Non-stationary temporal characterization of the temperature profile of a soil exposed to frost in south-eastern Canada

The objective of this work was to compare time and frequency fluctuations of air and soil temperatures (2-, 5-, 10-, 20- and 50-cm below the soil surface) using the continuous wavelet transform, with a particular emphasis on the daily cycle. The analysis of wavelet power spectra and cross power spectra provided detailed non-stationary accounts with respect to frequencies (or periods) and to time of the structure of the data and also of the relationships that exist between time series. For this particular application to the temperature profile of a soil exposed to frost, both the air temperature and the 2-cm depth soil temperature time series exhibited a dominant power peak at 1-d periodicity, prominent from spring to autumn. This feature was gradually damped as it propagated deeper into the soil and was weak for the 20-cm depth. Influence of the incoming solar radiation was also revealed in the wavelet power spectra analysis by a weaker intensity of the 1-d peak. The principal divergence between air and soil temperatures, besides damping, occurred in winter from the latent heat release associated to the freezing of the soil water and the insulation effect of snowpack that cease the dependence of the soil temperature to the air temperature. Attenuation and phase-shifting of the 1-d periodicity could be quantified through scale-averaged power spectra and time-lag estimations. Air temperature variance was only partly transferred to the 2-cm soil temperature time series and much less so to the 20-cm soil depth.