On modelling the thermal conductivity of soils using normalized-multi-variable pedotransfer functions

A comprehensive analysis of 6-published and 15-new Kersten (Ke) functions, i.e. normalized soil thermal conductivity (λ) expressions, was conducted using a complete λ data base of 40 Canadian soils. It was confirmed that Ke depended mainly on the degree of soil saturation (Sr), while additional dependency on volumetric content of sand (θsa) as the second variable and organic matter (θo-m) as the third variable , was marginal. Furthermore, a few Ke(Sr) functions did not fully meet the fundamental requirements at Sr boundaries, i.e. and . However, accurate λ estimates were still obtained within small Ke deviations, i.e. and . After applying a least square regression analysis to 21 functions, the following Ke(Sr) were found to be the highest ranking: From the novel Ke functions, two earned notable attention, namely: the 1st and 3rd Ke functions from the above list. The former is an extension to full Sr range for the original model by Johansen, while the latter is a simple power-exponential function. The λ estimates obtained by the functions listed above closely followed experimental data of a majority of 40-Canadian soils and Standard Sands. Standard deviation (SD) was used to determine the predictive performance of the Ke(Sr) functions: 17-coarse soils SDave ≈ 0.19 W m−1 K−1, 22-fine soils SDave ≈ 0.11 W m−1 K−1, and Standard Sands SDave ≈ 0.16 W m−1 K−1. In addition, the highest ranking functions, listed above, underwent validation against soil data from different places and dissimilar geneses. In general, the obtained estimates of λ closely follow experimental data: Chinese soils (SDave ≈ 0.160 W m−1 K−1), American soils (SDave ≈ 0.125 W m−1 K−1). However, uncertain λ estimates were obtained for soils of diverse geneses (volcanic origin).