Calibration-constrained Monte Carlo analysis of highly parameterized models using subspace techniques

Tonkin, Matthew and Doherty, John (2009) Calibration-constrained Monte Carlo analysis of highly parameterized models using subspace techniques. Water Resources Research, 45 12: B10-1-B10-17. doi:10.1029/2007WR006678

Author Tonkin, Matthew
Doherty, John
Title Calibration-constrained Monte Carlo analysis of highly parameterized models using subspace techniques
Journal name Water Resources Research   Check publisher's open access policy
ISSN 0043-1397
Publication date 2009-01
Year available 2009
Sub-type Article (original research)
DOI 10.1029/2007WR006678
Volume 45
Issue 12
Start page B10-1
End page B10-17
Total pages 18
Editor Praveen Kumar
Place of publication Washington , D.C., U.S.A.
Publisher Amer Geophysical Union
Collection year 2010
Language eng
Subject C1
970109 Expanding Knowledge in Engineering
090702 Environmental Engineering Modelling
Abstract We describe a subspace Monte Carlo (SSMC) technique that reduces the burden of calibration-constrained Monte Carlo when undertaken with highly parameterized models. When Monte Carlo methods are used to evaluate the uncertainty in model outputs, ensuring that parameter realizations reproduce the calibration data requires many model runs to condition each realization. In the new SSMC approach, the model is first calibrated using a subspace regularization method, ideally the hybrid Tikhonov-TSVD "superparameter'' approach described by Tonkin and Doherty (2005). Sensitivities calculated with the calibrated model are used to define the calibration null-space, which is spanned by parameter combinations that have no effect on simulated equivalents to available observations. Next, a stochastic parameter generator is used to produce parameter realizations, and for each a difference is formed between the stochastic parameters and the calibrated parameters. This difference is projected onto the calibration null-space and added to the calibrated parameters. If the model is no longer calibrated, parameter combinations that span the calibration solution space are reestimated while retaining the null-space projected parameter differences as additive values. The recalibration can often be undertaken using existing sensitivities, so that conditioning requires only a small number of model runs. Using synthetic and real-world model applications we demonstrate that the SSMC approach is general (it is not limited to any particular model or any particular parameterization scheme) and that it can rapidly produce a large number of conditioned parameter sets.
Keyword Steady-state flow
Transmissivity fields
Watershed model
Inverse problem
Q-Index Code C1
Q-Index Status Confirmed Code

Document type: Journal Article
Sub-type: Article (original research)
Collections: 2010 Higher Education Research Data Collection
School of Civil Engineering Publications
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Citation counts: TR Web of Science Citation Count  Cited 54 times in Thomson Reuters Web of Science Article | Citations
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Created: Thu, 03 Sep 2009, 08:57:54 EST by Mr Andrew Martlew on behalf of School of Civil Engineering