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The Schaer test case is described in two
references - Schaer et al, 2002: A
New Terrain-Following Vertical Coordinate Formulation for Atmospheric
Prediction Models. Monthly Weather Review, Vol. 130, 2459-2480;
Klemp et al, 2003: Numerical
Consistency of Metric Terms in Terrain-Following Coordinates.
Monthly Weather Review, Vol. 131, 1229-1239. The Schaer et al
(2002) reference presents results from a number of different test
cases (the results for the test case below can be found on pages
2475-2477). The Klemp et al (2003) paper deals exclusively with
this test and presents the analytical solution for the test along with
an extensive discussion of model design issues related to this
test. A detailed discussion of this test as it relates to
semi-Lagrangian models is given in Girard et al 2005: Finescale Topography and the MC2 Dynamics
Kernel, Monthy Weather Review, Vol 133, 1463-1477.
Depicted below are the analytic solution along
with solutions illustrating models with consistent and
inconsistent numerics. The COAMPS solutions show that even on a
very coarse grid (relative to the terrain), the correct solution can
still be captured and problems with metric inconsistencies are still
obvious.
9 January 2004, W. Skamarock
7 October 2005, Updated, W. Skamarock
9 December 2005, Updated, W. Skamarock
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