Preprints
https://doi.org/10.5194/tc-2021-73
https://doi.org/10.5194/tc-2021-73

  25 Mar 2021

25 Mar 2021

Review status: this preprint is currently under review for the journal TC.

Elements of future snowpack modeling – part 2: A modular and extendable Eulerian–Lagrangian numerical scheme for coupled transport, phase changes and settling processes

Anna Simson1, Henning Löwe2, and Julia Kowalski1,3 Anna Simson et al.
  • 1AICES Graduate School, RWTH Aachen University, Schinkelstr. 2a, 52062 Aachen, Germany
  • 2WSL Institute for Snow and Avalanche Research SLF, Flüelastr. 11, 7260 Davos, Switzerland
  • 3Computational Geoscience, Geoscience Centre of the University of Göttingen, Goldschmidtstr. 1, 37077 Göttingen, Germany

Abstract. A coupled treatment of transport processes, phase changes and mechanical settling is the core of any detailed snowpack model. A key concept underlying the majority of models is the notion of layers as deforming material elements that carry the information on their physical state. Thereby an explicit numerical solution of the ice mass continuity equation can be circumvented, however at the downside of virtual no flexibility in implementing different coupling schemes for densification, phase changes and transport. As a remedy we consistently recast the numerical core of a snowpack model into an extendable Eulerian–Lagrangian framework for solving the coupled non-linear processes. In the proposed scheme, we explicitly solve the most general form of the ice mass balance using the method of characteristics, a Lagrangian method. The underlying coordinate transformation is employed to state a finite-difference formulation for the superimposed (vapor and heat) transport equations which are treated in their Eulerian form on a moving, spatially non-uniform grid that includes the snow surface as a free upper boundary. This formulation allows to unify the different existing view points of densification in snow or firn models in a flexible way and yields a stable coupling of the advection-dominated mechanical settling with the remaining equations. The flexibility of the scheme is demonstrated within several numerical experiments using a modular solver strategy. We focus on emerging heterogeneities in (two-layer) snowpacks, the coupling of (solid-vapor) phase changes with settling at layer interfaces and the impact of switching to a non-linear mechanical constitutive law. Lastly, we discuss the potential of the scheme for extensions like a dynamical equation for the surface mass balance or the coupling to liquid water flow.

Anna Simson et al.

Status: final response (author comments only)

Comment types: AC – author | RC – referee | CC – community | EC – editor | CEC – chief editor | : Report abuse
  • RC1: 'Comment on tc-2021-73', Anonymous Referee #1, 06 May 2021
  • RC2: 'Comment on tc-2021-73', Anonymous Referee #2, 15 May 2021

Anna Simson et al.

Anna Simson et al.

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Short summary
This companion paper deals with numerical particularities of partial differential equations underlying one dimensional snow models. In this second part we include mechanical settling and develop a new hybrid (Eulerian-Lagrangian) method for solving the advection-dominated ice mass conservation on a moving mesh alongside with Eulerian diffusion (heat and vapor) and phase changes. The scheme facilitates a modular and extendable solver strategy while retaining control on numerical accuracy.