The dependence of energy dissipation on spatial resolution in a viscous-plastic sea-ice model

We present sea-ice kinetic energy budgets to quantify the relative importance of the various energy sinks in a viscous-plastic sea-ice model. To this end, we study two idealized model domains where energy dissipation associated with shear and axial (ridge/lead building) deformation can be analyzed independently. We find that when only shear deformation is present - either at the domain boundary induced by the no-slip boundary condition or within the model domain induced by gradients in the surface air stress - the energy dissipated through friction reduces in relative importance as the spatial resolution of the model is increased. In the limit where the spatial resolution tends to zero, the simulated sea ice drift tends to the analytical solution - giving us confidence in the numerical implementation of the governing differential equation. Increasing spatial resolution leads to a localization of deformation along the shear lines effectively increasing the area over which energy is input by the wind which is not compensated for by frictional shear dissipation. For instance at 40 km spatial resolution, 64% and 29% of the input power is dissipated through shear deformation and water drag respectively, while at 5 km spatial resolution 54% and 43% of the input power is dissipated by the respective processes. These values approach the respective values of 53% and 47% found analytically for this particular model configuration. The overall result is a 64% increase in the domain total sea-ice kinetic energy when the spatial resolution is increased from 40 km to 5 km due to the finer representation of shear lines. In convergence, the mean kinetic energy and potential energy do not depend meaningfully on the spatial resolution. In this case, the structure of the thickness and concentration fields effectively sets the velocity gradient near the boundary provided that the plastic deformation wave associated with the ridge building process is resolved.