An exact solution for a steady, flowline marine ice sheet

Abstract

AbstractG. Böðvarsson’s 1955 plug-flow solution for an Icelandic glacier problem is shown to be an exact solution to the steady form of the simultaneous stress-balance and mass-continuity equations widely used in numerical models of marine ice sheets. The solution, which has parabolic ice thickness and constant vertically integrated longitudinal stress, solves the steady shallow-shelf approximation with linear sliding on a flat bed. It has an elevation-dependent surface mass-balance rate and, in the interpretation given here, a contrived location-dependent ice hardness distribution. By connecting Böðvarsson’s solution to the Van der Veen (1983) solution for floating ice, we construct an exact solution to the ‘rapid-sliding’ marine ice-sheet problem, continuously across the grounding line. We exploit this exact solution to examine the accuracy of two numerical methods, one grid-free and the other based on a fixed, equally spaced grid.