On mass conservation for ice sheets

TL;DR

This paper introduces a new continuum-mechanical formulation for ice sheets that improves mass-balance calculations and reduces velocity errors, aiding more accurate modeling of ice sheet dynamics.

Contribution

It presents a novel formulation that encompasses all material processes and derives a quasi-mass-balance relation to enhance ice sheet modeling accuracy.

Findings

Reduces velocity errors in high surface gradient regions

Provides an analytic velocity for model verification

Improves mass-balance calculations in ice sheet models

Abstract

A new continuum-mechanical formulation is proposed which encompasses all material processes within and surrounding an ice sheet. Using this formulation, the balance of mass and free-surface relations for ice sheets are derived and elaborated upon. The resulting three-dimensional mass-balance relation is then integrated vertically to produce an ice-sheet quasi-mass-balance relation in the horizontal plane, and is demonstrated to reduce velocity errors in regions with high magnitude surface gradients. An analytic velocity satisfying the corrected mass-balance relation is formulated as a means to verify future numerical ice-sheet models.