A new empirical model for the estimation of soil thermal conductivity

  • Jie RenEmail author
  • Lili Men
  • Wenbing Zhang
  • Jie Yang
Original Article


Soil thermal conductivity (λ) is an important thermal property which serves as an indicator for the coupling of soil, water, heat, and solutes in a numerical model. The objective of this study is to develop a new empirical model for estimating soil thermal conductivity. There are several methods for estimating λ available, but they are complicated and can produce relatively large errors. Using published datasets, the performance of the new estimate was evaluated along with nine other normalized models, and the advantages and disadvantages of each model and its relevant soil types were analyzed and compared. The results showed that the new empirical model is suitable for studying the thermal conductivities of soils of different textures. In the comparisons, it had the best performance among the ten models considered, with a minimum standard deviation (SD) of 0.074 W m−1 K−1, the coefficient of determination (R2) from 0.929 to 0.983 with a mean of 0.964, and relative error (Re), from 5.210 to 9.900% with a mean of 7.335%. The new model has been shown to improve the reliability of estimation of soil thermal conductivity and has application in agricultural science, environmental science, earth science and engineering research.


Soil Thermal conductivity Empirical model Soil water content 

List of symbols


A, B, C, D, E

Campbell model parameters


Mass fraction of clay particles


Mass fraction of sand particles


Mass ratio of organic matter


Mass fraction of silt particles


Soil porosity

a, b, m

Lu et al. (2007) model parameters

c, d, e, f

Su et al. (2016) model parameters

J, L

He et al. (2017) model parameters


Measured value


Sample mean


Model simulated value


Number of independent λ records


Number of model fitting parameters



Ewen and Thomas model parameters

κ, χ, η

Côté and Konrad model parameters

µ, φ

Lu et al. (2014) model parameters


Soil thermal conductivity (W m−1 K−1)


Volumetric water content


Particle density


Specific weight

α, β

The new model parameters









Soil solids




Other minerals





Degree of saturation


Kersten number


Standard deviation


Coefficient of determination


Relative error


Particle size distribution


Heat pulse



This work was supported by the National Natural Science Foundation of China (Grant No. 51679194) and Open Research Fund of Key Laboratory of Failure Mechanism and Safety Control Techniques of Earth-Rock Dam of the Ministry of Water Resources (Grant No. YK319011).

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.State Key Laboratory of Eco-hydraulics in Northwest Arid Region of ChinaXi’an University of TechnologyXi’anChina
  2. 2.College of Water Resources and Hydro-electric EngineeringXi’an University of TechnologyXi’anChina

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