A Fourier Spectral Method to Measure the Thermal Diffusivity of Soil

Abstract

It is well established that amplitude decays and phase shifts as a function of depth, frequency, and thermal diffusivity when a periodic surface temperature signal conducts into the ground. In historical practice, this principle has often been employed to estimate soil thermal diffusivity using observations of the dominant diurnal and annual temperature signals. We describe and demonstrate a method to infer thermal diffusivity over a broad bandwidth in the frequency domain using high fidelity time-series ground temperature records. We draw information from thermal signals generated by meteorological events over weeks and months, as well as the dominant diurnal signal. Both the decay in amplitude and shift in phase of each frequency band contribute points to plots that define linear functions relative to a parameter that incorporates frequency and depth. Linear regression through the points gives the magnitude and uncertainty of the slope of the function, where the slope is equal to the inverse square root of the average thermal diffusivity over the sampled time-period and depth interval. This allows statistical quantification of the uncertainty in the thermal diffusivity estimate. Furthermore, our method delineates depth intervals where nonconductive processes significantly affect heat transfer. Examples are presented for a dry desert soil in South Australia and the floor of a tropical alpine forest in Mexico.