Simulation of ice-sheet melting

A simple model is presented where the temperature, extent and thickness of sea ice is predicted in a numerical simulation. The model is based on Newton’s law of cooling with added terms to account for black-body emission by the ice and solar and atmospheric radiation. The ice is assumed to be an ellipsoid, with the temperature being uniform throughout. Coupled equations are developed for the temperature of the ice and the water beneath it. A second model is presented based on the one-dimensional heat equation, where the ice is considered as a uniform, infinitely large slab of ice. The added terms in the first model are used as boundary conditions and the ice initially set to have a uniform temperature throughout. The first model predicts that the ice sheet is completely melted in less than a month. This is largely due to the initiail assumption that the temperature of the ellipsoidal ice is uniform. The second model predicts a melting time in the order of a month, depending on the number of layers of ice used. The fast melting time is a consequence of assuming that the temperature of the water beneath the ice sheet remains constant during the melting and heating processes. While the models are simple and reasonably fast computationally, more realistic time-scales can be obtained through revision of the initial assumptions and the development of a more complicated model.