Unified approaches for flood estimation

根据过去的降雨量预测河流的流量是水文学中的一个基本问题，也是洪水估算等许多应用的关键。在过去的几十年里，许多计算模型被提出来解决这个问题。目前，环境署等机构用于估计洪水风险的最先进方法包括物理（流体动力学）、概念（径流）和统计建模。物理模型的适用性是有限的，因为它们需要详细的数据和高计算能力。因此，往往选择概念和统计模型，因为它们可以准确地拟合现有数据。然而，基于数据的模型往往是由不同机构独立开发的，往往缺乏适当的理论背景。尽管能够很好地拟合给定河流的真实数据，但在应用于不同条件（例如，另一条河流，不同季节或异常条件，如极端降水）时，它们往往不准确。模型的假设和约束往往没有得到严格的评估，因此我们不知道对每个模型的限制有清楚的理解。该博士项目旨在开发数学工具，以扩展目前对水文模型假设及其局限性的理解，并为开发更具理论合理性的模型奠定基础。可以区分三个主要目标。第一个目标是建立一个数学框架，提供一系列情景下的标度律和分析预测。它将以简化的方式基于真实世界系统的表示，可以使用渐近方法。论文制定报告的初步结果将通过引入不同类型的流量之间的耦合，更现实的集水区几何形状和随时间变化的降雨量系列进行扩展。第二个目标是利用作为第一个目标获得的一系列简单情景的参考解决方案，评估不准确的来源和不同类别简化模型的局限性。我们试图了解常用模型的不同简化如何反映简单水文系统的真实的行为，以及这些模型的预测分歧。在《论文拟订报告》中已经查明了概念模型的一些不一致之处，但扩大所分析的设想方案的范围可能有助于获得更一般性的结论，并将其扩大到更广泛的一类模型，即统计和物理模型。最终目标是利用第一个和第二个目标的结论来开发理论上更合理的洪水估计计算方法，这可能会更好地处理数据可用性有限的情况。主要应用包括在无测量河流（流量未测量）中的洪水估计，以及考虑到气候变化对水文循环的未来影响的模型开发。通过这种方式，我们希望证明，严格的数学方法在这项研究中开发的水文模型的进一步发展可能会产生重大影响。

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.