Propagation of linear surface air temperature trends into the terrestrial subsurface

The thermal regime of the continental subsurface contains the record of the most recent changes in the energy balance at the ground surface. Borehole paleoclimatology methods can be applied to infer past ground surface temperature changes and to estimate the heat storage of the subsurface, thus contributing to ascertain the overall energy budget of the climate system. A crucial point is to understand the nature of the coupling between the atmosphere and the ground. Previous studies have examined air and ground temperature relationships working under the assumption that linear trends in surface air temperature should be equal to those measured at depth within the terrestrial subsurface. Here, a purely conductive model of heat conduction is used to show that surface trends are attenuated as a function of depth within conductive media, therefore invalidating the above assumption. The model is forced with synthetic linear surface temperature trends as the time varying upper boundary condition; synthetic trends are either noise free or include additions of Gaussian noise at the annual time scale. It is shown that over a 1000 year period, the trend is linearly damped with depth in both the noise-free and noise-added cases. However, when 100-year intervals are considered, the linear damping of the trend at depth is lost. An error estimate for the corresponding underground trend variation is determined by performing a Monte Carlo simulation. Using ECHO-G general circulation model output as a more realistic simulated data set, the damped trend behaviour as a function of depth is observed, although it is not linear. The use of air and soil temperature data collected over 99 years in Armagh, Ireland and 29 years in Fargo, North Dakota also do not show subsurface temperature trends that are equal to the surface trend. Over time scales smaller than 100 years and when noise is taken into account, damping of the temperature trend at depth is no longer observed due to the impact of annual variability on the trend estimates. It is therefore possible to observe the same trends at depth and at the surface, but such observations are not an indication that the ground and surface trends are directly coupled.