Journal Article

PreJuSER-21348

http://join2-wiki.gsi.de/foswiki/pub/Main/Artwork/join2_logo100x88.png Parameter estimation by ensemble Kalman filters with transformed data: Approach and application to hydraulic tomography

Schoniger, A. ; Nowak, W. ; Hendricks-Franssen, H. J.FZJ*

2012
AGU Washington, DC

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Please use a persistent id in citations: http://hdl.handle.net/2128/20538  doi:10.1029/2011WR010462

Abstract: Ensemble Kalman filters (EnKFs) are a successful tool for estimating state variables in atmospheric and oceanic sciences. Recent research has prepared the EnKF for parameter estimation in groundwater applications. EnKFs are optimal in the sense of Bayesian updating only if all involved variables are multivariate Gaussian. Subsurface flow and transport state variables, however, generally do not show Gaussian dependence on hydraulic log conductivity and among each other, even if log conductivity is multi-Gaussian. To improve EnKFs in this context, we apply nonlinear, monotonic transformations to the observed states, rendering them Gaussian (Gaussian anamorphosis, GA). Similar ideas have recently been presented by Beal et al. (2010) in the context of state estimation. Our work transfers and adapts this methodology to parameter estimation. Additionally, we address the treatment of measurement errors in the transformation and provide several multivariate analysis tools to evaluate the expected usefulness of GA beforehand. For illustration, we present a first-time application of an EnKF to parameter estimation from 3-D hydraulic tomography in multi-Gaussian log conductivity fields. Results show that (1) GA achieves an implicit pseudolinearization of drawdown data as a function of log conductivity and (2) this makes both parameter identification and prediction of flow and transport more accurate. Combining EnKFs with GA yields a computationally efficient tool for nonlinear inversion of data with improved accuracy. This is an attractive benefit, given that linearization-free methods such as particle filters are computationally extremely demanding.

Keyword(s): J

Note: The authors would like to thank the German Research Foundation (DFG) for financial support of the project within the Cluster of Excellence in Simulation Technology (EXC 310/1) and within the International Research Training Group "Nonlinearities and upscaling in porous media" (NUPUS, IRTG 1398) at the University of Stuttgart.

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Contributing Institute(s):

1. Agrosphäre (IBG-3)

Research Program(s):

1. Terrestrische Umwelt (P24)

Appears in the scientific report 2012

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Database coverage:
; ; Current Contents - Agriculture, Biology and Environmental Sciences ; Current Contents - Life Sciences ; Current Contents - Social and Behavioral Sciences ; JCR ; NCBI Molecular Biology Database ; SCOPUS ; Science Citation Index ; Science Citation Index Expanded ; Thomson Reuters Master Journal List ; Web of Science Core Collection

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