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

各项目须发展一套以物理为基础的水文模式，以模拟洪水事件。它们的系统动力学是由一大组非线性微分方程来描述的，这些方程与排水景观的溪流和河流的自相似网络相耦合。为了能够在具有重大社会影响和气候尺度效应的尺度上研究洪水（例如，2008年经历严重洪水的爱荷华河流域等约50,000平方公里的流域），数值求解器需要一种高效且可扩展的算法。探索大气输入与景观属性（包括土壤、植被和河网拓扑）之间复杂的尺度相互作用需要非线性动力系统的工具。模型分析结果的确认需要对大量的经验数据集进行分析。该项目以一种进一步调查和解释洪水复杂行为的方式解决了所有这些问题。理解幂律是如何在洪水事件中产生的，对于在不断变化的环境条件下预测洪水频率具有重要意义。这将对世界上大部分地区的水利基础设施设计产生深远的影响。基于对全国众多流量测量仪的流量观测数据的统计分析，文献中已经记录了年流量峰值（因此，通常是洪水）的上尾分位数与流域面积有关。然而，幂律指数的依赖性并没有与地区及其气候的物理特征联系起来。因此，由于这些特征可能会因人类干预（例如城市化）或气候变化而改变，我们预测未来洪水频率的能力在很大程度上是推测性的，或者充其量是临时的。越来越多的证据表明，个别洪水事件也表现出与流域面积有关的幂律。建立洪水发生所必需的物理过程与洪水分位数幂律指数之间的联系将加强对洪水频率的预测。这一建议的重点是扩展数学工具，以建立这些联系，提高我们对洪水行为的理解。

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.