Hybrid Ensemble Kalman Filter and Markov Chain Monte Carlo Implementations for Non-Gaussian Data Assimilation

Abstract

This paper proposes two efficient matrix-free ensemble Kalman filter implementations for non-linear Data Assimilation (DA). Starting with an ensemble of model realizations, the proposed methods employ Markov chains and Gaussian kernels to sample from posterior error distributions. The first method employs a Random-Walk to propose candidates, while the second one does it via the pre-conditioned Crank-Nicholson (pCN) proposal distribution. For the pCN formulation, an iterative matrix-free method is employed to generate samples from the proposal distribution. The posterior ensemble can then be built similar to that of the posterior ensemble Kalman filter implementation. Experimental tests are performed
by using the Lorenz-96 model. Two observational operators are employed: a non-smooth operator and an exponential one. For full observational networks, prior and posterior errors differ by order of magnitudes. In terms of Root-Mean-Square-Errors, prior errors are decreased by several order of magnitudes for observation coverages of 70%, 80%, and 90% model components.