Four-dimensional ensemble Kalman filtering

Ensemble Kalman filteringwas developed as away to assimilate observed data to track the current state in a computational model. In this paper we showthat the ensemble approach makes possible an additional benefit: the timing of observations, whether they occur at the assimilation time or at some earlier or later time, can be effectively accounted for at low computational expense. In the case of linear dynamics, the technique is equivalent to instantaneously assimilating data as they are measured. The results of numerical tests of the technique on a simple model problem are shown.