

On an Adaptive Filter Based on Forecast Errors Modelling for SSH Data Assimilation and its Comparison with Optimal Interpolation Method
Hong Son Hoang^{(1)} , Rémy Baraille^{(1)} , Yves Morel^{(1)} , Michel Gavart^{(1)} , Michel Assenbaum^{(1)} , Nicolas Filatoff^{(1)} , and Olivier Talagrand^{(2)}
^{(1)}
SHOM/LEGOS,
18 Av E. Belin,
31401,
France
^{(2)} LMD/ENS, 24 rue Lhomond, 75231, France
Abstract
Defining the gain is a key problem in
application of filtering technique for data assimilation
in meteorology and oceanography. Due to insurmountable difficulties
related to very high dimensions of the system state and uncertainties
in modelling model error, simple sequentiel algorithms like
OI schemes are widely used in comparison with other advanced methods
(Kalman filter ...) because of its less time consuming and
less computer memory. The performance of the OI scheme depends essentially on specification of the forecast error covariance matrix (ECM)(or background covariance matrix).
Usually the ECM is chosen apriori as a constant matrix. The question on how to specify the ECM is of first importance since it determines
a performance of the filter. This question will be addressed in this talk in the context of SSH data assimilation for oceanic models.
The approach used here is based on modelling the forecast errors.
It will be shown that the procedure of modelling forecast error
is quite similar to that done in the construction
of breeding modes. The filter gain can be derived : (i)
either by using only the forecast perturbations derived
from integration of the numerical model alone (without using the observations). The filter with the gain obtained in this way (it is in some sense an OI algorithm) will be applied after to
assimilate the observations; (ii) or by integrating the model from
a set of analysed and perturbed states and evolving the gain
during the assimilaion process. The forecast errors will be used to estimate some parameters of the parametrized ECM and thus, to initialize the gain structure. It will be shown that the proposed filter performs much better than the standard CooperHaines filter. A considerable improvement of the filter performance can be achieved also by employing the adaptive technique based on parametrization of the gain derived from the modelled forecast errors.
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