Mapping Uncertainty in the Borehole Method of Climate Reconstruction

Borehole temperature-depth profiles contain information about surface ground temperatures (SGT) a region has experienced in the past, and therefore provide complementary information to the more customary surface air temperature (SAT) record of climate change. Using temperature-depth measurements from boreholes, researchers have been able to extend local, regional, and hemispheric estimates of surface temperature variations by several centuries. The borehole method relies on the conduction of heat in the upper few hundred meters of the earth's crust; mathematically, conduction is a compressive (information losing) mapping. When solving the inverse heat conduction problem (reconstructing SGT from temperature-depth measurements), one is forced to deal with the non-uniqueness issues this compressive mapping creates. Several researchers have suggested that the most robust mean of dealing with the uniqueness problem is to limit the number of parameters in the solution. Taken to the extreme, this means using the temperature-depth information (in connection with the SAT record) to find a single parameter, the pre-observational mean temperature (POM). Alternatively, one can seek to parameterize SGT changes in terms of rates of change over long time periods (century intervals), the few-parameter estimation technique of Huang et al. [1996]. However, even when only a limited number of parameters are sought in the inversion, a certain amount of a priori information must be assumed. We are interested in how uncertainties in this a priori information are mapped into uncertainties in the solution. We perform numerical simulations to investigate how uncertainties in borehole temperature-depth measurements, data reduction parameters, SAT records, and thermal constraints (all used as a priori information in recovering a POM from a temperature-depth log) are mapped into the solution space of the borehole method of climate reconstruction.