A STEADY-STATE KALMAN FILTER FOR ASSIMILATING DATA FROM A SINGLE POLAR ORBITING SATELLITE

A steady-state scheme for data assimilation in the context of a single , short period (relative to a day), sun-synchronous, polar-orbiting sa tellite is examined. If the satellite takes observations continuously, the gains, which are the weights for blending observations and predic tions together, are: steady in time. For a linear system forced by ran dom noise, the optimal steady-state gains (Wiener gains) are equivalen t to those of a Kalman filter. Computing the Kalman gains increases th e computational cost of the model by a large factor, but computing the Wiener gains does not. The latter are computed by iteration using pri or estimates of the gains to assimilate simulated observations of one run of the model, termed ''truth,'' into another run termed ''predicti on.'' At each stage, the prediction errors form the basis for the next estimate of the gains. Steady state is achieved after three or four i terations. Further simplification is achieved by making the gains depe nd on longitudinal distance from the observation point, not on absolut e longitude. For a single-layer primitive equation model, the scheme w orks well even if only the mass field is observed but not the velocity field. Although the scheme was developed for Mars Observer, it should be applicable to data retrieved from Earth atmosphere satellites, for example, UARS.