# Séminaire

**Titre :**Uncertainty Quantification: The generalized Wiener-Hermite polynomials

**Nom du conférencier :**Mohamed JARDAK

**Son affiliation :**Laboratoire de Météorologie Dynamique/IPSL, Ecole Normale Supérieure, 24 rue Lhomond, 75005 Paris

**Laboratoire organisateur :**LMD

**Date et heure :**16-12-2010 14h30

**Lieu :**Salle E314, LMD-ENS, Département des Géosciences, 24 rue Lhomond, 75005 Paris

**Résumé :**

Most physical, biological, geophisical, economic and financial processes, etc, involve some degree of uncertainty. Uncertainty quantification (UQ) is the task of determining statistical information about the outputs of a process of interest, given only statistical (i.e., incomplete) information about the inputs.

In the geophysics community, an enormous amount of work has been spent in developing large, complex numerical models of the oceans and atmosphere. The necessity of the inclusion of stochastic physics has been recognized as a missing aspect in climate simulation, weather uncertainty prediction and in the closure of inhomogeneous geophysical turbulence. These developments have uncovered new problems in the numerical solution and diagnostic analysis and verification of model simulations and predictions. We naturally pose the more general question of how to model uncertainty and stochastic input, and how to formulate algorithms in order for the simulation output to reflect accurately the propagation of uncertainty.

Several uncertainty quantification methods have been developed. On one side of the spectrum there is the Monte Carlo Method amounting to a number (usually a large number) of deterministic solves, which does not require any change to the numerical code, but is inefficient. On the other side there is the Polynomial Chaos Method, where uncertainty is regarded as generating a new dimension and the solution as being dependent on that dimension. Implementation of the polynomial Chaos method in an existing code requires some programming effort. However, solution of the resulting system of equations is in general quite fast.

In this talk we will present the spectral stochastic method also known as the Polynomial Chaos Method as non conventional method to account, assess and quantify the uncertainty. We will show the discretization techniques involved in implementing the Polynomial Chaos Method. For the purpose of illustration, examples of application of the method will be shown.

**Contact :**

Riwal Plougonven, LMD-ENS, 24 rue Lhomond, 75005 Paris

tel: 01 44 32 27 31