An Analytical Solution to the One‐Dimensional Heat Conduction–Convection Equation in Soil

Abstract

Soil heat transfer occurs by conduction and convection. Soil temperatures below infiltrating water can provide a signal for water flux. In earlier work, analysis of field measurements with a sine wave model indicated that convection heat transfer made significant contributions to the subsurface temperature oscillations. In this work, we used a Fourier series to describe soil surface temperature variations with time. The conduction and convection heat transfer equation with a multi‐sinusoidal wave boundary condition was solved analytically using a Fourier transformation. Soil temperature values calculated by the single sine wave model and by the Fourier series model were compared with field soil temperature values measured at depths of 0.1 and 0.3 m below an infiltrating ponded surface. The Fourier series model provided better estimates of observed field temperatures than the sine wave model. The new model provides a general way to describe soil temperature under an infiltrating water source.