Consistent climate fingerprinting

The optimal fingerprinting methodology of Allen and Tett (Clim Dyn 15:419–434, 1999) was criticized by McKitrick (Clim Dyn 58:405–411, 2022) who argued that it fails to yield unbiased and consistent coefficient estimates, and the associated residual consistency test (RCT) is uninformative regarding the regression model validity. Chen et al. (Clim Dyn 62:1439–1446, 2023) concurred on key points but showed that consistency could be established under certain conditions. I argue herein that they are sufficiently restrictive as to reaffirm the practical invalidity of the Allen and Tett method. Chen et al. also derived an asymptotic distribution of the RCT. Their result implies the critical values used up to now may be incorrect. I propose an alternative fingerprinting method based on the Instrumental Variables procedure with consistent standard errors and I demonstrate its potential in an application to twentieth century temperature data. I find the modeled anthropogenic signal is detected but needs to be scaled down by 35 to 60%, whereas the modeled natural signal needs to be scaled up 2- to fourfold, to reconcile optimally with observations.