Journal of Hydrology (2007) 340, 105– 118
available at www.sciencedirect.com
journal homepage: www.elsevier.com/locate/jhydrol
Global water-balance modelling with WASMOD-M:
Parameter estimation and regionalisation
Elin Widén-Nilsson
a,*
, Sven Halldin a, Chong-yu Xu
a,b
a
Department of Earth Sciences, Air, Water and Landscape Sciences, Uppsala University, Villavägen 16,
SE-752 36 Uppsala, Sweden
b
Department of Geosciences, University of Oslo, P.O. Box 1047, Blindern, NO-0316 Oslo, Norway
Received 15 September 2005; received in revised form 15 December 2006; accepted 3 April 2007
KEYWORDS
Global model;
Water balance;
Runoff;
Regionalisation;
Distributed
Summary Limitations in water quantity and quality are among the greatest social and
economic problems facing mankind. However, difficulties in estimating the global longterm average runoff have led to differences of as much as 30% when integrated to the
whole earth. Model estimates of runoff are especially uncertain for the 50% of the global
land surface lacking consistent runoff data. In this study, we present the WASMOD-M global water-balance model, constructed to provide robust runoff estimates both for gauged
and ungauged basins. WASMOD-M is a conceptual water-budgeting model with two statevariables and five tunable parameters. A simple parameter-value estimation procedure
allowed ‘‘acceptable’’ parameter values to be identified both for the majority of gauged
basins, and for most ungauged basins. Acceptable global simulations could be accomplished with continentally constant parameter values but at the cost of compensating
errors on a basin scale. A ‘‘standard’’, spatially-distributed parameter-value set was
derived for a ’’best’’ global simulation. Of the simulated 59132 0.5 · 0.5 cells, 45%
got ‘‘good’’ parameter values as a by-product of regionalisation, 41% from regionalisation, whereas 14% were given a default value set. This global set allowed simulation of
the 1915–2000 world water balance. The simulation was in the same range as previously
published model results and compilations of runoff measurements. Long-term average
within-year runoff variations agreed well with previously published results for most of
the studied runoff stations although WASMOD-M was only calibrated against long-term
average runoff. Improvement of WASMOD-M and other global water-balance models
should be simplified by a common definition of basin boundaries and areas, as well as runoff. Further, modelling progress will depend on improved global datasets of precipitation
and runoff regulation.
ª 2007 Elsevier B.V. All rights reserved.
* Corresponding author.
E-mail addresses: elin.widen@hyd.uu.se (E. Widén-Nilsson), sven.halldin@hyd.uu.se (S. Halldin), chongyu.xu@geo.uio.no (C.-y. Xu).
0022-1694/$ - see front matter ª 2007 Elsevier B.V. All rights reserved.
doi:10.1016/j.jhydrol.2007.04.002
106
Introduction
The world population is learning to cope with limited water
resources. In spite of its central importance to mankind, the
difference between estimates of global runoff is around 30%
and up to 70% for individual continents (GRDC, 2004). Access to high-quality water-balance data from local to global-scales is one of the most important prerequisites for
the planning of sustainable development. Such data are,
however, completely lacking in many developing countries
(GRDC, 2005). This makes water-balance measurement
compilations and model estimates unreliable for those regions and focuses attention on methods to extrapolate to
regions where information is lacking (IAHS, 2003).
Global-scale problems have motivated, in the last 10–15
years, development of global water-balance models. Problems
that require global-scale water data include climate-change
impact, virtual water trade, water conflicts in multinational
river basins and rapidly increasing water demand from a
growing world population (Döll et al., 2003; Arnell, 2003;
Oki and Kanae, 2006). Global water-balance models may
also provide a basis to establish long-term data-collection
programmes in places where these are missing.
In climate-change studies, global water-balance models
can be important tools in developing consistent hydrological
properties and variability over large spatial domains (Arnell,
1999b, 2004; Vörösmarty et al., 2000a; Alcamo and Henrichs, 2002). Understanding of land-surface processes and
their parameterisation in general circulation models (GCMs)
has improved but large uncertainties still remain (Kabat
et al., 2004), particularly concerning runoff. Many GCMs
treat runoff as a residual discarded from the land surface
to the ocean after each time step. Water flows are primarily
considered at the interfaces between the atmosphere and
the ocean on one hand and the land surface on the other.
GCMs are still the only way to provide consistent long-term
input data to global water-balance models but the quality of
GCM precipitation remains insufficient with respect to
amount as well as to occurrence (Mearns et al., 1995; Bates
et al., 1998; Xu, 1999a; Arora, 2001).
Present-day global water-balance models work with a
spatial resolution of 0.5 · 0.5 latitude–longitude and
monthly input data (Fekete et al., 1999a; Arnell, 2003; Döll
et al., 2003). Validation data are restricted by the large degree of regulation of the many major water courses which,
without information on operational rules, cannot be simulated. Since, global data, especially time series, have
incomplete information on regulation of large rivers (Vörösmarty et al., 1997; Nilsson et al., 2005), it is difficult to
know whether runoff variability refers to regulated or to
natural conditions. Additionally, anthropogenic influences,
such as water abstractions can considerably alter the runoff
in the downstream parts of a basin (Döll et al., 2003).
Hence, validation must primarily be done on long-term
average runoff data. The robustness of water-balance models can suffer from problems of overparameterisation and
equifinality (Franks et al., 1997) with such limitations in input and validation data.
Since, neither global-change predictions nor runoff in
ungauged basins can be studied in vitro, one way to increase
the goodness of water-balance predictions and extrapola-
E. Widén-Nilsson et al.
tions is to subject models to internal tests that reveal their
capacity to predict spatial and temporal variations of
changes in water-balance components. In this paper we
present the new WASMOD-M (M for macro-scale) global
water-balance model based on the WASMOD (Water And
Snow balance MODeling system) catchment model (Xu,
2002). We selected WASMOD as our starting point because
its simple structure and few parameters were in line with
the global-modelling data limitations. As summarised in Xu
(2002), different versions of WASMOD have shown a high level of generality from applications at variously-sized catchments in Europe, Asia and Africa. Studies have shown that
its model parameters can be correlated with catchment
characteristics (Xu, 1999b, 2003; Muller-Wohlfeil et al.,
2003) such as land-cover fractions and soil texture. WASMOD
(Xu, 1999c), together with the models of Refsgaard and
Knudsen (1996) and Donnelly-Makoweckia and Moore
(1999), are also the only water-balance models that we have
been able to locate that passed the full split-sample-proxybasin test proposed by Klemeš (1986).
The first objective of this study was to complement
existing global water-balance models with a new one (one
way to improve uncertainty estimates of global and continental runoff is by comparing independent models and compilation methods). Furthermore, a methodology for
regionalisation of parameter values of the ungauged basins
of the world, which amount to 50% of the global land surface
in the Global Runoff Data Centre (GRDC, 2005), should be
outlined. A third objective was to find out if one, or a very
small number of parameter-value sets, could be used to produce acceptable global and continental water balances, i.e.
to find out how simple a model could be designed that reasonably reflects the global water balance.
Global models and data requirements
Simulation of the global water balance can be done with different types of models. The global water-balance models
are simple models, transferring precipitation to evaporation
and runoff. The three main global water-balance models are
WBM (Vörösmarty et al., 1989, 1996, 1998), Macro-PDM (Arnell, 1999a, 2003) and WGHM (Döll et al., 2003; Kaspar,
2004), a submodel of WaterGAP (Döll et al., 1999; Alcamo
et al., 2003). WASMOD-M, as presented here, is a new model
in this category. Runoff is also produced by globally operating dynamic vegetation models like LPJ (Gerten et al.,
2004), and Soil-Vegetation-Atmosphere-Transfer (SVAT)
models like VIC, used as a land-surface scheme in some
atmospheric GCMs (Liang et al., 1994; Nijssen et al.,
2001a). Routing models like HD (Hagemann and Dümenil,
1998) simulate global runoff when combined with atmospheric GCMs.
Principally, parameter-value tuning is necessary for all
models because of limited data quality, complexity of processes, and subgrid spatial heterogeneity (Döll et al.,
2003) even though it would ideally be avoided (Arnell,
1999a). Nijssen et al. (2001b) report on the improvements
in model performance found when land-surface-parameterisation schemes and macroscale hydrological models were
calibrated against runoff. This was true for conceptual as
well as for physically-based models.
Global water-balance modelling with WASMOD-M
The three main global water-balance models have different approaches to calibration or tuning. WBM has parameter
values assigned a priori (Vörösmarty et al., 1998) and it is
not calibrated. The parameter values are related to vegetation and soil properties, or assumed constant. Vörösmarty
et al. (1998) use WBM to compare different estimates of potential evaporation. Fekete et al. (1999a) apply runoff-correction factors in gauged cells to make inflow to
downstream areas equal to measured flow. For calibration
of WTM, the water-transport model in WBM, the reader is
referred to Vörösmarty et al. (1989), Vörösmarty and Moore
(1991), and Vörösmarty et al. (1996).
Arnell’s (1999a, 2003) approach is to avoid calibration as
much as possible. Macro-PDM parameter values are estimated from spatial databases or assumed constant from
the literature values and using knowledge of previous applications of the model (Arnell, 2003). Six of the 13 parameters
are globally uniform and 7 are functions of soil texture and
vegetation (Arnell, 2003). When developing the model, Arnell (1999a) did some tuning to set values and test model
sensitivity. The tuning process includes tests of precipitation datasets and potential evaporation calculations and is
done against long-term average runoff and long-term average within-year runoff patterns.
The approach of Döll et al. (2003) is to calibrate only one
WGHM parameter, which regulates runoff based on effective precipitation and available soil water. Calibration is
carried out against measured long-term average runoff to
get a simulated maximum error of 1%. This goal is achieved
for all 724 stations after applying one or two correction factors in 339 cases to ensure that the downstream stations get
simulated runoff similar to the measured. Döll et al. (2003)
regionalise their calibrated parameter with multiple regression against long-term average temperature, freshwater
area, and length of non-perennial river stretches. A subset
of the calibration basins is included in the regression but
correction factors are not regionalised. The other WGHM
parameter values are globally uniform or related to land
cover and its associated properties (e.g. albedo and rooting
depth), leaf mass, slopes, soil/bedrock properties and climate variables (e.g. temperature).
Availability and preparation of input data files is a major
problem in global water-balance modelling. Uncertainties
and differences in model-input data, especially precipitation, are major sources of uncertainty in model output. Arnell (1999a) states that, with a rudimentary sensitivity
analysis of Macro-PDM for Europe, macro-scale models are
primarily constrained by the quality of the input data, while
‘‘estimated model parameters and model form are less significant’’. Döll et al. (2003) list erroneous input data (primarily precipitation but also radiation) as the first reason
for the need of calibrating WGHM. Kaspar (2004) proves,
through careful sensitivity analysis of WGHM, that other factors are more important for the model uncertainty than the
precipitation errors, although the results would improve
with precipitation corrected for gauge undercatch. Fekete
et al. (2004) use WBM to study the impact of different precipitation datasets on runoff estimation. Vörösmarty et al.
(1998) test different potential evaporation functions for
the same purpose. These two WBM studies show the need
for accurate precipitation inputs for water balance calculations and that arid and semiarid regions are very sensitive to
107
precipitation input while the sensitivity for potential evaporation functions is more pronounced in humid areas.
Materials and methods
Data preparation
The global water-balance model WASMOD-M was driven by
the freely available CRU TS 2.02 climate data (Mitchell
et al., 2004). Basin boundaries and areas, flow paths, and
continent boundaries were taken from STN-30p (Vörösmarty
et al., 2000b). These datasets have grid cells with identical
projection and 0.5 · 0.5 latitude–longitude resolution but
differing land-sea masks. The CRU climate dataset includes
land-surface cells with smaller land-surface fractions than
the STN-30p physiographic dataset. We used, conservatively, the land mask implicitly defined by STN-30p (59132
cells). Seven cells in this were not covered by CRU and
climate values of these were set to an average of the eight
surrounding cells. CRU climate data cover the period 1901–
2000 whereas long-term runoff averages from GRDC (2004,
2005) are based on different time periods during the 20th
century. Some gauging stations include data from the 19th
century.
Climate-input data to WASMOD-M comprised gridded
monthly values of precipitation, temperature and water-vapour pressure. Precipitation-correction factors were calculated for gauge losses as quotients for each cell between
corrected and uncorrected precipitation (Willmott et al.,
1998; Legates and Willmott, 1990) as a long-term average
for each month. We only used correction factors between
1 and 3.4. The correction increased total global precipitation by 9%. Measured runoff from 663 gauging stations in
257 basins discharging to oceans or large lakes was used
for parameter-estimation and model validation. The runoff
data were included in ’’UNH/GRDC Composite Runoff Fields
V1.0’’ (Fekete et al., 1999b, 2002), where station positions
are slightly relocated to fit into their 0.5 flow paths. The
STN-30p dataset delineates 6132 basins, of which 4226 are
small covering one or two cells only. 257 of these 6132 basins correspond to 50% of the global surface area and have
runoff data from gauging stations that have been running
for variable time periods, none of which were reported beyond 1997. Related to the actively discharging area only,
the coverage is 72% instead of 50% (Fekete et al., 2002).
Almost all large rivers are regulated (Vörösmarty et al.,
2004; Nilsson et al., 2005) such that natural peak- and
low-flow characteristics are modified. Regulation data are
often unavailable since dam and reservoir operation commonly involve competing economic interests and can also
be in conflict with downstream water-supply needs (Brakenridge et al., 2005). Many hydrological models, therefore, do
not include regulation effects. Flow data from regulated rivers are sometimes naturalised, i.e. recalculated to their
natural behaviour by subtracting anthropogenic effects like
abstraction and damming, to overcome this problem, but no
global database of naturalised streamflow exists. We used
long-term-average runoff in this study instead of time series
to minimise the effect of the regulation problem on model
calibration. We assumed that regulation did not affect average flow volumes, a non-valid assumption in warm and arid
108
E. Widén-Nilsson et al.
areas with substantial evaporation loss from river stretches
and reservoirs, e.g. in the Nile. We did also not correct for
water extraction, a problem, e.g. in the Yellow River and
Colorado River basins.
The combination of precipitation and runoff data showed
that some basins had physically unreasonable runoff coefficients. We estimated parameter values only from basins
with runoff coefficients between 1% and 85%. Regions where
these problems were abundant were excluded altogether,
e.g. Alaska and the Colorado River basin.
Model description
WASMOD-M updates the storage of water in each cell by
adding precipitation and subtracting calculated evaporation
and runoff. Gridded datasets of precipitation, temperature
and potential evaporation are used as input to calculate the
runoff from each cell. WASMOD-M calculates snow accumulation and melt, actual evaporation, and separates runoff
into a fast and a slow component with a monthly time step.
The model allows snow, rain and also melting to simultaneously occur in the same month. The model has 4–6
parameters (model constants; Table 1), depending on the
presence of snow or not, of which 5 have been varied in
the parameter-estimation procedure. All units are mm
month1 unless stated otherwise.
Potential evaporation
Potential evaporation (ep) is pre-processed and used as input. Xu (2002) reviews different potential evaporation equations depending on data availability. In this case it was
calculated from air temperature, Ta(C), and relative
humidity, RH (%) calculated from temperature and watervapour pressure:
2
ep ¼ E c ðT þ
a Þ ð100 RHÞ
ð1Þ
where T þ
a ¼ maxðT a ; 0Þ. The parameter Ec was set to 0.018
(mm month1 C2) globally.
(
Snow accumulation and melt
Snow and rainfall as well as snowmelt and accumulation
vary exponentially between two temperature thresholds
(Tm and Ts). The snow equations were applied only for grid
cells where at least one monthly average temperature fell
below 4 C:
(
2 !)þ
Ta Ts
snow ¼ P 1 exp ð2Þ
Ts Tm
rain ¼ P snow
melt ¼ ðsnowpackold =Dt þ snowÞ
(
2 !)þ !
Tm Ta
;1
min
1 exp Ts Tm
snowpack ¼ snowpackold þ ðsnow–meltÞ Dt
ð4Þ
ð5Þ
where P is precipitation and Dt=1 month. {x}+ means
max(x,0), and {x} means min(x,0).
Evaporation
Direct water loss (dl) to the atmosphere is calculated from
potential evaporation and rainfall. The variable ‘‘land moisture’’ (in mm) represents the storage of water available for
evaporation and runoff in the next time step. The name is
introduced to make a clear distinction to the well-defined,
local-scale, soil-physical entity ‘‘soil moisture’’. Available
water is calculated from active rain, i.e. rainfall minus
direct loss, and snowmelt. Actual evaporation (evaptot) is
calculated from land moisture, potential evaporation (ep),
and direct loss:
(
dl ¼ ep ð1 erain=ep Þ ep > 1
ð6Þ
dl ¼ ep
ep 6 1
active rain ¼ frain dlgþ
available water ¼ land moistureold =Dt þ active rain
þ melt
water=ðep-dlÞ
evap ¼ minfððep-dlÞ ð1 Aavailable
ÞÞ; available waterg ep-dl > 1
c
evap ¼ ep-dl
ep-dl 6 1
Table 1
ð3Þ
ð7Þ
ð8Þ
ð9Þ
The complete set of parameters in the WASMOD-M global water-balance model
Parameter
Governing
Values
Ts(C)
Tm(C)
Ac()
Ps(month1)
Snowfall (Eqs. (2) and (4))
Snowmelt (Eqs. (2) and (4))
Actual evaporation (Eq. (9))
Slow runoff (baseflow, Eq. (11))
Pf(mm1)
Fast runoff (storm flow, Eq. (12))
1.5, 3.5
1.5, 3.5
0.35, 0.55, 0.75
0.00005, 0.0001, 0.0015, 0.004, 0.01, 0.025, 0.05,
0.14, 0.19, 0.25, 0.4, 0.6, 0.8, 0.9
0.000005, 0.00001, 0.0001, 0.0005, 0.001, 0.0025,
0.005, 0.0095, 0.0145, 0.025
The combination of all values generate 1 680 globally-fixed parameter-value sets.
One additional parameter, Ec (Eq. (1)), governs the pre-processing of temperature and humidity data into potential evaporation. This
parameter was set to 0.018 (mm month1 C2).
Global water-balance modelling with WASMOD-M
evaptot ¼ fevap þ dlgþ
109
ð10Þ
where Ac () is a tuneable parameter.
Slow and fast runoff, and water balance
The slow runoff is a base flow, provided by land moisture
whereas the fast runoff is provided by both land moisture
and water added (i.e. melt + active rain) during a time step.
Both runoffs are described by linear reservoirs:
slow ¼ Ps land moistureold
fast ¼ P f land moistureold ðmelt þ active rainÞ
ð11Þ
ð12Þ
where Ps (month1) and Pf (mm1) are tuneable parameters.
The grid cell runoff, which is the sum of slow and fast
runoff, is routed downstream without delay along the flow
network, i.e. flow is summed along the flow paths for each
time step. There is no interaction between upstream and
downstream runoff generation, i.e. all cells are
independent:
runoff ¼ slow þ fast
ð13Þ
The water balance is finally achieved by updating land moisture in each cell:
land moisture ¼ land moistureold þ ðactive rain
þ melt-evap-runoffÞ Dt
ð14Þ
Parameter-value estimation in gauged basins
Simulation results with different parameter values were
compared against observed long-term average runoff, to
find acceptable parameter values. Parameter values that
produced unreasonable state-variable (snowpack and land
moisture) values were discarded. The primary goal of the
estimation was not to produce the best possible runoff in
all gauged basins but to produce sets of acceptable parameter values in each cell that could be used to regionalise,
i.e. to estimate parameter values in neighbouring ungauged-basin cells.
WASMOD-M was first run with a combination of globallyuniform parameter-value sets, covering the range of ‘‘reasonable’’ values for each parameter (Table 1). These were
deduced from previous studies using the WASMOD catchment model (Vandewiele et al., 1992; Xu et al., 1996; Xu,
2002). The most sensitive parameters were given the broadest range of possible values (Table 1). The combination of
the discrete values for all the parameters resulted in 1680
simulations. All the sets of values that produced acceptable
runoff for a gauged basin were selected at first. Then, when
the regionalisation procedure was completed, the best
parameter-value set for each gauged basin was selected
for the final simulation.
Parameter-value sets were considered ‘‘acceptable’’, if
the simulated basin runoff differed by less than ±20%, or
5 mm in dry areas, respectively, from the measured value,
given that land moisture, snowpack, and change in snowpack had to be reasonable during the simulation period.
Land moisture was not allowed to exceed 1000 mm in any
month while the snowpack limit was 1200 mm. The average
land moisture and snowpack, respectively during the first
simulation year (1915) was not allowed to differ more than
200 mm and 100 mm, respectively compared to the average
of the last simulation year (2000). These limits were based
on previous model experience (Vandewiele et al., 1992;
Xu et al., 1996; Xu, 2002).
In basins with more than one gauging station, an interstation algorithm allowed cells to be tuned to the runoff generated between stations if the runoff coefficient was
acceptable. Interstation runoff was not considered if the
sum of headwater and simulated interstation runoff produced unacceptable results, i.e. volume error larger than
±20%. The interstation algorithm was also overruled if it increased the error at the downmost gauging station compared to a calibration for the whole basin against runoff
at this station.
Regionalisation
Regionalised parameter-value sets were assigned to grid
cells belonging to ungauged basins and to gauged basins
where no acceptable sets were found in the calibration
runs. Regionalisation is probably best for surrounding areas
close to gauged areas. Thus, regionalisation was conducted
by searching for a common parameter-value set among all
acceptable sets in surrounding gauged areas. Surrounding
cells were found in a window (Fig. 1), which was moved over
cells without or with non-acceptable parameter-value sets.
A rectangular window form was used because climate varies
more with latitude than with longitude. The most commonly
occurring parameter-value set among the gauged basins in
this window was selected for each given cell. If two or more
parameter-value sets were equally common, the combination that gave the lowest error in the neighbouring cells
was selected. Cells where no gauged basin or common
parameter-value set was found within the moving window
were given a single, default value set. Cells belonging to
stations where the 20%-error limit was not reached were
not regionalised but given the best available parameter-value set with an error above 20%.
The default parameter-value set was subjectively derived from a map (not shown) of acceptable parameter values for all gauged and regionalised cells. The map showed a
few dominating parameter-value sets close to the areas
with missing values. The most abundant of these was chosen
as default.
Simulations
All simulations started with globally uniform initial values of
land moisture and snowpack. A 14-year warming-up period,
1901–1914, was used to obtain physically reasonable statevariable values. The time step used was 1 month and simulations were evaluated for the time period 1915–2000.
Simulations were first performed for regionalisation. This
required a simulation for each of the 1680 parameter-value
sets. Only data from gauged areas were saved for further
analysis.
Estimation of global and continental water balances was
carried out in four steps. Continental runoff was cumulated
using the continental boundaries in STN-30p and one geographically-distributed global parameter-value set, which
was called the ‘‘standard simulation’’ set, was compiled to
110
E. Widén-Nilsson et al.
Figure 1 River basins of the world: (1) Gauged basins with acceptable runoff (black) and unacceptable (dark grey) simulations.
The latter include areas with unacceptable runoff coefficients as well as simulation problems and (2) Ungauged basin with
regionalised parameter values (light grey) and with a default set of parameter values (white). Regionalised parameter-value sets
were selected from cells within a 17 · 39-cell rectangle (seen in the southern Atlantic) moved over all land areas lacking acceptable
model-parameter values.
give a ’’best’’ estimate. In this first step we selected parameter-value sets from the 1680 globally uniform sets to give the
best fit to long-term average runoff in all gauged basins, and
from the regionalisation procedure for the remaining basins.
In a second step, an uncertainty analysis of this ‘‘standard simulation’’ was performed. This was done using the
original simulations with all 1680 parameter-value sets. Sets
that produced simulations within ±20% of the sum of all
measured runoff were analysed to see if a single globallyuniform parameter-value set could be used to acceptably
simulate not only global but also continental runoff. Total
global and continental runoff with the ‘‘standard simulation’’ was compared with previously published estimates.
Although, the model was not explicitly tuned to withinyear runoff patterns, its capability to capture these with
the ‘‘standard’’ simulation was compared to published simulations in a third step. A set of 15 gauging stations was selected that could be compared with results in at least two
previous publications using other models.
The final step in producing a good runoff estimate was to
allow state-variable values to exceed their limits, if necessary many fold, if acceptable runoff could not be achieved
otherwise.
Results
Regionalisation
The simulations with 1680 globally uniform parameter-value
sets produced acceptable results for the whole upstream
area that comprises the mainstream sub-basins of 485 of
the 663 stations (Fig. 1). The 178 non-accepted stations
were divided into the following four categories: In the first
category, 57 stations lacked input and validation data that
produced acceptable runoff coefficients. The other three
categories were the result of either data or model deficiencies: No acceptable parameter-value sets could be found for
29 stations, i.e. they exceeded the 20%-error limit criterion;
23 stations had unreasonable state variables for all parameter-value sets (e.g. the snowpack or the land moisture grew
too large); 69 stations had no acceptable parameter-value
set with acceptable state-variables.
After applying the interstation algorithm (‘‘Parametervalue estimation in gauged basins’’ Section), parameter values could be set for 531 of the total 663 stations. Since,
some of them were substituted by parameter values from
downstream stations, the number of parameter-value sets
was finally 429. These correspond to 42% of all cells. The
regionalisation procedure allowed another 41% of all cells
to get parameter values. A total of 14% of all cells could
not be addressed by the regionalisation procedure. The
remaining 3% of all cells belonged to stations that did not
reach the ±20% error limit, but had an acceptable runoff
coefficient and at least one parameter-value set with
acceptable state-variables. These stations were given the
parameter-value set that gave the lowest error, but above
20%.
Regionalisation was fully successful in 46% of the cells,
i.e. there existed a common parameter-value set for all station cells in the window. Regionalisation was partly successful in 42% of the cells, i.e. a common parameter-value set
could be identified in the majority of station cells in the
window. Regionalisation was less successful for 12% since
parameter-value sets could only be found for less than half
of the station cells in the window when only parameter values common for at least two basins were accepted.
The regionalisation failed for 14% of the land-surface
cells (Fig. 1) for two reasons. Areas bordering the Arctic,
Central America, the southern tip of South America, parts
of Northern Africa and Saudi Arabia, Indonesia and New Zeeland were too far away from station cells with the given size
of the moving window. No common parameter-value set
could be found in parts of Turkey, eastwards towards central Asia, in south-central Australia and some small areas
in Asia, Africa and America.
Global and continental water balances
Globally, 717 of the total 1680 parameter-value sets produced runoff within ±20% of the measured values integrated
Global water-balance modelling with WASMOD-M
111
Discussion
10000
Model performance, parameter-value estimation
and regionalisation
8000
3
km /yr
6000
4000
2000
Africa
Asia
Oceania
Europe
N. Am.
S. Am.
Figure 2 Sums of gauged continental runoff: Measured runoff
(circles) and simulated runoff (stars) with the WASMOD-M global
water-balance model using a tuned, geographically distributed
parameter-value set, and interval between max and min
simulated runoff (lines) with 717 globally-fixed parameter sets
producing global runoff within ±20% of the measured.
over all gauged areas (Fig. 2). With a ±1%-error limit, 54 sets
remained. Simulations with these 717 parameter-value sets
integrated the different continents to a globally acceptable
runoff. However, none of these globally-uniform sets could
produce acceptable simulations of runoff from all continents. The best globally-uniform parameter-value set,
based on results for each continent, produced continental
runoff errors up to 48%. All acceptable globally-uniform
parameter-value sets produced overestimated runoff from
Europe. All sets caused state-variable problems at some
point, and some basins even showed problems with all
parameter-value sets, e.g. stations in the Amazon, Cauvery,
Columbia, and Danube basins.
Runoff was well simulated with WASMOD-M for all continents (Table 2, Fig. 3) with the geographically distributed
parameter-value set, which produced runoff within ±20% of
the measured for 455 of the total 663 gauging stations. Simulation results within ±1% were achieved for 276 stations.
Continental and global runoff values were in the same
range as measurement compilations and comparable investigations (Table 2). Runoff was simulated 3–23% better for
individual continents with continentally-uniform parameter
values, than with the globally distributed parameter-value
set, but at the cost of compensating errors at the basin
scale.
Within-year runoff variations
The long-term average within-year variations were reasonably well captured for most of the 663 stations. There was
a general tendency that simulated runoff varied more than
the measured (e.g. Mackenzie in Fig. 4), while there were
a few examples of the opposite (e.g. Yenisey in Fig. 4).
There was also a tendency for around 40% of the gauging
stations that the simulated peak flows occurred earlier than
the measured (e.g. Mackenzie, Mississippi and Guadalquivir
in Fig. 4), while a delayed peak only occurred at 15% of the
stations.
One objective in this study was to see how simple a model
could be to yield acceptable continental and global runoff
simulations, given available input and validation data. It
was not expected that a globally-uniform parameter-value
set would be able to produce acceptable continental runoff.
In this study, one set of geographically-distributed parameter values, estimated with a simple procedure, was able to
simulate a global runoff, that agreed well with measurement compilations and comparable simulation studies, as
well as with runoff at the calibration stations. In spite of
its simplicity, it may be questioned if WASMOD-M also is
overparameterised as long as only long-term average runoff
is used for validation. Tuning the model against within-year
runoff variations (like Arnell, 1999a), evaporation patterns
(Vörösmarty et al., 1998), or climatic water balance (Dai
and Trenberth, 2002) would probably allow identification
of more parameter values, but these additional calibration
data are still uncertain.
Snowpack and land moisture problems could depend on
the model, input data, or validation data. We experienced
state-variable problems for 23 stations in seven basins on
four continents in the simulations with globally-uniform
parameters: North America, South America, Europe and
Asia. Nine additional stations in four basins that were excluded because of unreasonable runoff coefficients received
regionalised parameter values that produced state-variable
problems. The problems we experienced with land moisture
in the Amazon basin can be compared to the correction factors Döll et al. (2003) introduced in the same basin to
achieve an acceptable calibration.
Problematic model-parameter values in sub-basins of larger river systems are not much discussed in the literature,
but implicitly shown by Döll et al. (2003), who introduce a
multiplicative correction factor, limited to 100%, for upstream gauging stations to assure that all downstream stations get simulated runoff similar to the measured. Also
Fekete et al. (1999a) introduce such a factor, ranging between 0.01 and 100 (and beyond), when necessary.
The globally distributed parameter values used by WASMOD-M in its ‘‘standard simulation’’ were a by-product of
the regionalisation procedure. This procedure was able to
set parameter values for the majority of the ungauged basins in the world. The global runoff pattern produced by
the ‘‘standard‘‘ parameter-value set, where around 50%
of the cells were regionalised or given a default parameter
value, showed a reasonable pattern (Fig. 3). A cell-by-cell
comparison to other model results would probably show
big differences since WASMOD-M used constant parameter
values within basins in contrast to the WBM, Macro-PDM
and WGHM models, where parameter values are varied
according to non-runoff factors such as vegetation and soil
type.
Since, around 45% of the regionalised cells had common parameter values for all stations within the regionalisation window, these would not be very sensitive to a
missing station. The 10% regionalised cells that got values
112
E. Widén-Nilsson et al.
Table 2 Global and continental runoff estimates in km3/year (many data may not be directly comparable because of different
continental boundaries and averaging periods)
Continent
Areaa
(106 km2)
Data-based estimates
Combined
estimates
Model estimates
K78
L79
BR75
S97
GRDC04
F02
F99bm
O01
D03
G04
W
Europe
Asia
Africa
North America
South America
Oceania
10.1
44.0
30.1
22.4
17.9
8.66
2970
14,100
4600
8180
12,200
2510
3110
13,190
4225
5960
10,380
1965
2564
12,467
3409
5840
11,039
2394
2900
13,508
4040
7770
12,030
2400
3083
13,848
3690
6294
11,897
1722
2772
13,091
4517
5892
11,715
1320
2822
11,425
5567
5396
11,240
1308
2191
9385
3616
3824
8789
1680
2763
11,234
3529
5540
11,382
2239
–
–
–
–
–
–
3669
13,611
3738
7009
9448
1129
Global
(except
Antarctica)
133
44,560
38,830
37,713
42,648
40,533
39,307
37,758
29,485
36,687
40,143
38,605
N
N
X
X
Xb
N
N
Nc
N
Nc
N
K78
L79
BR75
S97
GRDC04
F02
F99bm
O01
D03
G04
W
N
X
Korzun et al. (1978), Table 157, time period not specified.
L’vovich (1979), Table 20, time period not specified.
Baumgartner and Reichel (1975), Table XXXV, time period not specified.
Shiklomanov (1997), Table 4.2, time period 1921–1985.
GRDC (2004), time period ‘‘approximately’’ 1961–1990.
Fekete et al. (2002), Table 3, model WBM and data, almost equal to Fekete et al. (1999b), time period not specified.
Fekete et al. (1999b), model WBM, time period not specified.
Oki et al. (2001), Table 2, land-suface models and TRIP routing model, time period 1987–1988.
Döll et al. (2003), Table 1, model WGHM, time period 1961–1990.
Gerten et al. (2004), Table 2, model LPJ, time period 1961–1990.
WASMOD-M, time period 1961–1990.
endorheic basins included.
exorheic basins only.
a
Grid cell area and continental boundaries from Fekete et al. (1999b), endorheic basins included. These areas are only valid for the W
estimate (F02 and F99bm is calculated for 1.6% fewer grid cells). Oceania is defined as Australia, New Zeeland, Papua New Guinea and
some small Islands. W simulation is only made for a minor part of Greenland, which is included in the North America values.
b
It is assumed,that this estimate excludes endorheic basins (not clearly stated in the original publication).
c
It is assumed that these estimates include endorheic basins (not clearly stated in the original publication).
Figure 3 Global average (1915–2000) runoff simulated with the WASMOD-M global water-balance model. The simulation is based
on a parameter-value set tuned from 485 globally-distributed gauging stations. The dots indicate endorheic basin outlets.
from a minority of the surrounding stations might have
been sensitive to the selection of proxy stations. The size
of the regionalisation window was the result of a subjec-
tive balance between the need to cover large areas while
at the same time avoiding regions with too different
properties.
Global water-balance modelling with WASMOD-M
Mackenzie
Congo
50
250
40
200
30
113
Huang He
30
80
Lena
1.5
Maas
Amazon
400
60
1
25
150
500
300
40
20
100
10
0
20
50
Jan Apr Jul Oct
0
200
0.5
20
0
Jan Apr Jul Oct
100
Jan Apr Jul Oct
0
Jan Apr Jul Oct
0
Jan Apr Jul Oct
15
Mississippi
20
Wisla
Sénégal
8
35
00
10
6
30
80
30
60
4
20
5
40
25
2
10
20
0
Jan Apr Jul Oct
0
Loire
4
3
Jan Apr Jul Oct
0
Yenisey
120
80
100
2
Guadalquivir
1.5
80
0
20
Jan Apr Jul Oct
Chang Jiang
100
60
80
60
10
1
1
0
40
40
5
0.5
20
20
Jan Apr Jul Oct
Jan Apr Jul Oct
Brahmaputra
15
60
40
0
Danube
40
20
Jan Apr Jul Oct
0
Jan Apr Jul Oct
0
Jan Apr Jul Oct
0
Jan Apr Jul Oct
0
Jan Apr Jul Oct
Figure 4 Long-term within-year variations in runoff and precipitation (grey bars) from 15 representative gauging stations at 6
continents averaged over different time periods (in units of 1000 m3 s1). Measured monthly runoff (white dots) and simulated with
WASMOD-M (black dots) based on a parameter-value set tuned from 485 globally-distributed gauging stations. Note different
ordinate scales.
It should be investigated if the difference between measurement-based and model estimates is related to different
handling of ungauged basins. Oki et al. (1995) conclude in
their global assessment that runoff is lower in ungauged
than in gauged areas. Additionally, Fekete et al. (2002) report, by combining observation data and simulations with
the WBM model, that the ungauged actively discharging
areas are wetter than the gauged ones.
WASMOD-M has not been subjected to consistency tests
such as parameter independency, heteroscedasticity,
split-sample-proxy-basin test that the WASMOD catchment
model has passed (Xu, 1999c), but few other global models
present such results. One rare example is given by Nijssen
et al. (2001b) in the test of their regionalisation algorithm,
based on climatic zones. In this application of the model,
we used less input data than other global models. The present version of WASMOD-M does not account for, e.g. time
delays along river networks, evaporation losses from dams
and rivers, flood inundation, anthropogenic water abstraction, river regulation, river routing, subgrid variability, glacier dynamics, permafrost and capillary rise. Future model
development may include additional processes and input
data if validation data and consistency checks can substantiate them.
Data problems
Comparison of global water-balance models is difficult because, in contrast to GCMs, there are no common definitions
of data structure, content and quality, time periods and
temporal resolution. Data-related problems can be divided
into three classes: (i) geographical boundaries and positions, (ii) runoff- and precipitation-data quality, differing
time periods, and spatial mismatch, and (iii) unknown or
unavailable anthropogenic runoff influences.
Geographical boundaries and positions
There are several databases of global and continental river
flow nets and/or runoff, e.g. STN-30p/GRDC (given by
Fekete et al. (1999b) Hydro1k (USGS, 2004) and GHCDN
(Dettinger and Diaz, 2000) and provided by NCAR (Bodo,
2001a,b). However, these commonly show differences in
114
routing, basin-area sizes, and boundaries. The positioning of
gauging stations is not identical in different databases and
the stations are sometimes given relocated longitude–latitude information to fit into the spatial resolution of the grid
net (e.g. GRDC/STN-30p). Basin areas for given gauging stations can sometimes differ considerably (Renssen and
Knoop, 2000), which causes problems in validation of digital
river networks and results in different runoff estimates in
model comparisons.
There are also different definitions and boundaries. Oceania, e.g. is defined by different sources as including or
excluding parts of Australia, New Zealand, Papua New Guinea and various small islands (e.g. Nijssen et al., 2001b). In
addition to the border to Oceania, the borders of Asia with
Europe often differ, e.g. by the assignment of Turkey (Nijssen et al., 2001b; Döll et al., 2003). Arctic areas (especially
Antarctica and Greenland) are commonly excluded in modelling studies but included in global compilations of runoff
measurements.
Runoff from rivers to oceans (exorheic) makes up the major part of the global runoff. Other contributions come from
groundwater flow to oceans, river flow to inland basins
(endorheic) and groundwater flow to inland basins. Korzun
et al. (1978) estimate the amount of river flow which evaporates and comes from percolation into rivers. It is not always clear which of these components are included in
various global and continental runoff estimates (Table 2).
Global runoff also varies with time (e.g. Shiklomanov,
1997) and not all estimates include information about the
time period for the calculation (Table 2).
Inconsistent runoff and precipitation data and differing
time periods
Combinations of precipitation and runoff data from different
sources and time periods cause unreasonable runoff coefficients. Problems with runoff coefficients are reported previously (e.g. Fekete et al., 1999a; Nijssen et al., 2001b). In
contrast to Nijssen et al. (2001b), who exclude the Yukon River in Alaska because of a too small runoff coefficient of 0.25,
we found very high runoff coefficients ranging from 0.75 to
1.93 for most Alaskan basins. Like us, Nijssen et al. (2001b)
describe the neighbouring Brahmaputra and Irrawaddy basins
as problematic, whereas we were not able to confirm their
runoff coefficient problems in the Columbia River basin.
Although, problems with runoff coefficients are mostly
caused by inconsistent data, some relate to model deficiencies. Negative runoff coefficients in interstation sub-basins
can be caused by differing measuring techniques, anthropogenic water withdrawal, river-bed seepage and evaporation
from open-water bodies in warm climates. Use of averaged
runoff data from different time periods to calculate the runoff coefficient could also cause problems.
Unknown and unavailable anthropogenic runoff
influences
Most hydrologic models mimic natural variations of waterbalance components. Regulation of rivers by dams, re-routing of water to other basins, and water extraction are major
anthropogenic influences that considerably disrupt the natural water balance. Vörösmarty et al. (1997) and Nilsson
et al. (2005) quantify the influence of dams and the degree
E. Widén-Nilsson et al.
of regulation of large rivers and find that dams globally impact 83% of the global runoff, and represent a 700% increase
in the standing stock of natural river water, with residence
times for individual impoundments spanning from one day to
several years. Lehner and Döll (2004) elaborate a new global
database of lakes, reservoirs and wetland, but we are still
far away from a trustworthy global database of time series
accounting for anthropogenic influences of the global water
cycle. Hence, even a perfect fit between simulated and
measured runoff needs to be evaluated critically and should
not be overrated.
Global runoff estimates
WASMOD-M runoff simulations with the ‘‘standard’’, i.e. the
geographically-distributed best-fitting, parameter-value set
produced global and continental runoff within the range of
other models and measurement compilations (Table 2). Larger areas were simulated acceptably with WASMOD-M
(Fig. 1) rather than with WGHM (see Fig. 2 in Döll et al.,
2003), possibly as a consequence of WGHM simulating yearly
runoff within ±1% of the measured, while the WASMOD-M
limit was set to ±20%. Most areas that Döll et al. (2003) accept without correction were also accepted with WASMODM. WGHM simulates runoff acceptably in Rio Madeira in the
Amazon basin and River Rhine, where WASMOD-M did not.
More examples can be found of the opposite, e.g. in many
northern basins, where WGHM underpredicts, but also in
the Murray, Oranje and West African rivers. One explanation
is that WGHM uses uncorrected precipitation input, causing
an underestimation for snow-covered areas. Moreover, five
parameters were tuned in WASMOD-M compared to one in
WGHM.
Most other global models underestimate runoff in snowcovered areas (Macro-PDM – Arnell, 1999a; WBM – Fekete
et al., 1999a; WGHM – Döll et al., 2003; TRIP with different
land-surface models – Oki et al., 1999; LJP – Gerten et al.,
2004), usually because of underestimated precipitation. At
the same time most of these models overestimate runoff
in arid basins, e.g. because open-water evaporation is not
considered. In the study presented here, WASMOD-M did
not follow these patterns, probably because of our parameter-value estimation.
The difference between the largest and smallest global
runoff estimates in Table 2 exceeds the highest continental
runoff estimate. The model estimates, including WASMODM’s, are generally lower than the estimates based only on
measurements. The total simulated runoff with WASMOD-M
included runoff to inland drainage basins, but excluded runoff from Antarctica and 89% of Greenland. It is comparable to
the measurement compilation of L’vovich (1979) who only
considers runoff to oceans, but higher than WBM (Fekete
et al., 1999b), WGHM (Döll et al., 2003), VIC (Nijssen
et al., 2001b; Table 4) and the TRIP routing scheme combined
with different land-surface models (Oki et al., 2001). On the
other hand, it is lower than LPJ (Gerten et al., 2004) and
UNH/GRDC Composite Runoff Fields V1.0 (Fekete et al.,
1999b). The low value of total simulated runoff reported by
Oki et al. (2001) should partly be related to the short time
period (1987–1988). WASMOD-M also simulates low runoff,
92% of the 1961–1990 average value, for this period.
Global water-balance modelling with WASMOD-M
115
Table 3 Characteristics of runoff-gauging stations selected because of their occurrence in previous articles. The minimum
regulation capacity is defined as the quotient of usable water amount, excluding non-usable bottom water to the discharge
before any substantial human manipulations (Nilsson et al., 2005). Regulation capacity does not say anything about the actual
operation of dams (Nilsson et al., 2005)
Gauging station
River
Country
Areaa (km2)
Start year
End year
Regulation
capacity
Regulation delayb
Norman Wells
Vicksburg
Óbidos
Mackenzie
Mississippi
Amazon
Canada
USA.
Brazil
1,570,000
2,964,252
4,640,300
1966
1965
1928
1984
1983
1996
Alcala del Rio
Montjean
Borgharen
Guadalquivir
Loire
Maas
Spain
France
Netherlands
46,995
110,000
21,300
1913c
1863c
1911c
1994
1979
1990
1–3 months
1 week–1 month
1 week–1 month
in Orinocco
1 week–1 month
Tczew
Ceatal Izmail
Bakel
Kinshasa
Wisla
Danube
Sénégal
Congo
194,376
807,000
218,000
3,475,000
1900c
1921
1904c
1903b
1994
1985
1989
1983
Igarka
Bahadurabad
Yenisey
Brahmaputra
Poland
Romania
Senegal
Congo
(Kinshasa)
Russia
Bangladesh
12%
15.5%d
3% (lumped
with Orinocco)
34%e
1.5%
5% (lumped
with Rhine)
4%
4.6%d
24%d
0%
2,440,000
636,130
1936
1969
1995
1992
1–3 months
1–7 days
Huayuankou
Datong
Stolb
Huang He (Yellow R.)
Chang Jiang (Yangtze)
Lena
China
China
Russia
730,036
1,705,383
2,460,000
1946
1923
1978
1988
1986
1994
18%d
8% (lumped
with Ganges)
51%d
12%d
3%
1–7 days
1–3 month
1–7 days
6–12 months
1–3f months
1–3 months
a
Areas taken from GRDC, distributed through Fekete et al. (1999b).
Vörösmarty et al. (1997).
c
The measured data are averages from a longer time period than the simulated (starting 1915).
d
These values are minimum values as dam data-collection was stopped because the rivers fell into the highest biological impact class
(Nilsson et al., 2005).
e
Silgado Dorado et al. (1991).
f
before completion of the Three Gorges Dam project.
b
Even if there is a general tendency that global runoff
estimates based only on measurements are higher than
modelled ones, there are at least three reasons why the
difference should be even larger. Runoff to internal
basins is commonly excluded in compilations of runoff
measurements. The exorheic runoff simulated with WASMOD-M is equal to the runoff compiled from measurements by Baumgartner and Reichel (1975). There should
also be a difference between those measurement compilations that include groundwater runoff into oceans and
those that do not. Some of the measurement compilations
include evaporation from rivers and dams, which is not
included in any model with the exception of WGHM (Döll
et al., 2003).
Continental runoff estimates of WASMOD-M were generally in the same range as previous estimates (Table 2), with
the exception of a larger runoff from Europe and a lower
runoff from South America. This could partly be explained
for Europe where Döll et al. (2003) and Arnell (1999a) find
the Willmott et al. (1998) precipitation-correction too high.
For South America, we think that the difference was caused
by problems in finding acceptable parameter values for the
major part of the Amazon River basin without accepting
unreasonably high land moisture values. South American
runoff was higher when the land-moisture limitation was
disregarded. The low runoff from Oceania was most likely
caused by a limited continental area, since the WASMOD-M
estimate only included Papua New Guinea, not the whole island of New Guinea. The combined WASMOD-M estimate
from Asia and Oceania was in the same range as others.
Runoff from selected basins
Comparison between observed and simulated within-year
variations in runoff is complicated by river regulation. Nilsson et al. (2005) show that almost all large river basins are
regulated and that it is difficult to get reliable time-series
data on regulation. Since, our WASMOD-M simulations did
not include time-delayed routing, this negatively influenced
the capacity to mimic within-year variations in basins with
monthly or yearly delays. Regulation effects and missing
time-delayed routing likely cause a higher variation of the
simulated runoff as compared to the measured runoff
values.
WASMOD-M was reasonably successful in simulating the
average within-year runoff variations (Fig. 4, Table 3)
although it was only calibrated against average runoff. WASMOD-M produced a good simulation for, e.g. Wisla at Tczew.
Runoff in the Amazon River basin at Óbidos and in Danube at
Ceatal–Izmail was not well simulated with WASMOD-M where
all tested parameter values resulted in too high land moisture. The parameter-value sets for Óbidos and Ceatal-Izmail
116
were set by regionalisation, which explained the poor simulation results. Good simulations could be achieved for both stations when too high state-variable values were accepted.
Conclusions
A global water-balance model, WASMOD-M, was constructed
on the basis of the well-tested WASMOD catchment model.
WASMOD-M is characterised by a simple structure and a
small number of tuneable parameters, but may still be overparameterised when considering the availability of global
input and validation data. WASMOD-M was successful in
temporally and spatially reproducing global and continental
runoff with a parameter-value estimation procedure that
was primarily intended to produce regionalised parameter
values. It was not possible to simulate continental runoff
with a single, globally-uniform parameter-value set, but a
continentally-uniform set for each continent was sufficient
for acceptable results. A distributed parameter-value set
was needed to correctly simulate individual basins,.
Parameter values were estimated for individual basins
and the set of acceptable parameter-value sets achieved
this way was used to regionalise parameter values to the
50% of the world land surface lacking globally consistent
runoff data. We suggest that an international collaboration
should be established to compare runoff estimates from
models and measurement compilations for all ungauged basins of the world. Such collaboration should identify common definitions of basin and continental areas and runoff
measures as well as inclusion or exclusion of endorheic runoff, groundwater seepage, etc. to allow for unambiguous
comparisons.
Global water-balance modelling is primarily constrained
by data. Thus, a stronger focus on international collaboration is needed on global and continental databases. Higherquality precipitation data (see, e.g. the local evaluations of
Achberger et al., 2003) are especially needed to decrease
the uncertainty in global and continental water balances.
Improved data on anthropogenic runoff modifications are
also much needed to evaluate model skill in capturing
within-year patterns.
Acknowledgement
This work was funded by the Swedish Research Council
Grants 629-2002-287 and 621-2002-4352. We are grateful
to all those groups and individuals who supplied data directly from Internet and to Dr. Tim Mitchell who provided
the CRU data, respectively. Mr. Lebing Gong helped in preparing Figs. 2 and 4. We thank Dr. Balazs Fekete and two
anonymous reviewers for their valuable manuscript comments and Prof. Keith Beven for commenting the manuscript and checking the language.
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