CLIMATE DYNAMICS

Probability of extreme heat waves

What is the probability and dynamics of extreme heat waves, for instance the heat wave over western Europe in 2003? Such events are very rare, but have a huge impact on societies, economy and nature. Because those events are so rare, we can not rely on empirical data from the past. Due to the complexity of the turbulent atmosphere dynamics and the low probability of observing these events, brute-force numerical simulations are also of limited use. The proposed project aims at the first use of techniques and algorithms based on large deviation theory (from statistical mechanics), designed specifically to determine the rare probabilities and corresponding trajectories in complex dynamical systems.

The 2015 heat wave over France (NOAA's Climate Prediction Center).

Abrupt climate changes

While the present Earth climate has been extremely stable during the whole Holocene period, paleoclimate data show that the Earth has experienced drastic and abrupt climate changes in the past. Some of these abrupt climate changes, for instance transitions between glacial and interglacial periods, have probably been triggered by changes in the Earth orbital parameter (Milankovich cycles). However some others, for instance the Dansgaard-Oeschger, or the Heinrich events (see picture below) during the last glacial period are abrupt climate changes that have not been triggered by changes of external parameters. 

Temperature in Greenland and the North Atlantic during the last glacial period showing Dansgaard-Oeschger and Heinrich abrupt temperature changes (picture from S. Rahmstorf, Nature 2002, data from Grootes et al 1993 and Sachs at al 1989)

Those abrupt climate changes are examples of the climate system internal variability. Such events are probably related to the turbulent dynamics of the ocean and more precisely to its overturning circulation. Predicting such transitions in turbulent dynamics is a challenge as it requires to have an extremely well resolved climate model, and at the same time to run it on tens of millennial time scales. In order to develop the numerical and theoretical tools to address this challenge and to be able to study abrupt climate changes in turbulent dynamics, we have addressed the simplest problem of climate changes for Jupiter’s troposphere (see picture below).

Jupiter's troposphere jets and white oval anticyclones. During the period 1939-1940 one of Jupiter's jet disappeared and led to the appearance of white ovals (Rogers 1995). As Jupiter lost one of his jets, Jupiter's climate abruptly changed (Markus 2005)

While this kind of jet instability can not be studied using direct numerical simulations of turbulent flows, because it appears so rarely, we can devise dedicated algorithms to predict the transition probability between different climates on Jupiter, using tools from statistical mechanics and large deviation theory. (see the point Large deviation theory for atmosphere jets below)

Transitions between attractors with 3, 4 and 2 jets in a quasigeostrophic model of turbulent atmosphere in a regime similar to Jupiter's troposphere one (Bouchet Simonnet, see the seminar below)

This allows us to sample thousands of transitions, and to compute transition rates and transition paths between attractors. This new tools is opening a large new field of research in climate science, for a class of problems that involve rare events that are impossible to study using conventional tools. (See the point Large deviation theory for atmosphere jets below)

Large deviation theory for atmosphere jets: Seminar given during the Workshop on Instantons and Extreme Events in Turbulence and Dynamical Systems, held at Rio de Janeiro in December 2015 [movie] [slides]

See also the computation part of our research on large deviations and rare events.

Is their a common principle behind the self organization of jets, cyclone, anticyclones, and ocean currents in turbulent atmospheres and oceans

It is striking to observe the strong analogies between the emergence of cyclones, anticyclones, jets, and currents on any turbulent flows dominated by the Coriolis force, such as the Earth atmosphere, the Earth ocean, or Jovian planet atmospheres. When these flows are in a inertial regime (when the time scale for forcing and dissipation are much larger that the time scale for the inertial turbulence), one can actually explain the formation of these structures using equilibrium statistical mechanics. They then appear as maximum entropy states. This gives an amazing explanation for the emergence of these structure and predicts their detailed properties. These ideas have been successfully applied to model the Great Red Spot of Jupiter, ocean mesoscale vortices, and some of the ocean currents.  To learn more about this approach.