Mapping uncertainties through the POM-SAT model of climate reconstruction from borehole data

Abstract. Borehole temperature-depth profiles contain information about the ground surface temperature (GST) history of a locale and can be employed in climate reconstruction. The borehole method of climate reconstruction assumes that the dominant heat transport mechanism in the upper few hundred meters of the earth's crust is conduction; mathematically, conduction is a compressive (information losing) mapping from the temperature-time space of GST to the temperature-depth profile (T−z). Because the mapping is compressive, multiple GST histories can map into the same T−z profile; the solution suffers from non-uniqueness. One means of dealing with the non-uniqueness problem is to limit the number of parameters sought in the solution space. However, even when only a single parameter (the pre-observation mean GST, or POM) is sought in the inversion, a certain amount of a priori information must be introduced prior to inverting for a GST history. In the POM-SAT method, a priori information introduced includes the surface-air temperature history (SAT), the thermal diffusivity of the conductive medium, and the reducing parameter used to remove the background (non-climatic) heat flux. I perform a set of Monte Carlo analyses to investigate how uncertainties in these a priori model parameters are mapped into the solution space of the POM-SAT method of climate reconstruction. Results indicate that uncertainties in the thermal diffusivity are generally reduced by an order of magnitude when mapped to the POM. Uncertainties in the SAT time series are approximately equivalent in magnitude to their projection onto the POM. However, uncertainties in the adjustment for the background (non-climatic) thermal regime are magnified by an order of magnitude in the POM solution-space. These results suggest a degree of prudence should be exercised in interpreting surface temperature histories from reduced borehole data.