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Convective Trails may have a large effect on climate. They form rapidly propagating high altitude cirrus and the burned gases absorb infrared light resulting in a change of temperature in the atmosphere. To study the temperature in the earth atmosphere subjected to electromagnetic radiations, one may use the Radiative Transfer equations coupled with the Navier-Stokes equations. The problem has 7 dimensions; however with minimal simplifications it is equivalent to a small number of integro-differential equations in 3 dimensions. A numerical implementation using an H-matrix compression scheme allows us to measure the effect of clouds and airplane contrails on the temperature in the atmosphere. The result is very fast and the method is capable of handling variable absorption and scattering functions of spatial positions and frequencies.

The talk will not deal with the mathematical technicality of the method but will put these developments in perspective within the general problem of climate modeling.

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Olivier Pironneau is a French mathematician who is a professor at the Universit¨¦ Pierre et Marie Curie and member of the French Academy of Sciences. Pironneau is a worldwide recognized expert in computational fluid dynamics, scientific computing, computational engineering, optimal design, numerical analysis and partial differential equations. He is a member of French Academy of Sciences since 2002 and associate member of the Russian Academy of Sciences since 2004. He was awarded the Ordre National du M¨¦rite and he is also the recipient of the Marcel Dassault Prize and Blaise Pascal Prize by the French Academy of Sciences.

French Academy of Sciences (Acad¨¦mie des Sciences in French) was established in 1666.

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