Bayesian Inference: Kernel-Based Model for Surface Temperature Reconstruction in Ice Borehole Thermometry

作者：Kshema Shaju, Thomas Laepple, Peter Zaspel · 发表于：arXiv (Cornell University) · 年份：2026 · 研究领域：Climate change and permafrost、Cryospheric studies and observations、Geothermal Energy Systems and Applications

Reconstructing past surface temperature from shallow ice borehole temperature profiles requires solving an ill-posed inverse problem while quantifying uncertainties arising from measurements and prior assumptions. Bayesian formulations enable probabilistic reconstruction of surface temperature histories and uncertainty quantification. Existing reversible jump-Markov chain Monte Carlo approach based on adaptive piecewise-linear surface temperature models can, however, be computationally demanding. Here, we introduce a kernel-based surface temperature model that enables the use of a parallel ensemble Markov chain Monte Carlo sampler for efficient exploration of the solution space and quantification of the posterior. Using synthetic experiments, we investigate the effects of kernel configuration, measurement uncertainty, measurement density, and temporal smearing on reconstruction performance. We find that reconstruction quality is largely insensitive to the number of kernels once the kernel basis is sufficiently dense. Reducing measurement uncertainty substantially improves reconstructions, whereas increasing the number of borehole temperature measurements provides only marginal benefit. Finally, we evaluate the method using realistic surrogate climate histories that combine long-term temperature changes with stochastic climate variability. The kernel-based surface temperature model cannot represent short-term variability and therefore cannot fully explain the realistic measure...