Data Assimilation Challenges Posed by Nonlinear Operators: A Comparative Study of Ensemble and Variational Filters and Smoothers

Abstract

The ensemble Kalman filter (EnKF) and the 4D variational method (4DVar) are the most commonly used filters and smoothers in atmospheric science. These methods typically approximate prior densities using a Gaussian and solve a linear system of equations for the posterior mean and covariance. Therefore, strongly nonlinear model dynamics and measurement operators can lead to bias in posterior estimates. To improve the performance in nonlinear regimes, minimization of the 4DVar cost function typically follows multiple sets of iterations, known as an outer loop, which helps reduce bias caused by linear assumptions. Alternatively, iterative ensemble methods follow a similar strategy of periodically relinearizing model and measurement operators. These methods come with different, possibly more appropriate, assumptions for drawing samples from the posterior density, but have seen little attention in numerical weather prediction (NWP) communities. Last, particle filters (PFs) present a purely Bayesian filtering approach for state estimation, which avoids many of the assumptions made by the above methods. Several strategies for applying localized PFs for NWP have been proposed very recently. The current study investigates intrinsic limitations of current data assimilation methodology for applications that require nonlinear measurement operators. In doing so, it targets a specific problem that is relevant to the assimilation of remotely sensed measurements, such as radar reflectivity and all-sky radiances, which pose challenges for Gaussian-based data assimilation systems. This comparison includes multiple data assimilation approaches designed recently for nonlinear/non-Gaussian applications, as well as those currently used for NWP.