PEST News

20th March, 2010. BEOPEST for Windows

A beta version of BEOPEST for Windows is now available from the downloads page.

BEOPEST was introduced to the PEST family of programs by Willem Schreuder of Principia Mathematica. Information on Unix BEOPEST, including download instructions for Unix source code, as well as Willem’s documentation, is available here.

BEOPEST was originally written for use on Unix platforms but, with some help from Doug Rumbaugh from Environmental Simulations, has also been ported to Windows. Since then, I have added some refinements to the Windows version of BEOPEST. Because source code is shared between the Unix and Windows versions of BEOPEST, these refinements will eventually make their way back to the Unix version. However at the present state of development the Windows and Unix versions are a little different in that run management and run management reporting are not the same between the two versions. Also the Unix version does not offer restart capabilities. Hopefully, when the present developmental phase is complete, these differences will no longer exist.

At the time of writing it has been well over a year since Willem developed his original version of BEOPEST. I have to admit that while I was very interested in what he had done, my interest did not extend to studying its intimate details, nor gaining the necessary knowledge to understand TCP/IP communications in the Windows setting. It was then my opinion that the traditional Parallel PEST did a good enough job in the Windows environment, and there was no reason to replace something that worked satisfactorily with anything new. Three things changed my mind about that:

• the need to reduce all impediments to the use of large number of parameters when quantifying model predictive uncertainty;
• the ubiquitous use of multicore processors in modern machines; and
• the explosion in availability of cloud computing resources.

All of these require a more efficient and more flexible parallelization paradigm than that provided by Parallel PEST. BEOPEST provides such a paradigm. Hence it is my intention to build on the wonderful work that Willem did in adding BEOPEST enhancements to PEST code by continuing to support and improve these enhancements.

For those interested, BEOPEST is featured in the ground water literature. See:

Hunt, R.J., Luchette, J., Shreuder, W.A., Rumbaugh, J., Doherty, J., Tonkin, M.J. and Rumbaugh, D., 2010. Using the cloud to replenish parched groundwater modeling efforts. Rapid Communication for Ground Water, doi: 10.1111/j.1745-6584.2010.00699

Click here to download this article free of charge for a limited time.

John Doherty

4th February, 2010. Release of PEST Version 12

Version 12 of PEST features the introduction of a new operational mode. Prior to version 12, PEST could run in one of three modes, these being:

• estimation;
• predictive analysis;
• regularization.

A fourth mode, named “Pareto” mode, can now be implemented.

The “Pareto front” is a term borrowed from optimization theory. It is used in contexts where more than one objective function must be simultaneously minimized. The Pareto front constitutes a kind of trade-off curve. It is the locus of points in parameter space where one objective function cannot be lowered without raising another. It thus represents a set of compromise solutions to a multi-component optimization problem.

In simple situations where there are only two objective functions, the Pareto front may look something like this.

The Pareto front.

However in real-world situations it can be more complex (even if there are still only two objective functions). Knowing something about its shape can provide a modeller with some useful (and often surprising) information on a model’s ability (or inability) to simultaneously satisfy more than one set of constraints through variation of its parameters.

The Pareto concept becomes very interesting, and very informative, when applied to the important tasks of post-calibration predictive uncertainty analysis on the one hand, and enforcement of Tikhonov regularization constraints on the other hand. New aspects of PEST’s design facilitate its use in both of these applications.

When used for exploration of predictive uncertainty, the modeller proposes an hypothesis. He/she then asks “is it possible for certain good or bad thing to happen, given all that I know about system processes (as encapsulated in the model), and all that I know about system properties (as encapsulated in calibration constraints and expert knowledge)”? PEST is then run in Pareto mode to test the hypothesis. Perhaps this will demonstrate that the hypothesis can be rejected. Alternatively, it is possible that the hypothesis cannot be rejected completely, but can instead be rejected only at a certain level of confidence. This level of confidence will depend on the extent to which historical model-to-measurement fit must be violated and/or parameters must be assigned unlikely values if the prediction is to materialize. Using PEST’s Pareto mode, a trade-off curve can be rapidly built for a number of predictions of ever-increasing badness or goodness. The “cost” of incurring these predictions in terms of calibration misfit and/or parameter unbelievability is tested and displayed in a Pareto curve. This allows the modeller to make a quantitative or qualitative judgement of the level of confidence associated with each such prediction. This, in turn, can provide valuable support for model-based decision-making.

When applying Tikhonov constraints in a context of highly-parameterized inversion, another trade-off situation exists. In this case model-to-measurement fit must be traded off against the amount of heterogeneity that must be introduced to a parameter field to achieve that fit. In idealized settings, statistical metrics can be used to characterize model-to-measurement misfit and parameter field heterogeneity, these determining the optimum trade-off point. In real-world contexts, where model-to-measurement misfit is dominated by structural noise of unknown statistical properties, and where the likelihood or otherwise, as it pertains to different levels of parameter heterogeneity, must be judged qualitatively rather than statistically, trading-off calibration fit against parameter heterogeneity becomes a subjective matter. In making this judgement, a modeller gets to learn a lot about the model and about the system being simulated by the model. The information that PEST provides when run in Pareto mode provides the modeller with the information that he/she needs to support the making of this decision.

Also new in version 12 of PEST is a comprehensive model postprocessor named OBS2OBS. OBS2OBS is to model outputs what the existing PAR2PAR utility is to model parameters. It allows complex mathematical postprocessing of model outputs to take place before these are compared with user-supplied observations. Its uses include (among other things):

• formulation of one-sided penalty functions, this being useful when imposing “soft bounds” on parameters, or on linear/nonlinear combinations of parameters;
• formulation of non-linear penalty functions, where the objective function component pertaining to one or more observations is zero for certain values of these observations but rises rapidly (and possibly in a nonlinear fashion) once a certain threshold is crossed;
• fitting of complex functions of one or many model outputs to the same functions of field data as a means of filtering out structural noise.

21st July, 2009. Release of PEST Version 11.11

Version 11.11 of PEST has the following new features.

• Better handling of model run failure as parameters are upgraded. If a model rejects a new set of upgraded parameters and fails to run to completion, PEST can be instructed provide it with another set of upgraded parameters instead of terminating execution with an error message.
• Five point derivatives stencil. Both maximum precision and minimum error variance options are available. The latter can prove useful in mitigating the deleterious effects of bad model performance on finite-difference derivatives calculation.
• Vastly reduced memory requirements for parallel run queue. The parallel run queue is now stored as a direct access binary file. This allows Parallel PEST to accomodate much larger numbers of parameters and observations than was possible before this.
• Improved run distribution amongst slaves. Slaves can be allocated to different groups. Where possible, PEST allocates model runs to members of different groups before allocating runs to members of the same group.
• Improved SVD-assist model run efficiency. Prior information can be added to a base parameter PEST control file after the Jacobian for that file was calculated; when PEST undertakes SVD-assisted parameter estimation, the super-parameter Jacobian for the first iteration is still supplied for free.