Glacial Flow Velocity Glens Law Calculator

Glen's law is the constitutive equation for ice: the strain rate responds to applied deviatoric stress as a power law, strain rate equals A times stress raised to n, with n close to 3. The nonlinearity matters enormously. Because the exponent is 3, a doubling of stress produces roughly an eightfold increase in deformation rate, so thick or steep ice does not merely flow a little faster, it flows in a different regime. The stress driving that deformation is the gravitational driving stress, rho times g times H times the sine of the surface slope. Its most striking feature is how narrow the natural range is: across alpine glaciers and ice sheets alike, driving stress clusters between about 50 and 150 kPa, because ice thickens or steepens until it can deform fast enough to carry the mass delivered to it. Depth-integrating the deformation profile under the shallow ice approximation gives the surface speed as 2 A tau to the n times H divided by n plus 1. The rate factor A is strongly temperature dependent, near 3.5 times 10 to the minus 25 per Pa cubed per second at -10 degrees C and roughly an order of magnitude smaller at -30 degrees C, with an activation energy near 60 kJ per mole in cold ice and much higher within a few degrees of melting. Alpine glaciers typically move 10 to 200 m per year, while Jakobshavn Isbrae has exceeded 10000 m per year. The shallow ice approximation used here omits longitudinal stress gradients and lateral drag from valley walls, treats basal sliding as a fixed fraction rather than a physical process, and ignores crystal fabric, which can enhance flow by a factor of up to ten.

The debate over how glaciers move predates any measurement of ice rheology. In the 1840s James David Forbes argued that glaciers behave as viscous fluids, against John Tyndall's view that motion came from fracture and regelation. Resolving it required laboratory data on ice itself. John W. Glen, working at the Cavendish Laboratory in Cambridge, ran uniaxial creep tests on polycrystalline ice and published the results in 1952 and, definitively, in the Proceedings of the Royal Society in 1955, finding that steady-state strain rate scales with stress raised to a power between roughly 3 and 4. John Nye translated the laboratory result into glacier mechanics almost immediately, deriving in the 1950s the depth profile of deformation velocity and the relations that became the shallow ice approximation, later formalised more rigorously by Kolumban Hutter in 1983. Field verification came from borehole inclinometry, notably deformation measurements through the Athabasca Glacier in the early 1960s, which recovered the predicted concentration of shear in the lowest fraction of the ice column. The tabulated values of the rate factor A used by modellers today trace largely to the compilation in Cuffey and Paterson's Physics of Glaciers. The exponent itself remains under active revision, with recent analyses of Antarctic ice-shelf strain rates arguing that n may sit closer to 4 in low-stress, shelf-like settings.