Bayesian hierarchical modeling for temperature reconstruction from geothermal data

TL;DR

This paper introduces a Bayesian hierarchical model for reconstructing past surface temperatures from borehole data, accounting for model and measurement errors, and applying it to data from Utah to estimate temperature histories over 400 years.

Contribution

It develops a novel Bayesian hierarchical framework that incorporates model errors and prior information for paleoclimate temperature reconstruction from geothermal data.

Findings

Produced temperature histories with uncertainty estimates for 400 years.

Demonstrated the effectiveness of hierarchical modeling in combining multiple borehole data.

Performed sensitivity analyses to validate the robustness of the results.

Abstract

We present a Bayesian hierarchical modeling approach to paleoclimate reconstruction using borehole temperature profiles. The approach relies on modeling heat conduction in solids via the heat equation with step function, surface boundary conditions. Our analysis includes model error and assumes that the boundary conditions are random processes. The formulation also enables separation of measurement error and model error. We apply the analysis to data from nine borehole temperature records from the San Rafael region in Utah. We produce ground surface temperature histories with uncertainty estimates for the past 400 years. We pay special attention to use of prior parameter models that illustrate borrowing strength in a combined analysis for all nine boreholes. In addition, we review selected sensitivity analyses.