AI 中文总结
研究利用基于核的地表温度模型，结合并行系综马尔可夫链蒙特卡罗采样器，通过合成实验和实际气候历史评估，探讨影响冰芯温度重建性能的因素，为浅冰芯气候重建提供有效框架，同时考虑模型近似不确定性。
AI 中文摘要
从浅冰芯温度剖面重建过去的地表温度需要解决一个不适定的反问题，同时量化测量和先验假设产生的不确定性。贝叶斯公式能够对地表温度历史进行概率重建和不确定性量化。然而，现有的基于自适应分段线性地表温度模型的可逆跳跃马尔可夫链蒙特卡罗方法计算量很大。本文引入了一种基于核的地表温度模型，该模型能够使用并行系综马尔可夫链蒙特卡罗采样器来有效探索解空间并量化后验。通过合成实验，研究了核配置、测量不确定性、测量密度和时间模糊对重建性能的影响。结果表明，一旦核基足够密集，重建质量对核的数量基本不敏感。减少测量不确定性可显著改善重建，而增加冰芯温度测量数量的益处不大。最后，使用结合了长期温度变化和随机气候变异性的实际替代气候历史对该方法进行评估。基于核的地表温度模型无法表示短期变异性，因此不能完全解释实际测量，这突出了考虑这种近似不确定性的必要性。似然性经过调整以纳入地表温度模型的近似不确定性，从而产生具有可靠后验不确定性的稳健重建。总体而言，结果表明基于核的贝叶斯反演为基于浅冰芯的气候重建提供了一个有效的框架。
英文摘要
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 measurements, highlighting the need to account for this approximation uncertainty. The likelihood is adapted to include the approximation uncertainty of the surface temperature model, yielding robust reconstructions with reliable posterior uncertainties. Overall, our results demonstrate that kernel-based Bayesian inversion provides an efficient framework for shallow ice borehole based climate reconstructions.
