AN APPROXIMATE KALMAN FILTER FOR OCEAN DATA ASSIMILATION - AN EXAMPLEWITH AN IDEALIZED GULF-STREAM MODEL

A practical method of data assimilation for use with large, nonlinear, ocean general circulation models is explored. A Kalman filter based o n approximations of the state error covariance matrix is presented, em ploying a reduction of the effective model dimension. the error's asym ptotic steady state limit, and a time-invariant linearization of the d ynamic model for the error integration. The approximations lead to dra matic computational savings in applying estimation theory to large com plex systems. We examine the utility of the approximate filter in assi milating different measurement types using a twin experiment of an ide alized Gulf Stream. A nonlinear primitive equation model of an unstabl e east-west jet is studied with a state dimension exceeding 170,000 el ements. Assimilation of various pseudomeasurements are examined, inclu ding velocity, density, and volume transport at localized arrays and r ealistic distributions of satellite altimetry and acoustic tomography observations. Results are compared in terms of their effects on the ac curacies of the estimation. The approximate filter is shown to outperf orm an empirical nudging scheme used in a previous study. The examples demonstrate that useful approximate estimation errors dan be computed in a practical manner for general circulation models.