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

CMG 研究：探索洪水幂律：开发数值和分析工具

• 批准号: 1025483
• 负责人: Witold Krajewski
• 金额: $ 70.53万
• 依托单位: University of Iowa
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2010
• 资助国家: 美国
• 起止时间: 2010-09-15 至 2014-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1025483&HistoricalAwards=false
• 关键词: CMG; Research; Quest; Power; Laws

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.

PI 应开发能够模拟洪水事件的基于物理的水文模型。它们的系统动力学由大量非线性微分方程描述，这些方程通过排水景观的溪流和河流的自相似网络耦合。为了能够研究与重大社会影响和气候规模效应相适应的洪水规模（即约 50,000 平方公里的流域，例如 2008 年经历严重洪水的爱荷华河流域），数值求解器需要高效且可扩展的算法。探索大气输入与景观特性（包括土壤、植被和河网拓扑）之间的复杂尺度相互作用需要非线性动力系统工具。模型分析结果的确认需要对大量经验数据进行分析。该项目以进一步调查和解释洪水复杂行为的方式解决所有这些问题。了解洪水事件中幂律如何产生对于不断变化的环境条件下的洪水频率预测具有重要意义。这将对世界大部分地区的水基础设施设计产生深远的影响。根据对全国众多流量计的水流观测结果进行统计分析，文献中记载，年度水流峰值（因此通常是洪水）的上尾分位数显示了与流域面积有关的幂律。然而，幂律指数的依赖性与该地区的物理特征及其气候无关。因此，由于这些特征可能会因人为干预（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充其量只是推测或临时的。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增强对洪水频率的预测。该提案的重点是扩展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。