Testing a finite-difference model for soil heat transfer by comparing numerical and analytical solutions

Soil temperature influences most physical, chemical and biological processes that occur in soil. Analytical models (AMs)—exact analytical solutions of the soil heat flux equation—only exist to very specific conditions. Finite-difference models (FDMs) are applicable to more general conditions. Since FDMs are not exact, but approximate, they must be preliminarily tested by comparing their simulated results with those from AMs, if available. In previous literature, such tests have been done briefly, mainly through data-plots. The general objective of this study was the development of comprehensive procedures to perform such tests: (i) comparison of models by data-plots and statistical indices; (ii) searching for sources of apparent errors (AEs)—a concept introduced here; (iii) determination of the number of simulated periods (years) that the model computer program should run before output is recorded; and (iv) studying the influence of time-step and space-step magnitudes on the model performance. An explicit one-dimensional FDM was tested. Simulations represented soils of different thermal properties. Simulation results showed that: (i) statistical indices values consistently quantified the qualitative data-plot observations; (ii) AEs could be corrected by considerations on the first soillayer temperature and by choosing a sufficiently large simulation depth; (iii) no more than five periods are necessary for the FDM tested here; and (iv) adequate choice of time and space steps reduces errors and also reduces computing time.