Comparison between the accuracies of a new discretization method and an improved Fourier method to evaluate heat transfers between soil and atmosphere

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Abstract
To improve and evaluate the accuracy of Fourier methods for the analysis of the energy exchanges between soil and atmosphere, we have developed first a Fourier method that takes into account the nonneutrality corrections and the time variation of the air temperature and which improves the linearization procedures and, second, a new discretization method that does not imply any linearization. The Fourier method, which gives the exact solution of an approximated problem, turns out to have the same order of accuracy as the discretization method, which gives an approximate solution of the exact problem. These methods reproduce the temperatures and fluxes predicted by the Tergra model as well as another set of experimental surface temperatures. In its present form, the Fourier method leads to results that become less accurate (mainly for low wind speeds) under certain conditions, namely, as the amplitude of the daily variation of the air and surface temperatures and their differences increase and as the relative humidities of the air at about 2 m and at the soil surface differ. Nevertheless, the results may be considered as generally satisfactory. Possible improvements of the Fourier model are discussed.