A vertically integrated model with phase change for aquifers in cold firn

Abstract

Surface meltwater from glaciers and ice sheets contributes significantly to sea-level rise, yet the processes governing its transport and retention within cold firn remain poorly constrained, particularly in multiple dimensions. Here we present a multidimensional, vertically integrated modeling framework for aquifers in cold firn that incorporates phase change and residual trapping of liquid water. This mathematical framework, together with its numerical implementation, extends terrestrial groundwater models to describe aquifers expanding within otherwise cold firn, highlighting the analogous physics governing both systems. We derive semi-analytical solutions for finite-volume aquifers and validate them against numerical simulations and higher-fidelity model results. These solutions elucidate key features of meltwater dynamics and provide benchmarks for firn hydrologic models. We further demonstrate the three-dimensional expansion of an aquifer in cold, heterogeneous firn. Both the semi-analytical and numerical results show that lateral aquifer propagation slows at lower initial firn temperatures due to porosity reduction and associated loss of liquid water from freezing. Overall, this framework provides new insights into the formation and expansion of firn aquifers in percolation zones and helps clarify how subsurface meltwater storage modulates meltwater fluxes, surface mass loss, and contributes to global sea-level rise.