Abstract
 Top of page
 Abstract
 1. Introduction
 2. Method of Analysis: Water Mass Balance Equation
 3. Data Used in This Study
 4. Results
 5. Summary
 Acknowledgments
 References
 Supporting Information
[1] Since its launch in March 2002, the Gravity Recovery and Climate Experiment (GRACE) mission has been measuring the global time variations of the Earth's gravity field with a current resolution of ∼500 km. Especially over the continents, these measurements represent the integrated land water mass, including surface waters (lakes, wetlands and rivers), soil moisture, groundwater, and snow cover. In this study, we use the GRACE land water solutions computed by Ramillien et al. (2005a) through an iterative inversion of monthly geoids from April 2002 to May 2004 to estimate time series of basinscale regional evapotranspiration rate and associated uncertainties. Evapotranspiration is determined by integrating and solving the water mass balance equation, which relates land water storage (from GRACE), precipitation data (from the Global Precipitation Climatology Centre), runoff (from a global land surface model), and evapotranspiration (the unknown). We further examine the sensibility of the computation when using different model runoff. Evapotranspiration results are compared to outputs of four different global land surface models. The overall satisfactory agreement between GRACEderived and modelbased evapotranspiration prove the ability of GRACE to provide realistic estimates of this parameter.
1. Introduction
 Top of page
 Abstract
 1. Introduction
 2. Method of Analysis: Water Mass Balance Equation
 3. Data Used in This Study
 4. Results
 5. Summary
 Acknowledgments
 References
 Supporting Information
[2] Temporal change of evapotranspiration (ET) provides precious indications of the global water cycle and climate change, as well as important boundary conditions for climate models. Unfortunately, there are no globalscale in situ measurements of ET. Algorithms for deriving ET from the raw satellite observations require locationspecific calibration, making them very difficult to apply globally. In global land surface models (LSMs), ET is modeled through different empirical approaches, e.g., using the Penman equation [de Marsily, 1981], through parameterization of the latent heat flux [Ducoudré et al., 1993; Milly and Shmakin, 2002] according to the bulk equation introduced by Monteith [1963]. At large scales, the temporal distribution of ET is a function of climatic conditions, soil moisture availability, the vegetation type as well as the area of the surface water (wetlands and rivers). These surface conditions are poorly known for globalscale modeling. Existing models provide substantially dissimilar estimates at monthly, seasonal and even annual timescales [Verant et al., 2004].
[3] Recent results of the total land water storage based on the GRACE (Gravity Recovery and Climate Experiment) space mission [Rodell and Famiglietti, 1999; Tapley et al., 2004; Wahr et al., 2004; Schmidt et al., 2006; Ramillien et al., 2005a] suggest that the variations of continental water storage are mainly seasonal and the largest amplitudes are located in the large tropical basins of Africa and South America, in the South East Asia during monsoon events, as well as in the highlatitude regions of the Northern hemisphere due to the snow. These patterns are consistent with those provided by global LSMs, such as the water gap global hydrology model (WGHM) [Döll et al., 2003], the land dynamics model (LAD) [Milly and Shmakin, 2002], the Global Land Data Assimilation System (GLDAS) [Rodell et al., 2004a] and the organizing carbon and hydrology in dynamics ecosystems model (ORCHIDEE) [Verant et al., 2004]. Rodell et al. [2004b] computed time series of ET over the Mississippi River basin, using the land water information from the monthly GRACE geoids combined with precipitation and runoff data. Rodell et al. [2004b] showed that the GRACEderived ET is comparable to the estimates provided by the ECMWF (European Center for Medium range Weather Forecasting) reanalysis and the GLDAS models.
[4] In this paper, we compute time variations of basinscale ET rates (and associated uncertainties) by time integrating, and then solving, the water mass balance equation, using land water solutions derived from GRACE [Ramillien et al., 2004, 2005a] and independent information on precipitation and runoff. We present estimates of ET, and associated errors, for sixteen drainage basins from April 2002 up to May 2004. For validation, we compare the ET estimates with predictions from global LSMs.
2. Method of Analysis: Water Mass Balance Equation
 Top of page
 Abstract
 1. Introduction
 2. Method of Analysis: Water Mass Balance Equation
 3. Data Used in This Study
 4. Results
 5. Summary
 Acknowledgments
 References
 Supporting Information
[5] For a given watershed, the instantaneous equation of the water mass balance is
where P, , R are precipitation, water mass storage and runoff respectively. These terms are generally expressed in terms of water mass (mm of equivalent water height) or pressure (kg/m^{2}) per day. Time integration of equation (1) between times t_{1} and t_{2} (the starting and the ending dates of the considered period, with Δt = t_{2} − t_{1}, assumed to be ∼30 day, the average time span over which the GRACE geoids are provided) gives
In equation (2) above, ET is expressed in mm/day. If we have highfrequency sampled data (e.g., daily data for precipitation), the classical method of the “rectangle” summation has been applied to integrate precipitation P and runoff R over the Δt time interval. ΔW is the variation of the water mass inside the drainage basin area between t_{1} and t_{2}. This term is directly computed as the difference between two monthly GRACE solutions:
The GRACEbased land water solutions computed by Ramillien et al. [2005a] are spherical harmonics of a surface density function F(θ, λ, k) that represents the global map of W:
In equation (4), θ and λ are colatitude and longitude, k is a given monthly solution. n and m are degree and order, _{nm} is the associated Legendre function, and C_{nm}^{F}(t) and S_{nm}^{F}(t) are the normalized coefficients of the decomposition. In practice, the spherical harmonic development cutoff N used for the land water solutions of Ramillien et al. [2005a] is limited to degree 30. This corresponds to a spatial resolution of 660 km.
[6] Instead of using the “timepiecewise” approach proposed earlier by Rodell et al. [2004b] that requires highfrequency data (and those were not available) to evaluate equation (3), we linearly approximate the water mass variations of month ‘k’ as
Missing monthly land water solutions data (due to the lack of GRACE geoids) are simply interpolated from the previous and the next months.
[7] Precipitation and runoff data are provided as monthly grids of 1° × 1° (see section 3). Thus to be consistent with the land water solutions, we develop gridded P and R data into spherical harmonics, lowpass filter at degree 30 and recompute gridded data using equation (4).
[8] Sixteen river basins are considered in this study. Their location is shown in Figure 1. The contour of each basin is based on a mask of 0.5° resolution from Oki and Sud [1998]. For each month ‘k’, gridded ΔP, ΔR, and ΔW are spatially averaged over each river basin according to:
where F_{k} represents either ΔP, ΔR or ΔW. δλ and δθ are grid steps in longitude and latitude respectively (generally δλ = δθ), and R_{e} is mean Earth's radius (∼6378 km).
[9] Once each quantity is averaged spatially, it is easy to compute mean ET using equation (2). Monthly ET values were further divided by a factor of 30 to convert the unit of mm/month into mm/day.
[10] As equation (2) is linear and neglecting interpolation errors in equation (5), one can easily compute associated absolute errors from the relative uncertainties ɛ_{P} and ɛ_{R} on P and R respectively:
σ_{W} is the total error for a single month GRACE solution. Relative uncertainty on precipitation fields ɛ_{P} is assumed ∼11% [Rodell et al., 2004b]. However, modeled runoff data are much more uncertain, especially in large lowland watersheds such as the Amazon basin. In situ measurements of Amazon discharges vary by 30%: observed annual averages are 155,000 m^{3}/s [Vörösmarty et al., 1996], and 170,000–200,000 m^{3}/s [Dunne et al., 1998; Mertes et al., 1996; Meade et al., 1991].
[11] Regional runoff from different models, even for wellconstrained regions like in the US, can vary up to a factor of four [Lohmann et al., 2004]. This suggests the situation must be worse elsewhere. Thus we considered ∼30% as realistic values for ɛ_{R}.
[12] Wahr et al. [2004] estimated σ_{W} to be ∼18 mm for 750 km spatial average GRACEbased land water solutions. Ramillien et al. [2005b] found σ_{W} ∼ 15 mm for the final a posteriori uncertainties on the land water solutions, at the spatial resolution of 660 km. As we use a geographical mean to average the land water signal over each basin, _{W} < 1 mm. Thus, for each monthly estimate, the contribution of the land water to the total budget error (equation (7)) should be no much than 0.07 mm/day.
4. Results
 Top of page
 Abstract
 1. Introduction
 2. Method of Analysis: Water Mass Balance Equation
 3. Data Used in This Study
 4. Results
 5. Summary
 Acknowledgments
 References
 Supporting Information
[23] Figure 2 presents GRACEbased ET time series for each of the 16 selected river basins. The ET estimates presented in Figure 2 use the WGHM runoff for the computations. For comparison, are also plotted modelbased ET (from WGHM, GLDAS, LAD and ORCHIDEE). In view of the short time span considered here, the signal is dominated by the seasonal signal. Maximum of the ET seasonal cycle occur in July for Northern hemisphere river basins and in January in the Southern hemisphere. These are in the range 3–4 mm/day for all basins (at the spatial resolution of ∼660 km). These GRACEbased ET seasonal variations are consistent with model predictions as well as observations. In the central Amazon basin for example, a 3.6 mm/day seasonal amplitude was found by Costa and Foley [1999].
[24] Table 1 presents the results of statistical comparisons between GRACEderived and modelbased ET. The RMS (rootmeansquare) differences are averaged over the overlapping months over the 2002–2004 period. In general, RMS differences between GRACEbased and modelbased ET are less than 1 mm/day, except for the Brahmaputra watershed, a relatively small basin, where RMS differences range from 1.46 to 1.65 mm/day. The lowest RMS difference is found with the ORCHIDEE model over the Mississippi basin (∼0.29 mm/day rms). This result for the Mississippi basin is comparable with that from Rodell et al. [2004b]. These authors derived a time series of the ET rate changes by lowpass filtering the GRACE geoids according to the Wahr et al. [1998] method. They also found a good agreement with the GLDAS model for monthly means (∼0.83 mm/day rms) (spatial resolution of 750 km). As this basin is well covered by field observations, this comparison confirms the great value of GRACE for estimation ET.
Table 1. Statistical Comparisons Between the Time Series of the GRACEBased ET Rate (This Study) and the ET Rate Values Provided by Four Global Land Surface Models (GLDAS, LAD, ORCHIDEE, and WGHM) for Each Studied Basin for Bias and RMS Differences and Comparisons for Amazon and Mississippi Basins Using Different Runoff Data as Input (WGHM and LAD)Basin  GRACE Versus 

GLDAS  LAD  ORCHIDEE  WGHM 

Bias, mm/d 

Amazon  0.23  −0.31  0.5  0.37 

Amur  −0.13  −0.15  0.36  0.09 

Brahmaputra  0.32  −0.37  0.7  0.21 

Congo  0.02  −0.48  0.33  1.77 

Danube  −0.09  −0.26  0.39  0.38 

Ganges  −0.11  −0.64  0.1  0.15 

Hwang Ho  −0.03  −0.43  0.09  0.06 

Mekong  0.08  −0.68  0.43  0.09 

Mississippi  −0.16  −0.59  0.25  0.07 

Niger  0.39  −0.11  0.36  0.37 

Nile  −0.16  −0.59  0.25  0.14 

Ob  −0.23  −0.26  0.2  −0.12 

Parana  −0.04  −0.46  0.77  0.35 

Volga  −0.11  −0.1  0.41  0.02 

Yangtze  −0.11  −0.44  0.6  0.07 

Yenisey  −0.18  −0.05  0.38  0.04 



RMS, mm/d 

Amazon  0.8  0.65  0.46  0.78 

Amur  0.61  0.59  0.4  0.42 

Brahmaputra  1.46  1.47  1.65  1.3 

Congo  0.5  0.58  0.5  0.55 

Danube  0.99  0.97  0.6  0.7 

Ganges  0.66  0.97  0.71  0.6 

Hwang Ho  0.43  0.5  0.42  0.36 

Mekong  0.53  0.49  0.75  0.6 

Mississippi  0.48  0.49  0.29  0.32 

Niger  0.45  0.95  0.55  1.34 

Nile  0.48  0.49  0.29  0.64 

Ob  0.75  0.94  0.34  0.82 

Parana  0.46  0.66  0.53  0.47 

Volga  0.99  0.9  0.55  0.85 

Yangtze  0.53  0.51  0.53  0.41 

Yenisey  0.75  0.73  0.5  0.75 

Runoff  GRACE Versus 

GLDAS  LAD  ORCHIDEE  WGHM 

RMS, mm/d 
WGHM(Mississippi)  0.48  0.49  0.29  0.32 
LAD (Mississippi)  0.53  0.53  0.33  0.35 
WGHM (Amazon)  0.8  0.65  0.46  0.6 
LAD (Amazon)  0.91  0.64  0.6  0.77 
[25] In order to test the impact of the R model values to compute ET (and associated uncertainties), we consider two different river basin cases: the Amazon basin which suffers from lack of observations (we then assume the model error is large in this region), and the Mississippi basin which is well covered by in situ data (thus error on R should be small).
[26] We present GRACEbased ET values using monthly runoff data from two different models (WGHM and LAD) in Figures 3a and 3b. As seen on Figures 3a and 3b, considering LAD runoff produces higher ET than using WGHM runoff: the mean difference between WGHM and LAD curves is a constant bias over the considered time span (1.5 mm/day and 0.40 mm/day for Amazon and Mississippi basins respectively). Besides, the ET rate obtained by using WGHM runoff remains the closest to the mean value proposed by Costa and Foley [1999] for the Amazon River basin.
[27] Figures 4a and 4b present ET uncertainties (equation (7)) for the two basins (Amazon and Mississippi). As expected by the accuracy of the model runoff in these two regions, extreme errors (1.8 mm/day, ∼50% relative error) are found in the Amazon basin. In the case of the Mississippi basin, the maximum error reaches ∼0.55 mm/day (around June 2003) that corresponds to 20% of the amplitude of ET rate. Accuracy of the ET rate estimates should be clearly improved when the quality of the input runoff data from models increases.