A variational method for orographic filtering in NWP and climate models

Numerical models of the atmosphere are known to experience problems with near-grid-scale orographic forcing, particularly the formation of spurious grid-point storms. These problems can seriously undermine the accuracy and stability of model integrations, so possible methods for reducing them are of interest. Previous studies indicate that filtering the orographic field is effective in addressing these issues, and they motivate this work. Two potential disadvantages of orographic filtering are the loss of height from important barrier ridges and the adjustment of sea points to non-zero height. To counter these effects, a new variational filtering method is developed, which emulates a class of linear filters but allows the imposition of other conditions on the filtered orography. The properties of the method are explored analytically and confirmed in practice. A representative range of filtered/constrained orographies are then evaluated in a global, nonlinear shallow-water model, under a variety of flow regimes. The results indicate that the benefits of orographic filtering increase as the flow becomes more nonlinear and more balanced; since atmospheric flows are generally more nonlinear and more balanced than the model used here, this evidence is taken to support the use of orographic filtering in an NWP context. The benefits of extra filtering constraints are weakly supported, but they need further evaluation.