A Locally Mass Conserving Monotonic Filter for Use in Semi-Lagrangian Models

A new locally mass conserving and shape-preserving anti-diffusive filter to be applied in semi-Lagrangian type models has been designed. The filter successively redistributes local mass in a way bringing the resulting values closer to target values. The target values, in turn, are specified from a non-linear anti-diffusion of the original non-filtered forecast. To achieve monotonicity the target values are furthermore constrained to be located within a certain range which is given by the minimum and maximum value of the upstream grid points surrounding the semi-Lagrangian departure point.

The filter has been combined with the recently developed locally mass conserving semi-Lagrangian (LMCSL) scheme. A number of tests simulations in one and two dimensions demonstrate that the combined scheme is stable and shape preserving. Furthermore the accuracy is enhanced considerably as compared to the original LMCSL scheme, particularly near sharp changes in gradients. Based on a number of objective verification scores it has been found that the filtered test simulations generally correspond to a 10 to 400 {percent} increase in resolution.

The cost of the scheme is not negligible but it is much smaller than the additional cost needed to increase the resolution of the (non-monotonic) unfiltered scheme to a comparable overall accuracy.