A 2D model for simulating heterogeneous mass and energy fluxes through melting snowpacks

Abstract

Accurate estimation of the water flux through melting snowpacks is of primary importance for runoff prediction. Lateral flows and preferential flow pathways in porous media flow have proven critical for improving soil and groundwater flow models, but though many physically-based layered snowmelt models have been developed, only 1D matrix flow over level ground is currently accounted for in snow models. Snowmelt models that include these processes may improve snowmelt discharge timing and contributing area calculations in hydrological models. A two-dimensional snow model (SMPP – Snowmelt Model with Preferential flow Paths) is presented that simulates heat and water flows through both snowpack matrix and preferential flow paths, as well as snowmelt and refreezing of meltwater. The model assumes thermodynamic equilibrium between solid and liquid phases and uses the latest improvements made in snow science to estimate snow hydraulic and thermal properties. A finite volume method is applied to solve for the 2D heat and water equations. The use of a water entry pressure for dry snow combined with consideration of the impact of heterogeneities in surface fluxes and internal snow properties – density, grain size and layer thickness – allowed calculation of the formation of preferential flow paths in the snowpack. The simulation of water flow through preferential flow paths resulted in liquid water reaching the base of the snowpack earlier than for a homogeneous wetting front. Moreover, the preferential flow paths in the model increased the exchange of energy between the snow surface and the internal snowpack, resulting in faster warming of the snowpack. A sensitivity analysis, conducted on the snow internal properties showed that initial conditions such as density and temperature, should be carefully measured in the field to accurately estimate liquid water percolating through the snowpack. Furthermore, two empirical coefficients used in the water flow equation were showed to greatly impact model outputs. This heterogeneous flow model is an important tool to help understand snowmelt flow processes in complex and level terrains and to demonstrate how uncertainty in snowmelt-derived runoff calculations might be reduced.