Year of Award


Document Type


Degree Type

Master of Science (MS)

Degree Name

Computer Science

Department or School/College

Department of Computer Science

Committee Chair

Jesse V. Johnson

Commitee Members

Joel Harper, Mike Rosulek


cryosphere, modelling, variational techniques


University of Montana


A complete simulation of flowing ice requires knowledge of both the fundamental physical principles that govern the stress and energy balances and a framework for assimilating data into a model to help estimate unknown parameters. Modelling ice is complex, due to the large spatial extent of ice sheets, the multiple scales at which relevant physics operate, and the coupling between heat, stress, and ice rheology. As such, it is usually necessary to make approximations to the equations governing ice flow. At the same time, it is important to have an understanding of the specific assumptions that lead to these approximations. We develop a variational principle for Stokes flow, and neglect certain components in order to obtain the variational principle for the first-order approximation for ice flow. This result is fundamentally the result of assuming bed slopes to be much less than surface slopes, and that vertical resistive stresses are negligible. From a practical standpoint, using automatic differentiation tools on this functional yields a compact model of ice flow that automatically incorporates correct boundary condition. This model is compared to well known benchmark tests. We also present an improved model of ice thermodynamics that operates on enthalpy rather than temperature, avoiding many of the difficulties associated with phase change. We derive a method for inverting the Blatter-Pattyn ice sheet model in order to solve for the rate of basal sliding. This method uses the adjoint equations of the forward model to obtain the gradient of an error functional, and this is minimized using a quasi-Newton method. These methods are applied to an instrumented streamline of the Greenland ice sheet. We perform numerical experiments on this geometry in order to assess the sensitivity of thermal conditions at the ice sheet bed to perturbations in unknown parameters. The basal thermal regime is sensitive to changes in geothermal heat flux, with the location of the transition zone between cold and temperate ice being linear sensitive to changes in it. The temperature field of the ice sheet is insensitive to downstream changes in sliding speed due to the short length scales over which longitudinal coupling acts.



© Copyright 2013 Douglas John Brinkerhoff