Propagation of linear surface air temperature trends into the terrestrial subsurface

[1] 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 collecte