# 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, MatthewDoherty, John Calibration-constrained Monte Carlo analysis of highly parameterized models using subspace techniques Water Resources Research   Check publisher's open access policy 0043-13971944-7973 2009-01 2009 Article (original research) 10.1029/2007WR006678 45 12 B10-1 B10-17 18 Praveen Kumar Washington , D.C., U.S.A. Amer Geophysical Union 2010 eng C1970109 Expanding Knowledge in Engineering090702 Environmental Engineering Modelling 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. Steady-state flowTransmissivity fieldsGroundwater-flowWatershed modelInverse problemMass-transportUncertaintyMethodologyPrediction C1 Confirmed Code

 Document type: Journal Article Article (original research) 2010 Higher Education Research Data Collection School of Civil Engineering Publications

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