Data Assimilation Method, its Application and Stability

Abstract

The authors data assimilation method, namely, generalized Kalman filter (GKF) method, its application and stability is considered. The problem of stability of a dynamic system with data assimilation formulated for a sequence of random variables forming a Markov chain is considered. The stability formulation for this problem is suggested as the problem of the convergence of the corresponding Markov chain when the number of its members goes to infinity. Necessary and sufficient conditions of this convergence are proved. A number of numerical experiments with the specific dynamic system, namely with the ocean model circulation HYCOM and the GKF method are conducted and discussed. The stability of the GKF method was proofed.