Efficiency of a POD-based reduced second order adjoint model in 4-D VAR data assimilation

D.N. Daescu, I. M. Navon

Order reduction strategies aim to alleviate the computational burden of the four dimensional variational data assimilation by performing the optimization in a low order control space. The proper orthogonal decomposition (POD) approach to model reduction is used to identify a reduced order control space for the two dimensional global shallow water model. A reduced second order adjoint (SOA) model is developed and used to facilitate the implementation of a Hessian-free truncated Newton (HFTN) minimization algorithm in the POD-based space. The efficiency of the SOA/HFTN implementation is analyzed by comparison with the quasi-Newton BFGS and a nonlinear conjugate gradient algorithm. Several data assimilation experiments that differ only in the optimization algorithm employed are performed in the reduced control space. Numerical results indicate that first order derivative methods are effective during the initial stages of the assimilation; in the later stages, the use of the second order derivative information is of benefit and the HFTN provided significant CPU time savings when compared to the BFGS and CG algorithms. Further experiments are required to validate the approach for comprehensive global circulation models.