Unified approaches for flood estimation

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.

Combining specialised modelling techniques with complex data analysis in order to deliver prediction with quantified uncertainties lies at the heart of many of the major challenges facing UK industry and society over the next decades. Indeed, the recent Government Office for Science report "Computational Modelling, Technological Futures, 2018" specifies putting the UK at the forefront of the data revolution as one of their Grand Challenges.

The beneficiaries of our research portfolio will include a wide range of UK industrial sectors such as the pharmaceutical industry, risk consultancy, telecommunications and advanced materials, as well as government bodies, including the NHS, the Met Office and the Environment Agency.

Examples of current impactful projects pursued by students and in collaboration with stake-holders include:

- Using machine learning techniques to develop automated assessment of psoriatic arthritis from hand X-Rays, freeing up consultants' time (with the NHS).

- Uncertainty quantification for the Neutron Transport Equation improving nuclear reactor safety (co-funded by Wood).

- Optimising the resilience and self-configuration of communication networks with the help of random graph colouring problems (co-funded by BT).

- Risk quantification of failure cascades on oil platforms by using Bayesian networks to improve safety assessment for certification (co-funded by DNV-GL).

- Krylov regularisation in a Bayesian framework for low-resolution Nuclear Magnetic Resonance to assess properties of porous media for real-time exploration (co-funded by Schlumberger).

- Machine learning methods to untangle oceanographic sound data for a variety of goals in including the protection of wildlife in shipping lanes (with the Department of Physics).

Future committed partners for SAMBa 2.0 are: BT, Syngenta, Schlumberger, DNV GL, Wood, ONS, AstraZeneca, Roche, Diamond Light Source, GKN, NHS, NPL, Environment Agency, Novartis, Cytel, Mango, Moogsoft, Willis Towers Watson.

SAMBa's core mission is to train the next generation of academic and industrial researchers with the breadth and depth of skills necessary to address these challenges. SAMBa's most sustained impact will be through the contributions these researchers make over the longer term of their careers. To set the students up with the skills needed to maximise this impact, SAMBa has developed a bespoke training experience in collaboration with industry, at the heart of its activities. Integrative Think Tanks (ITTs) are week-long workshops in which industrial partners present high-level research challenges to students and academics. All participants work collaboratively to formulate mathematical
models and questions that address the challenges. These outputs are meaningful both to the non-academic partner, and as a mechanism for identifying mathematical topics which are suitable for PhD research. Through the co-ownership of collaboratively developed projects, SAMBa has the capacity to lead industry in capitalising on recent advances in mathematics. ITTs occur twice a year and excel in the process of problem distillation and formulation, resulting in an exemplary environment for developing impactful projects.

SAMBa's impact on the student experience will be profound, with training in a broad range of mathematical areas, in team working, in academic-industrial collaborations, and in developing skills in communicating with specialist and generalist audiences about their research. Experience with current SAMBa students has proven that these skills are highly prized: "The SAMBa approach was a great template for setting up a productive, creative and collaborative atmosphere. The commitment of the students in getting involved with unfamiliar areas of research and applying their experience towards producing solutions was very impressive." - Dr Mike Marsh, Space weather researcher, Met Office.