Bayesian Quantification of Covariance Matrix Estimation Uncertainty in Optimal Fingerprinting

TL;DR

This paper introduces a Bayesian framework for quantifying uncertainty in covariance matrix estimation within optimal fingerprinting, improving detection confidence and calibration over traditional methods.

Contribution

It proposes a Laplacian basis function parameterization for the covariance matrix, allowing uncertainty propagation and better calibration compared to principal component methods.

Findings

Achieves better-calibrated coverage rates in CMIP6 validation.

Detects anthropogenic warming with higher confidence in observational data.

Reduces variability over climate model choices.

Abstract

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.