Handling Nonlinearity in an Ensemble Kalman Filter: Experiments with the Three-Variable Lorenz Model

Abstract

Abstract An ensemble Kalman filter (EnKF) is optimal only for linear models because it assumes Gaussian distributions. A new type of outer loop, different from the one used in 3D and 4D variational data assimilation (Var), is proposed for EnKF to improve its ability to handle nonlinear dynamics, especially for long assimilation windows. The idea of the “running in place” (RIP) algorithm is to increase the observation influence by reusing observations when there is strong nonlinear error growth, and thus improve the ensemble mean and perturbations within the local ensemble transform Kalman filter (LETKF) framework. The “quasi-outer-loop” (QOL) algorithm, proposed here as a simplified version of RIP, aims to improve the ensemble mean so that ensemble perturbations are centered at a more accurate state. The performances of LETKF–RIP and LETKF–QOL in the presence of nonlinearities are tested with the three-variable Lorenz model. Results show that RIP and QOL allow LETKF to use longer assimilation windows with significant improvement of the analysis accuracy during periods of high nonlinear growth. For low-frequency observations (every 25 time steps, leading to long assimilation windows), and using the optimal inflation, the standard LETKF RMS error is 0.68, whereas for QOL and RIP the RMS errors are 0.47 and 0.35, respectively. This can be compared to the best 4D-Var analysis error of 0.53, obtained by using both the optimal long assimilation windows (75 time steps) and quasi-static variational analysis.