Unified approaches for flood estimation

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Predicting the flow in the river given past rainfall is a fundamental problem in hydrology, key to many applications such as flood estimation. Over past decades many computational models were proposed to address this problem. The current state-of-the-art approaches used by e.g. the Environmental Agency for estimating flood risk include physical (hydrodynamical), conceptual (rainfall-runoff), and statistical modelling. The applicability of physical models is limited, as they require detailed data and high computational power. Therefore, conceptual and statistical models are often chosen as they can be accurately fitted to available data. The data-based models however are often developed independently by different institutions and often lack proper theoretical background. Despite being able to fit real-world data for given river very well they are often inaccurate when applied for different conditions (e.g. for another river, different season or for unusual conditions, like extreme precipitation). Models assumptions and constraints are often not critically assessed therefore we don't know have clear understanding of the limits of each model. The PhD project aims at developing mathematical tools to extend current understanding of the hydrologic models' assumptions and their limitations, as well as to build foundations for development of more theoretically-justified models. Three main goals can be distinguished. The first goal is to develop a mathematical framework providing scaling laws and analytical predictions over a range of scenarios. It will be based on representation of real-world systems in a simplified way, for which asymptotic methods can be used. Preliminary results from Thesis Formulation Report are going to be extended by introducing coupling between different types of flows, more realistic catchment geometries and time-varying rainfall series. The second goal is to assess the sources of inaccuracy and limitations of different classes of simplified models using the reference solutions for a range of simple scenarios obtained as the first goal. We seek to understand how different simplification of commonly used models reflect the real behaviour of simple hydrologic systems and where these model's prediction diverge. Some inconsistencies of conceptual models were already identified in the Thesis Formulation Report, but extending the range of analysed scenarios may allow to obtain more general conclusions and extend them to a wider class of models, namely statistical and physical models. The final goal is to use the conclusion from the first and second goal to develop more theoretically-justified computational methods for flood estimation, which could potentially better handle situations with limited data availability. Key applications include flood estimation in ungauged rivers (where flow is not measured), and developing models taking into account the future effect of climate change on the hydrologic cycle. This way we hope to demonstrate that rigorous mathematical approach developed in this research may have significant impact on further development of hydrologic models.