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Nonlinear Processes in Geophysics An interactive open-access journal of the European Geosciences Union

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https://doi.org/10.5194/npg-2018-18
© Author(s) 2018. This work is distributed under
the Creative Commons Attribution 4.0 License.
Research article
23 Mar 2018
Review status
This discussion paper is a preprint. It is a manuscript under review for the journal Nonlinear Processes in Geophysics (NPG).
Application of ensemble transform data assimilation methods for parameter estimation in nonlinear problems
Sangeetika Ruchi and Svetlana Dubinkina Centrum Wiskunde & Informatica, P.O. Box 94079, 1098 XG Amsterdam, The Netherlands
Abstract. Over the years data assimilation methods have been developed to obtain estimations of uncertain model parameters by taking into account a few observations of a model state. However, most of these computationally affordable methods have assumptions of Gaussianity, e.g. an Ensemble Kalman Filter. Ensemble Transform Particle Filter does not have the assumption of Gaussianity and has proven to be highly beneficial for an initial condition estimation and a small number of parameter estimation in chaotic dynamical systems with non-Gaussian distributions. In this paper we employ Ensemble Transform Particle Smoother (ETPS) and Ensemble Transform Kalman Smoother (ETKS) for parameter estimation in nonlinear problems with 1, 5, and 2500 uncertain parameters and compare them to importance sampling (IS). We prove that the updated parameters obtained by ETPS lie within the range of an initial ensemble, which is not the case for ETKS. We examine the performance of ETPS and ETKS in a twin experiment setup, where observations of pressure are synthetically created based on the know values of parameters. The numerical experiments demonstrate that the ETKS provides good estimations of the mean parameters but not of the posterior distributions and as the ensemble size increases the posterior does not improve. ETPS provides good approximations of the posterior and as the ensemble size increases the posterior converges to the posterior obtained by IS with a large ensemble. ETKS is very robust while ETPS is very sensitive with respect to the initial ensemble. An issue of an increase in the root mean square error after data assimilation is performed in ETPS for a high-dimensional test problem is resolved by applying distance-based localization, which however deteriorated the posterior estimation.
Citation: Ruchi, S. and Dubinkina, S.: Application of ensemble transform data assimilation methods for parameter estimation in nonlinear problems, Nonlin. Processes Geophys. Discuss., https://doi.org/10.5194/npg-2018-18, in review, 2018.
Sangeetika Ruchi and Svetlana Dubinkina
Sangeetika Ruchi and Svetlana Dubinkina
Sangeetika Ruchi and Svetlana Dubinkina

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Short summary
Accurate estimation of subsurface geological parameters, e.g. permeability, is essential for the oil industry. This is done by combining observations of pressure with a mathematical model using data assimilation. We show that computationally affordable ensemble transform data assimilation methods are suitable for the parameter estimation. Particle filter is superior to Kalman filter for estimation of a small number of parameters and is equivalent for estimation of a large number of parameters.
Accurate estimation of subsurface geological parameters, e.g. permeability, is essential for the...
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