Efficient nonlinear model reduction for improved predictive uncertainty quantification and optimal design of monitoring networks in coupled groundwater-surface water systems

• Applicant: Dr. Thomas Wöhling
• Subject Area: Hydrogeology, Hydrology, Limnology, Urban Water Management, Water Chemistry, Integrated Water Resources Management
• Term: from 2014 to 2018
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 257317078

The reliable simulation and prediction of interacting flow and transport processes in complex coupled groundwater-surface water systems often requires PDE-based numerical models with spatially distributed parameters, which may exhibit a varying degree of non-linearity. They are data hungry, computationally demanding, and typically only little is known a priori about the true parameter values of these models. Global-search parameter-estimation schemes can require a large number of repeated model runs. Predictive uncertainty analysis or model-based optimization tasks - particularly the optimisation of monitoring networks - suffer from even larger problems. This becomes infeasible for complex physically-based process models, and model simplification is often the only choice to make such models accessible for the named purposes. Several promising model simplification methods have been developed to reduce the computational effort of physically-based models. This includes inversion-based upscaling and formal mathematical model reduction. However, many challenges must be met before these methods can be robustly applied to real cases in groundwater-surface water contexts. Most of all, there is additional error introduced by the model simplification which can invalidate the simplified models in the light of available data. The overall goals of model simplification are to obtain substantial reduction in computational effort, yet with only small errors. For example, the predictive probability distribution must still contain the true values (i.e., small error bias), and should not be unnecessarily wide to compensate for that bias (i.e., small error variance). The proposed project seeks to address these challenges in the context of modelling groundwater-surface water interaction and for the optimization of corresponding monitoring networks. Using two real-world case studies, we will first conduct a benchmark exercise to analyse the relative performance of existing methods (i.e., eigenmodels, proper orthogonal decomposition methods, and inversion-based upscaling) in terms of calibration performance, prediction performance, and the performance in optimization tasks. Secondly, efficient model reduction methods will be developed or extended for application to non-linear groundwater-surface water problems, which is the main goal of this proposal. Here, we will also adapt the Karhunen-Loève transformation of the prior parameter distributions to obtain simplified parameter distributions and thus reduced simulation times. Finally, we will apply the newly developed non-linear model reduction scheme for optimizing monitoring networks to reduce the uncertainty of groundwater - surface water predictive simulations and compare the results to equivalent solutions as achieved with a complex model.

• DFG Programme: Research Grants
• Participating Persons: Professor Dr.-Ing. Olaf A. Cirpka; Professor Dr.-Ing. Wolfgang Nowak