11 - Numerical modeling

Summary

Numerical modeling is a way of solving complex sets of equations that cannot be solved analytically.In finite difference modeling the infinitesimal step (e.g. dx) in the governing differential equation is replaced by a finite step (e.g. "∆x" ), and the variation over this step is assumed to be linear. Integration starts at a boundary and continues stepwise across the domain. In finite element and finite volume models, the domain is discretized into elements of unequal size and equations are written relating parameters on the boundaries of these elements. This results in a system of equations that must be solved simultaneously.Because the deformation rate in a glacier is a function of temperature, and conversely, full solutions require coupling of energy balance and momentum balance equations.Examples are given involving the role of subglacial permafrost in ice sheet behavior, estimation of prior ice sheet behavior from characteristics measured in ice cores and boreholes, and use of non-deterministic models to estimate sea level rise.