Regression-based optimal fingerprinting techniques for climate change detection and attribution require the estimation of the forced signal as well as the internal variability covariance matrix in order to distinguish between their influences in the observational record. While previously developed approaches have taken into account the uncertainty linked to the estimation of the forced signal, there has been less focus on uncertainty in the covariance matrix describing natural variability, despite the fact that the specification of this covariance matrix is known to meaningfully impact the results. Here we propose a Bayesian optimal fingerprinting framework using a Laplacian basis function parameterization of the covariance matrix. This parameterization, unlike traditional methods based on principal components, does not require the basis vectors themselves to be estimated from climate model data, which allows for the uncertainty in estimating the covariance structure to be propagated to the optimal fingerprinting regression parameter. We show through a CMIP6 validation study that this proposed approach achieves better-calibrated coverage rates of the true regression parameter than principal component-based approaches. When applied to HadCRUT observational data, the proposed approach detects anthropogenic warming with higher confidence levels, and with lower variability over the choice of climate models, than principal-component-based approaches.

中文翻译：

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最优指纹中协方差矩阵估计不确定性的贝叶斯量化

用于气候变化检测和归因的基于回归的最佳指纹技术需要估计受迫信号以及内部变异协方差矩阵，以便区分它们对观测记录的影响。虽然以前开发的方法已经考虑到与强制信号估计相关的不确定性，但对描述自然变异性的协方差矩阵中的不确定性的关注较少，尽管已知协方差矩阵的规范会有意义地影响结果。在这里，我们提出了一个使用协方差矩阵的拉普拉斯基函数参数化的贝叶斯最优指纹框架。这种参数化与传统的基于主成分的方法不同，不需要从气候模型数据估计基向量本身，这允许估计协方差结构的不确定性传播到最佳指纹回归参数。我们通过 CMIP6 验证研究表明，与基于主成分的方法相比，该方法实现了对真实回归参数的更好校准覆盖率。当应用于 HadCRUT 观测数据时，与基于主成分的方法相比，所提出的方法以更高的置信度检测人为变暖，并且在气候模型的选择上具有更低的可变性。我们通过 CMIP6 验证研究表明，与基于主成分的方法相比，该方法实现了对真实回归参数的更好校准覆盖率。当应用于 HadCRUT 观测数据时，与基于主成分的方法相比，所提出的方法以更高的置信度检测人为变暖，并且在气候模型的选择上具有更低的可变性。我们通过 CMIP6 验证研究表明，与基于主成分的方法相比，该方法实现了对真实回归参数的更好校准覆盖率。当应用于 HadCRUT 观测数据时，与基于主成分的方法相比，所提出的方法以更高的置信度检测人为变暖，并且在气候模型的选择上具有更低的可变性。