A review and evaluation of 39 thermal conductivity models for frozen soils

Abstract Frozen soil thermal conductivity (λeff) is a critical thermo-physical property that is required for environmental, earth science, geotechnical and geo-environmental applications and associated numerical modeling. Measurement of λeff in frozen soils is difficult and prone to errors, especially near the freezing/thawing point of soil water (e.g., −4 to 0 °C). Available steady-state or transient methods to measure λeff based on the soil temperature response to applied heat often result in melting of soil ice, violating the conduction-only assumptions of these methods and result in biased λeff measurements. Therefore, the choice of λeff models is often influence by their ease of implementation. A great number of such models have been developed during the last few decades since the latest comprehensive review of frozen soil thermal conductivity models in the early 1980s. There is a need to revisit this topic by comparing the models and evaluating their performance to provide information to the novice and expert alike, in order to guide them on their advantages, limitations and applications. A total of 39 models were categorized as: 1) linear and non-linear regression models (8 models); 2) physical models (6 models); 3) mixing models (6 models); 4) normalized models (17 models); and 5) models of other types based on their characteristics (2 models). These models were assessed with a large compiled dataset consisting of 331 λeff measurements taken at temperatures