The drainage of glacier and ice sheet surface lakes

TL;DR

This paper develops a model for supraglacial lake drainage driven by dissipation, revealing conditions for drainage, oscillatory filling-draining cycles, and the influence of physical parameters on these processes.

Contribution

It introduces a novel coupled model combining flow dynamics and channel evolution to explain supraglacial lake drainage mechanisms.

Findings

Drainage occurs when water supply exceeds a critical rate due to shock migration.

Drainage can be cyclic, with lakes filling and draining repeatedly.

Drainage behavior depends on parameters like water supply, uplift, and channel roughness.

Abstract

Supraglacial lakes play a central role in storing melt water, enhancing surface melt, and ultimately in driving ice flow and ice shelf melt through injecting water into the subglacial environment and facilitating fracturing. Here, we develop a model for the drainage of supraglacial lakes through the dissipation-driven incision of a surface channel. The model consists of the St Venant equations for flow in the channel, fed by an upstream lake reservoir, coupled with an equation for the evolution of channel elevation due to advection, uplift, and downward melting. After reduction to a `stream power'-type hyperbolic model, we show that lake drainage occurs above a critical rate of water supply to the lake due to the backward migration of a shock that incises the lake seal. The critical water supply rate depends on advection velocity and uplift (or more precisely, drawdown downstream of the lake) as well as model parameters such as channel wall roughness and the parameters defining the relationship between channel cross-section and wetted perimeter. Once lake drainage does occur, it can either continue until the lake is empty, or terminate early, leading to oscillatory cycles of lake filling and draining, with the latter favoured by large lake volumes and relatively small water supply rates.