Section: Research Program
Introduction
Recent events have raised questions regarding the social and economic implications of anthropic alterations of the Earth system, i.e. climate change and the associated risks of increasing extreme events. Ocean and atmosphere, coupled with other components (continent and ice) are the building blocks of the Earth system. A better understanding of the ocean atmosphere system is a key ingredient for improving prediction of such events. Numerical models are essential tools to understand processes, and simulate and forecast events at various space and time scales. Geophysical flows generally have a number of characteristics that make it difficult to model them. This justifies the development of specifically adapted mathematical methods:

Geophysical flows are strongly nonlinear. Therefore, they exhibit interactions between different scales, and unresolved small scales (smaller than mesh size) of the flows have to be parameterized in the equations.

Geophysical fluids are non closed systems. They are openended in their scope for including and dynamically coupling different physical processes (e.g., atmosphere, ocean, continental water, etc). Coupling algorithms are thus of primary importance to account for potentially significant feedback.

Numerical models contain parameters which cannot be estimated accurately either because they are difficult to measure or because they represent some poorly known subgrid phenomena. There is thus a need for dealing with uncertainties. This is further complicated by the turbulent nature of geophysical fluids.

The computational cost of geophysical flow simulations is huge, thus requiring the use of reduced models, multiscale methods and the design of algorithms ready for high performance computing platforms.
Our scientific objectives are divided into four major points. The first objective focuses on developing advanced mathematical methods for both the ocean and atmosphere, and the coupling of these two components. The second objective is to investigate the derivation and use of model reduction to face problems associated with the numerical cost of our applications. The third objective is directed toward the management of uncertainty in numerical simulations. The last objective deals with efficient numerical algorithms for new computing platforms. As mentioned above, the targeted applications cover oceanic and atmospheric modeling and related extreme events using a hierarchy of models of increasing complexity.