Parameter Estimation and Uncertainty Analysis: Principles and Practice

Course Overview

This five-day course, led by John Doherty (author of PEST), covers modern inversion and uncertainty analysis techniques for subsurface flow models. Hands-on sessions show how to implement theory using the PEST and PEST++ suites.

A key focus is the distinction between numerical modelling that is undertaken to understand how groundwater systems work and decision-support groundwater modeling. While the latter must inform real-world management, it must do so under uncertainty—since subsurface properties can never be perfectly known. The goal is not perfect prediction, but bias-free decision-making that acknowledges risk.

Topics include:

  • History matching and data assimilation

  • Appropriate model complexity and parameterization

  • Non-stationary geostatistics

  • Data Space Inversion (DSI) – a powerful, efficient method for uncertainty analysis without parameter tuning

Course Details and Registration information

  • Speaker: Dr. John Doherty
  • Date: September 1-5, 2025 (5 days, 9 am to 5 pm)
  • Location: University of Neuchâtel, building UniMail, Room E301-304
  • Cost:
    • WES PhD School members: no fee
    • Others (please contact School.Earth-Water@unine.ch for confirmation):
      • Academic participants: 150 CHF per day
      • Industrial, government, etc.: 500 CHF per day
  • Registration:
    • Please fill in the REGISTRATION FORM before August 1st, 2025
    • Registration is on a first-come, first-served basis.

What you will Receive

All participants will receive:

  • all slides that are presented in the course
  • the “PEST Book”
  • copies of publications on PEST/PEST++
  • extra workshops to complete in their own time.

Course Outline

Below is a course outline. However the material that is covered in the course will respond to the needs of those who attend. Time will be set aside for participants to discuss their own problems. Furthermore, participants are welcome to contact John after the course to continue discussions on matters that are important to them.

  • Introductions
  • Discussion and reflections on decision support modelling
  • Brief review of linear algebra and geostatistics
  • What is the metric for successful calibration?
  • How Bayes theorem is applied in groundwater modelling
  • Predictive uncertainty and predictive error
  • Old style calibration; parameter parsimony
  • Highly parameterized inversion and regularization
  • Subspace methods including singular value decomposition
  • Tikhonov regularization
  • Pilot points as a parameterization device
  • Construction of covariance matrices for parameter regularization and uncertainty analysis
  • Efficiencies gained through dimensional reduction

About the Presenter

John Doherty is the author of PEST and PEST-support utility software. Until recently, he also contributed heavily to GMDSI, an industry-sponsored initiative to boost awareness and education on the principles and practice of decision-support groundwater modelling; see https://www.gmdsi.org

Over his career of nearly 50 years, John has worked in the private, public and Tertiary sectors. He holds a PhD degree in Geophysics from University of Queensland and a Doctorate of Science from University of Neuchatel. He holds an adjunct professorial position at Flinders University where he currently supervises a number of PhD students.

However John as spent most of his career as a consultant, where he leads is own (one man) company, Watermark Numerical Computing. Through his company, John has assisted colleagues worldwide in building, history-matching and deploying models that address issues that have included extraction sustainability, high and low enthalpy geothermal, contaminant containment and remediation, and environmental impacts of mining and coal seam gas extraction.

  • Principles of uncertainty analysis
  • Nonstationary geostatistics
  • Generating random hydraulic property fields for structured and unstructured grids through spatial convolution
  • Linear uncertainty analysis
  • Ensemble smoothers: theory and practice
  • Direct predictive hypothesis-testing
  • Uncertainty in uncertainty: parameterizing the prior
  • Conceptual points and pilot points
  • Data space inversion
  • Ensemble space inversion
  • Hierarchical inversion
  • History-matching-induced predictive bias and its avoidance
  • When to use what method
  • Optimization under uncertainty
  • Data worth analysis
  • Structural overlay parameters
  • Some considerations for contaminant transport modelling
  • Some considerations for low enthalpy geothermal modelling
  • “Group therapy”: participants discuss their own problems

How to Get There

The UniMail building is part of the Faculté des Sciences at the University of Neuchâtel. The address is Rue Emile-Argand 11, 2000 Neuchâtel. The building’s opening hours can be found here.

To reach the building from the Neuchâtel train station (Gare Nord), take bus line 107 and get off at the Portes Rouges stop. From there, cross the bridge, and you’ll find the UniMail building. Alternatively, you can walk directly from the train station via Esplanade de l’Europe, which takes about 15-20 minutes.

Download the course programme