On an adaptive filter for altimetric data assimilation and its application to a primitive equation model, MICOM

In a reduced-order adaptive filtering approach, we demonstrate a possibility to overcome two major difficulties in estimating oceanic circulation: a very high dimension of the system state and uncertainties in specification of the model error statistics. This approach is based essentially on the assumption that a particular parametrized gain matrix has been selected and the tuning parameters are adjusted by minimizing the mean prediction error. In the present paper we apply a reduced-order adaptive filter for solving the problem of assimilating altimetric sea surface height into a primitive equation model: the Miami isopycnic coordinate ocean model (MICOM). A gain structure is described which is proven to be very efficient in the twin experiments. The assimilation algorithm to be employed in the identical twin experiment is a reduced-order filter whose reduced state consists of the layer thickness. The velocity update is calculated from the geostrophic hypothesis. The gain structure for the non-adaptive filter is obtained on the basis of three principal hypotheses: (H1) analysis error for the system output is cancelled in the case of noise-free observations (as is done naturally in a standard Kalman filter for noise-free observation); (H2) conservation of linear potential vorticity; (H3) no correction for the velocity at the bottom layer. The initial values of the parameters in the gain will be selected in such a way that the filter behaves exactly as the Cooper’Haines filter (CHF) at the first data update step. It is shown that the adaptive filter, which relaxes one or several of the above hypotheses, is capable of producing the better estimates for the ocean state (layer thickness and velocity) compared to that produced by the CHF in all layers, surface or subsurface. Numerical experiments demonstrate the excellent capacity of the adaptive filter to extract useful information from surface observations for inferring the oceanic circulation in the MICOM.