Minimum relative entropy: Theory and application to surface temperature reconstruction from borehole temperature measurements

Abstract

In this paper we extend the minimum relative entropy (MRE) method to reconstruct ground surface temperature changes (GST) from borehole temperature measurements (BHT). The application of MRE to recovering GST is promising and provides an alternative to other inverse methods in geophysics. The relative entropy formulation provides the advantage of allowing for a prior bias in the estimated pdf and 'hard' bounds if desired. Test cases showed good recoveries of the GST. The method was utilized in recovering GST from two data sets in Canada. The Lac Dufault data gave very consistent results for different choices of a priori information and bounds. The Mariner results were not as good quality. This method has only recovered past ground surface temperatures, which does not directly provide information regarding climate change. However, results contained herein show fairly uniform temperatures until the past 100 to 500 years and in more recent times about a 4°C rise in temperature, consistent with previous published results.