This page directs you to a number of educational videos prepared by John Doherty, author of PEST. Each video lasts for about an hour. Some of these videos cover use of PEST. Others are far more general, and are worth watching whether or not you use PEST; they allow you to understand some of the basics of data assimilation, and the important role that it plays in decision support modelling.
Thanks to GMDSI for sponsoring these videos.
What is PEST
This video provides an overview of PEST and the three families of utility software that accompany it. It also provides a brief discussion of the demands of decision-support environmental modelling, for this is the context in which PEST operates.
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What is Calibration?
This short video discusses what it means to calibrate a groundwater (or other) model. Calibration implies uniqueness. The quest for uniqueness is not a quest for truth. Uniqueness of solution of an ill-posed inverse problem requires regularization. If properly applied, regularization yields a solution to that problem which is of minimized error variance. However the potential for error in a calibrated parameter field, and in model predictions made by a calibrated model, can still be high.
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Vectors and Statistics
This video provides a short refresher on some aspects of matrix and vector algebra that we all learned at school but have since forgotten. It then does the same for a few basic statistical concepts. It is useful to watch this video before watching some of the other videos in this series.
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Well-Posed Inverse Problems
This video shows how parameters can be estimated when model calibration constitutes a well-posed inverse problem. However in groundwater modelling, well-posedness does not occur unless preceded by manual regularization. This is not recommended practice, for reasons discussed in the video. Nevertheless, the discussion is good preparation for other videos which focus on solution of ill-posed inverse problems. Of particular interest is the discussion on how to extend linear theory to calibration of nonlinear models.
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Problems with Manual Regularization
This video extends the discussion of the preceding video, while laying the foundation for ensuing videos. It explains how calibration based on manual regularization, whether performed automatically by software such as PEST or done manually by a modeller, may fail to find a parameter field that is of minimized error variance. It also shows that calibration achieved through manual regularization does not provide a good foundation for post-calibration uncertainty analysis. This is because the relationships between estimated and true hydraulic properties cannot be resolved when regularization is undertaken manually. The “cost of uniqueness” cannot therefore be assessed.
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Singular Value Decomposition
Singular value decomposition (SVD) is explained. Also explained is the important role that SVD can play in solving an ill-posed inverse problem, and the insights that it can provide into what calibration of a groundwater model can and cannot achieve. Important concepts such as the null space are also discussed. An explanation is provided of how over-fitting to a calibration dataset can occur, and why this is a bad thing.
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Tikhonov Regularization
The importance of Tikhonov regularization in solution of an ill-posed inverse problem in general, and in calibration of a groundwater model in particular, is explained. Also explained is its ability to achieve a solution to an inverse problem that is of minimized error variance through the role that it bestows on expert knowledge and site characterization in achieving that solution.
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Pilot Points
Pilot points are often employed as a parameterization device for groundwater models. This is because they can provide a sound basis for highly-parameterized inversion, while restricting parameters to a number which is low enough to allow filling of a Jacobian matrix using finite difference derivatives. The video discusses options for their emplacement, and how Tikhonov regularization is best applied in estimation of pilot point parameters. The video finishes with an example which demonstrates how, despite our best efforts to introduce geologically-meaningful Tikhonov regularization to the groundwater model calibration process, important hydrogeologically-significant structures may remain invisible to it.
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Getting the Most out of PEST - Part 1
This is the first video of a two-part series whose intention is to provide PEST users with some information on how to use PEST, and some of its supporting software, to best effect. This video covers the PEST control file, the difference between singular value decomposition and SVD-assist, and easy ways to add Tikhonov regularization to a PEST control file.
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Getting the Most out of PEST - Part 2
This second video of a two-part series covers calculation of finite-difference derivatives, defences against model output numerical granularity, some aspects of observation weighting, termination criteria, Marquardt lambda settings, and the use of some important PEST support utilities.
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Basic Geostatistics - Part 1
This is the first of a two-part series. It discusses correlated random variables. It shows how knowledge of one such variable conditions estimation of the other, and reduces its uncertainty. These principles are then applied to regionalized random variables to demonstrate the concepts behind random parameter field generation and kriging. The semivariogram, and its relationship to the spatial covariance function, are also discussed.
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Basic Geostatistics - Part 2
In this continuation of the first video of this series, links between geostatistics and history matching of groundwater models are explored. The use of geostatistical concepts and tools in model calibration, and in calibration-constrained uncertainty analysis are also discussed. Some shortcomings of traditional geostatistics, and how these have been addressed by newer geostatistical concepts such as multiple point geostatistics, are also explained.