Improved reconstruction of soil thermal field using two-depth measurements of soil temperature

The accurate estimation of soil thermal field is crucially important because soil temperature is a key parameter widely used in many related fields. This paper proposed an improved heat-conduction-equation (HCE) method to reconstruct soil thermal field using two-depth measurements of soil temperature. The revised HCE method employed a direct approach as well as an indirect approach to estimate both the daily average soil temperature (DST) and the instantaneous soil temperature (IST), during which the annual temperature cycle and the diurnal temperature cycle are combined. Two validation experiments (i.e., Test-1 and Test-2) were performed with soil temperature measurements at five stations chosen from the Soil Climate Analysis Network (SCAN). The results show that the revised HCE method improves the accuracy of modeling soil thermal field in comparison to its traditional form. The root mean square errors (RMSEs) of the ISTs estimated by the traditional HCE method range from 1.0 to 2.1 °C (2.4 to 4.8 °C) in Test-1 (Test-2); while the errors of the revised HCE method by the indirect approach are reduced to less than 1.0 °C in both Test-1 and Test-2; the errors by the direct approach are further reduced to less than 0.7 °C in both Test-1 and Test-2. The improved method has further potential to estimate soil heat flux, a variable that can be inferred using soil temperature gradients associated with soil apparent thermal conductivity.