Sequential data assimilation techniques in oceanography

We review recent developments of sequential data assimilation techniques used in oceanography to integrate spatio-temporal observations into numerical models describing physical and ecological dynamics. Theoretical aspects from the simple case of linear dynamics to the general case of nonlinear dynamics are described from a geostatistical point-of-view. Current methods derived from the Kalman filter are presented from the least complex to the most general and perspectives for nonlinear estimation by sequential importance resampling filters are discussed. Furthermore an extension of the ensemble Kalman filter to transformed Gaussian variables is presented and illustrated using a simplified ecological model. The described methods are designed for predicting over geographical regions using a high spatial resolution under the practical constraint of keeping computing time sufficiently low to obtain the prediction before the fact. Therefore the paper focuses on widely used and computationally efficient methods.