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needed at hydrometeorological scales of *10 km or better. Examples of soil moisture
downscaling based on data assimilation are provided by Reichle et al. (
2001
), Sahoo et al.
(
2012
), and Zhou et al. (
2006
). Also, Reichle and Koster (
2003
) addressed the propagation
of observational soil moisture information to unobserved regions.
3.2 Partitioning of Terrestrial Water Storage Observations
Passive microwave (e.g., AMSR-E) retrievals have been used in conjunction with land
surface models to better characterize snow (Sect.
3.1
) and soil moisture (Sect.
3.4
).
Gravimetric measurements such as from GRACE can provide monthly, basin-scale
([150,000 km
2
) estimates of changes in TWS (Sect.
2.2
). Since TWS is vertically inte-
grated and includes groundwater, soil moisture, snow, and surface water, TWS retrievals
offer significant insights into the regional- and continental-scale water balance and,
through data assimilation, the potential to learn more about hydrological processes.
Besides the obvious spatial downscaling challenge presented by the basin-scale GRACE
TWS retrievals, another challenge for the assimilation of GRACE-based TWS is the
partitioning of the vertically integrated TWS retrievals into water cycle component vari-
ables. Like the horizontal downscaling of AMSR-E SWE retrievals discussed in the pre-
vious section, the partitioning of TWS retrievals can be accomplished through assimilation
using an appropriate observation operator. In this case, the observation operator aggregates
the fine-scale model estimates of soil moisture, groundwater, and snow to basin-scale TWS
estimates. This observation operator enables the computation of the observation-minus-
forecast residuals (or innovations) in the (basin-scale, TWS) space of the observations. The
observation operator is also needed for the computation of the Kalman gain that transforms
the innovations back into the space of the fine-scale model variables. Similarly, the
required temporal aggregation of the model output to the monthly scale of the assimilated
TWS retrievals is accomplished through the observation operator.
This concept was illustrated by Forman et al. (
2012
), who assimilated GRACE TWS
retrievals over the Mackenzie River basin located in northwestern Canada (Fig.
3
) using an
updated version of the GEOS-5 LDAS developed by Zaitchik et al. (
2008
). The assimi-
lation estimates were evaluated against independent SWE and river discharge observations
(Sect.
2.3
). Results suggest improved SWE estimates, including improved timing of the
subsequent ablation and runoff of the snow pack. For example, Fig.
4
shows the
improvements in SWE estimates resulting from the assimilation of GRACE TWS retri-
evals. The white bars represent model results without assimilation, whereas the gray bars
represent results with assimilation. The labels on the y-axis of each subplot represent sub-
basins of the Mackenzie River basin. As shown in Fig.
4
, the assimilation of GRACE TWS
retrievals generally reduced the mean difference and RMSE between the model and the
independent CMC SWE estimates (Sect.
2.3
). The reductions are greatest in the Liard
basin, where the greatest amount of snow accumulation occurs. Here, the mean difference
with the CMC estimates is reduced through GRACE data assimilation by 30 % (from 13.2
to 9.3 mm) and the RMSE is reduced by 18 % (from 24 to 19.6 mm). Smaller reductions
occur in the other sub-basins. The correlation coefficient of the SWE anomalies (not
shown) suggests a slight degree of degradation resulting from assimilation, but further
analysis shows there is no statistically significant difference at the 5 % level. In summary,
the assimilation of GRACE TWS information into the Catchment land surface model
reduces the mean difference and RMSE in SWE estimates without adversely impacting
estimates of interannual variability.
