Conduction-dominated heat transport of the annual temperature signal in soil

[1] Conductive heat transport of temperature signals into the subsurface is a central assumption of ground surface temperature (GST) reconstructions derived from present-day temperatures in deep boreholes. Here we test this assumption and its implications for annual relationships between GST and surface air temperature (SAT) by analyzing two decades of shallow soil temperature (0.01 - 11.7 m) and SAT time series measured at Fargo, North Dakota. We spectrally decompose each of these temperature time series to determine the amplitude and phase of the annual signal at each depth. Conductive heat transport of a harmonic temperature signal in a homogeneous medium is characterized theoretically by exponential amplitude attenuation and linear phase shift with depth. We show that transport of the annual signal in the soil at Fargo follows these theoretical characterizations of conduction closely: the depth dependence of both the natural logarithm of the amplitude and the phase shift are highly linear. Interval wave velocities and thermal diffusivities calculated as functions of depth suggest a diffusivity gradient in the upper meter of the soil. We estimate the annual signal at the ground surface by extrapolating amplitude and phase shift regression lines upward to the surface. We compare this estimate of the annual signal at the ground surface to the annual signal contained in the SAT and show the ground surface signal to be attenuated similar to 20% and negligibly phase shifted relative to the SAT.