An improved scheme to suppress spurious orographic resonance in semi-lagrangian models

Semi-Lagrangian schemes, as are widely used in numerical weather prediction, exhibit a spurious resonance for time steps that result in Courant numbers C > 1. The spurious resonance is caused by orographic forcing and can be removed by off-centring the discretised equations in time. This approach leads to increased numerical damping everywhere in the domain and may adversely affect accuracy even in regions of little orography. In this thesis, the off-centring approach is revisited and the traditional off-centring scheme validated. In an attempt to reduce the additional numerical damping while maintaining stability, the traditional scheme is then modified by limiting the off-centring to a subset of equations. After extensive numerical tests in a shallow water model, the schemes are then further modified to vary the additional damping across the computational domain as a function of the orography. Based on the findings in the shallow water model, a new scheme is implemented in a global climate model (GCM) and the impact of the new scheme assessed in detail.