Collaborative Research: SGER--Dynamical Origins of Statistical Scaling in Floods on Real Networks-An Exploratory Diagnostic Analysis

近十年来，一种新的洪水非线性地球物理理论--标度理论--已经发展起来。它的明确目标是从划分自然地形的山坡-渠道连接的守恒方程和相关物理过程中预测洪水中的空间统计功率定律。在许多关于区域洪水频率的经验研究中，年洪峰流量统计与流域面积之间以及最近在个别降雨-径流事件中观察到了幂函数关系。初步分析表明，基于事件的尺度指数与年洪水分位数尺度指数密切相关。这两组指数之间的密切关系暗示了一个非常重要的假设，即不仅可以从物理过程中预测单个RF-RO事件的洪水尺度参数，而且可以通过考虑一年中的多个事件来预测年度洪水的洪水尺度参数。智力优势：在理想化确定性自相似网络中的研究表明，随着流域面积的增加，统计幂定律渐近出现。它们不是控制洪水的物理方程中的组成部分。这导致了一个关键的科学假设，即洪水中的幂定律的物理起源于渠道网络的自相似(自亲和)，这也是广泛观察到的网络的分形结构及其Horton关系的基础。目前的挑战是将这一理论推广到现实网络中。为了实现这一重要目标，我们建议使用亚利桑那州核桃峡谷和密西西比州古德温克里克这两个农业研究服务局盆地的现有数据来测试诊断框架。其核心思想是在一组分布式参数假设下从物理过程预测幂定律。然后将预测与观测到的幂定律进行比较，以诊断我们物理假设的有效性，并提出一组新的假设。为了预测洪水中的尺度律，求解了一个质量守恒方程，该方程描述了自然地形中坡道连接尺度上的物理过程，并计算了网络中每个连接的流量过程。为了求解质量守恒方程，我们将使用我们的研究小组在过去五年开发的基于地理信息系统的数字流域建模框架。这些目标是探索性的，旨在建立一种“概念证明”。广泛的影响：科学共识已经增长，即全球变暖是真实存在的，而且在很大程度上是由人类活动造成的。对行星水文气候的这种人为扰动正在造成一种非平稳的变化，这排除了根据长期历史降雨量和河流流量数据进行统计洪水预测的可能性。在美国和世界其他国家，为了水资源管理的目的，统计水文模型中经常使用历史水文数据。因此，非平稳气候下的水文预报给未来的水资源管理带来了巨大的问题。洪水尺度理论正在发展新的科学基础，特别适用于在全球变暖引起的非静态水文气候变化这一新问题的背景下进行洪水预测。洪水尺度理论的科学基础可以概括为包括与水耦合的生态和生物地化过程，例如河岸蒸发蒸腾，并在不断变化的水文气候中进行预测。

A new nonlinear geophysical theory of floods, henceforth called the scaling theory, has been developing for nearly a decade. It has the explicit goal to predict spatial statistical power laws in floods from conservations equations and related physical processes at the scale of hillslope-channel links that partition a natural terrain. In many empirical studies of regional flood frequencies, power law relationships have been observed between annual peak discharge statistics and drainage areas, and recently in individual rainfall-runoff events. Preliminary analyses show that event-based scaling exponents and the annual flood quantile scaling exponents are closely related. A close relationship between these two sets of exponents suggests a very important hypothesis, namely that it is possible to predict flood-scaling parameters from physical processes not only for individual RF-RO events, but also for annual floods by considering multiple events in a year.Intellectual Merit: Research in idealized deterministic self-similar networks has shown that statistical power laws emerge asymptotically as drainage area goes to infinity. They are not built into the physical equations governing floods. It has led to a key scientific hypothesis that power laws in floods have their physical origins in the self-similarity (self-affinity) of channel networks, which is also the basis for the widely observed fractal structure of networks and their Horton relations. The current challenge is to generalize the theory to real networks. To achieve this important goal, we propose to test a diagnostic framework using existing data from two Agricultural Research Service basins, Walnut Gulch, Arizona and Goodwin Creek, Mississippi. The key idea is to predict power laws from physical processes under a set of distributed parametric assumptions. Then compare the predictions with observed power laws for diagnosing the validity of our physical assumptions, and proposing a new set of assumptions. For predicting scaling laws in floods, a mass conservation equation, which parameterizes physical processes at the scale of hillslope-channel links in a natural terrain, is solved and flow hydrographs are computed for every link in a network. For solving the mass conservation equation, we will use a GIS-based digital watershed-modeling framework that our research group has developed in last five years. The objectives are exploratory in nature and are designed to establish a "proof of concept".Broader Impacts: Scientific consensus has grown that global warming is real and in substantial part is caused by human activities. This anthropogenic perturbation to the planetary hydro-climate is causing a non-stationary change, which precludes making statistical flood predictions from long-term historic rainfall and stream flow data. Historical hydrologic data are routinely used in statistical hydrologic models for the purposes of water resources management in the United States and other countries of the World. Therefore, hydrologic predictions in a non-stationary climate present an enormous problem for future management of water resources. The scaling theory of floods is developing new scientific foundations that would be particularly suited to make flood predictions in the context of the emerging problem of non-stationary hydro-climate change due to global warming. The scientific foundations of the scaling theory of floods can be generalized to include ecological and bio-geo-chemical processes that are coupled to water, for example, riparian evapotranspiration, and to make predictions in a changing hydro-climate.