Gaussian Framework and Optimal Projection of Weather Fields for Prediction of Extreme Events

Extreme events are the major weather-related hazard for humanity. It is then of crucial importance to have a good understanding of their statistics and to be able to forecast them. However, lack of sufficient data makes their study particularly challenging. In this work, we provide a simple framework for studying extreme events that tackles the lack of data issue by using the entire available data set, rather than focusing on the extremes of the data set. To do so, we make the assumption that the set of predictors and the observable used to define the extreme event follow a jointly Gaussian distribution. This naturally gives the notion of an optimal projection of the predictors for forecasting the event. We take as a case study extreme heatwaves over France, and we test our method on an 8,000-year-long intermediate complexity climate model time series and on the ERA5 reanalysis data set. For a-posteriori statistics, we observe and motivate the fact that composite maps of very extreme events look similar to less extreme ones. For prediction, we show that our method is competitive with off-the-shelf neural networks on the long data set and outperforms them on reanalysis. The optimal projection pattern, which makes our forecast intrinsically interpretable, highlights the importance of soil moisture deficit and quasi-stationary Rossby waves as precursors to extreme heatwaves.