All existing approaches to the analysis and interpretation of borehole temperatures in terms of a ground surface temperature history are based on the one-dimensional theory of heat conduction. Deviations from this idealization are manifest as noise in the interpretation. We present numerical experiments that explore the effects of three-dimensional subsurface heterogeneity on ground surface temperature histories inferred from borehole temperature profiles. Inversions of steady state temperature profiles containing such three-dimensional ''noise'' reveal that in an inversion formulation incorporating a priori information, spurious temperature histories can emerge when the a priori constraints on subsurface temperatures and thermophysical properties are too tight, i.e., when arbitrarily small variations in subsurface temperatures and thermophysical properties are interpreted to have significance for the derived climate history. Relaxation of the a priori constraints enables an effective muting of the spurious histories. Similar experiments conducted on synthetic transient signals confirm the steady state results but also reveal that relaxation of the a priori constraints will also lead to a loss of signal if the level of relaxation is excessive.

Our experiments suggest that relaxation of constraints on thermal conductivity is more efficient than relaxation of borehole temperatures in suppressing artifacts arising from the three-dimensional effects. We identify a range of constraints in which reasonable noise suppression and signal recovery are both achieved and then reprocess data from 22 Canadian boreholes for which surface temperature histories had earlier been derived by ourselves and others. Our reprocessed results reveal a remarkably simple surface temperature history common to much of eastern Canada. This history comprises a recent warming interval commencing in the nineteenth century, in which the surface temperature increased by some 1--4¿C. Approximately 0.5--1.0¿C of this increase was a recovery from a preceding cooler interval in which the temperature was below the long-term mean. The remainder of the increase represents warming that exceeds the long-term mean. ¿ American Geophysical Union 1995