Title: Data assimilation into groundwater contaminant models using an ensemble variational approach

Authors: M. EL GHARAMTI (King Abdullah University of Science and Technology, KAUST, Thuwal, KSA)
U. ALTAF (King Abdullah University of Science and Technology, KAUST, Thuwal, KSA)
I. HOTEIT (King Abdullah University of Science and Technology, KAUST, Thuwal, KSA)
A. W. HEEMINK (Delft Institute of Applied Mathematics, Delft University of Technology, Delft, Netherlands).

The adjoint method has been used very often for variational data assimilation. Using the available data, the control variables in the model are identified by minimizing a certain cost function that measures the differences between the model outputs and the data. In order to obtain a computationally efficient procedure, the minimization is performed with a gradient-based algorithm where the gradient is determined by solving the adjoint problem. The computational cost to run the adjoint model often exceeds several forward model runs which in return is computationally inefficient. The second drawback of the adjoint method is the programming effort required for the implementation of the adjoint model code.

We propose a new variational data assimilation approach based on model reduction using Proper Orthogonal Decomposition (POD), which avoids the implementation of the adjoint of the tangent linear approximation of the original nonlinear model. An ensemble of the forward model simulations is used to determine the approximation of the covariance matrix and only the dominant eigenvectors of this matrix are used to define a model subspace. By projecting the original model onto this subspace, an approximate linear model is obtained. The adjoint of the tangent linear model is replaced by the adjoint of this linear reduced model. Thus the adjoint model is run in reduced space with negligible computational cost. Once the gradient is obtained in reduced space it is projected back in full space and the minimization process is carried in full space.

In the presentation we will introduce the ensemble approach to variational data assimilation. The characteristics and performance of the method will be illustrated with a number of real life data assimilation applications with ground water contaminant models. For such models, we will develop a procedure to estimate some important model parameters such as the permeability of the underground geologic rocks in addition to various subsurface contaminant state estimates.

GMAO Head: Michele Rienecker Global Modeling and Assimilation Office NASA Goddard Space Flight Center

Curator: Nikki Privé Last Updated: May 27 2011