Fachbereich Geowissenschaften

Optimal Design of Monitoring in Coupled Hydrosystems

How should monitoring systems be designed to minimise the overall uncertainty of how to model coupled hydrosystems?

PhD Researcher: Anneli Guthke, née Schöniger
Supervisors: Wolfgang Nowak (University of Stuttgart), Thomas Wöhling (University of Tübingen/WESS), Walter Illman (University of Waterloo)

Project Description

The goal of this PhD project is to develop an optimal design (OD) method for large coupled hydrosystem models with uncertainty in structure, parameters and forcing terms. OD aims to identify the “best” additional measurements (data types and measurement locations in space and time) that will return the highest data utility, generally defined as the highest reduction of prediction uncertainty.

In order to explicitly account for conceptual or structural uncertainty, we propose to consider several plausible, competing conceptual models and to select the best one on an objective basis (model selection) or determine an averaged estimate (model averaging). When performing model averaging, weights are assigned to each individual model based on goodness-of-fit criteria and the principle of parsimony. In addition to within-model variance (due to parameter and measurement uncertainty), structural uncertainty can be quantified as between-model variance. In a Bayesian framework (Bayesian model averaging, BMA), not only an averaged estimate of competing structural models is obtained, but a full probability distribution of the predicted quantity. This provides a basis for environmental risk assessment.

The core development of this thesis will be to extend the BMA concept to treat weights as uncertain quantities with prior and conditional joint probability distributions. This upgrade reflects the limited information of data for the model selection purpose. We will use this new technique to assess the significance of the determined weights, the confidence of model selection and the accuracy of the quantified structural uncertainty.

With a focus on model selection toward improved system understanding, optimal design strategies shall be developed that aim at minimizing the overall prediction uncertainty and maximize the confidence in the assigned weights (i.e., minimize the uncertainty related to the model structure selection). To this end, a new objective function for optimal monitoring has to be formulated that measures the information gain on BMA weights.

We will apply this framework to compare between complex and oversimplified hydrogeological models and thus provide a statistical tool for the decision which model complexity is needed and what data will be most informative, keeping in mind computational limitations of high-dimensional coupled hydrosystem applications.

Conference Talks & Posters

  • Lötgering-Lin, O., Hopp, M., Gross, J., Schöniger, A. & Nowak, W.: Prediction of pure component and mixture viscosities using PCP-SAFT and entropy scaling. - Talk at SAFT 2015, Houston, May 2015
  • Schöniger, A., Wöhling, T., Samaniego, L. & Nowak, W.: On the various (good and bad) ways to evaluate Bayesian model weights. - Talk at EGU GA Vienna, Apr 2015
  • Nowak, W., Wöhling, T. & Schöniger, A.: Lessons learned from a past series of Bayesian model averaging studies for soil/plant models. - Talk at EGU GA Vienna, Apr 2015
  • Schöniger, A.: Multi-model approaches to quantify conceptual uncertainty in environmental modelling. - Talk at International Conference on Integrated Hydrosystem Modelling, Tübingen, Apr 2015
  • Nowak, W., Schöniger, A., Wöhling, T. & Samaniego, L.: Model selection on solid ground: Comparison of techniques to evaluate Bayesian evidence. - Talk at AGU Fall Meeting San Francisco, Dec 2014
  • Schöniger, A., Wöhling, T. & Nowak, W.: How to address measurement noise in Bayesian model averaging. - Poster at AGU Fall Meeting San Francisco, Dec 2014
  • Schöniger, A., Wöhling, T. & Nowak, W.: How reliable is Bayesian model averaging under noisy data? Statistical assessment and implications for robust model selection. - PICO-Presentation at EGU GA Vienna, Apr 2014
  • Schöniger, A., Nowak, W. & Wöhling, T.: Do Bayesian model weights tell the whole story? New analysis and optimal design tools for maximum-confidence model selection. - Talk at AGU Fall Meeting San Francisco, Dec 2013
  • Wöhling, T., Schöniger, A., Geiges, A., Nowak, W. & Gayler, S.: Evaluating experimental design for soil-plant model selection using a Bootstrap Filter and Bayesian model averaging. - Talk at AGU Fall Meeting San Francisco, Dec 2013


  • Motavita D.F., Chow R., Guthke A., Nowak W. (2019): The Comprehensive Differential Split-Sample Test: A stress-test for hydrological model robustness under climate variability. Journal of Hydrology, doi: 10.1016/j.jhydrol.2019.03.054
  • Höge, M., Guthke, A., Nowak, W. (2019): The Hydrologist's Guide to Bayesian Model Selection, Averaging and Combination. Journal of Hydrology, 572, 96-107, doi: 10.1016/j.jhydrol.2019.01.072
  • Lötgering-Lin, O., Schöniger, A., Nowak, W., Gross, J. (2016): Bayesian model selection helps to choose objectively between thermodynamic models: A demonstration of selecting a viscosity-model based on entropy scaling. Industrial & Engineering Chemistry Research 55 (38), 10191–10207, doi: 10.1021/acs.iecr.6b02671
  • Nowak, W., Guthke, A. (2016): Entropy-based experimental design for optimal model discrimination in the geosciences. Entropy 18(11), 409, doi: 10.3390/e18110409
  • Schöniger, A., Wöhling, T. & Nowak, W. (2015), A statistical concept to assess the uncertainty in Bayesian model weights and its impact on model ranking, Water Resources Research, 51, 7524–7546, doi: 10.1002/2015WR016918
  • Wöhling, T., Schöniger, A., Gayler, S. & Nowak, W. (2015), Bayesian model averaging to explore the worth of data for soil-plant model selection and prediction, Water Resources Research, 51, 2825–2846, doi: 10.1002/2014WR016292
  • Schöniger, A., Illman, W. A., Wöhling, T. & Nowak, W. (2015), Finding the right balance between groundwater model complexity and experimental effort via Bayesian model selection, Journal of Hydrology, 531(1), 96-110, doi: 10.1016/j.jhydrol.2015.07.047
  • Schöniger, A., Wöhling, T., Samaniego, L. & Nowak, W. (2014), Model selection on solid ground: Rigorous comparison of nine ways to evaluate Bayesian model evidence, Water Resources Research, 50, 9484–9513, doi: 10.1002/2014WR016062