Melt pond drainage through Arctic sea ice

Sea ice is a porous material that covers much of the Arctic ocean and insulates it from the atmosphere. In summer, vast tracts of the ice surface are covered by melt ponds, formed of melted snow and ice, which subsequently drain. Melt ponds reflect less solar radiation than bare or snow-covered ice and so their presence enhances ice melt. The formation and subsequent drainage of melt ponds is heavily dependent on the availability of drainage pathways in the ice interior, which are mostly formed of brine channels. Brine channels can either freeze, allowing for the retention of pond water, or melt, facilitating drainage. Understanding the physical controls on this process is crucial to understanding how melt ponds evolve and hence for representing them effectively in large-scale climate models. In this thesis, we present a series of models for melt-pond drainage in which we treat the ice as a mushy layer and characterise the critical transition between the freezing and melting of brine channels. First, we consider a 1D radial model, where the effects of drainage through the channel are parameterised. We derive analytic formulae relating a critical channel radius controlling closure, opening and, hence, drainage to the dimensionless parameters of the system. We consider three different parameterisations for the effect of channel drainage, compare fixed- and evolving-salinity models and compare planar and axisymmetric geometries. Second, we use a more physically-representative 2D model to investigate the extent to which 2D results can be understood using our 1D model. We use our model to investigate many aspects of the summer ice evolution related to pond drainage, including desalination. Third, we extend our 2D model to consider how drainage is affected by tributary channels which often attend larger brine channels. Finally, we discuss the implications of our results and avenues for future research.