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.