A Study of the Spurious Orographic Resonance in Semi-Implicit Semi-Lagrangian Models

Abstract

The semi-implicit semi-Lagrangian (hereafter SISL) numerical integration scheme has been widely adopted in atmospheric models as it permits, without loss of accuracy, the use of time steps much larger than those permitted by the Courant?Friedrichs?Lewy criterion for the corresponding Eulerian models. However, it is known that there is a problem with orographic forcing in SISL models, since spurious numerical resonance can occur in mountain regions for Courant numbers larger than unity. Several solutions to this problem have been proposed, but so far none has completely solved the problem. In recent work by Ritchie and Tanguay, two different treatments of the orographic forcing term, the semi-Lagrangian and the spatially averaged Eulerian (SAE), were analytically and numerically investigated. It was found that when the SAE method is used, the orographic resonance problem is less severe. The reason for this improvement is further investigated here and it is shown to be due to the modified growth characteristics of the resonance with the SAE treatment.