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Monthly and Daily Variations of Continental Water Storage and Flows 409

an input parameter depending on vegetation, land cover type, elevation, degree of

industrialization etc.

2.2.2 Reservoir Algorithm

For 487 reservoirs with a total storage capacity of about 4,000 km

, a reservoir oper-

ation algorithm was integrated into WGHM based on the approach of Hanasaki et al.

(2006). Information on reservoir type (irrigation or non-irrigation), surface area and

storage capacity was taken from the Global Lakes and Wetlands Database (GLWD)

(Lehner and Döll, 2004). The algorithm requires the deﬁnition of a reservoir-speciﬁc

operational year. The start of the operational year is deﬁned as the ﬁrst month of a

release period when the mean monthly inﬂow into the reservoir is smaller than the

mean annual inﬂow. Mean values for monthly and annual inﬂow were generated

from a previous model run covering the period 1961–1990 and not taking reservoir

operations into account.

At the beginning of an operational year, the annual total release R

for the fol-

lowing year is estimated based on actual water storage and mean annual inﬂow:

ﬁrst

α ·C

· I

mean

(2)

where S

ﬁrst

is the storage at the beginning of the operational year, α is a constant

parameter set to 0.85, C is the storage capacity and I

mean

is the long-term average

annual inﬂow. For large non-irrigation reservoirs, monthly releases are assumed to

be constant during the operational year. For large irrigation reservoirs, the water

demand in the downstream area (calculated as the sum of industrial, domestic, live-

stock and irrigation water use in a maximum distance of 5 cells downstream of the

reservoir) is also taken into account. Monthly ﬂuctuations in reservoir release occur

if there is a seasonal distribution of water demand. In the case of small non-irrigation

and irrigation reservoirs, monthly release is assumed to be inﬂuenced, addition-

ally by monthly inﬂows, such that overﬂow and storage depletion are minimized. If

monthly inﬂow exceeds storage capacity, overﬂow is generated.

2.3 Climate Input Data

For the period 1901–2002, WGHM is generally driven by monthly climate data

from the Climate Research Unit (CRU). The CRU TS 2.1 data set provides gridded

data for several climate variables like precipitation, number of rain days, tempera-

ture and cloudiness from 1901 to 2002 with a spatial resolution of 0.5

◦

(covering the

global land surface). This dataset is based on station observations and uses anomaly

analysis for the spatial interpolation (Mitchell and Jones, 2005; New et al., 1999,

2000). For precipitation, another global data set was used. The Global Precipitation

Climatology Centre (GPCC) provides a gridded monthly precipitation product for

the global land surface which is available from 1951 to 2004 with a spatial resolution

of 0.5

◦

(Full Data Set Version 3, Rudolf and Schneider, 2005). It is based on a larger

410 K. Fiedler and P. Döll

number of station observations than the CRU data and covers the time period of

the ﬁrst GRACE results. For the years 2005–2007, the so-called GPCC Monitoring

Product was used, which is based on a smaller number of station observations with a

less intensive data processing. To run the model for the GRACE period 2002–2007,

monthly temperature and cloudiness data from the ECMWF operational forecast

system were used as model input. In the standard version of WGHM, monthly pre-

cipitation is distributed equally over the number of rain days within one month.

For the GRACE period, daily precipitation data from ECMWF were scaled with

GPCC monthly precipitation totals to create a daily precipitation dataset to be used

as model input. Scaling numerical weather forecast data against observations is sup-

posed to improve the quality of the daily data product since forecast data are highly

uncertain especially with regard to precipitation intensity and peak values.

The above mentioned monthly precipitation data are not corrected for measure-

ment errors; precipitation, in particular snow, is generally underestimated due to

mainly wind induced undercatch. As this has a strong inﬂuence on simulated snow

water storage, precipitation was corrected using mean monthly catch ratios from

Adam and Lettenmaier (2003) and taking actual monthly temperatures into account

(see Döll and Fiedler, 2008, for details).

3 Results

3.1 Impact of Dynamic Flow Velocity Algorithm on River

Discharge and Storage

The ﬂow velocity is a very sensitive parameter for the calculation of both river dis-

charge and water storage variations. To investigate the effect of using a dynamic

ﬂow velocity approach instead of a constant global value, different model runs were

carried out. Here, the Amazon basin is chosen as an example. Using a constant

ﬂow velocity of 1 m/s within the model and thus representing the standard model

version, seasonal water storage variations are underestimated when compared to

GRACE observations (Fig. 1). Furthermore, there is a time shift of one to two

months between the modelled and observed river discharge as well as between cal-

culated water storage change and GRACE observations. In reality, the ﬂow regime in

the Amazon basin is strongly inﬂuenced by seasonal ﬂooding of ﬂoodplains which

delays discharge peaks. However, seasonal ﬂooding is currently only modelled in

a very simple way within WGHM, and is probably underestimated. If the constant

ﬂow velocity is lowered to 0.3 m/s, the time lags of modelled river discharge and

water storage change in the Amazon basin are much improved. For water storage

variations, the model values are signiﬁcantly increased by up to 100% and are in

good correlation with GRACE amplitudes (Fig. 1).

Using the dynamic ﬂow velocity algorithm with a roughness value of 0.04 shows

very similar results to the standard model version because the applied formula leads

to a comparable mean ﬂow velocity value. However, increasing roughness to a value

Monthly and Daily Variations of Continental Water Storage and Flows 411

Amazon at Obidos

100

200

300

400

500

600

700

800

900

Jan-05 Jan-06 Jan-07

discharge [km³/month]

Amazon Basin

–250

-200

–150

–100

–50

100

150

200

250

Jan-05 Jan-06 Jan-07

water storage change [mm w.eq.]

observation

dynamic flow velocity (roughness 0.04)

dynamic flow velocity (roughness 0.1)

constant flow velocity (1m/s)

constant flow velocity (0.3m/s)

GRACE

Fig. 1 River discharge and water storage change calculated with WGHM for the Amazon Basin

showing the impact of different ﬂow velocity algorithms

of 0.1 and thus decreasing the calculated ﬂow velocity leads to a signiﬁcant improve-

ment with respect to the timing of river discharge and water storage peaks and the

absolute values of water storage change for the Amazon basin. This may not be the

case for other basins with a typically higher ﬂow velocity. Since river bed rough-

ness is a very sensitive parameter for the calculation of ﬂow velocities, a spatially

distributed value should be applied in the future.

3.2 Impact of Reservoir Algorithm on River Discharge

and Storage

In order to estimate the inﬂuence of the new reservoir algorithm on modelled water

storage variations and river discharge, several model runs were carried out: two

anthropogenic model runs taking water use into account and modelling reservoirs

as reservoirs (ANT) or reservoirs as lakes (ANT-LAKE), without reservoirs but still

considering water use (USE) and a naturalized ﬂow run (NAT) without reservoirs

and use. For selected large river basins (like Colorado, Columbia, Volga, Ganges

and Mississippi, with signiﬁcant water use and/or reservoirs) both the total water

storage as well as the partitioning of water storage among the different compart-

ments (snow, soil, groundwater, surface water) differ between model runs. However,

monthly variations in total water storage do not change signiﬁcantly.

River discharge in the above ﬁve basins, however, is affected signiﬁcantly by

reservoirs and water use. The Colorado and the Columbia River are chosen here as

examples: eight reservoirs in the Colorado River Basin representing a total storage

capacity of 80 km

and 16 reservoirs in the Columbia River Basin with 73 km

storage volume are actually included within the reservoir algorithm.

Figure 2 showsthe results of different model runs for the long term mean period

1961–1990. Including reservoir operations strongly i mproves the mean monthly

412 K. Fiedler and P. Döll

Columbia River at The Dalles

Jan

Feb

Mar

Apr

May

Jun

Jul

Aug

Sep

Oct

Nov

Dec

mean monthly discharge [km³/month]

Colora do River at Lee s Ferry

0.5

1.5

2.5

3.5

4.5

Jan

Feb

Mar

Apr

May

Jun

Jul

Aug

Sep

Oct

Nov

Dec

mean monthly discharge [km³/month]

observation

ANT

ANT-LAKE

USE

NAT

naturalized flow data

Fig. 2 Mean monthly discharge (1961–1990) for Columbia and upper Colorado River using dif-

ferent model versions of WaterGAP to show the impact of reservoir operation and water use

(

∗

naturalized ﬂow data for Columbia River based on Haddeland et al., 2006, representing mean

over 1980–1990)

river discharge when compared to observations. The root mean squared error

(RMSE) decreased from 4.3 (ANT-LAKE) to 3.1 (ANT) for the Columbia River and

from 0.27 (ANT-LAKE) to 0.13 (ANT) for the upper Colorado River. The annual

peak decreased and the seasonal ﬂow regime changed due to reservoir operations

showing the typical behaviour of reservoirs used for hydropower generation with an

increase of winter ﬂows and a decrease of spring ﬂood. Without reservoirs (USE),

the seasonal ﬂow pattern changes because discharge seasonality is not dampened by

large surface water bodies, and because evaporation also decreases. The naturalized

ﬂow (NAT) shows the highest discharge volumes and seasonality as there is also no

human water use in this run.

Independent estimates of naturalized ﬂow data are available for both basins. For

Columbia River at The Dalles, the agreement between modelled naturalized ﬂow

values (NAT) and independent estimates (Haddeland et al., 2006) is quite good.

Naturalized ﬂow data for Colorado River at Lees Ferry from USBR (US Department

of the Interior – Bureau of Reclamation) differ signiﬁcantly from the modelled nat-

uralized ﬂow with a peak difference of about 100%, but the model still manages to

capture a large amount of the damping effects of reservoirs (and water use) on river

discharge.

3.3 Daily Variations of Water Storage

Since the internal time step of WGHM is one day, global continental water storage

change can also be calculated on a daily basis. It is, however, a common phe-

nomenon that climate or weather model data like those from ECMWF underestimate

Monthly and Daily Variations of Continental Water Storage and Flows 413

daily precipitation variability. There are too many wet days with a very low amount

of precipitation, and precipitation peaks are underestimated. This is one of the rea-

sons why simulated daily values of water storage and discharge are so unreliable

that they should not be considered further for hydrological analyses at continen-

tal and global scales. However, it is meaningful to investigate which effect the

computed pattern of daily storage variations has on GRACE signal processing

(Han et al., 2004).

A clear aliasing effect of sub-monthly hydrological mass variations that leads to

errors in the computed monthly gravity anomalies was detected. However, this effect

is small compared to other effects inﬂuencing the total GRACE error like ocean tides

or short term mass variations from the atmosphere and oceans. In addition, daily

water storage variations may still be underestimated by WGHM due to the climate

input data used. Furthermore, sub-daily variations which are larger than daily vari-

ations at least f or small spatial scales are not taken into account by WGHM. Since

the use of daily water storage variations for de-aliasing did not lead to a signiﬁ-

cant improvement of GRACE data processing, daily model results of water storage

variations were not further investigated.

4 Best Estimate of Continental Water Storage and Flows

The standard model version of WGHM is calibrated against long-term average river

discharge at 1,235 observation stations (i.e. 1,235 drainage basins) world-wide with

the runoff coefﬁcient γ as a calibration parameter. It determines how much of the

effective precipitation is transformed into runoff, depending on the degree of soil

water saturation. Additionally, two tuning factors are applied if γ cannot be adjusted

within a predeﬁned range (see Hunger and Döll, 2008, for details).

Another approach is the multi-objective calibration against monthly time series

of river discharge and GRACE continental water storage for the world’s 29 l argest

river basins. For each river basin, the most sensitive six model parameters were iden-

tiﬁed and then calibrated using a global optimization method (Werth et al., 2009).

To obtain a best global-scale estimate of continental water storages and ﬂows,

both approaches are combined. For all grid cells within the 29 largest river basins,

the parameter values of the standard model version are replaced by the values

determined by multi-objective calibration.

5 Conclusions

In this study, monthly and daily variations of continental water storage and river dis-

charge were calculated with the WaterGAP global hydrological model (WGHM).

Daily water storage variations were calculated to improve de-aliasing of GRACE

data. However, using these data for de-aliasing did not lead to a signiﬁcant

improvement of GRACE data processing.

414 K. Fiedler and P. Döll

New algorithms were added to obtain improvements with respect to modelled

monthly water storage and discharge values. The integration of a new reservoir

operation s cheme signiﬁcantly improved model results. Reservoir storages and river

discharge in basins with large reservoirs showed a better agreement with observa-

tions but the effect on total water storage variations was very small. With the new

algorithm, WGHM can now simulate the impact of reservoirs and water use from

surface water bodies on river discharge in a more realistic way.

Applying a dynamic ﬂow velocity instead of a constant global value showed

reasonable results and revealed the sensitivity of the approach to the river bed rough-

ness parameter. It also became obvious that an improved algorithm for ﬂoodplain

water storage modelling is required in some basins like the Amazon, and preferable

to a mere parameter tuning (like velocity or river bed roughness). A ﬁrst analysis

of the results of the multi-objective calibration by Werth et al. (2009) showed that a

good ﬁt to GRACE observations and river discharge by adjusting the six most sensi-

tive WGHM parameters is not possible in all river basins (e.g. Murray, St. Lawrence,

Nelson and Niger). This indicates that structural changes of the model or improved

input data and observations are necessary.

Future work will focus on investigating the reasons for discrepancies between

WGHM results on the one hand and GRACE observations and observed discharge

on the other hand. Next steps in model development will include the implementation

of spatially distributed roughness values as input parameters for the dynamic ﬂow

velocity approach. Furthermore, the data base for reservoirs included in the reservoir

operation algorithm will be regularly revised.

References

Adam JC, Lettenmaier DP (2003) Adjustment of global gridded precipitation for systematic bias.

J. Geophys. Res. Atmos., doi: 10.1029/2002JD002499.

Allen PM, Arnold JG, Byars BW (1994) Downstream channel geometry for use in planning-level

models. Water Resour. Bull. 30, 663–671.

Döll P, Fiedler K (2008) Global-scale modeling of groundwater recharge. Hydrol. Earth Syst. Sci.

12, 863–885.

Döll P, Kaspar F, Lehner B (2003) A global hydrological model for deriving water availability

indicators: Model tuning and validation. J. Hydrol. 270(1–2), 105–134.

Güntner A, Stuck J, Werth S, Döll P, Verzano K, Merz B (2007) A global analysis of

temporal and spatial variations in continental water storage. Water Resour. Res., doi:

10.1029/2006WR005247.

Haddeland I, Skaugen T, Lettenmaier DP (2006) Anthropogenic impacts on continental surface

water ﬂuxes. Geophys. Res. Lett., doi: 10.1029/2006GL026047.

Han SC, Jekeli C, Shum CK (2004) Time-variable aliasing effects of ocean tides, atmosphere, and

continental water mass on monthly mean GRACE gravity ﬁeld. J. Geophys. Res. Solid Earth,

doi: 10.1029/2003JB002501.

Hanasaki N, Kanae S, Oki T (2006) A reservoir operation scheme for global river routing models.

J. Hydrol. 327, 22–41.

Hunger M, Döll P (2008) Value of river discharge data for global-scale hydrological modeling.

Hydrol. Earth Syst. Sci. 12, 841–861.

Lehner B, Döll P (2004) Development and validation of a global database of lakes, reservoirs and

wetlands. J. Hydrol. 296, 1–22.

Monthly and Daily Variations of Continental Water Storage and Flows 415

Mays LW (1996) Water Resources Handbook, McGraw-Hill, New York.

Mitchell TD, Jones PD (2005) An improved method of constructing a database of monthly climate

observations and associated high-resolution grids. Int. J. Climatol. 25, 693–712.

New M, Hulme M, Jones P (1999) Representing twentieth-century space-time climate variability.

Part I: Development of a 1961–90 mean monthly terrestrial climatology. J. Clim. 12, 829–856.

New M, Hulme M, Jones P (2000) Representing twentieth-century space-time climate variabil-

ity. Part II: Development of 1901–96 monthly grids of terrestrial surface climate. J. Clim. 13,

2217–2238.

Rudolf B, Schneider U (2005) Calculation of gridded precipitation data for the global land-

surface using in-situ gauge observations, Proceedings of the 2nd Workshop of the International

Precipitation Working Group IPWG, Monterey October 2004.

Schulze K, Hunger M, Döll P (2005) Simulating river ﬂow velocity on global scale. ADGEO 5,

133–136.

Werth S, Güntner A, Petrovic S, Schmidt R (2009) Integration of GRACE mass variations into a

global hydrological model. Earth Planet Sci. Lett. 277, 166–173.

Calibration of a Global Hydrological

Model with GRACE Data

Susanna Werth and Andreas Güntner

1 Introduction

Since 2002, the US-German satellite gravity mission GRACE (Gravity Recovery

and Climate Experiment) monitors the Earth’s gravity ﬁeld and traces mass redistri-

butions close to the Earth’s surface (Reigber et al., 2005; Tapley et al., 2004). Time

series of global maps of surface mass anomalies are derived from monthly GRACE

gravity ﬁelds represented by coefﬁcients of a spherical harmonic representation.

Due to the global coverage and the previously unrivaled accuracy, GRACE derived

mass variations give insight into processes of the Earth’s subsystems. After removal

of mass variations due to tides and non-tidal atmospheric and oceanic transport pro-

cesses, GRACE time-variable gravity data mainly represent water mass variations

on and beneath the land surface, i.e., total continental water storage change (TWSC)

(see a recent overview by Schmidt et al., 2008a). Therefore, GRACE data are widely

used to improve understanding and modeling of the Earth’s water cycle through the

observation of hydrological mass changes on the continents. For example, previ-

ous studies analyzed the contribution of TWSC to sea level variations (Ramillien

et al., 2008) and the impact of climate variability or extremes on water storage

(e.g. Andersen et al., 2005) or they considered components of the continental water

cycle (evapotranspiration by Ramillien et al., 2006; runoff by Syed et al., 2007;

groundwater in Rodell et al., 2007; snow in Frappart et al., 2006). Other studies

applied TWSC data from GRACE to validate large-scale hydrological models (for a

recent overview see Güntner, 2008). For example, a good general correspondence to

GRACE was found for the WaterGAP Global Hydrology Model (WGHM), though

seasonal TWSC signal amplitudes tend to be smaller in WGHM than in GRACE

(e.g., Schmidt et al., 2006).

Beyond the mere comparison, a new challenge in hydrological modeling is model

improvement by the full integration of GRACE data into the modeling process.

S. Werth (B)

Helmholtz Centre Potsdam GFZ German Research Centre for Geosciences,

14473 Potsdam, Germany

e-mail: swerth@gfz-potsdam.de

417

F. Flechtner et al. (eds.), System Earth via Geodetic-Geophysical Space Techniques,

Advanced Technologies in Earth Sciences, DOI 10.1007/978-3-642-10228-8_36,



Springer-Verlag Berlin Heidelberg 2010

418 S. Werth and A. Güntner

Güntner (2008) recently exposed some of the conditions to be met for a successful

combination strategy. As ﬁrst examples, Zaitchik et al. (2008) assimilated GRACE

TWSC into a land surface model for the Mississippi river basin and Werth et al.

(2009a use GRACE data t o calibrate the global hydrological model WGHM.

In this study, we present the fundamental steps to be performed for the calibra-

tion of the global hydrological model WGHM (Sect. 2.1) using GRACE TWSC

estimations and river discharge data. These steps comprise the selection of ade-

quate calibration parameters (Sect. 2.2), the derivation of GRACE time series at the

scale of river basins with an optimized error budget (Sect. 2.3) and the multi-criteria

calibration approach (Sect. 2.4). Finally, results of the calibration are presented

and analyzed, also with respect to identifying of possible structural model errors

(Sect. 3).

2 Methods

2.1 Hydrological Model

The WaterGAP Global Hydrology Model (WGHM, Döll et al., 2003) is a concep-

tual global water balance model that simulates the continental water cycle with a

daily time-step and a spatial resolution of 0.5

◦

, excluding the regions of Antarctica

and Greenland. Water storage compartments represented in WGHM include canopy,

soil water, snow, groundwater and surface water bodies. In this study, WGHM is

forced by monthly climate data such as air temperature and cloudiness of ECMWF

(European Center for Medium-Range Weather Forecast) and precipitation data of

GPCC (Global Precipitation Climatology Center). Disaggregation of climate data

to the daily modeling time step is done within the model by simple rules. The

basic model version used in this study was calibrated (i.e. tuned) by adjusting a

runoff coefﬁcient parameter against observed river discharge at 1,235 gauging sta-

tions worldwide (Hunger and Döll, 2008). A detailed analysis of spatio-temporal

variations of water storage as simulated with WGHM was given by Güntner

et al. (2007).

2.2 Parameter Sensitivity Analysis

The conceptual equations of WGHM comprise around 30 different parameters that

belong to different hydrological storage and ﬂow processes. In the original model

version, only the runoff parameter was tuned to long-term annual averages of

observed river discharge. All other parameters were ﬁxed to physical or empir-

ical values (Döll et al., 2003). In this calibration study, TWSC as an additional

observable is used besides river discharge to constrain t he simulation results and

to tune additional model parameters. Especially water storage processes t hat are

dominant in a certain river basin are to be considered and respective parameters

to be calibrated. For example, snowfall is negligible in the Amazon basin whereas

Calibration of a Global Hydrological Model with GRACE Data 419

surface water transport is of high importance. In order to select adequate calibration

parameters, a parameter sensitivity analysis for both river discharge and TWSC was

undertaken for WGHM. 2,000 parameter sets were generated with Latin-Hypercube

sampling procedure and the model was run with each parameter set. By analyzing

the impact of each parameter to the model output, process and parameter sensitivi-

ties were found to vary with the region. For example, parameters governing surface

water transport and evapotranspiration are the most sensitive in the Amazon basin.

In river basins in high latitudes, for instance, parameters driving snow accumulation

and melt are among the most sensitive parameters. We also found for many areas

that different parameters were the most sensitive ones for the simulation of water

storage change and river discharge, respectively.

We conclude that depending on the predominant storage compartments, differ-

ent parameter should be calibrated for each river basin. The six most sensitive

parameters to both river discharge and TWSC were selected for the multi-objective

calibration approach. For the Amazon basin, these parameters belong to surface

water processes (runoff coefﬁcient, river velocity and wetland depth), groundwa-

ter (baseﬂow coefﬁcient), soil (rooting depth) and interception (maximum canopy

water height) (see also Werth et al., 2009a).

2.3 GRACE Data and Filter

GRACE data are provided as monthly coefﬁcients of a spherical harmonic repre-

sentation of the gravity ﬁeld. The application of ﬁltering techniques to GRACE

data is indispensable because of errors in the gravity ﬁelds in particular for sig-

nal components of higher harmonic degree, i.e., higher spatial resolution. Filtering

causes a damping of the signal inside the region of interest and the leakage of sig-

nals from outside into the resulting time series for the region of interest (Swenson

and Wahr, 2002). Numerous ﬁlter methods of different assumptions and design with

different error characteristics are available in the literature (see examples below).

A ﬁlter method that provides a reasonable balance of satellite and leakage errors

in the GRACE data is desirable to obtain an optimal separation of errors from the

signal. Applying a standard ﬁlter method (a Gaussian smoother of 500 km ﬁlter

width), Schmidt et al. (2008b) developed a method to determine dominant signal

components of the GRACE signal which were s uccessfully applied by Werth et al.

(2009a) for a calibration of WGHM. In this study, we identiﬁed and used another

ﬁlter method for hydrological model calibration, considering the improvement of

hydrological models and the evaluation of GRACE data as an iterative process.

To this end, we evaluated widely used ﬁlter methods and their parameter by

comparing ﬁltered data sets of GRACE and hydrological models (here WGHM).

Four isotropic and anisotropic methods were analyzed: (1) a standard isotropic

ﬁlter method is the widely-used Gaussian ﬁlter (GF). Designed for gravity ﬁeld

application by Jekeli (1981), its intensity is determined by the ﬁlter width r

, rep-

resenting the radius at which the ﬁlter weighting function declines to 50% of its

maximum value. (2) A ﬁlter (OF) by Swenson and Wahr (2002) minimizes the