A POD-based ensemble four-dimensional variational assimilation method

Abstract

In this paper, a POD-based ensemble four-dimensional variational data assimilation method (referred to as PODEn4DVar) is proposed on the basis of the proper orthogonal decomposition (POD) and ensemble forecasting techniques. The ensemble forecasts are conducted to obtain the model perturbations (MPs) and their corresponding observation perturbations (OPs). Under the assumption of the linear relationship between the MPs and the OPs, the POD transformation is applied to the OP space rather than the MP space directly, which substantially decreases the computational costs. The optimal MP and its corresponding OPs is thus represented by the transformed MP ensemble and their related OP orthogonal base vectors to fit the 4-D observation innovations in the assimilation window. Further, the implementation of the forecast model ensemble update is successfully implemented by replacing the single 4-D observation innovation with the ensemble of innovation vectors. The feasibility and effectiveness of the PODEn4DVar are demonstrated in an idealized model with simulated observations. It is found that the PODEn4DVar is capable of outperforming both 4DVar and the EnKF under both perfect and imperfect-model scenarios with lower computational costs compared with EnKF.