The increasing availability of remote sensing products for all components of the terrestrial water cycle makes it now possible to evaluate the potential of water balance closure purely from remote sensing sources. We take precipitation (P) from the TMPA and CMORPH products, a Penman-Monteith based evapotranspiration (E) estimate derived from NASA Aqua satellite data and terrestrial water storage change (ΔS) from the GRACE satellite. Their combined ability to close the water budget is evaluated over the Mississippi River basin for 2003–5 by estimating streamflow (Q) as a residual of the water budget and comparing to streamflow measurements. We find that Q is greatly overestimated due mainly to the high bias in P, especially in the summer. Removal of systematic biases in P reduces the error significantly. However, uncertainties in the individual budget components due to simplifications in process algorithms and input data error are generally larger than the measured streamflow.
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 Quantifying the terrestrial water budget over large spatial scales is key to understanding the availability of water resources, the potential for hydrologic extremes such as floods and droughts, and the interactions of the land surface with the atmosphere and climate. However, obtaining water balance components from ground based measurements alone remains a challenge, in terms of both accuracy and in achieving budget closure. This is especially true at larger scales and in less developed regions, where the paucity of gauges and measurement stations, and their inherent inaccuracies, generally prevents budget closure. To overcome this, retrievals from remote sensing have the potential to provide spatially continuous estimates of components of the terrestrial water cycle over regional to global scales [Alsdorf and Lettenmaier, 2003]. An outstanding science question is whether these individual component estimates are of sufficient accuracy to provide budget closure and thus give reliable information about the variation of the terrestrial water cycle?
 The terrestrial water budget is composed of the fluxes of precipitation (rain and snowfall), evapotranspiration (soil and canopy water evaporation, plant transpiration and snow sublimation), and runoff (surface and subsurface flow), together with storage on the land surface (snow pack, vegetation canopy, lakes, wetlands, rivers, etc) and subsurface (soil moisture, groundwater). These components are related through equation (1) which states that the fluxes of precipitation (P), evapotranspiration (E) and runoff (Q) are balanced by the change in water storage (S) at the Earth's surface:
 There exist a multitude of products from recent and current satellite missions that quantify these components, either individually or as an aggregate estimate, at various time and space scales [McCabe et al., 2008]. Precipitation is regularly retrieved from multi-sensor microwave and infrared data, using a variety of techniques [e.g., Huffman et al., 2007; Joyce et al., 2004]. Evapotranspiration can be estimated from considerations of the surface energy balance given remote sensing inputs of net radiation and surface meteorology [Su et al., 2005] and initial large scale estimates are becoming available [e.g., Mu et al., 2007]. Changes in total surface and subsurface storage can be derived using gravity anomaly measurements [Swenson and Wahr, 2002]. Streamflow and surface water storage can be estimated using laser altimetry and interferometric synthetic aperture radiometry technologies [Alsdorf and Lettenmaier, 2003].
 This paper presents first estimates of the large scale terrestrial water budget purely from remote sensing sources. We focus on the Mississippi basin in the central U.S., one of the best observed continental-scale regions globally, and for which model based and reanalysis estimates of the various budget components are also available for comparison. Assessments are made for the period 2003–5 that spans part of the Earth Observing System (EOS) era and the availability of retrievals for most components of the water budget. We take precipitation from the Tropical Rainfall Measuring Mission (TRMM) Multi Satellite Precipitation Analysis (TMPA) [Huffman et al., 2007] and the CMORPH [Joyce et al., 2004]. Total water storage is taken from the Gravity Recovery and Climate Experiment (GRACE). Evapotranspiration is calculated using a remote sensing Penman-Monteith based approach (RS-PM) [Mu et al., 2007] using EOS radiation and surface meteorology. Streamflow is relatively accurately monitored for the Mississippi using in-situ gauge measurement, and as no regular remote sensing based retrievals are made for this river, we use this as a target for budget closure. Elsewhere in the world, remote sensing retrievals of water stage and streamflow are likely the only feasible method, especially for regions dominated by wetlands, seasonal inundation and dynamic channeling [Alsdorf et al., 2007] and certainly for ungauged rivers.
 We first evaluate each of the remotely sensed datasets against observations and off-line data taken from the North American Land Data Assimilation System (NLDAS) and atmospheric reanalysis data taken from the North American Regional Reanalysis (NARR). We then use the remotely sensed data to calculate the runoff as a residual of the water budget and compare this to gauge measurements. Finally we evaluate the error in budget closure using estimated errors for each component, either from given instrument error estimates or calculated based on errors relative to the best estimates available from observations and models. This work is a first step in understanding the potential of remote sensing to accurately quantify the terrestrial water cycle over large scales and perform budget closure from independent data sources.
2. Data and Methods
2.1. Remote Sensing Products
 The TMPA [Huffman et al., 2007] combines multiple satellite estimates of precipitation and gauge analyses into a set of 0.25-degree, 3-hourly products. The datasets cover 50°N–50°S and are available from 1998. Although a combined gauge product (3B42) which is scaled to monthly gauge data does exist, we use the real-time product (3B42RT) which is based on satellite data only and thus reflects our ability to monitor over data sparse regions and in real time.
 The CMORPH method [Joyce et al., 2004] blends microwave based precipitation estimates with infra-red imagery to produce half-hourly, 8 km (at the equator) fields, with 3-hourly, 0.25-degree data available back to 2002. The infra-red imagery is used to propagate the data in time between available retrievals of relatively high quality passive microwave estimates, whilst morphing the shape and intensity of the precipitation features through interpolation.
 The GRACE satellite [Tapley et al., 2004] has been monitoring changes in the Earth's gravity field since its launch in 2002 by measuring the distance between two orbiting satellites. Variations in these fields can be attributed to changes in terrestrial water storage after removal of atmospheric and ocean bottom pressure changes [Tapley et al., 2004]. We use the University of Colorado CSR RL04 time series of approximately 30-day mass anomalies for the Mississippi using a 750km Gaussian half-width averaging kernel [Wahr et al., 1998].
 Remote sensing estimates of daily E were derived following the revised RS-PM formulation presented by Mu et al.  which is based on the Penman-Monteith equation [Monteith, 1965]. Inputs of radiation, meteorology and vegetation characteristics are taken from remote sensing data from the Atmospheric Infrared Sounder (AIRS), the Clouds and the Earth's Radiant Energy System (CERES), and the Moderate Resolution Imaging Spectroradiometer (MODIS) aboard the NASA Aqua platform. Instantaneous estimates of E are calculated at the satellite overpass time (1:30pm local time) and then extrapolated to daily values assuming a constant daytime evaporative fraction [Crago and Brutsaert, 1996] and using hourly net radiation data from the NLDAS, which are based in part on modeled data. An ensemble of estimates that represents the uncertainty in the remote sensing inputs was generated by using combinations of inputs from different sensors. Full details of the implementation of the RS-PM approach are given elsewhere [Ferguson et al., 2008].
2.2. Comparison Data
 The NLDAS [Mitchell et al., 2004] runs multiple land surface models, including the VIC model, forced by an observation-based meteorological dataset at 1/8th degree for the conterminous U.S. The NLDAS precipitation is merged from the Climate Prediction Center daily gauge analyses and National Weather Service Stage II gauge-radar data. We use the NLDAS P and VIC estimates of Q, E and S to evaluate the remote sensing products. VIC simulation parameters were recently updated using the calibration method of Troy et al.  which matches simulated runoff to a distributed estimate of actual runoff, based on U.S. Geological Survey (USGS) observations for 1130 small basins across the U.S. The VIC simulated output therefore offers reasonable estimates of the water budget components.
 The NARR [Mesinger et al., 2006] is an atmospheric-land reanalysis from 1979 to present and covers the North American continental region and surrounding ocean area at a spatial resolution of 32km. We use the atmospheric data (moisture convergence, precipitable water and P) to infer E as a residual of the atmospheric water budget.
 Daily streamflow measurements from the U.S. Army Corps of Engineers (USACE) for the Vicksburg gauging station on the Mississippi river are used as the target for budget closure. We also compare against the USGS small basin data that were interpolated by Troy et al.  to the whole continental U.S. using monthly runoff ratios calculated with NLDAS precipitation.
 For all evaluations except those involving the GRACE data, the time scale is the calendar month. The GRACE data are given as mass anomalies for approximately 30-day observation periods at irregularly spaced intervals. Calculations involving the GRACE data must therefore take into account these unique temporal sampling characteristics. We calculate the change in storage (ΔS) as the difference between two GRACE data points which represents the average change in storage between the observation periods. Following Rodell et al. , corresponding values of P, E and Q are calculated as the average of the set of running mean accumulations of daily values, of length equivalent to the difference in the dates of the two GRACE observations, which fall between the two observation periods.
 We first evaluate each of the remote sensing products against observations, model data and reanalysis. Figure 1 shows monthly time series for 2003–5 of P, E, Q and ΔS averaged over the Mississippi basin. For precipitation, the two remote sensing products are generally biased high relative to NLDAS, especially in the summer. The biases are 1.2 and 0.7 mm day−1 for the TMPA and CMORPH, respectively. RMS errors are 1.4 and 1.3 mm day−1, respectively. During the winter, there is somewhat better agreement but large spread among the two products. The TMPA has the highest bias in the winter. The evaporation estimates from VIC and NARR (inferred) show good agreement (bias = 0.1 mm day−1, rmse = 0.3 mm day−1). They are both forced by essentially the same precipitation (the NARR assimilates gauge precipitation that has commonality with the NLDAS gauge data inputs), but otherwise are independent. The RS-PM ensemble mean data are also in good agreement with the VIC and NARR data. They are slightly higher in the winter and peak later in the summer, and are therefore slightly lower in the early summer and higher in the late summer. The monthly bias is 0.1 mm day−1 and rmse is 0.3 mm day−1 relative to VIC.
Figure 1 also shows Q for VIC and observations from the USACE Vicksburg measurements and the USGS small basin gridded data. The VIC model is calibrated against the gridded data and thus shows a good match [Troy et al., 2008]. The match with the USACE Vicksburg data is reasonable, with some overestimation because the USACE data includes water management effects (which tend to reduce flow) that are not included in the VIC model. These comparisons provide confidence in the VIC estimates of E and ΔS. Lastly, the time series of ΔS is shown and indicates a reasonable correspondence between VIC and GRACE, although the amplitude of the VIC seasonal cycle tends to be larger, especially in the summertime (likely due to spatial leakage in the GRACE signal and lack of accounting for reservoir effects in the VIC model), also noted by Tang et al.  for two western U.S. basins.
 Runoff as derived as a residual of the land water budget (equation (1)) using the remote sensing estimates of P, E and ΔS is shown in Figure 2, and compared to the USACE streamflow measurements. The data values are calculated for the GRACE observation times. The residual values greatly overestimate the measured data (bias = 1.4 mm day−1, rmse = 1.7 mm day−1) and VIC data (bias = 1.3 mm day−1, rmse = 1.6 mm day−1), in part because of the overestimation by TRMM and CMORPH in the summer. The lower amplitude of the GRACE ΔS relative to VIC also contributes to the overestimation, although there is greater uncertainty in the true value of ΔS compared to uncertainty in the true value of P (see hereafter). The small overestimation of E by the RS-PM method relative to the VIC and NARR tends to reduce the high bias in the residual Q.
 To further quantify the source of the error in the inferred Q values, and thus the budget non-closure, we look at the errors in the individual components and their combined total error (Figure 3). Each of the remotely sensed products is in error because of the accuracy of the instrument, the sampling characteristics of the orbital path and resolution, and the errors and simplifications in the retrieval algorithm and temporal scaling. The total error in the basin averages (ignoring uncertainties due to the distribution of errors at the sub-basin and daily scale) is made up of systematic bias and random error:
where X is the true value, X′ is the remote sensing estimate, b is the bias and ɛ is random error. For the TRMM and CMORPH P, there is an obvious positive bias, especially in the summer (Figure 1). For the RS-PM E, the bias is systematic (except for the summer of 2003) but small. For ΔS, the GRACE data show a slight underestimation in the summer and winter relative to VIC, although there seems to be no systematic bias. We remove the systematic bias in the remote sensing estimates of P and E to see how much improvement is made to the residual Q estimate. The term b is estimated as the mean difference from the NLDAS estimate for P over a 30-day moving window. This is subtracted from the remote sensing estimate and the residual Q is recalculated (Figure 2, blue line). The bias and rmse of the bias corrected data relative to the VIC residual Q are 0.02 mm day−1 and 0.5 mm day−1 (equivalent to approximately 59,000 and 1,475,000 ML day−1, respectively).
 The remaining random error is assumed to be normally distributed with standard deviation derived from the uncertainty in the different remote sensing products. For P, this is taken as the difference between the bias corrected versions of TRMM and CMORPH, and for E as the difference in the upper and lower bounds of the RS-PM ensemble (in the absence of an alternative remote sensing method for estimating E). For GRACE we use the absolute error value given by Tapley et al.  of 25 mm for a 750km kernel half width which represents the quadrature sum of the errors in two GRACE anomaly solutions that are required to calculate the change in storage. 95% confidence limits on the residual Q are calculated as ±2σ, where σ is the standard deviation of the random errors, which are applied as relative errors to each term of equation (1). Following Rodell et al. , the relative error in Q is the quadrature sum of errors in each component:
where υX is the relative error (absolute error/exact value) in component X.
 To show the contribution of each remote sensing component to the overall error and uncertainty in the residual streamflow estimate, Figure 3 shows the residuals and 95% uncertainty estimates using all the remote sensing inputs (P bias corrected) as well as when using each remote sensing input on its own with the other components taken from VIC. The range in uncertainty for the total error is between 0.4 and 2.9 mm day−1, with the largest errors coming from GRACE (up to 2.4 mm day−1) and the least in the combined TRMM/CMORPH data (up to 1.4 mm day−1). The best fit to the USACE data are when using only E from remote sensing (bias = 0.1 mm day−1, rmse = 0.3 mm day−1), although the uncertainty during the summer is quite large (up to 1.9 mm day−1), especially when compared to the mean USACE streamflow of 0.5 mm day−1.
4. Summary and Conclusions
 We have used remote sensing estimates of precipitation, evapotranspiration and change in storage to calculate the closure of the terrestrial water budget for the Mississippi basin for 2003–5. Comparison of the individual budget terms with observations, off-line model estimates and atmospheric reanalysis at monthly scales indicates large overestimation by the two precipitation products, especially in the summer. For evapotranspiration, the RS-PM ensemble mean is comparable to the VIC and NARR inferred values, whilst the uncertainty, given by the ensemble spread, encompasses the VIC and NARR values. The VIC and GRACE values of ΔS are generally similar with the latter having a smaller amplitude. Although part of these differences may be because the VIC model does not take into account changes in groundwater, the uncertainties in the GRACE data are generally much greater. Water budget closure using only remote sensing data was evaluated by calculating streamflow as the residual of the water budget equation, which showed a large overestimation of measured streamflow, due mainly to the overestimation of precipitation. After removal of systematic biases in P, the budget non-closure was greatly reduced. The remaining uncertainty due to instrument and retrieval error, data processing and input uncertainty was estimated for each component and may account for the remaining budget non-closure. However, the total uncertainty was generally greater than the measured streamflow. We conclude that achieving budget closure from remote sensing is not possible at this time, due to large biases in remotely sensed precipitation and large uncertainty in remotely sensed terrestrial water storage. This is likely also the case for other regions and when using other products. Continued improvements in remotely sensed products, such as the recently released gauge-calibrated real time TMPA, may however, reduce the non-closure. Additionally, data assimilation may offer a potential way forward, especially when it incorporates a closure constraint [Pan and Wood, 2006].