We present a method to characterize soil moisture freeze-thaw events and freezing/melting point depression using permittivity and temperature measurements, readily available from in situ sources. In cold regions soil freeze-thaw processes play a critical role in the surface energy and water balance, with implications ranging from agricultural yields to natural disasters. Although monitoring of the soil moisture phase state is of critical importance, there is an inability to interpret soil moisture instrumentation in frozen conditions. To address this gap, we investigated the freeze-thaw response of a widely used soil moisture probe, the HydraProbe, in the laboratory. Soil freezing curves (SFCs) and soil thawing curves (STCs) were identified using the relationship between soil permittivity and temperature. The permittivity SFC/STC was fit using a logistic growth model to estimate the freezing/melting point depression (T-f/m) and its spread (s). Laboratory results showed that the fitting routine requires permittivity changes greater than 3.8 to provide robust estimates and suggested that a temperature bias is inherent in horizontally placed HydraProbes. We tested the method using field measurements collected over the last 7 years from the Environment and Climate Change Canada and the University of Guelph's Kenaston Soil Moisture Network in Saskatchewan, Canada. By dividing the time series into freeze-thaw events and then into individual transitions, the permittivity SFC/STC was identified. The freezing and melting point depression for the network was estimated as T-f/m = - 0.35 +/- 0.2,with T-f = - 0.41 +/- 0.22 degrees C and T-m = - 0.29 +/- 0.16 degrees C, respectively.

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.

Recently, there has been a revival in the development of models simulating coupled heat and water transport in cold regions. These models represent significant advances in our ability to simulate the sensitivity of permafrost environments to future climate change. However, there are considerable differences in model formulations arising from the diverse backgrounds of researchers and practitioners in this field. The variability in existing model formulations warrants a review and synthesis of the underlying theory to demonstrate the implicit assumptions and limitations of a particular approach. This contribution examines various forms of the Clapeyron equation, the relationship between the soil moisture curve and soil freezing curve, and processes for developing soil freezing curves and hydraulic conductivity models for partially frozen soils. Where applicable, results from recent laboratory tests are presented to demonstrate the validity of existing theoretical formulations. Identified variations in model formulations form the basis for briefly comparing and contrasting existing models. Several unresolved questions are addressed to highlight the need for further research in this rapidly expanding field. (C) 2013 Elsevier Ltd. All rights reserved.