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Improving flood prediction in sparsely gauged catchments by
the assimilation of satellite soil moisture into a rainfall-runoff
model
Camila Alvarez
Submitted in total fulfilment of the requirements of the degree of
Doctor of Philosophy
Department of Infrastructure Engineering
The University of Melbourne
April 2016
Produced on archival quality paper
ii
Abstract
This thesis explores the assimilation of remotely-sensed soil moisture (SM-DA) into a
rainfall-runoff model for improving flood prediction within data scarce regions. Satellite
soil moisture (SM) observations are used to correct the two main controlling factors of the
streamflow generation: the wetness condition of the catchment (state correction scheme)
and the magnitude of rainfall events (forcing correction scheme).
The core part of the research focuses on the state correction scheme. A simple rainfall
runoff model (the probability distributed model, PDM) is used for this. The soil water
state of PDM is corrected by assimilating active and passive satellite SM observations
using an ensemble Kalman filter. Within this framework, the efficacy of different existing
tools for setting up the state correction scheme are evaluated, and new techniques to
address some of the key challenges in the assimilation of surface satellite SM observations
into hydrological models are introduced.
Various options for the state correction scheme were implemented and enhanced throughout the thesis. The proposed schemes consistently led to improved streamflow ensemble
predictions for a case study. In the final state correction scheme, the ensemble root mean
square error was reduced by 24% at the catchment outlet, the false alarm ratio was reduced by a 9%, and the skill and reliability of the streamflow ensemble were improved after
SM-DA. The state correction scheme was also effective at improving the streamflow ensemble prediction within ungauged inner locations, which demonstrates the advantages of
incorporating spatially distributed SM information within large and poorly instrumented
catchments.
I showed that since stochastic SM-DA is formulated to reduce the random component of the
SM error (and therefore does not address systematic biases in the model), the efficacy of the
state correction schemes was restricted by the model quality before assimilation. This is
critical within a data scarce context, where streamflow predictions suffer from large errors
coming from the poor quality data used to force and calibrate the model. Additionally,
due to the higher control that SM exerts in the catchment runoff mechanisms during
minor and moderate floods, the state correction scheme had more skill when the low flows
were evaluated. Consequently, SM-DA improved mainly the quality of the streamflow
ensemble prediction (skill, reliability and average statistics of the ensemble) but did not
significantly reduced the existing biases in the peak flows prediction. These results reveal
one key limitation of the proposed approach: improving flood prediction by reducing
random (and not systematic) errors in the SM state of a rainfall-runoff model, while SM
is probably not the main controlling factor in the runoff generation during major floods
within the study catchment.
Addressing the above limitation, I set up a forcing correction scheme that aimed at reiii
ducing the errors in the rainfall data (the rainfall input, in addition to the infiltration
estimates from the model, are probably the main factors controlling the accuracy of flood
predictions). I adopted for this the soil moisture analysis rainfall tool (SMART) proposed by Crow et al., (2009). In SMART, active and passive satellite SM were assimilated
into the Antecedent Precipitation Index model to correct a near real-time satellite rainfall, which was subsequently used to force PDM (without state correction). The results
showed that remotely sensed SM was effective at improving mean-to-high daily satellite
rainfall accumulations, which in turn led to a consistent improvement of the streamflow
prediction, especially during high flows.
The efficacy of the state correction and the forcing correction schemes were compared
within 4 catchments. For most cases, the reduction of model SM error by the assimilation of satellite SM led to improved streamflow prediction compared with the correction
of the forcing data. This was true for both the low flows and high flows. The outperformance of the state correction scheme during high flows is counterintuitive with the
stronger influence that rainfall probably has during floods, and differs from previous studies. I interpreted these different results by various factors including the methodological
configuration (rainfall-runoff model, model error quantification, etc.), the quality of the
satellite rainfall data and the quality of the satellite SM retrievals. In agreement with
the literature, the combination of the forcing and the state correction schemes further
improved flood predictions.
The significance of this thesis is in providing novel evidence (based on real data experiments) of the value of satellite soil moisture for improving both an operational satellite
rainfall product and the streamflow prediction within data scarce regions. Additionally, I
highlighted a number of challenges and limitations within the forcing and state correction
schemes. I introduced new techniques to overcome some of these challenges and proposed
future strategies to further address them. This contributes to advancing towards a reliable
data assimilation framework for improving operational flood prediction within data scarce
regions.
iv
Declaration
This is to certify that:
1. The thesis comprises only my original work towards the PhD.
2. Due acknowledgement has been made in the text to all other material used.
3. The thesis is fewer than 100,000 words in length, exclusive of tables, figures, bibliographies and appendices.
Camila Alvarez
November 2015.
v
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Preface
This thesis is framed within the project Development of a new-generation flood forecasting
system using observations from space, funded by Australian Research Council and Bureau
of Meteorology under Linkage Project LP110200520 agreement.
The project aims to demonstrate the potential role that satellite-derived rainfall and soil
moisture products may play in improving continuous daily streamflow forecast of fluvial
flooding at semi-arid catchments in Australia. The motivation is to address the deficiency of geophysical data for implementing rainfall-runoff modelling and in particular,
two key informational gaps in gauge-based precipitation measurements over inland catchments and soil wetness measurements over the Australian continent. The hypotheses are
that (1) rainfall accumulations derived from the constellation of geostationary and polar
orbiting active and passive satellites can be used to provide near real-time rainfall to drive
hydrological modelling with full continental coverage at daily time scales; (2) active and
passive microwave satellite-derived soil moisture can be used to provide daily information
on the antecedent soil wetness of a catchment with direct influence on runoff generation;
and (3) by using satellite-derived data, forecasts of the river discharge at a sparsely-gauged
or ungauged catchment outlet can be enhanced. It is therefore the objective to develop
and implement a flood forecasting scheme that ingests satellite-derived precipitation and
soil moisture near real-time data sets to produce discharge forecasts under an operational
environment. With applications to Australia regions in mind, the implementation and
evaluations are conducted at the semi-arid, poorly instrumented flood-prone regions in
Australia.
Within this context, this thesis investigates a data assimilation framework that uses active and passive satellite SM observations to improve flood prediction within data scarce
regions.
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Acknowledgements
This thesis is the result of 4 years of intensive work and large personal growth. This goal
was achieved thanks to a sum of key factors.
I had the pleasure of working with Dongryeol and Andrew, who enthusiastically shared
their expertise and experience. They provided me with constant guidance, support and
trust throughout these years. They had a fundamental role in the development of my
academic/researcher profile.
I had valuable contributions from Wade, David and Chun-Hsu, which had direct impacts
in the quality of my research.
These years as PhD candidate were intense and exhausting, but also very exciting. The
University of Melbourne was a great place to develop my career, I was surrounded by great
colleagues and friends, and a very friendly and challenging academic environment. And
Melbourne is the best place that I could think of to spend this challenging time, lots of
biking, yoga, parks, playgrounds, and the best coffee.
My PhD was supported by Becas Chile from CONICYT. I am very grateful for the important effort that my country dedicates to developing advanced research. I will strive
to effectively reward their investment by contributing to the growth of science, and to a
sustainable development of Chile.
Finally, I had the most fundamental support from my family. My parents and in-laws with
their constant support and love. Specially my mum, who came to help us with parenting
& life in the hectic last weeks of our PhDs (Robert’s and mine). My healthy and happy
daughters, Blanca and Eloisa, who were a key aspect of the whole PhD experience and
taught me the most important lessons about parenthood, life and happiness. And my
beloved Robert, with his wisdom, his constant support, companionship, affection, shelter,
trust, humour, and love during this adventure, and in life.
Gracias a todos!
ix
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Contents
List of Figures
xv
List of Tables
xvii
Chapter 1 Introduction
1
Structure of the thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Chapter 2 Background
1
Microwave remote sensing of soil moisture . . . .
2
Hydrologic data assimilation . . . . . . . . . . .
3
Satellite soil moisture data assimilation (SM-DA)
4
State correction schemes . . . . . . . . . . . . . .
4.1 Model error representation . . . . . . . . .
4.2 Model error parameter estimation . . . . .
4.2.1 Ensemble verification criteria . . . . .
4.2.2 Maximum a posteriori approach . . .
4.2.3 Adaptive filtering techniques . . . . .
4.2.4 Triple collocation-based estimation .
4.2.5 Summary . . . . . . . . . . . . . . . .
4.3 Satellite SM observation operator . . . . . .
4.3.1 Profile soil moisture estimation . . . .
4.3.2 Observation rescaling . . . . . . . . .
4.3.3 Observation error estimation . . . . .
5
Forcing and dual correction schemes . . . . . . .
6
Summary and overall approach . . . . . . . . . .
1
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Chapter 3 Impacts of observation error structure in SM-DA
1
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2
Study area and data . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3
Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.1 Rainfall-runoff model . . . . . . . . . . . . . . . . . . . . . . . . .
3.2 EnKF formulation . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3 Satellite soil moisture rescaling and observation error estimation
3.4 Model error estimation . . . . . . . . . . . . . . . . . . . . . . . .
4
Results and discussion . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.1 Model calibration . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2 Model and observation error estimation . . . . . . . . . . . . . .
4.3 Assimilation experiments . . . . . . . . . . . . . . . . . . . . . .
5
Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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Chapter 4 Impacts of observation rescaling in SM-DA
1
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2
Study area and data . . . . . . . . . . . . . . . . . . . . . . . . .
3
Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.1 Rainfall-runoff model . . . . . . . . . . . . . . . . . . . . . .
3.2 EnKF formulation . . . . . . . . . . . . . . . . . . . . . . .
3.3 Model error representation . . . . . . . . . . . . . . . . . .
3.4 Estimation of SSM and SWI . . . . . . . . . . . . . . . . .
3.5 Observation rescaling and error estimation . . . . . . . . .
3.6 Evaluation of data assimilation results . . . . . . . . . . . .
4
Results and discussion . . . . . . . . . . . . . . . . . . . . . . . .
4.1 Model calibration . . . . . . . . . . . . . . . . . . . . . . . .
4.2 Error model parameter calibration . . . . . . . . . . . . . .
4.3 Rescaled SSM and SWI . . . . . . . . . . . . . . . . . . . .
4.4 Data assimilation results . . . . . . . . . . . . . . . . . . . .
4.4.1 Effects of observation error assumptions in DA results
4.4.2 Effects of different rescaling in DA results . . . . . . .
4.4.3 Effects of soil moisture product used in DA results . .
5
Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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Chapter 5 Lumped vs semi-distributed model configurations
1
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2
Study area and data . . . . . . . . . . . . . . . . . . . . . . . . . .
3
Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.1 Lumped and semi-distributed model schemes . . . . . . . . .
3.2 EnKF formulation . . . . . . . . . . . . . . . . . . . . . . . .
3.3 Error model representation . . . . . . . . . . . . . . . . . . .
3.4 Error model parameters calibration . . . . . . . . . . . . . . .
3.5 Profile soil moisture estimation . . . . . . . . . . . . . . . . .
3.6 Rescaling and observation error estimation . . . . . . . . . .
3.7 Evaluation metrics . . . . . . . . . . . . . . . . . . . . . . . .
4
Results and discussion . . . . . . . . . . . . . . . . . . . . . . . . .
4.1 Model calibration . . . . . . . . . . . . . . . . . . . . . . . . .
4.2 Error model parameters and ensemble prediction . . . . . . .
4.3 SWI estimation and rescaling . . . . . . . . . . . . . . . . . .
4.4 Satellite soil moisture data assimilation . . . . . . . . . . . .
5
Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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Chapter 6 Dual correction scheme
1
Introduction . . . . . . . . . . . . . . . . . . . . .
2
Study Area and Data . . . . . . . . . . . . . . . .
3
Methods . . . . . . . . . . . . . . . . . . . . . . . .
3.1 Rainfall-Runoff Model . . . . . . . . . . . . .
3.2 Forcing Correction Scheme . . . . . . . . . .
3.3 State Correction Scheme . . . . . . . . . . . .
3.3.1 Satellite Soil Moisture Data Processing
3.3.2 EnKF Formulation . . . . . . . . . . .
3.4 Dual Correction Scheme . . . . . . . . . . . .
3.5 Schemes Evaluation . . . . . . . . . . . . . .
4
Results . . . . . . . . . . . . . . . . . . . . . . . .
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4.1 Rainfall Correction . . . . . . . . .
4.2 Satellite Data Processing . . . . .
4.3 Streamflow Prediction Evaluation .
Discussion . . . . . . . . . . . . . . . . .
Conclusions . . . . . . . . . . . . . . . .
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Chapter 7 Discussion and Conclusions
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Challenges in satellite SM data processing
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Challenges in model error representation .
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Main findings . . . . . . . . . . . . . . . .
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Conclusions . . . . . . . . . . . . . . . . .
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Contributions . . . . . . . . . . . . . . . .
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Appendix A Publications
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References
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List of Figures
Chapter 2
9
Figure 1 Factors affecting satellite soil moisture retrievals . . . . . . . . . . . . . . 11
Figure 2 DA schematic diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
Chapter
Figure 1
Figure 2
Figure 3
Figure 4
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Warrego river catchment . . . .
Discharge prediction time series
Rescaled observations . . . . .
Assimilation results . . . . . .
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Chapter
Figure 1
Figure 2
Figure 3
Figure 4
Figure 5
Figure 6
Figure 7
Figure 8
Figure 9
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The Warrego river catchment . . . . . . . . . . .
The PDM scheme . . . . . . . . . . . . . . . . .
Hydrograph of observed and predicted discharge
Observed daily runoff ratio . . . . . . . . . . . .
Rescaled SSM . . . . . . . . . . . . . . . . . . . .
Simulated soil moisture and rescaled SSM, SWI .
NRMSD . . . . . . . . . . . . . . . . . . . . . . .
Major flood prediction . . . . . . . . . . . . . . .
Moderate flood prediction . . . . . . . . . . . . .
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The Warrego river basin . . . . . . . . . . . . . . . . . . . . . . . .
Periods of record of the different data sets . . . . . . . . . . . . . .
The PDM scheme . . . . . . . . . . . . . . . . . . . . . . . . . . .
Simulated and observed daily streamflow . . . . . . . . . . . . . .
Lag-correlation between simulated streamflow and θ . . . . . . . .
Lag-correlation between simulated streamflow and daily rainfall . .
Rank histograms . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Satellite SM data processing results . . . . . . . . . . . . . . . . .
T against soil depth found in previous studies . . . . . . . . . . . .
Streamflow and SM ensemble predictions before and after SM-DA
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Chapter 6
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Figure 1 Study catchments and rainfall gauges . . . . . . . . . . . . . . . . . . . . 83
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Mean daily bias in rainfall . . . . . . .
SMART evaluation . . . . . . . . . . .
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SM-DA results . . . . . . . . . . . . .
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Chapter 3
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Table 1 Evaluation metrics SM-DA . . . . . . . . . . . . . . . . . . . . . . . . . . 37
Chapter 4
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Table 1 Rescaled soil moisture observations . . . . . . . . . . . . . . . . . . . . . . 49
Table 2 Rescaled observation error . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
Chapter
Table 1
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Table 4
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Area and mean annual rainfall in study catchments . . . . . .
Model evaluation . . . . . . . . . . . . . . . . . . . . . . . . .
T and correlation coefficient between model and observed SM
SM-DA evaluation statistics . . . . . . . . . . . . . . . . . . .
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Table 1
Table 2
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Statistics of the reference run . . . . . . . . . . . . . . . . .
Statistics from the models forced with gauged-based rainfall
Model error parameters calibrated with MAP . . . . . . . .
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xviii
Chapter 1
Introduction
Floods have large negative impacts on society including the destruction of infrastructure
and crops, erosion, and in the worst cases, injury or loss of life (Thielen et al., 2009).
Moreover, the frequency of floods is increasing worldwide (Sivapalan et al., 2003). Particularly in Australia, floods correspond to the most costly natural disaster, with an average
annual cost estimated at $377 million (Middelmann-Fernandes, 2009). To reduce the tangible and intangible damage on public safety and society, flood warning systems are crucial.
These systems form part of a holistic approach that has gained important priority in the
political agenda in recent decades (Cloke and Pappenberger, 2009; Werner et al., 2009).
Flood warning systems are generally organised by sub-systems, including operational flood
forecasting, warnings to those at risk, and arrangements to communicate warning messages to people and organisations that need the information as a basis for their response
(Penning-Rowsell et al., 2000).
Operational flood forecasting is commonly provided by a government agency. Each agency
has its own set of tools to provide this service, which may include both qualitative or quantitative predictions. Qualitative predictions rely on weather forecasts and the knowledge
of historical flood events, while quantitative predictions rely on hydrologic forecasting
models 1 . These quantitative predictions can be deterministic or probabilistic. Deterministic predictions can use rainfall radar images, rainfall gauge observations or deterministic
rainfall forecasts to force hydrological models. Probabilistic predictions (also known as
ensemble prediction systems) use an ensemble of forcing data for medium term forecasts
(2-15 days). These ensembles aim to represent the forcing prediction uncertainties. The
forcing uncertainties have been commonly generated from perturbing the initial conditions and/or the parameters of numerical weather predictions (NWP) models (Cloke and
Pappenberger, 2009), although modern NWP models use stochastic physics. Among these
1
Model prediction refers to the output of the model at the following time step, which is obtained by
running the model with input forcing data at current time step. This concept is similar to model simulation.
Model forecast is used as the future prediction (or simulation) of the model that results from running the
model with forecast input data at a time greater than the current time step.
1
two types (deterministic and probabilistic streamflow predictions), there are event-based
predictions, where usually a team of experts is in charge of initialising and running a
model (or transfer function) to forecast the streamflow for the subsequent hours; and
continuous predictions, where a calibrated model for a particular catchment continuously
predicts the streamflow with a lead time that depends on the input weather forecast used
to force the model. While most quantitative flood forecasting systems worldwide started
as event-based deterministic predictions, given the key information that probabilistic predictions provide for risk assessment and decision making (Beven, 2011; Liu and Gupta,
2007; Robertson et al., 2013), an increasing number of systems, both continuous and eventbased, are moving towards ensemble prediction systems (Cloke and Pappenberger, 2009;
Krzysztofowicz, 2001).
In the case of Australia, the current event-based deterministic flood forecasting system,
managed by the Bureau of Meteorology, is migrating towards an operational continuous
deterministic modelling approach. An appropriate probabilistic modelling approach for
Australia is still under research. This thesis is framed within this context, and focuses on
continuous hydrological models within the context of data scarce regions. In particular (as
explained later), I aim to develop effective tools for reducing the uncertainties associated
with flood prediction in these areas by exploring the use of remotely sensed hydrological
observations.
Hydrological (or rainfall-runoff) models represent the processes operating within a catchment in order to predict the streamflow (including flood events) generated at the catchment outlet. These physical processes, also known as runoff mechanisms, determine the
catchment’s response to external forcing conditions such as rainfall (volume and intensity), temperature, solar radiation, wind speed and plant transpiration. Some of the key
factors influencing these mechanisms are the climate, static land surface features (e.g.,
soils, topography, landscape, vegetation and water bodies) and the initial conditions of
the catchment (e.g., wetness condition or soil moisture), which can be highly heterogeneous
(Beven, 2011). There exist a variety of rainfall-runoff models, ranging from very complex
and strictly physically based models to simpler conceptual models. However, one characteristic that they all share is that the accuracy of their predictions depends on the quality
of the data used to force and calibrate them. Therefore in an operational context of scaredata regions, where there is little and poor information about catchment characteristics
and forcing conditions, flood predictions can suffer from large uncertainties.
So we have on one hand the need for quality flood forecasting systems and on the other
hand, imperfect flood prediction models. The inherent uncertainties of these models must
be accurately quantified since this information is needed for risks assessment and decision
making (Liu and Gupta, 2007; Robertson et al., 2013). As a way of reducing model
uncertainties, since the early 1990s hydro-meteorologic observations have been used not
only as input variables of models but also as information to correct and update model
2
CHAPTER 1: INTRODUCTION
variables, in a process known as data assimilation (DA) (Hreinsson, 2008). DA techniques
are particularly useful in the context of flood forecasting because they allow real-time
updating of the forecasts as the event proceeds, which constrains the errors in subsequent
forecasts (Beven, 2011).
In the context of data scarce regions, it is appealing to explore remotely sensed observations of hydrological variables in DA. Given the key role that soil moisture (SM) has
on the catchment’s runoff mechanisms (Western et al., 2002), increasing attention has
been given to satellite SM microwave retrievals (e.g., Francois et al., 2003; Brocca et al.,
2010, 2012a; Alvarez-Garreton et al., 2013, 2014, 2015; Chen et al., 2014). In contrast to
in situ SM measurements (which are sparse and correspond to point measurements that
do not represent the heterogeneity over an area), satellite SM products provide spatially
distributed information of the water contained within the top few centimetres of soil, at
a global scale, and at regular and reasonably frequent time intervals. Additionally, satellite SM observations capture non-precipitation effects, which are not presented in most
hydrological models, such as irrigation (Kumar et al., 2015; Han et al., 2015a).
The existing satellite SM products have shown good agreement with ground data (Albergel
et al., 2009; Draper et al., 2009b; Albergel et al., 2010; Gruhier et al., 2010; Brocca et al.,
2011; Albergel et al., 2012), and there is an on-going development of satellite missions
dedicated to SM estimations (Liu et al., 2011). Although the information provided by these
satellites represents only the top few centimetres of soil (depth varying among different
sensors), when adequately processed, they can provide valuable information about deeper
layer SM (Brocca et al., 2011). Regarding the spatial resolution of these products (greater
than 25 km), studies have shown that despite their coarse resolution, these observations
can be used to represent catchment scale (>100 km) wetness conditions (Brocca et al.,
2012b). Moreover, these products have a revisit time of 1 to 3 days depending on latitude,
and the data can available within 3 h after being observed. This make them adequate for
many hydrological applications including flood forecasting (Wanders et al., 2014).
A common practice in satellite soil moisture data assimilation (SM-DA) is to combine SM
observations and SM predictions (a model state variable) to correct the model SM state
and to reduce the random component of its error (e.g., Francois et al., 2003; Brocca et al.,
2010, 2012a; Alvarez-Garreton et al., 2013, 2014, 2015; Chen et al., 2014). The rationale
is that processed satellite SM might be useful in improving the model’s representation
of SM, enabling more accurate prediction of the catchment response to rainfall and thus
better streamflow estimates. Despite their limitations, these studies have generally shown
positive results for reducing streamflow prediction uncertainty. On the other hand, other
studies have indicated that the assimilation of satellite soil moisture degrades the streamflow prediction (Parajka et al., 2006; Plaza et al., 2012; Kumar et al., 2014). While still
in development, satellite SM-DA state correction may be considered as a promising tool
for reducing the uncertainty in streamflow predictions. This approach would be specially
3
useful within data sparse regions, where there might be more value in remotely sensed
data, given the greater model uncertainties coming from poorer ground data. There are,
however, a number of key challenges that need to be addressed to implement such a scheme
successfully (in any context, not only within data sparse regions). The challenges include
accounting for the depth mismatch between model predictions and satellite observations,
representing and quantifying model and observation errors and setting up a robust data
assimilation scheme. In particular, there is still no agreement on the most effective techniques to quantify the model and the observation errors in the current state of the art
(Brocca et al., 2012a). Furthermore, there are challenges related to the downscaling processes required given the coarse resolution of satellite soil moisture products, the quality
control of satellite soil moisture and the satellite data discontinuity (Sahoo et al., 2013;
Ridler et al., 2014; Yin et al., 2014; Han et al., 2015b).
The efficacy of a SM-DA state correction scheme for improving streamflow prediction is
restricted by factors such as the inherent model limitations (coming from structural and
parameters uncertainties), the errors in forcing data, the experimental setup (e.g., model
error quantification, observation error quantification, satellite data processing techniques,
data assimilation scheme), and the specific catchment characteristics (e.g., soil type, location and land cover) (Massari et al., 2015). Since the aim of a SM-DA state correction
scheme is to reduce the errors in the model soil moisture, the reduction in streamflow uncertainty will depend on the error covariance between the soil water state and the output
streamflow. This error covariance will depend on the relative importance of soil moisture
compared with other factors in the runoff generation. In other words, it will depend on
the dominant runoff mechanisms within the catchment (such as saturation excess or infiltration excess). Therefore, the error covariance between SM and streamflow may become
weak when the errors in streamflow come mainly from errors in the rainfall input data
(Crow and Ryu, 2009) or from infiltration capacity estimates, such as in the case of very
intense runoff events (Wood et al., 1990). The contribution of input forcing uncertainty to
the streamflow errors becomes critical in ungauged or sparsely monitored locations, where
the available rainfall data generally comes from satellite products or numerical weather
prediction models.
Satellite rainfall information feature high temporal resolution, but usually contain important biases and errors (Yong et al., 2013; Zhou et al., 2014; Yong et al., 2015). Recent
studies have shown that these errors can potentially be reduced by using satellite SM observations (Pellarin et al., 2008; Crow et al., 2009; Brocca et al., 2013). The argument is
that given the information that the surface SM contains about recent rainfall events, the
rainfall can be constrained by satellite SM observations using simple water balance models. Although these studies have different approaches, they all have proved the potential
of improving satellite rainfall estimates by using satellite SM.
The demonstration of the potential of SM observations to correct errors in both the model
4
states and the forcing data has motivated recent studies to test dual (state and forcing)
correction schemes (e.g., Crow and Ryu, 2009; Chen et al., 2014; Massari et al., 2014). Due
to differences in the main runoff controlling factors, these studies have found that high-flow
estimations can be improved by correcting the rainfall forcing data, while low-flow events
and baseflow estimations are improved by the correction of initial soil moisture conditions
(Crow and Ryu, 2009; Chen et al., 2014). While these results suggest a promising future
for the further development of dual correction schemes (which is still an ongoing research
field), it remains unclear how they perform for different types of catchments. It is worth
noting that the use of soil moisture data to correct (or estimate) rainfall has limitations
during intense rainfall events due to the limited information that soil moisture provides
when the soil gets saturated (Chen et al., 2014). This may lower the effectiveness of
correcting rainfall data for flood forecasting. Moreover, the investigation of effective state
and forcing correction SM-DA schemes remains an ongoing research field.
Within the context described above, in this thesis I further explore the efficacy of using
satellite SM observations to improve flood prediction in data-scarce regions by applying
both state and forcing SM-DA correction schemes. I aim to test whether the spatially
distributed satellite soil moisture information can improve model predictions via data assimilation techniques. Various options for the components of an effective SM-DA scheme
are explored by working within 4 Australian catchments featuring a history of significant
flooding. These catchments have very distinct characteristics compared with most of the
catchments studied in SM-DA applications. Some of the techniques used during this research are adopted (and adapted) from previous studies and some of them are applied
for the first time in SM-DA applications. The significance of this research is in evaluating the efficacy of different existing tools for setting up a SM-DA scheme, in presenting
new techniques that address some key steps in SM-DA, and in providing (with real data
experiments) novel evidence of the efficacy of SM-DA for improving flood prediction in
data-scarce regions.
The research is divided into two main parts, each addressing one main research question.
To address these two main questions I define 9 sub-questions that target different aspects of
the problem. The first (and core) stage focuses on answering the following question:
Can we improve flood prediction by correcting the SM state of a rainfall-runoff model via
satellite SM data assimilation?
To answer this question, I explore several aspects of the assimilation schemes that can
affect the efficacy of SM-DA. The aspects include the impacts of different techniques
used to process the satellite data and the impacts of accounting for spatial distribution
of forcing data and channel routing. Specifically, I address 5 specific sub-questions (the
required information to understand the concepts behind the questions are presented in
Chapter 2):
1. How do the assumed observation error structures affect the efficacy of SM-DA for
5
improving streamflow prediction?
2. What are the impacts of different rescaling techniques (applied to remove systematic
biases between the model and the observation) on the efficacy of SM-DA?
3. Acknowledging that rainfall is presumably the main driver of flood generation in
semi-arid catchments, can we improve streamflow prediction by correcting the soil
water state of the model?
4. What is the impact of accounting for channel routing and the spatial distribution of
forcing data on SM-DA performance?
5. What are the prospects for improving streamflow within ungauged catchments using
satellite SM?
The second part of this research builds on the first part and focuses on the following
research question:
Can we further improve flood prediction by correcting both the satellite rainfall forcing data
and the model SM state via satellite SM data assimilation?
To answer this question, I explore the relative improvement in streamflow prediction coming from correcting the model states (via the state correction scheme used in the first stage)
and from correcting the rainfall forcing data (via a forcing correction scheme adopted from
the currently available techniques) in a dual state/forcing SM-DA. Within this stage, I
answer 4 sub-questions:
6. Can we improve the quality of an operational satellite rainfall product by the assimilation of satellite soil moisture?
7. Does this forcing correction scheme has a positive impact in streamflow prediction?
8. Can we improve streamflow prediction by the assimilation of satellite SM in a state
correction scheme?
9. What are the impacts in streamflow prediction of a combined state and forcing
correction scheme?
1
Structure of the thesis
This thesis is structured in 7 chapters. In the present chapter I give an overview of how
this research is framed, present the problem I am focusing on and its significance, the scope
of the research, and the defined research questions. I also provide a detailed explanation
of the structure of the thesis document. In Chapter 2 I summarise the background that
supports the research questions and provide a description of the methods used to address
them. I highlight which methods are currently being used in the literature and which
6
correspond to novel contributions of this thesis. The following 4 chapters address the
defined research questions. These chapters are published as peer-reviewed proceedings
and articles. They include their own introduction (with a description of the objectives,
scope and research questions), study area, data, methods, discussion and conclusions
sections. Complying with Thesis with Publication instructions from the University of
Melbourne (http://gradresearch.unimelb.edu.au/exams/publication.html), the format of
these chapters was maintained from their original publication sources.
In Chapter 3 I address sub-question 1 by analysing how different assumptions about the
structure of the satellite observation error affect the results of SM-DA in terms of streamflow prediction improvement. I present a real data experiment and test whether the
assumed degree of autocorrelation in the satellite observations error has any effect in the
streamflow prediction after SM-DA. Although the effects of incorrect observation error assumptions (structure and magnitude) in SM-DA have been previously studied (Crow and
van Loon, 2006; Crow and Reichle, 2008; Crow and Van den Berg, 2010; Reichle et al.,
2008), I provide new and different conclusions about those effects. I explain the apparent contradiction with previous studies through factors such as the different variable of
interest to evaluate the SM-DA results (previous studies have focused in the updated soil
moisture, while the work presented here focuses on the streamflow prediction), the large
errors in the streamflow prediction before SM-DA in this case, and the optimality of the
rescaling technique used to process the satellite data.
In Chapter 4 I address sub-question 2 by comparing the results of SM-DA state correction
schemes using different rescaling techniques to remove the systematic biases between model
SM and satellite SM observations. I test several commonly used rescaling techniques and
evaluate their effects in the updated streamflow. I also explore different assumptions
about the satellite observation error (related to sub-question 1). The contribution here
is twofold: i) I present new evidence of the advantages of assimilating satellite SM for
improving flood prediction in a semi-arid sparsely gauged catchment and ii) I provide
insights about the effects of different existing techniques to process the satellite SM data
in SM-DA results.
In Chapter 5 I address sub-questions 3, 4 and 5 by setting up a SM-DA state correction
scheme and comparing the results between lumped and semi-distributed model schematisations. With this comparison, I assess the effects of accounting for the spatial distribution
in forcing data and routing processes within a large study catchment. I also evaluate the
efficacy of SM-DA for improving flood prediction at ungauged sub-catchments. This work
introduces techniques which have not been applied in previous SM-DA studies, related to
model error representation and satellite SM data processing (observation error estimation
and rescaling). The contributions here include the presentation of these novel techniques
in a SM-DA context, the provision of new evidence of the efficacy of satellite SM-DA for
improving ensemble streamflow predictions in a sparsely instrumented catchment (and for
7
ungauged sub-catchments), and demonstrating that SM-DA skill is enhanced if the spatial
distribution in forcing data and routing processes are accounted for.
In Chapter 6 I address the last 4 sub-questions by comparing the relative skills of a
state correction SM-DA scheme, a forcing correction SM-DA scheme and a combined
state/forcing correction SM-DA scheme. The contribution here is to provide further evidence of the value of satellite soil moisture within data sparse regions. I demonstrate that
the quality of the satellite rainfall product is improved by the forcing correction scheme
during mean-to-high daily rainfall events, which in turn leads to an improved streamflow
prediction during high flows. I also show that for most catchments, the state correction
scheme outperforms the forcing correction scheme outputs, specially during low flows. In
agreement with previous studies, I show that in overall, the combined dual correction
scheme further improves the streamflow predictions. I also identify a number of challenges
and limitations within the proposed schemes.
In Chapter 7 I provide an overall discussion of the different findings of the thesis, summarise
the learning throughout the research and give recommendations based on the limitations
I have found. I highlight the main contributions and significance of the thesis, and present
ideas for future work. Finally, in Appendix A I provide a list of the publications and
conference presentations done throughout the research that supports this thesis.
8
Chapter 2
Background
In Chapter 2 I take the reader through the background that supports my two main research
questions. I provide a general review of the literature that puts my research within an
overall context. To minimise repetition with the background provided in the subsequent
chapters, the detailed explanation of the methods used in the thesis are cross-referenced
to the corresponding chapters.
To set up the soil moisture data assimilation (SM-DA) schemes, several key steps must be
addressed. This requires knowledge and understanding of the different components of the
SM-DA scheme, including satellite SM retrieval techniques and their associated errors,
various DA implementation steps (such as model and observation error representation,
the required satellite data processing, the updating technique, etc), and the hydrological
model used. In the following sections I cover this required background and highlight the
limitations and on-going research within each topic.
1
Microwave remote sensing of soil moisture
Remote sensing measures the radiation emitted and reflected from the Earth’s surface and
received at the satellite sensor. Each object has a unique combination of reflected, emitted, transmitted and absorbed radiation, which forms its spectral signature. Radiometry
corresponds to the measurement of this electromagnetic radiation, which is a consequence
of an objects material characteristics, which in the microwave region depend on its dielectric properties and temperature (Schmugge et al., 2002; Sharkov, 2003; Campbell and
Wynne, 2011).
Within the range of the electromagnetic spectrum, the L-∼X-band range (1 to 10 GHz)
from the microwave portion have been used for soil moisture sensing. Soil moisture retrieval techniques rely on the dielectric behaviour of liquid water, which has a substantially
greater dielectric constant than dry soil and hence a different radiative response. This dif9
ference is due to the electric dipole of water molecules, which responds to the applied
electromagnetic field. These highly polarised molecules have high dielectric constants in
the lower frequency region of the microwave region of the spectrum (about 80 at L-band
frequency), in contrast of dry soils that show low dielectric constants (about 3-4 at L-band)
(Schmugge, 1978; Carver et al., 1985; Schmugge, 1983; Engman and Chauhan, 1995). The
above results in water molecules having high reflectivity and low emissivity in this region, therefore, an increase in soil water content shows higher backscatter measurements
for radars (active sensors) and lower brightness temperatures for radiometers (passive sensors). Active sensors generally have higher spatial resolutions, but their ability to measure
soil moisture is significantly more affected by surface roughness, topographic features and
vegetation than passive sensors (Engman and Chauhan, 1995; Engman, 2000; Schmugge
et al., 2002).
Although the relationship between brightness temperature and soil moisture has a strong
theoretical basis, most algorithms used for quantifying this relation are empirical and
rely on ground data (Engman and Chauhan, 1995). Each microwave sensor uses its own
retrieval technique, depending on the sensor type, frequency observed, the associated microwave penetration depth, the sensor’s polarisation, and antenna scanning configurations
(Njoku and Entekhabi, 1996). These techniques are based on theoretical and/or empirical models and are under continuous development (Ahmad et al., 2010). The accuracy
of each algorithm relies on the identification and quantification of the interaction between soil moisture content, soil texture, surface roughness and vegetation cover (Jackson
and Schmugge, 1989; Njoku and Entekhabi, 1996; Engman and Chauhan, 1995; Engman,
2000).
The principal factors affecting soil moisture retrievals for passive sensors are shown in
a simplified scheme in Figure 1. The scheme shows that the received radiation at an
antenna (which comes from different sources) is transformed into brightness temperature
through radiometric techniques. The brightness temperature is then related to physical
properties of the observed scene through different physically based models and empirical
relationships that enable the identification of the different factors affecting the emitted
signal received from the scene, in order to finally estimate specific variables. Each of the
procedures showed in Figure 1 has associated uncertainties that must be accounted for
when using the final product.
In this thesis I am a final user of microwave remote sensing soil moisture products and
I will not go into further details of the data processing leading to these products. In
particular, I use soil moisture products from one active and two passive satellites sensors
with different retrieval algorithms (details are provided in Chapters 3, 4, 5 and 6). It is
however, important to recognise that the penetration depth of the microwave signals is of
few centimetres, thus the soil moisture estimates represent the top soil layer. The spatial
resolution of these products is coarse (greater than 25 km), however, it has been shown that
10
CHAPTER 2: BACKGROUND
TB is measured and instrumental error is added
Microwave remote sensor
Radiative transfer model
Soil dielectric model
SM product
TB is converted to the soil TB and then to the soil (plus water) dielectric constant
Physical scenario observed
Figure 1: Factors affecting satellite soil moisture retrievals
these observations can be used to represent catchment scale (>100 km) wetness conditions
(Brocca et al., 2012b). The revisit time of these satellites is 1 to 3 days, depending on
latitude, and the data can available within 3 h after being observed. This make them
adequate for many hydrological applications including flood forecasting (Wanders et al.,
2014).
2
Hydrologic data assimilation
Hydrologic (or rainfall-runoff) models conceptualise the streamflow generation processes
within a catchment based on a specific structure, set of parameters and input data. Depending on the model, different fluxes and states influencing the streamflow are estimated,
such as net rainfall, soil moisture, fast surficial flows, interflow, baseflow, groundwater, etc.
The models are a simplified representation of a real system, therefore their predictions are
prone to errors (Beven, 2011). Moreover, they also rely on the quality of the data used to
force them and to calibrate their parameters (especially when parameters are not physically measurable), which becomes critical in the context of data-scarce regions.
A popular approach to reduce the random errors in hydrological models is data assimilation
(DA). DA techniques use observations to inform and correct specific model components
(such as model states or parameters). As an example, Figure 2 shows a Kalman-based
simplified schematic of DA procedure (see below for Kalman filter description).
The basis of DA techniques relies on Bayes’ theorem, which establishes that for two events
A and B, with probability of occurrence P (A) and P (B), respectively, the probability
that both events occur is given by
P (A ∩ B) = P (A | B) · P (B) = P (B | A) · P (A)
(1)
Where P (A | B) is the conditional probability of occurrence of event A given that B
has occurred. Eq.1 leads directly to Bayes’ theorem, where the marginal probabilities
P (A) and P (B) are referred as prior probability density functions, and the conditional
11
Figure 2: Kalman-based DA schematic diagram: when an observation is available (black point), the
corresponding value simulated by the model (white point) is corrected and an updated value is calculated
(gray point) (Aubert et al., 2003).
probability P (B | A) is referred as posterior density function:
P (B | A) =
P (A | B) · P (B)
P (A)
(2)
Applying Bayes’ theorem to solve the DA problem, the posterior probability distribution
Ppost of the quantity of interest, x, given a set of uncertain observations, z, can be defined
as
Ppost (x | z) =
P (z | x) · Pprior (x)
P (z)
(3)
Based on this Bayesian estimation of the posterior distribution, a Kalman filter (KF)
(Kalman, 1960) can be formulated to reduce the errors in hydrologic models. The KF and
its derivations, along with particle filters and variational assimilation techniques (Liu and
Gupta, 2007), are the most commonly used DA schemes in hydrology. In the following, I
provide a brief description of these 3 approaches for the particular case of a state correction
framework (framework implemented in this research, as explained in Section 3).
1. The KF updating scheme determines state corrections (updating step) based on
the model and observations errors, which are assumed to be independent Gaussian
errors. As a simple Bayesian formulation, the KF estimates posteriori state values
(Ppost in Eq. 3) recursively over time by using incoming observations and a linear
background model to propagate the state variable. The KF compares Ppost (x) and
Pprior (x) (the state variable with and without the observation information) and
minimises the expected value of the square magnitude of their difference (i.e., KF is
a minimum mean-square error estimator).
The main limitation of this filter is that it requires linearity of the system for propagating the model errors from one time step to another (Evensen, 1994). Since
hydrological processes are highly non-linear, variations of the Kalman filter have
been developed in order to deal with this limitation including the Extended Kalman
Filter (EKF) and the Ensemble Kalman Filter (EnKF).
The EKF performs local linear approximation for propagating the model error co12
variance matrix. This algorithm has had some successful applications in hydrology,
although it can create instabilities or divergences due to the linear approximation of
non-linear processes (Clark et al., 2008). The EnKF is a Monte Carlo approximation of the traditional KF that non-linearly propagates a finite ensemble of model
trajectories (Reichle et al., 2002). This filter was introduced by Evensen (1994) as
an alternative of the EKF to deal with the limitations of the linear approximations
within strong non-linear systems. The Monte Carlo method consists in using a large
cloud of possible realisations to represent a specific probability density function. In
hydrological models, these ensembles are usually generated by perturbing the model
state variables, parameters and/or forcing data by a mean-zero Gaussian noise (Ryu
et al., 2009). The results obtained by Evensen (1994) using the EnKF were better
than the ones obtained in previous studies using the EKF, which was reflected in
better quality of the forecasts error statistic and lower calculation times. The EnKF
uses the updating equation of the traditional KF, but with the Kalman gain (Eq.14)
calculated based on the relative magnitude of the error covariances of the model and
observations (Burgers et al., 1998). As the error covariance information in the model
is propagated by a Monte Carlo ensemble, the EnKF can represent almost any type
of model errors (Crow and Van den Berg, 2010). The limitation of the EnKF is the
invalid Gaussian error in the non-Gaussian earth system models. In addition, the
EnKF cannot conserve the water balance and it may perturb the state variables into
some non-physical meaning values (Li et al., 2012; Moradkhani et al., 2012).
The formulation of an EnKF-based DA scheme has been widely detailed in the
literature (e.g., Burgers et al., 1998; Evensen, 1994; Reichle et al., 2002). In general,
when an observation is available, an ensemble of observations (θ obs ) is created by
perturbing the observed time series with a particular observation error (the structure
and magnitude of this error must be estimated for a specific application). Then, each
member i of the ensemble prediction of the variable of interest (θ, an ensemble of a
model state in this example) is updated by
θi+ (t) = θi− (t) + K(t) · (θiobs (t) − Hθi− (t)).
(4)
The superscripts “− ” and “+ ” denote the state prediction before and after the assimilation step, respectively. H is an operator that transforms the model state to the
measurement space. When the observations are processed to represent the model
space before the DA step (as is it consistently done in this thesis, see Section 4.3 and
Chapters 3 to 6), H reduces to the unity matrix. K is the Kalman gain, calculated
for each time step as
K(t) =
P− (t)
,
+ R(t)
(5)
P− (t)
where R(t) is the θ obs error variance and P− (t) is the error covariance of the model
state. This error covariance can be estimated at each time step based on state
13
ensemble mean, θ − (t), as
P− (t) =
i h
iT
1 h −
θ (t) − θ − (t) · θ − (t) − θ − (t) .
N −1
(6)
2. Particle filters (PF) are based in updating the probability density function (PDF)
of the model states. For this purpose, the posterior probability distribution of the
model states are drawn by discrete random sampling of particles with associated
weights. When an observation becomes available, the weights of the particles are
evaluated and updated. In this sense, while the Kalman filters deal directly with
the states of the model, particle filters update the particle weights, therefore they
can update simultaneously different components of the model (associated with the
updated particle). Given the latter, this technique has been used widely for simultaneously updating model states and parameters (Liu and Gupta, 2007; Hreinsson,
2008). PF are not limited to Gaussian PDFs and they can be applied to linear and
non-linear models. However, they required a large number of members to avoid the
collapse of the particle, which makes them computationally expensive (van Leeuwen,
2010). Weerts and El Serafy (2006) undertook a comparative analysis of EnKF
and PF for state updating with hydrological models and concluded that the EnKF
scheme was more suitable for flood forecasting. On the other hand, Dechant and
Moradkhani (2011); DeChant and Moradkhani (2012) did a comprehensive study to
test the effectiveness and robustness of the EnKF and PF on hydrologic forecasting
and they concluded that the PF is superior to the EnKF. The PF shows better results since it can relax the Gaussian assumption and keep the water balance intact
(Moradkhani et al., 2005a, 2012). Also, Matgen et al. (2010) used the PF for flood
forecasting/inundation.
3. Variational data assimilation techniques, in contrast to Kalman filters and particle
filters that have a sequential approximation, operate in a batch basis over a time
window that contains the observed data. These techniques in general minimise a
cost function constructed by an aggregation of errors from different sources (model
structure, observations, initial conditions, inputs and parameters) over the entire
assimilation window, assuming that errors are independent and additive. These
methods are very well suited for smoothing problems (characterising variables at
past times), but can also be implemented for filtering problems if the smoothing
scheme is defined sequentially each time new observations arrive. The disadvantage
of this technique for real time applications is that it can be computational inefficient
(Liu and Gupta, 2007).
Given the advantages and disadvantages of the DA techniques summarised above within
the context of flood prediction, in this research I adopt an EnKF-based approach. In
particular, I implement a state correction scheme in which the soil moisture state of a
hydrological model is updated by using satellite observations (details in Section 3).
14
3
Satellite soil moisture data assimilation (SM-DA)
Within the context of data scarce regions, remotely sensed observations of hydrological
variables are appealing datasets to use in DA. These observations provide temporally and
spatially distributed information about hydrological variables in areas where there is little
or no ground information, complementing standard measurements of rainfall, soil water
content, evapotranspiration, snow cover, vegetation cover, topography, water quality, areas
of groundwater recharge and discharge, etc. (Engman, 1996; Ritchie and Rango, 1996).
The successful use of satellite data is, however, subject to the reliability of retrieval techniques used for determining the hydrologic variables (Stewart et al., 1996), which will be
a determinant of the observations errors assessment.
The use of satellite soil moisture observations in hydrologic DA in particular, has been
increasingly explored (e.g., Francois et al., 2003; Brocca et al., 2010, 2012a; Chen et al.,
2014). This is for three main reasons: 1) SM is a key controlling factor in runoff response of
a catchment by influencing different processes including evaporative fluxes, infiltration and
percolation, surface runoff, interflow, and groundwater recharge (Engman and Chauhan,
1995; Schultz and Engman, 2000; Western et al., 2002; Njoku et al., 2003; Jia et al., 2009);
2) in-situ measurements of SM are scarce and they provide point information that does not
represent the heterogeneity over an area; and 3) there is on-going development of satellite
missions dedicated to SM estimations (Liu et al., 2011).
Sections 4 and 5 below review the two main approaches of satellite soil moisture data
assimilation (SM-DA). The first and most popular approach is the use of satellite SM
to correct the soil water states of hydrological models (state correction SM-DA). The
second and more recent approach is the use of satellite SM to correct satellite rainfall
observations, which can then provide better forcing data for hydrological models (forcing
correction SM-DA).
4
State correction schemes
The studies that investigate the use of satellite SM to correct SM states of models can be
broadly categorised into two main groups; the first group has mostly worked with land
surface models and has focused on improving surface SM or root-zone SM estimation (e.g.,
Crow and van Loon, 2006; Crow and Reichle, 2008; Crow and Van den Berg, 2010; Reichle
et al., 2008; Ryu et al., 2009). The second group (where this thesis fits) has focused on the
improvement of streamflow prediction from rainfall-runoff models (Francois et al., 2003;
Brocca et al., 2010, 2012a; Chen et al., 2014; Wanders et al., 2014). This Section describes
the main challenges of SM-DA within the latter group.
Improvements in streamflow predictions investigated by studies in the second group are not
15
exclusively influenced by better representation of SM. The rationale here is that satellite
SM can be used to correct the SM model prediction, enabling more accurate prediction of
the catchment’s response to rainfall and thus better streamflow estimates. The efficacy of
SM-DA state correction scheme is therefore influenced by the particular runoff mechanisms
which occur within the catchment (Alvarez-Garreton et al., 2015). Since SM-DA aims to
reduce the errors in the model soil moisture, the reduction in streamflow uncertainty will
depend on the error covariance between soil moisture and runoff. This error covariance
(which in the model space will be defined by the representation of the different sources of
uncertainty) may become marginal when the errors in streamflow come mainly from errors
in rainfall input data (Crow and Ryu, 2009). This physical constraint is case specific and
determines the potential skill of SM-DA for improving streamflow prediction.
An important challenge within this approach is that the satellite SM estimates represent
only a few top centimetres of soil (given the microwave penetration depths, see Section
1) whereas hydrological models generally represent the water content of deeper soil layers
(Parajka et al., 2006). These different SM representations must be addressed since data
assimilation schemes reduce random state errors by combining predictions and observations of a same physical variable. Addressing this problem, several studies have related
the top soil layer moisture with deeper layers by making various assumptions regarding
the vertical distribution of water content or by using land surface models (Parajka et al.,
2006; Draper et al., 2009a; Meier et al., 2011). Additionally, many hydrological models
have state definitions that differ from measured soil moisture. Consequently, the studied
model has to be carefully analysed and observation operators must be determined to relate
satellite measurements with model states in order to incorporate these observations in a
consistent way (Barrett and Renzullo, 2009).
Despite their limitations, state correction SM-DA applications have generally been shown
to reduce streamflow prediction uncertainty (e.g., Francois et al., 2003; Brocca et al., 2010,
2012a). Nevertheless, there are key challenges that need to be addressed to implement
such schemes and there is still no agreement on the most effective techniques to do so
(Crow and Van den Berg, 2010). These challenges include the adequate representation of
model errors; the estimation of those errors; the implementation of observation operators
that relate the satellite observations with the model states in a consistent way; and the
estimation of the satellite observation errors. Sections 4.1 to 4.3 provide a review of the
techniques used to address each of these challenges.
4.1
Model error representation
The main sources of uncertainty in hydrologic models come from the errors in the forcing data, the model structure and model parameters (Liu and Gupta, 2007). In SM-DA
applications, an adequate representation and estimation of these errors is critical since it
determines the value of the Kalman gain (Eq.14). Moreover, the improvement in stream16
flow prediction coming from a better representation of SM relies on the covariance between
the errors in SM states and the modelled streamflow, which directly depends on the specific representation and estimation of the model errors. Most SM-DA studies are based
on overly simplistic error models (Crow and Van den Berg, 2010). The general practice is
to capture the net effect of multiple error sources in an aggregated way by adding unbiased synthetic noise to forcing variables, model state variables and/or model parameters
(Reichle et al., 2008; Ryu et al., 2009; Brocca et al., 2010; Crow and Van den Berg, 2010;
Chen et al., 2011; Brocca et al., 2012a; Hain et al., 2012).
To represent the forcing uncertainty within a Monte-Carlo approach, the different input
data sets used by the model can be perturbed, such as temperature, potential evapotranspiration and rainfall. In the experiments carried out throughout this research, only
rainfall was perturbed. This choice was made for two reasons: 1) to minimise the number of unknown error parameters and 2) because rainfall is the most critical forcing data
affecting the streamflow generation within the study catchments. It should be noted that
the potential evapotranspiration also plays an important role in streamflow generation,
especially within the semi-arid catchments used in this study. Although this input data
was not explicitly perturbed to represent the forcing uncertainty, the errors in the actual
evapotranspiration (calculated based on PET and the SM state of the model) were implicitly accounted for when the SM state of the model was perturbed (see model structure
error below).
Regarding the uncertainty in rainfall data, this error is generally represented by a multiplicative error (McMillan et al., 2011; Tian et al., 2013). In particular, various SM-DA
studies (e.g., Brocca et al., 2012a; Chen et al., 2011) have represented the rainfall error
(p ) as
p ∼ lnN (1, σp2 ),
(7)
where σp is the standard deviation of the lognormal distribution.
The parameter uncertainty can be represented by perturbing selected model parameters.
The structure of these errors will depend on the nature of the parameter and the assumptions made in each application. The justification of the specific rainfall error and
parameter error structure adopted in each experiment of the thesis is provided in the
corresponding methodology section of Chapters 3 to 6.
Within the context of SM-DA applications, the model structural error is usually represented by perturbing the SM state of the model (the same variable that is updated in
the DA scheme). This error is commonly assumed to be spatially homogeneous additive
random error (e.g., Chen et al., 2011; Crow and Van den Berg, 2010; Hain et al., 2012;
Reichle et al., 2008):
s ∼ N (0, σs2 ),
(8)
17
where σs is the standard deviation of the normal distribution. This type of perturbation,
however, should be carefully implemented. Since the physical limits of SM (porosity as an
upper bound and residual water content as a lower bound) are represented in the model
space by the corresponding storage capacity, when the model SM prediction approaches
the limits of this storage, applying unbiased perturbation to SM can lead to a truncation
bias in the background prediction. This can result in mass balance errors and degrade
the performance of the DA scheme. Moreover, the Kalman filter assumes unbiased state
variables (Ryu et al., 2009).
This issue is of particular importance in arid regions like the study area (see area description in Chapters 4 to 6), where the soil water content can be rapidly depleted by
evapotranspiration and transmission losses, thus approaching the residual water content
of the soil. Addressing this issue, Ryu et al. (2009) proposed a truncation bias correction
that consists in running a single unperturbed model prediction (θ−0 ) in parallel with the
perturbed model prediction (θi,− ). At each time step, the mean bias of an N -member
ensemble prediction, δ(t), is calculated by subtracting θ−0 (t) from the ensemble mean:
δ(t) =
N
1 X −
θ (t) − θ−0 (t).
N i=1 i
(9)
Then, a bias corrected ensemble of state variables, θ̃i− (t), is obtained by subtracting δ(t)
from each member of the perturbed ensemble, θi− (t).
This truncation bias correction ensures unbiased state ensembles, however, some important but subtle effects remain that arise from the non-linear, bounded nature of hydrologic
models. Representing model errors by adding unbiased perturbation to forcing, model parameters and/or model states can lead to a biased streamflow ensemble prediction (e.g.,
Plaza et al., 2012; Ryu et al., 2009), compared with the unperturbed model run. This
biased streamflow ensemble prediction (hereinafter referred to as the “open-loop”) is degraded compared with the streamflow predicted by the unperturbed calibrated model. As
a consequence, improvement of the open-loop after SM-DA will in part be due to the
correction of bias introduced during the assimilation process itself.
This issue of bias in the streamflow open-loop introduced through perturbation of forcing,
etc. has not been explicitly treated in previous SM-DA applications. In Chapters 5 and
6, I address this by examining if the bias correction proposed by Ryu et al. (2009) can be
used to correct the bias issue in the streamflow open-loop.
4.2
Model error parameter estimation
It has been shown that inappropriate assumptions about the magnitude of model errors
results in sub-optimal performance of the DA scheme and in the degradation of the updated
predictions (Crow and van Loon, 2006; Crow and Reichle, 2008; Reichle et al., 2008).
18
Nevertheless, most SM-DA studies adopt error structures for the different perturbations
(such as the ones presented in Section 4.1) and then assume an arbitrary magnitude for
those errors, without examining the validity of either assumption. In the following sections,
I describe the most commonly used methods to estimate model error parameters within
SM-DA context.
4.2.1
Ensemble verification criteria
When a hydrological model is perturbed to generate an open-loop streamflow ensemble
(Qol ) that accounts for different sources of uncertainties, the characteristics of that ensemble should be examined to determine if it is a reliable estimate of the uncertainty. There
are some verification methods (commonly used in meteorology) to measure reliability or
consistency of ensembles, based on the observed streamflow (Qobs ) (De Lannoy et al.,
2006). For example, if the ensemble has enough spread, the temporal average (expressed
by an overbar) of the ensemble skill (skt ) should be similar to the temporal average of
the ensemble spread (spt ), i.e., sk/sp = 1 (Brocca et al., 2012a; De Lannoy et al., 2006),
where:
sk =
T
2
1 X
Qol (t) − Qobs (t) ,
T t=1
(10)
"
#
T
N
2
1 X x1 X
sp =
Qol (i, t) − Qol (t)
.
T t=1 N i=1
(11)
Additionally, if the observation is indistinguishable from a member of the ensemble,
the rap
tio between sk and the ensemble mean squared error (mse), normalised by (N + 1)/2N
should be equal to one (Brocca et al., 2012a; Moradkhani et al., 2005b), where:
"
#
T
N
1X 1 X
2
(Qol (i, t) − Qobs (t)) .
mse =
T t=1 N i=1
(12)
The above discharge ensemble verification criteria have been used in previous SM-DA
applications (e.g., Brocca et al., 2012a). The limitation here is that they assume that
the observed discharge has no error (or very small error compared with the model error),
which could lead to overestimation of the model error parameters.
4.2.2
Maximum a posteriori approach
The open-loop ensemble prediction can also be evaluated under a Bayesian inference procedure in order to maximise the probability of having the streamflow observation within
the open-loop streamflow. Wang et al. (2009) detailed such a procedure, called a maximum
a posteriori (MAP) scheme, which maximises the probability of observing historical events
given the model and error parameters. The description and equations to implement MAP
19
are provided in Chapter 5. It should be noted that this approach has not been applied in
previous SM-DA studies.
4.2.3
Adaptive filtering techniques
Another approach found in the literature to estimate the magnitude of model errors are
adaptive filtering techniques (Crow and Reichle, 2008; Reichle et al., 2008). These techniques evaluate normalised filter innovations in the updating step, ν, to correct the assumed model and observation errors:
ν(t) = p
θobs − θ−
P− (t) + R(t)
.
(13)
Where P is the background error variance in the model state θ, R is the error variance of
the observation θobs . In the KF theory, correct assumptions about the magnitudes of the
model and observation errors should result in serially uncorrelated filter innovations (white
noise) and the normalised innovations should have unit variance. While these techniques
have a strong theoretical basis, the convergence of model and observation error estimations
is slow (simulations periods of more than 5 years are required) and they are based on the
assumption that observation errors are uncorrelated, which is probably not the case with
satellite soil moisture observations (Crow and Van den Berg, 2010).
4.2.4
Triple collocation-based estimation
To overcome the limitations of adaptive filtering techniques, Crow and Van den Berg
(2010) proposed a new approach that used an estimated observation error variance (R̂,
coming from a triple collocation analysis, see Section 4.3.3) to constrain the unit-variance
restriction of ν (Eq.13) and estimate the model error variance P . Within the limitations
regarding the simplified representation adopted for the model error structure, Crow and
Van den Berg (2010) showed an improved estimation of model error in the presence of
autocorrelated observation errors, compared with adaptive filtering techniques.
4.2.5
Summary
Given the determinant role that the estimation of model errors plays in SM-DA, in this
thesis I strive to prevent arbitrary assumptions about the magnitude of these errors. For
this I apply different techniques. In Chapters 3 and 4, I use the ensemble verification criteria described in Section 4.2.1, which is simple to implement and not too computationally
expensive. To overcome the limitations of this approach and to introduce a new approach
within SM-DA applications, in Chapter 5 and 6, I implement MAP to estimate the model
error parameters. There is however, an important research gap here since the most suitable procedure to generate ensemble of streamflow predictions is still not assessed, and a
20
consistent inter-comparison between the available techniques has not been carried.
4.3
Satellite SM observation operator
As mentioned earlier, one of the key challenges in setting up a satellite SM-DA scheme is
converting surface soil moisture observations from the satellites into variables physically
or statistically compatible with the model soil moisture. This can be achieved by using an
observation operator. Such observation operator needs to address a few key issues. Firstly,
there is a dynamical difference between model SM prediction and satellite SM observations
related to the different depths that they represent that needs to be resolved. This can be
done by estimating a profile soil moisture based on surface observations. Secondly, after
a profile SM is estimated from the satellite SM (and therefore both the observations and
the model are representing the same physical variable), there are systematic differences
that need to be removed before assimilation. These differences are due to the distinct
modelling and observational approaches used, which typically lead to predictions with
different systematic relationships to the assumed truth (Yilmaz and Crow, 2013). Lastly,
the observation error of these transformed and rescaled observations must be estimated.
This error is usually assumed to be an additive random error with a variance of R (from
Eq.14).
The observation operator is defined here as the combination of techniques used to solve the
above three steps (profile soil moisture estimation, observation rescaling and observation
error estimation). Sections 4.3.1 to 4.3.3 review the methods commonly used to address
these steps and present the new methods we have proposed in this thesis.
4.3.1
Profile soil moisture estimation
The flux of water from the surface of the soil into deeper layers is dominated by soil properties, such as porosity, wilting point, field capacity and unsaturated hydraulic conductivity,
and by forcing data, such as rainfall and evapotranspiration (Richards, 1931). If there
is information available about the soil properties of the study area, a physically based
model can be applied to the surface observations to estimate this flux (eg. Richards, 1931;
Beven and Germann, 1982; Manfreda et al., 2014). However, this information is generally
not available. Addressing this challenge, Wagner et al. (1999) proposed an empirical relationship that linearly relates the variation in time of the root zone SM to the difference
between surface SM and root zone SM. This is done by applying an exponential smoothing
filter to the surface observations.
In this thesis I adopt the above filter (see methodology sections in Chapters 3 to 6), which
has been widely used to represent deep-layer SM based on surface observations (Wagner
et al., 1999; Albergel et al., 2008; Brocca et al., 2009, 2010, 2012a; Ford et al., 2013). The
filter estimates an average of profile saturation by recursively calculating a soil wetness
21
index (SWI) whenever a surface SM observation is available:
SWI(t) = SWI(t − 1) + G(t) [SSM(t) − SWI(t − 1)] ,
(14)
where SSM(t) is the satellite SM observation and G(t) is a gain term varying between 0
and 1 as:
G(t) =
G(t − 1)
.
t−(t−1)
G(t − 1) + e−( T )
(15)
T is a calibrated parameter that implicitly accounts for several physical parameters (Albergel et al., 2008). The common practice is to calibrate T by maximising the correlation
between SWI and the unperturbed model soil moisture (θ).
4.3.2
Observation rescaling
In order to optimally merge model predictions and observations, the systematic differences
between the two datasets must be removed. This is usually done as a pre-processing step
by rescaling the observations to match the model predictions in some statistical sense
(Reichle and Koster, 2004; Drusch et al., 2005; Yilmaz and Crow, 2013). If not done as
a pre-processing step, this rescaling can be expressed via H in Eq. 13 (to scale model
states to the observations). There are a variety of strategies for such rescaling. The most
common are those based on least squares regression (LR) (Crow et al., 2005), cumulative
distribution function (CFD) matching (Reichle and Koster, 2004) and variance (VAR)
matching (Yilmaz and Crow, 2013).
Only recently, Yilmaz and Crow (2013) applied a signal variance-based rescaling technique used as a pre-processing step in triple collocation (TC) analysis (Section 4.3.3) into
a synthetic SM-DA application. In their work, they assessed the relative performance
of TC-based rescaling and the above-mentioned techniques. The conclusion, based on
analytical and numerical analyses, was that when the TC requirements are met (enough
samples of three independent and coincident measurements/predictions of the same physical variable, with no cross-correlated errors), TC-based rescaling gives un-biased estimates
of the rescaling factors (Eq.19), while the rest of the techniques above provide sub-optimal
solutions. The solutions from LR-, CDF- and VAR-based rescaling techniques are very
close to optimal estimates when the errors in the reference and the matched datasets (i.e.,
model and observations) are assumed negligible compared to the real signal (high signal
to noise values) (Yilmaz and Crow, 2013).
The rescaling of satellite SM observations to statistically match the model SM prediction
is a necessary step in SM-DA applications. Most of these applications adopt a specific
technique (commonly following previous studies) and implement the DA scheme without
questioning the impacts of this decision. Addressing this gap, I adopt a real data approach
(further details in Section 6) and evaluate the impacts that different rescaling techniques
22
have in the updated streamflow coming from the assimilation of satellite soil moisture into
a rainfall-runoff model.
The specific question defined here is: what are the impacts of different rescaling techniques
in improving streamflow prediction after SM-DA? I answer this question in Chapter 4.
It is worth noting that the work presented in that chapter was developed before Yilmaz
and Crow (2013) emphasised the use of TC to rescale observations, therefore TC-based
rescaling was not included in the analysis. In the subsequent Chapters (5 and 6), I adopt
the TC-based technique to rescale the SWI derived from active and passive satellite SM
products into the model space.
4.3.3
Observation error estimation
The error associated with the different rescaled observations needs to be estimated for
Bayesian-based updating schemes, such as the EnKF (R from Eq.14). Quantifying this
uncertainty is a major challenge, especially given the lack of ground measurements of soil
moisture in most areas. Moreover, incorrect assumptions regarding these errors degrade
the performance of stochastic assimilation results (Reichle et al., 2008; Crow and Reichle,
2008; Crow and Van den Berg, 2010).
To estimate the errors in the observed soil moisture, one alternative would be to propagate
the errors through the retrieval algorithm and physical models used in the satellite soil
moisture estimation (Section 1), however this requires expert knowledge in remote sensing
and falls beyond the scope defined in this research.
In this thesis I adopt two approaches to estimate R. The first one consists on determining
an upper boundary of R and testing different values within that boundary (Chapters 3
and 4). The second one uses triple collocation (TC) technique to estimate the value of
R (Chapters 5 and 6). In this section, I describe these two approaches and highlight
how they are applied in order to obtain new insights about satellite error estimation in a
SM-DA context.
Regarding the structure of the observations error, there is a spatial and a temporal component that should be defined. A spatial correlation of the observation error can be expected
given the overlapping observations and the actual footprint of the satellite observations
(Wanders et al., 2012). Regarding the temporal structure of the observation error, most
SM-DA applications assume that satellite SM errors are temporally uncorrelated. This is
indeed one of the assumptions of the adaptive filtering approaches presented in Section
4.2.3. However, long-term comparisons between satellite SM retrievals and dense groundbased networks question this assumption (Crow and Van den Berg, 2010). The potential
temporal correlation in the observation error poses a contradiction that may have several
impacts in SM-DA. For example, it can lead to a sub-optimal characterisation of observation errors which can degrade the performance of the SM-DA scheme (Reichle et al., 2008;
23
Crow and Reichle, 2008; Crow and Van den Berg, 2010). Moreover, the temporal correlation of the observation error can be transferred into the model space in the updating step
(Eq.13), which would result in correlated errors between model and observations in the
following time step. This violates the EnKF assumption of independence between model
and observation errors (Evensen, 1994). To explore the magnitude of this problem within
a real data case, in Chapter 3 I investigate how different autocorrelation structures for
this error affect the SM-DA results, while assuming a known observation error variance R.
The specific question answered here is how assumed observation error structures affects
SM-DA efficacy for improving streamflow prediction?.
Among the SM-DA studies that do not assume arbitrary values for R, some studies have
used the variable variance multiplier (VVM) to dynamically estimate observation errors
(Leisenring and Moradkhani, 2012; Moradkhani et al., 2012; Yan et al., 2015). Additionally, and probably the most popular technique used to estimate this error is triple
collocation analysis. TC was introduced by Stoffelen (1998) and uses three collocated and
coincident independent datasets (with uncorrelated errors) for the same target variable
to determine the parameters of the linear model and estimate the measurement errors of
the three datasets. In reality, the datasets may contain error auto-correlations, which increases sampling errors. Additionally, the TC method needs a sufficient number of triplets
for statistical analysis. Zwieback et al. (2012) showed that for samples above 500, TC
estimates had 10% uncertainty, however, in some studies, fewer samples have been used
(e.g. Scipal et al., 2008; Dorigo et al., 2010).
In TC, triplets are usually composed of a model (θ) and two sets of observations (θobs1 and
θobs2 in the following example) that are assumed to be linearly related to a same truth Θ
as follows,
θ = Θ + θ
(16)
θobs1 = α1 Θ + β1 + 1
θobs2 = α2 Θ + β2 + 2
where α1 , α2 are the scaling factors and β1 , β2 are the intercepts of the linear equations
(the model is used as the reference dataset). 1 and 2 are the observation zero mean
random errors with variances of σ1∗2 and σ2∗2 , respectively. θ is the model zero mean
random error with variance σθ2 .
∗
if the observations are rescaled into the model space by θobs
= (θobsi − βi ) /αi and ∗i =
i
i /αi (with subscript i standing for 1 and 2), then the equations in Eq.16 can be combined
and re-arranged to be
∗
θ − θobs1
= θ − ∗1
∗
θ − θobs2
= θ − ∗2
(17)
∗
∗
θobs1
− θobs2
= ∗1 − ∗2 .
24
Following the TC procedure (Stoffelen, 1998), estimates of the model and observation
error variances (σθ2 , σ1∗2 and σ2∗2 , respectively) can be obtained by cross-multiplying the
equations in Eq.17, while assuming that the errors in the model and observations are
independent between the three datasets and in time, and that there are sufficiently large
number of triplets:
∗
∗
σθ2 = (θobs1
− θ) (θobs2
− θ)
∗
∗
∗
σ1∗2 = (θobs1
− θobs2
) (θobs1
− θ)
(18)
∗
∗
∗
σ2∗2 = (θobs1
− θobs2
) (θobs2
− θ).
The overbar denotes the average in time. The scaling factors and intercepts in Eq.16
must be resolved before the estimation of model and observation error variances in Eq.18.
Following the preprocessing techniques used in TC (see details in Yilmaz and Crow, 2013,
Appendix A), these factors can be estimated as
α1 =
θobs2 θ
θobs1 θobs2
and α2 =
θobs1 θ
.
θobs1 θobs2
(19)
The additive bias between the model and observations can be defined as B = E(θ) −
E(θobsi ) (with subscript i standing for 1 and 2). If the mean of the observations is modified
to match E(θ), the intercepts in Eq.16 become βi = (1 − αi )θ.
TC has been widely validated as a reliable technique to estimate observation errors when
the data requirements are met (e.g., Yilmaz and Crow, 2013; Su et al., 2014). The data
requirements are that there is a sufficiently large number of collocated data points from
three independent data series and that the linear relationships and error structures are
maintained throughout the analysis period. In real applications however, these conditions
are difficult to realise given the infrequent spatiotemporal sampling of satellite sensors (Su
et al., 2014).
Seeking to relax some of the data requirements of TC, Su et al. (2014) recalled the concept
of instrumental variable regression (the general case of TC) and proposed an alternative
implementation of this regression where a lagged variable was used as the third independent dataset in TC. This scheme (LV hereafter) features the important advantage of
requiring only two datasets and showed satisfactory results for active and passive SSM
products over Australia, when compared with TC results. In this thesis, I apply (for the
first time in SM-DA context) the LV scheme for periods when the model SM prediction
and only one satellite dataset is available or when the sampling requirement of TC are not
met (Chapter 5).
It is also common to assume that the satellite SM observation errors are time-invariant
(e.g., Reichle et al., 2008; Ryu et al., 2009; Crow and Van den Berg, 2010; Brocca et al.,
2010, 2012a); however, studies evaluating satellite SM products have shown an important
25
temporal variability in measurement errors (Loew and Schlenz, 2011; Su et al., 2014).
Since a data assimilation scheme explicitly updates the model prediction based on the
relative weights of the model and the observation errors, assuming a constant observation
error will lead to over-correction of the model state if the actual observation error is higher
than assumed, and vice versa.
To characterise the temporal behaviour of the observation error, the above techniques (TC
or LV) can be applied to specific time windows of the observations and model predictions
(for example, by grouping the triplets or doublets by month-of-the-year). There is however,
a trade-off between the sampling window (which defines the temporal characterisation of
the error) and the sample size (number of triplets in each subset). To address the issue
of temporally variant observation errors I develop an approach that involves seasonal
characterisation of the observation error by applying TC and LV to 4-month sampling
windows (further details in Chapter 5). This seasonal approach is novel in the context of
SM-DA.
5
Forcing and dual correction schemes
As introduced in Chapter 1, in addition to the popular state correction assimilation approach, recent studies have explored the use of satellite SM retrievals for filtering errors
present in satellite-based rainfall accumulation products (Crow and Bolten, 2007; Pellarin
et al., 2008; Crow et al., 2009; Brocca et al., 2013). Given that space-borne rainfall estimates provide the only possible source of near real time information for most global land
areas, the potential of these techniques is highly significant, especially for poor instrumented areas (Crow et al., 2009).
The premise of these studies is that soil moisture contains information about antecedent
rainfall that can be used to constrain rainfall estimates by using simple water balance models. Although these studies have slightly different approaches (further details in Chapter
6), they have all shown the potential for improving satellite rainfall estimates by using
satellite SM retrievals.
The above implies that the use of microwave soil moisture could enhance models predictions of runoff by the improvement of both the antecedent moisture conditions (which
theoretically determines the catchment infiltration capacity) via a state correction SM-DA
scheme coupled with the improvement of storm-scale rainfall totals (which represent the
most important meteorological input of a rainfall-runoff model) via a forcing correction
SM-DA scheme (Crow and Ryu, 2009). This has motivated recent studies to test these
dual forcing/state correction schemes (dual SM-DA). Massari et al. (2014) set up a simple scheme in which in-situ observations of SM were used to correct the rainfall (through
the SM2RAIN algorithm introduced by Brocca et al. (2014)) and to initialise the wetness
condition of a simple rainfall-runoff model. Their case study showed high potential for the
26
SM data to improve flood modelling.
Using a relatively more complex assimilation scheme and rainfall-runoff model, Crow and
Ryu (2009) set up a state correction SM-DA scheme integrated with a rainfall correction
scheme (using the Soil Moisture Analysis Rainfall Tool, SMART, introduced by Crow
et al. (2009)) in a series of synthetic twin experiments. The formulation of this dual
correction scheme avoids ”over-use” of the remotely sensed soil moisture in the analysis
(i.e., it avoids cross-correlation between forecasting and observing errors). The key point
is that the corrected precipitation is fed into an off-line model simulation (based on the
state update analysis) and not the state-update analysis itself. The results of this dual
SM-DA scheme were further supported by Chen et al. (2014) in a real data application.
Both studies showed that the satellite rainfall correction led to improvement in streamflow
prediction, especially during high flow periods. On the other hand, the soil water state
correction led mainly to improved base flow component (low flows simulation). The combined state/forcing correction scheme led to improvement of both the high and the low flow
components of the streamflow, outperform both the state-only and forcing-only correction
schemes. It remains unclear however, how well this dual SM-DA scheme performs for different catchment characteristics including climate and rainfall-runoff mechanisms.
Addressing this gap, in Chapter 6 I expand the evaluation of the dual SM-DA proposed
by Crow and Ryu (2009) within 4 large semi-arid catchments in Australia. I devise the
dual SM-DA scheme under an ungauged catchment scenario (without rain gauges, only
satellite data is used to force the model) to answer three research questions: 1) How much
can we improve streamflow prediction by the correction of satellite rainfall via SMART?
2) How much can we improve streamflow prediction by the assimilation of SSM in a state
correction scheme? 3) What are the impacts in streamflow prediction of a combined state
and forcing correction scheme?
6
Summary and overall approach
I have provided a general review of the main challenges that must be addressed to implement a SM-DA scheme. I described the most commonly used techniques to address each
of those challenges and mentioned which ones were adopted in Chapters 3 to 6 of this
thesis. As highlighted above, some of the adopted techniques were new in the context of
SM-DA. This forms part of the novel contributions of this thesis and includes:
• The correction of the unintended bias introduced in the generation of streamflow
ensemble predictions (described in Section 4.1 and implemented in Chapters 5 and
6). I apply the bias correction scheme proposed by Ryu et al., (2009) directly to
the streamflow prediction. I use the unperturbed model run to estimate the mean
bias in the streamflow (following Eq.9, but using streamflow instead of soil moisture)
and then correct each ensemble member by subtracting this mean bias. This prac27
tical tool ensures that the streamflow ensemble mean maintains the performance of
the unperturbed (calibrated) model run–thus avoiding artificial degradation of the
unperturbed model run by bias.
• The use of a maximum a posteriori approach to estimate model error parameters
(described in Section 4.1 and implemented in Chapters 5 and 6).
• The use of a lagged-variable approach to estimate satellite observation error (described in Section 4.3 and implemented in Chapter 5).
• A seasonal characterisation of the satellite SM error (described in Section 4.3 and
implemented in Chapter 5).
In addition to introducing these new techniques in the context of SM-DA applications,
the following chapters answer my two main research questions: 1) Can we improve flood
prediction by correcting a rainfall-runoff model SM state via satellite SM data assimilation?
2) Can we further improve flood prediction by correcting both the satellite rainfall forcing
data and the model SM state via satellite SM data assimilation?
The approach I have taken to answering these two main questions, which differentiates this
work from a large number of previous SM-DA applications, is to set up the experiments
using real data (observed satellite retrievals are used to feed the assimilation scheme
and observed streamflow to evaluate SM-DA results). Real data experiments have the
inherent challenge of not knowing the true information about model and observations
errors. This approach therefore, leads to sub-optimal SM-DA schemes; however, it provides
real evidence of the efficacy of using satellite SM to improve flood prediction.
While answering my first research question, I set up a series of real data experiments and
define 5 sub-questions related to different aspects of the state correction SM-DA scheme.
It should be noted that in this exploration, the rainfall data used to force the model is a
gauged-interpolated dataset. This avoids the incorporation of further errors in the system
coming from satellite rainfall products. A summary of the sub-questions, and a description
of how they are answered in Chapters 3 to 5, is presented below:
1. How do assumed observation error structures affect SM-DA efficacy for improving
streamflow prediction?
This question was introduced in Section 4.3 and targets the research gap regarding
the assumptions made about the structure of the satellite observation errors. While
in SM-DA applications it is commonly assumed that these errors are temporally
uncorrelated, studies dedicated to satellite SM error characterisation have put this
assumption in doubt (Crow and van den Berg, 2010). Temporal correlation in the
observations errors could lead to a sub-optimal characterisation of the observation
error and to the the violation of a key EnKF assumption. In Chapter 3, I evaluate
the magnitude of these potential impacts within a real data case.
28
2. What are the impacts of different rescaling techniques on the efficacy of SM-DA?
This question was introduced in Section 4.3 and targets the research gap regarding
the impacts that different rescaling techniques may have on SM-DA results. In
Chapter 4, I answer this question by setting up a real data case and testing several
commonly used techniques for rescaling the satellite observations into the model
space.
3. While rainfall is presumably the main driver of flood generation in semi-arid catchments, can we effectively improve streamflow prediction by correcting the soil water
state of the model?
This question is defined based on the study catchment selected in the experiments
presented in Chapter 5. The runoff mechanisms of the study catchment are likely to
be dominated by rainfall, as is the case for several large and sparsely instrumented
semi-arid catchments with an extensive history of flooding within Australia. Within
this context, I aim to examine and provide real evidence of the potential for improving flood prediction by correcting the antecedent wetness condition of the catchment
via SM-DA.
4. What is the impact of accounting for channel routing and the spatial distribution of
forcing data on SM-DA performance?
This question aims to reinforce the fact that a data assimilation scheme is designed
to reduce the random component of the model error and does not address systematic
errors (see Section 2). I explore the importance of the model quality before assimilation for enhancing the SM-DA performance by evaluating the results of SM-DA from
a lumped and a semi-distributed model configuration. These results are presented
in Chapter 5.
5. What are the prospects for improving streamflow within ungauged catchments using
satellite SM?
Given that the absence of co-located streamflow gauging stations is typical for most
locations in all catchments, I set up the experiments in Chapter 5 under an ungauged
(no stream gauges) scenario for the inner catchments of a semi-distributed model
scheme. I then evaluate the skill of SM-DA within these inner catchments, which
provided useful insights into this common situation.
To answer my second research question, I adopt one of the available forcing correction SMDA schemes (Section 5) and combine it with the state SM-DA developed in the first stage
of the thesis (Chapters 3 to 5). The dual forcing/state SM-DA scheme is implemented in
Chapter 6 where the following specific questions are answered:
1. Can we improve the quality of an operational satellite rainfall product by the assimilation of satellite soil moisture via SMART?
29
2. Does this forcing correction scheme has a positive impact in streamflow prediction?
3. Can we improve streamflow prediction by the assimilation of satellite SM in a state
correction scheme?
4. What are the impacts in streamflow prediction of a combined state and forcing correction scheme?
The above questions aim to assess the relative benefits of correcting independently and
simultaneously, the satellite rainfall forcing data and the model soil moisture state for the
purposes of improving flood prediction. I set up the experiments within 4 large semi-arid
catchments and present the results in Chapter 6 .
30
Chapter 3
Impacts of observation error
structure in SM-DA
This chapter was published as the following peer-reviewed proceeding paper:
C. Alvarez-Garreton, D. Ryu, A. W. Western, W. T. Crow, and D. E. Robertson. Impact
of observation error structure on satellite soil moisture assimilation into a rainfall-runoff
model. In J. Piantadosi, R. Anderssen, and J. Boland, editors, MODSIM2013, 20th International Congress on Modelling and Simulation. Modelling and Simulation Society of
Australia and New Zealand, pages 3071-3077, December 2013.
31
Impact of observation error structure on satellite soil
moisture assimilation into a rainfall-runoff model.
C. Alvarez-Garreton a , D. Ryu a , A. W. Western a , W. Crow b , D. Robertson c
a
Department of Infrastructure Engineering, The University of Melbourne, Parkville, Victoria, Australia
b
USDA-ARS Hydrology and Remote Sensing Laboratory, Beltsville, Maryland, United States
c
CSIRO Land and Water, Victoria, Australia
Email: calverez@student.unimelb.edu.au
Abstract: In the Ensemble Kalman Filter (EnKF) - based data assimilation, the background prediction of
a model is updated using observations and relative weights based on the model prediction and observation
uncertainties. In practice, both model and observation uncertainties are difficult to quantify thus have been
often assumed to be spatially and temporally independent Gaussian random variables. Nevertheless, it has
been shown that incorrect assumptions regarding the structure of these errors can degrade the performance of
the stochastic data assimilation.
This work investigates the autocorrelation structure of the microwave satellite soil moisture retrievals and
explores how assumed observation error structure affects streamflow prediction skill when assimilating these
observations into a rainfall-runoff model. An AMSR-E soil moisture product and the Probability Distribution
Model (PDM) are used for this purpose.
Satellite soil moisture data is transformed with an exponential filter to make it comparable to the root zone
soil moisture state of the model. The exponential filter formulation explicitly incorporates an autocorrelation
component in the rescaled observation, however, the error structure of this operator has been treated until now
as an independent Gaussian process. In this work, the variance of the rescaled observation error is estimated
based on the residuals from the rescaled satellite soil moisture and the calibrated model soil moisture state.
Next, the observation error structure is treated as a Gaussian independent process with time-variant variance;
a weakly autocorrelated random process (with autocorrelation coefficient of 0.2) and a strongly autocorrelated
random process (with autocorrelation coefficient of 0.8). These experiments are compared with a control
case which corresponds to the commonly used assumption of Gaussian independent observation error with
time-fixed variance.
Model error is represented by perturbing rainfall forcing data and soil moisture state. These perturbations are
assumed to represent all forcing and model structural/parameter errors. Error parameters are calibrated by
applying two discharge ensemble verification criteria. Assimilation results are compared and the impacts of
the observation error structure assumptions are assessed.
The study area is the semi-arid 42,870 km2 Warrego at Wyandra River catchment, located in Queensland,
Australia. This catchment is chosen for its flooding history, along with having geographical and climatological
conditions that enable soil moisture satellite retrievals to have higher accuracy than in other areas. These
conditions include large area, semi-arid climate and low vegetation cover. Moreover, the catchment is poorly
instrumented, thus satellite data provides valuable information.
Results show a consistent improvement of the model forecast accuracy of the control case and in all experiments. However, given that a stochastic assimilation is designed to correct stochastic errors, the systematic
errors in model prediction (probably due to the inaccurate forcing data within the catchment) are not addressed
by these experiments. The assumed observation error structures tested in the different experiments do not exhibit significant effect in the assimilation results. This case study provides useful insight into the assimilation
of satellite soil moisture retrievals in poorly instrumented semi-arid catchments.
Keywords: Data assimilation, soil moisture, satellite retrievals, rainfall-runoff model, hydrology.
32
C. Alvarez-Garreton et al., Impacts of observation error structure in soil moisture data assimilation
1
I NTRODUCTION
Accurate soil moisture predictions can lead to better modelling of hydrological processes including runoff,
groundwater recharge and evapotranspiration. For example, it was shown that runoff prediction could be improved by assimilating antecedent soil moisture into rainfall-runoff modelling (Crow et al., 2005). Nonetheless, the improvement in model skill resulting from assimilating soil moisture observations (on-site or remotely
sensed) into rainfall-runoff models has not been fully assessed due to three main limitations: observation uncertainties, temporal resolution and the spatial mismatch between observations and soil water content from
rainfall-runoff models (Brocca et al., 2012).
Ground measurements of soil moisture are scarce in most regions, which positions satellite retrievals as a potential solution for improving soil moisture representation. However, satellite soil moisture retrievals have in
general higher uncertainty than ground measurements, a coarser spatial resolution and represent only the top
few centimetres of soil, all factors that need to be accounted for their use. Exploring tools for improving runoff
predictions using satellite soil moisture retrievals has become very popular. The success of stochastic assimilation relies on several factors including whether soil moisture is a dominant control on the runoff generation
process in the catchment, the representativeness and accuracy of the observations, and having an adequate
representation of model and observation errors. It has been shown that incorrect assumptions regarding the
model structure and observation errors can degrade the performance of the stochastic data assimilation (Crow
and van Loon, 2006; Crow and Reichle, 2008; Crow and van den Berg, 2010; Reichle et al., 2008; Ryu et al.,
2009). Up to date, for hydrologic applications, the error structure of these observations has not been carefully
investigated and their assimilation into rainfall-runoff models has been undertaken using the observed time
series (i.e., one single realisation from stochastic process) and assuming a time invariant error variance.
In this study, we show how observation error structure assumptions affect the improvement in assimilation
skill using a soil moisture product from the Advance Microwave Scanning Radiometer (AMSR-E) and the
probability distributed model (PDM). Additionally, we treat the observation as a stochastic process represented by a Monte Carlo - based ensemble. For this we set up an ensemble Kalman filter (EnKF) scheme.
The depth mismatch between observed soil moisture (few centimetres of soil) and the predicted soil moisture
(depth depending on the calibrated model parameters, but more comparable to the root zone layer) is addressed
by applying an exponential filter to the surface observations (Wagner et al., 1999). This filter transforms the
surface soil moisture into a profile soil moisture through the estimation of a soil wetness index (SWI). Subsequently, systematic differences between the SWI and the predicted soil moisture are removed by a linear
regression rescaling. In different assimilation experiments, the observation error structure is treated as a sequentially independent Gaussian process or as an autocorrelated random process. For evaluating the impacts
of these assumptions in the assimilation results, one control case and 3 experiments are defined. The control
case corresponds to the commonly used assumption of time invariant variance of the observation error and the
assimilation of the observed time series (single realisation). Experiment 1 assumes Gaussian independent error
in the observation and treats the observation as a stochastic process so the assimilation is made based on an
ensemble of observations. Experiments 2 and 3 assume a “weakly” autocorrelated observation error (Exp.2)
and a “strongly” autocorrelated observation error (Exp.3). The assimilation of these two last experiments uses
the observed time series (single realisation). Assimilation results are compared and evaluated for the different
observation error structure assumptions.
2
S TUDY AREA AND DATA
The study area is the Warrego River catchment (42,870 km2 ), located in south west Queensland, Australia (see
Fig.1). The mean annual precipitation over the catchment is 520 mm and it has a long history of flooding, with
at least 10 major events in the last 100 years that have caused extensive inundation of towns and rural lands
(http://www.bom.gov.au/qld/flood/brochures/warrego).
Rainfall data was obtained from the Australian Water Availability Project (AWAP), which covers the period
from 1900-up to date and has a spatial resolution of 0.05◦ (Jones et al., 2009). Hourly streamflow records for
Warrego at Wyandra gauge were collected from the Queensland Department of Natural Resources and Mines
website (http://watermonitoring.derm.qld.gov.au) for 1967-2013 period. The soil moisture dataset was obtained from the Advance Microwave Scanning Radiometer (AMSR-E), version 5 C/X-band, 0.25◦ resolution
level 3 product for the period 07/2002-10/2011 (Owe et al., 2008).
33
10°S
1:80,000,000
Augathella
15°S
#
Charleville
20°S
#
##
##
###
# #
#
#
Wyandra
25°S
Cunnamulla
30°S
35°S
Towns
40°S
#
Rainfall station
Warrego River catchment
AMSR-E grid
115°E 120°E 125°E 130°E 135°E 140°E 145°E 150°E 155°E
Figure 1. Warrego river catchment
3
M ETHODS
3.1 Rainfall-runoff model
The probability distributed model (PDM) is a conceptual rainfall-runoff model that has been widely used in
hydrologic research (Moore, 2007). The model treats soil water content as a probability distributed variable.
Then, two cascade reservoirs are used for representing surface storage and one routing reservoir for representing sub-surface runoff generation. The main inputs of the model are rainfall and potential evaporation. A
detailed description of the model structure and formulations is presented by Moore (2007). Here, a lumped
model of the catchment and a daily time step is used. The model is calibrated by using a genetic algorithm
(Chaturvedi, 2010) with an objective function based on the Nash-Sutcliffe statistic.
3.2 EnKF formulation
The Kalman filter is a Bayesian estimator that sequentially updates model background predictions with available observations. The updating step is based on the relative values of the uncertainties (error covariance)
existing in the model and the observations. In the ensemble Kalman filter (EnKF), the error covariance is
explicitly calculated from Monte Carlo-based ensembles. For a state-updating assimilation approach, the state
ensemble is created by perturbing forcing data and/or the state of the model with unbiased errors.
−
−
−
Let θ− (t) = {θ1,t
, θ2,t
, ..., θN,t
} be the perturbed model soil moisture state ensemble prediction (background
prediction) before the updating step for time step t, where N is the number of ensemble members. Given
that there is no knowledge of the real state values, the ensemble average is use as reference to estimate the
0
−
prediction error. The error of member i (θ−
i,t ), the abnormality matrix of the ensemble (θM (t)), and the
covariance matrix of the state model errors (Pt− ), for each time step t, are calculated by:
0
−
θ−
i,t = θi,t −
N
1 X −
θ
N i=1 i,t
;
0
0
0
−
−
−
−
θM
(t)0 = {θ1,t
, θ2,t
, ..., θN,t
} ;
Pt− =
T
1
−
θ− (t)0 × θM
(t)0
N −1 M
(1)
When a soil moisture observation is available, the SWI is estimated and rescaled (see Section 3.3), and each
member of the state ensemble is updated by the rescaled observation, θobs(EF ) (t), using the following expression:
+
−
−
θi,t
= θi,t
+ K(θobs(EF ) (t) − H(θi,t
))
with
K=
Pt− H T
HPt− H T + Rt
(2)
where K is the Kalman gain, H is the observation operator that relates the modelled state to the measured
variable. As the observation is rescaled separately prior to the state updating, H reduces to the identity matrix
in this work. Rt is the error variance of the rescaled observation for time t.
3.3 Satellite soil moisture rescaling and observation error estimation
Satellite soil moisture retrievals (θobs ) represent the top few centimetres of the soil, while the rainfall-runoff
model soil moisture state accounts for a significantly deeper layer. The depth of the modelled storage depends
on the calibrated model parameters, but typically it is comparable with the root zone soil moisture. For
transferring θobs information into the soil water content space of the model (θ), we use the exponential filter
proposed by Wagner et al. (1999). This filter assumes that the variation in time of the root zone soil moisture is
linearly related to the difference between surface soil moisture and root zone soil moisture. The filter estimates
a profile average saturation degree by recursively calculating a soil wetness index (SWI) every time there is a
34
satellite soil moisture retrieval θobs (Brocca et al., 2010):
SW I(t) = SW I(t − 1) + Gt [θobs (t) − SW I(t − 1)]
with
Gt =
Gt−1
t−(t−1)
−
T
(3)
Gt−1 + e
Gt is a gain term varying between 0 and 1. T is a calibrated parameter representing the time scale of the SWI
variation. SWI is then linearly rescaled in order to meet the same mean and standard deviation as the root zone
soil moisture from the model (θ). The rescaled observation is named θobs(EF ) .
The estimation of observation uncertainties is a major challenge, especially given the lack of ground measurements of soil moisture in most areas. In this study we propose to determine an upper boundary of the rescaled
observation error variance. If we assume that the error is independent of the measurement (i.e., orthogonal),
0
we can express the variance of the rescaled observation as V ar(θobs(EF
) ) = V ar(θobs(EF ) ) + R, where R is
0
the rescaled observation error variance from Eq. 2 and V ar(θobs(EF ) ) is directly calculated from the rescaled
0
data. Given that the variance is always positive, we can use V ar(θobs(EF
) ) as the upper boundary of R. In a
first stage, R is considered to be equal to the upper boundary.
Once we have the variance of the rescaled soil moisture error (R), the following experiments are defined in
order to explore how error structure assumptions affect the assimilation results:
•
•
•
•
Control case: error is treated as a fixed, time invariant variance.
Exp.1: error is treated as white Gaussian process lacking auto-correlation.
Exp.2: error is treated as a “weakly” autocorrelated process, with lag-1 day coefficient AR(1)=0.2.
Exp.3: error is treated as a “strongly” autocorrelated process, with lag-1 day coefficient AR(1)=0.8.
The random component of the autocorrelated errors in Exp.2 and Exp.3 is assumed to be zero mean autocorrelated Gaussian noise, the spread of which is calculated by constraining the temporal mean of the rescaled
observation ensemble covariance to be equal to R.
3.4
Model error estimation
Model error is represented by perturbing forcing precipitation data with an independent multiplicative lognormally distributed error (mean 1 and standard deviation σp ), and by perturbing the soil moisture with
independent additive normally distributed error (mean 0 and standard deviation σsm ). These perturbations
consider input forcing, model parameter and model structure error sources. Model error parameters (σp and
σsm ) are calibrated by running the open-loop (perturbing forcing and soil moisture state, but without assimilating rescaled soil moisture observations) for 100 ensemble members (N), and evaluating the following two
discharge ensemble verification criteria:
i) If the ensemble spread is large enough, the temporal average of the ensemble skill (skt ) should be similar
to the temporal average of the ensemble spread (spt ), i.e., sk/sp = 1 (Brocca et al., 2012; De Lannoy et al.,
2006), where:
sk =
T
2
1 X
Qsim (t) − Qobs (t)
T t=1
and
sp =
"
#
T
N
2
1 X 1 X
Qsim (i, t) − Qsim (t)
T t=1 N i=1
(4)
ii) If the observation is indistinguishable from a member
of the ensemble, the ratio between sk and the ensemp
ble mean-square-error (mse) should be equal to N + 1/2N (Moradkhani et al., 2005; Brocca et al., 2012),
where:
"
#
T
N
1 X 1 X
2
mse =
(Qsim (i, t) − Qobs (t))
T t=1 N i=1
4
(5)
R ESULTS AND DISCUSSION
4.1 Model calibration
Figure 2 presents the simulated and observed discharge time series for both the calibration and verification
periods. These results reveal that calibrated model underestimates the observed peak flows and overestimates
low flows. A likely factor that contributes to the performance of the model is the poor density of rainfall gauges
within the catchment, which results in low quality gridded rainfall data for the area. Model performance
can also be related to the objective function used for calibration (maximising the Nash-Sutcliffe efficiency)
(Gupta and Kling, 2011). Given the semi-arid nature of the catchment, rainfall-runoff generation processes
35
Calibration period: 1967−2001 (NS= 0.49) Verification period: 2002−2013 (NS =0.57)
8
Obs
Model
Q (mm/day)
6
4
2
0
Apr71
Oct76
Mar82
Sep87
Mar93
Sep98
Feb04
Aug09
Figure 2. Discharge prediction time series, the dashed black line indicates the end of calibration period.
are likely to be dominated by the soil water content of the catchment, which would explain why many rainfall
events do not result in discharge (this can be seen by comparing runoff ratios with rainfall intensity and with
modelled soil moisture, not shown here). Presumably, given the poor representation of the forcing data, the
model structure and conceptualisation are not able to correctly represent this saturation excess runoff process.
Due to the lack of ground data for improving rainfall representation over the catchment, and the likely high
dependency of runoff generation processes on the soil water content of the catchment, the assimilation of
satellite soil moisture offers an important opportunity for improving the model discharge prediction.
4.2 Model and observation error estimation
The linear rescaling described in Section 3.3 was trained using the first two years of data (2002-2004) and
then updated in each time step. The parameter T of the exponential filter (eq. 3) was calibrated for the same
training window. The rescaled observation time series is presented in Figure 3, and has a correlation coefficient
of 0.82 with the modelled soil moisture for the verification period. The standard deviation of the associated
residuals (stdres ) is 0.05 m3 /m3 (expressed as volumetric percentage of the calibrated soil moisture storage of
630 mm). These results reveal the strong concordance between the model soil moisture state and the rescaled
surface soil moisture observation. The observation error variance is estimated as 1360 mm3 . The adopted
standard deviation of the random component of the “weak” and “strong” autoregressive processes (exp. 2
and 3) are 0.0574 m3 /m3 and 0.0351 m3 /m3 , respectively. These values fullfill the constraint of a temporal
observation variance equals to R. Following the methodology described in section 3.4, model error parameters
calibration results in σP = 0.3195 and σsm = 0.0248 m3 /m3 (volumetric percentage of soil moisture storage).
Soil moisture (mm)
Model
Rescaled
400
200
0
Jan04
Jan06
Jan08
Rescaled soil moisture (mm)
Calibration period
600
Jan10
Verification period
500
500
400
400
300
300
200
200
100
100
0
0
0 100 200 300 400 500
Model soil moisture (mm)
0 100 200 300 400 500
Figure 3. Rescaled observations, dashed black line indicates the end of training period.
4.3 Assimilation experiments
The evaluation of assimilation is undertaken for the period 06/2004-10/2011. The first half of the analysis
window, up to 03/2008, is characterised by small flow events (Period 1) while the second half (03/200810/2011) is characterised by larger flow events, having at least three major flood events (Period 2).
The assimilation results for experiment 3 are presented in Fig. 4, for these two separate periods. The green
dashed line represents the un-perturbed model (i.e. the predictions of the calibrated model, called “sim”). From
these graphs it can be seen that for small flow events (Period 1), the assimilation procedure is reducing the
36
Period 1
Q (mm/day) Exp. 3
2.5
obs
sim
O−L ens
O−L mean
updated ens
updated mean
2
1.5
1
0.5
0
09/04
03/05
10/05
05/06
11/06
06/07
Period 2
Q (mm/day) Exp. 3
8
6
4
2
0
12/07
07/08
01/09
08/09
03/10
09/10
04/11
Figure 4. Assimilation results for experiment 3 (observation error treated as a strong autocorrelated process,
with lag-1 day coefficient AR(1)=0.8).
Table 1. Evaluation metrics of assimilation results for control case and experiments
Experiment
Control case
Exp.1
Exp.2
Exp.3
*
RMSD sim
Period 1
Period 2
0.05
0.05
0.05
0.05
0.32
0.32
0.32
0.32
MRMSD open loop
Period 1 Period 2
(0.01)*
(0.02)*
0.11
0.44
0.11
0.45
0.12
0.44
0.12
0.47
MRMSD updated
Period 1
Period 2
(0.002)*
(0.005)*
0.07
0.36
0.06
0.34
0.08
0.36
0.08
0.36
NRMSD
Period 1 Period 2
(0.12)*
(0.06) *
0.65
0.80
0.56
0.76
0.65
0.82
0.65
0.77
95% confidence interval
open-loop spread and in general reducing the model overestimation of streamflow (when analysing the mean
of the open-loop and updated ensemble, compared with the observed discharge). For larger flow events events
(Period 2), the assimilation is mainly reducing the spread of the open-loop while the model underestimation is
not being corrected. The assimilation results of the control case and experiments 1 and 2 show similar relation
between the open-loop and updated ensembles (not shown here) and their evaluation metrics are summarised
in Table 1.
Table 1 presents the mean root mean square difference (MRMSD) and the normalised MRMSD (NRMSD)
for the different assimilation experiments for Periods 1 and 2. The NRMSD is calculated as the ratio between
the MRMSD from the open loop ensemble and the MRMSD from the updated ensemble. Additionally, the
RMSD of unperturbed model (sim) is presented in the Table. Data assimilation for the control case and the
experimental cases results in an improvement of around 40% in period 1 and of 20% in period 2, in terms of
MRMSD. Differences between the control case and the experiments are within the confidence intervals thus
they are not considered significant.
In general, the spread of the discharge ensemble is reduced by assimilating satellite soil moisture retrievals, but
the poor representation of the model, evaluated as the ensemble mean compared with the observed discharge, is
not consistently corrected (it only improves for specific events). Given that stochastic assimilation is designed
to correct stochastic errors, the model systematic errors (presumably coming from the poor representation of
precipitation over the catchment, given the lack of instrumentation within the area) are not addressed thus the
performance of the assimilation becomes marginal. Moreover, the different observation error structures tested
does not affect the assimilation results. This suggests that even though observation error structure theoretically
37
has a direct effect on an EnKF-based assimilation, when working with real data and the uncertainties inherent
in a poorly instrumented area, the effect is trivial.
5
CONCLUSIONS
This work has shown that the assimilation of satellite soil moisture retrievals derived from AMSR-E into PDM
results in a consistent improvement of the model predictions. This improvement is based on the reduction of the
model forecast uncertainty. Nevertheless, given that a stochastic assimilation is designed to correct stochastic
errors (which translates in the achieved reduction of model forecast uncertainty), the systematic poor model
performance (probably due to poor representation of forcing data within the catchment) is not addressed by
these experiments. While the spread of the ensemble discharge prediction is reduced after assimilation, the
ensemble mean is not always closer to the discharge observation. Moreover, the different observation error
structures tested here did not result in significant differences in the assimilation performance. This suggests
that when the model prediction accuracy and uncertainties are mainly controlled by high uncertainties in
forcing data, the assumptions of the observation error structure made in a state-update assimilation framework
have little effect. These findings enhance our understanding of the advantages and limitations of assimilating
satellite soil moisture observations into a rainfall-runoff model for improving streamflow prediction. In order
to address the systematic model predictions biases, while reducing the stochastic errors of the model, efforts
should be focused on combining the presented state-update assimilation scheme with some tool to reduce the
uncertainty in rainfall data.
ACKNOWLEDGEMENT
This research was conducted with financial support from the Australian Research Council (ARC Linkage
Project No. LP110200520) and the Bureau of Meteorology, Australia. We gratefully acknowledge the advise
and data provision of Chris Leahy and Soori Sooriyakumaran from the Bureau of Meteorology, Australia.
R EFERENCES
Brocca, L., F. Melone, T. Moramarco, W. Wagner, V. Naeimi, Z. Bartalis, and S. Hasenauer (2010). Improving runoff
prediction through the assimilation of the ASCAT soil moisture product. Hydrology and Earth System Sciences 14(10),
1881–1893.
Brocca, L., T. Moramarco, F. Melone, W. Wagner, S. Hasenauer, and S. Hahn (2012). Assimilation of surface- and rootzone ASCAT soil moisture products into rainfall–runoff modeling. Geoscience and Remote Sensing, IEEE Transactions
on 50(7), 2542–2555.
Chaturvedi, D. (2010). Matlab Program of Genetic Algorithms.
Crow, W. T., R. Bindlish, and T. J. Jackson (2005). The added value of spaceborne passive microwave soil moisture
retrievals for forecasting rainfall-runoff partitioning. Geophysical Research Letters 32, L18401.
Crow, W. T. and R. H. Reichle (2008). Comparison of adaptive filtering techniques for land surface data assimilation.
Water Resources Research 44, W08423–.
Crow, W. T. and M. J. van den Berg (2010). An improved approach for estimating observation and model error parameters
in soil moisture data assimilation (doi 10.1029/2010WR009402). Water Resources Research 46, W12519.
Crow, W. T. and E. van Loon (2006). Impact of Incorrect Model Error Assumptions on the Sequential Assimilation of
Remotely Sensed Surface Soil Moisture. Journal of Hydrometeorology 7, 421–432.
De Lannoy, G. J., P. R. Houser, V. Pauwels, and N. E. Verhoest (2006). Assessment of model uncertainty for soil moisture
through ensemble verification. Journal of Geophysical Research: Atmospheres (1984–2012) 111(D10).
Gupta, H. V. and H. Kling (2011). On typical range, sensitivity, and normalization of mean squared error and Nash-Sutcliffe
efficiency type metrics. Water Resources Research 47(10), W10601.
Jones, D. A., W. Wang, and R. Fawcett (2009). High-quality spatial climate data-sets for australia. Australian Meteorological and Oceanographic Journal 58(4), 233.
Moore, R. J. (2007). The PDM rainfall-runoff model. Hydrology & Earth System Sciences 11(1), 483–499.
Moradkhani, H., S. Sorooshian, H. Gupta, and P. Houser (2005). Dual state–parameter estimation of hydrological models
using ensemble Kalman filter. Advances in Water Resources 28(2), 135–147.
Owe, M., R. de Jeu, and T. Holmes (2008). Multisensor historical climatology of satellite-derived global land surface
moisture. Journal of Geophysical Research: Earth Surface (2003–2012) 113(F1).
Reichle, R. H., W. T. Crow, and C. L. Keppenne (2008). An adaptive ensemble Kalman filter for soil moisture data
assimilation. Water Resources Research 44(3).
Ryu, D., W. T. Crow, X. Zhan, and T. J. Jackson (2009). Correcting Unintended Perturbation Biases in Hydrologic Data
Assimilation. Journal of Hydrometeorology 10, 734–750.
Wagner, W., G. Lemoine, and H. Rott (1999). A method for estimating soil moisture from ERS scatterometer and soil
data. Remote Sensing of Environment 70(2), 191–207.
38
Chapter 4
Impacts of observation rescaling in
SM-DA
This chapter was published as the following article:
C. Alvarez-Garreton, D. Ryu, A. W. Western, W. T. Crow, and D. E. Robertson. The
impacts of assimilating satellite soil moisture into a rainfall-runoff model in a semi-arid
catchment. Journal of Hydrology, 519: 2763-2774, 2014.
39
The impacts of assimilating satellite soil moisture into a rainfall-runoff model in
a semi-arid catchment
C. Alvarez-Garretona , D. Ryua , A.W. Westerna , W.T. Crowb , D.E. Robertsonc
a Department
of Infrastructure Engineering, The University of Melbourne, Parkville, Victoria, Australia
Hydrology and Remote Sensing Laboratory, Beltsville, Maryland, United States
c CSIRO Land and Water, Highett, 3190 Victoria, Australia
b USDA-ARS
Abstract
Soil moisture plays a key role in runoff generation processes, and the assimilation of soil moisture observations into
rainfall-runoff models is regarded as a way to improve their prediction accuracy. Given the scarcity of in-situ measurements, satellite soil moisture observations offer a valuable dataset that can be assimilated into models; however,
very few studies have used these coarse resolution products to improve rainfall-runoff model prediction. In this work
we evaluate the assimilation of satellite soil moisture into the probability distributed model (PDM) for the purpose of
reducing flood prediction uncertainty in an operational context. The surface soil moisture (SSM) and the soil wetness
index (SWI) derived from the Advanced Microwave Scanning Radiometer (AMSR-E) are assimilated using an ensemble Kalman filter. Two options for the observed data are considered to remove the systematic differences between
SSM/SWI and the model soil moisture prediction: linear regression (LR) and anomaly-based cumulative distribution
function (aCDF) matching. In addition to a complete period rescaling scheme (CP), an operationally feasible real-time
rescaling scheme (RT) is tested.
On average, the discharge prediction uncertainty, expressed as the ensemble mean of the root mean squared difference (MRMSD), is reduced by 25% after assimilation and little overall difference is found between the various
approaches. However, when specific flood events are analysed, the level of improvement varies. Our results reveal
that efficacy of the soil moisture assimilation for flood prediction is robust with respect to different assumptions regarding the observation error variance. The assimilation performs similarly between the operational RT and the CP
schemes, which suggests that short-term training is sufficient to effectively remove observation biases. Regarding the
different rescaling techniques used, aCDF matching consistently lead to better assimilation results than LR. Differences between the assimilation of SSM and SWI, however, are not significant. Even though there is improvement
in streamflow prediction, the assimilation of soil moisture shows limited capability in error correction when there
exists a large bias of the peak flow prediction. Findings of this work imply that proper pre-processing of observed
soil moisture is critical for the efficacy of the data assimilation and its performance is affected by the quality of model
calibration.
Keywords: Data assimilation, soil moisture, flood prediction, satellite retrievals, rescaling, rainfall-runoff models.
1
1. Introduction
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Flood forecasting based on hydrologic models has
shown significant improvement over the past decades
as a result of a growth in the understanding of hydrological processes, computational power, and availability of various observations. Quantification and reduction of hydrologic models uncertainty still remain as key
challenges to be addressed given that processes such as
water resources management and decision-making rely
on the accuracy of model predictions (Liu and Gupta,
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2007). Since the early 1990s, various hydrologic observations have been used not only to calibrate and validate
models but also to update model variables in real time,
through a process known as data assimilation (DA).
Soil moisture observations, in particular, have been
used for updating the soil moisture and/or soil temperature states of models (e.g., Pauwels et al., 2001; Francois et al., 2003; Crow and van Loon, 2006; Reichle
et al., 2008; Crow and Ryu, 2009; Brocca et al., 2010;
Crow and van den Berg, 2010; Lee et al., 2011; Brocca
et al., 2012; Han et al., 2012). Accurate soil moisture
Preprint submitted to Journal of Hydrology
April 18, 2016
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predictions can lead to better modelling of hydrological processes including runoff, ground water recharge
and evapotranspiration. Nonetheless, there is no consensus about the improvement in streamflow forecasting skill from assimilating soil moisture observations
(on-site or remotely sensed) into rainfall-runoff models, because some key aspects of the assimilation framework have not been fully assessed to date. These include the correct quantification of model and observation uncertainties, the sparse observation time, the
rainfall-runoff model structure and the mismatch of spatial scales between observations and model state variables, the more suitable DA technique, and the assimilation performance as a function of climatic, soil and
land use conditions (Brocca et al., 2012).
Ground measurements of soil moisture are scarce
in most regions, thus satellite retrievals offer a valuable tool to estimate large-scale soil moisture content.
Passive microwave satellite soil moisture observations
in particular, generally have higher uncertainty than
ground measurements and a coarse spatial resolution,
and they represent water content only in the top few centimetres of soil (surface soil moisture or SSM hereafter).
Nevertheless, they provide soil moisture estimates with
a good spatial coverage at regular and reasonably frequent time intervals, which makes them suitable for
large-scale monitoring. Moreover, the current ESA Soil
Moisture Ocean Salinity (SMOS) (Barre et al., 2008)
and the upcoming NASA Soil Moisture Active/Pasive
(SMAP) (Entekhabi et al., 2010) missions are mainly
dedicated to the estimation of soil moisture, thus more
frequent and higher-quality observations are expected in
the near future.
The majority of studies assimilating satellite soil
moisture observations focus on improving soil moisture
profile estimation in land surface models (e.g., Pauwels
et al., 2001; Crow and van Loon, 2006; Reichle et al.,
2008; Crow and van den Berg, 2010; Chen et al., 2011;
Han et al., 2012). These models calculate water and energy balances for the soil surface, which results in the
partitioning of rainfall in surface runoff and infiltration.
They have a strong physical basis and therefore involve
complex parametrisation schemes. Conceptual rainfallrunoff models on the other hand, vary in complexity depending on the assumptions and simplifications made
regarding the hydrologic processes within the catchment (Beven, 2011). The simpler models can be suitable
for areas where little data is available. This group of
models generally uses rainfall and potential evapotranspiration as input data, energy fluxes are considered indirectly only to estimate evapotranspiration, and runoff
generation processes are conceptualised as a series of
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interconnected storages through the catchment (Chiew
et al., 1996), which requires a less complex parametrisation scheme than some available physically-based models (Loague, 2010; Mirus and Loague, 2013).
There have been some synthetic studies exploring the
advantages of assimilating pre-storm soil moisture observations into rainfall-runoff models (e.g., Crow and
Ryu, 2009; Lee et al., 2011), but relatively few studies have assimilated real observations. Exceptions include Pauwels et al. (2001, 2002) who assimilated SSM
derived from the European Space Agency (ESA) European Remote Sensing (ERS) satellites using a statistical correction assimilation method and found improvement in discharge prediction for both the lumped and the
distributed models tested. Francois et al. (2003) found
improvement in flood event simulation using a coupled
land surface-hydrological model after the assimilation
of SSM derived from ESA’s synthetic aperture radar
(SAR) using an extended Kalman filter. Brocca et al.
(2010) assimilated a soil wetness index (SWI) product derived from the Advanced Scatterometer (ASCAT)
onboard of the Metop satellite using a direct nudging
scheme, and found improvement in discharge prediction. More recently, Brocca et al. (2012) compared ensemble Kalman filter assimilations of the SSM and the
SWI derived from ASCAT, and found more significant
improvement in discharge prediction when the root zone
soil moisture product (SWI) was assimilated.
The efficacy of assimilating satellite soil moisture
retrievals into rainfall-runoff models relies on factors
such as the dominance of soil moisture in controlling
the runoff generation process, the accuracy of the observations, the effective rescaling of observations into
the model space, and the correct representation of uncertainties in model prediction. For example, it has
been shown that incorrect assumptions of the model
structural and observational errors (Crow and van Loon,
2006; Crow and Reichle, 2008; Reichle et al., 2008;
Ryu et al., 2009; Crow and van den Berg, 2010) and the
use of suboptimal rescaling schemes (Yilmaz and Crow,
2013) can degrade the performance of the stochastic
DA. Moreover, using model predictions to rescale biased observations can potentially transfer the model biases into the rescaled observation, which suggests that
the DA methods should explicitly take into account both
model and observation biases (Pauwels et al., 2013).
Most DA research working with rescaling of soil
moisture observations prior to assimilation (e.g., Crow
and van Loon, 2006; Crow and Reichle, 2008; Reichle
et al., 2008; Crow and van den Berg, 2010; Han et al.,
2012) have focused on long-term, continuous water balance modelling applications that are significantly dif-
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ferent from the event-based application of a hydrologic
model in an operational flood forecasting context. As
a result, it is not evident how relevant they are to operational stream flow forecasting and thus DA studies
specific to this particular application type are needed.
This paper addresses this gap.
In summary, there are a number of challenges to be
addressed in the assimilation of satellite soil moisture
into rainfall-runoff models. This study addresses some
of them and has the following main objectives: 1) to
provide new evidence of the improvement in flood prediction from assimilating real satellite SSM observations and a SWI derived from them, in a semi-arid catchment, in an operational context, and 2) to explore different rescaling techniques and their impacts in improving
discharge prediction.
In addressing our two main objectives, we compare
assimilations of SSM and SWI derived from the Advance Microwave Scanning Radiometer (AMSR-E) into
the probability distributed model (PDM). To remove
systematic differences between the observed soil moisture (SSM and SWI) and the soil moisture predicted by
PDM, different rescaling procedures are tested. These
include linear regression (LR) and anomaly-based cumulative distribution function (aCDF) matching. In the
aCDF scheme, seasonality is removed by grouping soil
moisture values into corresponding months and applying standard CDF matching to the separately grouped
values. We also test different periods for setting up the
rescaling: a real time approach (RT), which uses only
past and current information, thus is operationally feasible; and a complete period approach (CP) that uses all
the information available, which is more robust.
The study area chosen for this work is a sparselymonitored, large, semi-arid catchment. Quantitative operational flood forecasting is currently done using an
event-based model whenever a moderate or larger flood
is likely to occur. In this paper, we present an attempt at
providing continuous streamflow modelling within the
catchment, which makes effective use of satellite soil
moisture observations to improve predictions.
The paper is structured in five sections: Section 2 describes the study catchment and the data used; Section
3 describes the methodology, including a description of
the PDM, the ensemble Kalman filter used for the assimilation, the representation of the uncertainties in the
model, the estimation of SWI, the rescaling of SSM and
SWI, and the metrics used to evaluate the assimilation
results; Section 4 presents the results and discussion;
and Section 5 summarises the main conclusions of the
study.
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2. Study Area and Data
The study area is the semi-arid Warrego catchment
(42,870 km2 ), which is a sub-catchment of Wyandra
River catchment located in Queensland, Australia. This
catchment is chosen for its flooding history, along with
its geographical and climatological conditions, which
enables soil moisture satellite retrievals to have higher
accuracy than in other areas. These conditions include
the size of the catchment and having a semi-arid climate
and a low vegetation cover. Moreover, the catchment
features very sparse ground monitoring networks thus
satellite data can make more unique and valuable contribution compared to well instrumented catchments.
The catchment has summer dominated rainfall with
mean monthly rainfall of 80 mm in January, and 20
mm in August. Mean maximum temperature in January is above 30◦ C and in July below 20◦ C. The
runoff seasonality is characterised by peaks in summer months and minimum values in winter and spring.
The mean annual precipitation over the catchment is
520 mm and it has a long history of flooding with
at least 10 major events in the last 100 years that
have caused extensive inundation of towns and rural lands. Floods in the catchment are often related
to heavy rainfall events linked to La Niña. Major
towns within the entire Warrego river catchment are Augathella, Charleville, Wyandra (upstream to the Warrego at Wyandra gauge) and Cunnamulla (downstream
of Warrego at Wyandra gauge) (see Fig.1). Among
these towns, only Cunnamulla has flood protection
The current flood alert system within the catchment consists in a network of volunteer rainfall and
river height observers who communicate observations by telephone when specified threshold levels
have been exceeded, as well as automatic telemetry stations operated by the Bureau of Meteorology
(BoM), the Murweh Shire Council and the Department of Environment and Resource Management
Therefore, an automated continuous operational model
could provide valuable information about not only
major floods, but also moderate and minor flooding.
The rainfall data used in this work was obtained
from the Australian Water Availability Project (AWAP),
which covers the period from 01/1900-12/2013 and is
gridded at a spatial resolution of 0.05◦ Jones et al.
(2009).
Hourly streamflow records were collected
from the State of Queensland,
Department
of Environment and Resource Management
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42
10°S
1:80,000,000
Augathella
15°S
Charleville
20°S
Wyandra
25°S
Cunnamulla
30°S
35°S
40°S
Towns
Warrego River catchment
Rainfall station
115°E 120°E 125°E 130°E 135°E 140°E 145°E 150°E 155°E
Figure 1: The Warrego river catchment
236
(http://watermonitoring.derm.qld.gov.au) for 03/196712/2013. Daily discharge was calculated based on the
daily AWAP time convention (9AM-9AM local time,
UTC+10).
The surface soil moisture (SSM) dataset was obtained
from AMSR-E version 5 (C/X-band) Level 3 soil moisture product developed by the Vrije Universiteit Amsterdam with NASA at 0.25◦ resolution for the period
07/2002-10/2011 (Owe et al., 2008).
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3. Methods
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on two main factors: 1) the representativeness between
the satellite soil moisture and the soil water states of
the model, which is addressed by processing the satellite data (see Sections 3.4 and 3.5), and 2) the covariance between the errors in discharge and the soil water
states. Due to the inherent limitations of the conceptual
model, the links (based on solid physical processes) between the errors in soil moisture and discharge would
become more complex to analyse at the finer scales of
a semi-distributed scheme. Furthermore, for an initial
real-data assimilation experiment, the selected lumped
scheme would be a natural choice since it avoids the
specification of spatial cross-correlation of modelling
errors that is required if the model had a finer resolution than the assimilated observations. The spatially distributed catchment setup would require a more complex
DA with more parameters, and therefore less transparent assimilation results.
The model was run at a daily time step. This temporal
resolution was chosen considering the poor instrumentation and relatively long concentration time (approximately 6 days) within the catchment. The 10 parameters
of the model were calibrated using a genetic algorithm
(Chipperfield and Fleming, 1995) and an objective function based on the Nash-Sutcliffe model efficiency (NS)
(Nash and Sutcliffe, 1970).
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3.2. EnKF formulation
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3.1. Rainfall-runoff model
The probability distributed model (PDM) is a conceptual rainfall-runoff model that has been widely used
in hydrologic research and applications (Moore, 2007).
The model treats soil water content (S 1 in Fig.2) as a
distributed variable following a Pareto distribution function. Two cascade of reservoirs (S 21 and S 22 , Fig.2)
represent surface routing within the catchment, and one
subsurface reservoir (S 3 , Fig.2) represents sub-surface
runoff generation. The main inputs to the model are
rainfall and potential evapotranspiration. A detailed description of the model processes and formulations is
presented in Moore (2007).
Despite the large scale of the study catchment, the
DA experiments are set up by using a lumped scheme to
maintain a simple framework. This permitted to test the
hypothesis of this work—more accurate estimation of
soil water states in the model can be achieved by the assimilation of satellite soil moisture, which in turn can
lead to better streamflow prediction—with a reduced
number of contributing factors. Our hypothesis relies
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The Kalman filter is a Bayesian estimator that sequentially updates model background predictions with
available observations. The updating step is based on
the relative magnitudes of model and observation error variances. In the ensemble Kalman filter (EnKF),
P
Fast
runoff
E
S21
S22
Fast flow storages
S1
Qr (Fast flow)
Q
Recharge
Qs (Slow flow)
S3
Slow flow storage
Figure 2: The PDM scheme
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the error covariance is explicitly calculated from Monte
Carlo-based ensemble realisations. For a state-updating
assimilation approach, the state ensemble is created by
perturbing forcing data, parameters and/or states of the
model with unbiased error. As detailed in Section 3.3,
in this study the state ensemble was generated by perturbing rainfall data and the soil moisture prediction of
the model (water content in S 1 , Fig.2). Then, the water
content of S 1 was updated by using satellite soil moisture observations.
Model and observation uncertainties are propagated
by the EnKF thus the final discharge prediction is
treated as an ensemble of equally likely realisations.
The uncertainty of the discharge prediction can be derived from the ensemble, thus providing valuable information for operational flood alert systems.
If we define the model soil moisture state ensemble
in the background prediction as θ− (t):
−
−
θ− (t) = {θ1,t
, θ2,t
, . . . , θ−N,t },
Satellite surface soil moisture (SSM) observations and
a soil wetness index (SWI) derived from them were assimilated in separate runs to update θ− . Before being
assimilated, SSM and SWI were rescaled to remove systematic differences between the model and the observation (see Section 3.5), which is required for an optimal
state updating scheme (Yilmaz and Crow, 2013). When
a rescaled observation was available, the state ensemble
at time t was updated using the following expression:
r
θ+ (t) = θ− (t) + K(θobs
(t) − H(θ− (t))),
is the rescaled SSM or SWI and H is an operator that transforms the model state to the measurement.
As the observation was rescaled separately prior to the
state updating, H reduces to the identity matrix in this
work. The Kalman gain matrix K was calculated for
each time step by:
K=
(1)
where N is the number of ensemble members and
−
−
{θ1,t
, θ2,t
, . . . , θ−N,t } are the ensemble realisations of soil
moisture at time step t. The error of the member i at
time step t is estimated as:
N
1 X −
θ .
N i=1 i,t
(2)
The anomaly vector of the ensemble for time step t is
then given by:
− 0 − 0
θV − (t)0 = {θ1,t
, θ2,t , ..., θ−N,t 0 }.
(3)
The covariance matrix of the state model errors (P−t )
is directly estimated at each time step based on the
anomaly vector:
P−t =
1
θV − (t)0 × θV − (t)0 T .
N−1
(6)
where R is the observation error variance after rescaling.
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3.3. Model error representation
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(4)
P−t HT
,
HP−t HT + R
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−
θ−i,t 0 = θi,t
−
(5)
r
where θobs
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One of the main strengths of EnKF-based DA is that
it explicitly accounts for different sources of error such
as model error and observation error. As summarised in
Section 3.2, the background model prediction is updated
by using observations and relative weights based on the
model prediction and observation uncertainties. In practice, both model and observation uncertainties are difficult to quantify and they have often been assumed to be
spatially and temporally independent Gaussian random
variables.
In this work we followed the error model adopted
by the majority of previous soil moisture DA experiments, where model error is represented by reducing
the main sources of uncertainty (forcing data, structure
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of the model and parameter errors) into two main components: uncertainties in states or fluxes of the model
and uncertainties in forcing data (Reichle et al., 2002;
Crow and van Loon, 2006; Reichle et al., 2008; Crow
and Ryu, 2009; Kumar et al., 2009; Crow and Van den
Berg, 2010; Chen et al., 2011; Hain et al., 2012). In this
approach, errors from all sources in the model are represented by perturbing the forcing inputs and the states
of the model. i.e., both parameter and model structural errors are schematically represented by perturbing
model states (and/or fluxes). The above simplification
has the drawback of not explicitly treating the parameter uncertainties, which may play a critical role in the
model error representation. For example, the parameter
uncertainty is important in streamflow DA experiments
where there is a strong (and more direct) link between
streamflow prediction and model parameters, and there
is a variety of assimilation schemes formulated to deal
with it (Georgakakos et al., 2004; Moradkhani et al.,
2005, 2012). However, estimating optimal error model
parameters for the parameter uncertainty adds an important challenge, and sub-optimal specification of parameter uncertainty can further complicate the interpretation
of results from the soil moisture state error correction
scheme.
The uncertainties coming from forcing data were reproduced by perturbing precipitation data with a serially
independent multiplicative error following a log-normal
distribution (mean 1 and standard deviation σ p ). It was
assumed that there is no autocorrelation in the rainfall
error, which could be an oversimplification of the error
structure. Uncertainties coming from the structure and
the model parametrisation were represented by perturbing the soil moisture state of the model with a normally
distributed additive error (mean 0 and standard deviation σ sm ).
The error model parameters (σ p and σ sm ) were calibrated by running the open-loop (perturbing the forcing and soil moisture state, but without assimilating
rescaled soil moisture observations) with 500 ensemble members (N), and evaluating the following two discharge ensemble verification criteria:
i) If the ensemble spread is large enough, the temporal average of the ensemble skill (skt ) should be similar
to the temporal average of the ensemble spread (spt ),
i.e., sk/sp = 1 (De Lannoy et al., 2006; Brocca et al.,
2012), where:
T h
X
i2
1
Q sim (t) − Qobs (t)
T t=1


T
N
2 
1 X  x1 X sp =
Q sim (i, t) − Q sim (t)  .

T t=1 N i=1
sk =
ii) If the observation is indistinguishable from a member of the ensemble, the ratio between sk and the
ensemble mean squared error (mse), normalised by
√
(N + 1)/2N should be equal to one (Moradkhani et al.,
2005; Brocca et al., 2012), where:
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(7)
(8)
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

T
N

1 X  1 X
2
 .
(Q
mse =

sim (i, t) − Qobs (t)) 
T t=1  N i=1
(9)
By using the above discharge ensemble verification
criteria, we are assuming that the observed discharge
has no error (or very small compared to the model error), which might lead to an overestimation of σ p and
σ sm .
3.4. Estimation of SSM and SWI
The SSM derived from AMSR-E was averaged over
the entire catchment. In the downsampling procedure, averaged values of ascending (1:30AM local
time, UTC+10) and descending (1:30PM local time,
UTC+10) satellite passes were calculated for the entire catchment in days when more than 50% of the pixels, containing more than 50% of their areas within the
catchment, had valid data. Then, anomalies of averaged
ascending (AAA) and anomalies of averaged descending (AAD) datasets for the catchment were calculated
by subtracting their long-term temporal means. Daily
SSM was calculated as the average of AAA and AAD (if
both were available) or directly as either AAA or AAD
(if only one was available). Anomalies are used instead
of the actual ascending and descending averaged values
because there is bias between the two datasets (Brocca
et al., 2011; Draper et al., 2009), which would affect the
daily SSM calculation.
The observed SSM and the soil water content of PDM
represent different soil layers. Rainfall-runoff models in
general do not separately account for the SSM, instead
they work with soil moisture storage(s) representing significantly deeper layer(s). For PDM, the depth of the
soil water storage (S 1 from Fig.2) is determined by calibration, but it is rather comparable to the root zone soil
moisture. Satellite SSM by contrast, represent the top
centimetres of soil. In order to address this mismatch,
we estimated a soil wetness index (SWI) derived from
the SSM product, which has been widely used to represent deeper layer soil moisture (Wagner et al., 1999;
Albergel et al., 2008; Brocca et al., 2010, 2009).
The SWI was obtained by using the exponential filter proposed by Wagner et al. (1999), which assumes
that the variation in time of the root zone soil moisture
is linearly related to the difference between SSM and
root zone soil moisture. The filter estimates an average
of profile saturation by recursively calculating a SWI
whenever a satellite SSM retrieval is available (Brocca
et al., 2010):
S WI(t) = S WI(t − 1) + Gt [S S M(t) − S WI(t − 1)] ,
(10)
where Gt is a gain term varying between 0 and 1 as:
Gt =
t−(t−1) .
(11)
T
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T is a calibrated parameter representing the time scale of
SWI variation, which was obtained by maximising the
correlation between SWI and the soil moisture predicted
by the model.
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3.5. Observation rescaling and error estimation
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Gt−1
Gt−1 + e−
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In hydrologic DA, in order to optimally merge model
predictions and observations, the systematic differences
between these two data sets have to be removed. This
is usually done by rescaling the observations against
model predictions (Reichle and Koster, 2004; Drusch
et al., 2005; Yilmaz and Crow, 2013). The rescaling
approaches adopted in this work were linear regression (LR) (Crow et al., 2005) and a variation of the
cumulative distribution function (CDF) matching used
by Reichle and Koster (2004), which is referred to as
anomaly-CDF (aCDF) matching. The aCDF matching first removes the seasonal fluctuation of the modelpredicted and the observed soil moisture by calculating
anomaly from monthly mean soil moisture. CDF’s of
the anomalies are then matched to rescale observations
to model predictions.
In this work we tested the assimilation of four
rescaled observations: satellite SSM rescaled via LR (i)
and aCDF matching (ii), and SWI rescaled via LR (iii)
and aCDF-matching (iv). Two periods for setting up the
rescaling schemes were also considered: a “real time”
operational scheme where only data prior to the prediction time was used and a “complete period” scheme
where all the data was used. In the real time scheme
(RT), the first two years of observations were used for
rescaling initially, then this rescaling time window was
updated to include more recent observations. In this
way, rescaling is always based on all the past available data, while no ‘future’ information is used. The
real time rescaled SSM via LR and aCDF operators are
named SSM+LR(RT) and SSM+aCDF(RT), respectively. The
real time rescaled SWI via LR and aCDF are named
SWI+LR(RT) and SWI+aCDF(RT), respectively.
If all the available observations were used to evaluate the assimilation results, the complete period scheme
(CP) was estimated by applying LR and aCDF rescaling to the complete time series of model predictions
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and satellite soil moisture observations. While this
approach can capture the overall climatology of soil
moisture better, it is not operationally feasible because it uses ‘future’ information. The complete period
rescaled SSM via LR and aCDF are named SSM+LR(CP)
and SSM+aCDF(CP), respectively. The complete period
rescaled SWI via LR and aCDF are named SWI+LR(CP)
and SWI+aCDF(CP), respectively.
The error associated with the different rescaled observations needs to be estimated for the EnKF formulation
(R from eq.6). Quantifying this uncertainty is a major
challenge, especially given the lack of ground measurements of soil moisture in most areas. Moreover, it has
been found that incorrect assumptions of these errors
degrade the performance of the stochastic assimilation
results (Reichle et al., 2008; Crow and Reichle, 2008;
Crow and van den Berg, 2010).
In this study we determined an upper bound of the
rescaled observation error and tested a selection of error
variances within the bound. This allowed for evaluating the sensitivity of the assimilation results to different
magnitudes of observation error variances. In theory, if
r
we express a rescaled observation (θobs
) as the sum of
r,T
the “true” rescaled observation (θobs
) and the rescaled
r
observation error (obs
), and we assume error orthogonality, we can express the variance of the rescaled obr,T
r
r
servation as Var(θobs
) = Var(θobs
) + Var(obs
), where
r
r
Var(obs
) = R from eq.6. In this way, Var(θobs
)
can be considered as an upper bound of R. We used
this upper bound to test different values of R: R1 =
r
r
r
0.3Var(θobs
); R2 = 0.5Var(θobs
); R3 = 0.7Var(θobs
) and a
fixed value of R4 = 3% (expressed as standard deviation in units of volumetric percentage of the calibrated
r
soil moisture storage of 396 mm).Note that θobs
corresponds to either the rescaled SSM or the rescaled SWI,
r
thus Var(θobs
) is the variance of the rescaled time series.
3.6. Evaluation of data assimilation results
The evaluation of the different DA experiments was
based on the normalised root mean square difference
(NRMSD). The NRMSD was calculated as the ratio of
the mean root mean square difference (MRMSD) between the updated discharge ensemble members (Qup
sim )
and the observed discharge to the MRMSD between the
open loop (ensemble discharge prediction without assimilation, Qol
sim ) and the observed discharge:
q
NRMS D = q
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1
N
1
N
PN i=1
PN i=1
Qup
sim (i, t) − Qobs (t)
Qolsim (i, t) − Qobs (t)
2
2 ,
(12)
where N is the number of ensemble members (in these
experiments, N=1000).
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The NRMSDs from the different assimilation experiments were evaluated and compared based on four main
factors: 1) the different observation error variances considered, 2) the real time and the complete period approaches used for rescaling, and the different rescaling technique used (LR and aCDF), and 3) the different
products assimilated (SSM or SWI).
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4. Results and discussion
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4.1. Model calibration
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The common period of rainfall and discharge records
for the catchment is 1967-2013. The period 1967-2001
was used for calibration and 2002-2013 for verification.
The NS model efficiency for calibration and verification
periods were 0.53 and 0.69, respectively. Fig.3 presents
the simulated and observed discharge time series for the
catchment and the daily flow duration curve.
These results reveal that the calibrated model underestimates some of the observed peak flows and consistently overestimates low and zero flows. One of the
key factors responsible for the large prediction error is
the low density of rainfall gauges within the catchment,
which results in a low quality gridded rainfall data for
the area. Another key factor to consider is the model
structural error coming from a deficient representation
of the runoff generation processes within the catchment.
As we run a lumped model for the entire catchment, the
spatial heterogeneity of rainfall over the catchment is
ignored and the runoff mechanisms are represented by
a single combination of storages depths for the entire
area. The lumped model structure is therefore another
main source of uncertainty and an important limitation
of the selected scheme. Moreover, neglecting rainfall
spatial heterogeneity probably contributes to the systematic underestimation of peak flows.
Given the semi-arid climate of the catchment and
the dominance of surface runoff in the total streamflow
(baseflow component is negligible), the initial rainfallrunoff generation process is likely dominated by the antecedent soil water content of the catchment. There are
a number of rainfall events that did not result in measurable discharge during the study period because the
catchment did not reach the wetness threshold needed
for runoff generation. One potential issue is whether or
not the model structure and conceptualisation is able to
correctly represent this saturation excess runoff process.
To asses the impact of catchment wetness (soil moisture content) on the runoff generation behaviour, and
to establish whether there is a threshold hydrological
response, satellite SSM observations can be compared
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to the discharge at the catchment outlet (Brocca et al.,
2013). In this work, both simulated and observed daily
runoff ratios (calculated for daily rainfall over 1 mm)
were compared with the modelled soil moisture content
of the catchment (at the previous time step) and with
the satellite SSM observed in the catchment (at the previous time step). These results are presented in Fig.4
and show that both the observed and simulated runoff
start, and continuously increase, when the modelled soil
moisture has reached a value of approximately 60 mm
and the observed satellite SSM has reached 0.1 vol/vol.
The highly scattered nature of these plots is similar to
the findings of Brocca et al. (2013), in which the semiarid catchment featured a more scattered relationship
than the more humid catchments. The non-linear relation between runoff (modelled and observed) and soil
moisture (modelled and observed), as well as the identified threshold values, suggest that antecedent soil moisture exerts an important control in the runoff generation
mechanisms.
Despite the critical role of antecedent soil moisture in
runoff generation, the effect of antecedent soil moisture
content on flood generation is less apparent when it is
greater than the threshold values for runoff generation.
In Fig.4, the runoff ratios (for both modelled and observed cases) do not exhibit strong correlation with soil
moisture (modelled and observed) content beyond the
threshold values. To confirm this behaviour, we set up
a series of synthetic experiments (presented in AlvarezGarreton et al. (2013b), but not shown here) in which
input rainfall and model soil moisture were perturbed
with a range of different noise levels, using the error
model specifications from Section 3.3. Standard deviations varied between 0.1-0.6% for the rainfall error parameter (σ p ) and 0.01-0.06% for the soil moisture error parameter (σ sm ). Discharge error showed a similar
dependency on soil moisture and rainfall errors for the
low ranges of σ p and σ sm . However, when both rainfall
and soil moisture errors became large (which resulted
in large flood events given the multiplicative nature of
rainfall error), discharge error was considerably more
affected by rainfall. These results are consistent with
our runoff generation analysis, and suggest that when
the catchment is (relatively) dry, the combination of soil
moisture and rainfall would dominate runoff generation
processes. When the catchment has reached the wetness
required for runoff generation however, variation in discharge (and thus the error in discharge), which is mainly
dominated by surface runoff, is predominantly affected
by rainfall (and thus the error in rainfall).
Factors such as the lack of ground data for improving rainfall representation over the catchment, and the
0
Obs
Model
6
a)
50
4
100
2
0
Apr71
Oct76
Mar82
Sep87
Mar93
Sep98
Feb04
Aug09
Daily rainfall (mm)
Daily discharge (mm)
8
150
Log daily discharge (mm)
5
10
Obs
Model
b)
0
10
−5
10
−10
10
0
0.5
Excedence probability
1
Figure 3: a) Hydrograph of observed and predicted discharge. The dashed black line indicates the end of calibration and beginning of verification
period. b) Observed and modelled daily flow duration curve.
Daily runoff ratio (RR)
0.8
Model RR
Obs RR
Model RR
Obs RR
a)
b)
0.6
0.4
0.2
0
0
100
200
300 0
0.1
0.2
0.3
Satellite SSM (vol/vol)
0.4
Figure 4: Observed daily runoff ratio (Obs RR) and simulated daily runoff ratio (Model RR) plotted against a) simulated soil moisture and b)
satellite SSM. The dashed lines in panels a) and b) correspond to the identified threshold values.
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expected accuracy of satellite soil moisture retrievals
(given the low vegetation cover within the catchment),
provide potentially favourable conditions for achieving
significant forecast improvements using a state correcting DA framework. However, given the runoff generation processes within the catchment, we expect that the
improvement in skill from soil moisture DA would decrease for large floods. Moreover, the benefit of state
correction via DA may be marginal when the model
prediction contains large bias after calibration, because
rescaling observations can transfer the bias to the observations (Pauwels et al., 2013).
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4.2. Error model parameter calibration
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For the calibration of the error model parameters
we used the genetic algorithm (Chipperfield and Fleming, 1995) with ranges for σP and σ sm being 0.1-0.6
and 0.01-0.06 (% of the soil moisture storage), respectively. It should be noted that since the discharge error, as represented here, comes from two sources (rainfall and state uncertainties), a compensatory behaviour
between the two sources in the final discharge uncertainty is expected. In other words, there may be multiple pairs of rainfall and soil moisture errors that result in similar, if not identical, discharge error (also
known as equifinality in the set of parameters). Moreover, since we run a multi-objective calibration, we obtained a set of Pareto optimal solutions, representing
the trade-off of maximising the two different verification criteria (Gupta et al., 1998). Among the set of
Pareto solutions, we filtered the pair of error parameter
for which both objective functions had less than 20% of
error. The selected error parameters were σP = 0.37
and
σ sm =√ 0.032, which resulted in sk/sp = 1.18 and
sk/mse (N + 1)/2N −1 = 0.78.
4.3. Rescaled SSM and SWI
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Table 1: Characteristics of rescaled soil moisture observations: correlation coefficient with the modelled soil moisture (r), standard deviation of the associated residuals (std), and mean bias (bias) for the
entire period.
r
std (mm)
bias (mm)
SSM+LR(RT)
0.66
32
6
SSM+LR(CP)
0.64
33
0
SSM+aCDF(RT)
0.76
29
4
SSM+aCDF(CP)
0.76
26
0
SWI+LR(RT)
0.78
26
2
SWI+LR(CP)
0.78
26
0
SWI+aCDF(RT)
0.94
16
-2
SWI+aCDF(CP)
0.94
15
0
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652
653
654
655
656
657
Rescaled SSM and SWI, for the real-time and the
complete period approaches were estimated based on
the methodology described in Section 3.5. The T parameter that maximised the correlation between SWI
and the modelled soil moisture, which roughly represents a soil layer depth of 180 cm (by assuming a porosity of 0.46, taken from the A-horizon information reported in McKenzie et al. (2000), and the model soil
moisture storage of 396 mm), was 9 days. This T value
is within the range of the optimal values obtained by
Albergel et al. (2008) for soils with lower depths (30
cm depth with T between 1 and 23 days), similar to the
value found by Brocca et al. (2009) for a thinner layer
of soil (depth of 15 cm and T of 10 days, for one of the
study fields), and slightly lower than the values obtained
by Wagner et al. (1999) for depths of 20 and 100 cm (T
equal 15 and 20 days, respectively). This suggests that
the study catchment is reacting faster than the ones in
the latter studies, which is reasonable considering the
semiarid climatic condition and the surface runoff dominant mechanism of the study area.
Evaluation metrics of rescaled observations, including the correlation coefficient with the modelled soil
moisture (r), the standard deviation of the associated
residuals (std), and the mean bias (bias) for the entire
period are presented in Table 1. These results reveal
strong correlation between the modelled soil moisture
and the rescaled observations for all cases, with correlation coefficients greater than 0.64. Non-zero bias values in Table 1 are the result of the real-time rescaling
scheme, which uses only information prior to the current observation to set up the rescaling.
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To visualise some of the rescaled results, Fig.5 shows
the time series of real time rescaled products and Fig.6
presents scatter plots against modelled soil moisture.
Rescaled SWI has higher r and lower std with the
modelled soil moisture, compared to rescaled SSM,
which suggests a better representation of the root zone
soil moisture dynamics. This can also be seen in the
smoother time series of rescaled SWI compared to the
rescaled satellite observations (Fig.5) and is consistent
with Brocca et al. (2010).
High r and low std of residuals, however, does not
necessarily mean better rescaled observations and more
optimal Kalman update. Yilmaz and Crow (2013) evaluated LR and CDF-matching techniques based on their
skill in merging model predictions and observations
to create an analysis product with lower uncertainties
(which is the primary goal of DA). They found that both
LR and CDF-matching can give suboptimal solutions
when model predictions and observations have correlated errors, which violates the orthogonality assumption between their errors. This means that, when the
Soil moisture (mm)
Soil moisture (mm)
300
200
Model
SSM+LR
SSM+aCDF
a)
Model
SWI+LR
SWI+aCDF
b)
100
0
300
200
100
0
Jan04
Jan06
Jan08
Jan10
Figure 5: a) Rescaled SSM using the real time approach (rescaling is fit with data prior to the observation time). b) Rescaled SWI using real time
approach.
Rescaled soil moisture (mm)
300
250
SSM+LR
SSM+aCDF
SWI+LR
SWI+aCDF
200
150
100
50
0
0
a)
100
200
b)
300 0
100
200
300
Figure 6: The relationship between the simulated soil moisture and a) rescaled SSM and b) rescaled SWI. Rescaling has been done using the real
time approach (rescaling is fit with data prior to the observation time).
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high correlation between the model soil moisture and
rescaled observation originates from the correlated errors between them, the resulting Kalman update can be
worse than the pairs with lower correlation but with independent errors.
To test the sensitivity of the DA results to different estimates of the observation error variance (R), four R values, corresponding to 0.3, 0.5 and 0.7 times the rescaled
soil moisture variance and a fixed value of 3% are tried
in the DA. These R values, expressed as standard deviation in units of volumetric percentage of the calibrated
soil moisture storage (396 mm), are summarised in Table 2.
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Table 2: Rescaled soil moisture observation error standard deviation
scenarios, expressed as percentage of the model storage capacity (396
mm).
R1
R2
R3
R4
SSM+LR
3.8 4.8
5.7
3.0
SSM+aCDF
5.9 7.7
9.0
3.0
SWI+LR
4.6
5.9 7.0 3.0
SWI+aCDF
5.9
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4.4. Data assimilation results
Considering the main objective of this work—to
test the skill of assimilating satellite soil moisture
for improving flood predictions—major flood events
were selected for evaluation of the complete period.
Moderate floods were also considered to evaluate
the experiments in conditions where soil moisture
is assumed to play a more important role in runoff
generation compared to major floods conditions (see
Section 4.1). The selection of major and moderate
floods was made by using all events with a peak
discharge greater than the corresponding threshold values provided by the Bureau of Meteorology
(http://www.bom.gov.au/qld/flood/brochures/warrego)
for the Warrego at Cunnamulla and the Warrego at
Wyandra gauges (see Fig.1). The Bureau of Meteorology’s classification is based on the historical damage
produced by flooding. Flood events were included in
the classification if they were moderate or major at
either one or both gauges. This resulted in discharge
values in Warrego at Wyandra gauge above 0.55 and
2.05 mm for moderate and major floods, respectively,
which yielded three major floods and four moderate
floods for the 2001-2012 period.
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4.4.1. Effects of observation error assumptions in DA
results
We evaluated the sensitivity of the DA results to the
observation error variances by comparing the assimi-
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lation results using each of the four assumed R values
(see Table 2). Fig.7 presents the NRMSD after assimilation of the different rescaled products using the real
time rescaling (RT) approach, for the total period of
evaluation (2001-2012), the 3 major and the 4 moderate floods events. The NRMSD values in Fig.7 are plotted with their 95% confidence bounds. These results
reveal that the performance of the assimilation scheme
depends mainly on the rescaled observation used and
that the sensitivity to the assumed rescaled observation
error variance R is not noticeable. The NRMSD calculated with the updated ensemble after the assimilation of
rescaled SSM and SWI using the complete period (CP)
rescaling approach, shows a similar behaviour with respect to the assumed R (not shown here).
These findings differ from previous studies in which
incorrect observation error assumptions led to significant degradation of the assimilation results (Crow and
van Loon, 2006; Crow and Reichle, 2008; Crow and
van den Berg, 2010; Reichle et al., 2008), however,
those studies focused their evaluation on soil moisture
prediction and not on streamflow prediction, as this
work does. When evaluating results in terms of streamflow prediction improvement, Alvarez-Garreton et al.
(2013a) found that different assumed observation error
structures did not significantly affect the assimilation
results. The reduced sensitivity to the observation error specification can be explained by various factors including: 1) the errors in the model discharge prediction
limiting the sensitivity of the DA to observation errors;
2) the weak relation between the errors in soil water
states and discharge; and 3) inherent sub-optimality of
the rescaling procedures adopted in this work (Yilmaz
and Crow, 2013) that may not meet the orthogonality
assumed for estimating the upper bound of R, thus the
observation errors tested may be covering too small a
fraction of the R space.
4.4.2. Effects of different rescaling in DA results
An important finding to highlight from the assimilation experiments is that both the RT and the CP rescaling approaches yielded similar NRMSD (with differences not statistically significant at the 5% level). This
was true for the total period and also the major and moderate floods evaluated (NRMSD for the complete period rescaled observations are not plotted because they
are very similar to the graphs in Fig.7). Similar performance of RT and CP rescaling further supports the conclusions of Reichle and Koster (2004), and suggests that
the short time training window used in the RT rescaling
approach (2 years in this case) is sufficient to remove
systematic biases in satellite soil moisture retrievals and
1.5
Complete period
c)
Major flood 3
d)
1
1.5
R3
R4
SWI+LR
SSM+aCDF
SSM+LR
SWI+aCDF
SWI+LR
SSM+aCDF
SSM+LR
SWI+LR
SWI+aCDF
SSM+aCDF
SSM+LR
SWI+aCDF
SWI+LR
SSM+LR
SSM+aCDF
R1
R2
SWI+aCDF
0.5
0
Moderate flood 1
Moderate flood 2
Moderate flood 3
Moderate flood 4
e)
f)
g)
h)
1
SWI+aCDF
SWI+LR
SSM+aCDF
SSM+LR
SWI+aCDF
SWI+LR
SSM+aCDF
SSM+LR
SWI+LR
SWI+aCDF
SSM+aCDF
SSM+LR
SWI+aCDF
0
SWI+LR
0.5
SSM+aCDF
NRMSD
Major flood 2
b)
SSM+LR
NRMSD
a)
Major flood 1
Figure 7: NRMSD for a) the complete period of evaluation, b-d) the three major floods, and e-h) the four moderate floods after assimilation of the
four rescaled products (SSM+LR, SSM+aCDF, SWI+LR and SWI+aCDF), using the real time rescaling approach, and the four observations error
variances (R1, R2, R3 and R4).
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to provide rescaled observations which can effectively
improve model predictions in a DA scheme.
If we evaluate the assimilation experiments based on
the rescaling scheme used (LR and aCDF), we find consistently better performance of aCDF-rescaled products
compared with LR-rescaled products, for the total period of evaluation and the three major floods (Fig.7, panels a, b, c and d). The results for the moderate floods
do not show significant differences. The better performance of assimilating aCDF-rescaled observations can
be explained by the fact that the LR-based rescaling
smears out a small number of extreme values, resulting
in underestimated (rescaled) peak soil moisture values
(see Fig.6). This prevents the assimilation scheme from
taking advantage of using these high observed (and perhaps true) antecedent wetness values, especially before
floods. The aCDF matching approach by contrast, can
keep the information of the extreme observations by assuming non-linear relationship between the datasets and
by accounting for possible seasonality effects.
4.4.3. Effects of soil moisture product used in DA results
To evaluate and interpret the assimilation results
based on the different products assimilated (SSM and
SWI), it is worth highlighting the runoff mechanisms
within the study catchment. The main component of the
total runoff in the semi-arid study catchment is quick
(surface) runoff, which occurs only immediately after
rainfall events. Thus, while the overall pattern of SWI
is closer to the dynamics of soil moisture store (S1) of
PDM (see Figs. 5 and 6), which in turn determines
the dynamics of baseflow, the actual contribution of
baseflow to the runoff generation is trivial. In other
words, the total runoff mainly depends on the values
of S1 immediately prior to rainfall events. Therefore,
even when SWI shows a better overall agreement with
S1, for the specific times (or events selected in this research), SSM may provide similar information to represent surface runoff. If we evaluate the performance
of the filter when a linear regression scheme is used
to rescale SSM and SWI, Fig.7 indicates that assimilating SSM+LR and SWI+LR leads to similar NRMSD in
all the events analysed (with differences not statistically
significant at the 5% level), except for major flood 1. In
the case of the first major flood (Fig.7, panel b), the assimilation of SSM leads to an improvement of the open
loop, while assimilating SWI leads to degradation. The
same relations are found when comparing the assimilation of SSM+aCDF and SSM+aCDF, except during
moderate flood 1 (Fig.7, panel e), in which the assimilation of SWI+aCDF yielded greater improvement than
842
SSM+aCDF. As pointed out above, the different results
found in the assimilation of SSM and SWI during major
and moderate floods, are event specific and, given the
small number of events, it is difficult to generalise. It
is expected, however, that the assimilation of SSM and
SWI would lead to different performance if the objective
was to forecast low flows instead of floods. In this case,
the better representation of deep layer soil moisture provided by SWI may result in more valuable information
to correct S1 and improve runoff prediction.
In summary, the assimilation of SSM and SWI derived from satellite observations in general reduces the
uncertainty of model streamflow predictions by around
25% (Fig.7, panel a). However, for major flood events,
improvement was achieved only for combinations of the
assimilated product and rescaling approach (Fig.7, panels b, c and d). During moderate events on the other
hand (Fig.7, panels e, f, g and h), the performance of
the filter was less dependent on the different soil moisture products and the model discharge prediction was
improved by approximately 40% (except for moderate
flood 2, where there was no improvement nor degradation of the model). To visualise the effects of the assimilation in the streamflow ensemble prediction, Figs. 8
and 9 present the major and moderate floods before and
after assimilation of the SSM+aCDF product. These
graphs show that the updated model discharge prediction is more accurate compared to the open loop.
843
5. Conclusions
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Coarse resolution satellite soil moisture products are
globally available at a regular temporal resolution and
their reliability has been widely validated in recent years
(e.g., Albergel et al., 2012; Su et al., 2013). The assimilation of these products into rainfall-runoff modelling,
however, has been implemented only in a few studies
(e.g., Brocca et al., 2010; Meier et al., 2011; Brocca
et al., 2012; Chen et al., 2014; Wanders et al., 2014), despite the potential positive impacts of a better soil moisture representation in streamflow prediction.
Addressing this research gap, this paper presents an
evaluation of satellite soil moisture DA into a conceptual rainfall-runoff model (PDM) for the purpose of reducing flood prediction uncertainty in an operational
context. We compare assimilations of a surface soil
moisture (SSM) and a soil wetness index (SWI) derived from the AMSR-E. We explore different aspects
of the assimilation framework, including various rescaling options, the impact of observation uncertainty and
a systematic approach to model error characterisation.
Discharge (mm)
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2
openloop
openloop mean
updated
updated mean
obs
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0
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Figure 8: Major flood prediction before (open loop) and after assimilating SSM+aCDF(RT) (updated). Rescaling has been done using the real time
approach.
3
Discharge (mm)
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2
openloop
openloop mean
updated
updated mean
obs
08/09
Figure 9: Moderate flood prediction before (open loop) and after assimilating SSM+aCDF(RT) (updated). Rescaling has been done using the real
time approach.
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The study is undertaken in the semi-arid Warrego River
Basin in south central Queensland, Australia.
In general, the stochastic assimilation improves the
prediction for both moderate and major floods; however,
the improvement is higher and more consistent for moderate events. This is in agreement with the lower dependence of runoff generation on antecedent soil moisture
in large events. We also show that the stochastic assimilation efficacy depends more on the rescaling technique
than on the observation error specification. The low sensitivity to the observation error may be due to the large
systematic errors in the model. These systematic errors
can be explained by model structural errors or by the
poor calibration resulting from the lack of a dense rain
gauge network. Given that stochastic assimilation is designed to correct stochastic errors, the model systematic
errors are not addressed thus the performance of the assimilation becomes marginal and less sensitive to the
specified observation error. Moreover, if the error orthogonality assumption made for estimating the upper
boundary of the rescaled observation error R is not met,
this upper bound may be too small and therefore the different error values tested may be covering a small range
of possible R.
We addressed various options for processing the
satellite soil moisture prior to assimilation. We found
that removing systematic biases between the model and
the satellite observations using real time rescaling (with
2 years training window) and complete period rescaling approaches led to similar results. This suggest that
a short period of training is sufficient to remove bias
and effectively use the observations to improve model
prediction. The later has positive implications in the
effective use of short-time records from current and
near-future soil moisture satellite missions for improving rainfall-runoff streamflow predictions. We tested
two different techniques for rescaling, linear regression
(LR) and anomaly-based cumulative distribution function matching (aCDF), which assumes a non-linear relationship between datasets and accounts for seasonal effects. We found that the assimilation of aCDF-rescaled
observations performed consistently better than assimilating LR-rescaled observations. However, given the
known drawback of the rescaling techniques used here
(Yilmaz and Crow, 2013), the feasibility of implementing a triple collocation rescaling (that requires three
mutually independent datasets with sufficient temporal
length to accurately estimate the error characteristics)
should be explored in future work.
We also explored the impacts of assimilating SSM
and SWI derived from the satellite observations and
found that, given the specific runoff mechanisms within
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the catchment (semi-arid catchment with rapid response
to rainfall events, dominated by surface runoff), the better representation of deep layer soil moisture provided
by the SWI does not guarantee better assimilation results during moderate and major flood events. In fact,
the assimilation of SSM and SWI led to similar model
streamflow prediction improvement for the complete
period of evaluation and for most of the flood events
analysed. However, the small number of events precludes definitive conclusions about which of the two is
more suitable to improve flood prediction in this catchment.
Regarding the forcing and model (structure and parameter) errors characterisation, it was assumed that all
these sources of error were represented by perturbing
rainfall and soil moisture state. The parameters of these
perturbations were calibrated by applying two discharge
ensemble verification criteria. The observed discharge
error was discarded in the formulation. The assumption of having small observed discharge error compared
to the model error is strong (especially for flood events)
and can lead to severe overestimation of the errors in the
model. Future work should explore other techniques for
calibrating the error parameters that include the errors in
observed discharge and explicitly treat the uncertainties
in the model parameters.
We highlight that a limitation of this work, which
directly affects the skill of the assimilation scheme, is
the large bias in streamflow prediction for individual
flood events. As mentioned above, the bias found in the
model streamflow predictions comes mainly from errors
in forcing data, PDM structure, the lumped schematisation and the model parameters. In order to examine the
advantages of assimilating satellite-based soil moisture
into spatially distributed catchment setup, extension of
the state-updating scheme to a semi-distributed catchment system is currently in progress.
In addition to improving the spatial representation of
the model, there are tasks remaining to refine the presented data assimilation scheme: 1) To improve the
representation and estimation of the model error by
explicitly treating parameter uncertainty and accounting for the streamflow observation error; 2) To explore
physically based methods, based on Richard’s equation
(Richards, 1931), to transfer the surface satellite information into deeper layer soil moisture; and 3) To explore TC-based procedures to rescale the satellite observations. Lastly, more real-case studies are needed,
which contribute to build evidence and understanding of
the improvement skill of satellite soil moisture assimilation into rainfall-runoff models over a wide range of
catchment characteristics (catchment size, climatic con-
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ditions, dominant runoff mechanisms, ground data network availability, etc.).
Although the results presented here are site specific,
they provide novel evidence of the advantages of assimilating satellite-based soil moisture observations for improving flood prediction. Our findings imply that proper
pre-processing of observed soil moisture is critical for
the efficacy of the data assimilation and its performance
is affected by the the quality of model calibration. With
this, we are contributing to build knowledge and understanding that can lead us towards an optimal DA framework.
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Acknowledgments
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This research was conducted with financial support
from the Australian Research Council (ARC Linkage
Project No. LP110200520) and the Bureau of Meteorology, Australia. We gratefully acknowledge the advise
and data provision of Chris Leahy and Soori Sooriyakumaran from the Bureau of Meteorology, Australia.
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58
Chapter 5
Lumped vs semi-distributed model
configurations
This chapter was published as the following article:
C. Alvarez-Garreton, D. Ryu, A. Western, C.-H. Su, W. Crow, D. Robertson, and C.
Leahy. Improving operational flood ensemble prediction by the assimilation of satellite
soil moisture: comparison between lumped and semi-distributed schemes. Hydrology and
Earth System Sciences, 19(4):1659-1676, 2015.
59
Manuscript prepared for Hydrol. Earth Syst. Sci.
with version 5.0 of the LATEX class copernicus.cls.
Date: 6 March 2015
Improving operational flood ensemble prediction by the assimilation
of satellite soil moisture: comparison between lumped and
semi-distributed schemes.
C. Alvarez-Garreton1 , D. Ryu1 , A.W. Western1 , C.-H. Su1 , W.T. Crow2 , D.E. Robertson3 , and C. Leahy4
1
Department of Infrastructure Engineering, The University of Melbourne, Parkville, Victoria, Australia
USDA-ARS Hydrology and Remote Sensing Laboratory, Beltsville, Maryland, United States
3
CSIRO Land and Water, Australia
4
Bureau of Meteorology, Melbourne, Victoria, Australia
2
Correspondence to: Camila Alvarez-Garreton
(calvarez@student.unimelb.edu.au)
5
10
15
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25
30
Abstract. Assimilation of remotely sensed soil moisture data
(SM-DA) to correct soil water stores of rainfall-runoff models has shown skill in improving streamflow prediction. In the
case of large and sparsely monitored catchments, SM-DA is
a particularly attractive tool. Within this context, we assimilate satellite soil moisture (SM) retrievals from the Advanced
Microwave Scanning Radiometer (AMSR-E), the Advanced
Scatterometer (ASCAT) and the Soil Moisture and Ocean
Salinity (SMOS) instrument, using an Ensemble Kalman filter to improve operational flood prediction within a large
(>40,000km2 ) semi-arid catchment in Australia. We assess
the importance of accounting for channel routing and the
spatial distribution of forcing data by applying SM-DA to a
lumped and a semi-distributed scheme of the probability distributed model (PDM). Our scheme also accounts for model
error representation by explicitly correcting bias in soil moisture and streamflow in the ensemble generation process, and
for seasonal biases and errors in the satellite data.
Before assimilation, the semi-distributed model provided
a more accurate streamflow prediction (Nash-Sutcliffe efficiency, NSE=0.77) than the lumped model (NSE=0.67) at
the catchment outlet. However, this did not ensure good performance at the “ungauged” inner catchments (two of them
with NSE below 0.3). After SM-DA, the streamflow ensemble prediction at the outlet was improved in both the lumped
and the semi-distributed schemes: the root mean square error
of the ensemble was reduced by 22% and 24%, respectively;
the false alarm ratio was reduced by 9% in both cases; the
peak volume error was reduced by 58% and 1%, respectively;
the ensemble skill was improved (evidenced by 12% and
35
40
45
13% reductions in the continuous ranked probability scores,
respectively); and the ensemble reliability was increased in
both cases (expressed by flatter rank histograms). SM-DA
did not improve NSE.
Our findings imply that even when rainfall is the main
driver of flooding in semi-arid catchments, adequately processed satellite SM can be used to reduce errors in the model
soil moisture, which in turn provides better streamflow ensemble prediction. We demonstrate that SM-DA efficacy is
enhanced when the spatial distribution in forcing data and
routing processes are accounted for. At ungauged locations,
SM-DA is effective at improving some characteristics of the
streamflow ensemble prediction; however, the updated prediction is still poor since SM-DA does not address the systematic errors found in the model prior to assimilation.
1
50
55
Introduction
Floods have large costs to society, causing destruction of infrastructure and crops, erosion, and in the worst cases, injury
and loss of life (Thielen et al., 2009). To reduce flood impacts
on public safety and the economy, early and accurate alert
systems are needed. These systems rely on hydrologic models, whose accuracy in turn is highly dependent on the quality
of the data used to force and calibrate them. Therefore, in the
case of sparsely monitored and ungauged catchments, flood
prediction suffers from large uncertainties.
A plausible approach to reduce model uncertainties in the
sparsely monitored catchments is to exploit remotely sensed
60
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105
110
C. Alvarez-Garreton et al.: Assimilation of satellite soil moisture to improve flood prediction
hydro-meteorological observations to correct the states or
parameters of the model in a data assimilation framework.
Within this context, satellite soil moisture (SM) products are 115
appealing given the vital role of SM in runoff generation. SM
influences the partitioning of energy and water (rainfall, infiltration and evapotranspiration) between the land surface and
the atmosphere (Western et al., 2002). Satellite SM observations provide global scale information and can be obtained in 120
near real time at regular and reasonably frequent time intervals. This makes them valuable for improving the representation of catchment wetness. The accuracy of these observations has been assessed by a number of studies (Albergel
et al., 2009; Draper et al., 2009; Albergel et al., 2010; Gruhier 125
et al., 2010; Brocca et al., 2011; Albergel et al., 2012; Su
et al., 2013). In general, they have shown promising performance with moderate correlation between satellite SM and
ground data, but with significant bias at some locations.
In the last decade a large number of studies have explored 130
satellite SM data assimilation (SM-DA) to correct the soil
water states of models. These studies can be categorised into
two main groups; the first, and larger group, has focused on
the improvement of the SM predicted by the model (generally working with land surface models, e.g., Crow and van 135
Loon, 2006; Crow and Reichle, 2008; Crow and Van den
Berg, 2010; Reichle et al., 2008; Ryu et al., 2009). The second, and smaller group (where our study fits), has focused on
the improvement of streamflow prediction in rainfall-runoff
models (Francois et al., 2003; Brocca et al., 2010b, 2012; 140
Alvarez-Garreton et al., 2013, 2014; Chen et al., 2014; Wanders et al., 2014).
Studies from the first group evaluate the prediction improvement of the same variable that is updated in the assimilation scheme (SM). Improvements in streamflow pre- 145
dictions investigated by studies in the second group are not
exclusively influenced by better representation of SM. The
potential improvement of streamflow predictions in the latter
case is constrained by the particular runoff mechanisms operating within a catchment. Accordingly, even when a model 150
structure and parametrisation are capable of representing the
runoff mechanisms, improving streamflow prediction by reducing error in soil moisture depends on the error covariance
between these two components. This error covariance (which
in the model space will be defined by the representation of
the different sources of uncertainty) may become marginal
when the errors in streamflow come mainly from errors in 155
rainfall input data (Crow and Ryu, 2009). This physical constraint is case specific and determines the potential skill of
SM-DA for improving streamflow prediction. To understand
and assess this skill, further studies focusing on the improvement of streamflow prediction are needed with different
model characteristics, such as structure, parametrisation and 160
performance before assimilation; and with different catchment characteristics, such as climate, scale, soils, geology,
land cover and density of monitoring network. Among the
61
latter, semi-arid catchments present distinct rainfall-runoff
processes which have been rarely studied in SM-DA.
Here we address this gap by studying the Warrego River
catchment in Australia, a large and sparsely monitored semiarid basin. We set up the probability distributed model
(PDM) within the catchment, and assimilate passive and active satellite SM products using an Ensemble Kalman filter
(Evensen, 2003) for the purpose of improving operational
flood prediction. We devise an operational SM-DA scheme
to answer three main questions. 1) While rainfall is presumably the main driver of flood generation in semi-arid catchments, can we effectively improve streamflow prediction by
correcting the antecedent soil water state of the model? 2)
What is the impact of accounting for channel routing and the
spatial distribution of forcing data on SM-DA performance?
3) What are the prospects for improving streamflow prediction within ungauged sub-catchments using satellite SM?.
A series of SM-DA experiments using a lumped version of
PDM have already been undertaken in this study catchment
by Alvarez-Garreton et al. (2014). They found that assimilating passive microwave satellite SM improved flood prediction, while highlighting specific limitations in their scheme.
This paper expands on this previous result in a number of key
ways. We improve the representation of model error by explicitly treating forcing, parameter and structural errors. We
devise a more robust ensemble generation process by correcting biases in soil moisture and streamflow predictions.
We incorporate additional satellite products and apply instrumental variable regression techniques for seasonal rescaling
and observations error estimation. Furthermore, we employ
a semi-distributed scheme to evaluate the advantages of accounting for channel routing and the spatial distribution of
forcing data.
In this paper, Sect. 2 presents a description of the study
catchment and the data used. Section 3 presents the methodology, including a description of the rainfall-runoff model,
the EnKF formulation and the specific steps for setting up the
SM-DA scheme. These include the error model estimation,
estimation of profile SM based on the satellite surface data,
the rescaling of satellite observations and observation error estimation. Section 4 presents the results and discussion.
Section 5 summarises the main conclusions of the study.
2
Study area and data
The study area is the semi-arid Warrego catchment (42,870
km2 ) located in Queensland, Australia (Fig.1). The catchment has an important flooding history, with at least three
major floods within the last 15 years. The study area also features geographical and climatological conditions that enable
satellite SM retrievals to have higher accuracy than in other
areas. These conditions include the size of the catchment,
the semi-arid climate and the low vegetation cover. Moreover, the ground-monitoring network within the catchment is
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210
215
sparse thus satellite data is likely to be more valuable than in 220
well-instrumented catchments. The catchment has summerdominated rainfall with mean monthly rainfall accumulation
of 80 mm in January, and 20 mm in August. Mean maximum daily temperature in January is above 30◦ C and below 20◦ C in July. The runoff seasonality is characterised by 225
peaks in summer months and minimum values in winter and
spring. The mean annual precipitation over the catchment is
520 mm. Regarding the governing runoff mechanisms within
the study catchment, Alvarez-Garreton et al. (2014) showed
that streamflow has a negligible baseflow component and the 230
surface runoff is generated only when a wetness threshold is
exceeded. They concluded that soil moisture exerts an important control on the runoff generation mechanisms. In this
work, the runoff mechanisms analysis is deepened by looking at model predictions (Sect. 3.1).
235
Daily rainfall data was computed from the Australian Water Availability Project (AWAP), which has a
grid resolution of 0.05◦ (Jones et al., 2009). Hourly
streamflow records were collected from the State of
Queensland, Department of Natural Resources and Mines 240
(http://watermonitoring.dnrm.qld.gov.au) (Fig.1). Daily discharge was calculated based on the daily AWAP time convention (9am-9am local time, UTC+10h). The flood classification for the study catchment (at the catchment outlet,
N7) was provided by the Australian Bureau of Meteorol- 245
ogy as river height threshold values, corresponding to minor, moderate and major floods. These threshold values expressed as streamflow (mm/day) are 0.06, 0.55 and 2.05, respectively and relate to flood impact rather than recurrence
interval. The associated annual exceedance probability for 250
the minor, moderate and major floods at N7 are 15.7%, 3.1%
and 0.95%, respectively (calculated using the complete daily
streamflow record period). Potential evapotranspiration was
obtained from the Australian Data Archive for Meteorology
database. Daily values were estimated by assuming a uni- 255
form daily distribution within a month.
Three satellite products were used here. The first was the
Advanced Microwave Scanning Radiometer - Earth Observing System (AMS hereafter) version 5 VUA-NASA Land Parameter Retrieval Model Level 3 gridded product (Owe et al.,
2008). AMS uses C- (6.9 GHz) and X-band (10.65 and 18.7
GHz) radiance observations to derive near-surface soil moisture (2 to 3 cm depth) using a land-surface radiative transfer
model. The product used is in units of volumetric water con- 260
tent (m3 m−3 ) and has a regular grid of 0.25◦ .
The second product was the TU-WIEN (Vienna University of Technology) ASCAT (ASC hereafter) data produced
using the change-detection algorithm (Water Retrieval Package, version 5.4) (Naeimi et al., 2009). ASC transmits elec- 265
tromagnetic waves in C-band (5.3Gz) and measures the
backscattered microwave signal. The change-detection algorithm assumes that land surface characteristics are relatively
static over long time periods. Based on this, the differences
between instantaneous backscatter coefficients and the his- 270
62
3
torical highest and lowest values for a given incident angle,
are related to changes in soil moisture (Wagner et al., 1999).
The final SM estimate is provided in relative terms as the degree of saturation and has a nominal spatial resolution varying from 25 to 50 km.
The third satellite product was the Soil Moisture and
Ocean Salinity satellite (SMO hereafter), version RE01 (Reprocessed 1-day global soil moisture product) SM provided
by the Centre Aval de Traitement des Donnees. SMO uses
L-band (1.4 GHz) detectors to measure microwave radiation emitted from depth of up to approximately 5 cm. Nearsurface soil moisture is obtained in units of volumetric water
content (m3 m−3 ) at a spatial resolution of approximately 43
km by using the forward physical model inversion described
by Kerr et al. (2012). The overpass times of the AMS, ASC
and SMO satellites over the study catchment are 1.30am/pm,
10am/pm and 6am/pm local time (UTC+10h), respectively.
Figure 2 summarises the period of record of the different
datasets.
For each satellite dataset, a daily averaged SM was calculated for the complete catchment (or sub-catchment in the
case of the semi-distributed scheme). The areal estimate of
satellite SM over the catchment was given by averaging the
values of ascending and descending satellite passes on days
when more than 50% of the pixels had valid data. For the case
of the passive sensors (AMS and SMO), we subtracted the
long-term temporal mean of the ascending and descending
datasets to remove the systematic bias between them (Brocca
et al., 2011; Draper et al., 2009). Then, daily satellite SM
was calculated as the average between the mean-removed ascending and descending passes (if both were available) or
directly as the mean-removed available pass. For ASC retrievals, given the unbiased ascending and descending measurements, daily satellite SM was calculated from the actual
ascending and descending values averaged over the catchment.
3 Methods
3.1
Lumped and semi-distributed model schemes
The probability distributed model (PDM) is a conceptual
rainfall-runoff model that has been widely used in hydrologic research and applications (Moore, 2007), mainly over
temperate and humid environments. The model was selected
from amongst the set of models available within the flood
forecasting system managed by the Australian Bureau of Meteorology. This selection was based on both the suitability of
PDM to simulate ephemeral rivers (Moore and Bell, 2002)
and preliminary analysis comparing PDM against other models such as the Sacramento soil moisture accounting model,
which did not perform as well as PDM.
PDM is a parsimonious model where the runoff production is controlled by the absorption capacity of the soil (in-
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Fig. 1. The Warrego river basin located in Queensland, Australia (left panel). A close-up of the area is presented on the right panel. The
lumped PDM scheme is set up over the entire catchment, while the semi-distributed scheme divides the total catchment in 7 sub-catchments
(SC1 to SC7).
In this way, for a time t, the soil moisture over the entire
catchment, θ (water content of S1 ), can be expressed as the
summation of all the store capacities greater than C ∗ (t):
Satellite SM
Streamflow
Rainfall
SMOS
ASCAT
AMSR−E
N1
N3
N7
θ(t) =
AWAP
1975
1980
1985
1990
1995
2000
2005
2010
295
Fig. 2. Periods of record of the different datasets. The initial date of
the plot was set as the beginning of the streamflow data record
280
285
290
(1 − F (c)) dc.
(2)
0
1970
275
CZ∗ (t)
C ∗ (t + ∆t) = C ∗ (t) + P ∆t.
cluding canopy and surface detention). This process is conceptualised by a store with a distribution of capacities across 300
the catchment and the spatial distribution of these capacities
is described by a probability distribution (Moore, 2007). The
spatial variability of store capacities can be related to different soil depths, which was identified as the most dominant
factor governing runoff variability in a semi-arid catchment 305
(Jothityangkoon et al., 2001).
In the current formulation, the model treats soil moisture store (S1 in Fig.3) over the entire catchment as a distributed variable with capacities (c) following a Pareto distribution function, F (c). At a given time, the different stores 310
receive water from rainfall and lose water by evaporation
and groundwater recharge (drainage). The shallower stores
with less capacity than a critical capacity, C ∗ , start to generate direct runoff while the rest accumulates the water as
soil moisture. The proportion of the catchment that generates runoff can therefore be expressed in terms of the Pareto 315
density function, f (c), as
prob (c ≤ C ∗ ) = F (C ∗ ) =
ZC ∗
f (c)dc.
Note that the critical capacity C ∗ varies in a time interval ∆t
based on the net rainfall rate during that time, P ,
(1)
0
63
(3)
Direct runoff is calculated based on Eq. 1 and routed
through two cascade of reservoirs (S21 and S22 in Fig.3, with
time constants k1 and k2 , respectively). Subsurface runoff is
estimated based on the drainage from S1 and transformed
into baseflow by using a storage reservoir (S3 in Fig.3 with
time constant kb ). These are then combined as total runoff,
or streamflow. A detailed description of the model conceptualisation and the formulation of the different rainfall-runoff
processes is presented in Moore (2007).
PDM was set up using both a lumped scheme and a semidistributed scheme (see Fig.1). The semi-distributed scheme
was configured with 7 sub-catchments (SC1 to SC7), each
using the lumped version of PDM. The area and mean annual rainfall of each sub-catchment are summarised in Table
1. The river routing between upstream and downstream subcatchments in the semi-distributed scheme was represented
by a linear Muskingum method (Gill, 1978):
S = km (Ix + (1 − x)O) ,
(4)
where S is the storage within the routing reach, km is the
storage time constant, I and O are the streamflow at the beginning and end of the reach, respectively, and x is a weighting factor parameter. The time constant parameters of the
P
Direct
runoff
3.2
S21
E
Surface
runoff
S22
Fast flow storages
S1
Q Total
runoff
Drainage
Sub-surface
runoff
Baseflow
S3
Slow flow storage
355
Fig. 3. The PDM scheme
320
350
storages S21 , S22 and S3 (k1 , k2 and kb , respectively) were
scaled by the area of each sub-catchment, and km from the
360
Muskingum routing was scaled by the length of the river
channel between corresponding nodes. The remaining model
and routing parameters of the semi-distributed scheme were
treated as homogeneous.
EnKF formulation
The ensemble Kalman filter (EnKF) proposed by Evensen
(2003) has been widely used in hydrologic applications given
the nonlinear nature of runoff processes. In the EnKF, the error covariance between the model and observations is calculated from Monte Carlo-based ensemble realisations. In this
way, the model and observation uncertainties are propagated
and the streamflow prediction is treated as an ensemble of
equally likely realisations. The uncertainty of the streamflow
prediction can be derived from the ensemble, which provides
valuable information for operational flood alert systems.
In a state-updating assimilation approach, the state ensemble is created by perturbing forcing data, parameters and/or
states of the model with unbiased errors. As we will see
in Sect. 3.3, an N -member ensemble of model soil moisture, θ = {θ1 , θ2 , ...θN }, was generated by perturbing rainfall forcing data, the model parameter k1 , and θ. Then, the
soil water error of member i at time t was estimated as
0
−
θ−
i (t) = θi (t) −
Table 1. Area and mean annual rainfall of the catchments used in
the lumped and semi-distributed schemes.
365
325
330
335
340
345
Catchment
Area
(km2 )
Mean annual
rainfall (mm)
SC1
SC2
SC3
SC4
SC5
SC6
SC7
Total
14,670
4,453
8,070
5,431
4,067
2,130
4,049
42,870
492
532
596
524
503
467
418
512
370
375
The lumped and the semi-distributed models were calibrated by using a genetic algorithm (Chipperfield and Fleming, 1995) with an objective function based on the NashSutcliffe model efficiency (NSE) (Nash and Sutcliffe, 1970).
380
The models were calibrated for the period 01 January 1967
- 31 May 2003 and evaluation performed for the period 01
June 2003 - 02 March 2014. To make fair comparisons between the two model setups in a scenario where the inner
catchments are ungauged, the semi-distributed scheme was
calibrated using only the outlet gauge (N7 in Fig.1). The
performance of the calibrated models was evaluated based 385
on the NSE at the catchment outlet (N7, Fig.1) and at inner
nodes N1 and N3, in the case of the semi-distributed scheme.
To analyse the runoff mechanisms simulated by the
lumped and the semi-distributed schemes, we calculated the
lag-correlation between rainfall and streamflow, and between
antecedent SM and streamflow. This enables further understanding of the improvement in streamflow that can be ex- 390
pected by improving the simulated SM content through SMDA.
64
5
N
1 X −
θ (t),
N i=1 i
(5)
where the superscript “− ” denotes the state prediction prior
to the assimilation step. The error vector for time step t was
0
0
0
−
defined as θ − (t)0 = {θ1− (t) , θ2− (t) , ..., θN
(t) } and the error
−
covariance of the model state (P ) was estimated at each
time step as:
P − (t) =
T
1
θ − (t)0 · θ − (t)0 .
N −1
(6)
When a daily SM observation from AMS, ASC or SMO
was available, each member of the background prediction
(θ − ) was updated. Before being assimilated, each of the
three observation datasets was transformed to represent a
profile SM and then rescaled to remove systematic differences between the model and the transformed observations
(details in Sects. 3.5 and 3.6). We sequentially assimilated an
N -member ensemble of the transformed and rescaled AMS,
ASC and SMO (named θ ams , θ asc and θ smo , respectively)
and updated each member of θ − with the following 3 steps:
1. If θ ams was available at time t,
θi+ (t) = θi− (t) + K1 (t) · (θiams (t) − Hθi− (t)),
(7)
where H is an operator that transforms the model state
to the measurement space. Since the additive and multiplicative biases between the model predictions and the
microwave retrievals were removed via rescaling in a
separate step (see Section 3.6), H reduced to a unit matrix. The Kalman gain K1 (t) was calculated as
K1 (t) =
P − (t)H T
,
HP − (t)H T + R1 (t)
(8)
where R1 (t) is the error variance of θ ams estimated
in the rescaling procedure (Sect. 3.6). If θ ams was not
available, θ + (t) = θ − (t).
6
2. If θ asc was available at time t, we updated the model
soil moisture with
θi++ (t) = θi+ (t) + K2 (t) · (θiasc (t) − Hθi+ (t)),
395
(9)
where K2 (t) was calculated as
P − (t)H T
K2 (t) =
.
HP − (t)H T + R2 (t)
2011; Brocca et al., 2012; Alvarez-Garreton et al., 2014) and
represented a spatially homogeneous rainfall error (p ) as
p ∼ lnN (1, σp2 ),
440
(10)
R2 (t) is the error variance of θ asc and P − is the model
error covariance re-calculated by applying Eq.(6) to the 445
updated soil moisture θ + (t). If θ asc was not available,
θ ++ (t) = θ + (t).
400
3. If θ smo was available at time t, we updated the model
soil moisture with
450
θi+++ (t) = θi++ (t) + K3 (t) · (θismo (t) − Hθi++ (t)),
where K3 (t) was calculated as
405
K3 (t) =
P − (t)H T
.
HP − (t)H T + R3 (t)
(12)
455
R3 (t) is the error variance of θ smo and P − is the model
error covariance re-calculated by applying Eq.(6) to the
updated soil moisture θ ++ (t). If θ smo was not avail- 460
able, θ +++ (t) = θ ++ (t).
410
415
(11)
In the case of the semi-distributed scheme, during the
updating steps described above, each sub-catchment was
treated independently and no spatial cross-correlation in the
satellite measurements was considered. The order of the
products assimilated in steps 1 to 3 was arbitrary; however, 465
we checked that different orders did not significantly affect
the SM-DA results.
3.3
Error model representation
470
420
425
430
435
The main sources of uncertainty in hydrologic models are
the errors in the forcing data, the model structure and the
incorrect specification of model parameters (Liu and Gupta,
2007). Generally, these errors are represented by adding unbiased synthetic noise to forcing variables, model state vari- 475
ables and/or model parameters.
The estimation of model errors is among the most crucial
challenges in data assimilation, as it determines the value of
the Kalman gain. In the case of a state updating SM-DA, the
ability of the scheme to improve streamflow prediction will 480
mainly depend on the covariance between the errors in SM
states and modelled streamflow, which directly depends on
the specific representation and estimation of the model errors.
To represent the forcing uncertainty, we adopted a multi- 485
plicative error model for the rainfall data (McMillan et al.,
2011; Tian et al., 2013). In particular, we followed the
scheme used in various SM-DA studies (e.g., Chen et al.,
65
(13)
where σp is the standard deviation of the lognormal distribution. The above representation assumes a spatially homogeneous fraction of the error to the rainfall intensity, which
could be an over simplification in a large area like the study
catchment. However, it avoids the estimation of additional
error parameters (e.g., spatial correlation parameter) in an already highly undetermined problem (see Sect. 3.4).
The parameter uncertainty was represented by perturbing
the time constant parameter (k1 ) for store S21 , a highly sensitive parameter of the model that directly affects the streamflow generation by influencing the water stored in both surface storages S21 and S22 (note that in the PDM formulation used, the time constant k2 is calculated as a function
of k1 ). Given the lack of prior information about the structure of the parameter error (k ), we adopted a normally distributed multiplicative error with unit mean and standard deviation of σk , following previous SM-DA studies working
with rainfall-runoff models (Brocca et al., 2010b, 2012).
Following the scheme used in most SM-DA experiments
(e.g., Reichle et al., 2008; Crow and Van den Berg, 2010;
Chen et al., 2011; Hain et al., 2012), the model structural
error was represented by perturbing the SM prediction (θ)
with a spatially homogeneous additive random error,
s ∼ N (0, σs2 ),
(14)
where σs is the standard deviation of the normal distribution.
The physical limits of SM (porosity as an upper bound
and residual water content as a lower bound) are represented
by the model through the storage capacity of S1 . When θ
approaches the limits of S1 , applying unbiased perturbation
to θ can lead to truncation bias in the background prediction. This can then result in mass balance errors and degrade
the performance of the EnKF (Ryu et al., 2009). Moreover,
the Kalman filter assumes unbiased state variables. This issue is of particular importance in arid regions like the study
area, where the soil water content can be rapidly depleted by
evapotranspiration and transmission losses, thus approaching the residual water content of the soil. To ensure that the
state ensemble remained unbiased after perturbation we implemented the bias correction scheme proposed by Ryu et al.
(2009).
The truncation bias correction consisted of running a single unperturbed model prediction (θ−0 ) in parallel with the
perturbed model prediction (θi,− ). At each time step, the mean
bias, δ(t), of the N -member ensemble prediction was calculated by subtracting θ−0 (t) from the ensemble mean, as follows (Ryu et al., 2009):
δ(t) =
N
1 X −
θ (t) − θ−0 (t).
N i=1 i
(15)
490
495
500
505
510
515
Then, a bias corrected ensemble of state variables, θ̃i− (t),
was obtained by subtracting δ(t) from each member of the
perturbed ensemble, θi− (t).
Although the latter resulted in unbiased state ensembles,
some important but subtle effects remain that arise from the 540
highly non-linear nature of hydrologic model. These need
to be guarded against in SM-DA. Representing model errors by adding unbiased perturbation to forcing, model parameters and/or model states can lead to a biased streamflow ensemble prediction (e.g., Ryu et al., 2009; Plaza et al., 545
2012), compared with the unperturbed model run. This biased streamflow ensemble prediction (open-loop hereafter)
is degraded compared with the streamflow predicted by the
unperturbed calibrated model. As a consequence, improvement of the open-loop after SM-DA will in part be due to the
correction of bias introduced during the assimilation process 550
itself.
To avoid overstating the SM-DA efficacy due to the above
issue, we applied the bias correction scheme directly to the
streamflow prediction (in both the open-loop and the assimilation runs). We used the unperturbed model run to estimate 555
a mean bias in the streamflow (following Eq. 15, but using
streamflow instead of soil moisture) and then corrected each
ensemble member by subtracting this mean bias. This practical tool ensures that the streamflow ensemble mean maintains the performance skill of the unperturbed (calibrated) 560
model run, thus avoiding artificial degradation of the unperturbed model run by bias. To our knowledge, this approach
has not been applied in SM-DA previous studies.
3.4
Error model parameters calibration
565
520
525
To calibrate the error model parameters (σp , σk and σs ), we
evaluated the open-loop ensemble prediction (Qol ) against
the observed streamflow at the catchment outlet. In this study
we used a maximum a posteriori (MAP) scheme, a Bayesian
inference procedure detailed by Wang et al. (2009) that max- 570
imises the probability of observing historical events given the
model and error parameters. In other words, it maximises the
probability of having the streamflow observation within the
open-loop streamflow.
575
Member i from the N -member open-loop can be expressed as
T
Qol
i (t) = Q (t) + m (t),
(16)
where Q is the (unknown) truth streamflow and m is the 580
error of the streamflow prediction and consists of forcing,
parameter and states errors:
T
530
m (t) = f (p (t), k (t), s (t)).
535
(17)
Q̂obs (t) = Qol (t) + m (t) + obs (t).
(18)
66
(19)
Following Li et al. (2014), obs was assumed to be a serially independent multiplicative error following a normal distribution (mean 1 and standard deviation of 0.2). Then, the
likelihood function (L) defining the probability of observing
the historical streamflow data given the calibrated model parameters (x), and the error model parameters (σp , σk and σs ),
was expressed as
L(Qobs |x, σp , σk , σs ) = Πn
t=1 p(Qobs (t)|Q̂obs (t)).
(20)
To maximise L, we applied a logarithm transformation to
it and maximised the sum over time of the transformed function. The probability density function (p) at each time step
was estimated by assuming that the ensemble prediction of
the observed streamflow, Q̂obs (t), follows a Gaussian distribution, with its mean and standard deviation computed using
the ensemble members. The period used to calibrate the error
model parameters was 01 January 1998 - 31 May 2003.
An important aspect to highlight about this error parameter calibration is that it is a highly underdetermined problem.
Only one data set (streamflow at N7) is used to calibrate the
error parameters, while there might be many combinations
of error parameters that can generate similar streamflow ensemble (equifinality on the error parameters).
3.5
Profile soil moisture estimation
The aim of the stochastic assimilation detailed in Sect. 3.2
is to correct θ, which is a profile average SM representing
a soil layer depth determined by calibration. By assuming a
porosity of 0.46, (A-horizon information reported in McKenzie et al. (2000)), and the model S1 storage capacity of 396
mm (420 mm) for the lumped (semi-distributed) scheme, this
profile SM roughly represents the upper 1 m of the soil. On
the other hand, the satellite SM observations represent only
the few top centimetres of the soil column (see Sect. 2). To
provide the model with information about more realistic dynamics of θ, we applied the exponential filter proposed by
Wagner et al. (1999) to the satellite SM to estimate the soil
wetness index (SWI) of the root-zone. SWI has been widely
used to represent deeper layer SM based on satellite observations (e.g., Albergel et al., 2008; Brocca et al., 2009, 2010b,
2012; Ford et al., 2014; Qiu et al., 2014). SWI was recursively calculated as:
SWI(t) = SWI(t − 1) + G(t) [SSM(t) − SWI(t − 1)] ,
(21)
where SSM(t) is the satellite SM observation and G(t) is a
gain term varying between 0 and 1 as:
G(t − 1)
.
t−(t−1)
−
T
G(t − 1) + e
585
Qobs (t) = QT (t) + obs (t).
Combining Eqs. 16 and 18, the model ensemble prediction
of the observed streamflow (Q̂obs ) is expressed as:
G(t) =
The observed streamflow at N7 (Qobs ) can be expressed as
a function of the same (unknown) truth and the streamflow
observation error (obs ),
7
(22)
T is a calibrated parameter that implicitly accounts for several physical parameters (Albergel et al., 2008). T was calibrated by maximising the correlation between SWI and the
8
590
595
unperturbed model soil moisture (θ) during the first year of 640
satellite data. This calibration period was selected to maximise the independent evaluation period (see Section 3.7);
however, more representative values are likely to be obtained if a longer period was used for calibration. SWI was
calculated independently for each of the AMS, ASC and 645
SMO datasets (named SWIAMS , SWIASC and SWISMO , respectively) and then rescaled to remove systematic differences with the model prediction (Sect. 3.6).
3.6
600
605
610
615
620
625
630
635
Rescaling and observation error estimation
The systematic differences (e.g., biases) between θ and the 650
SWI derived from each satellite product must be removed
prior to applying a bias-blind data assimilation scheme (Dee
and Da Silva, 1998). We applied instrumental variable (IV)
regression to resolve the biases and estimate the measurement errors simultaneously (Su et al., 2014a). In three- 655
data IV regression analysis, also known as triple collocation
(TC) analysis (Stoffelen, 1998; Yilmaz and Crow, 2013), the
model θ, the passive SWI and active SWI are used as the
data triplet. As the sample size requirement for TC is stringent (Zwieback et al., 2012), a pragmatic threshold of 100
triplet sample was imposed (Scipal et al., 2008). During pe- 660
riods when only one satellite product was available (i.e., before ASC) or when the sample threshold for TC was not met,
a two-data set IV regression using lagged variables (LV) was
applied as a practical substitute (Su et al., 2014a). The LV
analysis was performed on the model θ and a single satellite 665
SWI, with the lagged variable coming from the model.
In most SM-DA experiments, the error in satellite SM has
been treated as time-invariant (e.g., Reichle et al., 2008; Ryu
et al., 2009; Crow and Van den Berg, 2010; Brocca et al.,
2010b, 2012; Alvarez-Garreton et al., 2014); however, studies evaluating satellite SM products have shown an important temporal variability in the measurement errors (Loew 670
and Schlenz, 2011; Su et al., 2014a). Since a data assimilation scheme explicitly updates the model prediction based
on the relative weights of the model and the observation errors, assuming a constant observation error may lead to overcorrection of the model state if the actual error is higher, and 675
vice versa.
Temporal characterisation of the observation error can be
achieved by applying TC (or LV) to specific time windows
of the observations and model predictions (for example,
by grouping the triplets or doublets by month-of-the-year).
There is however, a trade-off between the sampling window
(which defines the temporal characterisation of the error) and 680
the sample size (number of triplets in each subset). In an operational context this trade-off becomes more critical since
only past observations are available. After analysing the temporal variability of the observation errors using the complete
period of record (not shown here), we found that a 4-month
sampling window can reproduce seasonality in errors while 685
ensuring sufficient data samples for the TC and LV schemes.
67
With this analysis we also assessed the suitability of using
LV, which yielded similar results to TC although some positive bias in LV error variance estimates relative to TC was
noted (not shown here).
Summarising, the procedure for rescaling and error estimation consists of:
1. From the start of the AMS dataset, we grouped LV
triplets (SWIAMS (t), θ(t) and θ(t − 1)) into three subsets: Dec-Mar, Apr-Jul and Aug-Nov.
2. We applied LV and thus, estimated the observation error
variance and rescaling factors for a given 4-month subset only when a minimum of 100 samples was reached
(after one year of AMS dataset). After the first year
of AMS, new seasonal triplets were added into the
corresponding 4-month data pool (retaining all earlier
triplets) and LV was applied to the updated subset.
3. When ASC was available, LV triplets (SWIASC (t), θ(t)
and θ(t − 1)) subsets were formed following step 1 criteria and LV was applied after the 4-month data pools
had more than 100 samples, following step 2.
4. In parallel with step 3, TC triplets were formed using the
two available satellite datasets (SWIAMS (t), SWIASC (t)
and θ(t)) and grouped into the 4-month subsets defined
in step 1. TC was applied only when the 4-month data
pools contained more than 100 samples (after approximately 3 years of ASC data).
5. Steps 3 and 4 were repeated when SMO was available. The triplets for TC in this case were given by
SWIASC (t), SWISMO (t) and θ(t).
6. Once steps 1-5 were complete, a single time series of
observations error variance and rescaling factors was
constructed for each satellite-derived SWI by selecting
TC results when available, and LV results if not. This
criterion was adopted because LV is susceptible to bias
due to auto-correlated errors in the model SM (Su et al.,
2014a). The rescaled observations from AMS, ASC and
SMO were named θams , θasc and θsmo , respectively.
3.7 Evaluation metrics
To evaluate the SM-DA results, we used six different metrics. Firstly, the normalised root mean squared difference
(NRMSE) was calculated as the ratio of the root mean square
error (RMSE) between the updated streamflow ensemble
(Qup ) and the observed streamflow to the RMSE between
the open-loop (ensemble streamflow prediction without assimilation, Qol ) and the observed discharge:
NRMSE =
1
N
1
N
PN qPT
i=1
PN
i=1
2
up
t=1 (Qi (t) − Qobs (t))
qP
T
t=1
Qol
i (t) − Qobs (t)
2 ,
(23)
690
695
where N = 1000 is the number of ensemble members. The 735
NRMSE provides information about both the spread of the
ensemble and the performance the ensemble mean, which is
considered as the best estimate of the ensemble prediction.
Moreover, as it is calculated in linear streamflow space, it
gives more weight to high flows.
To further evaluate the performance of the ensemble mean,
we calculated the Nash Sutcliffe efficiency (NSE) for the en- 740
tire evaluation period as follows (example for the open-loop
case):
2
P ol
t Qobs (t) − Q (t)
NSEol = 1 − P
2 ,
t Qobs (t) − Qobs
(24)
745
where Qol
700
is the open-loop ensemble mean. Similarly, NSEup
was calculated by applying Eq.(24) to the updated ensemble
mean (Qup ).
We also estimated the probability of detection (POD) of
daily flow rates (not flood events) exceeding minor, moderate 750
and major floods, for the open-loop and the updated ensemble mean, as follows (example for the open-loop case):
PODol =
705
710
720
(25)
755
15.7%
where the symbol # represents the number of times. Qobs
is the observed streamflow corresponding to a minor flood
classification. This corresponds to a flow (not flood) frequency of 15.7% (see Sect. 2). Similarly, PODup was calculated by applying Eq.(25) to the updated ensemble mean
760
(Qup ). We estimated the false alarm ratio (FAR) for daily
flows as (example for the open-loop case):
FARol =
715
#(Qol >= Q15.7%
& Qobs >= Q15.7%
)
obs
obs
,
#(Qobs >= Q15.7%
)
obs
)
#(Qol >= Q15.7%
& Qobs < Q15.7%
obs
obs
.
#(Qobs < Q15.7%
)
obs
(26)
Similarly, FARup was calculated by applying Eq.(26) to the 765
updated ensemble mean.
Finally, we calculated the aggregated peak volume error
(PVE, in mm) of the ensemble mean, for days when the observed streamflow was above a minor flood classification (t∗
days in Eq. 27). An example for the open-loop, PVE was cal- 770
culated as
PVEol =
X
Qol (t∗ ) − Qobs (t∗ ) .
(27)
t∗
725
730
To evaluate the skill of the streamflow ensemble prediction
before and after SM-DA, we calculated the continuos ranked 775
probability score (CRPS; Robertson et al., 2013). CRPS is
used as a measure of the ensemble errors. In the case of the
deterministic unperturbed run, CRPS reduces to the mean absolute error. The reliability of the ensembles was also evaluated by inspecting the rank histograms of the ensemble fol- 780
lowing Anderson (1996). A reliable ensemble should have a
uniform histogram while a u-shape (n-shape) histogram indicates that the ensemble spread is too small (large) (De Lannoy et al., 2006).
The evaluation period for the SM-DA was 01 June 2003 785
- 02 March 2014. This period is independent of all scheme
component calibration periods (see Sects. 3.1, 3.4 and 3.5).
68
4
9
Results and discussion
4.1 Model calibration
The streamflow at the outlet of the study catchment (N7 in
Fig.1) features long periods of zero-flow, a negligible baseflow component and sharp flow peaks after rainfall events,
when the catchment has reached a threshold level of wetness
(see observed streamflow in Fig.4).
The simulated streamflows from the lumped and the semidistributed schemes are presented in Fig.4. To help visualisation of these time series, the calibration and evaluation
periods were plotted separately. The evaluation period was
further separated into two sub-periods, evaluation sub-period
1 (01 June 2003 - 30 April 2007), characterised by having
only moderate and minor floods, and evaluation sub-period
2 (30 April 2007 - 02 March 2014), which had three major flooding events. The plots show that both the lumped
and the semi-distributed models are generally able to capture
the hydrologic behaviour of the catchment. As expected, the
spatial distribution of forcing data and the channel routing
accounted for by the semi-distributed scheme enhanced the
overall performance of the model, with lower residual values
through time (panels a.2, b.2 and c.2 in Fig.4) and consistently improved the simulation of peak flows.
Table 2 presents the evaluation statistics for the streamflow prediction in the calibration and evaluation periods, for
both the catchment outlet and the inner catchments (notice
that N1 does not have data in the calibration period). The
different statistics in this table consistently show that, at the
catchment outlet, the semi-distributed has consistently better performance than the lumped scheme in terms of RMSE,
NSE, PEV and CRPS. Both schemes show better statistics in
the evaluation period due to the higher flows over that period.
The good performance of the semi-distributed scheme at
the catchment outlet was not reflected at the inner catchments. To explore the reasons for such bad performance,
we separately calibrated the model parameters in those subcatchments by using all the available N7, N1 and N3 observations. The results (not shown here) revealed that in this
case, the model was able to adequately simulate streamflow
in those sub-catchments (NSE in evaluation period of 0.78,
0.69 and 0.84 at N1, N3 and N7 nodes, respectively). Based
on this, we argue that the problem of the poor model performance in the “ungauged” inner catchments is most likely
due to sub-optimal parameter estimation (due to the limited
information about catchment heterogeneity provided by the
integrated catchment streamflow response) and unlikely to be
due to errors in the input data or model structure.
To focus the analysis of the catchment runoff mechanisms
on periods with flood events, the lag-correlation between the
daily streamflow simulated at N7 and θ (Fig.5), and between
daily streamflow and the daily rainfall (Fig.6), was calculated
15.7%
for daily streamflow values greater than Qobs
, or minor
5
100
0
10
Q (mm d−1)
Residuals
(mm d−1)
Feb71
Feb75
Feb79
Feb83
Feb87
Feb91
Feb95
Feb99
Feb03
0
b.1)
1
20
0.5
40
0
1
Rainfall (mm d−1)
−10
Feb67
60
b.2)
0
−1
May03
Q (mm d )
8
−1
150
a.2)
0
1.5
Residuals
(mm d−1)
0
Obs
Lumped model
Semi−distributed model 50
a.1)
May04
May05
May06
0
c.1)
6
20
4
40
2
60
0
5
Rainfall (mm d−1)
Residuals
(mm d−1)
Q (mm d−1)
10
Rainfall (mm d−1)
10
80
c.2)
0
−5
Apr07
Apr08
Apr09
Apr10
Apr11
Apr12
Apr13
Fig. 4. Simulated and observed daily streamflow (Q) and model streamflow prediction residuals (simulated minus observed) at the catchment
outlet (N7). (a.1) and (a.2) present the calibration period. (b.1) and (b.2) present evaluation sub-period 1, which has only moderate and minor
flood events. (c.1) and (c.2) present evaluation sub-period 2, which has 3 major flood events. The daily rainfall plotted on the right axis
correspond to the averaged rainfall over the entire catchment.
790
flood level. The lumped scheme indicates a stronger link between θ and streamflow than the semi-distributed scheme.
This is represented by higher r values in panel a compared
with panels b-h in Fig.5. Conversely the link between rain- 795
69
fall and streamflow is weaker in the lumped scheme (lower r
values in panel a compared with panels b-h in Fig.6). These
different representations of the catchment runoff response
will have a direct impact on the skill of SM-DA to improve
Table 2. Model evaluation at the catchment outlet (N7) and at the
inner catchments (N1 and N3), for calibration and evaluation periods. RMSE and PVE statistics are in units of mm.
Statistic
Lumped scheme
(N7)
0.53
0.3
0.46
NSEcalib
NSEeval
0.52
0.67
0.59
0.77
0.28
0.39
-1.89
PODcalib
PODeval
0.79
0.93
0.76
0.91
0.54
0.76
0.73
FARcalib
FAReval
0.09
0.11
0.10
0.11
0.07
0.15
0.14
PVEcalib
PVEeval
-70.86
1.30
-39.99
34.75
-100.53
168.23
115.52
CRPScalib
CRPSeval
0.29
0.56
0.28
0.33
0.92
0.58
0.49
r
h) Semidist−SC7
5
Lag (d)
5
Lag (d)
5
Lag (d)
5
Lag (d)
10 0
10 0
10 0
10
r
4.2 Error model parameters and ensemble prediction
a) Lumped
b) Semidist−SC1
c) Semidist−SC2
d) Semidist−SC3
e) Semidist−SC4
f) Semidist−SC5
g) Semidist−SC6
h) Semidist−SC7
5
Lag (d)
5
Lag (d)
5
Lag (d)
5
Lag (d)
0.4
820
0.6
r
g) Semidist−SC6
Fig. 6. Lag-correlation coefficient (r) between the simulated
streamflow at N7 (mm d−1 ), and the daily rainfall (mm d−1 ) of
the entire catchment (a) and the 7 sub-catchments (b)-(h).
0
0.4
0.2
10
825
Fig. 5. Lag-correlation coefficient (r) between the simulated
streamflow at N7 (mm d−1 ), and θ (mm d−1 ) from the lumped (a)
and the semi-distributed (b)-(h) model schemes.
830
810
f) Semidist−SC5
0.4
0
0
0.2
805
e) Semidist−SC4
0.4
0.2
0.6
800
d) Semidist−SC3
0
815
10 0
c) Semidist−SC2
0.2
r
0.18
0.18
10 0
b) Semidist−SC1
0.6
0.19
0.21
10 0
a) Lumped
0.6
Semi-distributed scheme
(N7)
(N1)
(N3)
RMSEcalib
RMSEeval
0
0
11
streamflow prediction. A strong relationship between θ and
streamflow prediction suggests strong correlation between 835
their errors, and therefore, greater potential improvement of
streamflow resulting from an improved representation of θ.
If we assume that the semi-distributed scheme provides
a better representation of runoff response within the entire
catchment (based on its better model performance at the out- 840
let), Figs. 5 and 6 also suggest that daily rainfall is the main
control on runoff generation and thus has a stronger impact in the streamflow prediction than soil moisture. Figure
5 shows that flood prediction strongly depends on antecedent
soil moisture for up to the preceding 3 days. The strong correlation found at lag-0 suggests that the real time SM correction given by the proposed SM-DA would be a good strategy 845
to improve flood prediction.
70
The calibrated error parameters for the lumped and the semidistributed schemes are σp = 1.286 mm and 0.977 mm; σs =
0.099 and 0.03 and σk = 0.084 and 0.018, respectively. σs
is expressed as a percentage of the total storage capacity
(396 mm in the lumped scheme and 420 mm in the semidistributed scheme) and σk is expressed as a percentage of
the calibrated parameter k1 .
The rank histograms of the generated ensemble prediction (open-loop) are presented in Fig.7. The histograms at
the catchment outlet (N7) are either n-shape or displaced to
one side, for both the lumped and semi-distributed model
schemes (Figs.7a and 7b, respectively). This suggests that
the open-loop ensembles are slightly biased (with respect to
the observed streamflow) and feature wider spread than an
ideal ensemble. The width of the spread will be critical for
the evaluation of SM-DA (Sect. 4.4) since any decrease of
the spread would be considered as an improvement of the
ensemble prediction.
The wider spread of the open-loop ensembles at the catchment outlet could be due to factors such as an over-prediction
of error parameters by the MAP calibration algorithm, or the
representation of the model error with time-constant error parameters. The latter becomes critical given the distinct behaviour of the intermittent streamflow response within the
catchment, which could indicate distinct behaviour in the
model errors as well.
The ensemble predictions at the inner nodes N1 and N3
(Figs.7c and 7d, respectively) feature high bias with respect
to the observed streamflow (note that observations at N1 and
N3 were not used to calibrate the error parameters). The large
bias at these inner nodes result from the large errors in the
calibrated model in SC1 and SC3 (see Sect. 4.1).
4.3 SWI estimation and rescaling
The satellite SM derived from AMS, ASC and SMO are presented in Fig.8a, for the lumped model. The satellite datasets
No of observations
12
100
a) Lumped−N7
b) Semidist−N7
c) Semidist−N1
d) Semidist−N3
Open−loop
50
0
Updated
0
20 40 60 80 100 0 20 40 60 80 100 0 20 40 60 80 100 0 20 40 60 80 100
Ensemble Percentile
Ensemble Percentile
Ensemble Percentile
Ensemble Percentile
Fig. 7. Rank histograms of the open-loop and updated streamflow ensemble predictions. (a) presents the results from the lumped scheme at
node N7. (b)-(d) present the results from the semi-distributed (semidist) scheme at nodes N7, N1 and N3.
850
855
860
865
870
875
880
885
feature significantly higher noise than the modelled θ. This
can be explained by factors such as random errors in the
satellite retrievals (Su et al., 2014b), and the rapid varia- 890
tion of water content in the surface layer of soil due to infiltration and evapotranspiration losses. Figure 8b presents
the SWI derived from the satellite products, after seasonal
rescaling (θams , θasc and θsmo ). This plot shows better
agreement between model and observations due to SWI filtering/transformation, even when the higher noise in the
rescaled SWI time series is still present.
Figure 8c shows the seasonal observation error variance,
and reveals a clear variation in the error with time. The variation of the seasonal error values is due to the alternative use
of TC or LV and to the increasing sample size of each seasonal pool (see Section 3.6), which should reduce the uncertainties coming from finite sample size. One limitation of this
procedure is its assumption that the errors vary seasonally
without inter-annual variability. Since there are inter-annual
cycles (wet and dry years), one may also expect the errors to
vary with year. Ideally, moving-window estimation with win895
dows smaller than 3 months should be considered, but that
would cause greater sampling uncertainties for the TC and
LV estimates. The inverse relationships between θams and
θasc error variances at some times could be due to the passive retrieval by AMS compared with the active ASC, among
900
other factors.
A common error standard deviation value used in previous
SM-DA studies is 3% m3 m−3 (e.g., Chen et al., 2011). This
constant error, when transformed according to the soil moisture storage capacity of the model and the soil porosity (see
905
Section 3.5) gives an error variance of 667 (750) mm2 for
the lumped (semi-distributed) scheme. As a simple comparison, these values are within the range of the error variance
estimated through seasonal LV/TC; however, a comprehensive analysis of the impacts of accounting for seasonality in
910
SM-DA is beyond the scope of this work.
Table 3 summarises the results of the SWI calibration and
seasonal rescaling for the lumped model, showing the T parameter for each SWI and the correlation coefficient (r) between θ and the satellite SM before and after SWI transfor915
mation and rescaling (θobs ). These results confirm the visual
71
assessment of plots in Fig.8 by showing an important increase in the linear correlation coefficient with θ when satellite SM is transformed into SWI. The correlation is further
increased after rescaling, which illustrates that there is clear
benefit from performing seasonal bias correction. Note that
applying a constant rescaling factor would have no impact on
on the correlation between θ and θobs .
Table 3. Parameter T and correlation coefficient between model SM (θ) and satellite SM, before and
after SWI transformation and rescaling. Results are
presented for the entire catchment.
Dataset
T
(days)
AMS
ASC
SMO
3
11
40
r between θ and
Satellite SM SWI θobs
0.65
0.77
0.46
0.74
0.92
0.79
0.94
0.97
0.93
The optimal T values (Table 3) are difficult to validate
since there is no ground data to compare with and, given that
it has been shown that they strongly depend on the physical processes of the study site (Ceballos et al., 2005), direct
comparison with other studies cannot be made reliably. Indeed, previous studies have shown a wide range of optimal
T values for soil depths ranging between 10 and 100 cm.
As an example, in Fig.9 we have summarised the optimal T
found in 5 different studies (Albergel et al., 2008; Brocca
et al., 2009, 2010a; Ford et al., 2014; Wagner et al., 1999).
Previous studies have shown that optimal T value increases with layer depth (e.g., Brocca et al., 2010a). Results
presented here show an increased T value for SMO, which
would be inconsistent with L-band having a deeper penetration than AMS C-band (to limit the comparison within passive retrievals). We speculate that these differences might be
due various factors, including the different retrievals methods
(which have quite different assumptions pertaining to spatial
heterogeneity) and the influence that radio-frequency interference noise. Moreover, to the best of our knowledge, the
existing studies examining the dependence of T on the soil
depths are usually based on a single satellite product against
13
350
θ (mm d−1)
300
250
0.5
a)
Model
AMS
ASC
SMO
0.3
200
0.2
150
0.1
100
0
50
−0.1
0
350
300
θ (mm d−1)
0.4
−0.2
Satellite SM (m3 m−3 d−1)
b)
Model
θams
asc
250
θ
200
θ
smo
150
100
Obs. error variance (mm2 d−1)
50
0
1000
θams
800
c)
θasc
smo
θ
600
400
200
0
Jun02
Jun03
Jun04
Jun05
Jun06
Jun07
Jun08
Jun09
Jun10
Jun11
Jun12
Jun13
920
925
930
in situ measurements at variable depths. Hence it is difficult to compare our results against these studies due to the
increased complexity due to different sensing and retrieval
methods.
There are some key theoretical issues that should be considered when using SWI as a profile SM estimator. Firstly,
the parameter T in Eq.(22) was estimated by maximising
the correlation between SWI and θ, which could introduce
cross-correlated errors between them. This would violate the
IV regression assumption of no correlation between the errors among the triplets (Sect. 3.6). A way to overcome this
issue, if data requirements are met, would be to estimate a 935
profile SM independently of the rainfall-runoff model prediction, for example by using a physically-based model to
transfer surface SM into deeper layers (e.g., Richards, 1931;
Beven and Germann, 1982; Manfreda et al., 2014).
Secondly, the SWI formulation explicitly incorporates au- 940
tocorrelation terms, which would result in autocorrelated er-
72
Optimal T (d)
Fig. 8. (a) shows the model soil moisture on the left axis (θ) and the satellite soil moisture observations in the right axis. (b) shows the soil
moisture on the model space, after the three satellite datasets were transformed into a soil wetness index (SWI) and then rescaled by using
TC or LV (θams , θasc and θsmo ). (c) shows the rescaled satellite SM observations error variance.
40
Wagner et al., 1999
Albergel et al., 2008
Brocca et al., 2009
Brocca et al., 2010a
Ford et al., 2014
20
0
0
50
Soil depth (cm)
100
Fig. 9. Optimal T parameter against soil depth found in previous
studies.
rors in the observation, which violates an EnKF assumption: independence between observation and prediction errors. The autocorrelation in the observation error can be
transferred to the updated θ + during the SM-DA updating
step. In that case, the θ − background prediction error covariance at time t + 1 would be correlated to the error of the
rescaled SWI at time t + 1. In contrast with the first issue
14
945
950
955
960
965
listed above, the violation of the EnKF assumption can not
be avoided by replacing SWI with a physically-based model,
since the latter would result in profile SM strongly correlated
with previous states as well. Indeed, given the physical mechanisms of water flux in the unsaturated soil, this problem will
be present whenever a profile SM estimated from satellite
SM is used as an observation in an EnKF-based data assimilation framework. A way to overcome this could be to work
with models that explicitly account for the water in the top
few centimetres of soil and therefore can directly assimilate
a (rescaled) satellite retrieval. However, the errors in satellite
SM retrievals are probably already autocorrelated (Crow and
Van den Berg, 2010).
Breaching some of the EnKF-based scheme and/or the
IV-based rescaling assumptions could theoretically degrade
the performance of the SM-DA scheme, when the variable
analysed is soil moisture (Crow and Van den Berg, 2010;
Reichle et al., 2008; Ryu et al., 2009). In this context, the
performance of SM-DA with respect to the improvement in
streamflow has been under-investigated. Alvarez-Garreton et
al. (2013, 2014) show that in terms of streamflow prediction,
SM-DA seems to be less sensitive to violation of these as- 995
sumptions. Both the lower sensitivity and the apparent contradiction with previous studies analysing soil moisture prediction performance highlight the need for further studies focusing on SM-DA for the purposes of improving streamflow
1000
prediction from rainfall-runoff models.
4.4
970
975
980
985
990
Satellite soil moisture data assimilation
The ensemble predictions of streamflow and θ, before and
after SM-DA, for both the lumped and the semi-distributed1005
schemes at N7, are presented in Fig.10. The truncation bias
correction (Sect. 3.3) was successful in creating an unbiased
θ ensemble when the unperturbed model approached the soil
water storage bounds (Figs.10a.2 and 10b.2).
The rank histograms at N7, N1 and N3 are presented in1010
Fig. 7. For all the evaluated nodes, the ensemble predictions
are more reliable after SM-DA (flatter histograms compared
with the open-loop). The consistent overestimation of the observed streamflow in the open-loop ensembles (diagonal histograms displaced towards the higher ensemble percentiles)1015
is partially addressed by the SM-DA.
The evaluation statistics for the SM-DA are summarised
in Table 4. The streamflow data of the inner catchments (N1
and N3) are used only for evaluation purposes in the semidistributed scheme, therefore they are representative of “un-1020
gauged” inner catchments.
The NRMSE in Table 4 (all values below 1) demonstrates
that the SM-DA was effective in reducing the streamflow prediction uncertainty (RMSE) across all gauged and ungauged
catchments. The reductions in the RMSE ranged from 17 to1025
24% for the different evaluation nodes. The NRMSE combines precision improvement (i.e., reduction of ensemble
spread) with prediction accuracy improvement (i.e., enhance-
73
Table 4. SM-DA evaluation statistics calculated at the catchment
outlet (N7) and at the inner catchments (N1 and N3).
Statistic
Lumped scheme
(N7)
Semi-distributed scheme
(N7)
(N1)
(N3)
NRMSE
0.78
0.76
0.81
0.83
NSEol
NSEup
0.67
0.64
0.77
0.78
0.28
0.26
-1.75
-1.39
PODol
PODup
0.96
0.94
0.92
0.93
0.56
0.55
0.69
0.69
FPol
FPup
0.11
0.10
0.11
0.10
0.07
0.06
0.12
0.11
PVEol
PVEup
5.63
-2.37
35.30
34.93
-96.87
-109.66
56.42
40.71
CRPSol
CRPSup
0.32
0.28
0.26
0.23
0.74
0.73
0.20
0.24
ment of ensemble mean performance) resulting from the SMDA. Given that the ensemble open-loop spread was larger
than an ideal ensemble (based on the n-shaped rank histograms in Fig.7), the reduction of the ensemble spread may
be in part artificial.
The performance of the ensemble mean was assessed by
computing the NSEol and NSEup (Table 4). At the catchment
outlet, the NSE of the ensemble mean after SM-DA only
improved for the semi-distributed scheme. At the ungauged
catchments, SM-DA was effective at improving the performance of the ensemble mean only at N3, compared with the
open-loop. However, the performance of the model in that
catchment was still poor. This can be explained by the systematic errors present in the model for those catchments before assimilation, which were not addressed by the SM-DA.
The POD values at the catchment outlet (N7) show that
before and after SM-DA, the model is consistently capable
of detecting minor floods. Although this does not demonstrate an advantage of the SM-DA scheme proposed here, it
does reflect the adequacy of the model ensemble prediction
for simulating minor (and larger) floods. Consistently with
previous results, the prediction of the semi-distributed model
at the inner catchments is poorer in terms of detecting minor floods. The lower FAR values after SM-DA demonstrates
the efficacy of the scheme in reducing the number of times
the model predicted an unobserved minor flood, at both the
gauged and the ungauged catchments.
The open-loop PVE was improved (lower PVE values)
after SM-DA at N7 (for both the lumped and the semidistributed schemes) and at N3. This was not the case however, for inner node N1, at which the PVE was higher after SM-DA, compared with the open-loop. When compared
to the unperturbed model run (Table 2), the assimilation
of satellite soil moisture improved the performance of the
Q (mm d−1)
10
OL ens.
OL ens. mean
Updated ens.
Updated ens. mean
Obs.
a.2)
OL ens.
OL ens. mean
Updated ens.
Updated ens. mean
Unpert.
5
0
400
θ (mm d−1)
a.1)
300
200
100
Q (mm d−1)
0
Apr07
10
Apr08
b.1)
Apr09
Apr10
Apr11
Apr10
Apr11
OL ens.
OL ens. mean
Updated ens.
Updated ens. mean
Obs.
5
0
400 b.2)
θ (mm d−1)
15
OL ens.
OL ens. mean
Updated ens.
Updated ens. mean
Unpert.
300
200
100
0
Apr07
Apr08
Apr09
Fig. 10. Streamflow (Q in mm d−1 ) and soil moisture (θ in mm d−1 ) ensemble prediction at the catchment outlet, before and after SM-DA
for evaluation sub-period 2 (01 May 2007 - 02 March 2014), which had three major flooding events. (a.1) and (a.2) present the results for the
lumped model. (b.1) and (b.2) present the results for the semi-distributed model.
1030
1035
model in terms of PVE at all the nodes and for both the
lumped and semi-distributed schemes.
The skill of the ensembles after SM-DA was improved at
the catchment outlet by 12% and 13% (expressed by a reduc-1040
tion in CRPS) for the lumped and semi-distributed scheme
respectively, and by a 17% at N1. The skill of the updated
ensemble was also consistently higher than the unperturbed
model run (Table 2).
74
To summarise the efficacy of the SM-DA, we take into account the characteristics of the ensemble predictions (openloop and updated) in terms of the their mean, skill and reliability. Overall, SM-DA was effective at improving streamflow ensemble predictions in the gauged and the ungauged
catchments. By accounting for rainfall spatial distribution
and routing process within the large study catchment, we improved the model performance at the outlet compared with
16
1045
1050
a lumped homogeneous scheme.This led to greater improvements from the SM-DA for the semi-distributed model. The
latter was achieved even though the relationship between
θ and the streamflow prediction was weaker in the semi-1100
distributed scheme (Fig.5). The proposed SM-DA scheme
therefore, has the merits of improving streamflow ensemble
predictions by correcting the SM state of the model, even
when rainfall appears to be the main driver of the runoff
mechanism (see Sect. 4.1).
1105
5
1055
1060
1065
1070
1075
1080
1085
1090
1095
Conclusions
This paper presents an evaluation of the assimilation of pas-1110
sive and active satellite soil moisture observations (SM-DA)
into a conceptual rainfall-runoff model (PDM) for the purpose of reducing flood prediction uncertainty in a sparsely
monitored catchment. We set up the experiments in the large
semi-arid Warrego River Basin (>40,000 km2 ) in south cen-1115
tral Queensland, Australia. Within this context, we explore
the advantages of accounting for the forcing data spatial distribution and the routing processes within the catchment.
The framework proposed here rigorously addressed the
two main stages of a SM-DA scheme: model error repre-1120
sentation and satellite data processing. We applied the different methods in the context of a sparsely monitored large
catchment (i.e., limited data), under operational streamflow
and flood forecasting scenarios (i.e., not future information
1125
is used in any of the presented methods).
The model error representation was the most critical step
in the SM-DA scheme, since it determined the error covariance between observations and model state, and thus the
potential efficacy of SM-DA. Moreover, the SM-DA evalu-1130
ation was done against the open-loop ensemble prediction.
We addressed key issues of the ensemble generation process
by correcting truncation biases in soil moisture and streamflow predictions. This prevented an unintended degradation
of the open-loop ensembles coming from perturbing a highly
non-linear model. The open-loop ensembles at the catchment
outlet provide key information about prediction uncertainty,1135
which is required for assessing risks associated with water
management decisions (Robertson et al., 2013). These ensembles showed a slight bias with respect to the observed
streamflow and featured a wide spread. Further exploration
of model error representation (sources of error and the structure of those errors) and error parameter estimation is required to improve the characteristics of the open-loop ensem1140
ble prediction.
In the satellite data processing, we highlighted that the use
of an exponential filter to transfer surface information into
deeper layers may potentially lead to violation of some of
TC and EnKF assumptions (Sect. 4.3). Possible solutions to1145
overcome this would be to use more physically-based methods to transfer satellite SM into deeper layers or to use a
rainfall-runoff model that explicitly accounts for the surface
75
soil layer that can directly assimilate a (rescaled) satellite
SM product. However, both solutions are constrained by the
ancillary data available for satisfactory implementation of a
physically-based model. In the rescaling and error estimation procedure, we applied seasonal TC and LV to avoid
error-in-variable biases. Applying these to correct biases in
the SWI, showed improved agreement between observed and
modelled SM. This seasonal approach is novel in the context
of SM-DA and tends to lead to closer agreement between
model and observations. Further investigation is required to
assess the impacts and importance of accounting for seasonality in rescaling and error estimation.
The evaluation of the SM-DA results led to several insights. 1) The SM-DA was successful at improving the openloop ensemble prediction at the catchment outlet, for both the
lumped and the semi-distributed case. 2) Accounting for spatial distribution in the model forcing data and for the routing
processes within the large study catchment improved the skill
of the SM-DA at the catchment outlet. 3) The SM-DA was
effective at improving streamflow prediction at the ungauged
locations, compared with the open-loop. However, the updated prediction in those catchments was still poor, because
the systematic errors before assimilation are not addressed
by a SM-DA scheme.
This work provides new evidence of the efficacy of SMDA in improving streamflow ensemble predictions within
sparsely instrumented catchments. We demonstrate that SMDA skill can be enhanced if the spatial distribution of forcing data and routing processes within the catchment are accounted for in large catchments. We show that SM-DA performance is directly related to the model quality before assimilation. Therefore we recommend that efforts should be
focused on ensuring adequate models, while evaluating the
trade-offs between more complex models and data availability.
Acknowledgements. The authors wish to thank one anonymous reviewer, Dr. Uwe Ehret and the Chief-Execute Editor Dr. Erwin
Zehe for their constructive comments and suggestions on the earlier
draft of the paper. This research was conducted with financial support from the Australian Research Council (ARC Linkage Project
No. LP110200520) and the Australian Bureau of Meteorology. C.
Alvarez-Garreton was supported by Becas Chile scholarship.
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78
Chapter 6
Dual correction scheme
This chapter was re-submitted to Water Resources Research after moderate revisions, as
the following article:
Alvarez-Garreton C., Ryu D., Western A.W., Crow W.T., Su, C.-H., and Robertson D.E.
Dual assimilation of satellite soil moisture to improve streamflow prediction in data-scarce
catchments. Submitted.
Abstract
This paper explores the use of active and passive microwave satellite soil moisture products
for improving streamflow prediction within 4 large (>5,000km2 ) semi-arid catchments in
Australia. We use the probability distributed model (PDM) under a data-scarce scenario
and aim at correcting two key controlling factors in the streamflow generation: the rainfall
forcing data and the catchment wetness condition. The soil moisture analysis rainfall tool
(SMART) is used to correct a near-real time satellite rainfall product (forcing correction
scheme) and an ensemble Kalman filter is used to correct the PDM soil moisture state
(state correction scheme). These two schemes are combined in a dual correction scheme
and we assess the relative improvements of each.
Our results demonstrate that the quality of the satellite rainfall product is improved by
SMART during moderate-to-high daily rainfall events, which in turn leads to improved
streamflow prediction during high flows. When employed individually, the soil moisture
state correction scheme generally outperforms the rainfall correction scheme, especially for
low flows. Overall, the combined dual correction scheme further improves the streamflow
predictions (reduction in root mean square error and false alarm ratio, and increase in
correlation coefficient and Nash-Sutcliffe efficiency). Our results provide new evidence of
the value of satellite soil moisture observations within data-scarce regions. We also identify
a number of challenges and limitations within the schemes.
79
1
Introduction
Flood prediction in sparsely monitored and ungauged catchments can suffer from large uncertainties given the quality of the data used to force and calibrate the models. Addressing
this challenge, a number of studies have explored data assimilation methods to integrate
various existing observations from the ground and satellites into streamflow models (e.g.,
Moradkhani et al., 2005b; Liu and Gupta, 2007; Lievens et al., 2015; Lopez et al., 2015;
Mendoza et al., 2012; Wanders et al., 2014).
Within this context, and given the essential role that soil moisture (SM) plays in the
runoff generation (Western et al. (2002) and references therein), significant attention has
been given to satellite SM observations. Microwave retrievals of SM provide near real time
estimates of the water content from the top few centimetres of soil, at a global scale every
1-3 days. Moreover, satellite SM estimates have shown good agreement with ground data
(Albergel et al., 2009; Draper et al., 2009b; Gruhier et al., 2010; Brocca et al., 2011; Su
et al., 2013).
A popular approach has been to use satellite SM in a state correction scheme (e.g., Francois
et al., 2003; Brocca et al., 2010, 2012a; Alvarez-Garreton et al., 2013, 2014; Chen et al.,
2014; Wanders et al., 2014; Alvarez-Garreton et al., 2015; Massari et al., 2015). The rationale is that processed satellite SM can be used to update the SM state of rainfall-runoff
models, enabling more accurate prediction of catchment response to precipitation and
thus better streamflow. These studies have generally shown positive results for reducing
streamflow prediction uncertainty, although important limitations have been identified.
The limitations influencing the efficacy of the state update schemes include the limited
knowledge and skill gaps in structural and parameter uncertainties, the errors in forcing
data, the particular runoff mechanisms within the catchment (Alvarez-Garreton et al.,
2015), the experimental setup (e.g., model error quantification, observation error quantification, satellite data processing techniques, data assimilation scheme), and the specific
catchment characteristics (e.g., soil type, location and land cover) (Massari et al., 2015).
Since the aim of a state correction scheme is to reduce the errors in the model SM, the
reduction in streamflow uncertainty will depend on the error covariance between these
two components. This error covariance may be weak when the errors in streamflow come
mainly from errors in the rainfall input data (Crow and Ryu, 2009). The latter becomes
critical in locations without rain gauges, where the available rainfall data generally comes
from satellites.
Satellite rainfall products provide near real-time information with high temporal resolution, which can be used for flood forecasting and monitoring. This information, however,
contains bias and errors that are usually corrected by using rain gauges (Yong et al., 2013;
Zhou et al., 2014; Yong et al., 2015). To dispense with the need for weather stations (which
are not available in large part of the world), recent studies have shown that these products
80
CHAPTER 6: DUAL CORRECTION SCHEME
can potentially be improved by using satellite SM observations (Crow and Bolten, 2007;
Pellarin et al., 2008; Crow et al., 2009, 2011; Pellarin et al., 2013; Brocca et al., 2013, 2014;
Wanders et al., 2015; Zhan et al., 2015). The argument is that given the information that
surface SM contains about antecedent rainfall events, the magnitude of these events can be
estimated by satellite SM retrievals through water balance models. Although these studies have different approaches, they have all shown the potential improvement of rainfall
estimates by using satellite SM.
The potential of SM observations to correct errors in both the model states and the forcing data has motivated recent studies to test these dual forcing/state correction schemes
(dual SM-DA). For example, Massari et al. (2014) set up a scheme in which in-situ SM observations were used to correct the rainfall (through the SM2RAIN algorithm introduced
by Brocca et al. (2013)) and to initialise the wetness condition of a simple rainfall-runoff
model. Their results showed high potential for SM data to improve flood modelling in a
case study.
Using a more complex assimilation scheme and rainfall-runoff model, Crow and Ryu (2009)
set up a state SM-DA scheme integrated with a rainfall correction scheme (via the antecedent version of the soil moisture analysis rainfall tool, SMART, introduced by Crow
et al. (2009)) in a series of synthetic twin experiments. To prevent the potential introduction of cross-correlation between observations and forecasting errors coming from the
dual use of satellite SM, Crow and Ryu (2009) applied the rainfall correction offline (i.e.,
the corrected rainfall is not used within the analysis cycle used to update SM states).
The results of this dual SM-DA scheme were further supported by Chen et al. (2014) in
a real data application over 13 study catchments in the central United States, with areas
ranging between 700 and 10,000 km2 . Both studies showed that the satellite rainfall correction led to improvement in streamflow prediction, especially during high flow periods.
Conversely, the soil water state correction mainly led to improvement of the base flow
component (low flows periods). The combined state and forcing correction scheme led to
improvement of both the high and low flow components of the streamflow; outperforming
both the state and forcing correction scheme in isolation. However, it remains unclear how
this dual SM-DA scheme performs for different catchment characteristics (such as climate
and rainfall-runoff mechanisms) and under different experimental conditions (such as the
data assimilation setup, model structure and quality of the forcing data).
In this paper we expand the evaluation of the dual SM-DA proposed by Crow and Ryu
(2009) by using very distinct catchments and different experimental conditions than Chen
et al. (2014). In contrast to previous studies [e.g., Crow and Ryu, 2009; Crow et al., 2011;
Chen et al., 2014; Massari et al., 2014], we focus on large semi-arid catchments in Australia
with a history of relatively frequent flooding. Additionally, these catchments are sparsely
instrumented thus streamflow prediction is a great challenge. One of the catchments
was previously studied by Alvarez-Garreton et al. [2014, 2015] while exploring effective
81
Table 1: Study catchments characteristics.
Catchment
Warrego
Comet
Thomson
Barcoo
Outlet stream
gauge
Warrego River at Wyandra
Comet River at The Lake
Thomson River at Longreach
Barcoo River at Blackall
Record
initial year
1967
1972
1969
1969
Mean annual
rainfall (mm)
537
723
516
570
Area
(km2 )
42,870
10,470
57,734
5,758
state correction schemes for improving flood prediction. In this paper we expand the state
correction scheme proposed by Alvarez-Garreton et al. [2014, 2015] by incorporating three
other catchments and by combining the data assimilation scheme with a rainfall correction
scheme. Also, this is the first work that applies the dual data assimilation scheme to the
semi-distributed rainfall-runoff modelling. We devise the dual SM-DA scheme under an
scenario without rain gauges (only satellite data is used to force the model) to answer
four main questions: 1) Can we improve the quality of an operational satellite rainfall
product by the assimilation of satellite soil moisture using SMART? 2) Does this rainfall
correction scheme have a positive impact on streamflow predictions? 3) Can we improve
streamflow prediction by the assimilation of satellite SM in a state correction scheme? 4)
What are the impacts on streamflow prediction of a combined state and forcing correction
scheme?
To set up the experiments, we use the probability distributed model (PDM) forced with
the Tropical Rainfall Measuring Mission (TRMM) Multisatellite Precipitation Analysis
(TMPA) rainfall products. We assimilate passive and active satellite SM products to correct the PDM soil moisture state (state correction scheme via an ensemble Kalman filter,
EnKF) and to correct the satellite rainfall (forcing correction scheme via SMART).
2
Study Area and Data
The study area consists of four catchments in Queensland, Australia: the Warrego, Comet,
Thomson and Barcoo (Figure 1). These catchments were selected for their flooding history,
along with their low density of rainfall gauge networks. Some of the main characteristics
of the catchments, including the mean annual rainfall (calculated using 3B42 dataset,
described below), area and stream gauge at the outlet, are summarised in Table 1. The
catchments are located in arid, steppe, hot climatic region (Peel et al., 2007) and feature
summer-dominated rainfall (Figure 2). Moreover, since the ground-monitoring network
within the catchments is sparse (rainfall gauges are shown in Figure 1), satellite SM data
is likely to be more valuable than in well-instrumented catchments.
Streamflow records were collected from the State of Queensland, Department of Natural Resources and Mines (http://watermonitoring.dnrm.qld.gov.au/ ) for each outlet gauge
(Table 1). Potential evapotranspiration was obtained from the climatological 0.05◦ grid82
1:80.000.000
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Rainfall gauge
20°S
30°S
Study catchments
Warrego
Comet
120°E
40°S
Thomson
Barcoo
130°E
140°E
150°E
200
150
Warrego
Comet
Thomson
Barcoo
100
100
50
0
150
Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
50
Mean monthly PET (mm)
Mean monthly rainfall (mm)
Figure 1: Study catchments and rainfall gauges.
Figure 2: Seasonal rainfall (bars) and potential evapotranspiration (lines) of the study catchments, calculated for the period January 1998 to August 2013.
ded data provided by the Australian Bureau of Meteorology (Australian Data Archive
for Meteorology database) and daily values were estimated by assuming a uniform daily
distribution within a month.
Satellite rainfall data were obtained from the Tropical Rainfall Measurement Mission
(TRMM) Multisatellite Precipitation Analysis (TMPA) (Huffman et al., 2007). We used
the 0.25◦ resolution corrected TMPA research product (3B42, period 01 January 1998 - 31
December 2013) and the near real-time operational product (3B42-RT, period 01 January
2000 - 28 November 2013), which is derived exclusively from satellite-based observations.
A daily averaged time series was calculated for each study sub-catchment (sub-catchments
delineation are presented in Figure 3). The 3B42-RT product was corrected using SMART
(section 3.2). To evaluate the correction scheme, we used the gauge-interpolated rainfall dataset of the Australian Water Availability Project (AWAP) (Jones et al., 2009) as
the benchmark rainfall. The near real-time satellite product was also used to force the
rainfall-runoff models. These runs were used as the reference to evaluate the different data
assimilation schemes (section 3.5).
Satellite SM products were obtained from one active and two passive sensors. The active
sensor product was the TU-WIEN (Vienna University of Technology) Advanced Scatterometer (ASCAT, ASC hereafter) data produced using the change-detection algorithm
83
(Water Retrieval Package, version 5.4) (Naeimi et al., 2009), for the period 04 January
2007 - 14 July 2013. One passive sensor product was the Advanced Microwave Scanning
Radiometer - Earth Observing System (AMSR-E, AMS hereafter) version 5 VUA-NASA
Land Parameter Retrieval Model, Level 3 gridded product (Owe et al., 2008) for the period
29 July 2002 - 03 October 2011. The second passive sensor product was the Soil Moisture
and Ocean Salinity satellite (SMOS, SMO hereafter), version RE02 (Re-processed 1-day
global SM) product provided by Centre Aval de Traitement des Donnees for the period
16 January 2010 - 01 January 2014.
A daily averaged SM value was calculated for each product over the study sub-catchments
(Figure 3). The areal SM estimate over a catchment was calculated by averaging the
values of ascending and descending satellite passes on days when more than 50% of the
catchment had valid data. For AMS and SMO, we subtracted the long-term temporal
mean of the ascending and descending datasets before areal SM estimation to remove the
systematic bias between them (Brocca et al., 2011; Draper et al., 2009b).
3
3.1
Methods
Rainfall-Runoff Model
The probability distributed model (PDM) is a parsimonious rainfall-runoff model that has
been widely used in hydrologic research and applications (Moore, 2007). PDM belongs to
the set of models within the flood forecasting system managed by the Australian Bureau
of Meteorology. The model estimates a profile average SM (θ) within the catchment
(water content of S1 in Figure 4) by conceptualising the soil water store S1 with varying
capacities across the catchment. In this study, the spatial heterogeneity of the store
capacities was represented by a Pareto distribution function. The SM component and the
net rainfall (total rainfall minus evaporation and drainage) define the separation between
direct runoff and sub-surface runoff. Direct runoff is transformed into surface runoff by two
reservoirs (S21 and S22 in Figure 4). Subsurface runoff is estimated based on the drainage
from S1 and transformed into baseflow by using a one-storage reservoir (S3 in Figure 4).
Surface runoff and groundwater flow are combined as total runoff (streamflow hereafter).
A detailed explanation of the model conceptualisation is presented in Moore (2007) and
the description of the formulation used in this research is provided in Alvarez-Garreton
et al. (2015).
A semi-distributed scheme using PDM was set up at a daily time step for each of the
study catchments (see Figure 3). The time constant parameters of reservoirs S21 , S22 and
S3 (k1 , k2 and kb , respectively) were scaled by the area of each sub-catchment. Following
Alvarez-Garreton et al. (2015), the river routing between nodes was represented by a linear
Muskingum method (Gill, 1978) with a storage time constant km . This parameter was
84
Warrego
0
50
SC2
SC1
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SC6
.
SC6
SC5
SC1
!
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SC5
SC4
!!
SC6
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Nodes
SC8
Sub-catchments
1:8.000.000
!
SC7
!
SC1
SC3
Barcoo
SC3
!
SC6
!
!
!
!! SC8
!SC7
!
!
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1:8.000.000
SC4
SC4
!
Comet
SC2
SC3
SC7
!
Thomson
!!
SC5
1:8.000.000
Km
200
100
!
SC5
SC4
!
!!
SC2
SC3
SC1
1:8.000.000
Figure 3: Semi-distributed schemes within the study catchments.
P
Direct
runoff
S21
E
S22
Surface
runoff
Fast flow storages
S1
Q Total
runoff
Drainage
Sub-surface
runoff
S3
Baseflow
Slow flow storage
Figure 4: The PDM scheme.
scaled by the length of the river channel between consecutive nodes. The rest of the model
and routing parameters were treated as homogeneous within each study catchment.
To calibrate the model parameters, we forced the model with 3B42 rainfall dataset and
used half of its entire period of record to calculate the objective function, which was based
on the Nash-Sutcliffe model efficiency (NSE) (Nash and Sutcliffe, 1970). In particular,
we divided the complete period in wet and dry years (based on mean annual rainfall
from Table 1) and selected half the wet and half the dry years as calibration period. The
calibration was done by using a genetic algorithm (Chipperfield and Fleming, 1995).
3.2
Forcing Correction Scheme
Following Crow et al. (2011), we implemented the soil moisture analysis rainfall tool
(SMART) to correct the 3B42-RT satellite rainfall dataset. This corrected rainfall dataset
was used to force the PDM in the forcing correction and the dual correction schemes
(see schematic in Figure 5). In general terms, SMART uses the antecedent precipitation
index (API) model to estimate a SM proxy. This proxy is corrected by using satellite
SM observations via a Kalman filter. The Kalman filter innovations are then used to
correct the potential errors in the satellite rainfall data used to force the API model. The
API model is used here because SMART was shown to perform better when applied to a
linear water balance model lacking saturation (which is a non-linear process represented
85
by rainfall-runoff models). This was one of the key findings in Crow et al. [2011], where a
more complex land surface model was used that did not enhance the correction of rainfall
accumulations. The expected improvement coming from a more realistic modeling of soil
moisture (which accounted for the energy balance control on soil water loss, soil saturation
and runoff generation) was uncertain given the challenges in evapotranspiration modeling
approaches and the multilayered model with finite soil water capacities.
The API model at day t was formulated as
API(t) = γ(t)API(t − 1) + P (t),
(1)
where P is the 3B42-RT rainfall data and γ(t) is a dimensionless loss coefficient that
varies according to the day of the year (D):
γ(t) = 0.8 + 0.05(2πD(t)/365).
(2)
The coefficients in (2) aim to capture radiation and climatological temperature effects.
Their values were adopted from Chen et al. (2014). Following Crow and Ryu (2009),
prior to being assimilated into the API model, satellite SM observations were rescaled
into the API space by using a cumulative distribution function. When a rescaled AMS,
ASC and/or SMO observation (Θams , Θasc and Θsmo , respectively) was available at time
t, API was updated using three sequential steps (the time t was omitted in the following
equations when all the terms corresponded to the same time step):
1. If Θams was available at time t,
API+ = API− + K f (Θams − API− ).
(3)
The superscripts minus and plus denote before and after updating, respectively. K f
is the Kalman gain (superscript f refers to forcing scheme) calculated at each time
step as
Kf =
T−
.
+Σ
(4)
T−
Where Σ is the scalar error variance of the observation Θams , fixed at 0.042 mm3 mm−3 .
The use of fixed observation error variance follows previous studies applying SMART
(Chen et al., 2014; Crow and Ryu, 2009; Crow et al., 2011). Since λ (10) is calibrated
for each sub-catchment, the difference in (relative) SM error estimates is compensated within the calibration process. T − is the scalar error variance for the API
forecast at time t, calculated as
T − (t) = γ 2 (t)T + (t − 1) + Z + P 2 (t).
(5)
T + is the updated API error variance, calculated whenever API was updated, as
T + = (1 − K f )T − .
(6)
86
The term Z + P 2 (t) in (5) is the model background uncertainty added in each time
step, which assumes greater error in API prediction when P is greater than zero.
Following Crow et al. (2011) and Chen et al. (2014), Z was fixed at 3 mm2 and at 5 (dimensionless). If Θams was not available at time t, API+ = API− , i.e., no
correction was done.
2. If Θasc was available at time t,
API++ = API+ + K f (Θasc − API+ ).
(7)
In this step, K f was calculated by (4) where Σ was the scalar error variance of Θasc ,
fixed at 0.042 mm3 mm−3 . Similarly to step 1, if API+ was updated by (7), T − was
also updated by (6). If Θams was not available at time t, API++ = API+ .
3. If Θsmo was available at time t,
API+++ = API++ + K f (Θsmo − API++ ).
(8)
Similarly to the previous steps, K f was calculated by (4), but now using Σ as the
scalar error variance of Θsmo , fixed at 0.042 mm3 mm−3 . If API++ was updated by
(8), T − was also updated by (6). If Θsmo was not available at time t, API+++ =
API++ .
After the above 3-step updating scheme, the analysis increments δ were defined for each
time step t as
δ = API+++ − API− .
(9)
Following Crow et al. (2011), the rainfall accumulation [P ] was corrected by
[P ]c = [P ] + λ[δ].
(10)
The superscript c denotes after correction. The square brackets represent non-overlapping
accumulation windows. To ensure that SM observations corrected only past rainfall accumulations, the length of these windows was varied so that the last day of the window
had a SM observation. The parameter λ in (10) is constant in time, and was calibrated
for each sub-catchment by minimising the root-mean-square error between [P ]c and the
3B42 rainfall product. Negative values of [P ]c were reset to zero.
Following Chen et al. (2014), we applied a 2 mm threshold value for rainfall correction
when [P ] was zero (i.e., the correction step in (10) was done only if λ[δ] > 2). The latter is
done since SMART analysis tends to create spurious very low rainfall due to positive noise
in the SM observations, which results in increased false alarm ratios in rainfall events.
The consequence of this is that real rainfall values smaller than 2 mm can be discarded,
however, these low-intensity rainfall values are unlikely to make significant impacts on the
streamflow prediction with the given high evapotranspiration of the study regions.
87
To get a daily corrected rainfall time series, we redistributed the corrected accumulations
in proportion to the original daily rainfall. To remove positive bias due to the resettingto-zero step, the corrected rainfall was multiplicatively rescaled to match the long-term
mean of P . The corrected 3B42-RT dataset using SMART is called 3B42-RTC .
3.3
State Correction Scheme
To set up the state correction scheme (schematic in Figure 5), we followed the procedure
developed by Alvarez-Garreton et al. (2015). The rainfall dataset used in this scheme
was the uncorrected 3B42-RT. In summary, the scheme consisted of using satellite SM
observations to correct the model SM (θ hereafter) via a stochastic data assimilation
framework using an ensemble Kalman filter (EnKF) (Evensen, 2003). Prior to being
assimilated, the satellite data was processed to provide consistent information about θ’s
dynamics. In the following we provide a description of the satellite data processing and
the EnKF implementation.
3.3.1
Satellite Soil Moisture Data Processing
Given the active and passive sensors microwave penetration depths, satellite SM observations represent only the top few centimetres of soil. Furthermore, θ is an average profile
SM representing a deeper layer. Therefore, the depth that θ represents depends on soil
properties and model parameters, and is unique for each sub-catchment and PDM scheme.
By assuming a porosity for the study catchments ranging between 0.45 and 0.5 (A-horizon
information reported in McKenzie et al. (2000)) and S1 storage capacity ranging from 200
to 280 mm (obtained from calibrated model parameters for the different catchments), θ
represents roughly a depth varying between 400 and 600 mm.
To address the depth mismatch between satellite and model, we applied the exponential
filter proposed by Wagner et al. (1999) to the satellite SM observations and obtained a
soil wetness index (SWI) of the root-zone. The use of SWI to characterise the dynamics
of the root zone SM based on surface observations has been successfully evaluated in a
number of studies (e.g., Albergel et al., 2008; Brocca et al., 2009, 2010; Ford et al., 2013).
We calculated the SWI for each satellite dataset and each sub-catchment by using the
following recursive formulation:
SWI(t) = SWI(t − 1) + G(t) (SSM(t) − SWI(t − 1)) ,
(11)
where t is the daily time step, SSM is the satellite observation (AMS, ASC or SMO) and
G is a gain term varying between 0 and 1 calculated as
G(t) =
G(t − 1)
.
t−(t−1)
G(t − 1) + e−( T )
(12)
The parameter T accounts for several physical parameters defining infiltration and per88
colation processes (Albergel et al., 2008). T was calibrated for each satellite product and
each sub-catchment. The calibration was done by maximising the correlation coefficient
between SWI and the model SM (θ) over the entire period of record of the corresponding
satellite product.
Once the SWI was calculated for AMS, ASC and SMO, we applied instrumental variables
(IV) regression (Su et al., 2014) to remove the systematic (multiplicative and additive)
biases between each SWI and θ and to estimate the observation errors. Following AlvarezGarreton et al. (2015), we applied the triple collocation (TC) analysis (Stoffelen, 1998;
Yilmaz and Crow, 2013) to rescale the SWI and estimate its observation error variance.
The TC-based method has been used as an optimal rescaling method and error estimator
if assumed assumptions are met (Yilmaz and Crow, 2013) and it has been increasingly
applied in hydrologic data assimilation applications (Dorigo et al., 2010; Alvarez-Garreton
et al., 2015; Chen et al., 2014; Crow and Yilmaz, 2014). Data triplets for TC comprised
of the model θ and two SWI time series (derived from a passive and an active sensor,
respectively). We implemented TC with an imposed threshold sample of 100 (Scipal
et al., 2008). For the periods where only one satellite product was available, or when the
threshold for TC triplets was not met, a two-data IV regression was used as a practical
substitute. The two-data IV, also known as lagged variables (LV) (Su et al., 2014), was
applied to the model θ, a single satellite SWI, and a 1-day lagged variable coming from
the model θ.
As a simplification of the seasonal approach proposed by Alvarez-Garreton et al. (2015), in
this study we applied TC and LV to the complete period of record of AMS, ASC and SMO.
This bulk approach provided a scalar observation error variance and constant rescaling
factors for each of the SWI datasets. The rescaled SWI datasets for AMS, ASC and SMO
were named θams , θasc and θsmo , respectively. Finally, ensembles of 500 members were
calculated for the three rescaled datasets (θ ams , θ asc and θ smo , respectively) by adding
a Gaussian noise with mean zero and the error variance obtained from the TC and LV
analyses. As discussed in section 5, the adopted bulk estimations may have implications
for the observation error characterisation and data assimilation results.
3.3.2
EnKF Formulation
In the EnKF, the errors in the model and the observations are calculated from MonteCarlo ensemble realisations. To implement the state-correction scheme, every time there
was a 500-member ensemble of observations available (θams , θasc and/or θsmo estimated
via the satellite data processing described in section 3.3.1), each member of a 500-member
ensemble of predictions (θ) at time t was sequentially updated using (t was omitted from
the following equations since all the terms corresponded to the same time step):
89
1. If θams was available at time t,
θi+ = θi− + K(θiams − Hθi− ).
(13)
The subscript i indicates a member of the ensemble of predictions and observations.
The minus and plus denote θi values before and after updating, respectively. The H
is an operator that transforms the model state into the measurement space. Given
the pre-processing applied to the satellite SM products (section 3.3.1), H reduced
to a unit matrix (and therefore was omitted from the following equations). The
Kalman gain K was calculated at each time step as
K=
C
,
C +E
(14)
where E is the θams rescaled observation error variance estimated from IV analyses
(section 3.3.1) and C is the scalar error covariance of the background prediction θ− .
C was calculated at each time step as
C=
T
1
θ− − hθ− i · θ− − hθ− i ,
N −1
(15)
where hθ− i is the ensemble mean at time t. If θams was not available, θ+ = θ− , i.e.,
no correction was done.
2. If θasc was available at time t,
θi++ = θi+ + K(θiasc − θi+ ).
(16)
To calculate K we applied (14), where E corresponded to the θasc observation error
variance estimated from IV analyses and C was re-calculated by applying (15) to
the updated soil moisture θ+ . If θasc was not available, θ++ = θ+ .
3. If θsmo was available at time t,
θi+++ = θi++ + K(θismo − θi++ ).
(17)
Consistently with the previous steps, K was calculated by (14), where E corresponded to the θsmo observation error variance and C was calculated by applying
(15) to the updated soil moisture θ++ . If θsmo was not available, θ+++ = θ++ .
During the sequence of three updating steps, each sub-catchment was treated independently and no spatial cross-correlation in the satellite measurements was considered. The
order of the satellite products used in the 3-step sequential assimilation was arbitrary,
however different orders were tested with no significant variation in results.
Following Alvarez-Garreton et al. (2015), to generate the model background ensemble
prediction (θ− ) we applied un-biased perturbations to the rainfall forcing data, the model
parameter k1 and the model SM prediction (θ). These perturbations aimed to represent
the main sources of model error, coming from the forcing data, the model parameters and
90
the model structure.
The error models adopted for each perturbation followed a number of previous SM-DA
experiments (e.g., Chen et al., 2011; Brocca et al., 2012a; Alvarez-Garreton et al., 2014)
and consisted in a serially independent log normal multiplicative error (mean 1, standard
deviation σp ) for the rainfall data, a serially independent Gaussian additive error (mean
0, standard deviation σk ) for parameter k1 , and a serially independent Gaussian additive
error (mean 0, standard deviation σs ) for the model soil moisture. To avoid truncation
biases while applying the θ perturbation, we implemented the bias correction scheme
proposed by Ryu et al. (2009) to the SM ensemble. This bias correction ensures unbiased
state ensembles; however, given the non-linear processes represented by the hydrological
model, the perturbation process can still generate biased streamflow ensemble prediction.
This can degrade the performance of the EnKF (Ryu et al., 2009). To remove the biases in
streamflow caused by the forcing and state ensemble perturbations, we followed AlvarezGarreton et al. (2015) and also applied the bias correction scheme to the streamflow
ensembles (of the subcatchment outlets and routing channels).
The error model parameters (σp , σs and σk ) were assumed to be homogeneous within each
study catchment and were calibrated using a maximum a posteriori likelihood approach
(MAP) (Wang et al., 2009) for the period 01 January 1998 - 31 December 2003. MAP has
been used as an objective method to estimate reliable model error parameters (AlvarezGarreton et al., 2015; Li et al., 2014). With this approach we maximised the likelihood
(aggregated over time) of having the observed streamflow within the model streamflow
ensemble prediction. In the MAP scheme, the error in the observed streamflow at the
outlet of each study catchment was assumed to follow a serially independent multiplicative gaussian error (mean 1, standard deviation 0.2). Further details about model error
formulations and MAP calibration can be found in Alvarez-Garreton et al. (2015).
3.4
Dual Correction Scheme
The dual correction scheme combined the forcing correction scheme (section 3.2) with the
state correction scheme (section 3.3). The streamflow prediction for a given time step
was obtained by running the state correction scheme and then using the average of the
updated θ ensemble (and the average of the model ensemble states that were not updated)
to initialise a new PDM run, this time forced with 3B42-RTC coming from the SMART
forcing correction scheme. Following Crow and Ryu (2009), the state outputs of this last
single run of PDM were discarded (not fed back to the state correction scheme) to avoid
cross-correlation between model and observation errors. Figure 5 presents a diagram of
the dual correction scheme.
91
Reference
3B42-RT
Forcing
correction
scheme
3B42-RT
PDM
AMS, ASC,
SMO
PDM
PDM
Qsim
Qsim
Ensemble
mean
Qsim
θ+
θ-
DP
θams, θasc,
θsmo
EnKF
3B42-RT
Dual
correction
scheme
3B42-RTC
SMART
AMS, ASC,
SMO
3B42-RT
State
correction
scheme
Qsim
AMS, ASC,
SMO
PDM
3B42-RTC
θ+
θ-
Ensemble
mean
PDM
Qsim
θ+
DP
θams, θasc,
θsmo
EnKF
Figure 5: Diagram of the reference evaluation run and the 3 correction schemes. The red single-lined boxes
correspond to deterministic variables while the blue double-lined boxes correspond to stochastic variables
(ensembles). The circle labelled DP indicates the data processing of the satellite SM observations detailed
in section 3.3.1
.
3.5
Schemes Evaluation
The reference model run used to evaluate the different correction schemes was the unperturbed model forced with 3B42-RT dataset. The use of the near-real time satellite rainfall
product to force the reference run reflects our aim to evaluate the efficacy of the correction
schemes under a data scarce scenario.
Given that the streamflow from the reference run, the forcing correction scheme (section
3.2) and the dual correction scheme (section 3.4) are deterministic predictions, the state
correction scheme (which provides an ensemble of updated streamflow predictions) was
evaluated in terms of its ensemble mean.
The evaluation period was July 2002 to November 2013, which was determined by the
availability of the satellite datasets (section 2). The streamflow prediction from the reference run and the 3 correction schemes (forcing correction, state correction and dual
correction schemes) were evaluated based on the Nash-Sutcliffe efficiency (NSE) (Nash
and Sutcliffe, 1970), the root mean square error (RMSE) and the correlation coefficient
(R). In particular, we calculated the difference (in percentage) between the statistics of
92
the streamflow from the different correction schemes and the reference run.
To evaluate the improvement from the different schemes during high and low flows periods,
the three statistics were calculated in natural space (more sensitive to high flows) and logtransformed space (more sensitive to low flows). Following Massari et al. (2015), to avoid
exclusion of the zero-flow periods when applying the log transformation, an arbitrary
fraction of the mean daily observed streamflow (Qobs /40) was added to the streamflow
time series (observed and simulated) before calculating their logarithm.
Additionally, we estimated the false alarm ratio (FAR) as the number of times (#) the
model streamflow prediction exceeded a threshold value (Q∗ ), while the observed streamflow was less than Q∗ :
FAR =
#(Qsim >= Q∗ & Qobs < Q∗ )
.
#(Qobs < Q∗ )
(18)
Q∗ was set as the daily flow rate corresponding to a minor flood classification. The
flood classification for the study catchments was provided by the Australian Bureau of
Meteorology as river height threshold values. These relate to flood impact rather than
recurrence interval. The threshold values for minor floods, expressed as streamflow (mm
day−1 ) for Warrego, Comet, Thomson and Barcoo catchments are 0.06, 0.1, 0.02 and 0.14
, respectively. Similarly, we estimated the probability of detection (POD) of these flow
rates as
POD =
#(Qsim >= Q∗ & Qobs >= Q∗ )
,
#(Qobs >= Q∗ )
(19)
The rainfall correction scheme was further evaluated in terms of the corrected rainfall
dataset. For this we used the gauge-interpolated AWAP rainfall as a benchmark dataset
and calculated 5 statistics for the 3B42-RT dataset before and after SMART correction.
The statistics used here were the mean daily bias, the coefficient of determination R2 , the
RMSE, the FAR and the POD. In this case, FAR and POD were calculated based on daily
rainfall threshold values specified in section 4.1.
4
4.1
Results
Rainfall Correction
To categorise the evaluation of SMART into meaningful ranges, we analysed the histograms
of daily rainfall for the benchmark rainfall dataset (AWAP). Figure 6 shows the frequency
of daily rainfall accumulations within four representative sub-catchments (each from one of
the four study catchments). To calculate the histograms we filtered daily accumulations
greater than 2 mm, which resulted in 532, 658, 444 and 553 daily records for the four
sub-catchments, respectively (panels a to d in Figure 6). These plots reveal that for
93
Frequency
0.6
a) Warrego (SC1)
b) Comet (SC3)
c) Thomson (SC4)
d) Barcoo (SC5)
0.4
0.2
0
0
20
40
60
Rainfall (mm day - 1)
0
20
40
60
0
20
40
60
0
20
40
60
Figure 6: Histograms of the benchmark daily AWAP rainfall accumulations larger than 2 mm over 4
representative sub-catchments.
all the sub-catchments more than 50% of the daily rainfall values are within the first
histogram bin, which corresponds to 2 to 7 mm (each histogram bin corresponds to a 5
mm increment). Almost 20% (slight variation across the catchments) of the daily records
range between 7 and 12 mm and the rest is distributed above 12 mm. Based on this, the
evaluation statistics of the forcing correction scheme (section 3.5) were calculated within
these three ranges. FAR and POD in particular were calculated with (18) and (19), using
the upper and lower ranges bounds as threshold values, respectively.
To illustrate the tendency of the satellite rainfall estimates to over or under predict daily
rainfall events, in Figure 7 we present the mean daily bias of the rainfall before and after
SMART correction (using AWAP as the benchmark dataset) for each sub-catchment within
the 4 study catchments (29 sub-catchments in total, see Figure 3). The plots in Figure 7 do
not represent long-term biases, but rather the mean daily bias within specific evaluation
ranges. Before SMART correction, the near real-time satellite product generally over
predicted daily accumulations of rainfall for the low-to-mean ranges (panels a and b). For
the high rainfall events (panel c), the behaviour of the satellite product before correction
was the opposite, there was a fairly consistent under-prediction of daily accumulations.
This over-prediction of low rainfall events and under-prediction of high rainfall events is
consistent with the literature (Ebert et al., 2007).
To interpret the plots in Figure 7, we should recall that SMART is formulated to reduce
the random component of the error in the satellite rainfall data, and thus a reduction in
long-term biases should not be expected. However, since the plots illustrate the mean
biases within specific ranges, some variation of the general tendency to over or under
predict rainfall events at some locations was identified after SMART correction. For the
lowest rainfall range (panel a), the over-prediction of daily accumulations was reduced
within 90% of the catchments after applying SMART (up to 15% of reduction in positive
biases). For the second rainfall range (panel b) the impacts of SMART correction were
not so consistent. Almost half of the cases where there was over prediction of rainfall
estimates (20 in total) were improved after applying SMART. Similarly, almost half of the
under prediction cases (8 in total) were improved after SMART correction (e.g., 2 subcatchments within Warrego, 1 sub-catchment within Comet and 1 sub-catchment within
Thomson). For the high rainfall range (panel c) there was consistent negative bias in
3B42-RT, which was not reduced after applying SMART. The latter could be due to the
94
Bias (mm day - 1)
Bias (mm day - 1)
Bias (mm day - 1)
3
a) 2 to 7 mm day -1
2
1
0
3
b) 7 to 12 mm day-1
3B42-RT
2
3B42-RT c
1
0
-1
c) >12 mm day-1
0
-5
-10
0
5
10
15
20
25
30
Sub-catchment
Figure 7: Mean bias in daily rainfall before and after SMART correction within the study catchments:
Warrego (sub-catchments 1 to 7), Comet (8 to 15), Thomson (16 to 23) and Barcoo (24 to 29). The mean
bias was calculating for daily accumulations of the benchmark dataset varying between 2 to 7 mm (panel
a), 7 to 12 mm (panel b) and above 12 mm (panel c).
limited information that SM provides when the surface soil gets saturated, and to the
tendency of under-estimate peak rainfall events coming from SMART’s core formulation
(further discussion in section 5).
Figure 8 presents the statistics calculated for 3B42-RT before (x-axes) and after SMART
correction (y-axes), for the 3 rainfall ranges defined above and for the 29 study subcatchments. Additionally, the R2 and the RMSE were calculated for the complete range
of daily rainfall accumulations. The coefficient of determination R2 between 3B42-RT and
AWAP for the 3 rainfall ranges (panels a, b and c in Figure 8) and for the complete rainfall
accumulation range (panel d) increased after SMART correction. The improvement was
moderate, but consistent throughout most catchments (it should be noted that different
scales in x- and y-axes were used for the different rainfall ranges). The low R2 values in
panel a are consistent to the larger errors found in 3B42-RT product for daily accumulations below 10 mm (Pipunic et al., 2015). In terms of the RMSE, the forcing correction
scheme reduced the satellite rainfall data error, across all catchments and all daily rainfall
ranges (panels e, f, g and h in Figure 8). The contrasting results between reduced RMSE
(panel g in Figure 8) and increased mean biases (panel c in Figure 7) for the high rainfall
range is consistent with the SMART core formulation. SMART was effective at reducing
the error variance of the rainfall estimates (random component of the satellite rainfall
error), which is reflected by a reduction in RMSE; however, the existing biases in the original dataset were not significantly impacted by the scheme. Positive results after SMART
correction were also observed in the increased POD (panels i, j and k) and decreased FAR
(panels l and m) statistics, across all catchments and all daily rainfall ranges.
95
2 to 7 mm day - 1
0.15
7 to 12 mm day- 1
0.1
a)
>12 mm day - 1
b)
0.4
Complete range
c)
d)
0.6
R2
0.1
0.05
0
RMSE (mm)
10
0.4
0
0.05
0
0.1
e)
0
0.05
0.1
14 f)
8
12
6
10
0
20
0
0.5
0.3
10
g)
0.4
0.6
h)
8
16
6
8
4
80
POD (%)
0.5
0.2
0.05
5
10
10
80
i)
15
12
12
80
j)
75
16
4
20
k)
70
60
65
65
FAR (%)
5
70
75
80
60
60
4
l)
4
3
3
2
2
2
3
4
5
1
70
80
m)
50
50
0.04
10
Warrego
Comet
Thomson
Barcoo
70
70
5
60
70
80
n)
0.02
1
2
3
4
0
0
0.05
Figure 8: Sub-catchment wise evaluation of SMART analyses using AWAP as the benchmark dataset.
Y-axes presents the corrected 3B42-RTC statistics and x-axes the uncorrected 3B42-RT statistics. The 3
columns show the results for the indicated daily rainfall ranges. The 4 rows present the results for R2 ,
RMSE, POD and FAR statistics, respectively.
In summary, although SMART led to increased rainfall mean biases at some locations for
specific ranges of rainfall events (Figure 7), overall the scheme improved the quality of the
satellite rainfall data (Figure 8). In particular, the positive impacts within high rainfall
events (increased R2 and POD, decreased RMSE) suggest that this could be a suitable
scheme to improve the prediction of high streamflow events.
4.2
Satellite Data Processing
Figure 9 summarises some of the satellite data processing results, panel a shows the parameter T from equation 12 that maximised the correlation coefficient (presented in panel
b) between the model SM and SWI for each sub-catchment and each satellite product.
The parameter T varied within a range of 3 to 42 days, which is consistent with the range
of values found in previous studies (e.g., Albergel et al., 2008; Brocca et al., 2009; Ford
et al., 2013). These variations in T could be due to a series of factors, including the particular sub-catchment physical processes, the retrieval method of the satellite product, the
quality of the SM predicted by the model, and the different periods of time used for the calibration. Across all sub-catchments, and similarly to previous findings (Alvarez-Garreton
et al., 2015), T values were larger for the SMO product, which would be inconsistent with
L-band having a deeper penetration than AMS C-band (to limit the comparison within
passive retrievals). This might be due to factors including the different retrieval meth96
50
a)
T (days)
40
30
20
10
0
1
b)
R
0.9
0.8
0.7
0.6
E (vol/vol) 2
2.5
2
×10 -3
c)
AMS
ASC
SMO
1.5
1
0.5
0
0
5
10
15
Sub-catchment
20
25
30
Figure 9: Satellite data processing results for the Warrego (sub-catchments 1 to 7), Comet (8 to 15),
Thomson (16 to 23) and Barcoo (24 to 29). Panel a shows the calibrated parameter T used in the SWI
estimates. Panel b presents the correlation coefficient between AMS, ASC and SMO-derived SWI and the
model soil moisture. Panel c presents the observation error variance in the observation space.
ods (which have quite different assumptions pertaining to spatial heterogeneity) and the
influence of radio-frequency interference noise.
The observation error variances for SWI derived from AMS, ASC and SMO, respectively,
are presented in panel c, Figure 9. SMO-derived SWI generally outperformed the others
two sensors, which is consistent with its higher correlation with the model (panel b).
The passive AMS product showed the largest error across the study sub-catchments. It
should be noted that the errors presented in Figure 9 come from TC analyses, the results
from LV procedure (applied when there was only one satellite product available or when
the sample threshold for TC was not met) maintained a similar comparative relationship
among sensors; however, the magnitude of the error was consistently higher. This overestimation of the observation errors by LV is consistent to previous studies (Su et al., 2014;
Alvarez-Garreton et al., 2015) and it is likely to be explained by error autocorrelation of
the lagged variables used in the triplets. This will have the impact of giving greater weights
to the model predictions in the assimilation.
4.3
Streamflow Prediction Evaluation
The statistics of the reference runs used to evaluate the different assimilation schemes are
presented in Table 2. It can be seen from this table that the quality of the streamflow
prediction in most of these catchments was poor, with low NSE and R values (calculated
using both the raw and the log-transformed streamflow values). The only catchment
that showed good quality statistics is the Comet. The poor performance of the model in
97
Table 2: Streamflow prediction statistics for the reference runs calculated using the raw streamflow values
(r) and for the log-transformed values (l).
NSE
(r)
(l)
0.30 0.40
0.70 -0.30
0.28 0.10
0.24 -0.03
Catchment
Warrego
Comet
Thomson
Barcoo
R
(r)
0.58
0.87
0.55
0.50
(l)
0.74
0.56
0.75
0.62
RMSE
(r)
0.34
0.78
0.21
0.53
(mm)
(l)
1.11
1.49
1.51
1.21
FAR
(r)
0.07
0.22
0.23
0.10
POD
(r)
0.85
0.81
0.95
0.73
Table 3: Streamflow prediction statistics from the models forced with gauged-based rainfall data. (r) refers
to the raw streamflow values and (l) to the log-transformed values.
Catchment
Warrego
Comet
Thomson
Barcoo
NSE
(r)
(l)
0.85 0.69
0.74 0.21
0.54 0.56
0.43 0.25
R
(r)
0.92
0.89
0.77
0.66
(l)
0.87
0.71
0.86
0.73
RMSE
(r)
0.15
0.73
0.17
0.46
(mm)
(l)
0.80
1.16
1.06
1.04
FAR
(r)
0.05
0.15
0.17
0.06
POD
(r)
0.92
0.81
0.96
0.79
the study catchments was mainly due to the low quality of the forcing rainfall data (the
near real-time 3B42-RT product). This was confirmed by the higher statistics obtained
after calibrating the models with the (higher quality) gauged-interpolated AWAP dataset
(presented as reference in Table 3). The relevance of using these reference runs is that
they represent the data scarce scenario within most areas in the world. The calibrated
model error parameters (σp , σs and σk ) for the study catchments are presented in Table 4.
It can be seen from this table that Comet catchment presents the lowest error in rainfall,
which is consistent with the better performance in streamflow prediction.
The results of the different assimilation schemes are presented in Figure 10. Overall, the
use of (processed) satellite SM to correct the model SM and/or the forcing rainfall led
to an improvement over the reference model runs. In terms of NSE and RMSE, there
was a wide range of improvement for both the high flows (panels a, e) and the low flows
(panels b, f). In 3 out of 4 high flow cases and all the low flow cases, the state correction
scheme outperformed the forcing correction scheme. The combined dual scheme further
improved the results, irrespective of wether the high flows or low flows were emphasised in
the evaluation. The only case where this relation changed was for the high flows in Comet
catchment (panel a), where the forcing scheme consistently showed a greater positive
impact in streamflow prediction. The counterintuitive behaviour of the dual scheme in
Table 4: Model error parameters calibrated with MAP
Catchment
Warrego
Comet
Thomson
Barcoo
σp
0.98
0.70
0.85
0.89
98
σs
0.03
0.03
0.02
0.02
σk
0.10
0.05
0.08
0.03
Raw flow
Log flow
∆ NSE
a)
b)
0.2
0.1
0
∆ RMSE
∆R
0.2
∆ FAR
0
c)
0.2 d)
0.1
0.1
0
0
0.1
0.1
e)
0
0
-0.1
-0.1
-0.2
0.2
-0.2
g)
f)
Wa
Co
Th
Ba
0
-0.2
-0.4
0.1
∆ POD
fDA
sDA
dDA
5
h)
0
-0.1
Wa
Co
Th
Ba
Figure 10: Data assimilation results of the forcing correction scheme (fDA), the state correction scheme
(sDA) and the dual correction scheme (dDA). The statistics in the left column (panels a, c, e, g and h)
were calculated using the raw streamflow values. The statistics in the right column (panels b, d and f)
used log-transformed streamflow values.
the Comet catchment could be due to a combinations of factors, including the better
initial performance of the model, the higher quality of the rainfall data, the catchments
runoff mechanisms, the quality of the satellite SM within the catchment. Based on the
improvements in R, the dual correction scheme in general outperformed the other two
schemes. This is the true for 2 out of 4 high flow cases (panel c) and for 3 out of 4 low
flow cases (panel d).
The dual correction scheme also led to a consistent decrease of the FAR (panel g in Figure
10) within all the study catchments. By applying this dual correction scheme, the number
of incorrectly predicted minor floods was reduced by 10 to 30%. If these predictions were
to be applied to feed operational flood alert systems, this improvement in FAR would
have a significant impact. In terms of POD (panel h), the data assimilation schemes had a
much lower (negative and positive) impact on the streamflow prediction (less than 10% of
POD variation). The POD is only improved in Comet catchment, where the dual scheme
showed the highest effect. For the other catchments there was a decrease of POD after
the state and dual correction schemes.
99
5
Discussion
The results presented here demonstrate that active and passive satellite SM retrievals
have the potential to improve an operational satellite rainfall product (3B42-RT). We
also showed that assimilating the satellite SM observations into the streamflow modelling
generally had positive impacts in the quality of the streamflow prediction. Finally, by
combining the forcing and state correction schemes we further improved the streamflow
predictions for most study catchments. These outcomes are consistent with previous
studies (Crow and Ryu, 2009; Chen et al., 2014; Massari et al., 2014).
Overall, the assimilation of SM retrievals via SMART improved the rainfall estimates
over the study catchments, with a decrease in RMSE and FAR, and an increase in R2
and POD within most sub-catchments (Figure 8). Similarly to previous studies (Crow
et al., 2011; Chen et al., 2014), SMART showed limitations during wet conditions. This
resulted in the under-prediction of some high intensity rainfall events (increased negative
biases in panel c, Figure 7). As mentioned in section 4.1, this could be due to the limited
information about rainfall that SM provides when the surface soil is wet. This key issue
affects not only SMART, but also other correction schemes aiming to estimate (or reduce
the error in) rainfall based on SM information (e.g., Brocca et al., 2013; Zhan et al., 2015).
Another reason for the under-prediction of rainfall peaks could be the precipitation error
variance minimisation approach used by SMART (the Kalman filter). It has been shown
that an error variance minimisation algorithm increases the conditional bias of the rainfall
estimates, which is manifested by an underestimation of strong rainfall (Ciach et al.,
2000).
When the SM was near the lower limit of the volumetric water content (dry conditions),
SMART consistently reduced the over-prediction of small rainfall events (decreased positive bias in panel a, Figure 7). This suggests that, in contrast to previous studies (e.g.,
Crow et al., 2011; Chen et al., 2014), the noise in the SM retrieval signal was not misinterpreted by SMART as rainfall. The better performance of SMART during low intensity
rainfall events could be explained by the different climatology of our study region and by
the different quality of the satellite products (rainfall and SM products).
The impact of SMART correction in the streamflow modelling was assessed in section
4.3. The overall improvement of the forcing data via SMART was successfully transferred
into the streamflow modelling. Similar to previous studies (Crow and Ryu, 2009; Chen
et al., 2014), during high flow periods SMART led to a consistent positive impact on the
streamflow modelling across all catchments (increased NSE, R and a reduced RSME in
Figure 10). Therefore, even when some peak rainfall values were under predicted at some
locations (negative mean biases in Figure 7), the corrected rainfall featured consistently
lower errors than the near real-time satellite rainfall (Figure 8). This resulted in an
improved overall performance of the rainfall-runoff model after SMART rainfall correction.
100
The low flow estimations were also improved after SMART; however, the improvement was
less significant than during high flows. This was expected given the higher control that
rainfall exerts in the streamflow generation during intense events.
The correction of the model SM state by the assimilation of satellite SM led to a significant improvement in the prediction of low flows (panels b, d and f in Figure 10). The
improvement during high flows was less for most cases (panels a, c and e in Figure 10),
which is consistent with the higher control that the catchment wetness condition has in
the streamflow generation during low flow periods. Our results agree with various studies demonstrating the potential of these observations for enhancing streamflow modelling
(e.g., Brocca et al., 2010; Alvarez-Garreton et al., 2014; Wanders et al., 2014; AlvarezGarreton et al., 2015; Massari et al., 2015). Notwithstanding this evidence, there are key
choices to be made in setting up the SM data assimilation schemes that can have significant impacts on their results. As clearly described by Massari et al. (2015), these schemes
are highly influenced by local conditions and methodological issues. The latter should be
carefully taken into consideration before drawing general conclusions.
Regarding our methodology, the first key step to set up the state correction scheme was
the satellite data processing (section 3.3.1). The use of the exponential filter to estimate
the SWI of the root zone based on surface observations was a simple solution that has
shown positive results in several studies (e.g., Albergel et al., 2008; Brocca et al., 2009;
Ford et al., 2013). However, there are some issues related to the autocorrelation in the
observation errors and the potential cross-correlation with the model SM errors that have
been highlighted when SWI is used within a data assimilation scheme (Brocca et al.,
2010; Alvarez-Garreton et al., 2015). There is an important research gap here since the
implications of the latter issues have not yet been assessed, and the use of other profile SM estimation methods (e.g., Richards, 1931; Manfreda et al., 2014) have not been
tested within this data assimilation context. The rescaling of the observations and the
quantification of their errors was performed here by a triple collocation based approach
(TC and LV detailed in section 3.3.1), which has been assessed as an optimal rescaling
procedure if assumptions are met (Yilmaz and Crow, 2013). In particular, we applied TC
and LV to the complete observation period (bulk estimation of rescaling parameters and
observation errors), which does not consider the temporal variability (e.g., seasonality) in
the observation errors (Draper and Reichle, 2015; Su and Ryu, 2015). This simplification
could potentially lead to overcorrection of the model state if the actual error is higher,
and vice versa. To address this, some studies have applied seasonal rescaling and error
estimation (Alvarez-Garreton et al., 2015) or have separately treated anomalies and seasonality within the TC implementation (Chen et al., 2014). Despite these attempts to
address the temporal variation in the observation errors, further investigation is required
to assess the impacts of rescaling assumptions and simplifications in satellite SM data
assimilation.
101
A practical implication of the highlighted limitations within the satellite data processing is
that lower errors estimated for a particular dataset (e.g. SMO-derived SWI in Figure 9) do
not necessarily imply a better performance of the product in the data assimilation schemes.
Therefore, a comparative assessment of the skill of the different satellite SM products
to improve streamflow prediction in the proposed schemes cannot be drawn from these
results (such comparison would require to run the assimilation schemes independently for
the different satellite products). Acknowledging this limitation, the benefit of sequentially
assimilating the three satellite products is that since we are using a statistically optimal
updater, integrating multiple observations should provide better results. Additionally,
given the different period of record of the SM products, using the three products enables
a longer evaluation period for the assimilation schemes.
The second key step in the state correction scheme was the representation and quantification of the model errors, which has a direct impact in the data assimilation results
(Massari et al., 2015). There are a number of methods to quantify model errors such as
the assumption of arbitrary error parameter values (Chen et al., 2014), the maximisation
of ensemble verification criteria (De Lannoy et al., 2006; Brocca et al., 2010; Massari et al.,
2015), the auto-tuned land data assimilation system proposed by Crow and Yilmaz (2014)
and the maximisation of the likelihood of having the streamflow observations within the
streamflow ensemble prediction (Alvarez-Garreton et al., 2015; Li et al., 2014) (adopted
in this study). The evaluation of these techniques and their impacts on the assimilation of
SM into rainfall-runoff models has not been studied deeply. In particular, the reliability
and quality of the generated open-loop ensembles (in Monte Carlo-based applications)
used to evaluate the data assimilation results are usually not assessed. In our case, since
we based the evaluation on deterministic predictions (as explained in section 3.5), the skill
of the stochastic state correction scheme in terms of ensemble prediction characteristics
was not assessed.
Despite the highlighted limitations and challenges within the forcing and state correction
schemes, our experiments demonstrated that the streamflow prediction for these sparsely
gauged locations is improved by the assimilation of satellite soil moisture. The state correction scheme generally showed higher positive impact on the streamflow prediction than
the forcing correction scheme, for both high flows and low flows. This larger improvement during high flows contrasts with previous studies (Crow and Ryu, 2009; Chen et al.,
2014) where the forcing correction scheme generally outperformed the state correction for
high flows. This could be due to several factors including differences in rainfall-runoff
mechanisms between catchments, the quality of the forcing data before correction, the
quality of the satellite SM products and the different experimental methodologies. Finally, we showed that the combination of a better representation of the catchment wetness
condition (via state correction scheme) with higher quality forcing data (via forcing correction scheme) in most cases outperformed the results of separately applying either data
assimilation scheme (Figure 10).
102
Finally, it should be noted that while the proposed schemes were able to improve the
quality of an operational satellite rainfall product and the PDM SM state, which in turn
led to better streamflow predictions, the streamflow predictions after the dual SM-DA
scheme still did not outperform the case where the gauge-based rainfall data was used as
input forcing (evaluation scores presented in Table 3). This implies that while satellite
SM may be useful for improving satellite rainfall products and SM states of hydrological
models within data scarce regions, it is more critical to have a higher quality forcing data
for accurate streamflow prediction in the study regions.
6
Conclusions
We explored the use of active and passive satellite SM products for improving the streamflow prediction of a rainfall-runoff model (PDM) within 4 large semi-arid catchments.
We set up our experiments under a scenario without rain gauges to represent the data
scarcity in most areas worldwide, which led to poor streamflow predictions before assimilation. Within this context, two key variables controlling the runoff generation were
corrected by the assimilation of the surface SM observations: the satellite rainfall forcing
data and the PDM soil moisture state.
The forcing correction used SMART (Crow et al., 2011) and the results showed a consistent
improvement in the the operational satellite rainfall (increased R and reduced RMSE and
mean bias). In general, the use of the corrected rainfall data to force the rainfall-runoff
models improved the streamflow prediction (increased NSE, R2 and decreased RMSE),
especially during high flow periods.
The state correction scheme generally showed a higher positive impact on the streamflow
prediction compared with the forcing correction scheme, especially for low flows. The
combined dual correction scheme enhanced the benefits of the individual schemes, which
led to an improved prediction of both low and high flows.
We have highlighted a number of limitations within the forcing and state correction
schemes that should be addressed to advance towards a robust data assimilation framework. Although our results are case specific and depend on the catchment characteristics,
degree of instrumentation and the experimental set up, they provide new evidence of the
value of satellite SM for improving both an operational satellite rainfall product and the
streamflow prediction within data scarce regions.
Acknowledgements
This research was conducted with financial support from the Australian Research Council
(ARC Linkage Project No. LP110200520) and the Bureau of Meteorology, Australia. C.
103
Alvarez-Garreton was supported by a Becas Chile scholarship. We are grateful to all who
contributed to the data sets used in this study. We thank Chris Leahy and Soori Sooriyakumaran from the Australian Bureau of Meteorology for providing catchment and AWAP
rainfall data, and gratefully acknowledge their advice. AMSR-E data were produced by
Richard de Jeu and colleagues at Vrije University Amsterdam and NASA. ASCAT level
3 data were produced by the Vienna University of Technology within the framework of
EUMETSAT’s Satellite Application Facility on Support of Operational Hydrology and
Water Management from MetOp-A observations. The SMOS version RE02 data were
provided by Centre Aval de Traitement des Donnees. he TMPA data were provided by
NASA Goddard Earth Sciences Data and Information Services Center (GES DISC). We
also thank the anonymous reviewers and associate editor for their comments which have
improved the quality of this paper.
104
Chapter 7
Discussion and Conclusions
This research aimed to improve flood forecasting in catchments with low on-ground data
availability by using space observations. Active and passive satellite soil moisture (SM)
products were assimilated a into a rainfall-runoff model to improve hydrologic model
streamflow predictions. Remotely sensed SM was used to correct two key variables controlling the streamflow generation: the catchment wetness condition (via a state correction
scheme) and the rainfall forcing data (via a forcing correction scheme).
The core part of the research focused on the state correction scheme (Chapters 3, 4 and 5).
To set up this scheme, I used a simple rainfall runoff model (the probability distributed
model, PDM) and corrected the soil water state of the model by assimilating active and
passive satellite SM observations. Each of the required steps to set up an effective soil
moisture data assimilation (SM-DA) scheme were rigorously addressed. These steps were
categorised into two main topics: the satellite SM data processing and the model error
representation. Several aspects within each topic were explored and different techniques to
address them were applied. Some of the techniques were adopted from previous studies and
some were introduced in this thesis (the innovative aspects of the research are summarised
in Section 5).
After setting up a SM-DA state correction scheme that was effective at improving streamflow predictions, in Chapter 6 the scheme was coupled with a forcing correction scheme.
In the forcing correction scheme, the near real-time satellite rainfall product used to force
PDM was corrected by assimilating satellite SM via the soil moisture analysis rainfall tool
(SMART) proposed by Crow et al. (2009). This dual correction scheme was evaluated
within 4 large sparsely gauged catchments.
The following sections provide a description of the key challenges and limitations found
throughout the research, a summary of the main findings, the conclusions of the thesis,
including my recommendations for future work, and finally a list of the key contributions
of this thesis.
105
1
Challenges in satellite SM data processing for DA
The satellite soil moisture products were processed to resolve three key issues within the
state correction scheme: 1) the depth mismatch between the soil moisture represented by
the satellite retrievals (i.e., the top few centimetres of soil) and by the model (usually a
deeper layer), 2) the presence of systematic biases between the observations and the model
predictions, and 3) the need to quantify the statistical properties of random observation
error (and model error, as explained in Section 2).
The reason for having a depth mismatch between model and observations relies on the
selected conceptual rainfall-runoff model used in this research. The selected PDM uses
only one tank to represent the soil water storage. One of the main challenges of using
such a parsimonious model is that the satellite data must be processed in such a way that
the model can ingest information compatible with the conceptual storage (deep layer of
soil). This would not be necessary if a land surface model that explicitly represents the
first top layer of soil water storage was used instead, such as VIC/Noah (Kumar et al.,
2014; DeChant and Moradkhani, 2015). However, there are some limitations in applying
a distributed land surface model in data-scarce regions such as the study catchments. For
example, the calibration of such a model given the poor hydro-meteorological data (quality
and quantity) can lead to unrealistic parameters and over parametrisation issues.
The depth mismatch was addressed by applying the exponential filter proposed by Wagner
et al. (1999) to the surface satellite observations to estimate a soil wetness index (SWI) of
the root zone soil moisture. This was a simple solution that has shown positive results in
several studies (e.g., Albergel et al., 2008; Brocca et al., 2009; Ford et al., 2013). However,
there are some issues that have been highlighted when SWI is used within a data assimilation scheme. For example, SWI can introduce autocorrelation in the observation errors
that can lead to cross-correlation with the background soil moisture errors (Brocca et al.,
2010; Alvarez-Garreton et al., 2015) (further discussed below). The implications of this
in SM-DA have not been assessed yet. Moreover, there are more physically-based profile
soil moisture estimation methods which have not been tested within a data assimilation
context (e.g., Richards, 1931; Manfreda et al., 2014).
There is a plethora of techniques to remove the systematic (additive and multiplicative)
biases between the model soil moisture and the SWI derived from the observations. Here,
I applied a number of them throughout the research, including: linear rescaling (LR,
Chapters 3 and 4), anomaly-based cumulative distribution function (aCDF) matching
(Chapter 4), three-data set instrumental variable regression (triple collocation, Chapters
5 and 6) and a two-data set instrumental variable regression (lagged variables, Chapters
5 and 6).
In Chapter 4, I showed that the assimilation of aCDF-rescaled observations performed
consistently better than assimilating LR-rescaled observations. However, this was a single
106
CHAPTER 7: DISCUSSION AND CONCLUSIONS
real-data case study thus generalised conclusions were not drawn. A few other studies
have evaluated different rescaling techniques in SM-DA with varied results. For example,
Massari et al. (2015) compared LR, CDF and variance matching techniques and found little
impact in SM-DA results when assumptions of model error were correct. Yilmaz and Crow
(2013) demonstrated that triple collocation (TC) was the optimal rescaling technique,
if the procedure requirements were met. These requirements include having sufficient
linearly related independent triplets and zero error autocorrelation in the observations
(non-zero error auto-correlation is allowed, but it increases the sampling error of TC
estimates).
Despite the increasing use and evaluation of the above techniques, a deep investigation
leading to strong conclusions about the impacts of the different rescaling techniques in the
updated streamflow predictions has not been undertaken yet. Such a complex investigation
should consider that SM-DA results are highly influenced by a large number of experimental considerations (i.e., model structure, quality of the model parameters, quality of the
forcing data, quality of the satellite soil moisture data, satellite data processing, model
error characterisation, etc.) and specific catchment characteristics (i.e., climate, geology,
topography, runoff mechanisms, location, etc.). In this sense, the experiments carried out
in this research contribute to address this gap by implementing different rescaling techniques. Moreover, I worked within semi-arid large catchments, which feature very distinct
runoff mechanisms from most catchments studied in SM-DA.
Another unsolved issue is that the systematic differences between model and observations
may have a temporal component (e.g., seasonality) (Draper and Reichle, 2015; Su and
Ryu, 2015), which has been rarely taken into consideration within SM-DA applications.
Addressing this, in Chapter 5 I applied seasonal rescaling and found positive outcomes
in terms of the updated streamflow prediction. Nevertheless, I highlighted that further
investigation was required to assess the importance and impacts (if any) of this seasonal
approach compared to the commonly used bulk rescaling.
The final step in the satellite data processing was the quantification of the (rescaled)
observation errors. Quantifying errors requires the assumption of a certain error structure,
and incorrect assumptions can degrade the performance of the data assimilation (Reichle
et al., 2008; Crow and Reichle, 2008; Crow and Van den Berg, 2010). In most SM-DA
applications, an independent Gaussian error is assumed, which disregards the potential
autocorrelation in the observation errors. Error autocorrelation in the observations can
lead to error correlation between the observations and the background model forecast,
which violates a critical EnKF assumption (Alvarez-Garreton et al., 2015). This would
be especially critical when a SWI is used to represent deep-layer soil moisture, since
its formulation explicitly incorporates autocorrelation terms. Exploring this, different
error autocorrelation structures were tested in Chapter 3, however results showed little
impact on the updated streamflow for the case study. I explained this low sensitivity
107
through factors such as the large errors in the model, the arbitrary procedure used to
estimate the observation error variance, and the error correlation between the model and
the raw satellite observations that probably exists before data processing. These findings
are broadly consistent with Crow and van den Berg (2010), who found that soil moisture
analysis was not further improved via the introduction of the Colored Kalman Filter (which
explicitly accounts for observation error auto-correlation), despite the clear presence of
error auto-correlation in the assimilated observations.
Given the results from Chapter 3, for the subsequent chapters I adopted an independent
Gaussian structure for the observation error and concentrated on quantifying its variance
using different procedures. In Chapter 4, I assumed orthogonality between the rescaled
observations and their errors and determined an upper bound of the observation error
variance. Different error variances within the bound were tested; however, little impact on
the updated streamflow was found (Alvarez-Garreton et al., 2015). This new procedure
was adopted later by Massari et al. (2015), who suggested that the optimal choice of the
observation error variance had a strong connection with the accurate representation of
the model error. It should be noted that this error estimation procedure is arbitrary and
does not consider an evaluation of the satellite observation quality (Alvarez-Garreton et al.
(2015) and Massari et al. (2015) evaluated the quality of the error estimates in terms of the
updated streamflow). In the following Chapters 5 and 6, the error quantification procedure
was improved by applying instrumental variable regressions. In particular, I applied triple
collocation, TC (Stoffelen, 1998; Yilmaz and Crow, 2013), and lagged variables (Su et al.,
2014) when TC requirements were not met. These procedures simultaneously resolved the
rescaling of the observations and the quantification of the observation errors. As mentioned
above, given the evidence of temporal changes in the variance of the observation errors
(Draper and Reichle, 2015; Su and Ryu, 2015), in Chapter 5 I explicitly represented
the seasonality in the satellite errors by applying seasonal TC and LV. Although those
results demonstrated a significant seasonality in the satellite observations errors, it was
not clear what the impact of representing this within SM-DA context was, hence further
investigation is needed.
Assessing the impacts of observation error seasonality in SM-DA fell beyond the scope
of this thesis, thus in Chapter 6 the error quantification procedure was simplified by
applying bulk TC and LV. This reduced the number of assumptions and to simplify the
interpretation of results in the (already complex) dual correction scheme.
2
Challenges in model error representation
A consistent representation of the errors in the model is an important and major challenge
in SM-DA. On the one hand, there are several sources of error in a rainfall-runoff model,
including the model structure, the model parameters and the quality of the forcing data.
108
On the other hand, there is usually very limited data to evaluate the model predictions
and quantify these errors, which makes the problem highly underdetermined. Solving this
problem involves several arbitrary decisions and assumptions that may significantly affect
SM-DA results. The most critical are the selection of the error sources to quantify, the
assumptions about the structure of those errors, and the assumed (or estimated) quality
of the observed data used to evaluate the model predictions. Furthermore, after the above
above assumptions are made, there are different techniques to represent those errors and
to estimate their parameters (described in Chapter 2, Section 4.2), with little agreement
on the most suitable procedure to achieve this.
The estimation of the error parameters has a direct impact in SM-DA, since they influence the error covariance between the model soil moisture and the predicted streamflow.
Moreover, most stochastic SM-DA applications evaluate their schemes using the openloop as the reference run (open-loop refers to the ensemble of predictions resulting from
perturbing the selected error sources with the estimated error parameters). Despite the
significant impacts that the error parameters estimation may have in SM-DA, the quality
of these open-loop simulations is usually not a major focus of investigation in SM-DA
applications.
In this research I firstly made some decisions about which errors to represent and how.
Then, an ensemble verification approach to estimate the error parameters of the rainfall
forcing data and the model SM was adopted (Chapters 3 and 4). Advancing towards
a more consistent error representation, in Chapters 5 and 6 I added a (sensitive) model
parameter into the error sources, which directly affected the surface runoff estimation
(main component of the total streamflow generated by the study catchments). I also
introduced a maximum a posteriori approach to quantify the error parameters, which
resulted in a more reliable open-loop ensemble (evaluated in Chapter 5 by using rank
histograms).
Another challenge within this error characterisation procedure is that perturbing components of the model (such as the forcing data, parameters and/or states) with un-biased
errors may introduce bias in the open-loop streamflow prediction. This unintended bias
is due to two main reasons: the truncation of SM state ensembles and the non-linear,
bounded nature of hydrological models. This can result in mass balance errors and degrade the performance of the SM-DA scheme. The truncation bias was removed by applying the bias correction scheme proposed by Ryu et al., (2009) to the SM state ensembles
(Chapters 4, 5 and 6). To remove the biases caused by non-linearities in the model, I
applied a similar bias correction scheme to the streamflow prediction ensembles (Chapters
5 and 6).
In summary, the representation and estimation of model errors is a necessary and key step
in SM-DA. Given that this is one of the several steps required in SM-DA, most applications adopt a specific technique (based on previous studies) to estimate the model errors
109
without comparing different techniques or without deeply evaluating the estimated error
parameters. This investigation contributes towards assessing the most suitable techniques
to generate reliable streamflow prediction ensembles and understanding their impacts in
SM-DA.
3
Main findings
The results of this research demonstrated that the assimilation of remotely sensed SM to
correct the model’s SM state consistently led to improved streamflow predictions. While
these improvements were significant, an important limitation was clearly evident. Stochastic data assimilation is formulated to reduce the random component of the errors and
therefore does not address systematic biases in the model, therefore, the efficacy of the
state correction scheme was restricted by the model quality before assimilation (Chapter
4). Consequently, SM-DA mainly improved the quality of the streamflow ensemble prediction (skill, reliability and averaged statistics) but did not significantly reduced the existing
biases in the peak flows prediction (Chapters 3, 4 and 5). The state correction scheme was
also effective at improving the streamflow ensemble prediction within ungauged internal
locations, which demonstrates the advantages of incorporating spatially distributed SM
information within large and poorly instrumented catchments (Chapter 5).
Given the particular runoff mechanisms within the study catchments, the state correction
scheme led to varied improvements in the streamflow prediction. The streamflow at the
outlet of the study catchments features long periods of zero-flow, a negligible base flow
component and sharp flow peaks after rainfall events, when the catchment have reached
a threshold level of wetness. Given these characteristics, SM exerts a higher control
on catchment runoff generation during minor and moderate floods, therefore the state
correction scheme showed more skill when the low flows were evaluated. SM-DA improved
major floods to a lesser extent (Chapter 4 and 6). These results reveal one key limitation
of this approach: it aims at improving flood predictions by correcting the SM state of a
rainfall-runoff model, however, SM is probably not the main controlling factor in the runoff
generation during large floods (within the study catchments used in this research).
Addressing the above limitation, I set up a forcing correction scheme that aimed at reducing the errors in the rainfall data (Chapter 6). The rainfall data, in addition to the
infiltration estimates from the model, are probably the main factors controlling the accuracy of flood predictions. I demonstrated that remotely sensed SM was effective at improving a near-real time satellite rainfall product (in particular, the medium-to-high daily
rainfall accumulations), which in turn led to a consistent improvement of the streamflow
prediction, especially during high flows. When comparing both schemes individually, results showed that the skill of the state correction scheme was, for most cases, greater at
improving streamflow prediction than when the corrected rain was used to force the model
110
(without state correction). This was true for both the low flows and high flows. Finally,
when the forcing and the state correction schemes were combied, flood predictions were
further improved.
4
Conclusions
This thesis investigated and assessed the value of coupling satellite soil moisture products
into the streamflow modelling for improving flood prediction. A real-data experimental
approach was used as a platform for developing and testing a variety of innovations to
improve SM-DA. With this, I provided new evidence of the advantages of exploiting this
spatially distributed information within data scarce regions.
The main challenges for implementing an effective SM-DA scheme were highlighted and
some of the limitations found in the current practices were identified. To overcome these
limitations, I propose the following strategies for future research:
• I suggest further exploration and assessment of the suitability of different rescaling
techniques to remove the systematic biases between the model and the observations.
To achieve a robust inter comparison, this exploration should include a range of
different catchment characteristics (size, climate, controlling runoff characteristics,
etc.) compared under similar SM-DA frameworks (i.e., implementing consistent
techniques for the estimation of observation and model errors).
• I suggest further exploring and assessing the importance of accounting for nonstationarity in the satellite errors within SM-DA applications.
• I recommend further assessing the impacts in SM-DA of the error autocorrelation
in SWI, when the latter is used as a profile soil moisture estimator. Additionally,
since an improved profile soil moisture estimation should have a positive effect on
the SM-DA efficacy for improving streamflow, I recommend testing other methods
to estimate the root zone soil moisture based on surface observations (e.g., Richards,
1931; Manfreda et al., 2014).
• I recommend exploring the suitability of assimilating satellite soil moisture into more
complex hydrological models that explicitly account for the water storage of the top
soil layer. In this way, the profile soil moisture estimation based on surface satellite
observations would not be a necessary step.
• There is an important research gap in the generation of streamflow ensemble predic-
tion, therefore I suggest exploring suitable strategies to consistently represent model
errors and estimate the error parameters.
• Finally, I strongly recommend that a subsequent approach should combine the pro-
posed SM-DA framework (which exploits spatially distributed information about the
111
catchment wetness condition and therefore has benefits for improving streamflow prediction throughout the catchment and, in particular, at ungauged inner locations),
with the assimilation of the observed streamflow at available stream gauges. The
assimilation of observed streamflow has shown to be effective at improving flood
prediction at the catchment outlet, however, this does not necessarily improve (or
even degrade) predictions at ungauged sub-catchments (Mendoza et al., 2012; Li
et al., 2015). The combination of these two data assimilation schemes was recently
explored by Wanders et al. (2014) with positive results for a case study, which encourages further investigation.
The assimilation of satellite soil moisture observations into a hydrologic model is not a
simple task. It requires addressing several challenges and there is no agreement on the most
suitable strategies. Moreover, the outcomes of a SM-DA scheme are highly influenced by
the particular catchment characteristics and methodological procedures, therefore general
conclusions should be drawn only with great care.
Acknowledging these limitations, this thesis provides new evidence of the value of remotely sensed soil moisture for improving flood prediction within data scarce regions. I
discussed the current practices to implement the state and the forcing correction schemes.
I highlighted their main limitations and proposed new strategies to address them.
5
Contributions
There are several scientific and practical contributions of this research. Different existing
tools to set up a SM-DA state correction scheme were evaluated; new techniques to address some of the key challenges in SM-DA were introduced; an effective dual correction
scheme for improving flood prediction was implemented, which combined a state and a
forcing correction schemes; and various real data experiments were presented, providing
novel evidence of the efficacy of SM-DA for improving flood prediction in data-scarce
regions.
In particular, the new techniques introduced to overcome some of the limitations found in
the state correction scheme included:
• The correction of the unintended bias introduced in the generation of streamflow
ensemble predictions (Chapters 5 and 6).
• The use of a maximum a posteriori approach to estimate model error parameters
(Chapters 5 and 6).
• The use of a lagged-variable approach to overcome TC requirements and estimate
satellite observation error (Chapters 5 and 6).
• The explicit representation of seasonality within the satellite SM errors (Chapter 5).
112
The framework proposed in this thesis improved the prediction of floods during the last
decade within 4 Australian catchments. This framework can be implemented within an
operational flood alert system, which would provide valuable information to reduce risks
associated with floods within data scarce regions.
113
114
Appendix A
Publications
Journal articles refereed
1. Alvarez-Garreton C., Ryu D., Western A.W., Crow W.T., Su, C.-H., and Robertson
D.E. Dual assimilation of satellite soil moisture to improve streamflow prediction in
data-scarce catchments. Submitted to Water Resources Research.
2. Alvarez-Garreton C., Ryu D., Western A.W., Su, C.-H., Crow W.T., Robertson D.E.
and Leahy C. Improving operational flood ensemble prediction by the assimilation
of satellite soil moisture: comparison between lumped and semi-distributed schemes.
Hydrol. Earth Syst. Sci., 19, 1659-1676, doi:10.5194/hess-19-1659-2015, 2015.
3. Alvarez-Garreton C., Ryu D., Western A.W., Crow W.T. and Robertson D.E. The
impacts of assimilating satellite soil moisture into a rainfall-runoff model in a semiarid catchment. Journal of Hydrology, doi:10.1016/j.jhydrol.2014.07.041, 2014.
Conference papers refereed
1. Alvarez-Garreton C., Ryu D., Western A.W., Crow, W.T., and Robertson D.E.:
Impact of observation error structure on satellite soil moisture assimilation into a
rainfall-runoff model, in: MODSIM2013, 20th International Congress on Modelling
and Simulation. Modelling and Simulation Society of Australia and New Zealand,
edited by Piantadosi, J., Anderssen, R., and Boland, J., pp. 3071-3077, 2013.
Conference presentations
1. Alvarez-Garreton C., Ryu D., Western A.W., Crow, W.T., Su, C.-H., and Robertson
D.E., 2014. Improving Flood Prediction By the Assimilation of Satellite Soil Mois115
ture in Poorly Monitored Catchments. 47th American Geophysical Union (AGU).
HM13M-04, 15-19 December, San Francisco, US.
2. Ryu, D., Alvarez-Garreton C., 2014. Conjunctive Use of Satellite Precipitation and
Soil Moisture for Hydrologic Predictions in Ungauged Regions. Smart Water Grid
International Conference, Incheon, Republic of Korea.
3. Alvarez-Garreton C., Ryu D., Western A.W., Su, C.-H., Crow, W.T., and Robertson D.E., 2014. Improving Flood Prediction By the Assimilation of Satellite Soil
Moisture in Poorly Monitored Catchments. Asia-Oceania Top University League on
Engineering(AOTULE) Conference. 26-28 November, Melbourne, Australia.
4. Alvarez-Garreton C., Ryu D., Western A.W., Crow, W.T., Robertson D.E. and
Leahy C., 2013. Effects of forcing uncertainties in the improvement skills of assimilating satellite soil moisture retrievals into flood forecasting models. International
Geoscience and remote sensing symposium (IGARSS). WE2.T03.4.
116
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