Calibration-constrained Monte Carlo analysis of highly parameterized models using subspace techniques
Article first published online: 15 JAN 2009
Copyright 2009 by the American Geophysical Union.
Water Resources Research
Volume 45, Issue 12, December 2009
How to Cite
2009), Calibration-constrained Monte Carlo analysis of highly parameterized models using subspace techniques, Water Resour. Res., 45, W00B10, doi:10.1029/2007WR006678., and (
- Issue published online: 15 JAN 2009
- Article first published online: 15 JAN 2009
- Manuscript Accepted: 5 NOV 2008
- Manuscript Revised: 31 MAY 2008
- Manuscript Received: 16 NOV 2007
- Monte Carlo;
- uncertainty analysis;
- parameter estimation
 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.