It is important to realize that snow is really a three phases medium: it might contain at the same time water in its solid phase (the ice crystals matrix), in its liquid phase (interstitial water) and in its gaseous phase (water vapor in the pore space). As the liquid water can move through the ice matrix, it transports mass as well as potentially energy. Depending on the conditions, it might also significantly alter the microstructure of the snow pack. Therefore it is very important to be able to simulate how this liquid water moves through the snow layers.

Matrix flow and preferential flow

Liquid water can move through the snow pack in two distinct ways: through matrix flow or through preferential flow. They are fundamentally different and have very different time scales.

Matrix flow

Matrix flow represents how the liquid water moves through the pore space of the ice matrix. This capillary motion is dominated by surface tension effects. Such a flow is highly dependent on the tortuosity of the ice matrix, the water column pressure head and changes of such properties which can lead to capillary barriers. The kind of flow moves the bulk of the mass in a gradual process.

Preferential flow

A second kind of liquid water transport mechanism is through preferential flow. This is a 2 dimensional effect where at some places the liquid water is able to locally flow much deeper into the snow pack. Although highly relevant for its impact on the snow microstructure and for its impact on snow stability, this transport mechanism only carries a minority of the liquid water mass. But by providing liquid water in deeper layers much faster, it can contribute to triggering a weak layer or accumulate liquid water at a capillary barrier (ponding) that could later refreeze and build an ice layer.

Modeling

In Snowpack, water transport can currently either be modeled with the bucket approach or by solving the Richards equations.

scheme

In the bucket scheme, each layer has an irreducible liquid water content. When liquid water content exceeds this value, it is moved to the next layer instantaneously (as if it is an overflowing bucket). This scheme is computationally very efficient, but does not reproduce certain flow features like capillary barriers, while also assuming infinite flow rates. For snow layers, the irreducible water content is determined following Coleou and Lesaffre (1998). For soil, the irreducible water content is determined following the function in soilFieldCapacity(), where it is parameterized as a function of grain size.

equation

When using Richards equation, the Darcy flow for unsaturated media is solved (Wever et al., 2014). This approach reproduces several flow features in a more physics-based way. For example, capillary barriers can inhibit downward percolation, and the percolation speed is more realistically simulated. To determine water retention, the van Genuchten parameterization is used for the relationship between pressure head and liquid water content. For snow, the model used is based on Yamaguchi et al. (2012). Note that it is possible to specify another model by modifying the source code. To determine the saturated hydraulic conductivity, the parameterization by Calonne et al. (2012) for permeability is used. The unsaturated hydraulic conductivity is subsequently determined from the saturated hydraulic conductivity using the Mualem model.

For soil, the soil type is specified using grain size, according to the following table: https://snowpack.slf.ch/Soil-with-Richards-equation/. The soil type sets the van Genuchten parameters, the saturated hydraulic conductivity as well as porosity.

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