EVALUATION OF HORIZONTAL GRADIENTS IN SIGMA-COORDINATE SHALLOW-WATER MODELS

Evaluating horizontal gradients in three-dimensional shallow water mod els that use bottom-following sigma coordinates can lead to large erro rs near steep bathymetry. A technique that has been proposed to minimi ze this problem involves computing horizontal gradients in cartesian c oordinates, while treating all other terms in a sigma coordinate frame work. We study this technique through both truncation error analysis a nd numerical experimentation, and compare it to the direct application of sigma coordinates. While the Cartesian coordinate method has bette r convergence properties and generally smaller truncation errors when horizontal gradients are zero, the sigma coordinate method can be more accurate in other physically relevant situations. Also the Cartesian coordinate method introduces significant numerical diffusion of variab le sign near the bottom (where physical diffusion is particularly smal l), thus potentially leading to instabilities. Overall we consider the sigma coordinates to be the best approach.