A GENERALIZED FAMILY OF SCHEMES THAT ELIMINATE THE SPURIOUS RESONANT RESPONSE OF SEMI-LAGRANGIAN SCHEMES TO OROGRAPHIC FORCING

The one-parameter three-time-level family of O(Delta t(2))-accurate sc hemes, introduced in Rivest et al. to address the problem of the spuri ous resonant response of semi-implicit semi-L-agrangian schemes at lar ge Courant number, has been generalized to a two-parameter family by i ntroducing the possibility of evaluating total derivatives using an ad ditional time level. The merits of different members of this family ba sed on both theory and results are assessed. The additional degree of freedom might be expected a priori to permit a reduction of the time t runcation errors while still maintaining stability and avoiding spurio us resonance. Resonance, stability, and truncation error analyses for the proposed generalized family of schemes are given. The subfamily th at is formally O(Delta t(3))-accurate is unfortunately unstable for gr avity modes. Sample integrations for various members of the generalize d family are shown. Results are consistent with theory, and stable non resonant forecasts at large Courant number are possible for a range of values of the two free parameters. Of the two methods proposed in Riv est et al. for computing trajectories, the one using a piecewise-defin ed trajectory is to be preferred to that using a single great-circle a re since it is more accurate at a large time step for some members of the generalized family.