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Inverse Modelling in Earth
and Environmental Sciences

ABC/J Summer School 2016

Geoverbund ABC/J Summer School 2016 targets researchers, practitioners, and students in earth and environmental sciences that would like to advance their knowledge about inverse modelling methods and how such methods can be used to quantify uncertainty, and diagnose, detect and resolve structural inadequacies in statistical, conceptual and physically based models. The course provides an introduction to new concepts, algorithms and computational frameworks for estimating parameter, model, and predictive uncertainty from experimental data. Registration is requested until 17 June 2016 at the latest.

© Daniel FeltenCopyright: Daniel Felten

Call for registration

Date & venue

August 29 - September 2, 2016

RWTH Aachen University
Division of Earth Sciences and Geography
Lochnerstraße 4-20
Lecture room (room 503 on floor 5, right entrance of the building) and CIP-Pool (room 507 on floor 5, left entrance of the building)
52064 Aachen

How to get there


The course objectives are to familiarize the participants with new algorithms that have been developed to estimate model parameters from experimental data using inverse modelling. Evenly important is the estimation of the uncertainty of the estimated parameters. In inverse modelling, parameters are estimated by minimizing an objective function that quantifies the difference between the model predictions and the observations or measurements. The models that are used in earth and environmental sciences generally predict non-linear and coupled processes. The non-linearity of the models makes that the objective function may be characterised by multiple local optima. Therefore, global optimisation algorithms that search the parameter space in an efficient way are required to find a global optimum. Often, measurements of different state variables, fluxes and indirect information about the model parameters are available. In order to reconcile these different information sources with model predictions, a multi-objective optimization procedure is required. Data are afflicted with uncertainty and contaminated by ‘errors’ and a process model is always a simplified representation of reality. This uncertainty and simplification are propagated in an uncertainty of the estimated model parameters and the model predictions.
In this course, algorithms for efficient sampling of the parameter space, treating multi-objective optimisation problems, and estimating parameter and model prediction uncertainty in the presence of model error will be presented and applied in practical exercises.

Prerequisites and target group

The course targets researchers and students in earth and environmental sciences that want to interpret experimental data using process models. Prior to the course, a set of papers and reading material developing the theory behind the algorithms that will be covered in the course will be made available.


  • Introduction to inverse modelling
  • Classical single objective optimization and linearized parameter uncertainty estimation
  • Global search algorithms
  • Multi-objective optimization
  • Parameter uncertainty using Markov Chain Monte Carlo simulation
  • Data assimilation using joint parameter and state estimation
  • Working towards your own inverse modelling application

Teaching methods

Reading material on the theory will be made available before the course starts. The morning sessions will be used to explain the theory and the working of the algorithms. In the afternoon sessions, the algorithms will be applied in exercises on PC. For the afternoon sessions, a working knowledge of MATLAB is required.

Program & timetable

Monday August 29Numerical/analytic models, and concepts, theory, and application of linear and nonlinear least squares
Tuesday August 30Concepts, theory, and applications of global optimization
Concepts, theory, and applications of multiple objective optimization
Wednesday August 31Concepts, theory, and applications of Bayesian inference
Thursday September 1Approximate Bayesian computation: Summary metrics
Friday September 2Data assimilation

Daily timetable
09.00 – 10.30Lecture room
10.30 – 11.00Coffee break
11.00 – 12.30Lecture room
12.30 – 13.30Lunch break (sandwich lunch provided)
13.30 – 15.00Computer room/CIP-pool
15.00 – 15.30Coffee break
15.30 – 17.00Computer room/CIP-pool

Lecture room: to be announced
Computer room/CIP-Pool: room 507 on floor 5


Jasper Vrugt
University of California Irvine, USA

Sander Huisman
Forschungszentrum Jülich, Germany

Registration procedure and deadline

Please fill out the registration form including a short letter of motivation and send it by e-mail with the subject 'ABC/J Summer School 2016' to until 30 June 2016 at the latest (registration deadline). Applicants will be informed by e-mail whether they receive a place, presumably by end of June. Please contact the coordination office in case you should have any further question.


A contribution of 300 EUR is charged for external participants from academia and 1,000 EUR for participants from the private enterprise sector, respectively. Members of Geoverbund ABC/J are exempt from charges. Please click at the provided links to check for i) member institutions of Geoverbund ABC/J: RWTH Aachen University, University Bonn, University of Cologne, Forschungszentrum Jülich or ii) participating master programs: RWTH Aachen University, University Bonn, University of Cologne. Payment details, travel and accommodation information will be given with the notifications. All participants need to cover their expenses for travel and accommodation by themselves. Catering during the event (coffee breaks and sandwich lunch) will be provided.