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This work develops a new multifidelity ensemble Kalman filter (MFEnKF)algorithm based on linear control variate framework. The approach allows forrigorous multifidelity extensions of the EnKF, where the uncertainty in coarserfidelities in the hierarchy of models represent control variates for theuncertainty in finer fidelities. Small ensembles of high fidelity model runsare complemented by larger ensembles of cheaper, lower fidelity runs, to obtainmuch improved analyses at only small additional computational costs. Weinvestigate the use of reduced order models as coarse fidelity control variatesin the MFEnKF, and provide analyses to quantify the improvements over thetraditional ensemble Kalman filters. We apply these ideas to perform dataassimilation with a quasi-geostrophic test problem, using direct numericalsimulation and a corresponding POD-Galerkin reduced order model. Numericalresults show that the two-fidelity MFEnKF provides better analyses thanexisting EnKF algorithms at comparable or reduced computational costs.

A Multifidelity Ensemble Kalman Filter with Reduced Order Control Variates