A model of the weathering crust and microbial activity on an ice-sheet surface

Abstract

Abstract. Shortwave radiation penetrating beneath an ice-sheet surface can cause internal melting and the formation of a near-surface porous layer known as the weathering crust, a dynamic hydrological system that provides home to impurities and microbial life. We develop a mathematical model, incorporating thermodynamics and population dynamics, for the evolution of such layers. The model accounts for conservation of mass and energy, for internal and surface-absorbed radiation, and for logistic growth of a microbial species mediated by nutrients that are sourced from the melting ice. It also accounts for potential melt–albedo and microbe–albedo feedbacks, through the dependence of the absorption coefficient on the porosity or microbial concentration. We investigate one-dimensional steadily melting solutions of the model, which give rise to predictions for the weathering crust depth, water content, melt rate, and microbial abundance, depending on a number of parameters. In particular, we examine how these quantities depend on the forcing energy fluxes, finding that the relative amounts of shortwave (surface-penetrating) radiation and other heat fluxes are particularly important in determining the structure of the weathering crust. The results explain why weathering crusts form and disappear under different forcing conditions and suggest a range of possible changes in behaviour in response to climate change.

A model of the weathering crust and microbial activity on an ice-sheet surface

“…In the present study, we extend our work from Woods and Hewitt [24] to seek timedependent solutions of the weathering crust model presented in that study. We begin in Section II by summarising the model and presenting the model equations relevant for this work.…”

“…In Woods and Hewitt [24], we presented a fully three-dimensional continuum model for the evolution of the weathering crust, accounting for mass conservation, energy conservation and internal shortwave radiation. We model the porous weathering crust and the solid ice below it, as shown in Figure 1.…”

“…It is assumed that all such surface meltwater immediately runs off laterally into nearby surface streams. As done in [24], we transform coordinates to Z = h(t) − z, the depth below the ice surface. The equations are presented using the Z coordinate, where the ice surface is now at Z = 0.…”

“…Until now, there have been limited attempts to model the weathering crust [21][22][23][24], and these have tended to focus on specific aspects. Schuster [21], Hoffman et al [22,23], Woods and Hewitt [24] all present one-dimensional (vertical) models forced by the surface energy balance components (e.g. shortwave and longwave radiation and turbulent heat fluxes).…”

“…Hoffman et al [22,23] modelled the temperature within the ice using the heat equation with a heat source provided by internal shortwave radiation, gaining predictions of surface lowering and internal melt extent over time. The more complex continuum model we presented in Woods and Hewitt [24] models the surface lowering, internal and surface melt, weathering crust porosity and thickness, and internal ice temperature simultaneously, based on mass conservation, energy conservation, and internal shortwave radiation. That study focussed only on steady solutions.…”