A parametrization of a steady periodic solution of the Fourier equation to model soil temperature dynamics
In dry days the temperature of the upper soil layers presents a characteristic asymmetric periodic-like pattern with a minimum in the morning and a maximum in the afternoon. In view of estimating the conductive heat component of the surface energy balance, at local, basin, and global scales, in this study we use a periodic series solution of the Fourier equation to develop a simple procedure to accurately reconstruct the soil temperature and heat flux profiles. The method is based on weighting and phasing the Fourier harmonics by means of coefficients which do not depend on the soil thermal properties but only depend on the shape of the temperature boundary condition. The proposed coefficients can be regarded to as site independent and with good approximation universal. In order to calibrate and test the procedure, measurements of soil temperature, soil heat flux, and soil water content, collected during the CividatEX Experiment (summer 2012, summer 2013, and spring and summer 2014), in Italy, were used. The method accurately reproduced the temperature observations at three measurement depths within the upper 20 cm soil layer. Once assessed the soil thermal conductivity, the method proved to be effective also in reproducing the measured soil heat flux. The procedure was furthermore validated reconstructing with good results the soil temperature dynamics measured by an independent micrometeorological station in a different environment.