A Sampling Filter for Non-Gaussian Data Assimilation
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Data assimilation combines information from models, measurements, and priors to estimate the state of a dynamical system such as the atmosphere. The Ensemble Kalman filter (EnKF) is a family of ensemble-based data assimilation approaches that has gained wide popularity due its simple formulation, ease of implementation, and good practical results. Most EnKF algorithms assume that the underlying probability distributions are Gaussian. Although this assumption is well accepted, it is too restrictive when applied to large nonlinear models, nonlinear observation operators, and large levels of uncertainty. Several approaches have been proposed in order to avoid the Gaussianity assumption. One of the most successful strategies is the maximum likelihood ensemble filter (MLEF) which computes a maximum a posteriori estimate of the state assuming the posterior distribution is Gaussian. MLEF is designed to work with nonlinear and even non-differentiable observation operators, and shows good practical performance. However, there are limits to the degree of nonlinearity that MLEF can handle. This paper proposes a new ensemble-based data assimilation method, named the "sampling filter", which obtains the analysis by sampling directly from the posterior distribution. The sampling strategy is based on a Hybrid Monte Carlo (HMC) approach that can handle non-Gaussian probability distributions. Numerical experiments are carried out using the Lorenz-96 model and observation operators with different levels of non-linearity and differentiability. The proposed filter is also tested with shallow water model on a sphere with linear observation operator. The results show that the sampling filter can perform well even in highly nonlinear situations were EnKF and MLEF filters diverge.