Interpretable probabilistic forecast of extreme heat waves

Understanding and predicting extreme events is one of the major challenges for the study of climate change impacts, risk assessment, adaptation, and the protection of living beings. Extreme heatwaves are, and likely will be in the future, among the deadliest weather events. They also increase strain on water resources, food security and energy supply. Developing the ability to forecast their probability of occurrence a few days, weeks, or even months in advance would have major consequences to reduce our vulnerability to these events. Beyond the practical benefits of forecasting heat waves, building statistical models for extreme events which are interpretable is also highly beneficial from a fundamental point of view. Indeed, they enable proper studies of the processes underlying extreme events such as heat waves, improve dataset or model validation, and contribute to attribution studies. Machine learning provides tools to reach both these goals.

We will first demonstrate that deep neural networks can predict the probability of occurrence of long-lasting 14-day heatwaves over France, up to 15 days ahead of time for fast dynamical drivers (500 hPa geopotential height field), and at much longer lead times for slow physical drivers (soil moisture). Those results are amazing in terms of forecasting skill. However, these machine learning models tend to be very complex and are often treated as black boxes. This limits our ability to use them for investigating the dynamics of extreme heat waves.

To gain physical understanding, we have then designed a network architecture which is intrinsically interpretable. The main idea of this architecture is that the network first computes an optimal index, which is an optimal projection of the physical fields in a low-dimensional space. In a second step, it uses a fully non-linear representation of the probability of occurrence of the event as a function of the optimal index. This optimal index can be visualized and compared with classical heuristic understanding of the physical process, for instance in terms of geopotential height and soil moisture. This fully interpretable network is slightly less efficient than the off-the-shelf deep neural network. We fully quantify the performance loss incurred when requiring interpretability and make the connection with the mathematical notion of committor functions.

This new machine learning tool opens the way for understanding optimal predictors of weather and climate extremes. This has potential for the study of slow drivers, and the effect of climate change on the drivers of extreme events.