Tempered ensemble Kalman filter for strongly nonlinear observation operators

Abstract

Nonlinear relationships between model state variables and complex observations such as radar reflectivity or satellite radiances can degrade data assimilation schemes that rely on linear assumptions and Gaussian error statistics. This study investigates likelihood tempering coupled with the ensemble Kalman filter (TEnKF) to address these nonlinearities by assimilating observations iteratively with adjusted error covariances. Using the Lorenz-96 model and a strongly nonlinear observation operator designed to mimic the inherent challenges of radar reflectivity, we evaluate sensitivity to the number of iterations, ensemble size, and relative amount of information assimilated at each iteration. Results show that the TEnKF improves stability and performance with respect to the standard EnKF for nonlinear operators at modest computational cost. Larger improvements are found in challenging regimes such as small ensembles, sparse observing networks, and small observation-error variance. Moreover, most of the beneficial impact of tempering is obtained with two to three iterations, thus limiting additional computational overhead. Furthermore, a comparison with adaptive observation-error inflation reveals that, while both methods improve filter stability, the information-preserving nature of the TEnKF yields superior accuracy in sparse observing networks.