A vertically integrated snow/ice model over land/sea for climate models: 1. Development

Sea ice/snow and land snow models are developed using a vertically integrated formulation (VIF). The VIF model has the capability of simulating the nonlinear effects of heat storage and transfer through the layers of snow and ice, which are felt particularly in spring and fall, yet this is achieved without resorting to the addition of layers to the numerical scheme. For comparison, a stable multilayer model is developed and tested. It is demonstrated that the VIF shares the accuracy of the multilayer formulation, and at the same time benefits from computational flexibility typical of linear formulations. The validity of the VIF assumptions and their parameter dependence are analyzed using an analytically solvable example. It is suggested that the VIF model may be specifically suitable for the implementation in a variety of climate models and general circulation models. A simple parameterization is applied to include seasonal and latitudinal changes in the heat flux from the mixed layer to the ice layer. This flux, though small in magnitude on an annual and latitudinal average, has an important influence on the ice thickness and its seasonal cycle and was taken as a constant in previous sea ice modeling. Latitudinal dynamical sea ice transport is also included in a simple parameterized form.