Finescale topography and the MC2 dynamics kernel

The Canadian Mesoscale Compressible Community (MC2) model provided daily forecasts across the Alps at 3-km resolution during the Mesoscale Alpine Programme (MAP) field phase of 1999. Among the results of this endeavor, some have had an immediate impact on MC2 itself as it increasingly became evident that the model was spuriously too sensitive to finescale orographic forcing. The model solves the Euler equations of motion using a semi-implicit semi-Lagrangian scheme in an oblique terrain-following coordinate. To improve model behavior, typical approaches were tried at first. These included a generalization of the coordinate transformation to make the terrain influence decay much more quickly with height as well as the introduction of nonisothermal basic states to diminish the amplitude of numerical truncation errors. The concept of piecewise-constant finite elements was invoked to reduce coding arbitrariness. But it was later pointed out that the problem was very specific and due to a numerical inconsistency. The true height of model grid points is fixed and known in height-based coordinates. Nevertheless, it was discovered that for this semi-Lagrangian scheme to be consistent, the departure height is an unknown that must be obtained in the same manner as the other unknowns.