Remote Sensing of Environment

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1 Remote Sensing of Environment 115 (2011) Contents lists available at ScienceDirect Remote Sensing of Environment journal homepage: Reconciling the global terrestrial water budget using satellite remote sensing Alok K. Sahoo, Ming Pan, Tara J. Troy, Raghuveer K. Vinukollu, Justin Sheffield, Eric F. Wood Department of Civil and Environmental Engineering, Princeton University, Princeton, NJ, USA article info abstract Article history: Received 16 September 2010 Received in revised form 10 March 2011 Accepted 12 March 2011 Available online 29 April 2011 Keywords: Global terrestrial water budget Remote sensing Water budget closure Recent retrievals of multiple satellite products for each component of the terrestrial water cycle provide an opportunity to estimate the water budget globally. In this study, we estimate the water budget from satellite remote sensing over ten global river basins for We use several satellite and non-satellite precipitation (P) and evapo-transpiration (ET) products in this study. The satellite precipitation products are the GPCP, TRMM, CMORPH and PERSIANN. For ET, we use four products generated from three retrieval models (Penman Monteith (PM), Priestley Taylor (PT) and the Surface Energy Balance System (SEBS)) with data inputs from the Earth Observing System (EOS) or the International Satellite Cloud Climatology Project (ISCCP) products. GPCP precipitation and PM (ISCCP) ET have less bias and errors over most of the river basins. To estimate the total water budget from satellite data for each basin, we generate merged products for P and ET by combining the four P and four ET products using weighted values based on their errors with respect to nonsatellite merged product. The water storage change component is taken from GRACE satellite data, which are used directly with a single pre-specified error value. In the absence of satellite retrievals of river discharge, we use in-situ gauge measurements. Closure of the water budget over the river basins from the combined satellite and in-situ discharge products is not achievable with errors of the order of 5 25% of mean annual precipitation. A constrained ensemble Kalman filter is used to close the water budget and provide a constrained best-estimate of the water budget. The non-closure error from each water budget component is estimated and it is found that the merged satellite precipitation product carries most of the non-closure error Elsevier Inc. All rights reserved. 1. Introduction Quantifying the global terrestrial water and energy cycles is essential for improving our understanding of the coupled climate system, including characterizing the memories and feedbacks between key water and energy components, and thus improving our predictions of large scale weather and climate. These are fundamental goals of the World Climate Research Program (WCRP) Global Energy and Water Experiment (GEWEX), the U.S. National Aeronautics and Space Agency (NASA) Energy and Water Cycle Study (NEWS, 2004), and the U.S. National Oceanic and Atmosphere Agency Climate Program (NOAA, 2009). Furthermore, consistent documentation of the water cycle and its changes over time is needed for improved estimates of the availability of water resources, estimating the risk of hydrologic extremes such as floods and droughts, and understanding of the interactions of the land surface with the atmosphere and climate. In much of the developed world, there is a high level of sophistication in observing systems that incorporate insitu, satellite, model output and other technologies to provide high quality, long-term data records of water cycle variables. The export of these technologies to less developed regions has been rare, but it is Corresponding author. Tel.: address: sahoo@princeton.edu (A.K. Sahoo). these regions where information on water availability and change is most likely needed in the face of regional environmental change due to climate, land use and water management. In these data-sparse regions, in situ data alone are insufficient to develop a comprehensive picture of how the water cycle is changing. Therefore strategies that merge in-situ, model and satellite observations within a framework that results in consistent water cycle records are essential. Such an approach is envisaged by the Global Earth Observing System of Systems (GEOSS) but has yet to be applied (GEO, 2005). Satellite remote sensing is a key component in meeting this goal as it provides unprecedented spatial coverage and resolution, and especially for regions where in-situ measurements are sparse or non-existent. In recent years, retrievals of all components of the terrestrial water cycle have emerged and there is now potential for making continuous global observations of the terrestrial water cycle in real time (Alsdorf & Lettenmaier, 2003). The terrestrial water budget can be defined as the balance between the change in water storage (ΔS) and the difference between the incoming water fluxes of precipitation (P) and outgoing fluxes of evapo-transpiration (ET) and discharge (Q) at the Earth's surface: ΔS = P ET Q Each water budget component in Eq. (1) has different temporal dynamics. For example, precipitation has faster dynamics than storage ð1þ /$ see front matter 2011 Elsevier Inc. All rights reserved. doi: /j.rse

2 A.K. Sahoo et al. / Remote Sensing of Environment 115 (2011) change. Irrespective of the different temporal dynamics of each flux, Eq. (1) holds at any time interval. A number of products from recent and ongoing satellite missions exist that quantify these components, either individually or as an aggregate, at various time and space scales. Global precipitation is retrieved at very high spatial and temporal resolution by combining microwave and infrared satellite measurements (Huffman et al., 2007; Joyce et al., 2004; Kummerow et al., 2001; Sorooshian et al., 2000). Large-scale estimates of ET have been derived by applying energy balance, process and empirical models to satellite derived surface radiation, meteorology and vegetation characteristics (e.g. Fisher et al., 2008; Mu et al., 2007; Sheffield et al., 2010; Su et al., 2007). Time changing total surface and subsurface water storage can be derived from measurements from the Gravity Recovery and Climate Experiment (GRACE) satellites (e.g. Han et al., 2009; Muskett & Romanovsky, 2009; Rodell & Famiglietti, 1999). Satellite based retrievals of discharge can be obtained from altimeter data assimilated into river dynamics models, although these are currently restricted by small swath width and low temporal resolution. Future missions such as the Surface Water Ocean Topography (SWOT; Durand et al., 2010) that uses a Ka-band synthetic aperture radar (SAR) interferometer (KaRIN) will improve on this and provide near global coverage of major rivers and water bodies. Despite the promise of global high resolution monitoring of the terrestrial water budget, there still remain considerable challenges in providing physically consistent and accurate estimates (Sheffield et al., 2009). These include errors resulting from the satellite sensors, the retrieval algorithms, and the spatial (horizontal and vertical) and temporal representativeness of the retrievals. Furthermore, there is great uncertainty among estimates of individual components from different sensors/algorithms (Ferguson et al., 2010) and biases relative to in-situ measurements (Dinku et al., 2008; Sapiano, 2010; Sheffield et al., 2010; Shen et al., 2010). In concert, retrievals of individual components do not close the water budget (Gao et al., 2010; Sheffield et al., 2009). One possible reason is that any single satellite sensor/ instrument does not measure all the water budget components simultaneously. Nevertheless, given the multitude of satellite based products there is potential to evaluate the uncertainties in each individual component and to merge individual estimates into a physically consistent estimate of the global water cycle. In this study, we build on previous work on estimating the largescale terrestrial water cycle from satellite remote sensing (Gao et al., 2010; Sheffield et al., 2009) by reconciling individual biased estimates into a budget closure-constrained best estimate. The questions to be addressed are (1) How well do individual remote sensing retrievals represent P and ET over regional to continental river basins globally? (2) How consistent are the mean water budget closure imbalance attributions to individual water budget components over the globe? (3) Can individual biased estimates be optimally combined to ensure budget closure, given the uncertainties across estimates? We answer these questions by evaluating available satellite products over ten large river basins across the globe. The products are evaluated against in situ measurements and observation constrained model estimates. The individual products are then combined to quantify the budget closure error. Given the lack satellite estimates of river discharge, we use in-situ measurements as the target for water budget closure. Insitu measurements have a relatively low measurement error of the order of less than 10% (Bjerklie et al., 2003) and are thus well suited as a target. Finally we use a constrained filter to optimally merge the products to provide a closure constrained best estimate of the water budget. 2. Study area and period 2.1. Study area We choose ten major river basins that are well-distributed over the globe (Fig. 1) and represent a range of climates. The river basins are the Mackenzie, Yukon, Mississippi, Danube, Lena, Chang Jiang, Mekong, Niger, Murray Darling and Amazon. The Mackenzie, Yukon and Lena are high latitude basins whose hydrology is characterized by a snow-dominated winter season. The Niger and Murray Darling river basins are water limited whereas the Amazon river basin is a very wet system that is energy limited. The Mississippi and Danube are temperature mid-latitude basins. The Chang Jiang is the longest river in Asia and third longest in the world which is fed by glacier melt water. The Mekong is the longest river in the Southeast Asia and the twelfth longest in the world and this river basin is shared by six countries Study period This study is carried out for because of the availability of all the remote sensing satellite products and in-situ discharge measurements for this time period only. The satellite precipitation data are available back to approximately 2002 or earlier depending on the product. However, the majority of the satellite datasets used as Fig. 1. Geographic location of 10 river basins used in this study.

3 1852 A.K. Sahoo et al. / Remote Sensing of Environment 115 (2011) input to the evapo-transpiration products is taken from the National Aeronautics and Space Administration (NASA) Aqua satellite, which has been flying since Terrestrial water storage data are taken from the GRACE satellite (for details, see Appendix A), which are only available since Data and methodology P RS1, P RS2, ET RS1, ET RS2, Merging P in-situ1, P in-situ2, ET model1, ET model2, 3.1. Datasets Multiple satellite remote sensing datasets from various sources are used for each water cycle variable except water storage, which is only available from GRACE. Non-satellite data products that are based on in-situ measurements, off-line modeling or inferred from atmospheric reanalyses are used to estimate uncertainties in the satellite data products. These multiple non-satellite products are merged together by taking their mean for each water budget components and the nonsatellite merged products are assumed to represent our best estimates of each budget term. The uncertainties are then used in the water budget analysis and to merge the satellite datasets to form a best estimate of budget terms under a closure constraint. The datasets are listed in Table 1 with a brief summary below. Details of all the satellite and non-satellite products for each water budget component are given in the Appendix A. Eight precipitation data products (four satellite and four nonsatellite based) are considered. The satellite products are GPCP, TRMM, CMORPH and PERSIANN and the non-satellite products are CPC, CRU, WM and GPCC. Six ET data products are used of which four are satellite-derived products and two are non-satellite products. The satellite products are PM (ISCCP), PM (EOS), PT (EOS), and SEBS (EOS) and the non-satellite products are VIC and ERA-interim inferred. The satellite data products are generated by forcing the PM, PT and SEBS models with input satellite data. The acronyms in parentheses after each ET model indicates the input data source used to generate the ET product. Discharge data are taken from in-situ gauge observations from the Global Runoff Data Center (GRDC, 2010). Terrestrial water storage data are taken from the GRACE satellite products. Even though Eq. (1) holds at any time scale, the GRACE storage data are available at approximately monthly time scale and can only be considered for large river basins because of its coarse spatial resolution. Moreover, the in-situ discharge data are available at basin scale. Therefore, our study is focused on large river basins with monthly time scale due to the lack of availability of the high resolution data products for all components. All the data products are temporally and spatially averaged to monthly and river basin scale respectively Methods P RS, ET RS Q OBS, ds/dt RS Water Balance Constraint P, ET, Q, ds /dt Fig. 2. A flow-chart of the methodology used in this study. Fig. 2 shows a basic flowchart of the analysis. First, the individual satellite data products for P and ET are analyzed, and the uncertainties are calculated with respect to the non-satellite merged product (as explained in Section 3.1) for each river basin separately. All the satellite products (P RS1, P RS2 and ET RS1, ET RS2 ) are then merged together to produce a single satellite-only data product for P and ET (P RS and ET RS ) respectively. Q and ds/dt for each river basin are taken directly from the in-situ measurements (Q OBS ) and the GRACE satellite (ds/dt RS ) respectively for the water budget calculation. There are uncertainties in the river discharge in-situ measurement data because of a number of sources of errors, such as the water level measurements, the rating curves and changes in the channel morphology, which will vary from basin to basin. Without detailed error information for each gauge, we assume that these in-situ discharge measurements are without any bias and they contain 7% RMS error (Dingman, 2002). The terrestrial storage data from GRACE might contain some bias, which depends on the basin and spatial domain, but there is no other large-scale estimate available to evaluate this. Land surface modeling can be used to evaluate GRACE (e.g. Tang et al., 2010), although these models generally do not account for all storage components, such as groundwater. Hence, we consider GRACE to be un-biased and use the standard GRACE error value (Rodell et al., 2004; Table 1 Summary of the gridded datasets used in this study. Our study period is from 2003 to Some datasets may extend beyond our study period. Dataset Start year End year Spatial resolution Temporal resolution Reference GPCP Daily Adler et al. (2003) TMPA 3B42RT 1997 Present h Huffman et al. (2007) CMORPH km (at equator) 30 min Joyce et al. (2004) PERSIANN h Hong et al. (2004) CPC PREC\L 1950 Present 2.5 Monthly Chen et al. (2002) CRU TS Monthly Mitchell and Jones (2005) WM v Monthly Willmott and Matsuura (2010) GPCC Monthly Schneider et al. (2008) PM (ISCCP) h Sheffield et al. (2010) PM (EOS) km Daily Vinukollu et al. (2011) PT (EOS) km Daily Vinukollu et al. (2011) SEBS (EOS) km Daily Vinukollu et al. (2011) VIC h Sheffield and Wood (2007) ERA-interim T h Simmons et al. (2007) GRACE Basin (750 km) ~Monthly Swenson and Wahr (2006) GRDC ~1900 ~2006 Basin Monthly GRDC (2010)

4 A.K. Sahoo et al. / Remote Sensing of Environment 115 (2011) Sheffield et al., 2009). All the estimates for P, ET, Q and ds/dt are then passed through a water budget closure constraint algorithm where the closure constraint is introduced as an error free observation (Pan & Wood, 2006) Merging technique The different satellite estimates of P and ET are merged into single P and ET estimates. The merged estimate is a weighted average of all the satellite products and the weights are determined by their error levels. First, the error variance of each product is calculated using the mean of non-satellite estimates as the truth. The weights are determined by two conditions: (a) the weights sum up to 1; and (b) the weights are proportional to the inverse of the error variances. The weights are calculated as: w i = 1 σ 2 i = n j =1 1 σ 2 j where, w i is the weight for product i, σ i 2 is the error variance of product i, and n is the total number of products to merge. This weighting procedure ensures that the merged estimates have the minimal error variance (Luo et al., 2007) Enforcing water balance constraint The mass balance of water given by Eq. (1) indicates that there is closure among the components. However, it is well known that estimates of the water budget terms from individual sources do not preserve this balance when combined and result in a residual or imbalance term (e.g. Pan & Wood, 2006). The Constrained Ensemble Kalman Filter (CEnKF) has been proposed by Pan and Wood (2006) to impose a linear constraint on the estimates of water balance terms so as to force closure. CEnKF has a convenient two-step design where the first step is applied as a regular Ensemble Kalman Filter (EnKF) and ð2þ the second step (constraining step) is performed separately to make further state updates such that the water balance is closed. Essentially, the constraining works by distributing the imbalance back to all water budget terms according to their error levels and correlations. Water budget terms with larger errors are adjusted more, i.e. more of the imbalance is attributed to them, and vice versa. The CEnKF constraining procedure also works in non-ensemble form (Simon & Chia, 2002), and we apply this procedure after we merge satellite estimates. The final results presented here perfectly close the water balance given by Eq. (1). This provides an improvement over the unconstrained and merged estimates since it imposes a known physical constraint (mass balance) on the data, which cannot be applied to any product individually. 4. Results and discussion 4.1. Estimation of uncertainties in the original RS data We first assess each of the satellite P and ET products against the non-satellite merged products over the ten basins. Fig. 3 shows the mean seasonal cycle of the precipitation products calculated for 2003 to The non-satellite merged dataset is the average of the gaugebased CPC, CRU, WM and GPCC products. There is no spatial coverage for most satellite products at latitudes higher than ±50, therefore only the GPCP satellite product is shown over the Mackenzie, Yukon and Lena river basins. A distinct seasonal cycle (higher precipitation in summer and lower in winter) is shown by all satellite and nonsatellite merged products for all basins except the Murray Darling. The summer precipitation is much higher over low-latitude basins (Niger, Amazon, and Mekong; notice that the scale on the vertical axis is not same for all the basins). The satellite estimates differ significantly for individual river basins though the phase of the seasonal cycles agrees well. For example, the difference between Fig. 3. Mean seasonal cycle of various precipitation products over 10 river basins for the period 2003 to The satellite products are shown in dashed lines and the non-satellite merged product is shown in a solid line. The non-satellite merged product is a combination of all the non-satellite based products: CPC, CRU, WM and GPCC.

5 1854 A.K. Sahoo et al. / Remote Sensing of Environment 115 (2011) TRMM and PERSIANN mean precipitation is more than 70 mm in August over the Niger basin and the difference between the CMORPH and TRMM mean precipitation is more than 60 mm in February over the Danube basin. There is no consistency in the relative order of the satellite estimates datasets across the basins; e. g. TRMM estimates the highest P over the Danube whereas the GPCP estimates the highest P over the Mekong and PERSIANN estimates the highest P over the Niger. All the satellite products overestimate precipitation as compared to the non-satellite merged product. The monthly mean bias (mm month 1 ) ranges between 33 (Mississippi) and 4 (Murray Darling) for TRMM; 33 (Niger) and 7 (Mekong) for CMOPRH; 45 (Niger) and 13 (Danube) for PERSIANN; and 19 (Yukon) and 8 (Amazon) for GPCP. Similarly, the RMSE (mm month 1 ) ranges between 43 (Mississippi) and 17 (Murray Darling) for TRMM; 46 (Niger) and 20 (Chang Jiang) for CMOPRH; 61 (Niger) and 19 (Murray Darling) for PERSIANN; and 29 (Mekong) and 9 (Lena) for GPCP (see Table 2 for the complete list of bias and RMSE values). Among all the satellite precipitation estimates, the GPCP seasonal cycle follows most closely with the non-satellite merged dataset and it has comparatively lower bias and RMSE values (note that the GPCP dataset used here is the non-gauge corrected, satellite only version). Fig. 4 shows the mean seasonal cycle of the ET products calculated for 2003 to The seasonal cycles for the low-latitude basins (Mekong, Amazon and Murray Darling) are not as prominent as in the high latitude basins. The phase of the seasonal cycle is mostly consistent among the products except over the Amazon. The SEBS (EOS) ET product is always higher in the summer months over all basins. The SEBS (EOS) also gives negative ET during the winter months over the high latitude basins whereas the other satellite products estimate nearly zero, but positive, values. Therefore the difference in ET between the summer and winter peaks for the SEBS (EOS) is large over the high latitude basins. The monthly mean bias (mm month 1 ) ranges between 21 (Mekong) and 11 (Danube) for PM(ISCCP); 13 (Yukon) and 30 (Mississippi) for PM (EOS); 22 (Murray Darling) and 17 (Mississippi) for PT (EOS); and 53 (Chang Jiang) and 4 (Mackenzie) for SEBS (EOS). Similarly, the RMSE (mm month 1 ) ranges between 33 (Amazon) and 6 (Mackenzie) for PM (ISCCP); 37 (Mississippi) and 8 (Lena) for PM (EOS); 34 (Mekong) and 7 (Lena) for PT (EOS); and 60 (Chang Jiang) and 25 (Danube) for SEBS (EOS) in mm month 1 (see Table 3 for the complete list of bias and RMSE values). The large differences between the ET products are mainly due to the different sensitivities of each model to forcing uncertainty (Vinukollu & Wood, in preparation). For example, the SEBS model is sensitive to inconsistencies in the air and surface temperature inputs, whereas these are relatively unimportant for the PM model. In terms of partitioning of P into ET and Q, a significant portion of the precipitation water is partitioned to Q over low-latitude basins (Amazon, Chang Jiang and Mekong) whereas a significant portion of P is partitioned to ET over the other basins Merging of the satellite P and ET products The satellite estimates for P and ET show little agreement across the basins, although there is some consistency in the phase of their seasonal cycles. Hence we merge all the satellite products based on their relative uncertainties before estimating water budget. For brevity, we discuss the results in detail only for the Amazon and Mississippi, and provide a summary for the other basins. Figs. 5 and 6 show the merging results for P (left panel) and ET (right panel) over the Mississippi (Fig. 5) and Amazon (Fig. 6) river basins. For the Mississippi (Fig. 5, left panel), the GPCP precipitation is much lower than the other satellite products and is very consistent with the nonsatellite merged P time series over the whole time period. The TRMM estimate exhibits opposite phase during the winter of All the original satellite products estimate low P in the summer of 2006 and the biases for all the satellite products with respect to the nonsatellite merged product are also small during that time period. The seasonality is clearly evident in all the datasets. All the original ET products show a reasonable seasonality over the Mississippi river basin (Fig. 5, right panel) which corresponds to the seasonality seen in the P products. The SEBS (EOS) shows a smaller second peak for ET in the spring season as well. However, the ET estimates differ from each other by considerably large values relative to the differences for P.PM (EOS) has the lowest mean ET (b50 mm month 1 ) whereas the SEBS (EOS) has the highest ET (N100 mm month 1 ; note that the scale has been truncated for clarity). The maximum difference between these two products approaches 110 mm month 1 in the summer. The PM (ISCCP) and PT (EOS) have intermediate ET values. Overall, the PM (ISCCP) ET product is the closest to the non-satellite merged ET dataset. For the Amazon (Fig. 6, left panel), all the satellite P products show reasonable seasonal cycles (higher in summer and lower in winter) compared to the non-satellite merged dataset, although the summer peak for the satellite products (except GPCP) is about 1 2 months earlier. The P seasonal range is very similar across all products except in the summer season of 2004, when the PERSIANN and CMORPH products are high. The ET products over the Amazon are very different from each other (Fig. 6, right panel), in terms of the mean and seasonal cycle. The PM (ISCCP) and SEBS (EOS) ET estimates are much higher than the other products and the difference for these two estimates with respect to the other estimates range in the order of 30 to 50 mm month 1 in winter seasons. These two products show same seasonality and the estimates are similar to each other. The PT (EOS) product has the lowest ET values. It shows a marked seasonal cycle, but in opposite phase to the PM (ISCCP) and SEBS (EOS). The nonsatellite merged product and the PM (EOS) do not show any seasonality but do show a positive trend, which is larger for the PM (EOS) product. For the merged P and ET datasets (Figs. 5 and 6, bottom row), we use four satellite based P and ET products respectively. The shaded Table 2 Bias and RMSE values of different satellite precipitation (P) products with respect to the non-satellite merged product over ten river basins. Bias RMSE TRMM CMORPH PERSIANN GPCP TRMM CMORPH PERSIANN GPCP Mackenzie Yukon Mississippi Danube Lena Chang Jiang Mekong Niger Murray Darling Amazon

6 A.K. Sahoo et al. / Remote Sensing of Environment 115 (2011) Fig. 4. Same as Fig. 3, but for ET. The non-satellite merged product is a combination of all the non-satellite based products: ERA-interim Inferred and VIC. gray area, which envelopes the satellite merged time series, shows the range of the original satellite values that are included in the merged dataset. The pie charts on each graph show the relative contribution of each satellite product to the merged dataset. The merged P time series preserves the seasonality for both basins as seen in the individual P time series. The satellite merged P ranges between 30 and 160, and 80 to 280 mm month 1 for over the Mississippi and the Amazon, respectively. Similarly, the satellite merged ET ranges between 0 and 100, and 70 to 120 mm month 1 for the Mississippi and Amazon, respectively. The range of ET values among the satellite products is larger over both the Mississippi and the Amazon (as shown by the width of the shaded areas). Since the GPCP and PM (ISCCP) products closely follow the non-satellite merged P and ET products respectively over the Mississippi, their contributions to the respective satellite merged datasets are greater than the other Table 3 Bias and RMSE values of different satellite evapo-transpiration (ET) products with respect to the non-satellite merged product over ten river basins. Bias PM (ISCCP) PM (EOS) PT (EOS) SEBS (EOS) RMSE PM (ISCCP) PM PT SEBS (EOS) (EOS) (EOS) Mackenzie Yukon Mississippi Danube Lena Chang Jiang Mekong Niger Murray Darling Amazon satellite products. It is the same for the GPCP P and PT (EOS) ET over the Amazon river basin. Fig. 7 summarizes the results of merging for the satellite P products over the ten basins and the mean relative contribution of each product to the merged dataset. It should be noted that the relative contributions vary from month to month and that can be quite different from the mean relative contributions which is derived for the entire period of 2003 to The GPCP is the only available P product over the high latitude basins (Mackenzie, Yukon and Lena). Hence the satellite merged dataset consists of the GPCP P only. The satellite merged estimates show distinct seasonality over all the basins except Danube and Murray Darling river basins. As expected, the seasonality is opposite (e. g. Amazon and Murray Darling) for the southern hemisphere basins as compared to the northern hemisphere basins. The GPCP is given the highest weight over all basins, ranging between 31 and 61% for basins with multiple available products, reflecting the low bias in the product compared to the non-satellite merged dataset. The range among the satellite P products is much larger over the Mississippi and the Danube throughout the study period. For low latitude basins (Chang Jiang, Mekong, Niger and Amazon) the range is higher in the summer compared to the winter. Fig. 8 shows the corresponding results for the ET products. The ET time series is much smoother as compared to the P time series with distinct seasonality except over the Amazon and Mekong river basins. However, the range among satellite ET products is much larger than the range for P. This indicates that all the satellite products correctly predict the seasonality of ET, but not necessarily the magnitudes. The highest range in ET is found over the Murray Darling basin as shown by the wider shaded area. The ET values are near zero or negative in winter months over the high latitude basins, which is possible because of sublimation of snow, ice and frozen ground. PM (ISCCP) generally contributes the highest and SEBS (EOS) contributes the lowest to the satellite merged dataset.

7 1856 A.K. Sahoo et al. / Remote Sensing of Environment 115 (2011) Fig. 5. Results of precipitation (left panel) and evapo-transpiration (right panel) merging over the Mississippi river basin. The top row shows the original time series and the bottom row shows the merged time series of the original satellite data for P and ET for the period 2003 to The shaded area in the bottom figures shows the range of the values from various satellite products used in the satellite merged product. The inserted pie chart indicated the relative contributions of each P and ET component in the merged product Water balance closure Figs. 9 and 10 show the results for the water budget components and budget closure from the satellite only products for for the unconstrained (left panel) and constrained system (right panel). The respective satellite products are merged together for each water budget component and these merged satellite only water budget components are used to estimate the water budget closure. In the unconstrained system, the water budget calculated using data from various satellites will generally not close because of errors in individual products. In the constrained system, we force the closure of the water budget. The results are again shown for the Mississippi River (Fig. 9) and Amazon (Fig. 10) River basins. The top row shows the fluxes, the middle row shows the terrestrial water storage and the bottom row shows the imbalance after calculating the water budget (Eq. 1). The river discharge data are taken from the in-situ gauge observations, which represent the entire basin. The storage is calculated from the GRACE satellite product and then the standard error value is added to it. There is no bias correction applied to the discharge and storage terms. Over the Mississippi basin, Q is relatively small compared to ET, and P is generally higher than ET+Q, which implies an increase in storage or water balance error. ds/dt shows seasonality over the Mississippi basin with positive storage change in winter and negative change in summer. The change in storage values vary between 60 and 30 mm month 1. When the unconstrained water budget is calculated, it is found that it does not close over the Mississippi. The imbalance varies between about 0 and 70 mm month 1 and shows a seasonal cycle. The positive imbalance derives mostly from the higher P values relative to the other components. These imbalance values are distributed among each water budget component using the CEnKF method as described in Section to give a constrained water budget (Fig. 9, right panel). The readjusted fluxes and storage change values maintain similar seasonal cycles to the unconstrained water budget components but the magnitudes are shifted, indicating that our approach of constraining the water budget components does not alter their behavior. The water budget closure Fig. 6. Same as Fig. 5, but for the Amazon river basin.

8 A.K. Sahoo et al. / Remote Sensing of Environment 115 (2011) Fig. 7. Summary of the results of the merging of satellite P products over all the 10 basins and their mean relative contributions (inserted pie charts) to the merged product. The shaded area in the bottom figures shows the range of the values from various satellite products used in the satellite merged product. results are shown in the bottom right panel of Fig. 9, and shows perfect closure of the water budget. The pie chart reveals the relative attribution of the non-closure error to each water budget component (a higher value indicates a higher contribution of that component to the non-closure error). The majority of the non-closure error is attributable to the P estimate and this is also shown in the adjusted values for P in the upper right panel of Fig. 9 for which the constraint is applied (compare the two P time series in the top row). Fig. 10 shows the results for the Amazon. Again, notice the lack of seasonal cycle in the ET dataset in both the non-constrained and constrained system. The imbalance in the water budget closure is much larger than for the Mississippi (varying between 70 and 50 mm month 1 ). The storage change and water budget closure imbalance show seasonality over this basin. Most of the non-closure error is assigned to the P and ET components. Table 4 summarizes the non-closure for all basins, in terms of the seasonal range in the error. Fig. 11 summarizes the mean water budget non-closure error (imbalance) attribution for all ten basins. The percent values shown in each pie chart are calculated based on the absolute imbalance values and they are not normalized by the respective water budget component values. Very little imbalance is attributed to Q because the in-situ gauge measurements are assumed to have less uncertainty than the satellite products. In contrast, a major portion of the imbalance is attributed to P over all basins, which is up to 55% for the Yukon basin. This is because precipitation is the largest component of the water budget and the uncertainties across satellite products are higher than for other components. The bias correction impacts the magnitude of each water budget component significantly though it closely follows the partitioning ratio of P into ET and Q as we notice in the non-bias corrected case Impact of bias correction on satellite based estimates The seasonal biases for different satellite estimates with respect to the non-satellite merged estimate range very widely for both P and ET as we notice from Figs. 2 and 3 respectively. An obvious question arises: do we need to bias correct the individual satellite products before merging them together to estimate the water budget? In

9 1858 A.K. Sahoo et al. / Remote Sensing of Environment 115 (2011) Fig. 8. Same as Fig. 7, but for ET. another words, what is the impact of the bias correction on the water budget estimated from the satellite products? This section looks at the above question by comparing the original and bias corrected satellite derived results. The satellite products are bias corrected to the nonsatellite merged products for this study. It is reminded that the nonsatellite merged products are based on in-situ measurements for P, and estimates from land surface model simulations and inferred from atmospheric reanalysis for ET. Figs. 12 and 13 compare the water budget imbalance and components calculated from the original (top row) and bias corrected satellite products (bottom row) for the Mississippi (Fig. 12) and Amazon (Fig. 13). The imbalance calculated from the original satellite data is much higher throughout the study period and sometimes exceeds 50 mm month 1 for the Mississippi. In contrast, the imbalance is much lower for the bias corrected satellite products. This indicates that bias correction of the original satellite products helps to remove the higher imbalance values over the Mississippi. However, when the water budget closure constraint is applied in both the cases (removing the imbalance) and the nonclosure error is assigned to the water budget components, the readjusted results for the water budget components exhibit similar temporal variation and the values are not significantly different between the two cases. Over the Amazon (Fig. 13), the imbalance calculated from both the original and bias corrected satellite datasets are very similar to each other. This implies that the bias correction to the satellite products with respect to the non-satellite merged product is unable to remove the higher imbalance over this basin. As expected, the corrected water budget components after the water budget closure is very similar in both cases. It is evident that the bias corrected results are largely influenced by the quality of the non-satellite merged products. In well-instrumented regions like the Mississippi, the non-satellite merged products are relatively accurate, whereas their accuracy in the Amazon is relatively low due to the sparsity of gauges and unique riverine system. This is likely the case for many other parts of the world, especially in underdeveloped countries. On the other hand, the water balance closure constraint applied in this study may not quantify the water budget components correctly if a bias is present in those components prior to applying the water budget closure constraint. For example, if both P and ET are positively and equally biased, these biases would cancel each other in the water

10 A.K. Sahoo et al. / Remote Sensing of Environment 115 (2011) Fig. 9. The results for the water budget closure from the satellite only products for 2003 to 2006 period using the unconstrained (left panel) and constrained system (right panel) for the Mississippi river basin. The top row shows the fluxes, middle row shows the terrestrial water storage and the bottom row shows the imbalance after water budget estimation. The inserted pie chart shows the relative assignment of the non-closure error to various water budget components based on their relative uncertainties. budget to produce zero closure imbalances. In this case, the water budget constraint algorithm assumes that both the P and ET estimates are accurate and will not correct them, resulting in overestimates of these components. It is therefore an open question as to whether we need to bias correct the satellite products prior to applying the water budget closure constraint; knowing that the non-satellite merged products may have large uncertainties themselves and may do little to bias correct the satellite products and the water budget closure constraint might not quantify the uncertainties properly in the satellite products due to the bias. Nevertheless, we use the original satellite products for the water budget closure in this study, because (i) the variability and Fig. 10. Same as Fig. 9, but for the Amazon river basin.

11 1860 A.K. Sahoo et al. / Remote Sensing of Environment 115 (2011) Table 4 Range of water budget non-closure errors at all the ten river basins. Range of WB non-closure error (mm month 1 ) Mackenzie 18 to 32 Yukon 57 to 55 Mississippi 0 to 70 Danube 20 to 42 Lena 60 to 47 Chang Jiang 35 to 50 Mekong 32 to 73 Niger 5 to49 Murray Darling 32 to 43 Amazon 70 to 50 mean of the adjusted water budget components after applying the water budget closure constraint is very similar when using either the original or bias corrected satellite products and (ii) we assume that the uncertainties present in the adjusted water budget components, after imposing the water budget closure, are less than those of the non-satellite merged products that are used to do the bias correction. 5. Conclusion The goal of this study is to estimate the water budget from satellite derived products over ten river basins for the period We have considered multiple remote sensing estimates of precipitation, evapo-transpiration and change in storage. A non-satellite (including in-situ observations, land surface model data, and reanalysis data) merged (assuming zero bias in the non-satellite datasets) product, developed separately for P and ET, has been used as a target dataset to calculate the uncertainties in the satellite products. The seasonal cycles for most of the satellite P and ET products are generally consistent with each other and with the non-satellite merged products. This consistent pattern among the different products is attributed to the similar set of satellite instruments that most algorithms use to estimate the water cycle components. However, there are huge discrepancies in the absolute values among the products, which can be partly attributed to the different retrieval algorithms. All the satellite products tend to overestimate precipitation for most of the basins, especially in the summer. The GPCP P and PM (ISCCP) ET products are found to have less bias and uncertainties over most of the basins. When the water budget is calculated from the satellite products, there is non-zero closure, which is consistent with the findings from earlier satellite based water budget studies (Gao et al., 2010; Sheffield et al., 2009). This non-closure is attributable to a number of factors. The spatial and temporal resolution at which each water budget variable is generated can affect the errors in the individual variables (e.g. Kustas et al., 2004; McCabe & Wood, 2006) as well as mismatches between variables (e.g. the GRACE storage change term has the coarsest spatial and temporal resolution whereas the ET retrievals are generally made at 5 10 km and sub-daily resolution). The GRACE data may also suffer from the leakage of the signal from outside of the basin boundary (Swenson & Wahr, 2006), which will vary from basin to basin depending on size and shape. The dynamic range and Fig. 11. The summary diagram of mean imbalance attribution charts over all the 10 river basins. The percent values shown in each pie chart are calculated based on the absolute imbalance values and are not normalized by the respective water budget component values. See Fig. 1 for the name of the basins.

12 A.K. Sahoo et al. / Remote Sensing of Environment 115 (2011) Fig. 12. Comparison of the water budget imbalance and components calculated from the original (top row) and bias corrected satellite products (bottom row) for the Mississippi river basin. The left panel shows the imbalances and the right panel shows the adjusted water budget components after the water budget closure is applied. uncertainties associated with each retrieval algorithm for each variable can also influence the non-closure. For example, precipitation retrievals from different algorithms show large discrepancies, especially over complex terrain (e.g. Dinku et al., 2008) and for non-convective, wintertime precipitation (Ebert et al., 2007; Gottschalck et al., 2005; Tian et al., 2007). Finally, the differences in input data from different sensors or providers can have large impacts on the retrievals, for example on ET (Ferguson et al., 2010). The magnitude of the non-closure error varies from basin to basin (Table 4). It is greatest over the Amazon and lowest over the Mackenzie, Niger and Danube basins. This may be a reflection of the sparseness of in-situ measurements in the Amazon to which satellite estimates can be calibrated to. In fact, for the Amazon there are large uncertainties in water budget components from ground-based measurements (Costa & Foley, 1998; Fekete et al., 2004), and disagreement between observations, models and reanalyses in precipitation (Adler et al., 2001)and the magnitude of the seasonal cycle of ET (Jimenez et al., 2011). However, there is considerable variation in non-closure errors across the other basins with low error values for the Niger, for example, which is also less well monitored. In high latitudes where observations are also generally sparse and the water budget is complicated by cold season processes, the non-closure error is high for two basins (Lena and Yukon) but the least of all basins for the Mackenzie. Thus there appears to be no consistent relationship between budget closure error and observational density, climate, or even basin size. Irrespective of all the inconsistencies among the various data products, we enforce a water budget constraint scheme to close the water budget as derived from the satellite products and calculate the relative contribution of each water budget component to the closure imbalance error. Our approach ensures the closure of the water budget in this study. The precipitation products provide the largest source of the non-closure error, suggesting that the satellite precipitation has the largest uncertainties among the three satellite merged products. The attribution of most of the non-closure error to the precipitation component is very consistent across all the basins. This is a reflection of the spatial and temporal variability of precipitation and the difficulty in obtaining accurate retrievals from satellite measurements that have low temporal repeat sampling (e.g. Hossain & Anagnostou, 2004; Nijssen & Lettenmaier, 2004; Steiner et al., 2003) and are reliant on conversion of radiances to rain rates (McCollum et al., 2002). Discharge tends to have the lowest contribution to non-closure error, which is generally because of the relatively low uncertainties that are assigned based on literature values. The contribution of ds/dt is comparable to that of P, and even larger in the Lena basin, where the seasonal cycle of discharge is dominated by the spring snow melt (Troy & Wood, 2010), implying that uncertainties in the change in storage are important. There is a wide range of biases across the satellite estimates with respect to the non-satellite merged estimate. Therefore, we verified the impact of bias correction on our water budget calculation error. Fig. 13. Same as Fig. 12, but for the Amazon river basin.

13 1862 A.K. Sahoo et al. / Remote Sensing of Environment 115 (2011) The results indicate that the impact of bias correction depends on how skillful and accurate our target non-satellite merged estimate is over any river basin. Many continental river basins (especially in the least developed regions such as in Africa) do not have extensive in-situ observation networks and therefore, the non-satellite merged estimate over those basins might carry larger uncertainties, as discussed above for the Amazon. Thus, the bias correction to the satellite estimates based on the non-satellite merged product may not have any impact over those basins. The biases and random errors in the satellite estimates can be reduced through calibration, which will lead to a reduction in the budget closure error. For precipitation, satellite estimates can be calibrated to gauge measurements and this has been done for the algorithm calibration for the real-time version of the TRMM estimates in For ET, this is more problematic because of the lack of largescale measurements, although modeled and infrared data can be used as a target for calibration in regions where there is confidence in their estimates. However, our merging technique is robust and independent of whether the datasets are calibrated or not. To conclude, this study provides initial estimates of the closed water budget from satellite only products over ten continental river basins. We believe that these estimates from the merged satellite products carry significant amounts of information about the water cycle in these basins and can be used as the basis for monitoring, climate change analysis and diagnostic studies. Further work is needed to understand and attribute the source of the large discrepancies among different estimates (satellite, in-situ, model and reanalyses) of the water budget components in order to improve water budget closure further at basin to continental scales and identify where improvements to satellite retrieval systems are most needed. Acknowledgements This study is supported by National Aeronautics and Space Administration under Grants NNX08AN40A and NNX09AK35G to Princeton University. We thank the anonymous reviewer for the constructive comments to improve this manuscript. Appendix A. Datasets Appendix A.1. Precipitation Appendix A.1.1. GPCP The Global Precipitation Climatology Project (GPCP) Version 2.1 precipitation product is a merged product that includes the low-orbit satellite microwave, geostationary infrared and surface rain gauge observations of precipitation (Adler et al., 2003). The detailed merging technique is described in Adler et al. (1993). The data are available from 1979 to present, however the data prior to 1987 do not include any microwave observations. This global monthly data product is provided at spatial resolution. The product includes a satellite only dataset (without any gauge correction) as well, which we use in this study. Appendix A.1.2. TMPA 3B42RT The TRMM (Tropical Rainfall Measuring Mission) Multi Satellite Precipitation Analysis (TMPA) precipitation product is based on a combination of the observations from the Low Earth Observing (LEO) microwave (MW) and Geosynchronous Earth Orbit (GEO) infrared (IR) satellite estimates (Huffman et al., 2007). The product is 3-hourly, gridded dataset covering the region from 50 N to 50 S latitude lines. The microwave data produce better estimates of the precipitation due to their stronger relationship to precipitation, but they are coarse in space and time whereas the infrared data produce lower quality estimates, but at finer space time scale. Hence, the product first uses the microwave data wherever they are available and then fills in the areas with the IR datasets (Habib et al., 2009). TMPA produces two datasets: one is bias corrected (3B42v6) and the other is in real time without any gauge correction (3B42RT). We use the 3B42RT data product in this study. Appendix A.1.3. CMORPH CPC (Climate Prediction Center) Morphing Technique (CMORPH) products are derived using a morphing algorithm. First, this technique produces propagation vector matrices by computing spatial lag correlations on successive geostationary satellite infrared images and uses these propagation vectors to propagate the microwave derived precipitation estimates (Joyce et al., 2004). This technique only propagates the precipitation features, but performs timeweighting interpolation between the propagated features to determine the shape and intensity of the precipitation feature. This is a merging technique and is very flexible in its nature. The CMORPH products are available from 60 N to 60 S at fine spatial (0.08 ) and temporal (30 min) resolutions. Appendix A.1.4. PERSIANN Precipitation Estimation from Remotely Sensed Information using Artificial Neural Networks (PERSIANN) precipitation product is derived by merging various low altitude polar orbiting satellites from NASA, NOAA and DMSP and Geostationary infrared imagery using artificial neural network approach (Hsu et al., 1999; Sorooshian et al., 2000). The algorithm first extracts and classifies local texture features from the infrared images to a number of texture patterns, and then it associates those classified cloud texture patterns to the surface rainfall rates. PERSIANN model parameters are then adjusted from passive microwave rainfall estimates. PERSIANN precipitation product covers from 50 N to 50 S at 0.25 spatial resolution and hourly temporal resolution. Appendix A.1.5. CPC unified gauge dataset The CPC (Chen et al., 2002) precipitation dataset is created using a reconstruction technique where the precipitation over land (PREC/L) is derived by interpolating observations from around 17,000 stations collected in Global Historical Climatology Network (GHCN), and the Climate Anomaly Monitoring System (CAMS) datasets and the precipitation over ocean (PREC/O) is derived by EOF reconstruction of historical observations. The optimal interpolation (OI) algorithm is used for the interpolation of the observations over the land. The monthly data are available at spatial resolution from 1948 to present. Appendix A.1.6. CRU The Climate Research Unit (CRU) of the University of East Anglia (UK) produce a dataset of monthly surface-based climate parameters. Precipitation is one of the parameters included in that dataset which is generated from the available gauge datasets. The number of available precipitation gauges varies over the years: in 1901, 4957 gauges contribute to the dataset, peaking in 1981 with 14,579 gauges. The CRU inserts synthetic zero anomaly values in regions that are too far from observations (i.e. farther than 450 km), while the other schemes simply interpolate over the entire distance (New et al., 2000; Mitchell & Jones, 2005). The data are provided at 0.5 resolution globally. Appendix A.1.7. WM Cort Willmott and Kenji Matsuura (WM) of the University of Delaware produce a climatic data product from a large number of stations, both from the GHCN and from the archive of Legates and Willmott (1990). The data product includes monthly climatology and a monthly time series from 1900 to 2006 of the surface precipitation and air temperature. It is a land-only product. The data product is being improved continuously with better spatial interpolation