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however, that despite the spatial coverage of data, for computational reasons assimilation is
often performed per column, that is, using a 1-D filter. When the vertical columns (of snow
or soil) are horizontally connected through the model physics or assimilation statistics, this
is referred to as 3-D assimilation.
The assimilation of catchment-distributed soil moisture has often focused on the
improvement of the state or initial conditions (Pauwels et al.
2001
,
2002
) and parameters in
order to improve spatially integrated fluxes, such as discharge. However, it is also possible
to use soil moisture assimilation to correct rainfall estimates (Crow and Ryu
2009
). At the
global scale, soil moisture assimilation will become increasingly important when coupled
to the atmosphere for climate and seasonal predictions.
Spatially distributed studies initially focused on assimilation of retrievals with simple
techniques and gradually developed towards more complex schemes, with the inclusion of
forward models (observation operators) to directly assimilate, for example, microwave
observations. Initial soil moisture retrieval studies explored the performance of different
filter techniques, such as Newtonian nudging, statistical correction and statistical inter-
polation (Houser et al.
1998
; Pauwels et al.
2001
; Paniconi et al.
2003
; Hurkmans et al.
2006
), while during the last decade, variational and KF-based assimilation largely domi-
nated this research field because of the proven robustness and flexibility of these latter
techniques (Reichle et al.
2002a
,
b
).
A typical conceptual problem with spatially distributed assimilation is the use of coarse-
scale remotely sensed data to infer fine-scale information. There are many static disag-
gregation techniques that use auxiliary information to perform such a downscaling outside
the assimilation scheme. Performing dynamic disaggregation within the assimilation
scheme remains a research challenge. The latter concept consists of a 3-D filter with
inclusion of spatially correlated (fine-scale) state and (coarse-scale) observation prediction
errors and has been addressed in EnKF frameworks by Reichle et al. (
2001b
,
2013
),
Reichle and Koster (
2003
), Pan et al. (
2009
), De Lannoy et al. (
2010
) and Sahoo et al.
(
2013
).
An important issue connected to 3-D filtering for disaggregation is the use of local
observations to update neighbouring locations, for example, to propagate from observed
swaths to unobserved locations. Often, this problem is solved with spatial interpolation or
by relying on horizontal connections in the model equations (Walker et al.
2002
). Alter-
natively, such horizontal information propagation can be done within an assimilation
scheme that provides accurate error correlations between observed and non-observed
observations and forecasts (Reichle and Koster
2003
; De Lannoy et al.
2012
). De Lannoy
et al. (
2009
) used an adaptive KF to identify such spatial correlations, along with the
magnitude of the forecast error, to optimize filter performance. Han et al. (
2012b
) studied
the effect of spatial correlations in an OSSE (observing system simulation experiment)
with a local ensemble transform Kalman filter. Filter technical issues such as update
frequency (Walker and Houser
2004
) and error estimation have also been addressed in a
spatial context. Reichle and Koster (
2005
) demonstrated the validity of the concept that
assimilation results should be better than either the model or observations alone. After
re-scaling satellite observations from AMSR-E and SMMR to take bias out of the system,
Reichle et al. (
2007
) showed that satellite observations can contribute valuable informa-
tion, even if they are not accurate. Reichle et al. (
2009
) further assessed the quality of
assimilation products as a function of retrieval and land surface model uncertainty in an
OSSE and showed that soil moisture retrievals can have slightly less skill than the land
surface model and still contribute to an overall higher skill in the assimilation product. This
was confirmed in a real data assimilation study by Draper et al. (
2012
).
