Data assimilation with extremum Monte Carlo methods

This study presents the extremum Monte Carlo filter as a data assimilation method. The method can be regarded as a variant of the variational approach (three- and four-dimensional variational), where the state estimates are obtained by solving an optimization problem numerically over a space of prediction functions, instead of the state space itself. We discuss the general principle of the new technique and its use of machine-learning methods, such as feed-forward neural networks and tree-based gradient boosting. We further provide the details for its computationally efficient implementation, in both computing time and storage. The extremum Monte Carlo filter is illustrated for the well-known Lorenz-63 and Lorenz-96 models. A performance improvement is found relative to the ensemble Kalman filter for the Lorenz-96 model.