ADVANCES IN SEQUENTIAL ESTIMATION FOR ATMOSPHERIC AND OCEANIC FLOWS

What: Estimate the state of a fluid system - the atmosphere or oceans - from incomplete and inaccurate observations, with the help of dynami cal models. When: After the observations have been made and before mak ing a numerical forecast of the system. If the evolution of the system over some finite time is to be evaluated - i.e., if interested in cli mate rather than prediction - sequential estimation proceeds by scanni ng through the observations over the interval, forward and back. How: Admit that the dynamical model of the system isn't perfect either. Ass ign relative weights to the current observations and to the model fore cast, based on past observations, that are inversely proportional to t heir respective error variances. Yes, but: To compute the forecast err ors is computationally expensive. So what: Compromise! The thrust of t his review is to illustrate some smart ways of (i) near-optimal, but c omputationally still feasible implementation of the extended Kalman fi lter (EKF), while using (ii) the EKF for observing system design, as w ell as for estimating (iii) the state and parameters of (iv) unstable and strongly nonlinear systems, including (v) the coupled ocean-atmosp here system.