An analytical stretching function that combines the best attributes of geopotential and terrain-following vertical coordinates

Abstract

This work provides a function for discretising the vertical coordinate in ocean models that is designed to allow the user to define a fixed surface resolution, as one can in geopotential coordinate models, whilst retaining the benefits of terrain-following coordinates. This formulation has been termed the γ stretching function and provides an analytical solution that, in contrast with hybrid schemes, allows gradual coordinate changes in the vertical and horizontal. The early part of the paper describes the theoretical framework in which this can be done. Following this a series of steps that are required to effectively implement the coordinate have been described, and a full description of the implementation for a shelf model, the Forecasting Ocean Assimilation Model (FOAM) Atlantic Margin Model (AMM7), is given.This implementation is then used to quantify the impact of the γ stretching compared with the current stretching scheme. This shows the new stretching to have improved slope and hydrostatic consistency parameters. As would therefore be expected the γ stretching is shown to give rise to reduced horizontal pressure gradient errors in an idealised seamount test case. The benefits of a constant and shallow box for air–sea exchange are demonstrated, with the γ stretching giving enhanced diurnal ranges, increased sea surface temperatures and shallower mixed layer depths where the FOAM AMM7 is presently unable to well represent these properties.