Regularized Fingerprinting with Linearly Optimal Weight Matrix in Detection and Attribution of Climate Change

Abstract Climate change detection and attribution play a central role in establishing the influence of human activities on global warming. The widely used optimal fingerprinting framework can be formulated as a linear errors-in-variables regression in which the covariance of internal climate variability is estimated from climate model simulations. Existing regularized optimal fingerprinting approaches often underestimate the variance of the scaling factors, leading to confidence intervals that are too narrow and fail to achieve nominal coverage. In this paper, we first propose consistent variance estimators for the regression coefficients within the general class of linear shrinkage weight matrices, thereby addressing the undercoverage problem in conventional methods. Building on this result, we further derive a linearly optimal weight matrix that directly minimizes the asymptotic variances of the estimated scaling factors. Numerical studies confirm improved empirical coverage and shorter interval lengths. When applied to annual mean near-surface air temperature (1951–2020), the proposed method produces narrower and more reliable intervals and provides new insights in detection and attribution across different regional scales. Significance Statement Optimal fingerprinting is a central tool for detecting and attributing climate change by linking observed climate signals to external forcings. In practice, both the fingerprints and the spatiotemporal covariance structure of internal climate variability must be estimated from climate model simulations, creating errors-in-variables challenges that complicate statistical inference. Existing methods often lose the original optimality of fingerprinting and can produce confidence intervals with poor coverage. We propose a new estimation framework that retains optimality in a more general and realistic setting where the covariance matrix is completely unknown. Numerical studies demonstrate that the proposed method delivers reliable uncertainty quantification while remaining efficient, improving confidence in detection and attribution results.