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

Authors:
Lionel Mathelin;Christophe Desceliers;M. Yousuff Hussaini
Affiliations:
LIMSI-CNRS, Orsay, France 91403;Université Paris-Est, Laboratoire Modélisation et Simulation Multi-Echelle, MSME UMR 8208 CNRS, Marne-la-Vallée Cedex 2, France 77454;Computational Science and Engineering, Department of Mathematics, Florida State University, Tallahassee, USA 32306-4510
Venue:
Computational Mechanics
Year:
2011

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Abstract

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.