Estimating Soil Thermal Diffusivity Using Pedotransfer Functions with Nonlinear Regression

Ahmed Yehia Mady1, 2, *, Evgeny Shein1
1 Soil Physics and Reclamation Department, Faculty of Soil Science, Lomonosov Moscow State University, Moscow, 119991, Russia
2 Ain Shams University, Faculty of Agriculture, Soil Science Department, Cairo, 11241, Egypt

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Creative Commons License
© 2018 Mady and Shein.

open-access license: This is an open access article distributed under the terms of the Creative Commons Attribution 4.0 International Public License (CC-BY 4.0), a copy of which is available at: ( This license permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

* Address correspondence to this author at the Soil Physics and Reclamation Department, Faculty of Soil Science, Lomonosov Moscow State University, Moscow, 119991, Russia; Tel: 8916990-90-50; E-mail:


Background and Objective:

Pedotransfer Functions (PTFs) are widely used for estimating soil thermal diffusivity. Some attempts have been made to indirectly predict soil thermal diffusivity from the easily available fundamental soil physics properties. The aim of the work was not only to validate the usage of PTFs with Nonlinear Regression (NLR) for estimating soil thermal diffusivity (KD), but to select the best predictor variables used for determination of PTFs.

Materials and Methods:

Soil thermal diffusivity was measured at different values of water content using Kondratieff method. The parameters of the quadratic equation, which described the relation between thermal diffusivity and water content, were determined by the fitting curve and using PTFs (exponential equations) based on soil physical properties. The combination of different soil physical properties used as PTF model’s independent variables was tested. Three classes of PTFs were proposed using NLR to estimate KD were: KDPTF-1 (Sand+ Silt+ Clay), KDPTF-2 (Sand+ Silt+ Clay + Bulk density), and KDPTF-3 (Sand+ Silt+ Clay+ Bulk density + Organic matter).


The best class of PTF could be used for calculating the parameters of the quadratic equation and soil thermal diffusivity was KDPTF-1 which considered the percentage of sand, silt and clay, RMSE=2.94×10-8 m2/s, and GMER =1.05.


The quadratic and exponential equations represented the nonlinear regression equations, which could be used for estimating soil thermal diffusivity at different values of water content from easily available data on soil texture, bulk density, and organic matter content.

Keywords: Soil physical properties, Thermal parameters, Pedotransfer functions, Quadratic equation, Nonlinear regression equation, Thermal diffusivity.