VELOCITY AND STRESS-FIELDS IN GROUNDED GLACIERS - A SIMPLE ALGORITHM FOR INCLUDING DEVIATORIC STRESS GRADIENTS

A new and efficient algorithm for computing the three-dimensional stress and velocity fields in grounded glaciers includes the role of deviatoric stress gradients. A consistent approximation of first order in the aspect of ratio of the ice mass gives a set of eight field equations for the five stress and and three velocity components and the corresponding boundary conditions. A coordinate transformation mapping the local ice thickness on to unit). and approximating the derivatives in the horizontal direction by centred finite-differences yields five ordinary differential and three algebraic equations. This allows use of the method of lines, starting the integration with prescribed stress and velocity components at the base, and a simple iteration procedure converges rapidly. The algorithm can be used for a wide range of stress-strain-rate relations, as long as strain only depends on deviatoric and shear stresses and on temperature. Sensitivity tests using synthetic and realistic ice geometries show the relevance of normal deviatoric stresses in the solutions for the velocity components even for ice sheets. Stress and velocity fields may deviate substantially from the widely used shallow-ice approximation.