Quantifying uncertainties in the global mass balance of mercury

GLOBAL BIOGEOCHEMICAL CYCLES, VOL. 25, GB4012, doi:10.1029/2011GB004068, 2011
Quantifying uncertainties in the global mass balance of mercury
Asif Qureshi,1 Matthew MacLeod,2 and Konrad Hungerbühler1
Received 11 March 2011; revised 25 August 2011; accepted 1 October 2011; published 13 December 2011.
[1] We quantify uncertainties in the global mass balance of mercury and identify research
priorities to reduce these uncertainties. This is accomplished by developing a new spatially
resolved global multimedia model (WorM3) that quantitatively describes the fate of
mercury at a process level, and conducting an uncertainty analysis on its unit-world variant
which computes similar global estimates. In our modeling approach, all mass transfer
processes and reactions in ocean water, soil and vegetation, are represented as pseudo-first
order; reactions in air are represented using the ratios of observed concentrations of
mercury species. We use Monte Carlo analysis to estimate uncertainties in the unit-world
modeled global mass balance of mercury and quantitatively identify the input parameters
which contribute most to these uncertainties. A key finding is that uncertainties in input
parameters that describe the rates of reduction and oxidation reactions in surface ocean
contribute more than uncertainties in anthropogenic emissions to the total uncertainties in
atmospheric concentration and depositional fluxes of mercury. More research should
therefore be targeted toward understanding of these oceanic processes.
Citation: Qureshi, A., M. MacLeod, and K. Hungerbühler (2011), Quantifying uncertainties in the global mass balance of
mercury, Global Biogeochem. Cycles, 25, GB4012, doi:10.1029/2011GB004068.
1. Introduction
[2] Mercury is a pollutant of global concern because of its
potential to bioaccumulate in food webs and cause adverse
health effects. In the environment, mercury exists as three
different species groups with distinct properties, namely
elemental mercury [Hg(0)], divalent mercury [Hg(II)] and
methylated mercury (MeHg). Once emitted to the environment, mercury cycles continuously and reversibly between
the atmosphere, surface ocean, sub-surface ocean, soil and
vegetation. Mercury in circulation in these five environmental compartments can therefore be viewed as the “active
pool” of mercury.
[3] On a global scale, it is desirable to study this active
pool through global-scale modeling. However, most globalscale models currently in use (CTM-Hg: Seigneur et al.
[2001]; GRAHM (solved online): Dastoor and Larocque
[2004]; and ECHMERIT (solved online): Jung et al. [2009])
are primarily atmospheric chemical transport models (CTMs)
and lack a complete multimedia perspective. Only GEOSChem, another CTM for mercury, [Smith-Downey et al., 2010;
Soerensen et al., 2010; Strode et al., 2007] has been further
developed to include oceans and terrestrial components.
[4] The basis of all above models is general circulation
models (GCMs), which are useful for several applications
[e.g., Bey et al., 2001; Wild et al., 1995; Xiao et al., 2008].
However, a large number of inputs are required to support
1
Safety and Environmental Technology Group, ETH Zürich, Zürich,
Switzerland.
2
Department of Applied Environmental Science, Stockholm University,
Stockholm, Sweden.
Copyright 2011 by the American Geophysical Union.
0886-6236/11/2011GB004068
these applications and the heavily parameterized atmosphere, which comes at a big computational cost. None of
the global mercury models listed above have provided
uncertainty estimates on their estimated global mass balances for mercury, even though it is widely acknowledged
that there are important uncertainties in input parameters
and process descriptions. Model sensitivities to a few input
parameters have been estimated [Lamborg et al., 2002; Lin
et al., 2006, 2007; Smith-Downey et al., 2010], and uncertainties in the inventories and fluxes associated with the
ocean compartment have been reported based on an empirical approach for describing oceanic processes [Sunderland
and Mason, 2007]. These are important first steps, however, they are not sufficient to determine uncertainties in the
estimated global mass balances which are a function of both
sensitivity to, and the uncertainty and variability in, input
parameters [MacLeod et al., 2002]. Therefore, research
directions and model improvements to reduce uncertainties
should not be based on sensitivity results alone, but rather
on uncertainty analysis of the global mass balance of
mercury.
[5] In contrast to CTMs, uncertainty analysis of multimedia contaminant and fate models has been repeatedly
demonstrated [Bennett et al., 1999; Liu et al., 1999; Luo and
Yang, 2007; MacLeod et al., 2010; Matthies et al., 2004;
Moskowitz et al., 1996]. Currently, multimedia mass balance
models are widely used for estimating the global fate and
transport of organic chemicals [e.g., Armitage et al., 2009;
Lamon et al., 2009; MacLeod et al., 2005a; Schenker et al.,
2007, 2008]. While CTMs explicitly model air and water
flows in the environment at highly resolved temporal and
spatial scales and implicitly calculate the mass balance
of substance(s) being modeled, multimedia mass balance
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models use spatial and/or temporal averages of environmental flows estimated from GCMs and explicitly model the
mass balance of the substance [MacLeod et al., 2010]. The
multimedia approach has been successfully evaluated for
modeling regional mass balances of mercury and conducting
regional uncertainty analysis [MacLeod et al., 2005b;
Qureshi et al., 2009].
[6] In this work, we seek to estimate uncertainties in the
global mass balance of mercury using a multimedia
approach. We present a spatially resolved multimedia model
parameterized to explicitly describe mercury cycling in the
global active pool (the World Multimedia Mercury Model,
WorM3, WorM-cube). We model elemental and divalent
mercury, Hg(0) and Hg(II), species that are important
from a mass flux perspective. We simplify the modeling
of mercury species in the atmosphere by using observed
average ratios of concentrations between Hg(0) and Hg(II)
species to empirically describe atmospheric mercury reactions [MacLeod et al., 2005b; Qureshi et al., 2009; Toose
and Mackay, 2004]; reactions in other compartments and
all mass transfer processes are represented by means of
pseudo-first order rate constants and mass transfer velocities. We then conduct a Monte Carlo uncertainty analysis on
a unit-world variant of WorM3 that has high computational
efficiency (25 000 Monte Carlo simulations in <10 h on
a modern desktop computer). We use results from this
uncertainty analysis to (i) quantify uncertainties in the
global mercury mass balance, (ii) identify the sources of
these uncertainties, and (iii) identify critical knowledge gaps
and recommend research priorities that will reduce output
uncertainties (Figure 1).
2. Methods
2.1. Model Environment
[7] WorM3 has a spatial resolution of 15° ! 15° (see
Figure S1 in Text S2 of the auxiliary material), like a contemporary model used to evaluate the global fate and transport of organic chemicals (BETR-Global) [MacLeod et al.,
2005a, 2011].1
[8] Each WorM3 grid cell consists of five environmental
compartments: air, soil, vegetation, surface ocean and subsurface ocean (Figure 2; Figure S2 in Text S2). Inter-grid
flow is only modeled in the air compartment; horizontal
transport of mercury in oceans is not modeled since the
timescale for air-water exchange of mercury is much faster
than the typical timescale for transport of ocean water into
or out of a grid cell [e.g., Strode et al., 2007]. Model input
parameter values and the uncertainties associated with these
parameters are presented in Table 1. We have defined
uncertainty values to represent both uncertainty and variability in input parameters as well as to subjectively include
the uncertainties that may exist in the model’s description of
the considered processes.
[9] In our work, uncertainties are assumed to be lognormally distributed [Grönholm and Annila, 2007; Limpert
et al., 2001] and represented as dispersion factors (DFs).
This means that 95% of possible values lie in the range of
1
Auxiliary materials are available in the HTML. doi:10.1029/
2011GB00468.
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median divided by the DF to median multiplied by the DF.
The relation between output and input DFs for a sample
case is discussed in the auxiliary material (see section S1 in
Text S1).
2.2. Species Definitions and Interconversions
2.2.1. Air
[10] Four mercury species are modeled in the air compartment: elemental mercury, Hg(0), divalent mercury, Hg
(II)(g) (assumed to be the same as reactive gaseous mercury,
RGM), aqueous divalent mercury, Hg(II)(aq), and particulate mercury, Hg-p (see Figure S2 in Text S2). Of these,
Hg(0), and Hg-p, are described by the mass balance equations. The other two species are represented as constant
fractions of [Hg(0)], by means of concentration ratios
(CRs). These CR values are ratios of observed concentrations of Hg(0) and Hg(II)(g), or Hg(II)(aq) from field
studies. They implicitly describe the net rate of interconversion between mercury species [MacLeod et al., 2005b;
Qureshi et al., 2009; Toose and Mackay, 2004]. Their use is
valid if (i) the gross rates of interconversions between the
mercury species are faster than the rates of processes
transporting these species into or out of the air compartment
[e.g., Selin et al., 2007, Figure 1] or (ii) the conditions in the
air compartment are near steady state. Toose and Mackay
[2004] have further suggested that CRs may be used to
approximate reactions when the above two conditions are
not completely met. The use of concentration ratios eliminates the need for specifying rate constants for oxidation
or reduction of individual mercury compounds in the air
compartment. Instead, the net rate of interconversion is
deducible from the model output.
[11] Each WorM3 grid-cell is assigned a Hg(0):Hg(II)(g)
CR value in air either (i) based on observations of Hg(0) and
RGM made at one or more locations in that grid-cell, or (ii)
if no observations are available, chosen based on observations at locations with similar emissions, or (iii) assigned a
default value of 100, which is the median value used in our
uncertainty analysis on the unit-world variant of WorM3,
Unit-WorM3 (see section S2 in Text S1).
[12] Concentrations of Hg(II)(aq) are defined as a constant
fraction of [Hg(II)(g)], and [Hg(0)] as a result, [Hg(II)(g)]:
[Hg(II)(aq)] ≈ 1:100000 (Mercury deposition network,
http://nadp.sws.uiuc.edu/mdn/maps/, 2 Oct 2009; concentration of Hg(0) in air is of order ng m–3 and concentration
of Hg in rainwater is ng L–1, or mg m–3, i.e., 1000 times
greater than Hg(0)(g)). Further information on species definitions is provided in the auxiliary material (section S3 in
Text S1).
[13] We note that mercury depletion events (MDEs) occur
during summers in polar regions when Hg(0) is oxidized
rapidly to Hg(II)(g). This leads to a transient situation with a
lower concentration ratio of Hg(0):Hg(II)(g), which we
estimate using observations (section S2 and Table S1 in Text
S1). We assume that MDEs take place in all latitudes north
of 60°N in the Arctic region and all latitudes south of 60°S
in the Antarctic region. In WorM3, Arctic depletion events
are set to occur during model months 3–5 and Antarctic
depletion events during model months 10–12, in each of the
last ten years of industrial simulations (more information
about model simulation times is provided in section 2.4).
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Figure 1. Procedure adopted to determine the uncertainties in the global mass balance of mercury. In
Task 1, a spatially resolved multimedia model (WorM3) is developed. Concentrations estimated by the
model are then evaluated with data from the field. Comparison is also made with results from other spatially resolved global models. Following this, in Task 2, a unit-world model (Unit-WorM3) with an identical model structure, process descriptions and global inputs to WorM3 is developed. Global results from
this model are then evaluated with global results from the spatially resolved WorM3. Global results from
Unit-WorM3 are also compared with global results from other spatially resolved and box models. Following this, in Task 3, a Monte Carlo analysis is performed on the Unit-WorM3 to estimate the uncertainties in
the global mass balance of mercury and to identify the key processes. DF represents both uncertainty and
variability in inputs, as well as the uncertainty in process descriptions (see section 2.1). For example, the
redox reactions in sub-surface oceans are assigned a relatively large DF value, of 12–18, since information
on redox kinetics of mercury in sub-surface oceans is highly uncertain. Unit-WorM3 is essentially the
building block of WorM3. The spatially resolved WorM3 is constructed by interlinking many smaller
unit-worlds (regions).
Figure 2. Model environment of a single WorM3 grid-cell.
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Table 1. Model Input Parameters for the Spatially Resolved WorM3 and Its Unit-World Variant, Unit-WorM3a
Median Values Used
in the Spatially Resolved
and Unit-World Model
Parameter
Dispersion Factor
(DF) for the
Unit-World Model
References/ Remarks
Environmental Definitions
Total Surface Area (km2)
% covered by water
% soil covered by vegetation
(short grasses)
Leaf area index
Stomatal density (number of
stomata per mm2 of leaves)
Area of stomatal pores (mm2)
Surface Area Related
Variable for WorM3; 510 ! 106
1.01
for Unit-WorM3
3
1.01
Variable for WorM ; 71%
for Unit-WorM3
Variable for WorM3; 52% for
1.1
Unit-WorM3
1
4
150
3
100
Air
Mixing depth of surface ocean
Mixing depth of the sub-surface
ocean
Mixing depth of soil
Vegetation
6000
100
400
Aerosols in air
Suspended solids in surface
ocean
Suspended solids in
sub-surface ocean
Air in soil
Water in soil
Water in vegetation
1 ! 10"11
2 ! 10"6
5
Height/Depth (m)
1.05
3
3
0.2
0.2
1.5
4
Volume Fractions
3
10
[MacLeod et al., 2005a] DF: generic value
[MacLeod et al., 2005a] DF: generic value
[MacLeod et al., 2005a] DF: generic value
Generic value DF: [MacLeod et al., 2005a]
[Franks and Beerling, 2009; Poole et al., 1996]
DF: [Franks and Beerling, 2009]
[Franks and Beerling, 2009; Peschel et al., 2003]
DF: [Franks and Beerling, 2009]
[Lamborg et al., 2002; MacLeod et al., 2005a]
[Kara et al., 2003]
[Sunderland et al., 2009]
[MacLeod et al., 2005a]
Generic value
2 ! 10"6
10
[MacLeod, Riley and McKone, 2005a]
BETR-global [MacLeod et al., 2005b]
DF: Estimated
Same as surface oceans
0.2
0.3
0.2
1.5
1.5
1.1
[MacLeod et al., 2005b]
[MacLeod et al., 2005b]
[MacLeod et al., 2005b]
Mass Transfer Related Parameters
Wind velocity at 10 m (m s–1)
Schmidt number for HgCl2
(Hg(II)(g)) in air
Schmidt number for Hg(0) in air
Schmidt number for Hg(0) in water
Schmidt number for Hg-p in air
Prandtl number for air
Water temperature (K)
Relative humidity
Global average radiation (W m–2)
Ground resistance to Hg(0)
exchange (s m–1)
Ground resistance to Hg(II)(g)
deposition (s m–1)
Cuticle resistance to Hg(0)
exchange (s m–1)
Rain rate (m s–1)
Rain Scavenging ratio
Ocean mixing velocity (m s–1)
Particle sinking velocity in oceansc
(m s–1)
Soil water runoff velocity (m s–1)
Soil solids runoff velocity (m s–1)
Soil-vegetation mass transfer
Uptake of water by vegetation
(m s–1)
Air-Surface (Surface Ocean, Soil and Vegetation) Mass Transfer
2
http://www.ceoe.udel.edu/windpower/ResourceMap/
index-world.html, 26 November 2010
2.63
1.01
DF: generic value
5
1.06
625
3.2 ! 106
0.72
282
50
500
21400
1.2
1.01
1.01
1.01
1.015
1.5
1.5
3
DF: generic value
DF: generic value
DF: generic value
DF: generic value
Range: 5–13°C
DF: generic value
DF: generic value
[Marsik et al., 2007] DF: generic value
Estimated within the
model code
33400
3
DF: generic value
3
[Marsik et al., 2007] DF: generic value
6 ! 10"9
100000
3
10
0.06–0.56 m y–1
[MacLeod et al., 2005a]
Surface Ocean-Sub-Surface Ocean Mass Transferb
3.2 ! 10"8
3
[Wegmann et al., 2009] DF: generic value
6.1 ! 10"12
4
[MacLeod et al., 2005a]
1.08 ! 10"8
6.39 ! 10"12
Soil-Surface Ocean Mass Transfer
3
3
2.22 ! 10"7
3
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[Wegmann et al., 2009] DF: [MacLeod et al., 2005a]
[Wegmann et al., 2009] DF: [MacLeod et al., 2005a]
[MacLeod et al., 2005a]
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Table 1. (continued)
Parameter
Median Values Used
in the Spatially Resolved
and Unit-World Model
Dispersion Factor
(DF) for the
Unit-World Model
c
Rate Constants (s
Rate constant for oxidation of Hg(0)
to Hgnr(II) in surface ocean
Rate constant for conversion of
Hgnr(II) to Hgr(II) in surface ocean
Rate constant for reduction of Hgr(II)
to Hg(0) in surface ocean
Rate constant for oxidation of Hg(0)
to Hgnr(II) in sub-surface ocean
Rate constant for conversion of
Hgnr(II) to Hgr(II) in sub-surface
ocean
Rate constant for reduction of
Hgr(II) to Hg(0) in sub-surface
ocean
– 1
References/ Remarks
)
Surface Ocean
Variable for WorM3;
4.9 ! 10"6
Unit-WorM3
2.8 ! 10"5
Variable for WorM3;
1.3 ! 10"7 for
Unit-WorM3
4
[Qureshi et al., 2010] DF: [Qureshi et al., 2011]
4
[Qureshi et al., 2010] DF: [Qureshi et al., 2011]
6
[Qureshi et al., 2010], DF: [Qureshi et al., 2011]
Sub-Surface Ocean
12
Variable for WorM3;
4.9 ! 10"7 for
Unit-WorM3
2.8 ! 10"6
12
Variable for WorM3;
1.3 ! 10"8 for
Unit-WorM3
18
Median value: assumed to be one-tenth of that
of surface ocean.
We note that little is known about redox reactions
in sub-surface oceans. So we have chosen a
relatively higher DF for these processes,
three times as surface ocean.
Median value: assumed to be one-tenth of that
of surface ocean.
We note that little is known about redox reactions
in sub-surface oceans. So we have chosen a
relatively higher DF for these processes,
three times as surface ocean.
Median value: assumed to be one-tenth of that
of surface ocean.
We note that little is known about redox reactions
in sub-surface oceans. So we have chosen a
relatively higher DF for these processes,
three times as surface ocean.
Rate constant for reduction of
Hg(II) to Hg(0) in soil solids
Rate constant for reduction of
Hg(II) to Hg(0) in soil water
Rate constant for oxidation of
Hg(0) to Hg(II) in soil solids
Rate constant for oxidation of
Hg(0) to Hg(II) in soil water
1 ! 10"10
Rate constant for litterfall, from
vegetation
3.7 ! 10"8
Soil
10
"10
10
1 ! 10"12
10
"12
10
1 ! 10
1 ! 10
Median value: see main text, DF: generic
to span two orders of magnitude
Median value: see main text, DF: generic
to span two orders of magnitude
Median value: see main text, DF: generic
to span two orders of magnitude
Median value: see main text, DF: generic
to span two orders of magnitude
value,
value,
value,
value,
Vegetation
1.1
[MacLeod et al., 2005a]
Concentration Ratios in Air
Hg(0):Hg(II)(g)
Hg(II)(g): Hg(II)(aq)
3
Variable for WorM ;
100 for Unit-WorM3
100000
4
See section S2 and Table S1 in Text S1.
3
Median value: see main text; DF: generic value
–1
Emissions (t y )
Hg(0) + Hg(II)
Hg-p
2028
203
1.6
1.6
[Pacyna et al., 2006] DF: [Lindberg et al., 2007]
[Pacyna et al., 2006] DF: [Lindberg et al., 2007]
Partition Coefficients (kg water/ kg particles)
Hg(0)
Hgnr(II)
Hgr(II)
Surface Ocean Suspended Solids-Water Partition Coefficients
3
[MacLeod et al., 2005b]
3 ! 104
8 ! 104
20
[Allison and Allison, 2005; Babiarz et al., 2001;
Baeyens et al., 1997; Balls, 1989; Ferrara et al.,
1986; MacLeod et al., 2005b; Soerensen et al.,
2010; Stordal et al., 1996]
Most of the values lay in the range 104 and 106.
They represent a variety of water bodies including
freshwater lakes and streams, bay and estuarine
water, seawater and open ocean water.
5.3 ! 104
20
DF same as for Hgnr(II).
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Table 1. (continued)
Parameter
Median Values Used
in the Spatially Resolved
and Unit-World Model
Dispersion Factor
(DF) for the
Unit-World Model
References/ Remarks
Hg(0)
Hgnr(II)
Hgr(II)
Sub-Surface Ocean Suspended Solids-Water Partition Coefficients
3
Same as surface oceans.
3 ! 104
8 ! 104
20
Same as surface oceans.
4
5.3 ! 10
20
Same as surface oceans.
Hg(0)
Hg(II)
1 ! 105
6 ! 104
Hg(0)
Hg(II)
1 ! 101
1 ! 102
Soil-Water Partition Coefficients
10
10
[MacLeod et al., 2005b] DF: generic value
[Lyon et al., 1997; MacLeod et al., 2005b;
Selin et al., 2008] Literature range:
2.4 ! 103 – 6.5 ! 105
Vegetation Flesh-Water Partition Coefficients
10
[MacLeod et al., 2005b]
10
[MacLeod et al., 2005b]
a
Dispersion factors are used in the uncertainty analysis of Unit-WorM3 and represent global uncertainties. Uncertainties in all parameters listed in this
table are considered in the Monte Carlo analysis.
b
See Figure S2 in Text S2 for an illustration of how various mass transfer and reaction processes are represented in the model.
c
Bulk transport velocity can be calculated by dividing 6.1 ! 10"12 m s–1 by the volume fraction of suspended particles, 2 ! 10"6, equal to 3.05 !
10"6 m s"1, or 0.26 m d–1. When 95% dispersion ranges in both parameters are considered, the resulting bulk transport velocity varies approximately
between 0.007 m d–1 to 10.5 m d–1.
We evaluate our representation of depletion events by
comparing the area under the Hg(0) versus time curve
modeled for the last year of WorM3 simulation with the area
under a similar curve obtained by Cole and Steffen [2010]
from a 12-year observation summary. Comparison is made
for both depletion and non-depletion months.
2.2.2. Surface Ocean and Sub-surface Ocean
[14] Three mercury species groups are modeled in surface
and sub-surface ocean compartments: elemental mercury,
Hg(0), non-reducible divalent mercury, Hgnr(II), and reducible divalent mercury, Hgr(II) [Qureshi et al., 2010]. Partitioning between aqueous and particulate fractions of these
species is estimated using equilibrium partition coefficients
(see Table 1 for values and uncertainties and section S3 in
Text S1 for derivations).
[15] Mercury redox reactions in oceans (Table 1) are
estimated as 24-h average pseudo-first order rate constants
(see section S4 in Text S1). Resulting rate constant values
are in the range 7 ! 10"8 – 2.6 ! 10"7 (order 10"7 s–1) for
reduction, which lie in the lower range of values used
recently by Soerensen et al. [2010], 10"5 s–1 to 10"7 s–1. Our
rate constants for oxidation, 2.7 ! 10"6 – 9.8 ! 10"6 s–1, are
of a similar magnitude (order 10"6 s–1) to Soerensen et al.
[2010].
[16] No information was available on the redox rate
constants in sub-surface oceans. Their values in WorM3 are
arbitrarily assumed to be one-tenth of the respective values
in surface oceans. Dispersion factors are assumed to be three
times those used for surface oceans (Table 1).
[17] When Hg(II) (gas and aqueous) and Hg-p species
deposit from air to the surface ocean, they enter the Hgnr(II)
inventory of the surface ocean.
2.2.3. Soil and Vegetation
[18] Two mercury species groups are modeled in soil and
vegetation: Hg(0) and Hg(II). Aqueous and solids fractions
of the bulk mercury species are determined using respective partition coefficients and volume fractions (Table 1;
section S3 in Text S1). The pseudo-first order rate constant
for Hg(II) reduction was assigned a low value (10"10 s–1) in
both aqueous and solid phases (Table 1). This value is
similar to that used by Scholtz et al. [2003], 8 ! 10"11 s–1.
The rate constant for oxidation of Hg(0) was assumed to be
two orders of magnitude lower than the reduction rate
constant (10"12 s–1). No reduction or oxidation reactions are
assumed in the vegetation compartment.
[19] When the Hg(II) species run-off from soil to surface
ocean (Figure 2), they enter the Hgnr(II) inventory of surface
ocean.
2.3. Intermedia Transport Processes
[20] A resistance-to-mass transfer approach (section S5 in
Text S1) is used to determine the gaseous dry exchange
velocities for all mercury species. Mass transfer velocities are
then calculated as the inverse of the estimated resistances.
2.4. Other Inputs and Model Runs
[21] The model is driven with estimated anthropogenic
mercury emissions for the year 2000 [Pacyna et al., 2006;
http://www.amap.no/Resources/HgEmissions/HgInventoryData.
html, 5 March 2011]. Inputs describing the model environment, species interconversions, and species multimedia
fluxes are already discussed above. After the input parameters are set, mass balance differential equations (section S6
in Text S1) are solved dynamically in MATLAB using the
ode15s solver. All model runs were made on a desktop
computer.
[22] The model is spun up by simulating 9000 years of
pre-industrial conditions. We choose total pre-industrial
emissions as one-third of the current anthropogenic emissions [Sunderland and Mason, 2007]. The global mass balance at the end of 9000 years was satisfied to within
<0.002% in both WorM3 and its unit-world variant, UnitWorM3, (see Figure S5 in Text S2) for the base run using
median values in Table 1. The final concentrations from
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the pre-industrial simulations are then used as initial concentrations for industrial simulations. After simulating 40
years of industrial emissions, mercury depletion events are
triggered for the next ten years (only applicable to WorM3;
MDEs are not considered in Unit-WorM3 since it is a single
region, unit-world model). Model outputs obtained after 50
years of industrial simulations are compared with observations. The outputs are the environmental concentrations of
mercury and a complete mass balance accounting of mercury species in each of the individual 288 regions of
WorM3 and in the world as a whole.
[23] MDEs are considered only for the last ten years in
order to gain computational efficiency. Inclusion of these
events during this period lowers the modeled atmospheric
concentrations, however this effect is minor compared to
changes possible due to uncertainty in other sensitive input
parameters (see results from our uncertainty analysis in
section 3). Therefore, the inclusion of MDEs for the preindustrial simulation or in the entire industrial simulations
will not appreciably influence the conclusions derived from
the spatially resolved WorM3, or from the Unit-WorM3.
2.5. Results From the Spatially Resolved WorM3
[24] Results from WorM3 are in satisfactory agreement
with observations (see section S7 and Tables S3 and S4 in
Text S1 for a detailed discussion). For evaluating the modeled mercury concentrations in air, we use observations that
were not used for estimation of CR values in section 2.2.1. In
summary, Northern and Southern Hemispheric concentrations in air are well reproduced, as are the depositional
fluxes for North America and MDEs. Concentrations in
oceans are more variable, but WorM3 modeled concentrations in air and surface oceans are comparable to those
obtained from CTMs for mercury (see Tables S3 and S4 in
Text S1).
2.6. Uncertainty Analysis of the Global Mass Balance
for Mercury
[25] The unit-world variant of WorM3 (Unit-WorM3) was
used for uncertainty analysis of the global mass budget of
mercury. Unit-WorM3 has identical model structure and
global inputs (see Table 1 for median values and DFs; all
parameters listed in the table were tested in the Monte Carlo
analysis) as the spatially resolved WorM3. The DFs were
selected to reflect a combination of uncertainty and variability, and the underlying uncertainty about the way each
process is modeled. Thus, for example, we have assigned
higher DFs to processes describing reduction and oxidation
processes in the sub-surface ocean compared to the surface
ocean to reflect additional uncertainty inherent in extrapolating our limited knowledge of these processes to the subsurface ocean where very few empirical observations of
mercury speciation are available.
[26] The results from Unit-WorM3 compare very well with
the combined results of the 288 regions obtained from
WorM3 (Figure 3). The Unit-WorM3 MATLAB code was
linked to Crystal Ball software, and 25,000 Monte Carlo
simulations conducted to estimate median values and associated DFs for outputs that describe the natural global mass
balance of mercury, and to quantitatively identify the influential input parameters whose uncertainties contribute most
to the model output uncertainties. All files required to run
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these simulations can be downloaded at http://www.sustchem.ethz.ch/tools/worm3.
3. Results and Discussions
3.1. Uncertainties in the Global Mass Balance
for Mercury
[27] Results from the Monte Carlo analysis of UnitWorM3 modeled global mass balance, after 50 years of
industrial simulations, and the associated DFs are shown
in Figure 4a. In general, good agreement (Figure 4b) is
observed between results from the Monte Carlo analysis
of Unit-WorM3 and global estimates from spatially resolved
global models. The pre-industrial global mass balance,
associated DFs, and a comparison with global estimates from
spatially resolved global models are shown in Figure S10 in
Text S2.
[28] The global mass balance in Figure 4a illustrates
that the air compartment is characterized by lowest DF
values. We estimate a net conversion of Hg(0) to Hg(II) in
the atmosphere of 11 Mmol y–1 (in WorM3, this value is
#15 Mmol y–1), with a 95% dispersion range of 2 to
62 Mmol y–1. This compares favorably with the net Hg(0) to
Hg(II) conversion of 30 Mmol y–1 estimated using GEOSChem by Selin et al. [2007]. The atmospheric residence time
of Hg(0) in Unit-WorM3 is 7.6 months (WorM3 estimated
residence time is 8.2 months), with a 95% dispersion range
of 2.4 to 24 months. This also agrees well with the range
reported in literature, 8.4–20.4 months [Holmes et al., 2006;
Selin et al., 2007].
3.2. Influential Input Parameters and Implications
to Global Modeling and Fundamental Research
[29] Here, we identify the input parameters whose uncertainties contribute more than 5% to the uncertainty in
selected key model outputs (Figure 5). This information can
serve to guide research priorities to reduce uncertainties in
modeled global mass balances for mercury. Influential input
parameters for forty six other model outputs are presented in
the auxiliary material (Figures S11–S16 in Text S2). In all
model runs we considered uncertainties in all model input
parameters listed in Table 1.
3.2.1. Deposition Fluxes From Air to Surface Ocean
and Terrestrial Surfaces
[30] Uncertainty in the deposition flux of total mercury
from air to surface ocean (Figure 5a) is mainly influenced
by the uncertainties in input parameters that describe the
availability of aqueous reducible mercury in surface ocean
and the rate constants for reduction and oxidation of mercury
species. Uncertainties in wind velocity, which affect the
Hg(0) exchange mass transfer coefficient, and parameters
that describe mercury sources to and sinks out of the model
environment, emissions into air and sinking of mercury out
of the model system, are also important.
[31] Interestingly, uncertainty in the deposition flux of
total mercury to soil and vegetation (Figure 5b) is also
influenced by uncertainties in input parameters that govern
reactions or processes in surface ocean (#47% contribution
to output variance). This indicates a strong contribution of
oceanic processes in the overall uncertainties in mercury
cycling in the global environment. Uncertainties in inputs
that describe the total stomatal pore area available for
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Figure 3. Comparison of global estimates between the unit-world variant of WorM3 (Unit-WorM3) and
WorM3. Figure legend: SO = surface ocean, SSO = sub-surface ocean, veg = vegetation; parameters
written as Soil_/SO_/SSO_Hg(0) to Hgnr(II)/Hgnr(II) to Hgr(II)/Hgr(II) to Hg(0)/ Hg(0) to Hg(II)/ Hg(II)
to Hg(0) represent the rates of interconversions between different species in the respective compartments.
exchange of mercury between air and vegetation, leaf area
index, stomatal area and stomatal density, contribute about
45% to the variance in this output.
3.2.2. Evasion Flux From Surface Ocean to Air
[32] Uncertainty in the evasion flux of mercury from surface ocean to air (Figure 5c) is also governed by uncertainties in input parameters that describe redox and sinking
processes in surface ocean (up to 81% contribution to the
output variance) and mercury exchange with air compartment (17% contribution to output variance).
3.2.3. Concentrations in Air and Surface Ocean
[33] Uncertainty in the concentration of Hg(0) (and as
a consequence total mercury) in air (Figure 5d) is also governed by uncertainties in input parameters describing processes in surface ocean, which determine the amount of
Hg(0) available for evasion. It is also dependent on the
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Figure 4
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Figure 5. (a–g) Dispersion factors (DFs) of selected model outputs and the percent contribution by input
parameters (legends) to the variance in these model outputs. All results were obtained from the Monte
Carlo uncertainty analysis of Unit-WorM3 modeled global mass balance after 50 years of industrial simulations. Diameters of pies are proportional to the DFs. All parameters listed in Table 1 that are not explicitly illustrated in the legend of any particular pie are congregated together in the legend “all other
parameters” of the respective pie, as uncertainties in these input parameters contributed less than 5% to
the uncertainty in the particular output. Input parameters associated with the ocean compartments are presented in shades or patterns of blue, and those associated with the vegetation compartment in shades
of green. Influential input parameters for all other model outputs are provided in the auxiliary material,
Figures S11–S16 in Text S2. Conc. = concentration.
Figure 4. (a) Global mass balance for mercury obtained from the Monte Carlo uncertainty analysis on Unit-WorM3, after
50 years of industrial simulations. Italic numbers in parenthesis represent dispersion factors in the median values that are
listed outside the parenthesis. Fluxes are reported as Hg(0):Hg(II):Hg-p for air-to-surface transfer, and as Hg(0):Hgnr(II):
Hgr(II) for surface ocean/sub-surface ocean exchange. Run-off from soil to surface ocean contributes to the Hg(0) and
Hgnr(II) pool in surface ocean. Color codes for fluxes: Purple: Hg(0), orange: Hg(II)(g) or Hgnr(II), pink: Hg-p, brown
(except when illustrating the total mercury inventory in soil): Hgr(II). (b) Comparison of global estimates obtained in
Figure 4a from the Monte Carlo analysis on Unit-WorM3 with the global estimates from the spatially resolved multimedia
model WorM3 presented in this work, box modeling estimates of Lamborg et al. [2002], empirical estimates of Sunderland
and Mason [2007] and other recently reported chemical transport models that consider terrestrial components [Selin et al.,
2008; Smith-Downey et al., 2010; Soerensen et al., 2010]. In Figure 4b, a: surface ocean depth in Unit-WorM3 = 33–300 m,
in WorM3 = 100 m, in work by Lamborg et al. [2002] = 100 m, and in work by Soerensen et al. [2010] = 10–670 m;
b: depth of sub-surface ocean in Unit-WorM3 = 133–1200 m, in WorM3 = 400 m, in work by Lamborg et al. [2002] =
900 m, however, the results are illustrated for 400 m (multiplying their number by 400/900) and in estimates of
Sunderland and Mason [2007] = 1500 m (their top ocean compartment); c: total soil mercury pool in work by SmithDowney et al. [2010]; d: soil mercury pool excluding “recalcitrant” mercury in work by Smith-Downey et al. [2010];
e: values from Sunderland and Mason [2007] and Soerensen et al. [2010] represent deposition of Hg(II) and Hg-p only;
f: values from Sunderland and Mason [2007] and Soerensen et al. [2010] represent net flux. Vertical bars in Unit-WorM3
represent 95% dispersion range.
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uncertainties in reactions occurring in the atmosphere (as
signified by concentration ratio). Uncertainties in emissions,
ocean particle sinking and wind velocity, input parameters
that describe mercury sources, mercury removal and mercury
exchange processes are also important.
[34] Uncertainty in the concentration of total mercury in
surface ocean (Figure 5e) is governed by uncertainties in
processes that may lead to the sinking of mercury out of
the surface ocean compartment.
3.2.4. Total Mercury Residence Time in Air Against
Deposition
[35] Uncertainty in the residence time of total mercury in
air will be governed by the net contribution of parameters
that describe mercury concentration in air and deposition of
mercury from air to terrestrial surfaces. From this net effect,
we see (Figure 5f) that uncertainties in input parameters
wind velocity and leaf area index, which describe the
exchange velocities of mercury with terrestrial surfaces are
important, contributing 63% and 11% to the output variance,
respectively. Also, since Hg(II)(g) has a higher deposition
velocity than Hg(0), higher concentration ratio of Hg(0):
Hg(II)(g) will imply a higher retention in the atmosphere.
Therefore, this input parameter is also of importance
(#23% contribution to the variance in output).
3.2.5. Mercury Removal Flux Out of the Model System
[36] Uncertainty in mercury removal from the model
environment is most influenced by uncertainties in parameters that describe partitioning of mercury to particles in
sub-surface and surface oceans, and the sinking velocity of
these particles (Figure 5g). Also, uncertainties in emissions
govern this output, as higher the addition of mercury to the
model environment, higher will be its removal.
3.2.6. Implications for Global Modeling and Research
Needs
[37] From our uncertainty analysis we are able to identify
a limited number of input parameters whose uncertainties
contribute most to the uncertainties in global mercury
cycling. The processes described by these parameters are
(i) redox reactions in surface oceans, as defined by the
amount of reducible mercury present in surface oceans and
rate constants for reduction and oxidation in surface oceans;
(ii) air-vegetation exchange, as defined by the extent of leaf
area available for exchange and the stomatal characteristics
of the vegetation type; (iii) mercury mass transfer processes
as defined by wind velocity; (iv) mercury interconversion
reactions in the atmosphere, as defined by the concentration
ratio Hg(0):Hg(II)(g).
[38] The global mass balance for mercury would be better
constrained if the uncertainties in these processes could be
reduced. There is especially little information available on
the quantity of reducible mercury in surface oceans. Information on the rate constants for reduction and oxidation of
mercury species in surface oceans is sparse, and therefore
extrapolations to a spatially resolved model are highly
uncertain. Models such as WorM3 and GEOS-Chem use
information on solar radiation and/ or productivity to
scale the limited information on rate constants over the
whole globe. However, there has been no systematic
research to determine rate constants as a function of these,
and many other possibly important parameters such as dissolved organic carbon (DOC), DOC structure, salinity
and water temperature. Indeed, Pirrone et al. [2008] have
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noted reduction and oxidation reactions occurring in surface
oceans as processes of importance in the global mercury
cycle.
[39] Leaf area index, stomatal area and stomatal density
collectively describe the available stomatal pore area for
exchange of mercury species. Uncertainties in air-vegetation
mercury exchange can thus be assessed through fundamental
research on exchange of mercury with vegetation [e.g.,
Lyman et al., 2007; Stamenkovic and Gustin, 2009], intercomparison of methods used to estimate this exchange, and
use of spatial data [Smith-Downey et al., 2010].
[40] In a spatially resolved global model, the DFs in
wind velocity may be reduced by considering wind velocity
fields. In this regard, current CTMs for mercury are well
parameterized, although the temporal and spatial scales of
parameterization can perhaps be optimized based on the
questions being evaluated. It must also be noted that there is
an inherent uncertainty related to the method used to derive
the mass transfer velocity as a function of wind velocity.
Method intercomparison and evaluation [e.g., Qureshi et al.,
2011; Soerensen et al., 2010] will help to reduce this
uncertainty.
[41] Mercury interconversion reactions in the atmosphere
may be better constrained by establishing more observation
stations at various locations in the world (for use in WorM3,
or for evaluation and/ or parameterization of other global
models), or through improved understanding of atmospheric
mercury reactions [Lin et al., 2006, 2007] for use in CTMs
for mercury.
[42] We finally note that the output uncertainties are
determined by uncertainties in inputs and a different set of
input dispersion factors may lead to identification of different research priorities. Our Monte Carlo analysis was conducted without updating the distributions of model inputs
based on agreement with empirical data. This means that if
input distributions are not larger than those considered in
this work, output DFs represent a maximum output variance
that includes uncertainty and variability. A logical extension
of this work would be to constrain input uncertainties using
Bayesian updating [e.g., Schenker et al., 2009].
4. Conclusions and Future Outlook
[43] We have developed and presented a new spatially
resolved global multimedia model for mercury that uses a
simplified representation of the atmospheric compartment so
that the level of detail in all the compartments is kept similar.
Our descriptive modeling approach produces results that are
in satisfactory agreement with the available data on mercury
fluxes and concentrations in the environment. A unit-world
variant of the spatially resolved global model having small
calculations times produces similar results and is used to
conduct a Monte Carlo uncertainty analysis.
[44] Our uncertainty analysis provides uncertainty estimates in the global mass balance of mercury and suggests
that more fundamental research should be conducted on
processes describing the redox reactions in surface oceans,
exchange between the air and vegetation compartments and
interconversions in the atmosphere. Knowledge on these
processes will help considerably in reducing the uncertainties associated with global mercury modeling.
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[45] Acknowledgment. Funding for this work was provided by the
Swiss Federal Office for the Environment (Bundesamt für Umwelt, BAFU).
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