A theoretical extension of the soil freezing curve paradigm

Numerical models of permafrost evolution in porous media typically rely upon a smooth continuous relation between pore ice saturation and sub-freezing temperature, rather than the abrupt phase change that occurs in pure media. Soil scientists have known for decades that this function, known as the soil freezing curve (SFC), is related to the soil water characteristic curve (SWCC) for unfrozen soils due to the analogous capillary and sorptive effects experienced during both soil freezing and drying. Herein we demonstrate that other factors beyond the SFC-SWCC relationship can influence the potential range over which pore water phase change occurs. In particular, we provide a theoretical extension for the functional form of the SFC based upon the presence of spatial heterogeneity in both soil thermal conductivity and the freezing point depression of water. We infer the functional form of the SFC from many abrupt-interface 1-D numerical simulations of heterogeneous systems with prescribed statistical distributions of water and soil properties. The proposed SFC paradigm extension has the appealing features that it (1) is determinable from measurable soil and water properties, (2) collapses into an abrupt phase transition for homogeneous media, (3) describes a wide range of heterogeneity within a single functional expression, and (4) replicates the observed hysteretic behavior of freeze-thaw cycles in soils.