This paper presents a comparison of two reduced-order, sequential and variational data assimilation methods: the SEEK filter and the R-4D-Var. A hybridization of the two, combining the variational framework and the sequential evolution of covariance matrices, is also preliminarily investigated and assessed in the same experimental conditions. The comparison is performed using the twin-experiment approach on a model of the Tropical Pacific domain. The assimilated data are simulated temperature profiles at the locations of the TAO/TRITON array moorings. It is shown that, in a quasi-linear regime, both methods produce similarly good results. However the hybrid approach provides slightly better results and thus appears as potentially fruitful. In a more non-linear regime, when Tropical Instability Waves develop, the global nature of the variational approach helps control model dynamics better than the sequential approach of the SEEK filter. This aspect is probably enhanced by the context of the experiments in that there is a limited amount of assimilated data and no model error.
Deep Dive into Comparison of reduced-order, sequential and variational data assimilation methods in the tropical Pacific Ocean.
This paper presents a comparison of two reduced-order, sequential and variational data assimilation methods: the SEEK filter and the R-4D-Var. A hybridization of the two, combining the variational framework and the sequential evolution of covariance matrices, is also preliminarily investigated and assessed in the same experimental conditions. The comparison is performed using the twin-experiment approach on a model of the Tropical Pacific domain. The assimilated data are simulated temperature profiles at the locations of the TAO/TRITON array moorings. It is shown that, in a quasi-linear regime, both methods produce similarly good results. However the hybrid approach provides slightly better results and thus appears as potentially fruitful. In a more non-linear regime, when Tropical Instability Waves develop, the global nature of the variational approach helps control model dynamics better than the sequential approach of the SEEK filter. This aspect is probably enhanced by the context o
However the hybrid approach provides slightly better results and thus appears as potentially fruitful. In a more non-linear regime, when Tropical Instability Waves develop, the global nature of the variational approach helps control model dynamics better than the sequential approach of the SEEK filter. This aspect is probably enhanced by the context of the experiments in that there is a limited amount of assimilated data and no model error.
Operational oceanography is an emerging field of activity that is concerned with real-time monitoring and prediction of the physical and biogeochemical state of oceans and regional seas. Operational ocean prediction systems have been made feasible by the concomitance of several elements: the emergence of relatively reliable numerical models and of appropriate computing capabilities, the establishment of global ocean observation systems, and the progress achieved in data assimilation techniques. It is the latter of these advances that is addressed in this paper. In the geophysical context, data assimilation methods face a number of specific difficulties. In particular, due to the very large dimensions of the systems, the computational burden and the prescription of adequate error statistics are critical issues. In addition, there is a need to improve methods in the case of non-linear systems and/or non-gaussian statistics.
Data assimilation methods are generally classified into two groups according to the approach used: the sequential approach, based on the statistical estimation theory and the Kalman filter, and the variational approach (4D-Var), built from the optimal control theory. It is well known that the 4D-Var and Kalman filter approaches provide the same solution, at the end of the assimilation period, for perfect and linear models. These approaches are different however, mainly because the model is seen as a strong constraint in the 4D-Var approach and as a weak constraint in the sequential approach. In addition, the specification and time evolution of the error statistics, the length and structure of the forecast-analysis cycles, and the temporal use of observations may be quite different. In practice, due especially to non-linearity, these differences can result in significant discrepancies between the solutions provided by the two approaches.
The full Kalman filter cannot be used in actual geophysical systems, because specifying of the error covariance matrices is difficult and also involves huge computational costs and impractical matrix handling. The need to circumvent these difficulties has led to the development of reduced-order Kalman filters. Here, order reduction consists in reducing the size of the background error covariance matrix by selecting a number of directions in the state space along which the error variability is assumed to lie. In recent years, this approach has given birth in particular to the Ensemble Kalman Filter (EnKF) (Evensen, 1994), the Reduced-Rank-SQuare-RooT (RRSQRT) filter (Verlaan and Heemink, 1997), the Singular Evolutive Ex-tended Kalman (SEEK) filter (Pham et al., 1998, Verron et al., 1999) and the ESSE method (Lermusiaux and Robinson, 1999). These four methods basically differ in their strategies to approximate the error covariance matrix and/or the way in which they propagate the state error statistics. In the EnKF, the error statistics are propagated using a statistically relevant ensemble of states. The forecast error covariance matrix is not given explicitly. The SEEK and RRSQRT filters are based on a truncation of an eigendecomposition of the error covariance matrix, and partly differ in their initial choice of the approximate low-rank matrix, and with respect to its time evolution. The SEEK takes advantage of the fact that the ocean is a dynamic system with an attractor, and is not intended to make corrections in directions perpendicular to the attractor, which are naturally attenuated by the system. In this paper, the SEEK filter is chosen.
The variational 4D-Var method has long been used in meteorology (e.g. Rabier, 1998) and has been applied to several operational forecasting systems in its incremental form (Courtier et al., 1994), a form that is particularly suited to nonlinear systems. It has also been developed for oceanographic situations (e.g. Greiner and Arnault, 1998a, b;Vialard et al., 2002Vialard et al., , 2003;;Weaver et al., 2003). The method is costly and involves complex software development for the tangent linear and adjoint models. As with sequential estimation, lack of knowledge concerning the error statistics leads to the use of approximations and models for the background error covariance matrix. To solve the problem, the order reduction procedure can also be used for the 4D-Var to build the Reduced-4D-Var (Blayo et al., 1998).
This has been tested in a realistic configuration by Robert et al. (2005). In the Reduced 4D-Var, the control parameter (namely the initial condition) now belongs to a
…(Full text truncated)…
This content is AI-processed based on ArXiv data.
