Modeling horizontal diffusion with sigma coordinate system.

Accurate calculation of horizontal diffusive transport is important in modeling temperature, salinity, sediment, and pollutant transport in estuaries and the coastal ocean. Many three-dimensional estuarine and coastal ocean models employ a so-called sigma coordinate transformation because of its useful applications with irregular bathymetry. However, for steep bottom slopes, the conventional definition of horizontal diffusion causes spurious diffusive transport. In this paper, a new formula is presented and tested for salinity diffusion in a quiescent-sloping basin under no external forces. Results indicate that this formula produces almost no spurious diffusion, so that the initial salinity field remains unchanged after a 30-d simulation.