### abstract

- Diffusive heat flux at the soil surface is commonly determined as a mean value over a time period using heat flux plates buried at some depth (e.g., 5–8 cm) below the surface with a correction to surface flux based on the change in heat storage during the corresponding time period in the soil layer above the plates. The change in heat storage is based on the soil temperature change in the layer over the time period and an estimate of the soil thermal heat capacity that is based on soil water content, bulk density and organic matter content. One- or multiple-layer corrections using some measure of mean soil temperature over the layer depth are common; and in some cases the soil water content has been determined, although rarely. Several problems with the heat flux plate method limit the accuracy of soil heat flux values. An alternative method is presented and this flux gradient method is compared with soil heat flux plate measurements. The method is based on periodic (e.g., half-hourly) water content and temperature sensing at multiple depths within the soil profile and a solution of the Fourier heat flux equation. A Fourier sine series is fit to the temperature at each depth and the temperature at the next depth below is simulated with a sine series solution of the differential heat flux equation using successive approximation of the best fit based on changing the thermal diffusivity value. The best fit thermal diffusivity value is converted to a thermal conductivity value using the soil heat capacity, which is based on the measured water content and bulk density. A statistical analysis of the many data resulting from repeated application of this method is applied to describe the thermal conductivity as a function of water content and bulk density. The soil heat flux between each pair of temperature measurement depths is computed using the thermal conductivity function and measured water contents. The thermal gradient method of heat flux calculation compared well to values determined using heat flux plates and calorimetric correction to the soil surface; and it provided better representation of the surface spatiotemporal variation of heat flux and more accurate heat flux values. The overall method resulted in additional important knowledge including the water content dynamics in the near-surface soil profile and a soil-specific function relating thermal conductivity to soil water content and bulk density.