Title: Reduced-Order Strategies for Efficient 4D-Var Data Assimilation

Author: Răzvan Ştefănescu (Virginia Tech)
Adrian Sandu (Virginia Tech)

Our work proposes the use of the reduced order modeling (ROM) approaches to speed up the solu- tion of variational data assimilation problems with large scale nonlinear dynamical models. It is shown that a key ingredient for a successful reduced order solution to inverse problems is the consistency of the reduced order Karush-Kuhn-Tucker conditions with respect to the full optimality conditions. In particular, accurate reduced order approximations are needed for both the forward dynamical model and for the adjoint model. New bases selection strategies are developed for Proper Orthogonal Decom- position (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 findings. In case of Petrov- Galerkin reduced data assimilation, stabilization strategies must be considered for the reduced order models. The new hybrid tensorial POD/DEIM shallow water ROM data assimilation system provides analyses similar to those produced by the full resolution data assimilation system in one tenth of the computational time.

GMAO Head: Steven Pawson Global Modeling and Assimilation Office NASA Goddard Space Flight Center

Curator: Nikki Privé Last Updated: Feb 9 2015