New Fourier-series-based analytical solution to the conduction–convection equation to calculate soil temperature, determine soil thermal properties, or estimate water flux

• Present an analytical solution based upon the Fourier series boundary conditions for soil surface temperature.
• Simulate soil thermal diffusivity and water flux density with different methods.
• Compared different models for calculating soil temperature.

Temperature is an important physical variable of soil. Heat transfer in soils predominantly occurs due to conduction and convection. In this paper, we present a new analytical solution, based upon the Fourier series boundary conditions for soil surface temperature, in which the separation of variables for the heat conduction–convection equation was established. Data that had been collected from the Qinghai-Xizang (Tibet) Plateau (QXP) were used to calculate the thermal diffusivity and the liquid water flux density using different methods. The results of the soil thermal diffusivity using 5 cm as the upper boundary for the soil depth were used to calculate the soil temperature using both the single sine wave conduction and conduction–convection model and the Fourier series conduction–convection model. These results were then compared with the values for the temperature of the field soil measured at a depth of 10 cm. The average standard error of the estimate (SEE), the normalized standard error (NSEE) and Bias were 0.16 °C, 2.70% and 0.11 °C for the Fourier series conduction–convection method. The results indicate that the Fourier series model provides a better estimate of observed field temperatures than the sine wave model. This method provides a useful tool for determining soil thermal parameters, simulating soil temperature and the parameterization of land surface processes for modeling permafrost changes under global warming conditions.