Integrated Optimal Fingerprinting: Method Description and Illustration

The present paper introduces and illustrates methodological developments intended for so-called optimal fingerprinting methods, which are of frequent use in detection and attribution studies. These methods used to involve three independent steps: preliminary reduction of the dimension of the data, estimation of the covariance associated to internal climate variability, and, finally, linear regression inference with associated uncertainty assessment. It is argued that such a compartmentalized treatment presents several issues; an integrated method is thus introduced to address them. The suggested approach is based on a single-piece statistical model that represents both linear regression and control runs. The unknown covariance is treated as a nuisance parameter that is eliminated by integration. This allows for the introduction of regularization assumptions. Point estimates and confidence intervals follow from the integrated likelihood. Further, it is shown that preliminary dimension reduction is not required for implementability and that computational issues associated to using the raw, high-dimensional, spatiotemporal data can be resolved quite easily. Results on simulated data show improved performance compared to existing methods w.r.t. both estimation error and accuracy of confidence intervals and also highlight the need for further improvements regarding the latter. The method is illustrated on twentieth-century precipitation and surface temperature, suggesting a potentially high informational benefit of using the raw, nondimension-reduced data in detection and attribution (D&A), provided model error is appropriately built into the inference.