ANALYTICAL SOIL–TEMPERATURE MODEL

Abstract

The exponential‐sinusoidal one‐dimensional analytical model reasonably describes soil temperature profile. Surface temperature may be represented by the sum of two sinusoids, one related to annual and the other to daily temperature variations, each one having constant amplitude. We introduce here a correction for the temporal variation of daily amplitude, and demonstrate that the heat equation can still be solved analytically. We compared temperature predictions obtained from the novel and from the usual analytical solution, using the root mean squared error (RMSE). For individual days, at a depth z = 0.10 m, the maximum value was RMSE = 0.30°C; for whole months, the maximum value was RMSE = 0.29°C, and the minimum was RMSE = 0.06°C. The only additional information required to apply our novel equation is information on temporal variation of daily amplitude, so we suggest our equation should be preferred when such data are readily available.