Dynamical aspects of extremes in climate and ecosystems

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Dynamical aspects of extremes in climate and ecosystems: Assessing trends, spatial coherence and mutual interdependence
Reik V. Donner
with Janna Wagner, Viola Mettin, Susana Barbosa, Eva Hauber, Marc Wiedermann, Jonathan F. Donges, Niklas Boers and others
Tomsk, 30 June 2014
Young Investigators Group CoSy‐CC2 @ PIK
Complex systems methods for understanding causes and consequences of past, present and future climate change
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New methods for studying recent climate and paleoclimate data
Regime shifts / dynamical transitions in climate history
Spatio‐temporal pattern of climate and paleoclimate variability
Societal / cultural / ecological consequences of climate change
Reik V. Donner, RD IV Transdisciplinary Concepts & Methods
reik.donner@pik‐potsdam.de
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Agenda
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Extremes – why are they so important?
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Quantile trends as proxies for time‐dependent extremes
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Spatial patterns of extremes: Complex network analyses
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Do climate extremes determine extreme ecosystem responses?
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Take home messages
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1. Extremes – why are they so important?
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Relevance of extreme events
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Relevance of extreme events
Human societies and ecosystems are commonly adjusted to certain mean conditions, but exhibit tolerance with respect to certain ranges of values of relevant characteristics (e.g., precipitation – sewage systems, river runoffs – dams, etc.)
When such ranges are exceeded, negative response often sets in rather quickly and with a strong impact regarding the system’s functionality (e.g., vegetation depth, faunal migration, economic losses, breakdown of infrastructures,…).
Consequence: need better knowledge on future frequencies of extremes, their spatial and temporal organization and consequences for interconnected systems.
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2. Quantile trends as proxies for time‐dependent extremes
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Quantile regression
Traditional trend analysis: trends in the mean
 What about the rest of the distribution, especially the tails?
 Classical approach: time‐dependent extreme value statistics – data‐
demanding!
Useful tool: quantile regression analysis
• Estimates a (parametric or nonparametric) model for the conditional quantile functions of the data distribution as a function of time
• Generalization of ordinary least‐squares estimator replacing squared difference by asymmetric loss function
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Example: Monthly tide gauge data from the Baltic Sea
Result: higher quantiles rise faster, lower ones slower than the mean (in entire Baltic Sea)
(Barbosa, 2008)
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Results 1: linear quantile trends (10%/50%/90%) corrected for GIA
(Donner et al., 2012)
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Results 2: linear quantile trends (10%/50%/90%) relative to trend in mean
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Results 3: average nonparametric quantile trends corrected for GIA
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Results 4: average nonparametric quantile trends relative to mean
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Nonparametric quantile trends show long‐term variability
 Are quantile trends changing with time?
Question: Is there any systematic acceleration/deceleration of trends?
 Statistical tests (t‐test and Mann‐Kendall test for (in)/dependent data)
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Intermediate summary:
• Heterogeneous long‐term trends in the distribution of Baltic sea‐level: broadening, potentially stronger extremes
• Trends in sea‐level quantiles are not constant, but vary with time
• Consistent spatial pattern of long‐term quantile trends
Questions:
• Monthly variability does not cover time scales of interest (typically 1 day or below): extremes are contained in short‐term variability!
• Are trends in daily extremes consistent with those in monthly extremes? (Does temporal aggregation matter?)
• Are the results comparable to those of time‐dependent extreme value
theory?
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Example: Daily tide gauge data from the Baltic Sea
(Ribeiro et al., 2014)
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Example: Daily tide gauge data from the Baltic Sea
(Ribeiro et al., 2014)
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Examples for other climate variables
Daily temperatures (max/min/mean) – station data
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Daily temperatures (max/min/mean) – station data
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Daily mean temperatures DJF – ERA‐Interim
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More results (not shown, mostly unpublished):
• Daily precipitation values for Germany
• Daily runoff values for Germany (SWIM model)
• Daily mean/maximum/minimum temperatures for NCEP/NCAR, ERA‐
Interim, ERA‐40 and e‐Obs (MSc thesis Viola Mettin)
Planned:
• Effect of temporal aggregation on quantile trends for precipitation
• …
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3. Spatial patterns of extremes: Complex network analyses
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The starting point…
(Bull. Amer. Meteor. Soc., 2006)
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Networks are everywhere!
Complex networks appear in various scientific disciplines, including transportation sciences, biology, sociology, information sciences, telecommunication, engineering, economics, etc.
 Solid theory of statistical evaluation and modeling
 Efficient numerical algorithms and multiple complementary measures
 Knowledge of interrelations between structure and dynamics
 Investigate climate problems by making use of complex network approaches as an exploratory tool for data analysis and modeling
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Network theory: General terms
A graph (network) is described by
• a set of nodes (vertices) V
• a set of links (edges) E between pairs of vertices
• eventually a set of weights W associated with the nodes and/or links
Basic mathematical structure: adjacency matrix A
Aij=1  nodes i and j are connected by a link
Aij=0  nodes i and j are not connected by a direct link
 binary matrix containing connectivity information of the graph
 undirected graph: A symmetric
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Network theory: General terms
Degree centrality: number of neighbors of a vertex
Local clustering coefficient: relative fraction of neighbors of a vertex that are mutual neighbors of each other
Global clustering coefficient: mean value of the local clustering coefficient taken over all vertices
Transitivity: relative fraction of 3‐loops in the network
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Climate networks: Basic algorithm
Starting point: Spatially distributed climate time series (e.g. reanalysis data)
 Consider spatial locations as “nodes” (vertices) of a network
 Compute mutual correlations between time series = “weights” of links (edges) in a weighted network representation based on statistical associations (functional network!)
 Remove all links with “weak” correlations = unweighted network representation
 Apply measures from complex network theory for studying the topological properties of the resulting graphs and their evolution
Refinement: replace correlations by other more sophisticated interdependency measures (mutual information, event synchronization,…)
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Evolving global surface air temperature network
Climate network analysis for running windows in time: evolving climate networks
Global network characteristics show distinct temporal variability profile strongly related to ENSO
(Radebach et al., Phys. Rev. E, 2013)
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Evolving global surface air temperature network
Interesting observation: peaks in global network characteristics do not coincide 1:1 with El Nino episodes
Reason: peaks indicate the formation of “localized structures”
of high connectivity, which may also arise in some La Nina periods as well as after strong volcanic eruptions (common regional cooling trend – increase of correlations)
In turn, not all El Ninos are accompanied by peaks: functional discrimination between classical and Modoki El Ninos!
Transitivity, NINO3.4, strat. opt. depth
(Radebach et al., Phys. Rev. E, 2013)
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Networks of extreme moisture divergence
Investigation of spatio‐temporal structure of South American moisture divergence (E‐P) from MERRA
Simplified view:
• Positive extrema: strong evapo‐transpiration
• Negative extrema: heavy rainfall
(Boers et al., Clim. Dyn., in revision)
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Special interest: spatio‐temporal organization of extremes (i.e., moisture divergence above/below certain thresholds)
 Use event synchronization as similarity measure: normalized fraction of temporally close extremes observed at different grid points
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Mean daily moisture divergence
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10% quantile of daily moisture divergence (extreme precipitation)
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90% quantile of daily moisture divergence (extreme evapotranspiration)
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Local clustering coefficient for networks of extreme evapotranspiration
events
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Average size of connected components of contemporaneous evapotranspiration extremes
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Differences between classical (1) and Modoki (2) El Ninos
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Regional climate networks
Spatial backbone of Indian summer monsoon revealed by event synchronization of heavy rainfall (Malik et al., Climate Dyn., 2012)
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4. Do climate extremes determine extreme ecosystem responses?
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Coincidence analysis
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Related concept with rigorous statistical framework
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Uncorrelated events: analytical expressions for the probability distribution of number of co‐occurrences (Donges, Donner, et al., PNAS, 2011)
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Correlated events: analytics approximately valid for short‐term correlations – work in progress
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Coincidence analysis
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Uncorrelated events: analytics vs. numerics (N=10 reference events)
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Definition of events
Classical definition: fixed thresholds – only valid for stationary signals with constant background (e.g., no seasonal cycle)
Possible solution: Determine time‐varying threshold according to a given quantile conditioned to the phase of the seasonal cycle
1. Filtering / decomposition (SSA, wavelets, EMD,…) – corrects only for non‐
stationarity in mean, not in higher‐order moments
2. Quantile regression – determines time‐varying quantile threshold for event detection (accounts for trends and cycles)
3. Double‐kernel approach in time and magnitude (MSc thesis Eva Hauber)
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Definition of events
• Multivariate extremes (e.g. heat and water stress to plants)?
 alternative definition of events (e.g. based on copula concept) – work in progress
(Schölzel &
Friedrichs, NPG,
2008)
 more than just two types of extremes (cluster analysis)?!
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Application: Yearly extreme tree ring widths
 Tree ring width as a proxy for annual net primary production (Rammig et al. 2014): Do bad years correspond to extreme climatic conditions?
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Next steps
 Extension of this approach to much shorter time‐scales (PhD project Jonatan Siegmund):
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Remote sensing data (faPAR, NDVI)
Eddy covariance measurements (FLUXNET)
Ecosystem models (validation)
(sub)seasonally resolved tree ring data?
 Spatially resolved coincidence analysis between two variables: (coupled) complex network approach?!
 Necessary modifications: time lags, causality,…
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5. Take home messages
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Take home messages
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Statistical analysis of extremes provides new insights into their potential impacts on human societies and ecosystems
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Trend analysis for extremes: quantile regression methods
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Spatial patterns of extremes: event synchronization and complex networks
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Statistical relationships between extremes in more than one variable: coincidence analysis
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Many open points currently being addressed: temporal aggregation
effect, time‐dependent baseline states, multivariate extremes,…
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Further applications/collaborations are welcome!
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Dynamical aspects of extremes in climate and ecosystems

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