Colloquium
Date: 2 March 2022
Time 15.30-16.30
Venue: Seminar Hall
Mathematics for Climatology
Olivier Pironneau
"Université Pierre et Marie Curie, Laboratoire Jacques-Louis Lions".
02-03-22

---

Abstract

In this introductory talk we intend to review the current state of climate modeling, the di erent modules involved and the open problems.

It will hopefully be done from the standpoint of mathe- matics. This means that we will need to speak of meteorology versus climatology, chaos and attractors [7], ocean to atmosphere coupling [1], shallow water [2] and the quasi-geostrophic approximation[5][4] versus Navier-Stokes, local versus global models and  nally radiative transfer and the problem of clouds [3].

The author is a specialist of the Navier-Stokes equations [6] with contributions to their discretization on unstructured meshes and multi-fluids and more recently to the numerical solution of the radiative transfer equations [8].

In such a colloquium talk it will not be possible to plunge deep into any of the above mentions topics, but we intend to give hints to mathematicians who would like to know the past and future contributions of mathematics to climatology.

References

[1] T. Dubos, S. Dubey, M. Tort, R. Mittal, Y. Meurdesoif, and F. Hourdin. Dynamico-1.0, an icosahedral hydrostatic dynamical core designed for consistency and versatility. Geosci. Model Dev, 8:3131--3150, 2015.

[2] Thomass Dubos. Fundamental of oceanic and atmospheric motion. 2022.

[3] Andrew Fowler. Mathematical geoscience. Berlin: Springer, 2011.

[4] J.-L. Lions, R. Temam, and S. Wang. Geostrophic asymptotics of the primitive equations of the atmosphere. Topological Methods in Nonlinear Analysis, 4(2):253--287, 1994.

[5] J.L. Lions, R. Temam, and S. Wang. Mathematical theory for the coupled atmosphere-ocean models. Journal de Mathematiques Pures et Appliquees, 74(2), 1995.

[6] B. Mohammadi and O. Pironneau. Analysis of the k-epsilon turbulent model. Wiley, 1997.

[7] Christian Vidal Pierre Berg{\'e}, Yves Pomeau. L'ordre dans le chaos. Eyrolles, 2004.

[8] O. Pironneau. A fast and accurate numerical method for radiative transfer in the atmosphere. Compte Rendus de l'acad\'emie des sciences (Math), December 2021.