An Improved Numerical Approximation of the Horizontal Gradients in a Terrain-Following Coordinate System

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Abstract
The use of a fine vertical grid resolution near the surface may lead to a numerically inconsistent approximation of the horizontal gradient terms in a terrain-following coordinate system. This occurs when the distance between two vertical grid points is smaller than the elevation difference between two horizontally adjacent (in the terrain-following coordinate system) points. In this paper an improved numerical procedure is proposed which eliminates this inconsistency and significantly increases the accuracy of the numerical approximation. Results are compared with those obtained with the conventional forward and centered schemes. Abstract The use of a fine vertical grid resolution near the surface may lead to a numerically inconsistent approximation of the horizontal gradient terms in a terrain-following coordinate system. This occurs when the distance between two vertical grid points is smaller than the elevation difference between two horizontally adjacent (in the terrain-following coordinate system) points. In this paper an improved numerical procedure is proposed which eliminates this inconsistency and significantly increases the accuracy of the numerical approximation. Results are compared with those obtained with the conventional forward and centered schemes.

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