3.1. Stocks: TWS From GRACE 2003–2009
 The area-average TWS over the entire Eurasian pan-Arctic drainage region has a seasonal peak-to-peak amplitude of 10.6 cm, with similar values over the largest basins (Ob: 12.3 cm; Yenisei: 12.4 cm; Lena: 10.1 cm). Maximum TWS typically occurs in May, declines rapidly in boreal spring when snow melt sets in, and thereafter gradually reduces to its seasonal minimum between August and October (Figure 1). Over the GRACE time period, the TWS over all basins exhibits significant interannual variability. Such variability can arise from changes in net precipitation or discharge. An increase in TWS would be consistent with either an increase in P-ET, or a decrease in R; conversely, a decrease in TWS would require reduced P-ET or increased R (equation (1)). Additionally, changes of the TWS capacity through changes of soil properties can affect runoff, and also land-atmosphere fluxes through ET.
 For the Ob and Yenisei basin, as well as the Eurasian pan-Arctic watershed as a whole, there is a tendency for overall TWS increase from 2003 to 2009 (Figure 1). However, fitting a linear trend to the basin mean TWS is not warranted given the apparent interannual variations and the short record of observations. A seasonal Mann-Kendall trend test, adjusted for autocorrelation [Hirsch and Slack, 1984], reveals that linear trends fitted to the mean TWS in the Lena and Ob basins, as well as the total Eurasian watershed, are statistically not significant at the 95% level. Only for the Yenisei Basin is the linear trend of 0.32 cm/yr significant at 95% but rather small in amplitude. The data record, while short, suggests the presence of low-frequency variations of 2–2.5 years, which has also been reported for other large river basins [Schmidt et al., 2008]. Similar interannual TWS variations are also simulated with hydrological models, and therefore are likely caused by variations in the forcing of TWS anomalies (P or ET). Whether robust physical connections between the interannual variations and large-scale climate variations such as the Arctic Oscillation exist is still unclear [Serreze and Barry, 2005; Krokhin and Luxemburg, 2007], and considerably longer time series are needed to assess statistical significances. Compared to the Ob and Yenisei basins, the TWS over the Lena basin increased considerably more from 2003 to early 2007, but since early 2007 this signal has reversed sign. This quasi-trend behavior is at least qualitatively consistent with variations in P-ET over the Lena basin, which had a similar declining signal since 2007 (see detailed analysis of TWS controls in section 3.2). The spatial distribution of TWS trends over the entire time period from 2003 to 2009 reveals large-scale positive TWS trends (Figure 2a), but no continuous colocation between those trends and regions of permafrost (Figure 2c). For the Ob, Yenisei and the regions west of the Ob, the maximum increase is concentrated to the south of the permafrost areas in a band that spans the northern and middle parts of the basins. In the central Lena basin, the trend is colocated with areas of mostly discontinuous permafrost. The seasonal Mann-Kendall test reveals that a considerable fraction of the local trends above about 1 cm water-equivalent height are significant at the 95% level (Figure 2b).
Figure 2. (a) Trend component of terrestrial water storage over Eurasian drainage region (in cm of water/yr) calculated by simultaneously fitting constant, trend, annual, and semiannual as well as GRACE-specific aliasing periods of 161 and 1362.7 days [Ray and Luthcke, 2006] to the GRACE data from January 2003 to January 2010. (b) Grey-shaded areas show regions where the linear trend is significant at the 95% level based on a seasonal Mann-Kendall test, accounting for serial correlation [Hirsch and Slack, 1984]. (c) Permafrost distribution over the region [Brown et al., 1998].
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 In order to gain more insight into the spatiotemporal pattern of the nonseasonal TWS variations, we compute empirical orthogonal functions (EOFs) of the data [e.g., Hannachi et al., 2007] after subtracting a composite seasonal cycle from each grid point anomaly. The different EOF modes need not necessarily represent independent physical modes [e.g., Dommenget and Latif, 2002], and due to the short record length, the EOF/PC may change with a longer record. Sensitivity test on GRACE TWS show that the EOF/PC patterns do not change significantly if at least 60 months are used (not shown). The primary use of the EOF decomposition here is to reveal the centers of action of nonseasonal variations, to assess if these signals are collocated to regions of permafrost or related to anomaly patterns in the controls of TWS anomalies, and to facilitate a comparison of TWS simulated with state-of-the-art hydrology models.
 The EOF/PC decomposition of the entire drainage region (Figure 3) yields a first mode that extends across all basins, but lumps together different temporal variability of the individual basins. Therefore, we compute the EOF for each basin individually. The first EOF/PC modes of the three large basins show distinctively different behavior, in particular between the Ob and Lena basin, while the Yenisei comprises features of both extremes (Figure 3). The explained variances for the first mode range from 43 to 71%. About 4–10% of the Ob basin is underlain by permafrost, which gradually increases to 36–55% of the Yenisei basin, and to nearly complete coverage of 78–93% for the Lena basin. Since permafrost is largely absent in the Ob basin, the observed TWS anomalies cannot be related to changes in permafrost. Similarly, the changes in the Yenisei basin are centered over the nonpermafrost regions, and thus also not related to permafrost-specific TWS dynamics. The prominent variations with a period of 2 to 2.5 years in the principal component time series of Ob and Yenisei suggest a common atmospheric driving process or TWS response leading to the observed nonseasonal TWS anomalies, while the first EOF/PC mode of the Lena basin shows a relatively monotonous TWS increase until early 2007, and a weaker decline after 2007 (Figure 3). The strongest TWS increase occurred in 2004. That year is actually marked by comparatively low P-ET, with corresponding low discharge values based on gauge observations. The scenario of increasing TWS during decreasing P-ET invites speculations about TWS capacity changes in the Lena basin. Could permafrost thaw have expanded TWS capacities to account for the observed increase? In lack of direct large-scale observations, the answer remains speculative. Degradation of permafrost in the East Siberian regions has been documented based on in situ observations from 1930 through 1996 [Romanovsky et al., 2007], and with unabated warming over the last decade, it is likely that the subsurface ground has warmed even further. Additionally, winter snow thickness also plays an important role for subsurface temperatures. Thicker layers of snow in winter months effectively insulate the ground to prevent heat loss to the atmosphere, which also inhibits recovery of previously degraded permafrost. However, as surface and subsurface temperatures are only weakly correlated on time scales of less than 10 years [Romanovsky et al., 2007], TWS variations from GRACE are likely not strongly linked to concurrent surface temperature variations. This notion is supported by the lack of significant correlation between the nonseasonal surface temperature anomalies from JRA-25 and TWS anomalies from GRACE (not shown).
Figure 3. Mode 1 of the EOF/PC decomposition of the terrestrial water storage (TWS) anomalies (composite seasonal cycle subtracted) from GRACE, WGHM, and GLDAS-NOAH for total (top to bottom) Eurasian pan-Arctic, Ob, Yenisei, and Lena. The explained variance is given in each map as percentage of total variance. The PC time series at right are normalized by their standard variations, and the EOF spatial maps are scaled by the same factor. The units for the EOF spatial maps are in centimeters of water-equivalent height.
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 For the second EOF modes, the Yenisei and Lena exhibit a similar spatiotemporal behavior. The explained variances for this mode range from 12% to 33% (Figure 4). The second PC is dominated by events starting in 2007 lasting through 2009, as well as some energy at the beginning of the record in 2003. Spatially, the second EOF/PC is concentrated along the southern and northern edges of the basins with opposing signs. This spatial structure is at least partly due to the orthogonality constraint in the EOF/PC decomposition. However, the rotated EOF patterns did not change significantly, so they appear to be robust. The declining TWS in the southern parts of the basins and increasing TWS in the northern parts of the basins during 2007 is consistent with the observed anomalous precipitation pattern during 2007 [Shiklomanov and Lammers, 2009; Rawlins et al., 2009a], which is linked to an anomalous circulation pattern of low pressure over western and central Eurasia, in turn possibly related to a positive NAO phase [Rawlins et al., 2009a]. The reversal of the 2007 TWS signal starting in early 2008 suggests a common atmospheric change in P-ET in those areas.
Figure 4. Mode 2 of the EOF/PC decomposition of the terrestrial water storage (TWS) anomalies from GRACE, WGHM, and GLDAS-NOAH for total (top to bottom) Eurasian pan-Arctic, Ob, Yenisei, and Lena. See Figure 3 for details.
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 In the absence of any independent observations to which the GRACE observations can be compared against, we use data from two hydrology models to assess the TWS signals to gain some additional insight into the GRACE observations. The models used are the conceptual Watergap Global Hydrology Model (WGHM) [Döll et al., 2003] and the Land Surface Model NOAH running within the Global Land-Data Assimilation System (GLDAS-NOAH) [Rodell et al., 2004]. WGHM has water storage components for snow, soil moisture, groundwater and surface water in the river network, lakes and wetlands, whereas GLDAS-NOAH does not explicitly simulate groundwater and surface water. WGHM uses a heuristic approach to reduce groundwater recharge in permafrost areas, depending on the permafrost spatial extent and type (continuous, discontinuous, sporadic permafrost) in each 0.5 degree model cell [Döll and Fiedler, 2008]. GLDAS-NOAH includes a frozen soil scheme [Koren et al., 1999] for soil layers down to a depth of 2 m mainly to represent the latent heat balance of freezing and thawing top soil. Neither model, however, explicitly represents permafrost processes or temporal permafrost dynamics, such as permafrost extent, type, or active layer thickness.
 Simulated water storage variations reasonably match the GRACE TWS observations (compare interannual variations in Figure 1). TWS from WGHM tends to match the GRACE data better than GLDAS-NOAH, both in terms of a lower root-mean-square difference as well as a higher correlation (Figure 5). For the Ob basin, the nonseasonal spatiotemporal TWS patterns of GRACE and the models agree very well, both for EOF/PC 1 and 2 (Figures 3 and 4). The EOF correspondence is less favorable for the Yenisei basin, with considerable differences both between GRACE and the models and also between the two models. However, the dominant event in the second EOF/PC of the Yenisei from 2007 to 2009 mentioned above is similarly captured by GLDAS-NOAH while it is represented in the first EOF/PC by WGHM (Figures 3 and 4). In the Lena basin, GRACE and WGHM show a similar trend-like pattern in the first EOF/PC, while this feature is split between mode 1 and 2 for GLDAS-NOAH (Figures 3 and 4).
Figure 5. Taylor diagram [Taylor, 2001] summarizing the normalized statistics of the comparison of simulated TWS anomalies from GLDAS-NOAH and WGHM relative to the observed TWS anomalies from GRACE for the Eurasian pan-Arctic drainage region and the major drainage basins (time period January 2003 to December 2009). (left) Comparison of the full simulated time series; (right) comparison of nonseasonal variations (12 month moving averages). In both cases, WGHM has higher correlations with GRACE and tends to have a lower root-mean-square difference than GLDAS-NOAH (indicated by the distance from the observations). GLDAS-NOAH tends to match GRACE observations better in terms of the standard deviations. Note that the statistics here are normalized by the standard deviations of the GRACE observations and take into account the agreement of the spatial pattern as well as temporal behavior; the statistics of the basin-mean values only are very similar to the ones shown.
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 Differences between the models in simulating interannual TWS variations can be due to a variety of factors including model structure and driving forces, with precipitation input being among the most important [e.g., Slater et al., 2007]. As WGHM is driven by GPCC precipitation [Rudolf and Schneider, 2004] and GLDAS-NOAH by Climate Prediction Center Merged Analysis of Precipitation (CMAP) fields, intermodel differences can be caused by differences of these data sets, and deficiencies in the precipitation data sets may propagate into considerable mismatch of simulated TWS relative to GRACE TWS. The effect of differences in input data may exceed the effect of different storage components represented by the models, i.e., model structure. For EOF/PC patterns of mode 1, WGHM(TWS) and WGHM(snow+soil moisture) are more similar to each other and GRACE than is GLDAS(snow+soil moisture) to WGHM(snow+soil moisture) or GRACE (not shown). Thus, one cannot simply attribute the better match of WGHM and GRACE to the inclusion of groundwater and surface water storage in WGHM. Although these are two important storage components with different seasonal dynamics compared to snow and soil moisture storage in the study area [Güntner et al., 2007], their effect is less relevant for the interannual storage variations analyzed here, where differences in climate forcing data may obviously be more important for explaining the differences between GLDAS-NOAH and WGHM. In spite of the model differences, the EOF/PC decomposition of simulated nonseasonal TWS shows that the models are able to capture important features of the interannual GRACE TWS signal. The models are successful in this by using climate forcing as the only time-variable constraint to the model simulations, ignoring any seasonal or longer-term permafrost dynamics. These results give additional evidence that the observed water storage variations in the Eurasian pan-Arctic from GRACE are predominantly driven by variations of the P-ET budget.
3.2. Flows: Hydrological Budget in 2003–2009
 In this section, we assess the seasonal and nonseasonal variability of the budget terms in equation (1), and how well the different observational data sets close the terrestrial Eurasian pan-Arctic water budget from 2003 to 2009. The seasonal variations of P-ET, P, R and ET have previously been quantified in several studies (see, e.g., Serreze and Barry  for a summary), but the annual components of TWS change rates, dS/dt, have not due to the lack of direct, large-scale observations. Over longer periods, it is often assumed that TWS changes average out over nonglaciated regions (otherwise, there would be a net mass gain or loss in TWS). With observations from GRACE, we can now address the validity of this assumption, albeit the time series is still relatively short for hydrological applications where random fluctuations of P-ET or R can introduce long-term memory in TWS (because TWS is the integrated response to these fluxes). Nonetheless, the seasonal variations in TWS change rates on a basin scale from GRACE allow an independent assessment of the quality of the P-ET estimates and the measured basin discharge from gauges. Additionally, equation (1) represents an alternative to infer discharge over large drainage basins such as the Eurasian pan-Arctic, about one fourth of which is not or only poorly monitored with discharge gauges. Previously, the annual Eurasian pan-Arctic drainage basin discharge has been estimated at about 2970 km3/yr (centered on the GRACE period) by scaling the monitored areas to account for the unmonitored regions [McClelland et al., 2006]. Rearranging equation (1), the inferred discharge from JAR-25/GRACE yields a similar mean annual value of 2920 km3/yr. This value is, of course, almost entirely determined by atmospheric moisture fluxes as annual TWS change rates are nearly 2 orders of magnitude smaller than the total P-ET.
 For seasonal variations, the relative amplitudes and phasing of P-ET and dS/dt over the basins reflect the milder and wetter climatic conditions in the western parts (Ob) compared to the colder and drier eastern regions (Lena). In the more eastern parts of the region, a larger fraction of the precipitation falls as snow that accumulates during the winter months and rapidly melts in spring, and seasonal P-ET and TWS changes are offset compared to the western regions (Figures 6b–6d). The seasonal cycle of TWS changes rates is similar over all basins, reaching maximum values in November/December, and minimum values in June (maximum TWS loss rate) when the snow melts. For the Ob basin, seasonal TWS rates and P-ET closely follow each other in phase and amplitude (Figure 6b). This is expected because 74% of the annual precipitation goes into evapotranspiration and consequently only the remaining fraction is available for discharge into the Arctic Ocean [Serreze and Barry, 2005]. During June and July, net P-ET for the Ob basin becomes negative and terrestrial water becomes a source for atmospheric water. Since a considerable fraction of the TWS in the Ob is in the form of open surface water in wetlands, ET is not limited by available soil moisture and occurs close to its potential rate [Serreze and Barry, 2005]. Over the Yenisei and Lena basins, on the other hand, only about 55% and 45%, respectively, of the annual precipitation is lost through evapotranspiration, and P-ET generally does not attain negative values during summer months (Figures 6c and 6d). Note that higher R/P ratios are found over permafrost regions because the permeability of the soil is limited [Serreze and Barry, 2005]. Additionally, colder mean temperatures over the permafrost regions result in lower ET. The lower ratios of ET/P for the Yenisei and Lena, and the fact that P-ET and dS/dt are not in phase due to significant snow storage in winter result in a larger fraction of the precipitation going into runoff and discharge. Therefore, the inferred discharge estimate through the difference of P-ET and dS/dt has a higher signal-to-noise ratio for these two basins, whereas for the Ob, the inferred discharge is a comparatively small difference between two bigger components that are in phase. This causes the inferred discharge over the Ob basin to be in poor agreement with gauged discharge values (Figure 6). An additional error source for the Ob basin may come from the JPL-GRACE data set we use here to estimate TWS variations. Relative differences between the JPL-RL4.1 data set and other GRACE solutions (e.g., from the Center for Space Research, CSR) are bigger for the Ob basin than for the Yenisei and Lena on the seasonal time scale. The reasons for this are unclear and are under investigation. The inferred discharge estimates for the Yenisei and Lena basins (Figure 6) agree well with the gauge observations. The timing of the spring discharge coincides in both curves, but the inferred estimates are slightly below the gauge values. Bias-like differences exist in the late summer and winter months (discussed below).
Figure 6. Climatology of monthly mean fluxes (shown in Figure 7). (top) TWS change rates from GRACE (solid line) and net precipitation P-ET from JRA-25 (dashed line). (bottom) Inferred discharge (with shaded uncertainty estimate, computed by solving equation (1) for R) and gauged discharge (red line, relative uncertainty 10%). Note that the monthly gauge observations have been smoothed to account for the temporal sampling from GRACE; see section 2 for details. The mean annual net precipitation P-ET for Eurasia from JRA-25 is 3150 km3, while the mean annual inferred discharge is about 2920 km3.
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 As described in section 2, we derive P-ET estimates from the aerological budget of JRA-25 reanalysis data. In Figure 7, the basin-averaged precipitation time series of the GPCP data set [Adler et al., 2003] are also shown. From the difference to P-ET, one could infer ET (as, e.g., done by Serreze and Etringer ), which is generally the least known budget parameter over land. Instead of inferring ET, we focus on the budget closure with dS/dt from GRACE and P-ET from JRA-25, and observed discharge from gauges. GRACE measurements are independent from R and P-ET observations, and therefore yield important large-scale information over the sparsely observed high northern latitudes. During the cold winter months, ET over most parts of northern Eurasia is very small, and discharge into the Arctic Ocean is also at its minimum [Serreze and Etringer, 2003]. In this respect it is reassuring that basin-averaged P-ET from JRA-25 is never larger than P from GPCP, and very close to GPCP during the winter months (Figure 7, dashed lines).
Figure 7. Monthly mean TWS change rates (black with circles), net precipitation P-ET from JRA-25 (solid grey line), and precipitation P from GPCP (dashed grey line) for (top to bottom) pan-Arctic Eurasia, Ob, Yenisei, and Lena river basins. Monthly values for P-ET and P have been matched to GRACE estimates of dS/dt according to equation (3).
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 When averaging over entire river basins, TWS rates dS/dt should always be equal to or smaller than P-ET in the absence of any other TWS sources (otherwise R in equation (1) becomes negative, which is obviously not possible as rivers do not run backward). However, during some months, we obtain TWS change rates dS/dt from GRACE that are larger than precipitation from GPCP or P-ET from JRA-25. For those months, the inferred basin discharge (solving equation (1) for R) becomes negative, which is unphysical. Over the Lena and Yenisei basins, this situation occurs consistently during the cold winter months. Although the propagated errors for the inferred discharge typically include the zero value, the consistently below-zero inferred discharge values suggest the presence of a systematic bias (Figures 8c and 8d). Two scenarios could explain the discrepancies: either GRACE overestimates the mass gain during some winter months, or the basin-integrated precipitation is underestimated in the observations (which then also propagates into P-ET from JRA-25). It is difficult to explain why GRACE would consistently overestimate the mass gain during some winter months for the Yenisei and Lena. The spatial patterns of the TWS anomalies from GRACE could have some influence on the basin-integrated TWS amplitudes through spatial signal leakage [Swenson and Wahr, 2002]. However, we have evaluated several different averaging kernels, but they do not significantly affect the estimated TWS change rates. The leakage issue for GRACE data is not critical for the basins examined here as TWS anomalies tend to be of similar amplitude and in phase across basin boundaries [Klees et al., 2007]. Therefore, underestimation of basin-integrated net precipitation might cause the negative inferred winter discharge, but this is difficult to assess in lack of independent observations. Alternative reanalysis data (NCEP/NCAR aerological fluxes, as well as ERA-Interim forecast P-ET) also result in negative discharge estimates during some cold winter months. However, the reanalysis products assimilate similar atmospheric observations and therefore likely contain similar biases. A bias in the inferred discharge of opposite sign tends to occur during the late summer months of September and October, in particular for the Yenisei basin, but also over the Lena (Figures 8c and 8d). Here, the inferred late-summer GRACE/JRA-25 discharge is consistently larger than the gauge measurements. Again, this signal is also present when we use NCEP/NCAR or ERA-Interim P-ET estimates. During some years, a secondary discharge peak is also seen in the gauge measurements, but it is usually smaller than the secondary peak in the inferred discharge, and mostly not present at all during the GRACE period. Interestingly, hydrological models also tend to have a second discharge peak during September and October for these river basins [Slater et al., 2007; Werth and Güntner, 2010]. During those months, P-ET reaches its annual maximum, and precipitation is typically in the form of rain. Additionally, it is possible that a considerable amount of runoff bypasses the streams and is not accounted for by the installed gauges [Syed et al., 2007]. Alternatively, P-ET in the reanalysis data sets could be overestimated either by too much precipitation or too little evapotranspiration. Either hypothesis is speculative at this point, but should be further investigated. Besides naturally occurring variations, artificial reservoir impoundments can also affect the hydrological budget. While impoundments over the Eurasian Arctic basins have significantly influenced the phasing of the seasonal terrestrial water budget [e.g., Shiklomanov and Lammers, 2009], the inferred discharge biases (from GRACE and JRA25) cannot be attributed to dams because water storage changes in reservoirs affect the GRACE signal and are thus implicitly accounted for in the budgeting applied here.
Figure 8. Monthly mean basin discharge inferred from GRACE/JRA-25 and directly observed (where available). Observed discharge is from the ArcticRIMS project; the red dashed lines are the original monthly discharge observations, and the red solid lines are the monthly discharge observations matched to GRACE estimates of dS/dt according to equation (3).
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 Finally, we assess the budget closure of nonseasonal and interannual variations to shed some light on the conundrum of stream flow trends exceeding observed precipitation trends [Adam and Lettenmaier, 2008]. We computed annually accumulated fluxes of the observed quantities dS/dt, P-ET, and R by summing the monthly values in a 12 month moving window (Figure 9). Again, any trends should be treated with caution given the short GRACE record. For the milder western regions, most variability in P-ET is expected to be reflected in TWS changes due to the low runoff ratio. This is indeed the case for the Ob basin, where the interannual TWS change rates agree very well with net precipitation anomalies (Figure 9b). With the exception of 2007, annual discharge from gauges in the Ob does not exhibit any trends or significant interannual variability from 2003 to 2009. Although nonseasonal dS/dt and P-ET over the Ob basin agree well, the inferred discharge exhibits considerably more variability compared to the gauged discharge estimate, which may at least partly be due to TWS errors mentioned above. Moving farther east into the Yenisei basin, the correspondence between interannual variations of dS/dt and P-ET begins to vanish as discharge variations become more important with the increasing R/P ratio [Serreze and Barry, 2005], but due to missing provisional gauge observations for some months we cannot reliably assess the closure of the interannual budget over the Yenisei basin. The larger discrepancy between annual P-ET and dS/dt from 2007 to 2008 is consistent with the record discharge in 2007, such that a positive P-ET anomaly mainly fed runoff and discharge, and had less effect on TWS. The annually accumulated fluxes over the cold Lena basin reflect the higher R/P ratios associated with regions of high permafrost coverage [Serreze and Barry, 2005]. From 2003 to 2007, P-ET into the basin has a similar positive slope and variability compared to gauged discharge over the same time period. Additionally, trends and variability in annually accumulated P-ET are very close to those of P from GPCP (not shown), consistent with the notion that P-ET variations tend to be highly correlated with variations in P [Serreze and Barry, 2005]. Following the peak in 2007, gauged discharge shows only a very modest increase, while annual P-ET markedly declines after the 2007 peak. This decrease in P-ET after 2007 is reflected in the negative TWS change rate inferred from GRACE (Figure 9). Between 2003 and 2007, the Lena basin was in a water accumulation mode, since then, the TWS in the basin has been declining, albeit at a slower rate than it was gaining in the accumulation period.
Figure 9. Annually accumulated fluxes for (a) pan-Arctic Eurasia, (b) Ob river basin, (c) Yenisei river basin, and (d) Lena river basin. At each time point, the values represent the integrated fluxes of the preceding 12 months; for example, the value for September 2008 is the sum of the monthly values between October 2007 and September 2008.
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