Shallowice

Shallowice (often written as shallow-ice) refers to the shallow ice approximation (SIA), a mathematical simplification used in glaciology to model the flow of ice. The SIA assumes the ice thickness is small compared to horizontal length scales and that shear stresses in the vertical are dominant. Under these assumptions, the horizontal velocities are mainly produced by shear between the bed and the surface, and longitudinal (along-flow) stresses are neglected. This reduces the full Stokes flow equations to a tractable form, allowing ice flux to be expressed as a nonlinear function of ice thickness and surface slope, typically using Glen's flow law with exponent n ≈ 3.

In practice, SIA is used to simulate ice-sheet evolution where topography changes slowly in the direction of flow, such as continental ice sheets and large ice caps, and for long-term climate-scale calculations. The governing equation takes the form of a conservation law for ice thickness, balancing surface mass balance with export by ice flow. The flux increases rapidly with ice thickness and with steeper surface slopes.

Limitations include poor performance in regions where longitudinal stresses are important, such as near fast-flowing ice streams, outlet glaciers, margins, or complex geometry where the assumption of horizontal uniformity breaks down. Consequently, SIA is often used in combination with other approximations, such as the shallow shelf approximation (SSA) or higher-order models, to capture a wider range of dynamical behaviors.

See also: glaciology, Stokes equations, Glen's flow law, ice-sheet modeling, SSA.