When calibrating a model we try to determine the simplest, most realistic, parameter field that is compatible with the data, without throwing information away by employing a parameter field that is too simple. Regularised inversion gives us the ability to do this.
But a calibrated parameter field is not reality - for reality is far more complex than this. To the extent that any prediction depends on the complexities of reality that cannot be represented uniquely in the calibrated model, that prediction has a potential for error - sometimes the potential for a lot of error. This potential for error must be accounted for when making management decisions on the basis of model outcomes.
Predictions that are especially prone to error are those that are highly sensitive to system detail. These include:
PEST's ability to accommodate parameterization complexity gives it the ability to estimate parameter sets of minimum error variance. It also allows it to characterize that error variance (or uncertainty). Traditional methods of parameter estimation based on pre-calibration parsimonization simply cannot do this.
PEST and its utilities allow a user to undertake comprehensive linear and nonlinear parameter and predictive uncertainty analysis as an adjunct to calibration based on highly parameterized inversion.
Linear analysis is approximate, but powerful. It allows characterization not only of parameter and predictive uncertainty. It can also calculate other useful quantities such as the following.
PEST provides three options for nonlinear uncertainty analysis:
The last of these is achieved through PEST's unique, and extremely powerful, null space Monte Carlo technique. This methodology allows a user to generate many different set of parameters, all of which are reasonable, and all of which calibrate a model. Each of these parameter fields may include any level of detail - well beyond that which can be represented uniquely in a calibrated model. If a prediction is made using many such calibration-constrained parameter fields, the uncertainty of that prediction can be assessed.
Null space Monte Carlo is extremely efficient. Once a model has been calibrated once, the numerical burden of re-calibrating it many times using parameter fields of arbitrary complexity is minimal.
A comprehensive tutoral on model predictive uncertainty analysis using PEST is available from the downloads page.
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