Data assimilation with extremum Monte Carlo methods

Abstract 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.