A Test of an Upstream Spline Interpolation Technique for the Advective Terms in a Numerical Mesoscale Model

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Abstract
Upstream interpolation with a cubic spline is used to integrate the advective terms in a two-dimensional hydrostatic primitive equation model. The model is applied to study the problems of air flow over a mountain, and sea and land breezes. Results are compared against existing numerical models and against an identical model which uses a simple upstream differencing scheme for the advective terms. It was found that under certain atmospheric conditions, where the atmosphere is being continuously forced, accurate results may be obtained near the surface even with the simple upstream scheme. Also it is shown that a sophisticated planetary boundary layer parameterisation is needed in order to obtain accurate results in both the lower and upper troposphere.

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