Non-iterative numerical model of soil freezing

Increasingly, numerical models of varying complexity are used to simulate the thermal and water balance of soils exposed to freezing-thawing cycles. An important aspect of soil freezing modeling is the highly non-linear nature of the energy balance equation during phase transition. To handle the transformation between sensible and latent heat during freezing–thawing events, the majority of existing models employ the concept of apparent heat capacity. The main disadvantage of this approach is that the apparent heat capacity increases by several orders of magnitude at the freezing point, which complicates the numerical solution, possibly causing numerical oscillations and convergence problems.

An alternative approach was developed to facilitate the simulations of soil water flow and energy transport during sporadic freezing–thawing episodes, which are typical for the winter regime of humid temperate continental climate. The approach is based on an accurate non-iterative algorithm for solving highly non-linear energy balance equation during phase transitions. The suggested modeling approach abstracts from many complexities associated with the freezing phenomena in soils, yet preserves the principal physical mechanism of conserving the internal energy of the soil system during the phase transitions. When applied to simulate occasional freezing soil conditions, the model algorithm delivers the desired effect of slowing down the propagation of surface freezing temperatures into deeper soil horizons by converting water latent heat into sensible heat. The model also allows the evaluation of the extent and duration of frozen soil conditions – a crucial information for soil water flow modeling, as the frozen soil significantly reduces the soil hydraulic conductivity.

The proposed algorithm was successfully verified against analytical solutions for idealized freezing and thawing conditions and applied to both hypothetical and real field conditions.