A STUDY OF THE BEHAVIOR OF SEMI-LAGRANGIAN MODELS IN THE PRESENCE OF OROGRAPHY

Orography is incorporated into two global shallow-water numerical mode ls, the first (which is termed the (u, v) model) based on a semi-Lagra ngian vector discretization of the momentum equation, the second (whic h is termed the PV-D model) based on the semi-Lagrangian advection of potential vorticity. Both models are two-time-level and use the finite -difference approach. Linear analyses of both models are performed for the idealized situation of stationary flow over orography on an f-pla ne. In extension of the analysis of Rivest et al. the effects of spati al discretization are included. Spurious orographic resonance in the s ense of infinite amplitude is eliminated by the damping effects of spa tial interpolation, but spurious enhanced responses in the neighbourho od of the points at which resonance previously occurred still remain. The linear analyses indicate similar spurious enhanced responses for b oth models, which is confirmed by the numerical experiments. The spuri ous orographic noise in both models can be eliminated by a sufficient amount of uncentring, though it is shown that uncentring of either fir st order or second order can have negative impacts on the large-scale Rossby waves. The PV-D model formulation, however, allows the use of a scheme in which only the divergence and continuity equations are unce ntred, which minimizes such negative impacts.