A spatio-temporal Kalman filter for estimation of barotropic Rossby waves from altimeter data

We derive a true spatio-temporal distributed filter for estimation of barotropic Rossby waves from altimeter data. Previous work on this topic has used spatial discretisation to convert the problem to a large dimension Kalman filter. We also derive a Kalman filter but express it in the spatial domain directly. This preserves the partial differential equation structure offering computational advantages, but also gives considerable insight into the filter structure.