Past hemispheric temperature variations from a Bayesian hierarchical analysis of the global geothermal dataset

As they are not directly calibrated with meteorological series, underground temperature-depth profiles provide potentially useful constraints on past climate evolution. However, the global geothermal-climate dataset is spatially clustered and is based on measurements that span nearly 60 years.  Little information is available concerning uncertainties in measurements or site conditions which could impart non-climatic signals. Furthermore, the inversion for past temperatures is ill-posed meaning that solutions are non-unique and are sensitive to these uncertainties and to noise.

We developed a Bayesian hierarchical model to reconstruct climate from the global geothermal dataset. We employ a transdimensional formulation that tailors the inferred resolution of the temperature history in each location to the measurements. This avoids over-fitting through the inherent parsimony of Bayesian formulations. Additionally, we do not make any fixed assumptions about observational noise or a priori uncertainties. Instead, these are jointly inferred using a hierarchical setup.

When applied to 1012 profiles our method shows a long-term warming over the Northern Hemisphere in agreement with earlier studies. In the Southern Hemisphere recent warming follows an inferred period of stable temperatures from CE 1500-1800. Sensitivity tests show that these results are robust to choices of hyperpriors but that hard-wiring the level of observational noise influences the inferred amplitude of pre-20^th Century warming over the Northern Hemisphere.