Unified diagnostic evaluation of physics-based, data-driven and hybrid hydrological models based on information theory (UNITE)

• Applicants: Dr.-Ing. Uwe Ehret; Dr. Anneli Guthke
• Subject Area: Hydrogeology, Hydrology, Limnology, Urban Water Management, Water Chemistry, Integrated Water Resources Management
• Term: since 2022
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 507884992

Hydrological models traditionally rely on physical laws and expert knowledge, encoded in conceptual relationships or partial differential equations. However, such physics-based models often suffer from a too rigid structure and produce model structural errors, resulting in biased predictions. Recently, data-driven approaches to hydrological modeling have gained attention, because they directly extract the information contained in the data and do not suffer from model structural limitations. Especially deep learning methods have demonstrated high predictive capability in spatial extrapolation, but lack interpretability and a theoretical foundation for prediction under changing conditions. To address this, physics-informed data-driven approaches have emerged. By infusing expert knowledge, data-driven models gain interpretability and prognostic skill. We call any such approach on the modeling continuum between these two end members “hybrid models”. We claim that merging data-driven with physics-based modeling requires also new standards on the level of statistical evaluation: we need methodological advances to bring (lack of) information in physics-based models and information in data to the same scale. However, diagnostic tools specifically tailored to the performance of hybrid models are lacking to date. Established skill scores exist for individual modeling approaches, but it is unclear how to treat hybrid models. Due to that, there is little motivation to set up and compare competing hybrid models. However, we see a huge potential in analyzing sets of truly alternative models (varying in structure and modeling type, not just details of parameterization) for individual case studies, because from comparing the deficits of competing model structures, we can learn the most about gaps in our system understanding and in our current modeling skill. The goal of the proposed project is to develop a unified diagnostic evaluation framework (UNITE) for hybrid models based on information-theoretic measures. Due to its generality, information theory is a suitable framework to analyze and compare models from the entire continuum, and from any discipline. Information measures naturally expand from single- to multivariate cases and thus encompass both standard model evaluation by few output variables and comprehensive diagnostic evaluation of model trajectories in high-dimensional state spaces. We put our focus on methods that explicitly aim to identify and compare model-internal mechanisms, in order to promote scientific understanding and progress. This will ultimately lead to better models with better skill, no matter on which position of the model continuum this final model is. We will test and demonstrate the proposed toolbox on a comprehensive case study of rainfall-runoff modeling. Thinking beyond, this framework is expected to be useful for arbitrary types of dynamic hybrid models in a broad range of scientific disciplines with societal importance.

• DFG Programme: Research Grants
• International Connection: USA
• Cooperation Partner: Professor Dr. Hoshin Vijai Gupta
• Co-Investigator: Professor Mathias Niepert, Ph.D.