Bayesian approach to data assimilation based on ensembles of forecasts and observations

Abstract

Abstract Optimal assessment of geophysical fields with observational data and a mathematical model is a data assimilation problem. To solve it, a Bayesian approach is most often used. In the ensemble algorithms, ensembles of forecasts and observations are used to approximate the covariance matrices considered in the algorithm. If all probability densities are Gaussian, the problem is reduced to that of the ensemble Kalman filter. In the strongly non- Gaussian case, a particle method is used, which is based on a Bayesian approach. Ensembles are also used in this method. In the research devoted to the ensemble Kalman filter much attention is paid to deviation of ensemble elements from an average value – ensemble spread. In this paper, a comparative analysis of spread behavior over time when using different approaches to the improvement of the convergence of the algorithms is performed. The results of numerical experiments with a 1-dimensional test model are discussed. These results show that in stochastic filters the behavior over time of ensemble spread is close to the theoretical error estimate. Some of the approaches that improve convergence in the ensemble filter, such as additive inflation and multiplicative inflation, change the general formula for ensemble spread.