Collaborative Research: Investigating the Physical Origins of Spatial Statistical Scaling in Peak Streamflows from Event to Annual Time Scales

几十年来，均质地区和流域的水文研究表明，年最大径流量分布的分位数(如年平均最大流量、百年最大流量)与上游流域面积呈幂函数关系，指数通常在0.5~1.0之间。一种新的地球物理理论正在发展，以了解洪峰流量(洪水)在时空降雨量、径流生成过程和河网中的水传输动力学方面的这种非线性相关性(比例)。该理论的中心假设是，降雨-径流事件的峰值流量标度来自于大流域范围内自相似网络拓扑和几何中的质量和动量守恒方程的解。正在进行的研究建立在诊断的基础上，而不是广泛使用的根据数据拟合模型以最小化误差的做法。诊断的目的是在没有拟合的情况下理解数据、理论和计算机模拟之间的关系。根据诊断结果，可以引入新的假设，修改假设和重复诊断。在密西西比州古德温溪实验分水岭(GCEW)的事件时间尺度上，研究人员在诊断降雨、渗透和径流在坡度和洪水空间尺度关系截获方面的作用方面具有经验。这个项目是在他们公布的结果的基础上进行的，并将其扩展到年度时间尺度。他们正在使用概率(集合)框架诊断GCEW中的峰值流量比例关系。集合被定义为不同的过程线的集合，这些过程线来自相同的降雨场，但来自不同的初始山坡入渗和产流条件。之所以做出这个定义，是因为已发表的研究表明，山坡径流条件对GCEW等小流域的径流时间和尺度特征有很大影响。正在解决的两个关键问题是，“峰值流量的空间尺度对坡面入渗和产流过程中的空间变异性有多敏感？”《科学》(319,2008)最近发表的一篇文章称，“鉴于目前正在发生的水文气候变化的规模和普遍性，我们断言，平稳性已经死了，不应该再作为水资源风险评估和规划的主要默认假设。找到一个合适的继任者对于人类适应不断变化的气候至关重要”。河流网络的自相似性在气候变化的十年和百年时间尺度上变化很小。因此，无论气候平稳性是否成立，新出现的基于网络自相似性的峰流标度理论都适用。如果我们能够更好地了解流域的物理运行方式，以及如何利用物理过程和条件来预测观测到的峰值径流的空间尺度，那么这一理论就可以用于预测非平稳气候变化下的洪水。这项研究的成果也为国际水文科学协会的长达十年的研究计划(2003-2013年)“未测流域预测”(PUB)做出了根本性的贡献。

For decades, hydrologic studies in homogeneous regions and river basins have shown that quantiles of the annual peak streamflow distribution (e.g. the mean annual peak flow, the 100-year peak flow) have a power-law dependence on upstream basin area with an exponent that usually varies between 0.5 and 1.0. A new geophysical theory has been developing to understand this non-linear dependence (scaling) in peak flows (floods) in terms of space-time rainfall, runoff generation processes and water transport dynamics in channel networks. The central hypothesis of the theory is that scaling in peak flows for rainfall-runoff events arises from solutions of mass and momentum conservation equations in self-similar network topologies and geometries in the limit of large drainage areas.The research being pursued is built on diagnosis, in contrast to the widely used practice of fitting a model to data to minimize errors. The purpose of diagnosis is to understand the relationships between data, theory, and computer simulations without fitting. Based on diagnostic results, new hypotheses can be introduced, assumptions can be modified and diagnosis repeated. The researchers have prior experience in diagnosing the role of rainfall, infiltration, and runoff generation on the slopes and intercepts of spatial scaling relations for floods at the event time scale in the Goodwin Creek Experimental Watershed (GCEW), Mississippi. This project is building on their published results and extending them to an annual time scale. They are diagnosing peak streamflow scaling relations in GCEW using a probabilistic (ensemble) framework. An ensemble is defined as a collection of different hydrographs that are produced from the same rainfall field but from a different set of initial hillslope infiltration and runoff generation conditions. This definition is made because published research indicates that hillslope runoff conditions substantially impact the timing and scaling features of streamflows in small basins like GCEW. Two key questions being addressed are, "How sensitive is the spatial scaling of peak flows to spatial variability in hillslope infiltration and runoff generation?" and "How is the scaling of annual maximum peak flows connected to the scaling of peak flows in rainfall-runoff events."A recent article in Science (319, 2008) stated that, "In view of the magnitude and ubiquity of the hydro-climatic change apparently now under way, however, we assert that stationarity is dead and should no longer serve as a central default assumption in water-resource risk assessment and planning. Finding a suitable successor is crucial for human adaptation to changing climate". Self-similarity in river networks changes little over the decadal and centennial time scales of climate change. Consequently, the emerging scaling theory of peak streamflows, which is based on network self-similarity, applies whether or not climatic stationarity holds. If we can better understand how basins operate physically and how physical processes and conditions can be used to predict observed spatial scaling in peak streamflows, then the theory can be used to predict floods under a non stationary climate change. Results from this research are also making fundamental contributions to Prediction in Ungauged Basins (PUB), the decade-long research initiative (2003-2013) of the International Association of Hydrologic Sciences.