Geoscience Reference
In-Depth Information
measurements. Assimilated satellite observations include retrievals of land surface tem-
perature, soil moisture, snow water equivalent (SWE) and snow cover area (e.g., Van den
Hurk et al.
2002
; Andreadis and Lettenmaier
2006
; Slater and Clark
2006
; Bosilovich et al.
2007
; Dong et al.
2007
; Drusch
2007
; Ni-Meister
2008
; Reichle et al.
2008
; Houser et al.
2010
). Houser (
2003
) discusses the assimilation of land surface retrieved quantities and
radiances. Early reviews of land data assimilation have been provided by McLaughlin
(
2002
), Reichle (
2008
), Moradkhani (
2008
) and Houser et al. (
2010
).
Land data assimilation uses observations to constrain the physical parametrizations and
initialization of land surface states critical for seasonal-to-interannual prediction. These
constraints can be imposed in four ways: (1) by forcing the land surface primarily by
observations (such as precipitation and radiation), often severe atmospheric NWP land
surface forcing biases can be avoided (e.g., Saha et al.
2010
; Reichle et al.
2011
); (2) by
employing innovative land surface data assimilation techniques, observations of land
surface storages (such as snow, soil temperature and moisture) can be used to constrain
unrealistic simulated storages (e.g., Houser et al.
2010
; Reichle et al.
2013
); (3) by tuning
adjustable parameters (e.g., Pauwels et al.
2009
; Vrugt et al.
2012
); and (4) the land surface
physical structure itself can be improved through the data assimilation process when the
constant confrontation of model states against observations returns useful information
about structural deficits. Integration of soil moisture information from satellite instruments,
and ground-based and in situ observations of the land surface, using land data assimilation,
provides a comprehensive picture of the state and variability of the land surface.
4.2 Data Assimilation Methods
Three methods are commonly used for land data assimilation (Houser et al.
2010
): vari-
ational (3- and 4-dimensional, 3D-Var and 4D-Var); sequential (Kalman filter (KF) and
Extended Kalman filter (EKF)); and ensemble (Ensemble Kalman filter, EnKF). Bouttier
and Courtier (
1999
) provide details of these methods. Talagrand (
2010a
) and Kalnay
(
2010
) discuss more recent developments in variational methods and ensemble methods,
respectively.
In the 3-D variational (3D-Var) method, a minimization algorithm is used to find a
model state, x, that minimizes the misfit between x and the background state x
b
, and also
between the observation predictions H(x) and the observations y. The observation operator
H maps the model state x to the measurement space, where y resides. In 3D-Var, we seek
the minimum with respect to x of the penalty function, J, given by Eq. (
1
). The first term on
the right hand side (J
b
) quantifies the misfit to the background term, and the second term
(J
o
) is the misfit to the observations. If the observation operator is linear (written H), the
penalty function, J, is quadratic and is guaranteed to have a unique minimum.
J
¼
1
2
½
x
x
b
T
B
1
½
x
x
b
þ
1
2
½
y
H
ð
x
Þ
T
R
1
½
y
H
ð
x
Þ
ð
1
Þ
4-D variational (4D-Var) assimilation is an extension of 3D-Var in which the temporal
dimension is included, that is, 4D-Var is a smoother. In 4D-Var, observations are used at
their correct time. 4D-Var has two new features compared to 3D-Var. First, it includes a
model operator, M, that carries out the evolution forward in time. The first derivative, or
differential, of M, M, is the tangent linear model (if M is linear, represented by M, its
derivative is M). The transpose of the tangent linear model operator, M
T
, integrates the
adjoint variables backward in time. The tangent linear model is only defined under the
condition that the function J defined by Eq. (
1
) be differentiable—this is the tangent linear
