Relationship between thermal and electrical conductivity curves of soils with a unimodal pore size distribution: Part 1. A unified series-parallel resistor model

Soil thermal conductivity (lambda) and electrical conductivity (sigma) characterize heat and electricity conduction through soils. Both lambda and sigma are affected by similar factors, such as soil water content (theta), texture, bulk density (rho b), temperature, structure, and organic matter content. Little is known about the quantitative relationship between lambda and sigma, and how soil texture and rho b modify the relationship. In this part one of a two-part series, we examine the correlation between lambda(theta) and sigma(theta) curves and develop a new model for normalized sigma curves of soils with a unimodal pore size distribution. We introduce an Ohm's law analogy to describe the lambda and sigma curves conceptually, based on a cubic cell unit model. A unified series-parallel resistor model considering theta and rho b effects is established for both lambda(theta) and sigma(theta) curves by considering heat and electrical conduction pathways (solid, solid-liquid, and liquid pathways) in the hydration, menisci, and continuous liquid ranges. Simultaneous measurements of theta, lambda and sigma with thermo-TDR sensors on two soils are used to examine the model performance at various values of rho b and theta. The modeled and measured lambda (theta) and sigma (theta) curves provide consistent trends, and the normalized lambda and sigma values vs. degree of saturation confirm the existence of an earlier reported "mirror image" phenomenon between the functions.