295
This technique has been developed more specifically for eddy-resolving
ocean assimilation models in which the signal dominates in the small
scales. Figure 6 illustrates the surface signature and vertical extension
of the three dominant modes calculated with an eddy-permitting model
in the Gulf Stream region. Theses modes reflect to some extent the
anisotropic nature of the multivariate covariances associated with the
local dynamics, with smaller scales represented by higher modes.
The local representation of the error sub-space has been shown to be
particularly eective for capturing the mesoscale features of the turbulent ocean. In the example described by Pendu et al. [2002], an assimilative system based on local EOFs was implemented in a 1/3 South
Atlantic OPA model to perform hindcast experiments for the 1993-1996
period. The assimilated data are similar to those shown in figure 4, consisting of composite AVHRR observations of SST and altimetric measurements of the sea-level anomalies. The results show that the assimilation is able to successfully reproduce the Agulhas Rings present at
that time in the real ocean. In addition to correcting the variables observed at the surface, the three-dimensional multivariate properties of
the EOFs also permitted a correction of the non-observed variables in
the ocean’s interior. The beneficial impact of the assimilation was particularly impressive on the mean salinity in the Confluence region down
to about 1500 meters depth.
6.
Low-rank Kalman filters
Several low-rank filters based on static or evolving error sub-spaces
have been developed over the past ten years, such as the SEEK filter
introduced by Pham et al. [1998] and the Reduced-Rank-SQuare-RooT
(RRSQRT) formulation explored by Verlaan and Heemink [1997]. Many
features of the Ensemble Kalman Filter (EnKF) put forward by Evensen
[1994] can be discussed using a similar framework.
The Ensemble OI scheme [Evensen, 2003] and the SEEK filter with
static error sub-space are two sub-optimal schemes which preserve a
number of important properties of statistical estimation but require only
a small fration of the computer resources needed by the model. In contrast to those simplified schemes, the EnKF or the SEEK filter with
evolutive sub-space propagate the error statistics according to the model
dynamics, but they need the simultaneous integration of model states
perturbed along each direction of the error sub-space.
The consequences of using a low-rank error covariance matrix to compute the forecast and analysis steps of the KF are examined in the
following sections.
OCEAN DATA ASSIMILATION
This technique has been developed more specifically for eddy-resolving
ocean assimilation models in which the signal dominates in the small
scales. Figure 6 illustrates the surface signature and vertical extension
of the three dominant modes calculated with an eddy-permitting model
in the Gulf Stream region. Theses modes reflect to some extent the
anisotropic nature of the multivariate covariances associated with the
local dynamics, with smaller scales represented by higher modes.
The local representation of the error sub-space has been shown to be
particularly eective for capturing the mesoscale features of the turbulent ocean. In the example described by Pendu et al. [2002], an assimilative system based on local EOFs was implemented in a 1/3 South
Atlantic OPA model to perform hindcast experiments for the 1993-1996
period. The assimilated data are similar to those shown in figure 4, consisting of composite AVHRR observations of SST and altimetric measurements of the sea-level anomalies. The results show that the assimilation is able to successfully reproduce the Agulhas Rings present at
that time in the real ocean. In addition to correcting the variables observed at the surface, the three-dimensional multivariate properties of
the EOFs also permitted a correction of the non-observed variables in
the ocean’s interior. The beneficial impact of the assimilation was particularly impressive on the mean salinity in the Confluence region down
to about 1500 meters depth.
6.
Low-rank Kalman filters
Several low-rank filters based on static or evolving error sub-spaces
have been developed over the past ten years, such as the SEEK filter
introduced by Pham et al. [1998] and the Reduced-Rank-SQuare-RooT
(RRSQRT) formulation explored by Verlaan and Heemink [1997]. Many
features of the Ensemble Kalman Filter (EnKF) put forward by Evensen
[1994] can be discussed using a similar framework.
The Ensemble OI scheme [Evensen, 2003] and the SEEK filter with
static error sub-space are two sub-optimal schemes which preserve a
number of important properties of statistical estimation but require only
a small fration of the computer resources needed by the model. In contrast to those simplified schemes, the EnKF or the SEEK filter with
evolutive sub-space propagate the error statistics according to the model
dynamics, but they need the simultaneous integration of model states
perturbed along each direction of the error sub-space.
The consequences of using a low-rank error covariance matrix to compute the forecast and analysis steps of the KF are examined in the
following sections.
OCEAN DATA ASSIMILATION