Satellite monitoring of changes in terrestrial water storage provides invaluable information regarding the basin-scale dynamics of hydrological systems where ground-based records are limited. In the Bengal Basin of Bangladesh, we test the ability of satellite measurements under the Gravity Recovery and Climate Experiment (GRACE) to trace both the seasonality and trend in groundwater storage associated with intensive groundwater abstraction for dry-season irrigation and wet-season (monsoonal) recharge. We show that GRACE (CSR, GRGS) datasets of recent (2003 to 2007) groundwater storage changes (ΔGWS) correlate well (r = 0.77 to 0.93, p value < 0.0001) with in situ borehole records from a network of 236 monitoring stations and account for 44% of the total variation in terrestrial water storage (ΔTWS); highest correlation (r = 0.93, p value < 0.0001) and lowest root-mean-square error (<4 cm) are realized using a spherical harmonic product of CSR. Changes in surface water storage estimated from a network of 298 river gauging stations and soil-moisture derived from Land Surface Models explain 22% and 33% of ΔTWS, respectively. Groundwater depletion estimated from borehole hydrographs (−0.52 ± 0.30 km3 yr−1) is within the range of satellite-derived estimates (−0.44 to −2.04 km3 yr−1) that result from uncertainty associated with the simulation of soil moisture (CLM, NOAH, VIC) and GRACE signal-processing techniques. Recent (2003 to 2007) estimates of groundwater depletion are substantially greater than long-term (1985 to 2007) mean (−0.21 ± 0.03 km3 yr−1) and are explained primarily by substantial increases in groundwater abstraction for the dry-season irrigation and public water supplies over the last two decades.
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 The Gravity Recovery and Climate Experiment (GRACE) [Tapley et al., 2004] offers the opportunity to monitor monthly changes in total terrestrial water storage (ΔTWS) via satellite observations at regional scales starting from April 2002 [Cazenave and Chen, 2010]. ΔGWS is estimated from GRACE-derived ΔTWS after deducting the contribution of changes in remaining terrestrial water stores including soil moisture (ΔSMS), surface water (ΔSWS), and ice and snow (ΔISS) over a particular time period (t) (equation (1)):
 GRACE measurements record large-scale variations in ΔTWS. The application of GRACE measurements to space-limited areas (e.g., river basin) is associated with both bias (i.e., amplitude damping from mass inside the basin) and leakage (i.e., sensitivity to masses outside the basin) [Chambers, 2006; Swenson and Wahr, 2006; Klees et al., 2007; Longuevergne et al., 2010]. Multiplicative [Swenson and Wahr, 2006] and additive [Klees et al., 2007] approaches to account for bias and leakage have been developed using a priori information on terrestrial distributions in water stores derived from Land Surface Models (LSMs). Such data processing methods for GRACE data are critical when the basin area (Bengal Basin ∼138,000 km2) marginally exceeds the limits in the resolution (∼100,000 km2) of GRACE observations [Longuevergne et al., 2010].
 The Bengal Basin of Bangladesh and West Bengal (India) (Figure 1), the largest river delta in the world [Shamsudduha and Uddin, 2007], is an ideal location to test the robustness of GRACE-derived estimates of ΔGWS in the humid tropics for four reasons. First, the basin features dense networks of ground-based, surface water and groundwater level monitoring stations with which to resolve and test estimates of ΔGWS from ΔTWS [Shamsudduha et al., 2009; Steckler et al., 2010]. Second, a basin-wide database of storage coefficients, derived from 279 pumping-test records [Bangladesh Water Development Board, 1994; Shamsudduha et al., 2011], enables conversion of groundwater-level observations to ΔGWS. Third, substantial intra-annual (seasonal) and interannual changes in groundwater storage (see auxiliary material Figures S1 and S2 for dry and wet-season groundwater levels in Bangladesh) occur as a result of intensive groundwater abstraction for dry-season irrigation and wet-season (monsoonal) recharge [Shamsudduha et al., 2011]. Fourth, the basin's area in Bangladesh (∼138,000 km2) is around the limit in the resolution of GRACE observations. In addition, the Bengal Basin provides a representative case study for other Asian Mega-Deltas for which detailed ground-based monitoring records are unavailable.
 Here, we test the ability of GRACE satellite measurements to trace intra-annual (seasonal) and interannual ΔGWS in a highly seasonal, tropical humid hydrological system, the Bengal Basin, over the period of January 2003 to December 2007 using in situ (ground based) observations of groundwater levels [Shamsudduha et al., 2009] and distributed specific yield estimates [Shamsudduha et al., 2011]. Critically, we resolve contributions of ΔSWS and ΔSMS to ΔTWS using in situ observations of ΔSWS from a network of 298 river-level monitoring stations across Bangladesh [Steckler et al., 2010] and simulations of ΔSMS from three Land Surface Models (LSMs) (CLM, NOAH, VIC) provided by the Global Land Data Assimilation System (GLDAS) [Rodell et al., 2004]. Further, we evaluate the robustness of different GRACE data processing methods for resolving ΔGWS in a highly seasonal, tropical humid basin where variations in the dry and wet-season groundwater levels are substantial (mean annual amplitude 5.4 ± 2.6 m). Finally, we place estimates of recent (2003 to 2007) trends in ΔGWS in the context of long-term trends (1985 to 2007) derived from long-term in situ observations.
2. Datasets and Methods
2.1. GRACE Datasets
 In this study, we use both postprocessed gridded GRACE datasets and spherical harmonic (SH) products, provided by the Centre for Space Research (CSR) and Groupe de Recherche en Géodesie Spatiale (GRGS), to derive ΔGWS in the Bengal Basin. Gridded files include: (1) a monthly, 1° × 1° CSR GRACE time series data set masked over the Bengal Basin in Bangladesh (land grid version “ss201008”; see http://grace.jpl.nasa.gov/data/; hereafter referred to as CSR GRID) [Swenson and Wahr, 2006] wherein bias and leakage are compensated using a scaling factor to restore GRACE TWS signal amplitude for each grid; and (2) a 10 day, 1° × 1° GRGS GRACE time series data (version RL02; see http://grgs.omp.obs-mip.fr; hereafter referred to as GRGS GRID) [Lemoine et al., 2007; Bruinsma et al., 2010]; no scaling factor is applied for the GRGS GRID data. The scaling coefficients provided for each 1° bin of the CSR GRID data are intended to restore much of the energy removed by destriping, filtering, and truncation processes [Swenson and Wahr, 2006]. Unlike CSR GRID monthly data, GRGS GRID products do not require additional filtering [Biancale et al., 2006; Lemoine et al., 2007; Ramillien et al., 2008; Tregoning et al., 2008; Bruinsma et al., 2010]. SH-based products (hereafter referred to as CSR SH for CSR and GRGS SH for GRGS products) are processed based on methods described by Longuevergne et al. . Bias and leakage are calculated using the additive hypothesis of Klees et al. . In the Bengal Basin, GRACE error amounts to 5 cm and is estimated by computing variability in the oceans at the same latitude and by propagating LSM error into leakage corrections according to Longuevergne et al. . The estimated error might be slightly overestimated as variability in the oceans may still contain geophysical signals. We convert the 10 day GRGS GRID solutions to a monthly time series by taking the average values in order to directly compare them with other GRACE solutions used in this study. Missing GRACE TWS data in CSR (June 2003) and GRGS (January, February, and June 2003) time series products were imputed (i.e., infilling of missing values) using linear interpolation and monthly mean values.
2.2. Borehole Hydrograph and Groundwater Storage
 We use weekly time series records of borehole hydrographs from a subset of 236 shallow (mean well depth of 30 m below ground level (bgl)) monitoring wells (see auxiliary material Figure S3 for borehole location) to assess changes in the groundwater storage over two periods (January 2003 to December 2007; January 1985 to December 2007). The first period represents recent changes in groundwater storage that are directly comparable to satellite observations under GRACE. The second period represents the longest period of groundwater storage changes for which observational records of high quality (mean missing record <4.3%) and density are available.
 The annual range (annual maxima – annual minima) in observed groundwater levels or hydraulic heads in the regionally unconfined shallow aquifer (<100 m bgl) in the Bengal Basin is translated into an equivalent groundwater depth (GWD) to derive in situ ΔGWS. Groundwater levels in shallow aquifers in Bangladesh reach the peak around September following rain-fed recharge through the monsoon season after their deepest levels observed toward the end of dry-season irrigation [Shamsudduha et al., 2011]. Estimates of in situ ΔGWS are compared with GRACE-derived estimates according to equation (2) wherein is the trend in GWD and A is area of the same grid cells (n = 27) within the Bengal Basin of Bangladesh over which time series measurements of GRACE ΔTWS and ΔSMS data were collated:
 is calculated at each monitoring location using specific yield value and range in annual groundwater levels according to equation (3):
 Similar to GRACE-derived ΔGWS estimates we apply both linear (August to October) and multiple linear trends to estimate in situ ΔGWS over the entire Bangladesh. Spatially distributed values derive from 279 pumping test records [Shamsudduha et al., 2011] are applied across Bangladesh (see auxiliary material Figure S4 for the location of pumping test and spatial distribution of ). The mean value of the estimated in Bangladesh is 0.06 (range 0.01 to 0.2) with a standard deviation of 0.04. In light of uncertainty in values of in Bangladesh [Michael and Voss, 2009], we compare this estimates derived from distributed values with an upper limit uniform value of 0.10; such a high value (0.12) has similarly been applied regionally [Rodell et al., 2009] where in situ derived values are absent.
2.3. Surface Water Storage and Soil Moisture
 ΔSWS used in our analysis refers primarily to flood-water loads and river storage as there are no irrigation dams or reservoirs in Bangladesh [Water Resources Planning Organization, 2000]. The Bengal Basin in Bangladesh is, however, flood prone. Areas of up to one third of the country (∼48,000 km2) are inundated by flood water each year and two thirds of the country may be under water during extensive flood years [Steckler et al., 2010]. We generate monthly time series data of ΔSWS of a spatial resolution of 1° × 1° using daily river-stage observations from 298 monitoring stations throughout Bangladesh (auxiliary material Figure S5 for seasonal variations in the in situ ΔSWS). This procedure involves: (1) conversion of daily river-stage records to mean monthly time series; (2) interpolation (applying the Inverse Distance Weighting method using the GSTAT package in R programming language) of mean monthly river-level records (point data) over the entire Bangladesh on a regular grid size of 0.05° × 0.05°; (3) subtracting gridded surface water level data from a resampled 300 m digital elevation model data on a regular grid size of 0.05° × 0.05°, and (4) aggregating interpolated values over a larger grid size of 1° × 1° (n = 27) over a period of January 2003 to December 2007 to generate mean monthly time series of ΔSWS.
 Soil moisture is often the dominant contributor to ΔTWS variability in warm and temperate regions [Rodell et al., 2009]. We apply monthly time series soil moisture records from three simulations of the Global Land Data Assimilation System (GLDAS) [Rodell et al., 2004]. Time series records of ΔSMS of a spatial resolution of 1° × 1° derived from three LSMs such as CLM (v. 2) [Dai et al., 2003], NOAH [Ek et al., 2003], and VIC [Liang et al., 2003]. The total depth of ΔSMS in CLM (10 layers), NOAH (4 layers), and VIC (3 layers) models are 3.4 m, 2.0 m, and 1.9 m, respectively. In the absence of in situ ΔSMS data we use the ensemble mean of 3 LSMs-derived time series data to represent ΔSMS in the Bengal Basin; a similar approach was used to estimate ΔGWS in northwestern India by Rodell et al.  and central valley of California by Famiglietti et al. . None of these LSMs, however, includes groundwater storage [Dai et al., 2003; Rodell et al., 2004] or a specific module for surface water routing.
2.4. Disaggregation of GRACE ΔTWS
 Disaggregation of GRACE ΔTWS into GRACE-derived ΔGWS is carried out differently for GRID and SH products. For CSR GRID and GRGS GRID, we derive temporal changes in groundwater storage, ΔGWS, over the basin area (∼138,000 km2) in Bangladesh by (1) extracting GRACE ΔTWS, ΔSMS, and ΔSWS time series (January 2003 to December 2007) records for each 1° × 1° grid cell (n = 27; see auxiliary material Figure S6 for location), and (2) averaging these time series signals from all grids and applying the equation (1). Note that ΔSMS represents changes in soil moisture storage in all soil horizons and ΔSWS includes river and flood water storage. Changes in freshwater storage derived from ice and snow (ΔISS) are negligible in Bangladesh and not considered in this study. For CSR SH and GRGS SH, ΔGWS is resolved differently to reduce the propagation of uncertainties from bias and leakage variations on surface water and soil moisture. Equation (1) is applied to GRACE SH solutions to derive ΔGWS estimates. Bias (due to signal loss in internal water mass) and leakage (due to contribution from water mass outside of basin area) corrections are applied to GRACE-derived estimates of ΔGWS following the method described in the work of Longuevergne et al. . This method, however, requires information on ΔSMS and ΔSWS mass distribution in inside and outside of the basin area. The same filtering used for GRACE solutions (truncation at degree 60 and a 300 km Gaussian smoothing for CSR SH, truncation at degree 50 for GRGS SH) is applied to ΔSMS and ΔSWS before subtracting from the raw GRACE data (uncorrected for bias and leakage). Both spatial extent and mass variations in ΔSWS are known for the Bengal Basin. To account for temporal and spatial mass variability of ΔSWS outside of the Bengal Basin we use a global-scale model of surface water extent [Papa et al., 2010].
 Linear and multiple linear trends were estimated from the basin-averaged GRACE derived ΔGWS. Linear trends (i.e., simple linear regression) in ΔGWS were calculated using data from the latter part of the wet season (August to October) of each year as these represent net changes in groundwater storage after the dry-season irrigation for high-yielding rice (“Boro”) (Figure 1) cultivation and monsoon recharge have taken place [Shamsudduha et al., 2011]. Estimates of linear trend in observed ΔGWS can be biased by the strong seasonality (dry and wet season variations) present in the time series records. To capture the highly seasonal structure in the ΔGWS signal, multiple linear trends (i.e., multiple linear regression) were calculated through the annual means of time series where, in addition to time (t), both sine and cosine functions of time are included as covariates; where T is the total number of time unit (month) in the complete seasonal cycle of the time series. Other approaches to separate seasonality from trend and residual components in the time series (e.g., seasonal-trend decomposition based on filtering procedure) can be applied but accurate, bias-free (due to seasonality) decomposition will require longer time scales [Cleveland et al., 1990; Shamsudduha et al., 2009].
Figure 2 shows monthly time series anomalies in all GRACE derived ΔTWS, simulated ΔSMS from 3 LSMs and their average, observed groundwater levels and river-stage levels, and average monthly rainfall in Bangladesh for the period of January 2003 to December 2007. ΔTWS signals derived from basin-averaged gridded GRACE products (CSR GRID, GRGS GRID) compare favorably (r > 0.94, p value < 0.0001) with ΔTWS derived from GRACE SH data applying a basin function (CSR SH and GRGS SH) over the Bengal Basin in Bangladesh. Mean annual amplitudes in ΔTWS between 2003 and 2007 are 51 cm (CSR GRID), 52 cm (GRGS GRID), 49 cm (CSR SH) and 58 cm (GRGS SH). Although GRACE ΔTWS solutions are highly correlated, the amplitude is less well constrained and can vary by up to 15%. Variability among GRACE ΔTWS solutions (3.5 cm) is, however, within the estimated GRACE error (5 cm). The leakage correction error for the defined basin area is large and accounts for 3.5 cm of the estimated GRACE error.
 Substantial variations in magnitude are observed between ΔSMS signals derived from three LSMs (Figure 2c) and introduce considerable uncertainty in recovering ΔGWS from ΔTWS. The mean seasonal amplitude in ΔSMS varies among the LSMs: 8 cm (CLM), 26 cm (NOAH) and 20 cm (VIC). At the outset of the monsoon season, ΔSWS rises quickly whereas ΔGWS responds more slowly with a lag of ∼1 month to ΔSMS (Figure 2d). Overall, variations in individual water stores compare well with observed variability in monthly rainfall (Figure 2e). Figure 3 shows that the strong seasonality associated with the unimodal (monsoonal) distribution in annual rainfall is reflected in mean monthly time series records of GRACE-derived ΔTWS, modeled ΔSMS, and in situ ΔSMS and ΔGWS.
 Estimates of ΔGWS over the period of 2003 to 2007 from observed borehole hydrographs, and all GRACE datasets are plotted in Figure 4. Changes in groundwater storage over the period of 2003 to 2007, estimated from GRACE data sets and borehole (in situ) hydrographs, are strongly correlated (Figure 4; Table 1). The highest Pearson correlation (r = 0.93, p value < 0.0001) is observed between in situ ΔGWS and CSR SH derived ΔGWS time series. Time series records of ΔGWS derived from GRGS SH are also strongly correlated (r = 0.89, p value < 0.0001) to in situ ΔGWS in Bangladesh. Pearson correlations between in situ ΔGWS and GRGS (GRID and SH) derived ΔGWS are slightly lower than CSR datasets but cross-correlation analysis reveals that improved correlations (Table 1) are achieved by employing a time lag of 1 month in the time series (Table 1). The 1 month phase lag in time series of ΔGWS between GRGS-derived estimates and observed records in the highly seasonal hydrological system of Bengal Basin can be attributed to the leakage correction in GRACE processing methodologies. Phases of ΔSMS and ΔSWS time series are in advance with respect to ΔGWS and a slight error in leakage correction can introduce such a time lag. Calculated uncertainty in GRACE-derived ΔGWS, represented in Figure 4, results from 16 possible estimates (4 GRACE solutions × 4 ΔSMS estimates derived from 3 LSMs and the mean of these).
Table 1. Pearson Correlation Between Time-Series Data of Groundwater Storage Derived From Borehole and GRACE Measurementsa
In all pairs, the p value of correlation is <0.0001 suggesting statistically significant association. GWS Sy(dist) = borehole derived GWS with distributed Sy values; GWS Sy(0.10) = borehole derived ΔGWS with a uniform Sy of 0.10; and GWS Sy(mean) = borehole derived ΔGWS with the national mean Sy of 0.06.
Correlation coefficients between all GRACE-derived ΔGWS and borehole-derived ΔGWS for various Sy values (distributed, 0.10, and national mean of 0.06) are approximately the same. Application of different Sy to estimate ΔGWS from in-situ groundwater levels at the national scale only affects the annual amplitude of ΔGWS anomaly.
Values within brackets are correlation coefficients with a lag of 1 month.
 Linear trends and their standard errors in estimates of GRACE-derived and in situ ΔGWS averaged over the Bengal Basin in Bangladesh are summarized in Tables 2 and 3. Standard error in the simple linear regression is a measure of error (uncertainty) of an estimated coefficient (slope of trend line). Linear trends in wet-season (August–October) groundwater levels represent changes in ΔGWS as wet-season groundwater levels reflect groundwater storage after monsoonal recharge has taken place. The trend (January 2003 to December 2007) in ΔGWS based on wet-season groundwater levels is −0.52 ± 0.30 km3 yr−1 (± standard error of linear trend estimate) using distributed values; this rate of groundwater depletion increases to −1.06 ± 0.59 km3 yr−1 if a uniform value of 0.1 is applied. Multiple linear trends in annual means represent net changes in ΔGWS that can be influenced by declining groundwater levels or increased seasonality over time associated with increased groundwater-fed irrigation during the dry season. These in situ ΔGWS estimates therefore produce slightly higher rates of groundwater depletion (−0.85 ± 0.17 to −1.61 ± 0.32 km3 yr−1). GRACE-derived estimates of ΔGWS losses using a simulated mean ΔSMS range from −0.44 ± 1.24 to −2.04 ± 0.79 km3 yr−1 for wet-season trends and −0.52 ± 0.50 to −2.83 ± 0.42 km3 yr−1 based on trends in annual means.
Table 2. Trends (km3 yr−1) in Groundwater Storage Changes (ΔGWS) in the Bengal Basin of Bangladesh Derived From Borehole Hydrographsa
Linear Trends (Wet Season) With Distributed Sy
Linear Trends (Wet Season) With a Uniform Sy = 0.1
Multiple Linear Trends (Time-Series) With Distributed Sy
Multiple Linear Trends (Time-Series) With a Uniform Sy = 0.1
Linear trends were calculated in the wet-season (August to October) groundwater levels and multiple linear trends through the annual means. Pumping-test derived distributed specific yield (Sy) values and a maximum value of 0.1 were applied for these estimates.
−1.60 ± 0.38
−3.08 ± 0.69
−1.30 ± 0.22
−2.53 ± 0.41
−0.52 ± 0.30
−1.06 ± 0.59
−0.85 ± 0.17
−1.61 ± 0.32
−0.21 ± 0.03
−0.44 ± 0.06
−0.23 ± 0.02
−0.46 ± 0.03
Table 3. Trends (km3 yr−1) in Groundwater Storage Changes (ΔGWS) in the Bengal Basin of Bangladesh Derived From GRACE TWS Dataa
Linear Trends in Wet-Season Levels
Multiple Linear Trends in Annual Means
Note: CLM – Cumulative Land Model soil moisture; NOAH – NOAH model soil moisture; and VIC - Variable Infiltration Capacity model soil moisture; AvgSMS – Average soil moisture of three LSMs.
Linear trends (wet-season levels) and multiple linear trends (annual means) were calculated after separating soil moisture (ΔSMS) and surface water (ΔSWS) storages from GRACE-derived ΔTWS.
CSR GRID Derived Estimates
−3.37 ± 1.03
−3.89 ± 1.04
−3.50 ± 1.24
−3.59 ± 1.04
−3.39 ± 0.60
−2.79 ± 0.63
−3.03 ± 0.71
−3.07 ± 0.62
−1.06 ± 1.02
−1.83 ± 0.95
−2.57 ± 0.93
−1.82 ± 0.92
−2.21 ± 0.46
−2.33 ± 0.48
−2.53 ± 0.53
−2.36 ± 0.46
GRGS GRID Derived Estimates
−1.64 ± 1.31
−2.17 ± 1.46
−1.77 ± 1.34
−1.86 ± 1.32
−2.28 ± 0.74
−1.68 ± 0.83
−1.92 ± 0.83
−1.96 ± 0.77
+0.32 ± 1.26
−0.45 ± 1.37
−1.18 ± 1.20
−0.44 ± 1.24
−1.05 ± 0.59
−1.16 ± 0.66
−1.36 ± 0.63
−1.19 ± 0.60
CSR SH Derived Estimates
−3.81 ± 0.99
−4.34 ± 0.93
−3.94 ± 0.87
−4.03 ± 0.85
−4.07 ± 0.60
−3.47 ± 0.55
−3.72 ± 0.65
−3.75 ± 0.57
−1.28 ± 0.97
−2.05 ± 0.87
−2.79 ± 0.67
−2.04 ± 0.79
−2.69 ± 0.47
−2.80 ± 0.40
−3.00 ± 0.47
−2.83 ± 0.42
GRGS SH Derived Estimates
−1.59 ± 1.12
−2.11 ± 1.30
−1.72 ± 1.29
−1.82 ± 1.18
−1.22 ± 0.79
−0.62 ± 0.75
−0.87 ± 0.76
−0.91 ± 0.74
−0.19 ± 0.86
−0.96 ± 0.91
−1.70 ± 0.86
−0.95 ± 0.82
−0.38 ± 0.52
−0.49 ± 0.52
−0.69 ± 0.53
−0.52 ± 0.50
 Short-term changes in ΔGWS, estimated over the period for which GRACE data are available, are highly sensitive to the length of the time series. For example, trends in ΔGWS estimated for a shorter (2003 to 2006) period are nearly twice that calculated for the period of 2003 to 2007 (Tables 2 and 3). Long-term (1985 to 2007) trends derived from in situ ΔGWS rates are considerably lower (−0.21 ± 0.03 to −0.23 ± 0.02 km3 yr−1) than those calculated over the period of GRACE observations. The estimation of in situ ΔGWS from borehole hydrographs enables the identification of areas of rising and falling groundwater storage over both short (2003 to 2007) and long (1985 to 2007) periods of observation (Figure 5). Over both periods, there are decreasing trends in ΔGWS in central and northwestern parts of Bangladesh and rising trends in southwestern and coastal regions. Relative to long-term terms, trends in recent in situ ΔGWS have reversed in northern areas and intensified in central and northwestern regions.
 Intra-annual (seasonal) variations and interannual trends in ΔGWS derived from both gridded GRACE and GRACE SH datasets in the tropical, humid Bengal Basin compare very well with estimates of in situ ΔGWS derived from borehole observations (Table 1, Figure 4). Similarity in the signals of in situ and GRACE time series records of ΔGWS is characterized using their correlation coefficients, centered root-mean-square (RMS) difference and amplitude of variations (represented by standard deviations) and represented graphically in Figure 6 [Taylor, 2001]. High correlation coefficients (r > 0.85, p value < 0.0001) and low RMS error (<5 cm) suggest that all CSR GRACE datasets (both gridded and SH) closely match in situ observations among the GRACE-derived ΔGWS estimates. There are, however, a number of sources of uncertainty and underlying assumptions that are inherent to both techniques. Estimation of in situ ΔGWS assumes: (1) trends in groundwater levels do not result from inhomogeneities in observation records; and (2) values of used to convert groundwater levels to ΔGWS, are representative of the monitored aquifer. Estimation of GRACE-derived ΔGWS assumes: (1) an accurate estimate of ΔSMS contribution from LSMs and ΔSWS from observations to recover ΔGWS; and (2) water storage is well described by LSMs inside the area of interest and in the surrounding area to estimate bias and leakage effects. The second point is not obvious in a highly seasonal basin featuring large spatial and temporal variability in (water) mass. For example, variability among LSMs is not substantially reduced following the application of filters to GRACE data; variability expressed as a standard deviation that is 6.5 cm for raw LSM data, becomes 4.0 cm and 5.1 cm under CSR-like and GRGS-like filters, respectively. GRACE solutions consequently suffer from the propagation of uncertain storage variability (different for CSR and GRGS solutions) surrounding their region of interest. Indeed, this problem may explain the noted differences in seasonal amplitudes and leads to larger RMS error in ΔGWS recovery (6 cm) relative to the amplitude of seasonal variations (20 cm).
 Another difficulty in trend estimation in this region relates to leakage of glacier melt from the Himalayas [Matsuo and Heki, 2010]. Forward modeling indicates that leakage of glacial mass changes (+2%) from the Himalayas into the Bengal Basin region for the CSR solution whereas for the GRGS solution it is the reverse (−1%). The difference in sign may be explained by the hard truncation for the GRGS solution. Although the value is small, a large glacier mass loss of ∼50 cm yr−1 [Matsuo and Heki, 2010; Bolch et al., 2011] induces mass changes of + 1.38 km3 yr−1 for CSR GRACE data and −0.69 km3 yr−1 for GRGS GRACE data into the Bengal Basin. This explains why estimated trends in ΔGWS derived from GRGS (SH and GRID) data are systematically smaller than those for CSR (SH and GRID) data.
 Uncertainty in simulated ΔSMS associated with the choice of LSM (GLDAS) for GRACE disaggregation also contributes substantially (standard deviations from CLM, NOAH and VIC models are 3, 11, and 8 cm, respectively) to overall calculated uncertainty in ΔGWS. Seasonal variability in simulated ΔSMS is observed in LSMs derived time series datasets (auxiliary material Figure S7). NOAH model derived ΔSMS represents the greatest seasonal variability (i.e., annual amplitude) whereas CLM-derived ΔSMS shows the least seasonal variation. Our estimated ΔSMS (ΔTWS - ΔGWS - ΔSWS) shows strong correlations (r = 0.83, p value < 0.0001 for CSR GRID; r = 0.89, p value < 0.0001 for CSR SH) with the average ΔSMS derived from 3 LSMs. Individually, VIC model derived ΔSMS compare well with the estimated ΔSMS time series data. It is also unclear whether LSMs capture large interannual variability in the Asian monsoon associated with climatic teleconnections such as ENSO and IOD. Other uncertainties in GRACE-derived estimate of ΔGWS associated with the use of simulated (GLDAS LSMs) ΔSMS can arise from (1) under representation of ΔSMS in areas of thick unsaturated zone, and (2) over representation of ΔSMS in areas of very shallow groundwater table and substantial surface water storage. In the latter case, simulated ΔSMS may include parts of shallow groundwater and surface water storage due to poor compartmentalization of individual terrestrial water stores [Gulden et al., 2007]. In the Bengal Basin, areas featuring a deep unsaturated soil zone are minimal (present only in thick clay-covered Pleistocene terrace areas) as groundwater levels in Bangladesh predominantly occur at very shallow depths (see auxiliary material Figures S1 and S2). In this study, the use of an average value of simulated ΔSMS from 3 LSMs, however, minimizes the uncertainty in estimation of ΔGWS using GRACE satellite measurements.
 We demonstrate that resolving trends in ΔGWS is problematic over short (e.g., 4 to 5 year) periods in a highly seasonal basin where seasonality in water storage is greater than the trend. Seasonality (i.e., annual amplitude) in ΔTWS in the Bengal Basin generally results from monsoonal flooding during the wet season and intensive groundwater abstraction during the dry-season. The trend in estimated ΔGWS for a 5 year period (2003 to 2007) is approximately half of that estimated from 2003 to 2006. Additionally, estimation of trend in ΔGWS in the Bengal Basin can be problematic due to the presence of strong seasonality in the data set. We demonstrate that the strong seasonality in ΔGWS can however be captured well in multiple linear regression by using additional covariates (e.g., sine and cosine function of time) and error in trend estimates can be minimized (Tables 2 and 3).
 Critical to our estimation of ΔGWS from GRACE data in the Bengal Basin is the robust resolution of ΔSWS from in situ observations as ΔSWS accounts for 22% of the total variability in GRACE-derived ΔTWS. This contribution although very critical in humid tropics [Frappart et al., 2011] is often ignored in flood-prone regions around the world [Swenson et al., 2006; Rodell et al., 2007; Tiwari et al., 2009] as flood water is mostly unregulated or its effect on ΔTWS is assumed to be negligible relative to ΔSMS.
 Estimated rates of groundwater depletion in the Bengal Basin (−0.52 ± 0.30 to −1.61 ± 0.32 km3 yr−1 equivalent to −0.34 to −1.14 cm yr−1) are substantially lower than those recently estimated elsewhere on the Indian subcontinent by Rodell et al.  in semiarid, northwestern India (−4.0 cm yr−1), and Tiwari et al.  for Bangladesh, Nepal and West Bengal (India), their “zone D” (−2.5 cm yr−1). More recently, another study [Llovel et al., 2010] has reported trends in ΔTWS (August 2002 to July 2009) of −1.1 cm yr−1 and −1.5 cm yr−1 over the River Ganges and Brahmaputra Basins, respectively. Each of these studies attributes groundwater depletion to intensive groundwater-fed irrigation. In the Bengal Basin, more rapid groundwater storage depletion estimated for the period 2003 to 2007, relative to 1985 to 2007, is linked to substantial increases in groundwater abstraction for irrigation and urban water supplies [Hoque et al., 2007; Shamsudduha et al., 2009; Shamsudduha et al., 2011]. In situ measurements show further that groundwater depletion primarily occurs in central (Dhaka city) and northwestern Barind Tract areas of Bangladesh where a low-permeability surficial deposit (Madhupur Clay Formation; see auxiliary material Figure S4 and S8 for hydraulic properties of the shallow aquifer in Bangladesh) of variable thickness (6 to 40 m) inhibits direct rainfall-fed recharge [Shamsudduha et al., 2011].
 A curious finding is the more favorable comparison that is observed between wet-season trends in ΔGWS derived from GRACE (−0.44 ± 1.24 to −2.04 ± 0.79 km3 yr−1) and in situ observations using a high, uniform estimate (0.1) of (−1.06 ± 0.59 to −1.61 ± 0.32 km3 yr−1) rather than a spatially distributed value (mean: 0.06 ± 0.04) of (−0.52 ± 0.30 to −0.85 ± 0.17 km3 yr−1) derived from pumping tests. In the large Mississippi Basin, Rodell et al.  stress the importance of applying representative, distributed storage coefficients but, as recognized by a recent study [Sun et al., 2010], the determination of is challenging. values derived from pumping tests can be biased toward low values in two ways. First, elastic storage often dominates short pumping tests where confined or semiconfined exist locally and water table drainage has insufficient time to respond. Second, in situ estimates of , that sample an area of <0.5 km2 but are scaled up to a 1° × 1° grid cell (used in our analysis of in situ ΔGWS), do not represent the considerable variability in that naturally exists in alluvial aquifers. The influence of low- values may be exaggerated at regional scales as abstraction and resultant groundwater depletion are biased to areas of higher . Our deductions highlight the current but under explored uncertainty associated with the selection of storage coefficients to reconcile ΔGWS from GRACE, as an equivalent groundwater depth, with in situ monitoring observations from borehole hydrographs.
 In a highly seasonal hydrological system in the humid tropics, the Bengal Basin, we show that GRACE satellite measurements closely trace recent (2003 to 2007) intra-annual (seasonal) and interannual variations in groundwater storage (ΔGWS) indicated by in situ, ground-based observations (borehole hydrographs). Critical to this analysis is the resolution of ΔGWS from total water storage (ΔTWS) derived from GRACE using (1) changes in observed surface water storage (ΔSWS) derived from river stage records monitored at 298 gauging stations; and (2) changes in simulated soil moisture storage (ΔSMS) using 3 Land Surface Models (LSMs) (CLM, NOAH, and VIC). GRACE-derived ΔTWS in the Bengal Basin from 2003 to 2007 is explained well by changes in surface water storage (ΔSWS) (22%), changes in soil moisture storage (ΔSMS) (33%), and ΔGWS (44%). Groundwater depletion in the Bengal Basin estimated from in situ observations using a distributed specific yield ( ) ranges from −0.52 ± 0.30 km3 yr−1 (wet season trends) to −0.85 ± 0.17 km3 yr−1 (trend in annual means). These estimates are highly comparable (within error) to the range in estimates, −0.44 ± 1.24 to −2.04 ± 0.79 km3 yr−1 (wet-season trends) and −0.52 ± 0.50 to −2.83 ± 0.42 km3 yr−1 (trends in annual means), derived from different GRACE datasets (gridded and spherical harmonic (SH) products of CSR and GRGS). Of the 4 GRACE solutions, CSR SH derived ΔGWS shows the highest correlation (r = 0.93, p value < 0.0001) and the lowest (<4.0 cm) RMS error with in situ ΔGWS estimates with distributed specific yield. It remains unclear whether the small discrepancy between in situ and GRACE satellite estimates derives from uncertainties in resolving GRACE ΔGWS from ΔTWS or the representivity of storage coefficients derived from in situ pumping tests. Estimates of the linear trend in ΔGWS are highly dependent upon the length of the time series (e.g., 2003–2006 versus 2003–2007). Calculated trends are also strongly influenced by the annual variability in the amplitude; errors can arise from residual interannual variations once the seasonal component is removed from the time series. Long-term (1985 to 2007) trends in observed ΔGWS (−0.21 ± 0.03 to −0.23 ± 0.02 km3 yr−1) are considerably lower than recent (2003 to 2007) trends and indicate higher rates of groundwater depletion as a result of increased groundwater abstraction for irrigation and urban water supplies.
 We thank Sean Swenson (NASA, USA) and GRGS (France) for GRACE solutions. We acknowledge the support from Bangladesh Water Development Board (BWDB) in providing groundwater level and specific yield data. We thank Michael Steckler and Scott Nooner (LDEO of Columbia University) for providing quality-controlled BWDB river-stage data. We thank three anonymous reviewers for their constructive feedback and comments that helped to improve the quality of the manuscript. Support from the UK's Engineering and Physical Sciences Research Council (EPSRC) through a Dorothy Hodgkin Postgraduate Award (Ref. GR/AKFX-DHPA, 2007-2011), and a Geography Scholarship (Ref. 4387, 2010-2011) from the Harold Hyam Wingate Foundation, UK are kindly acknowledged.