According to everyone's experience, predicting the weather reliably for more than a few days seems an impossible task for our best weather agencies. Yet, we all know of examples of “weather sayings” that allow wise old persons to predict tomorrow’s weather without solving the equations of motion, and sometimes better than the official forecast. On a longer scale, climate model have been able to predict the variation of mean Earth temperature due to CO2 emission over a period of 50 year rather accurately.

In the late 50’ and 60’s, Lewis Fry Richardson, then Edward Lorenz set up the basis on the resolution of this puzzle, using observations, phenomenological arguments and low order models.

Present progress in mathematics, physics of turbulence, and observational data now allow to go beyond intuition, and test the validity of the butterfly effect in the atmosphere and climate. For this, we will use new theoretical and mathematical tools and new numerical simulations based on projection of equations of motion onto an exponential grid allowing to achieve realistic/geophysical values of parameters, at a moderate computational and storage cost.

The goal of this PhD is to implement the new tools on real observations of weather maps, to try and detect the butterfly effect on real data. On a longer time scale,, the goal will be to investigate the “statistical universality” hypothesis, to understand if and how the butterfly effect leads to universal statistics that can be used for climate predictions, and whether we can hope to build new “weather sayings” using machine learning, allowing to predict climate or weather without solving the equations.