Mathematical Geology

, Volume 28, Issue 2, pp 229–251 | Cite as

Analytical modeling of glacier dynamics

  • David B. Bahr


Flow velocities and stresses within a glacier are determined by inverting known surface velocities with a specified glacier geometry. The surface velocities depend only weakly on the unknown velocities at the bed of a glacier, so the inversion is illposed and unstable. This instability causes both numerical computation errors and data errors to grow dramatically with depth, usually masking the actual velocity and stress solutions. To control the numerical errors, an analytical modeling scheme is presented which modifies the method of mean weighted residuals (used in finite element techniques). The resulting scheme impairs convergence by producing powerseries solutions, but in an advantageous tradeoff, the coefficients to the power series can be determined analytically rather than numerically. This leads to arbitrary order analytical powerseries solutions to the internal stress state of glaciers. The symbolic powerseries solutions can be evaluated at any point in the glacier with negligible roundoff and discretization errors. Analytical model accuracy is confirmed with known stress solutions for several widely used constitutive relations for ice.

Key words

ice stream numerical error inversion ill-posed 


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Copyright information

© International Association for Mathematical Geology 1996

Authors and Affiliations

  • David B. Bahr
    • 1
  1. 1.Institute of Arctic and Alpine ResearchUniversity of ColoradoBoulder

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