A Comparison of Adaptive Kalman Filters for a Tropical Pacific Ocean Model

The Kalman filter is the optimal linear assimilation scheme only if the first- and second-order statistics of the observational and system noise are correctly specified. If not, optimality can be reached in principle by using an adaptive filter that estimates both the state vector and the system error statistics. In this study, the authors compare the ability of three adaptive assimilation schemes at estimating an unbiased, stationary system noise. The adaptive algorithms are implemented in a reduced space linear model for the tropical Pacific. Using a twin experiment approach, the algorithms are compared by assimilating sea level data at fixed locations mimicking the tropical Pacific tide gauges network. It is shown that the description of the system error covariance matrix requires too many parameters for the adaptive problem to be well posed. However, the adaptive procedures are efficient if the number of noise parameters is dramatically reduced and their performance is shown to be closed to optimal, that is, based on the true system noise covariance. The link between those procedures is elucidated, and the question of their applicability and respective computational cost is discussed.