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

Authors: HE, HAILONG - Northwest Agricultural & Forestry University; Flerchinger, Gerald; KOJIMA, YUKI - Gifu University; DYCK, MILES - University Of Alberta; LV, JIALONG - Northwest Agricultural & Forestry University

Submitted to: Geoderma
Publication Type: Peer Reviewed Journal
Publication Acceptance Date: 8/26/2020
Publication Date: 10/13/2020
Citation: He, H., Flerchinger, G.N., Kojima, Y., Dyck, M., Lv, J. 2020. A review and evaluation of 39 thermal conductivity models for frozen soils. Geoderma. 382. Article 114694. https://doi.org/10.1016/j.geoderma.2020.114694.
DOI: https://doi.org/10.1016/j.geoderma.2020.114694

Interpretive Summary: Soil thermal conductivity is a critical physical property required by environmental and earth science, geotechnical and geo-environmental applications and associated numerical modelling. Measurement of soil thermal conductivity in frozen soils is particularly difficult because of ice melting while making the measurements. Numerous algorithms exist to estimate thermal conductivity of frozen soils, but no known study has been conducted to compare an extensive set of these algorithms with a common data set. Therefore, a dataset was compiled of 27 widely differing soils from seven studies, and 19 different algorithms were applied to these this compiled dataset. While some algorithms were shown to perform better than others, none could represent the wide range of soils satisfactorily. Future studies that focus on conceptualization and development of new frozen soil thermal conductivity models for accurate and wide application is recommended.

Technical Abstract: Frozen soil thermal conductivity ('eff) is a critical thermophysical property that is required by environmental and earth science, geotechnical and geo-environmental applications and associated numerical modelling. Measurement of 'eff in frozen soils is difficult and prone to errors, especially at high subfreezing temperature range (e.g., -4 to 0 ºC). Available steady-state or transient methods measure 'eff based on the transport characterization of applied heat that result in melting of the ice and change of 'eff being measured. Therefore, mathematical algorithms become prevalent because its ease of use and wide applications. A great number of such algorithms have been developed during the last few decades since the latest comprehensive review of frozen soil thermal conductivity models in early 1980s. There is a need to revisit this topic by collating the models and evaluating their performance to provide information to the novice and expert alike to guide them on the development, advantages and limitations. A total of 39 models were collated and categorized into eight linear and non-linear regression models, six physical models, six mixing models, 17 normalized models and two models of other types based on their characteristics. These models were assessed with a compiled large dataset consisting of 331 measurements taken at temperatures <-4 ºC on 27 soils from seven studies. Three performance indices including root mean square error (RMSE), average deviations (AD) and Nash-Sutcliff Efficiency (NSE) were used to evaluate model performance. The results showed that models of BB1992, TZ2016, ZM2018 and WL2017 are 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 ºC-1 and AD = -0.04 W m-1 ºC-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.