Jacques Blum

A simplified reduced order Kalman filtering and application to altimetric data assimilation in Tropical Pacific

Several studies have demonstrated the effectiveness of the singular evolutive extended Kalman (SEEK) filter and its interpolated variant called singular evolutive interpolated Kalman (SEIK) filter in their capacity to assimilate altimetric data into ocean models. However, these filters remain expensive for real operational assimilation. The purpose of this paper is to develop degraded forms of the SEIK filter which are less costly and yet perform reasonably well. Our approach essentially consists in simplifying the evolution of the correction basis of the SEIK filter, which is the most expensive part of this filter. To deal with model instabilities, we also introduce two adaptive tuning schemes to control the correction basis evolution and adjust the variable forgetting factor. Our filters have been implemented in a realistic setting of the OPA model over the tropical pacific zone and their performance studied through twin experiments in which the observations are taken to be synthetic altimeter data sampled on the sea surface. The SEIK filter is used as a reference for comparison. Our new filters perform nearly as well as the SEIK, but can be 2–30 times faster. D 2002 Elsevier Science B.V. All rights reserved.

A semi-evolutive filter with partially local correction basis for data assimilation in oceanography

A new data assimilation scheme derived from the singular evolutive extended Kalman (Seek) filter is introduced. The novel feature of the new filter is its correction basis which is partially local in the sense that it consists of “global” and “local” vectors, the later obtained from a local empirical orthogonal functions (Eof) analysis. Such an analysis was introduced in order to better represent the local variability of the ocean. This not only significantly reduces the implementation cost but may also improve the representativeness of the correction basis of the filter.TheperformanceofthisschemeisevaluatedthroughtwinexperimentsconductedinarealisticsettingoftheOPAmodeloverthetropical Pacific zone.The results are compared against those of the Seekfilter.The newfilter is shown to perform better while it is up to six times faster. Adaptive tuning of the forgetting factor was also used, which enhances performance and improves the stability of the filter during model unstable periods.