Heat flux in frozen soils

Soil temperature is the driving force for a flux of energy in the soil profile, eq.(1.1). This flux, qh, has to be balanced by a change in the energy storage in the soil, eq. (1.2), described by the changes in latent heat content (left hand side terms). However, the calculation of the ratio between sensible and latent heat when the soil freezes is complicated by a depression of the freezing-point. When the temperature drops below 0 oC the energy storage in the soil is changed such that liquid water is converted to ice, i.e. change of latent heat, and simultaneous with the temperature decrease, i.e. change of sensitive heat. The latent heat of freezing, seen in eq. (1.2) as the second left term, is zero when the soil is completely unfrozen or frozen.

Treatment of frost in the soil is based on a function for freezing-point depression and on an analogy between the processes of freezing-thawing and drying-wetting, i.e., the liquid-ice interface is considered equal to the liquid-air interface (see Harlan, 1973). Thus, unfrozen water below zero can be associated with a matric potential and an unsaturated conductivity and therefore affects soil water flows (see switch FrostInteract). Freezing gives rise to a potential gradient which in turn forces a water flow depending on the prevailing conductivity. This causes a capillary rise of water towards the frost zone and it also allows drainage of snow melt through the frost zone when frozen soil temperatures are close to 0 °C.