## Crocus - Introduction

Sommaire

### Model purpose

Crocus is a unidimensional thermodynamic-based computer model able to simulate the energy and mass balance of the snowpack. Its main purpose is to accurately describe the time evolution of the physical properties of the inner snowpack (thermal conduction, radiative transfer) based on a semi-quantitative description of the time evolution of the morphological properties of the snow grains along with snow metamorphism. This approach allows to realistically simulate energy and water fluxes at the snowpack interfaces (ground and atmosphere).

### Short description

Forcing variables

In its basic configuration, Crocus recquires the following forcing variables at a hourly time step:

• Air temperature
• Air relative humidity
• Wind speed
• Snowfall rate
• Rainfall rate
• Incoming solar radiation (visible + near-infrared)
• Incoming atmospheric radiation (thermal infrared)

The basal heat flux can either be imposed (simulations in Alpine settings) or result from the coupling with a soil physical model.

Variables describing physical properties of the snow layers

Snow layers are described through the following variables

• Thickness
• Temperature in the middle of the layer
• Snow density
• Liquid water content
• Snow type

The snow type is described semi-quantitatively using notions such as the dendricity, sphericity, grain size and the physical history of the snow layer.

Model output

Model output consists in:

• integrated physical properties at the scale of the whole snowpack (snow depth, snow water equivalent, surface temperature, albedo ...)
• inner snowpack physical properties, from which a profile of the physical properties of snow can be inferred
• an overview of the energy and water flux at the snowpack boundaries (atmosphere and ground)

Interactive management of snow layers

The uniqueness of Crocus arises from its interactive management of the number of horizontal layers (referred to as “virtual snow layers”) allowing to optimally discretize the vertical profile of the physical properties of the snowpack. Indeed, when fresh snow deposits at the surface of the snowpack, its physical properties can widely differ from the underlying older snow. In addition, snow metamorphism drives the time evolution of the physical properties of snow layers in potentially widely different directions. Neverthless, to avoid having to deal with a very large number of virtual snow layers which would impair the model performance, two virtual layers possessing neighbooring physical properties can be aggregated into a single virtual layer. In contrast, a given virtual snow layer can be spit up whenever it is too close from the snow surface: this allows a more accurate description of heat and radiation transfer in the uppermost snowpack, thus a better simulation of the temperatur profile.

Constitutive physical laws

Below the main physical laws implemented in Crocus

• Thermal conduction: 1D solution of the heat equation
• $\partial/\partial t \left(\rho C_p T\right)=\partial^2/\partial z^2 \left(k T\right)+Q$,
where $\rho$ is the snow density, $C_p$ is the specific heat capacité, $T$ is the temperature, $k$ is the thermal conductivity and $Q$ represents a possible local heat source .
• Phase change, when snow temperature reaches 273.16 K
• Surface energy balance
• Snow metamorphism: the laws describing the temporal rate of change of the morphological properties of snow were obtained in the laboratory under various temperature gradient conditions, and also under wet metemorphism conditions .
• Liquid water percolation: the current approach uses a “bucket model” formalism whereby water percolates only from snow layers reaching a threshold in terms of liquid water content.
• Settling under the combined impact of the overlying weight of snow and snow metamorphism .
• de/e = - \sigma/\eta \times dt\$
where $e$ eis the layer thickness, $\sigma$ is the fvertical stress and $\eta$ is the newtonian viscosity .

Physical parametrizations

Physical variables implemented into the physical laws described above are often parameterized as a function of the prognotics variables. A few examples are given below:

• the specific heat capacity is parameterized as a function of temperature ,
• the effective heat conductivity is parameterized as a function of the snow density ,
• the snowpack albedo is equal to that of the uppermost snow layer. It is calculated for three spectral bands (0.3 - 0.8 $\mu$m, 0.8 - 1.5 $\mu$m and 1.5 - 2.8 $\mu$m). In the first band, the albedo depends on the optical diameter (which itself is empirically derived from the morphological properties of snow grains) and on the snow age - reflecting the progressive darkening of snow over time to the incorporation of impurities. In the other spectral bands, the albedo only depends on the optical diameter .

References

The Crocus model was originally described in two publications :

Brun E., E. Martin, V. Simon, C. Gendre C. and C. Coléou, An energy and mass model of snow cover suitable for operational avalanche forecasting, J. Glaciol., 35(121), 333-342, 1989.

Brun E., P. David, M. Sudul and G. Brunot, A numerical model to simulate snowcover
stratigraphy for operational avalanche forecasting, J. Glaciol., 38(128), 13-22, 1992.

The current version of Crocus is now integrated as a snow scheme of the lans surface model ISBA within the SURFEX interface. The following reference provides details on this implementation :

Vionnet, V., Brun, E., Morin, S., Boone, A., Faroux, S., Le Moigne, P., Martin, E., and Willemet, J.-M.: The detailed snowpack scheme Crocus and its implementation in SURFEX v7.2, Geosci. Model Dev., 5, 773-791, doi:10.5194/gmd-5-773-2012, 2012.