The one-dimensional snow cover model SNOWPACK (Lehning et al., 1999; Bartelt and Lehning, 2002; Lehning et al., 2002a, b), was primarily developed for the support of avalanche warning in Switzerland. However, this physical model is also used for other applications such as permafrost investigations (Lütschg et al., 2003), the assessment of snow – vegetation interactions, climate research (Rasmus and Räisänen, 2003; Bavay et al., 2009), mass- and energy balance calculations for arctic areas (Meirold-Mautner and Lehning, 2003) and calculations of chemical solute transport in snow (Waldner et al., 2003).

Physical processes

A graphical review of the physical processes described by the SNOWPACK model is given in the above figure. SNOWPACK is based on a Lagrangian finite element implementation and solves the instationary heat transfer and settlement equations. Phase changes and transport of water vapor and liquid water are included. Special attention is paid to the metamorphism of snow and its connection to mechanical properties such as thermal conductivity and viscosity. At present, SNOWPACK is the most advanced snow cover models worldwide in terms of microstructural detail. Therefore, first attempts are being made to estimate snow cover stability from SNOWPACK simulations (Lehning et al., 2003).

Structure of the physical modeling

Model Foundations

The SNOWPACK model is built around a 1D soil/snow/canopy column (see figure above). This in effect neglects lateral transfers and only considers vertical gradients and transfers. The snow is modeled as a three phase porous medium (ice/liquid water/water vapor) but can also contain an arbitrary amount of soil in order to simulate from purely soil layers to snow layers, including ice lenses, permafrost, ponding, etc. An arbitrary number of layers can be simulated, according to needs. Because of its lagragian grid, SNOWPACK can simulate very thin layers if needed (ice crust, hoar).

Model Hierarchy

At the core of the model, are a few state variables. These are used to model the microstructure, including its metamorphic developments. This in turns allows to build bulk constitutive properties that are necessary to compute the core conservation equations. Finally, a few "side models" provide the necessary connections to meteorological forcing, real world measurements and parameters and other properties. Therefore the model can be described by the following hierarchical structure (see figure below):

• a few state variables: density, temperature, liquid water content that must be known for each layer;
• from these state variables, four primary (independent) microstructure parameters are derived: grain size, bond radius, sphericity and dendricity. As a matter of convenience, the coordination number will also be computed and used. Equilibrium growth metamorphism and kinetic metamorphism will drive the temporal evolution of these parameters according to various models.
• from the microstructure parameters, the macroscopic properties will be computed: thermal conductivity and viscosity. This will include pressure sintering, the strain amplification on the necks and its feedback on the metamorphism as well as both linear and non-linear viscosity ranges.
• these bulk properties then allow computing the core equations: mass and energy conservation as well as the settling. The energy balance will include the solar radiation absorption, the sublimation/deposition of water vapor, the melting and refreezing of water as well as the heat conduction. By enforcing the three phase approach, only two mass conservations will be required: for the liquid water and the water vapor.
• finally, auxiliary models provide the necessary "glue": the snow surface and ground boundary conditions (using either Neumann to enforce fluxes or Dirichlet to enforce temperatures or even swapping between the two depending on the conditions), a new snow density parametrization (that depends on the local climate), an albedo and short wave absorption parametrization and a snowdrift model.
• some post-processing models will be added to provide more relevant outputs: a hardness model, several snow stability index, a snow classification.

The user can configure variants of these basic model concepts. The way of interaction is primarily through a configuration file but also changes to the source code by users are in principle possible. In any case, a sufficient understanding of the modeling concept will ensure a safe operation of the model.

Energy Balance

The figure below shows the various fluxes that are part of the energy balance of the SNOWPACK model. These are available in the output files as well as through the niViz interface.