On the numerical resolution in a thermodynamic sea-ice model

Abstract

The numerical integration of the heat-conduction equation is one of the main components in a thermodynamic sca-ice model. The spatial resolution in the ice normally varies from a minimum of three layers up to a few tens of layers. The temporal resolution varies from a few minutes up to hours. In this paper the impact of numerical resolution on the prediction of a one-dimensional thermodynamic ice model is studied. Analytical solutions for idealized cases were derived and compared with the numerical results. For the full ice model, groups of simulations were made, applying average climatic weather-forcing data corresponding to the ice-freezing, ice-thermal equilibrium and ice warm-up seasons. Special attention was paid to the effect of model spatial resolution. Early in the freezing season, the influence of resolution on model predictions is not significant. When the shortwave radiation becomes large, its absorption within the ice or snow cover was found to modulate the effect of numerical resolution on predictions of ice temperature and surface heat fluxes (e.g. the model run with a coarse spatial resolution yielded large daily variations in surface temperature). Resolution also affects the in-ice temperature profile. For process studies, a two-layer scheme for the solar radiation penetrating into the ice is suitable for a fine-spatial-resolution ice model.