ANALYTICAL MODELING OF GLACIER DYNAMICS

Flow velocities and stresses within a glacier are determined by invert ing known surface velocities with a specified glacier geometry. The su rface velocities depend only weakly on the unknown velocities at the b ed of a glacier, so the inversion is ill-posed and unstable. This inst ability causes both numerical computation errors and data errors to gr ow dramatically with depth, usually masking the actual velocity and st ress solutions. To control the numerical errors, an analytical modelin g scheme is presented which modifies the method of mean weighted resid uals (used in finite element techniques). The resulting scheme impairs convergence by producing power-series solutions, bur in an advantageo us trade-off, the coefficients to the power series can be determined a nalytically rather than numerically. This leads to arbitrary order ana lytical power-series solutions to the internal stress state of glacier s. The symbolic power-series solutions cart be evaluated at any point in the glacier with negligible round-off and discretization errors. An alytical model accuracy is confirmed with known stress solutions for s everal widely used constitutive relations for ice.