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 <−4 °C on 27 soils from seven studies, using steady-state or transient methods. Three performance indices including root mean square error (RMSE), average deviations (AD) and Nash-Sutcliff Efficiency (NSE) were used to evaluate performance of these models. The results showed that the models of Becker et al. (1992) (BB1992), Tian et al. (2016) (TZ2016), Zhang et al. (2018) (ZM2018) and Wang et al. (2017) (WL2017) were the best performing models in their affiliated category. However, none of the models performed satisfactorily, with NSE = 0.51, RMSE = 0.46 W m−1 °C−1 and AD = −0.04 W m−1 °C−1 for the best performing model among all the models investigated. Future studies that focus on conceptualization and development of new frozen soil thermal conductivity models for accurate and wide application is recommended.