Comparison of sequential updating, Kalman filter and variational methods for assimilating Rossby waves in the simulated Geosat altimeter data into a quasi-geostrophic model

A variational method is examined for assimilating linear Rossby waves to be observed in Geosat altimeter data into a quasi-geostrophic model and compared with both a simple sequential updating method and the Kalman filter method. A particular emphasis is given to the vertical transfer of surface information contained in the altimeter data. Data are taken from theoretical solutions of linear Rossby waves in a two-layer channel with the data sampling scheme of the Geosat altimeter. These simulated data are assimilated into the same model with a domain of 8 Geosat tracks for 5 cycles of 17-day repeats. In the variational method, a preparation procedure is carried out prior to the variational assimilation to give a good first guess. The control variables are the initial and boundary conditions. This procedure enables the variational method to reconstruct the Rossby wave solutions in both layers with less than 20% of initial rms errors after a few tens of iterations. In the sequential updating method, the upper-layer pressure is matched with the data, while the lower-layer potential vorticity is assumed to be unchanged at updating as done widely in the other work. Since vertical projection is inefficient with this assumption, the lower-layer field is not reconstructed well. The Kalman filter method “accumulates” information on error propagation as the assimilation proceeds, and becomes more efficient than the sequential updating method after a couple of repeat cycles. The assimilation of the simulated Rossby waves implies advantage and disadvantage of each method in assimilating more general mesoscale variability observed in altimeter data into a quasi-geostrophic model.