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.
