Stochastic data assimilation of the random shallow water model loads with uncertain experimental measurements

L. Mathelin (1) , Christophe Desceliers (2) , M.Yussuf Hussaini (3)

1 LIMSI - Laboratoire d'Informatique pour la Mécanique et les Sciences de l'Ingénieur
2 MSME - Laboratoire de Modélisation et Simulation Multi Echelle
3 FSU - Florida State University [Tallahassee]

This paper is concerned with the estimation of a parametric probabilistic model of the random displacement source field at the origin of seaquakes in a given region. The observation of the physical effects induced by statistically independent realizations of the seaquake random process is inherent with uncertainty in the measurements and a stochastic inverse method is proposed to identify each realization of the source field. A statistical reduction is performed to drastically lower the dimension of the space in which the random field is sought and one is left with a random vector to identify. An approximation of the vector components is determined using a polynomial chaos decomposition, solution of an optimality system to identify an optimal representation. A second order gradient-based optimization technique is used to efficiently estimate this statistical representation of the unknown source while accounting for the non-linear constraints in the model parameters. This methodology allows the uncertainty associated with the estimates to be quantified and avoids the need for repeatedly solving the forward model.

Mots clés: Parametric estimation; Stochastic inverse method; Polynomial chaos; Data assimilation; Maximum likelihood; Chaos representations; inverse problems

Domaines: Mécanique des fluides [physics.class-ph]; Mécanique des fluides [physics.class-ph]; Dynamique des Fluides [physics.flu-dyn]

L. Mathelin, Christophe Desceliers, M.Yussuf Hussaini. Stochastic data assimilation of the random shallow water model loads with uncertain experimental measurements. Computational Mechanics, 2011, 47 (6), pp.603-616. ⟨hal-00750190⟩