Abstract
One of the most fundamental problems in hydrology is predicting the river flow at a given river basin’s (catchment) outlet. A wide range of hydrological models have been developed to address this problem. They can be divided into physical, conceptual, and statistical models. While physical models, based on the fundamental laws of hydrodynamics, are often considered to be the most accurate, conceptual and statistical models are often preferred by practitioners due to their lower requirements of input data and computing power.However, it is known that statistical and conceptual models sometimes cope poorly with predicting risk in areas with limited data or in non-standard environments. Hundreds of models have been developed in the past decades, but there is a lack of research on the connections between different approaches. Typically, they are treated in isolation and without a clear understanding of the limits of each model.
The aim of this PhD thesis is to develop a unified mathematical framework for comparing hydrological models, in order to clearly understand the limitations of currently used rainfall-runoff and flood estimation models. The work presented in this thesis was done together with my supervisor, Philippe Trinh. We start by developing a minimal coupled surface-subsurface flow model that represents the key properties of UK catchments. Based on this benchmark model, we analyse the mechanism of river flow formation during a single rainfall using asymptotic methods. Our key achievement is developing an approximate analytic solution for scenarios that enhances our understanding of this system far beyond numerical solutions currently found in the literature.
The primary focus of our investigation revolves around the study of minimal catchment models, which are based on numerous oversimplifications compared to complex real-world catchments. However, the simplistic structure of these minimal scenarios enables us to identify fundamental differences in the formulation of various hydrological models, without being obscured by the complexity and our limited understanding of real-world flows. An open question remains: Can the conclusions drawn from the study of these simple benchmark scenarios be applied to address the core issue of modeling real-world flows? We delve into this question in the second part of this paper, especially since there is still uncertainty within the hydrological sciences community about the underlying physical mechanisms that a comprehensive catchment model should encompass.
Nevertheless, we argue that the analytic solutions we develop provide a versatile benchmark for assessing data-based conceptual and statistical models beyond what can be learned from standard numerical testing on available data. Our framework allows us to assess the performance of different models across a range of limiting situations, typically underrepresented in real-world observations. We demonstrate its potential applications by identifying the key limitations of currently used models in the UK, including the QMED estimation method from the Flood Estimation Handbook, the Probability-Distributed Model (PDM), Grid and Grid-to-Grid models.
We believe that this study is a step forward towards developing more theoretically justified and robust catchment models in the future, which would better handle situations in which the currently existing methods turn out to be inaccurate.
| Date of Award | 26 Jun 2024 |
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| Original language | English |
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| Supervisor | Phil Trinh (Supervisor) & Paul Milewski (Supervisor) |