On reducing the slope parameter in terrain-following numerical ocean models

Sigma coordinate ocean models, such as the Princeton Ocean Model, are a type of terrain-following model, which are currently being used in regions with large topographic variability such as entire ocean basins, shelf breaks, continental shelves, estuaries and bays. The main concern when using a terrain-following ocean model is to reduce the pressure gradient force error (PGFE). Regardless of the method of calculation of the pressure gradient, the PGFE will not be reduced to an acceptable value without first reducing the slope parameter, defined by the absolute value of the ratio of the difference between two adjacent cell depths and their mean depth. Here two methods for reducing the slope parameter are compared: a traditional two-dimensional smoothing with Gaussian filters and an alternative one-dimensional robust direct iterative technique. While both methods efficiently smooth the bottom topography so that the pressure gradient errors are reduced to acceptable levels, the alternative method is shown to have a unique advantage of maintaining coastline irregularities, continental shelves, and relative maxima such as seamounts and islands.