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Probing new sequential schemes for retrospective data assimilation in geophysics – PROSSDAG

Submission summary

1- Scientific background and objectives The goal of data assimilation is to combine optimally various sources of data, typically a model and observations, to estimate the state of a physical system. One of the main drawbacks of sequential data assimilation methods, such as the Kalman filter, is that they only use the direct model, and hence cannot anticipate the future evolution of the system to improve its estimation at a given time. The goal of this project is to study a method aimed at bypassing this limitation, and in which the assimilation process alternates between the direct and backward models. Such a method will have in particular the main advantage of a very simple numerical implementation, whereas the human implementation cost needed by the current data assimilation methods is increasingly growing. 2- Description of the project, methodology The first aspect of the project is to establish the properties and conditions for convergence of the system. The backward model is in general unstable (as illustrated by the diffusion equation), but thanks to assimilation, the observations can be used to constrain the backward model within a realistic range. It has already been proved (both theoretically and numerically) on a toy model (simplified oceanic model, large network of observations, degraded Kalman filter) that the backward model can be stabilized by adding a constraint that forces the data assimilation back to the observations. It remains necessary to extend this preliminary result to a more realistic case (primitive equations model, incomplete observations, SEEK filter). This step will be carried out by replacing the problem of data assimilation and BFN algorithm into the more general framework of the observation problem for dynamical systems developed the last fifty years in the automatic and control theory field. In these two domains, the observation and filtering problems are closely linked, and the recent development of nonlinear filters and observers provides an additional theoretical basis to this project, as it has recently allowed us to prove some theoretical convergence results on simple nonlinear EDO systems. The second aspect is to continue the numerical tests for simple models (Burgers equation, or baroclinic quasi-geostrophic ocean model), and with a simplified sequential assimilation method: Newtonian relaxation from the model to the observations (nudging). It will then be compared with the two classical assimilation methods (4D-Var and Kalman filter) in several twin experiments (the observations are extracted from the model runs, and the time and spatial distributions can be set arbitrarily) in which the observation network will be more and more sparse, which make it harder to control the backward model. Statistical interpolation and the Kalman filter, which are more sophisticated than simple nudging, will be tested in order to possibly address the deficiencies of nudging and improve assimilation. This numerical validation will be jointly carried out with the theoretical aspect mentioned in the previous paragraph. We will study at the same time the effect of the presence of data and/or model errors in the identification process. The third aspect is to implement the method for a general oceanic circulation model (OPA). This will be done in twin experiments, first with a complete observation network, then in the partial case; and first using nudging, then using the Kalman filter developped at LEGI (SEEK filter). Finally, the implementation will be carried out with real data. The results will be compared to those of 4D-Var and standard SEEK. It is also clear that this will be jointly carried out with the theoretical study of back and forth algorithms applied to oceanic circulation models. 3- Expected results The long-term objectives are on one hand to obtain convergence results for the various existing direct and backward methods, and compare this new class of algorithms to classical assimilation methods on the OPA model, the goal being to identify the real trajectory of the system at least as accurately and as efficiently as those methods. By obtaining theoretical results of convergence (possibly in simplified cases) and especially by the numerical validation with real sets of observations, it will be possible to achieve the development of this new class of data assimilation algorithms. The numerical validation should confirm the preliminary results of quite good identification of the model/data errors. This will provide to the oceanographic (and more generally geosciences) community an alternative class of realistic data assimilation algorithms, with a very simple implementation.

Project coordination

Didier AUROUX (Université)

The author of this summary is the project coordinator, who is responsible for the content of this summary. The ANR declines any responsibility as for its contents.

Partner

Help of the ANR 90,000 euros
Beginning and duration of the scientific project: - 36 Months

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