As well as traditional parameter estimation, PEST supports highly parameterized inversion. In doing this it employs similar technologies to those which are used in geophysical data analysis, image processing, and other fields where extracting all possible information from expensive datasets is of paramount importance.
Because of the limited information that is available in most environmental datasets, model calibration necessarily leads to a simplified parameter field compared with the complex, heterogeneous disposition of physical and chemical properties that characterizes real-world environmental systems. The trick is to do this simplification in such a way that the calibrated parameter field is of minimum potential wrongness. This does not mean that it is right - only that it is the simplest, sensible parameter set that is compatible with the data. Knowing that it will be wrong (as it must be as a simplified version of reality), it follows that in calibrating a model we must seek that parameter field for which its potential for wrongness is roughly symmetrically disposed with respect to it.
So how should the simplification that is necessary for model calibration be achieved? One option is to do this simplification manually before calibration commences. Alternatively, we can allow the simplification to take place as part of the calibration process itself. The latter is preferable for, if properly done, it can indeed guarantee a parameter set of minimum error variance.
It is through PEST's use of sophisticated mathematical regularization techniques that it is able to accommodate the use of hundreds, or even thousands, of parameters in the calibration process with unwavering numerical stability, and a guarantee of parameter reasonableness. The more parameters that are employed, the more flexibility that mathematical regularization techniques have in attaining simple parameter fields of maximum reasonableness.
Mathematical regularization techniques employed by PEST include the following.
The "SVD-assist" methodology is unique to PEST. It allows highly parameterized inversion to be employed in the calibration of complex environmental models with run-time efficiencies that are normally associated with the use of only a few parameters. Through the use of this device it is now commonplace to employ hundreds, or even thousands, of parameters in the calibration of complex three-dimensional models with heterogeneous parameter fields, even if these models take over an hour to run. Further gains in numerical efficiency are made if these model runs are parallelized.
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