A NEW HESSIAN PRECONDITIONING METHOD APPLIED TO VARIATIONAL DATA ASSIMILATION EXPERIMENTS USING NASA GENERAL-CIRCULATION MODELS

An analysis is provided to show that Courtier's et al. method for esti mating the Hessian preconditioning is not applicable to important cate gories of cases involving nonlinearity. An extension of the method to cases with higher nonlinearity is proposed in the present paper by des igning an algorithm that reduces errors in Hessian estimation induced by lack of validity of the tangent linear approximation. The new preco nditioning method was numerically tested in the framework of variation al data assimilation experiments using both the National Aeronautics a nd Space Administration (NASA) semi-Lagrangian semi-implicit global sh allow-water equations model and the adiabatic version of the NASA/Data Assimilation Office (DAO) Goddard Earth Observing System Version 1 (G EOS-1) general circulation model. The authors' results show that the n ew preconditioning method speeds up convergence rate of minimization w hen applied to variational data assimilation cases characterized by st rong nonlinearity. Finally, the authors address issues related to comp utational cost of the new algorithm presented in this paper. These inc lude the optimal determination of the number of random realizations p necessary for Hessian estimation methods. The authors tested a computa tionally efficient method that uses a coarser gridpoint model to estim ate the Hessian for application to a fine-resolution mesh. The tests y ielded encouraging results.