An Empirical Model for Estimating Soil Thermal Conductivity from Texture, Water Content, and Bulk Density

Abstract

Soil thermal conductivity (λ) models are needed frequently in studying coupled heat and water transfer in soils. Several models are available, but some are complicated and some produce relatively large errors. In this study, we developed a simple model for estimating λ from soil texture, bulk density (ρb), and water content (θ). Three parameters, α, β, and λdry, are included in the model, where λdry is determined by ρb and α and β are shape factors estimated from soil texture and ρb. Empirical relations were developed for α and β by fitting the model to heat‐pulse (HP) measurements of λ(θ) on seven soils of various textures. The model performance was evaluated with independent λ(θ) data from independent HP measurements and literature values. The results show that the model is able to express the λ(θ) curves from oven dry to saturation at fixed ρb values. When ρb is varied, the estimated λ data agree well with measured values. The root mean square errors are <0.15 W m−1 K−1, and the bias is within 0.10 W m−1 K−1. The new model has the potential for use in studying heat movement in soils of varying texture, bulk density, and water content and can be incorporated into numerical algorithms for describing coupled heat and mass transfer processes.

Thermal property values of a central Iowa soil as functions of soil water content and bulk density or of soil air content

“…Based on soil water content and thermal conductivity datasets, Lu et al () presented an empirical model relating λ to θ , ρ b and soil texture, as follows: where α and β were factors that affected the shape of the λ ( θ ) curve. They were estimated from soil particle‐size information and ρ b : where f cl and f sa were USDA‐fractions of clay and sand, respectively.…”

“…the slope of the λ ( θ ) curve), whereas the β parameter influenced the magnitude of λ . Additional details about the model can be found in Lu et al ().…”

A novel approach to evaluate soil heat flux calculation: An analytical review of nine methods

“… λ s and k s of the soil samples were then determined in the laboratory (about 20°C) at different fractions of volumetric water content ( θ ) when the samples were dried in an oven (blue circles in Figure ). Multiple studies have suggested an exponential relationship between the thermal properties and θ [ McCumber and Pielke , ; Chen and Dudhia , ; Wang et al , ; Guan et al , ; L. Wang et al , ; Lu et al , ]. Following an empirical relationship proposed in Lu et al [], the best fit relationship between λ s (W m −1 K −1 ) and θ , as shown in Figure a, can be described as where 0.20 W m −1 K −1 is the thermal conductivity of dry soil and 1.46 and 0.34 are shape factors of the fit curve, which are fitted using a global optimization algorithm [ Vrugt et al , ].…”

“…Following an empirical relationship proposed in Lu et al [], the best fit relationship between λ s (W m −1 K −1 ) and θ , as shown in Figure a, can be described as where 0.20 W m −1 K −1 is the thermal conductivity of dry soil and 1.46 and 0.34 are shape factors of the fit curve, which are fitted using a global optimization algorithm [ Vrugt et al , ]. Lu et al [] suggested that the shape factors vary with soil texture and bulk density; however, information about soil texture was not available for this study. Assuming a uniform soil texture in the 0–20 cm layer, equation was used to calculate λ s at each time step and at different depths.…”

On the prediction of the thermal conductivity of saturated clayey soils: Effect of the specific surface area

“…Hence, much effort has been made to develop models incorporating these soil parameters which can be evaluated from laboratory investigations (Mickley, 1951;Gemant, 1952;Woodside and Messmer, 1961;De Vries, 1963;Johansen, 1975;Campbell, 1985;Coté and Konrád, 2005;Lu et al, 2007;Lu et al, 2014). The majority of these empirical or semitheoretical relations need the soil solid thermal conductivity (λ s ) as an input parameter.…”