FirnPerc: An intermediate-complexity water percolation model for firn

Meltwater buffering in the firn of glaciers, ice caps and ice sheets is an important, yet relatively uncertain, process that determines their mass balance. In the firn layer, meltwater and rain percolate downwards until it is buffered in wet layers, refrozen, or runs off. The efficiency of water retention determines the ratio of refreezing to runoff, while the vertical distribution of refreezing has a long-lasting impact on the subsurface density, heat conductivity and temperature profile. An accurate representation of water buffering is particularly crucial for estimating future runoff from the Greenland Ice Sheet. There, the formation of ice lenses in the former percolation zone could dramatically reduce the buffering capacity of the firn layer. Current firn models either are empirically-based and struggle to represent the complex processes determining water buffering or are physics-based but computationally expensive due to strong non-linearities in the governing equations.

Here, we present the intermediate-complexity percolation model FirnPerc that aims to capture the relevant water processes in firn within a fast and stable computational framework. Matrix percolation through firn is represented as gravity-driven flow, neglecting capillary forces. In cases of low water content and water flux, model layers can be partially wetted and can therefore remain below the melting point on average for a while. When water flow stalls on ice lenses, the model can form a slush layer. Gradual water percolation through ice lenses is parameterised, with exponentially decreasing efficiency for increasing ice layer thickness. Finally, in the absence of an explicit horizontal flow description, slush water is assumed to run off very slowly. With these process parameterizations, FirnPerc can resemble important features of Greenlandic firn, such as fast, deep percolation at the start of the melting season, ice lenses with slush layers on top, and deep, water-rich year-round aquifers.