A Bayesian partition modelling approach to resolve spatial variability in climate records from borehole temperature inversion

Collections of suitably chosen borehole profiles can be used to infer large-scale trends in ground-surface temperature (GST) histories for the past few hundred years. These reconstructions are based on a large database of carefully selected borehole temperature measurements from around the globe. Since non-climatic thermal influences are difficult to identify, representative temperature histories are derived by averaging individual reconstructions to minimize the influence of these perturbing factors. This may lead to three potentially important drawbacks: the net signal of non-climatic factors may not be zero, meaning that the average does not reflect the best estimate of past climate; the averaging over large areas restricts the useful amount of more local climate change information available; and the inversion methods used to reconstruct the past temperatures at each site must be mathematically identical and are therefore not necessarily best suited to all data sets. In this work, we avoid these issues by using a Bayesian partition model (BPM), which is computed using a trans-dimensional form of a Markov chain Monte Carlo algorithm. This then allows the number and spatial distribution of different GST histories to be inferred from a given set of borehole data by partitioning the geographical area into discrete partitions. Profiles that are heavily influenced by non-climatic factors will be partitioned separately. Conversely, profiles with climatic information, which is consistent with neighbouring profiles, will then be inferred to lie in the same partition. The geographical extent of these partitions then leads to information on the regional extent of the climatic signal. In this study, three case studies are described using synthetic and real data. The first demonstrates that the Bayesian partition model method is able to correctly partition a suite of synthetic profiles according to the inferred GST history. In the second, more realistic case, a series of temperature profiles are calculated using surface air temperatures of a global climate model simulation. In the final case, 23 real boreholes from the United Kingdom, previously used for climatic reconstructions, are examined and the results compared with a local instrumental temperature series and the previous estimate derived from the same borehole data. The results indicate that the majority (17) of the 23 boreholes are unsuitable for climatic reconstruction purposes, at least without including other thermal processes in the forward model.