  Understanding extreme events and their probability is key for the study of
climate change impacts, risk assessment, adaptation, and the protection of
living beings. Forecasting the occurrence probability of extreme heatwaves is a
primary challenge for risk assessment and attribution, but also for fundamental
studies about processes, dataset and model validation, and climate change
studies. In this work we develop a methodology to build forecasting models
which are based on convolutional neural networks, trained on extremely long
climate model outputs. We demonstrate that neural networks have positive
predictive skills, with respect to random climatological forecasts, for the
occurrence of long-lasting 14-day heatwaves over France, up to 15 days ahead of
time for fast dynamical drivers (500 hPa geopotential height fields), and also
at much longer lead times for slow physical drivers (soil moisture). This
forecast is made seamlessly in time and space, for fast hemispheric and slow
local drivers. We find that the neural network selects extreme heatwaves
associated with a North-Hemisphere wavenumber-3 pattern. The main scientific
message is that most of the time, training neural networks for predicting
extreme heatwaves occurs in a regime of lack of data. We suggest that this is
likely to be the case for most other applications to large scale atmosphere and
climate phenomena. For instance, using one hundred years-long training sets, a
regime of drastic lack of data, leads to severely lower predictive skills and
general inability to extract useful information available in the 500 hPa
geopotential height field at a hemispheric scale in contrast to the dataset of
several thousand years long. We discuss perspectives for dealing with the lack
of data regime, for instance rare event simulations and how transfer learning
may play a role in this latter task.
