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 (S_r), while additional dependency on volumetric content of sand (θ_sa) as the second variable $Ke\left(S_{\text{r}},{\theta }_{\text{sa}}\right)$ and organic matter (θ_o-m) as the third variable $Ke\left(S_{\text{r}},{\theta }_{\text{sa}},{\theta }_{\text{o}-\text{m}}\right)$, was marginal. Furthermore, a few Ke(S_r) functions did not fully meet the fundamental requirements at S_r boundaries, i.e. $K{e}_{S_{\text{r}}=0}=0$ and $K{e}_{S_{\text{r}}=1}=1$. However, accurate λ estimates were still obtained within small Ke deviations, i.e.$K{e}_{S_{\text{r}}=0}=0\pm 0.02$ and $K{e}_{S_{\text{r}}=1}=1\pm 0.02$. After applying a least square regression analysis to 21 functions, the following Ke(S_r) were found to be the highest ranking:$Ke\left(S_{\text{r}}\right)=1+a·{\log }_{10}(b+S_{\text{r}}^c)$ $Ke\left(S_{\text{r}}\right)=0.5·\left[a+b·{\log }_{10}\left(S_{\mathrm{r}}\right)+\left|a+b·{\log }_{10}\left(S_r\right)\right|\right]$ $Ke\left(S_{\text{r}}\right)=S_{\text{r}}^{-a}·\exp \left(1-S_{\text{r}}^{-b}\right)$ $Ke\left(S_{\text{r}}\right)=\exp \left[a·(1-S_{\mathrm{r}}^{-b})\right]$ $Ke\left(S_{\text{r}}\right)=a·erfc\left[-b·\ln \left(S_{\text{r}}/a\right)\right]$.

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 S_r 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(S_r) functions: 17-coarse soils SD_ave ≈ 0.19 W m⁻¹ K⁻¹, 22-fine soils SD_ave ≈ 0.11 W m⁻¹ K⁻¹, and Standard Sands SD_ave ≈ 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 (SD_ave ≈ 0.160 W m⁻¹ K⁻¹), American soils (SD_ave ≈ 0.125 W m⁻¹ K⁻¹). However, uncertain λ estimates were obtained for soils of diverse geneses (volcanic origin).