Predicting extreme events is an important scientific and societal issue. The evolution of some weather patterns is easier to predict than others, but there are patterns in which the chances of certain extremes, such as the deadliest summer heat waves, are greater. We will focus on determining these patterns. Numerous techniques have been developed in data science and atmospheric sciences to tackle this challenge, and to provide a better physical understanding of the formation of these events.
In this thesis, we are mainly interested in characterizing the predictability of trajectories of chaotic systems such as those that describe the movements of the atmosphere. Predictability is a measure of how predictable a system is, for a given timescale. For example, the evolution of some meteorological patterns is predictable for several days in advance (high predictability), while others can change very quickly (low predictability). This means that the uncertainty linked to the initial conditions is less strong in the first case than in the second. How to characterize this uncertainty?
The study of predictability (in atmospheric sciences) is often placed in a probabilistic framework: we are interested in the probability of being in a particular state, knowing that we start from a given state which may be uncertain.
LSCE has developed a set of tools for stochastic simulations of meteorological variables to determine the probability densities of these variables, as well as statistical scores to assess the quality of the forecasts thus produced. In parallel, statistical mechanics algorithms developed at ENS Lyon enabled to simulate extreme events in an optimal way, based on important sampling principles.
We will therefore focus on determining the weather conditions that lead to extreme heat waves and their likelihood. The object of this thesis is to develop a statistical methodology to find the optimal parameters of climate simulation tools, and to determine the important variables from which heat waves are predictable. Another important aspect of the thesis will be to determine the impact of climate change on the predictability of these extreme events.
The thesis will stand at the interface between climate science, statistics and nonlinear physics. We will try to establish a balance between digital experiments and data analysis according to the results obtained in the first months of the thesis. The thesis will be funded by the ANR SAMPRACE project (https://samprace871353291.wordpress.com/). The work will be supervised by Dr. Pascal Yiou (LSCE), in collaboration with Dr. Freddy Bouchet (ENS Lyon).