Spectral analysis of air and ground temperatures at Fargo, North Dakota: conduction dominated propagation of the annual frequency signal

Surface air temperature (SAT) and ground temperature at various depths from 1 cm down to 1170 cm have been observed hourly for approximately the last twenty years at the North Dakota State University (NDSU) Microclimate Research Station (46° 54' N, 96° 48' W, elevation 273 m) in Fargo, North Dakota. Here we aggregate the NDSU SAT data and ground temperature data at each depth into time-series of daily means. We spectrally decompose each temperature time-series into Fourier components and then determine the phase and amplitude of the annual frequency component at each depth. The observed phase and amplitude of the annual signal versus depth are compared to expectations from a model of conductive heat transport in a homogeneous medium. A harmonic temperature signal propagating conductively through a homogeneous medium will display a linear phase shift and an exponential amplitude attenuation with depth. We show that the behavior of the annual frequency signal within the ground is clearly conductive: linear regression of the phase shift and natural logarithm of the amplitude yield fits within R² values of 0.996 and 0.999, respectively. We use the best-fit regression coefficients from the amplitude and phase shift data to determine an average thermal diffusivity of the soil of 3.7 \pm 0.1 \times 10^-7 m²/s, and an average wave velocity of the propagating annual signal of 3.3 \pm 0.5 cm/day.