4.1. Water Storage Changes from GRACE
 In this section we characterize the spatial-temporal variability in the observed water storage change signals from GRACE. The underlying causes of these variations are discussed in more detail in subsequent sections.
 Figure 1a shows that the time series of globally averaged TWSC peaks during NH Winter (DJF) with an amplitude of roughly 0.6 centimeters/month. Figure 1b shows the latitudinal distribution of seasonally averaged TWSC. A clear dominance of the strongest water storage change signals in a Southern Hemisphere (SH) 0° to 30° S latitudinal band is apparent for all the seasons, with lesser peaks in the NH subtropics and at 60°N. In the tropics, Summer (Winter) is dominated by increases (decreases) in TWSC, due to increases (decreases) in precipitation in response to seasonal migration of the ITCZ. In contrast, midlatitudes during JJA (DJF) are dominated by decreases (increases) in TWSC, due to increases (decreases) in evapotranspiration. The polar regions are similar to the tropics, but with slight JJA (DJF) increases (decreases) in TWSC, particularly in the NH. The amplitude of the seasonal cycle in the zonally averaged absolute value of TWSC (Figure 1c) has associated peaks in the corresponding regions.
Figure 1. (a) Monthly variations of globally averaged GRACE-derived TWSC estimates (black dots) are shown along with the fitted seasonal cycle (black solid line). (b) Zonally averaged TWSC estimates from GRACE for each season, JJA, SON, DJF and MAM. (c) Amplitudes of seasonal cycles fitted to the zonally averaged absolute value of TWSC estimates from GRACE.
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 The TWSC variations in the tropics shown in Figure 1b can be readily explained by the migration and strength of the Inter Tropical Convergence Zone (ITCZ), with maxima associated with enhanced precipitation. The hemispheric differences in the amplitudes of TWSC (±4–5 cm/month in SH; ±2 cm/month in NH) are manifestations of greater land precipitation in the SH in comparison to the NH, especially in equatorial South East Asia, South America and Africa [Adler et al., 2003]. Minima correspond to shifts in the subtropical depressions where evapotranspiration increases. In addition to the large fluctuations in the tropics, there is a NH midlatitude zone of much lower yet prominent variability in the range of ±1centimeter/month. Positive storage changes in DJF result from midlatitude polar frontal precipitation and snow storage. Snowmelt and evapotranspiration account for the decreasing (MAM) and negative (JJA, SON) peaks in this zone. Note that the TWSC variations during SON and MAM can be viewed as intermediate stages of the stronger end-members prevalent during JJA and DJF.
 The amplitude of seasonal cycle in zonally averaged value of TWSC (Figure 1c) provides perspective on the magnitude of the storage changes, both positive and negative, across the continents. The greatest variation in storage changes occur in the SH Tropics with an amplitude greater than 7 cm/month, followed by the NH Tropics (∼3.2 cm/month), the NH midlatitudes (∼2.4 cm/month) and the SH midlatitudes (almost 2 cm/month). Figure 1c further highlights where the principal zones for mass exchange between the land and the atmosphere or ocean occur, and that they are consistent with the major features of the atmospheric general circulation and global patterns of precipitation and evaporation [Hartmann, 1994; Peixoto and Oort, 1992]. This also includes the desert regions with zero or low TWSC (near 30° N and S).
 Figures 1b and 1c have two important implications for terrestrial hydroclimatology. The first is that global scale measurements of TWSC, available for the first time with GRACE, have identified significant regions of dynamic change, and that they are consistent with global patterns of weather and climate. The second, more subtle implication is that the GRACE mission has shown that terrestrial water storage responds in predictable ways to precipitation and evaporation processes, hence providing important “memory” of past atmospheric phenomena.
 Table 2 lists the annual means, amplitudes of fitted annual cycles and seasonal means of GRACE-based TWSC, averaged for each continent and the river basins shown in Figure 2. Although insignificant compared to the amplitude of the cycles, annual mean values over Europe, South America and Asia show a net accumulation of water mass with values of 0.32 cm/month, 0.30 cm/month and 0.08 cm/month respectively for the period of the GRACE data used here. On the other hand, even lesser depletion of total water storage is noted in Australia (−0.13 cm/month), North America (−0.06 cm/month) and Africa (−0.02 cm/month). The seasonal means again point to the influence of ITCZ migration on the distribution of land water storage, similar to what we have noted in Figure 1. While tropical basins in the NH gain water (e.g., Yangtze (2.44 cm/month), Ganges/Brahmaputra (4.65 cm/month), Orinoco (2.80 cm/month) and Niger (2.03 cm/month)) during JJA from enhanced precipitation, basins in the SH tropics and those in NH mid-to-high latitudes tend to lose water (e.g., Zambezi (−3.40 cm/month), Amazon (−2.80 cm/month), Congo (−2.74 cm/month), Ob (−2.80 cm/month) and Lena (−1.93 cm/month)) due to lack of precipitation and increased evapotranspiration. On the contrary, basins in the SH tropics tends to gain water during DJF while those in the NH tropics experience a net loss in storage, underscoring the dominant role of climate in defining the spatiotemporal heterogeneity of observed storage change. Furthermore, the amplitude of the annual cycles in South America (4.10 cm/month) stands out from those for the rest of the continents, including the Amazon basin (7.60 cm/month) which has the largest amplitude among the river basins. Amplitudes of variability secondary to those in the Amazon are found in Ganges/Brahmaputra (5.80 cm/month), Dniepr (5.28 cm/month) and Zambezi (5.18 cm/month) river basins.
Figure 2. River basins referred to in this study: (1) Mackenzie; (2) Mississippi; (3) Magdalena; (4) Orinoco; (5) Amazon; (6) Parana; (7) Volta; (8) Niger; (9) Congo; (10) Zambezi; (11) Nile; (12) Danube; (13) Dniepr; (14) Don; (15) Volga; (16) Ob; (17) Yenisei; (18) Lena; (19) Amur; (20) Ganges/Brahmaputra; (21) Yangtze; (22) Mekong; (23) Murray.
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Table 2. Estimates of Annual Mean, Amplitude of Fitted Annual Cycle and Seasonal Mean for the Continents and the Largest River Basins
|Region||Annual Mean, cm/month||Amplitude, cm/month||Seasonal Mean, cm/month|
 It is important to note here that, while it is necessary to smooth the Stokes coefficients from GRACE to reduce the noise in derived mass change fields, the process also suppresses the variability of the storage change signal. The length scale used for smoothing further affects the derived storage change estimates. While a large averaging radius can decrease the strength in the storage change signal [Chen et al., 2006], a smaller radius can produce spurious north-south stripes [Swenson and Wahr, 2006b]. Hence our estimates of mean (annual and seasonal) and amplitude of seasonal cycles based on the use of 1000 km half-width Gaussian averaging kernel are conservative characterizations of basin-to-continental storage changes observed by GRACE.
 To understand the relative contributions from the large river basins in Figure 2 toward the TWSC for an entire continent, ratios of the sum of absolute value of TWSC in a basin to that of the continent were computed for North America, South America, Africa and Asia. Figure 3 illustrates the relative contributions of some of the largest river basins toward the total storage change in North America, South America, Africa and Asia. Also shown in the figure is the percentage of continental area residing within each of the river basins. The results show that just a few of these river basins can account for a notable portion of the total storage change over the entire continent in which the basins are located. This is particularly noteworthy in continental South America, where the change in the Amazon basin is on average of about 45% of the continental storage change, and the aggregate (Amazon, Parana and Orinoco) contributes about 70% while the contributing area is ∼44% of the area of South America. To a lesser degree, similar results are also seen in Africa and Asia, where aggregated storage changes in the basins shown account for 50%, 35% of the continental water storage changes respectively.
Figure 3. Ratio of GRACE-derived TWSC in the listed river basin to that of the entire continent. Total represents the sum of ratios for the river basins considered in each continent. Also shown are (above each bar) the percentage of continental area occupied by each of the river basins.
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4.2. GRACE–GLDAS Comparisons
 In this section, we compare seasonal estimates of TWSC from GRACE to those from GLDAS [Rodell et al., 2004b]. For consistency with the GRACE data, TWSC from GLDAS was computed using equations (1)–(2). Although not a perfect reproduction of observations, global model output such as that from GLDAS captures the magnitude and variability of terrestrial hydrology sufficiently enough, so that in the absence of any similar, global observational data sets, it provides a reasonable opportunity for evaluation and understanding of the GRACE hydrology signal [Syed et al., 2004]. For comparison with GRACE, GLDAS-based TWSC estimates were converted into spherical harmonic coefficients, smoothed with a 1000 km half-width Gaussian averaging kernel and transformed into 1 × 1 degree gridded data.
 Global plots of seasonal storage change estimates obtained from GRACE and GLDAS are shown in Figure 4. GLDAS results used here are for the same period as the GRACE measurements. There is very good overall agreement between the two estimates with Root Mean Square Errors (RMSE) ranging between ∼1 cm/month in JJA and ∼0.7 cm/month in DJF. Some of biggest storage change signals, consistent with Figure 3, are occurring in the Amazon, Ganges/Brahmaputra, Congo river basins and over large regions of Northern Europe and Western North America. While there are some small differences in magnitude of the TWSC estimates, GLDAS performs reasonably in capturing the global spatial patterns of observed storage changes at seasonal timescales.
Figure 4. Spatial patterns of seasonally averaged TWSC (cm/month) from GRACE and GLDAS. On the basis of the seasonal averages computed for the period of April 2002 till July 2004.
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 Time series of TWSC from GRACE and GLDAS for four of the major river basins in continental North and South America are shown in Figure 5. Also included in the plots for Mississippi and Amazon basins are independent estimates of TWSC from a combined land-atmosphere water balance (LAWB) [Syed et al., 2005]. GLDAS estimates agree very well with GRACE, with RMSE values of ∼1.5 cm/month in Mississippi and Mackenzie and ∼2.5 cm/month in Amazon and Parana river basins. Estimates of storage change from GLDAS and LAWB also track each other fairly well in both the Amazon (RMSE = 4.5 cm/month) and Mississippi (RMSE = 1.6 cm/month) basins except for the periods of September-October in 2002 and late JJA 2003. Discrepancies between TWSC estimates from GLDAS and LAWB are attributed to errors in the horizontal divergence of water vapor (DivQ) and are discussed in detail by Syed et al. . Furthermore, model estimates of storage change are less variable than GRACE-derived storage changes, primarily due to the absence of contributions from surface and groundwater in the simulations.
Figure 5. TWSC estimates from GRACE (GRC) and GLDAS (GLD) in 4 of the largest river basins in continental North and South America. Also included for Mississippi and Amazon basins are TWSC from a Land-Atmosphere Water Balance (LAWB).
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 Overall, Figures 4 and 5 show good agreement in the spatial-temporal variability of TWSC estimates from GRACE and GLDAS. The differences in magnitude between the two estimates can either be due to model deficiencies, such as inadequate snow or missing surface or groundwater components in the models, or due to uncertainties in the GRACE data (e.g., due to processing, aliasing, instrument error, etc.). One consequence of the GRACE errors is that true water storage change signals may be enhanced or dampened in both regional and global scales [Swenson and Wahr, 2006b; Chen et al., 2006a; Seo and Wilson, 2005]. Nevertheless, we believe that the agreement between GRACE and GLDAS is sufficient, so that GLDAS output fields can be studied to better understand the processes contributing to terrestrial water storage variations.
4.4. Correlation Analysis
 Figure 11 shows the global and latitudinal distribution of the correlation coefficients between monthly GLDAS-based TWSC and the hydrologic fluxes for the entire length of the simulation. P acts as a positive flux in terrestrial water balance; hence areas with positive correlations are interpreted as areas where the values of TWSC are largely impacted by P. On the contrary, evapotranspiration and runoff are variables that deplete water storage; hence negative correlations are indicative of the regions where these processes are most effective in controlling magnitude and variability of the continental water storage changes.
Figure 11. Spatial and latitudinal distribution of the correlation coefficients between GLDAS-based TWSC and (a) P; (b) E; and (c) R.
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 A comparison of the three global correlation plots suggests that positive correlations between precipitation and water storage changes (Figure 11a, first column) have the maximum spatial coverage over the globe followed by the negative correlations between E and R (Figures 11b and 11c, first column). The latitudinal dependence of the controlling processes discussed in the previous section (Figures 9 and 10) is also evident here. The tropics are consistently dominated by the high positive correlations between P and TWSC while the TWSC estimates in the NH midlatitudes are correlated more with E than with P. Figure 11 shows a significant increase in correlation between E and TWSC (Figure 11b, second column) in the region between 30°–70° N/S and the concomitant decrease in correlation between P and TWSC (Figure 11a, second column). In addition, the dominance of snowmelt-derived runoff in the NH high latitudes is also distinctly discernible from the considerably higher absolute values of correlation between R and TWSC (Figure 11c, second column).