Application of a Semi-Lagrangian Integration Scheme to the Moisture Equation in a Regional Forecast Model

Abstract

Scale-dependent phase errors are characteristic of Eulerian advection schemes and can lead to significant erroneous dispersion, especially for features whose length scales are near the resolution limits of a numerical model. However, the corresponding errors are much smaller for a semi-Lagrangian scheme using a high-order interpolation technique. This property is exploited by introducing a semi-Lagrangian formulation in the moisture equation of the DRPN (Division de Recherche en Prévision Numérique) regional baroclinic finite element model. The impact of this change is assessed by comparing the resulting precipitation fields with those from the version of the model in which all variables are treated using the Eulerian formulation. It is found that the semi-Lagrangian scheme is better, with the improvement being partly attributable to the need for some horizontal diffusion to control noise associated with the Eulerian advection, while no such diffusion is necessary for the semi-Lagrangian scheme.