A model of hydraulic and energetic dynamics in a freezing soil with varying topography

This work presents a one-dimensional model of thermal and hydraulic dynamics in a soil column subjected to water phase change. The formulation includes the Generalized Richards equation for water conservation, the Nassar and Horton formulation for energy conservation, a volume conservation formulation associated to water/ice phase change and a formulation of snow bulk dynamics over the ground. The coupling of these processes may lead to soil expansion/contraction. Providing a modeling tool for this process has been the main motivation of this work. This is because topography dynamic during freezing/thawing cycles is an important issue in high latitude and altitude areas, as it has relevant impacts on environmental and human systems. However, modeling tools on this point are still rare, to our knowledge. The soil column is discretized in an adjustable number of layers. The time step can be adjusted as well. Input data include the soil stratigraphy, precipitation and air temperature. A preliminary evaluation of the model is proposed by using two analytical tests: One test performs a comparison between the model results and the analytical solution from the Richards equation (which describes the soil water fluxes) and the other test performs a comparison with the Neumann analytical solution (for unilateral freezing of a semi-infinite region). A set of pilot studies are also proposed to evaluate model performances during simple conditions, such as the complete freezing of a saturated soil column or the complete fusion of an ice-rich soil column.