Propagation of linear surface air temperature trends into the terrestrial subsurface

Previous studies have tested the long-term coupling between air and terrestrial subsurface temperatures working under the assumption that linear trends in surface air temperature should be equal to those measured at depth within the subsurface. A one-dimensional model of heat conduction is used to show that surface trends are attenuated as a function of depth within conductive media on time scales of decades to centuries, therefore invalidating the above assumption given practical observational constraints. The model is forced with synthetic linear 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, propagating surface trends are progressively damped with depth in both noise-free and noise-added scenarios. Over shorter intervals, the relationship between surface and subsurface trends is more variable and is strongly impacted by annual variability (i.e., noise). Using output from the FOR1 millennial simulation of the GKSS ECHO-G General Circulation Model as a more realistic surface forcing function for the conductive model, it is again demonstrated that surface trends are damped as a function of depth within the subsurface. Observational air and subsurface temperature data collected over 100 years in Armagh, Ireland, and 29 years in Fargo, North Dakota, are also analyzed and shown to have subsurface temperature trends that are not equal to the surface trend. While these conductive effects are correctly accounted for in inversions of borehole temperature profiles in paleoclimatic studies, they have not been considered in studies seeking to evaluate the long-term coupling between air and subsurface temperatures by comparing trends in their measured time series. The presented results suggest that these effects must be considered and that a demonstrated trend equivalency in air and subsurface temperatures is inconclusive regarding their long-term tracking.