"Whereas the depth of a temperature perturbation is related to the timing of surface changes, the shape of the perturbation reveals details of the surface temperature history. Positive temperature perturbations signify past warming; negative anomalies indicate cooling. The amount of surface warming or cooling can not be read directly from the temperature profile because of the attenuating and smearing features of heat conduction. Instead, the magnitude of surface temperature excursions that caused the subsurface anomaly are found by calculating perturbations for models with different surface temperature histories. A ground surface temperature history is selected that best explains the observed subsurface perturbation."
If the surface record is not properly calibrated, the borehole record will not be properly calibrated. The borehole records are not completely independent of the surface record, but Pielke's pressure measurements are independent and they show very little warming in the surface layer.
Instead, the magnitude of surface temperature excursions that caused the subsurface anomaly are found by calculating perturbations for models with different surface temperature histories. A ground surface temperature history is selected that best explains the observed subsurface perturbation."
Here's what I think this means, and I invite your comment: the way that a surface temperature history is generated using borehole temperatures is to create different theoretical surface temperature histories and then to use these histories to generate a borehole temperature (subsurface temperature) model. Then the model temperature curve is compared to the actual borehole temperature curve. The surface temperature history that generated the closest-fit of modeled borehole temperature to actual borehole temperature is chosen as the borehole "surface temperature" history.
Do you think that is accurate? If so, there is no calibrated surface temperature data that is being used as a reference for comparison. The only actual temperature data that is being examined are the borehole temperature logs.
Now, it makes some sense that as a starting point a surface temperature history similar to what has been observed at the surface would be one surface temperature history to use. But I would hope that the researchers would use alternative histories to verify the results and establish error bounds (the borehole temperature curves I have seen have shown upper and lower bounds).