The introduction of regularization capabilities to PEST brings with it tremendous benefits when calibrating most types of environmental models. In many cases it makes the difference between success and failure of the parameter estimation process. It is no exaggeration to say that, for some types of models, PEST's regularization capabilities allow nonlinear parameter estimation to be used in the calibration process for the first time.

In spatial models such as groundwater and geophysical models, regularization allows you to introduce constraints on parameter spatial variability to the parameterization process. These constraints may be based on geostatistical evidence, of just on intuition. Thus you can ask PEST to calibrate a ground water model in such a way that only enough heterogeneity is introduced to the model domain to ensure that a good fit between model outcomes and field measurements is obtained. Meanwhile you can use a superfluity of parameters (especially if you are using pilot-points) so that PEST can place the heterogeneity exactly where it is needed to ensure goodness. In this way, you don't have to guess where such heterogeneity is required through the use of a cumbersome zonation pattern based on the artificial concept of "piecewise constancy". If regularization constraints are properly applied, the fact that there is a redundancy of parameters does not hinder PEST. Numerical stability is still maintained. This functionality is available from no other parameter estimation software.

PEST's regularization capabilities are a real breakthrough when it comes to using nonlinear parameter estimation techniques with surface water models such as HSPF. One no longer must hold most parameters at "fixed values" (these values having often been determined on the basis of little more than guesswork) and use PEST to estimate just a few others. When using PEST in regularization mode you can estimate a large number of parameters, in each case supplying an item of "prior information" in the form of a preferred value for that parameter. In minimizing model-to-measurement discrepancies, PEST will vary parameters from these preferred values only to the extent required to achieve the desired level of fit between field measurements and model outcomes.

No matter in what context it is used, regularization works the same way. The user must inform PEST of the extent to which he/she will tolerate a model-to-measurement misfit as PEST attempts to calibrate the model and enforce the regularization constraints at the same time. PEST will not violate the misfit condition (unless it is quite impossible to achieve the desired level of fit). The result is the attainment of a sensible set of parameter values, and the prevention of problems arising from numerical instability of the inversion process.
When used in the calibration of a groundwater model, together with pilot points as a parameterization device, the results can be astounding.