A comparison of analytical and numerical model predictions of shallow soil temperature variation with experimental measurements

Abstract

In several fields of enquiry such as geothermal energy, geology and agriculture, it is of interest to study the thermal behaviour of shallow soils. For this, several analytical and numerical methodologies have been proposed to analyse the temperature variation of the soil in the short and long term. In this paper, a comparative study of different models (sinusoidal, semi-infinite and finite difference method) is conducted to estimate the shallow soil temperature variation in the short and long term. The models were compared with hourly experimental measured data of soil temperature in Leicester, UK, at depths between 0.75 and 2.75 m. The results show that the sinusoidal model is not appropriate to evaluate the short-term temperature variations, such as hourly or daily fluctuations. Likewise, this model is highly affected by the undisturbed ground temperature and can lead to very high errors. Regarding the semi-infinite model, it is accurate enough to predict the short-term temperature variation. However, it is useless to predict the long-term variation at depths greater than 1 m. The finite difference method (FDM) considering the air temperature as a boundary condition for the soil surface is the most accurate approach for estimating both short and long-term temperature variations while the FDM with heat flux as boundary condition is the least accurate approach due to the uncertainty of the assumed parameters. The ranges of errors for the sinusoidal, semi-infinite and FDM are found to be from 76.09 to 142.13%, 12.11 to 104.88% and 1.82 to 28.14% respectively.