The use of mathematical models of glaciers allows us to determine their dynamical and thermal properties for those regions not accessible to direct observation, as well as predicting their time evolution.
Through measurements done on the glacier surface or from satellite, we can determine geometrical, dynamical and thermal properties of the glacier surface such as velocity, strain or temperature. However, for determining such properties within the glacier body, without the need to dig boreholes, or in order to be able to predict the future behaviour of a glacier, we are forced to use models.
Based on physical hypothesis, we set the equations governing the dynamical and thermal regime of glaciers and their interactions with their environment (atmosphere, ocean, ground). The solution of such equations gives the velocity and temperature fields within the glacier. If these are dependent on time, the model allows us to make predictions on the future behaviour of the glacier (whether it will advance or retreat, whether it will gain or lose mass as a consequence of decreased or increased melting or snow accumulation, etc.).
However, the difficulty of the equations and the complex geometry of many glaciers implies that the equations of the thermo-mechanical model cannot be solved exactly, making necessary the use of numerical methods, which provide an approximate solution to the problem.