A data assimilation technique based on the π-algorithm

A practical implementation of the data assimilation algorithm based on the Kalman filter in its complete formulation is impossible due to high dimension of the associated equation sets and to nonlinearity of the predicted processes. The main direction in the implementation of the Kalman filter is an ensemble approach. Under the assumption of ergodicity of random forecast errors, an alternative algorithm with respect to the ensemble Kalman filter can be considered, in which probability averaging is replaced by time averaging. The proposes algorithm is based this assumption. The algorithm is easy to implement; however, its convergence, applicability to the data assimilation problems, and connection to the Kalman filter have not been studied. In the paper, applicability of the π-algorithm to data assimilation is considered on an example of a simple one-dimensional advection equation. Use of this simple equation allows comparing the classical Kalman filter algorithm with various practical approaches to its implementation.