A unified theoretic framework for reconstructing soil thermal field from single depth measurements

Most conventional numerical schemes for soil ground heat flux estimation rely on the knowledge of the temporal evolution of soil temperature. In this study we propose and test a novel scheme, which requires no information on soil temperatures to supplement the flux plate measurement. The proposed method is based on the fundamental solution of the one-dimensional heat equation and Duhamel's principle for the incorporation of inhomogeneous boundary conditions. Being completely independent of the soil temperature, the new scheme therefore avoids a potential source of error in measurements and in heat storage calculation. The only thermal property involved in the new scheme is the thermal diffusivity of the soil, which is a weak function of soil water content and can be approximated as constant with reasonable accuracy. For validation, the proposed method is compared to the conventional approach using a canonical one-dimensional heat conduction problem, as well as real field measurements. Results of comparison highlight that the new model is robust and capable of preserving the good accuracy of the conventional approach with reduced input information. In addition, the inclusion of the heat storage term in the ground heat indicates a clear improvement of the surface energy balance closure for field measurements. Furthermore, the proposed numerical algorithm can be extended to form a unified theoretic framework which embraces the existing numerical schemes in the literature for the reconstruction of the entire soil thermal (flux and temperature) field, from a single point measurement.