Modelling meltwater processes on ice sheets

Understanding the behaviour of ice sheets is of great interest, due to their response to changes in climate. The large ice masses of both the Antarctic and Greenland ice sheets have the potential to significantly increase global sea levels as the ice or its meltwater is transferred to the oceans (DeConto and Pollard 2016). A key factor, and the focus of this project, is how much of the surface meltwater produced by the ice sheet actually runs off into the oceans. This is affected by the layer of compacting snow at the top of the ice sheet, through which meltwater can percolate. It is possible for this meltwater to refreeze or form aquifers, preventing or delaying the meltwater reaching the ocean (Harper and others 2012). A model is needed to better understand these processes. This project will cover a variety of problems concerning the fluid- and thermodynamics within the snow layer.
There are currently several one-dimensional models for the compacting snow layer of ice sheets. Vandecrux and others (2020) compared nine such models, finding that there is considerable disagreement between the outputs of the different models themselves and the observed data. The aim of this project is to learn from these existing models (in particular the continuum model by Meyer and Hewitt (2017)) and create a mathematically sound continuum model for the compacting snow that agrees with field data.
Once this has been achieved, the model will be generalised to higher dimensions, allowing lateral flow of meltwater and vertical features of the snow and ice (such as pipes) to be captured. These are absent from the existing models, but have significant impacts on the flow of meltwater. A further development of the model will be to scale it up to the whole of Greenland. With this, it will be possible to answer the question of how much of the surface meltwater runs off into the oceans.
This project falls within the EPSRC Fluid Dynamics and Aerodynamics research area. It will develop a new theory for three-phase flow in a compacting medium undergoing phase change. It will exploit numerical and asymptotic methods for solving and analysing the complex systems of partial differential equations that describe these phenomena. The models developed in this project will have applications beyond snow and ice alone. The knowledge gained will be useful for other multiphase porous media flows involving phase change. Examples include models for cooking food (Halder and others 2011) and methane venting through the sea floor (Skarke 2014).