Estimation of mid-latitude Rossby waves using a simple ocean model and Kalman filtering with TOPEX/POSEIDON altimeter data

Long baroclinic Rossby waves are a mechanism by which mid-latitude oceans adjust to low frequency wind forcing. Observation of such large-scale planetary waves with Earth based observation systems has always been difficult. In this work, we describe a technique for inverse modeling of long baroclinic Rossby waves based on simulated annealing and Kalman filtering of TOPEX satellite altimeter data. The mid-latitude dynamics of the model are governed by the low-frequency forced quasi-geostrophic vorticity equation on a {dollar}beta{dollar}-plane, which limits sea surface height anomaly (SSHA) changes to those caused by radiation of long (nondispersive) Rossby waves and Ekman pumping. An additional local seasonal heating and cooling is introduced to account for the annual steric signal. The SSHA is the dependent variable, while free parameters predetermined by simulated annealing include the reduced gravity, the westward Rossby wave speed, and phase and amplitude of the local seasonal heating. A Kalman filter, based on the model dynamics forced with '93-'95 wind stress anomalies is used with TOPEX SSHA data and the annealed parameter estimates. The filter state vector is constructed along a line of latitude in each basin and is comprised of a mean phase speed from the annealing and the TOPEX SSHA observations at one degree resolution. Regions of free wave and Ekman pumping activity were identified by correlating individual terms to the time rate of change of the filtered SSHA after removing the estimate of the local heat flux. Free wave propagation was found to exist throughout most of the global oceans. Filtered phase speeds at high latitudes were faster than those predicted by linear Rossby wave theory as found in earlier subjective studies. To identify frequency components in the filtered TOPEX data, a multi-channel singular spectrum analysis (MSSA) techniques was used. Semiannual, annual, and interannual components were extracted. Correlations of the Rossby and Ekman terms with the reconstructed signals showed that semiannual and annual frequencies were dominated by wind forcing, while interannual waves may be forced by other mechanisms such as Kelvin wave reflection.