Non-Gaussian Data Assimilation Via Modified Cholesky Decomposition

This paper proposes an ensemble Kalman filter implementation for non-linear data assimilation. As in any ensemble based method, the moments of background error distributions are approximated by means of an ensemble of model realizations. The precision background covariance is estimated via a modified Cholesky decomposition in order to decrease the impact of sampling errors. Once all hyper-parameters are estimated, samples from the posterior distribution are estimated via a Markov-Chain-Monte-Carlo (MCMC) method. The MCMC implementation is enhanced by means of linear approximations of the observation operator. Posterior ensembles are then built by using a series of rank-one updates over prior Cholesky factors. Experimental tests are carried out by using the Lorenz 96 model. The numerical results evidence that, as the degree of the observational operator increases, the accuracy of the proposed filter is not affected and even more, for full observational networks, posterior errors are much lower than those of backgrounds, in some cases, by several order of magnitudes.