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.