A stochastic approach to supraglacial meltwater transport modeling

Supraglacial meltwater transport and subsequent drainage has been shown to dramatically influence ice dynamics and will be a key process in the cryospheric response to a changing climate [Bartholomew et al., 2010, Das et al., 2008]. However, meltwater transport modeling is complicated by the intrinsic spatial and temporal variability of glacier surfaces as well as the numerous choices for thermodynamic parameterizations and the governing transport equations. Several large-scale models use empirical thermodynamic parameterizations from available meteorological data, but suffer inaccuracies in meltwater volumes and transport patterns. Other modeling studies that use more physically-based thermodynamic parameterizations, like energy balance models, accurately estimate meltwater volumes, but still have been simplified to account for basin-scale effects and neglect the more complicated flow physics of a heterogeneous material [Luthje, 2006]. We account for the high degree of variability in meltwater transport modeling by coupling energy balance thermodynamics to stochastic differential equation methods (e.g., Focker-Planck Equation) which have been previously used to model hydrological processes in various settings including flow through heterogeneous porous media. We present a model of idealized domain and explore a suite of surface parameters (snow depth, firn depth, snow permeability, elevation, etc.) to produce runoff patterns and meltwater accumulation ponds which we qualitatively compare to available observations. We restrict our model to a supraglacial setting and make simple approximations about englacial mass loss sinks. The stochastic approach presented here is a first step towards approximating the complex nature of meltwater transport, storage, and runoff.