Soil heat flux estimation based on the finite-difference form of the transient heat flow equation

Abstract

Soil heat flux ( G) often aids in interpreting the response of plants to the growing environment, but methods of estimating G are needed that require limited soil temperature and physical property information. This study describes a method for estimating G by implicitly solving the finite-difference form of the transient heat flow equation for the apparent daily thermal conductivity. The derived apparent thermal conductivity and measured soil temperature gradient are applied to Fourier's law for estimating G. This method requires the measurement of soil bulk density and daily water content (for volumetric heat capacity) and hourly temperatures at three depths. Hourly G measured by heat flux plates buried at depths of 0.05 m in apple and peach orchards and 0.03 m in a barley stubble field were compared with G estimated using the harmonic method and our proposed finite-difference method. The finite-difference method performed better, as indicated by a smaller root-mean-square error (r.m.s.e.), than the harmonic method for 71 of the 83 daily data sets used in this study. The average r.m.s.e. in estimating hourly G for the 83 data sets was 10.9 W m −2 for the finite-difference method and 16.3 W m −2 for the harmonic method. Daily net warming or cooling of the soil was correctly estimated for 95% of the data sets using the finite-difference method. The harmonic method, however, results in no net warming or cooling of the soil when deviations are not accounted for in the periodicity.