Second Order Analysis in Data Assimilation

Wednesday, May 1, 2002 - 11:30am - 11:50am
Keller 3-180
Francois-Xavier Le Dimet (LMC-IMAG)
In variational data assimilation (VDA) for meteorological and/or oceanic models, the assimilated fields are deduced by combining the model and the gradient of a cost functional measuring discrepancy between model solution and observation, via a first order optimality system. However existence and uniqueness of the VDA problem along with convergence of the algorithms for its implementation depend on the convexity of the cost function. Properties of local convexity can be deduced by studying the Hessian of the cost function in the vicinity of the optimum thus the necessity of second order information to ensure a unique solution to the VDA problem. In particular we study issues of existence, uniqueness and regularization through second order properties. We then focus on second order information related to statistical properties and on issues related to preconditioning and optimization methods and second order VDA analysis. Predictability and its relation to the structure of the Hessian of the cost functional is then discussed along with issues of sensitivity analysis in the presence of data being assimilated. Computational complexity issues are also addressed and discussed.

* Ref: Le Dimet F.-X., I.M. Navon, D. Daescu: Second Order Information in Data Assimilation. Mont. Wea. Rev., March 2002