A direct approach to detection and attribution of climate change.

We present here a novel statistical learning approach for detection and attribution (D&A) of climate change. Traditional optimal D&A studies try to directly model the observations from model simulations, but practically this is challenging due to high-dimensionality. Dimension reduction techniques reduce the dimensionality, typically using empirical orthogonal functions, but as these techniques are unsupervised, the reduced space considered is somewhat arbitrary. Here, we propose a supervised approach where we predict a given external forcing, e.g., anthropogenic forcing, directly from the spatial pattern of climate variables, and use the predicted forcing as a test statistic for D&A. We want the prediction to work well even under changes in the distribution of other external forcings, e.g., solar or volcanic forcings, and therefore formulate the optimization problem from a distributional robustness perspective.