IJPAM: Volume 69, No. 1 (2011)

THE NEWTON METHOD IN PROBLEMS OF VARIATIONAL
DATA ASSIMILATION: APPLICATION TO
AN INFILTRATION MODEL

Pierre Ngnepieba$^1$, Desmond Stephens$^2$, Francois-Xavier Le Dimet$^3$
$^{1,2}$Department of Mathematics
Florida A&M University
Tallahassee, Florida, 32307, USA
$^1$e-mail: [email protected]
$^2$e-mail: [email protected]
$^3$Laboratoire Jean-Kuntzmann
University of Grenoble and INRIA
Grenoble Cedex, 38400, FRANCE
e-mail: [email protected]


Abstract. The problem of four-dimensional variational data assimilation (4D-Var) seeks to find an optimal initial field minimizing a cost function defined as the squared distance between model solutions and observations within an assimilation window. It requires minimization algorithms along with adjoint models to compute gradient information needed for the minimization. In this paper, an alternative method is suggested based on the implementation of the Newton algorithm stemming from the optimality system. This new method solves the 4D-Var-minimization problem efficiently, and it is equivalent to the LBFGS algorithm using the exact Hessian of the cost function. An application to the data assimilation problem in hydrology is presented. Numerical results are discussed.

Received: October 18, 2010

AMS Subject Classification: 65N30

Key Words and Phrases: Newton's method, data assimilation, infiltration, optimality system, adjoint, Hessian, Richards equation

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Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2011
Volume: 69
Issue: 1