A Thickness and Enthalpy Distribution Sea-Ice Model

The theory of sea ice thickness distribution developed by Thorndike et al. has been extended to include sea ice enthalpy distribution. The extended theory conserves both ice mass and thermal energy, in the form of the heat stored in the ice, by jointly solving a thickness-distribution equation and an enthalpy-distribution equation. Both equations have been implemented in a one-dimensional dynamic thermodynamic sea-ice model with 12 ice thickness categories following the numerical procedure of Hibler. The implementation of the enthalpydistribution equation allows the sea-ice model to account for any changes in the ice thermal energy induced by sea ice processes. As a result, the model is able to conserve not only the ice mass but also its thermal energy in the presence of ice advection, growth, melting, and ridging. Conserving ice thermal energy in a thicknessdistribution sea ice model improves the prediction of ice growth, summer ice melt in particular, and therefore ice thickness. Inability to conserve the thermal energy by not implementing the enthalpy-distribution equation, compounded with an effect of the surface albedo feedback, causes the model to underestimate ice thickness by up to 11% under various conditions of thermal and mechanical forcing. This indicates the importance of conserving energy in numerical investigations of climate.