Application of the semi-Lagrangian method to a multilevel spectral primitive-equations model

Abstract

It has previously been shown that semi-Lagrangian schemes can be applied to spectral models of the shallow-water equations using large time-steps (e.g., see Ritchie 1988). The present study considers the extension of this work to a multilevel spectral primitive-equations model. As a first step, an Eulerian vorticity-divergence spectral model is converted to an Eulerian model based on a vector momentum form of the equation of motion. From the latter, several semi-Lagrangian models are prepared: one using an interpolating semi-Lagrangian treatment of advection in the horizontal (referred to as 2DISL) while retaining Eulerian advection in the vertical, another using a 3-dimensional interpolating semi-Lagrangian formulation (referred to as 3DISL), and another which combines the 2DISL scheme in the horizontal and a non-interpolating semi-Lagrangian treatment in the vertical (referred to as NISLV). Medium-range intercomparison experiments are performed using models that include simple physical parametrizations. It is shown that the semi-Lagrangian semi-implicit approach can be applied accurately and stably to produce medium-range (5-day) forecasts using time-steps that are far larger than those permitted by the Courant-Friedrichs-Lewy (CFL) stability criterion for the corresponding Eulerian model. The NISLV version is found to be more accurate than the 3DISL one which apparently has excessive damping in the vicinity of the tropopause, where all the model fields change abruptly in the vertical.