Abstract
Abstract. Numerical simulation of glacier dynamics in mountainous regions using zero-order, shallow ice models is desirable for computational efficiency so as to allow broad coverage. However, these models present several difficulties when applied to complex terrain. One such problem arises where steep terrain can spuriously lead to large ice fluxes that remove more mass from a grid cell than it originally contains, leading to mass conservation being violated. This paper describes a vertically integrated, shallow ice model using a second-order flux-limiting spatial discretization scheme that enforces mass conservation. An exact solution to ice flow over a bedrock step is derived for a given mass balance forcing as a benchmark to evaluate the model performance in such a difficult setting. This benchmark should serve as a useful test for modellers interested in simulating glaciers over complex terrain.
Highlights
Numerical simulation of glaciers and ice sheets is essential for understanding the cryospheric response to a changing climate and is increasingly an integral part of modern climate change projections
Higher-order ice dynamical models are capable of simulating individual glaciers or large ice sheets, but presently their high computational demands restrict their use over domains required to simulate regional mountain glacier evolution
After revisiting a well-known mass conservation problem of finite difference models for glacier flow in mountainous regions, we have identified another complication which arises with very steep topography
Summary
Numerical simulation of glaciers and ice sheets is essential for understanding the cryospheric response to a changing climate and is increasingly an integral part of modern climate change projections. One approach is to explicitly simulate glaciers at a sub-kilometer resolution over large, ice-covered regions of the globe Such an approach demands models of ice dynamics capable of simulating mountain glaciers in computational domains containing many (e.g. 107) grid nodes over century-long model periods. Higher-order ice dynamical models are capable of simulating individual glaciers or large ice sheets, but presently their high computational demands restrict their use over domains required to simulate regional mountain glacier evolution. By reducing the complexity of the stresses that are simulated in a dynamical model, greater computational effort can be put into addressing large-scale problems at some cost to model accuracy One such model is the vertically integrated, shallow ice formulation discretized using finite differences Confirming that a shallow ice model can meet the benchmark described here along with the benchmarks for the transient simulation of a growing ice sheet described by Bueler et al (2005) is strongly recommended prior to conducting simulations of glaciers over rough topography
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