On the Kalman smoother approach to the stochastic ...

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XVI International Conference on Computational Methods in Water Resources (CMWR-XVI) Ingeniørhuset

On the Kalman smoother approach to the stochastic inverse problem of groundwater hydrology
Paper
Author:Franz Konecny <franz.konecny@boku.ac.at> (BOKU - University of Natural Resources and Applied Life Sciences)
Presenter:Franz Konecny <franz.konecny@boku.ac.at> (BOKU - University of Natural Resources and Applied Life Sciences)
Date: 2006-06-18     Track: Special Sessions     Session: Data assimilation in water resources modelling
DOI:10.4122/1.1000000226
DOI:10.4122/1.1000000227

Key words: Inverse problems, distributed parameter systems, infinite dimensional Kalman smoother, EM algorihm. In this presentation we are concerned with the estimation of the hydraulic conductivity profile on the basis of noisy observations of hydraulic heads. An augmented Kalman smoother is applied to the stochastic flow equation. The implementation of the smoother requires the solution of a Riccati type partial differential equation for the smoother covariance and a stochastic partial differential equation to obtain the optimal estimate of the augmented state. We discuss finite dimensional approximations of the smoothing problem and propose an EM algorithm for the estimation of the conductivity parameters.