Application of regularised optimal fingerprinting to attribution. Part I: method, properties and idealised analysis

Optimal fingerprinting has been the most widely used method for climate change detection and attribution over the last decade. The implementation of optimal fingerprinting often involves projecting onto k leading empirical orthogonal functions in order to decrease the dimension of the data and improve the estimate of internal climate variability. However, results may be sensitive to k, and the choice of k remains at least partly arbitrary. One alternative, known as regularised optimal fingerprinting (ROF), has been recently proposed for detection. This is an extension of the optimal fingerprinting detection method, which avoids the projection step. Here, we first extend ROF to the attribution problem. This is done using both ordinary and total least square approaches. Internal variability is estimated from long control simulations. The residual consistency test is also adapted to this new method. We then show, via Monte Carlo simulations, that ROF is more accurate than the standard method, in a mean squared error sense. This result holds for both ordinary and total least square statistical models, whatever the chosen truncation k. Finally, ROF is applied to global near-surface temperatures in a perfect model framework. Improvements provided by this new method are illustrated by a detailed comparison with the results from the standard method. Our results support the conclusion that ROF provides a much more objective and somewhat more accurate implementation of optimal fingerprinting in detection and attribution studies.