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Semi-Lagrangian semi-implicit techniques are now well established and used by an increasing number of meteorological centers. However, it is demonstrated by both analysis and numerical integration that there is a serious problem incorporating orographic forcing into semi-Lagrangian models, since spurious resonance can develop in mountainous regions for Courant numbers larger than unity. A solution, consisting of two classes of schemes, is proposed, analyzed, and then evaluated using a global shallow-water model. Simply off-centering the semi-implicit scheme eliminates the spurious resonances. Although this can be achieved with a first-order scheme, it is at the expense of decreased accuracy, and therefore a second-order scheme is recommended.
Rivest et al. (Tue,) studied this question.