CMG Research: On the Quest for Power Laws in Floods: Developing Numerical and Analytical Tools

PI应开发一个能够模拟洪水事件的基于物理的水文模型。他们的系统动力学描述了一个大的非线性微分方程组，耦合的自相似网络的溪流和河流排水景观。为了能够在与重大社会影响和气候尺度效应兼容的尺度上研究洪水（即约50，000平方公里的流域，如2008年经历严重洪水的爱荷华州河流域），数值求解器需要一个高效且可扩展的算法。大气输入和景观特性（包括土壤、植被和河流网络拓扑结构）之间复杂尺度相互作用的探索需要非线性动力系统的工具。模型分析结果的确认需要分析大量的经验数据集。该项目解决了所有这些问题，将进一步调查和解释洪水的复杂行为。理解如何在洪水事件中出现幂律对在不断变化的环境条件下进行洪水频率预测具有重要意义。这将对世界上许多地方的水利基础设施设计产生深远的影响。根据全国各地众多流量计的流量观测数据的统计分析，文献中记载了年流量峰值（因此，通常是洪水）的上尾分位数与流域面积呈幂律关系。然而，幂律指数的依赖性并没有与该地区的物理特征及其气候联系起来。因此，由于这些特征可能会因人类干预（例如城市化）或气候变化而发生变化，因此我们预测未来洪水频率的能力在很大程度上是推测性的，或者充其量是临时性的。越来越多的证据表明，个别洪水事件也显示幂律相对于流域面积。建立洪水成因所必需的物理过程和洪水分位数幂律指数之间的联系，将增强洪水频率的预测。这项提案的重点是扩大建立这些联系所必需的数学工具，并提高我们对跨尺度洪水行为的理解。

The PIs shall develop a physics-based hydrologic model capable of simulating flood events. Their system dynamics are described by a large set of non-linear differential equations that are coupled by the selfsimilar network of stream and rivers draining the landscape. To enable the study of floods at scales compatible with significant societal impacts and climate scale effects (i.e. ~50,000 km2 basins such as the Iowa River basin that experienced severe flooding in 2008), the numerical solver requires an efficient and scalable algorithm. The exploration of complex scale interactions between atmospheric inputs and landscape properties including soil, vegetation, and topology of the river network requires tools of nonlinear dynamical systems. The confirmation of the model analysis findings requires analysis of a large dataset of empirical data. This project addresses all these issues in a way that will further the investigation and explanation of the complex behavior of floods. Comprehension of how power laws arise in flood events has implications for flood frequency prediction under changing environmental conditions. This would have profound effects on the water infrastructure design in much of the world.Based on statistical analysis of streamflow observations from numerous stream gauges across the nation, it has been documented in the literature that the upper tail quantiles of annual streamflow peaks (thus, often floods) display power laws with respect to drainage area. However, dependence of the power law exponents has not been linked to physical characteristics of the regions and their climates. Therefore, as these characteristics might change due to human intervention (e.g. urbanization) or climatic changes, our ability to predict future flood frequency is largely speculative or ad-hoc at best. There is increasing evidence that individual flood events also display power laws with respect to drainage area. Establishment of links between the physical processesessential to flood genesis and the exponents of the power laws of flood quantiles would enhance prediction of flood frequency. This proposal focuses on expanding the mathematical tools essential to establishing those links and improving our understanding of flood behavior across scales.