Theoretical and Practical Issues of Ensemble Data Assimilation in Weather and Climate

Abstract

Practical and theoretical issues of ensemble data assimilation are presented and discussed. In presenting the issues, the dynamical view, rather than a typical statistical view, is emphasized. From this point of view, most problems in ensemble data assimilation, and in data assimilation in general, are seen as means of producing an optimal state that is in dynamical balance, rather than producing a state that is optimal in a statistical sense. Although in some instances these two approaches may produce the same results, in general they are different. Details of this difference are discussed. An overview of several fundamental issues in ensemble data assimilation is presented in more detail: dynamical balance of analysis/forecast, inclusion of nonlinear operators, and handling of reduced number of degrees of freedom in realistic high-dimensional applications. An ensemble data assimilation algorithm named the Maximum Likelihood Ensemble Filter (MLEF) is described as a prototype method that addresses the above-mentioned issues. Some results with the MLEF are shown to illustrate its performance, including the assimilation of real observations with the Weather Research and Forecasting (WRF) model.