Elements of future snowpack modeling – Part 1: A physical instability arising from the nonlinear coupling of transport and phase changes

˜The œcryosphere, vol. 16, pp. 903–923

Abstract

The incorporation of vapor transport has become a key demand for snowpack modeling in which accompanied phase changes give rise to a new, nonlinear coupling in the heat and mass equations. This coupling has an impact on choosing efficient numerical schemes for 1D snowpack models which are naturally not designed to cope with mathematical particularities of arbitrary, nonlinear partial differential equations (PDEs). To explore this coupling we have implemented a stand-alone finite element solution of the coupled heat and mass equations in snow using the computing platform FEniCS. We focus on the nonlinear feedback of the ice phase exchanging mass with a diffusing vapor phase with concurrent heat transport in the absence of settling. We demonstrate that existing continuum-mechanical models derived through homogenization or mixture theory yield similar results for homogeneous snowpacks of constant density. When snow density varies significantly with depth, we show that phase changes in the presence of temperature gradients give rise to nonlinear advection of the ice phase amplifying existing density variations. Eventually, this advection triggers a wave instability in the continuity equations. This is traced back to the density dependence of the effective transport coefficients as revealed by a linear stability analysis of the nonlinear PDE system. The instability is an inherent feature of existing continuum models and predicts, as a side product, the formation of a low-density (mechanical) weak layer on the sublimating side of an ice crust. The wave instability constitutes a key challenge for a faithful treatment of solid–vapor mass conservation between layers, which is discussed in view of the underlying homogenization schemes and their numerical solutions.

Authors 3

1. Konstantin Schürholt

   WSL Institute for Snow and Avalanche Research SLF

   Affiliation as printed

   WSL Institute for Snow and Avalanche Research SLF, Flüelastr. 11, 7260 Davos, Switzerland

2. Julia Kowalski Aachen AICES Graduate School

   RWTH Aachen University · Aachen Institute for Advanced Study in Computational Engineering Science · University of Göttingen

   Affiliation as printed

   AICES Graduate School, RWTH Aachen University, Schinkelstr. 2a, 52062 Aachen, Germany

   Computational Geoscience, University of Göttingen, Goldschmidtstr. 1, 37077 Göttingen, Germany

3. Henning Löwe corresponding

   WSL Institute for Snow and Avalanche Research SLF

   Affiliation as printed

   WSL Institute for Snow and Avalanche Research SLF, Flüelastr. 11, 7260 Davos, Switzerland