Using Pilot Points with MODFLOW and MT3D

When using PEST in "regularization mode" calibration of spatially-based models can be undertaken in new and exciting ways. When coupled with the use of "pilot points" as a method of spatial parameterization, PEST has new power. You can dispense with traditional notions of parameter parsimony, for PEST's regularization functionality will let you estimate many parameters, while ensuring that they all have reasonable values. Furthermore, you can dispense with the use of ugly and unrealistic zones, for PEST will find regions of spatial heterogeneity itself, introducing heterogeneity only where it is needed in order for model outputs to match field measurements.

The figure below shows the calibrated transmissivity field for a model built at an industrial site. Using PEST's regularization functionality, goodness of fit can be played against smoothness of the transmissivity field required to achieve calibration. Thus the modeler dictates how much heterogeneity is acceptable in the final two-dimensional transmissivity field based on his/her knowledge of the area and the noise content of the calibration dataset.

Transmissivity field calibrated against borehole water level measurements.

One of the truly exiting features of using pilot points is that they can be combined with the use of stochastic field generation techniques in order to produce a suite of spatial parameter distributions.  The entire suite of parameters can satisfy the geostatistics of an area, and calibrate the model. This allows the modeler to undertake "calibration constrained Monte-Carlo analysis" to explore the uncertainties surrounding key model predictions. The following two figures show transmissivity fields which also calibrate the above model. (This is a dramatic example of the non-uniqueness of the calibration process.) Many more such transmissivity fields could also be generated using this new "warping technology" made possible by basing parameterization on pilot points, and using PEST's regularization capabilities.

Stochastic field, "warped" by PEST to ensure that the model is calibrated.

Another transmissivity field which also calibrates the model.

For more information on pilot points and regularisation, see the following publication:

Doherty, J., 2003. Groundwater model calibration using Pilot Points and Regularisation,
Groundwater Vol.41 (2): 170-177