POD/DEIM reduced-order strategies for efficient four dimensional variational data assimilation

Journal Article · Sat Aug 15 04:00:00 EDT 2015 · Journal of Computational Physics

DOI:https://doi.org/10.1016/J.JCP.2015.04.030· OSTI ID:22465644

This work studies reduced order modeling (ROM) approaches to speed up the solution of variational data assimilation problems with large scale nonlinear dynamical models. It is shown that a key requirement for a successful reduced order solution is that reduced order Karush–Kuhn–Tucker conditions accurately represent their full order counterparts. In particular, accurate reduced order approximations are needed for the forward and adjoint dynamical models, as well as for the reduced gradient. New strategies to construct reduced order based are developed for proper orthogonal decomposition (POD) ROM data assimilation using both Galerkin and Petrov–Galerkin projections. For the first time POD, tensorial POD, and discrete empirical interpolation method (DEIM) are employed to develop reduced data assimilation systems for a geophysical flow model, namely, the two dimensional shallow water equations. Numerical experiments confirm the theoretical framework for Galerkin projection. In the case of Petrov–Galerkin projection, stabilization strategies must be considered for the reduced order models. The new reduced order shallow water data assimilation system provides analyses similar to those produced by the full resolution data assimilation system in one tenth of the computational time.

• OSTI ID: 22465644
• Journal Information: Journal of Computational Physics, Journal Name: Journal of Computational Physics Vol. 295; ISSN JCTPAH; ISSN 0021-9991
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
APPROXIMATIONS
FINITE DIFFERENCE METHOD
FLOW MODELS
FOUR-DIMENSIONAL CALCULATIONS
INTERPOLATION
KINETIC EQUATIONS
NONLINEAR PROBLEMS
SIMULATION
TWO-DIMENSIONAL CALCULATIONS
VARIATIONAL METHODS
WATER