Step-Mountain Technique Applied to an Atmospheric C-Grid Model,
or How to Improve Precipitation near Mountains
Gary L. Russell
2007: Monthly Weather Review, 135, 4060-4076,
doi:10.1175/2007MWR2048.1
Abstract
Starting with Arakawa and Lamb's second-order C-grid scheme, this paper
describes the modifications made to the dynamics to create a C-grid
atmospheric model with a variable number of cells for each vertical
column. Where mountains exist, grid cells are discarded at the bottom
of the column so that the mass per square meter of retained cells is
more nearly equal to that of horizontally adjacent cells. This leads
to the following chain of causes and effects: decreased mass variations
reduce the numerically induced alternating patterns in the horizontal
velocity components, which reduce erroneous vertical mass fluxes, which
reduce erroneous precipitation. In addition, horizontal flows above
mountains are smoother, the Ferrel cell is stronger, and the polar cell
is better organized. The C-grid performs geostrophic adjustment best
among the gridpoint schemes, being the most sensitive to
condensation-related heating perturbations. It also overreacts more
egregiously to numerical errors, particularly with respect to the
vertical mass flux, and consequently is often not used. Mesinger et
al. applied the step-mountain (eta coordinate) technique to an E-grid
scheme with excellent results. Its application to the C-grid reduces
numerical errors in the vertical mass flux resulting in improvements in
precipitation and other quantities.
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