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Analytical Solutions for Two-Dimensional Soil Heat Flow with Radiation Surface Boundary Conditions

Dep. of Soil Science, Univ. of British Columbia, 248-2357 Main Mall, Vancouver, BC, Canada V6T 1Z4

*Corresponding author.

ABSTRACT

Heat flow and temperature variations in soils are important in agriculture, forestry, and ecology. Nonuniform surface cover and variability in soil properties result in two-dimensional soil heat flow. This study derives analytical solutions for unsteady two-dimensional soil heat transfer problems with standard (constant temperature coefficient) and modified (temperature coefficient varies with position) radiation surface boundary conditions. Solutions are periodic in time and horizontal direction. The structure of the solutions guarantees that soil temperatures are smooth functions of position and time, even if the temperature coefficient or forcing function in the radiation boundary condition are discontinuous. Calculated soil temperatures, heat flux densities, and surface energy balance components for bare wet strips alternating with strips covered with either chalk, black plastic, or clear plastic were found to vary strongly with time and position. For diurnal variations, lateral heat flow only significantly affected temperatures in the middle of strips narrower than 0.2 m. Sensitivity of soil temperature to changes in soil thermal properties increased as the temperature coefficient in the surface boundary condition decreased. Both cases showed that spatial differences in albedo, surface resistance, and aerodynamic resistance spatially alter the surface energy balance and soil thermal regimes, including surface temperature and heat flux density.

Contribution from the Dep. of Soil Science, Univ. of British Columbia.

Received for publication June 30, 1991.

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