Grid‐point response to the incremental strategy for variational applications

Abstract

AbstractThe incremental approach is an efficient way to reduce the computational cost of four‐dimensional variational assimilation. In this approach, the discrepancy between the forecast fields and the observations is calculated with a full physics model at high resolution, but the minimization is performed at a lower resolution with a simplified physics model. The incremental approach is also used in sensitivity‐analysis applications where errors in the initial conditions are estimated a posteriori by replacing observations by a subsequent analysis. The incremental strategy as used in typical sensitivity analyses with observations corresponding to a full model state is re‐examined in the context of a grid‐point model by establishing how the grid‐transfer operations in grid‐point space influence the convergence properties of the whole incremental process. We show that two incremental grid‐point formulations are possible. In the first formulation, the tangent‐linear perturbations are interpolated at high resolution to be compared with the forecast errors. In the second one, the forecast errors are interpolated to low resolution before the minimization. Using a one‐dimensional study and identical twin experiments in three dimensions, we study the impact of aliasing associated with the grid‐transfer operations on the two incremental formulations. They are both affected by the misinterpretation of unresolved forecast errors leading to a contribution to resolved forecast errors. However, the first formulation has the property of damping this aliasing contribution and this effect is stronger with higher‐order grid‐transfer operators. Copyright © 2002 Royal Meteorological Society.