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A Multifidelity Ensemble Kalman Filter with Reduced Order Control Variates

This work develops a new multifidelity ensemble Kalman filter (MFEnKF) algorithm based on linear control variate framework. The approach allows for rigorous multifidelity extensions of the EnKF, where the uncertainty in coarser fidelities in the hierarchy of models represent control variates for the uncertainty in finer fidelities. Small ensembles of high fidelity model runs are complemented by larger ensembles of cheaper, lower fidelity runs, to obtain much improved analyses at only small additional computational costs. We investigate the use of reduced order models as coarse fidelity control variates in the MFEnKF, and provide analyses to quantify the improvements over the traditional ensemble Kalman filters. We apply these ideas to perform data assimilation with a quasi-geostrophic test problem, using direct numerical simulation and a corresponding POD-Galerkin reduced order model. Numerical results show that the two-fidelity MFEnKF provides better analyses than existing EnKF algorithms at comparable or reduced computational costs.