A dual-weighted trust-region adaptive POD 4D-VAR applied to a FEM shallow-water equations model

Abstract

A limited-area finite-element model of the nonlinear shallow-water equations is used to solve an inverse problem where the initial conditions are optimized in presence of observations being assimilated in a time interval. We then consider a reduced-order model of the above inverse problem, based on proper orthogonal decomposition (POD), referred to as POD 4-D VAR. A dual-weighted method for efficient POD snapshot selection is coupled with a trust-region adaptivity approach. Numerical results obtained point to an improved accuracy in all metrics tested when dual-weighing choice of snapshots is combined with POD adaptivity of the trust-region type. Results of ad-hoc adaptivity of the POD 4-D VAR turn out to yield less accurate results than trust-region POD when compared with the high-fidelity model. Directions of future research will be outlined.