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

几十年来，在同质区域和河流流域的水文研究表明，年洪峰流量分布的分位数（例如，平均年洪峰流量，100年洪峰流量）具有幂律依赖于上游流域面积的指数，通常在0.5和1.0之间变化。一个新的地球物理理论已经发展到了解这种非线性的依赖关系（缩放）在高峰流量（洪水）的时空降雨，径流产生过程和渠道网络中的水运输动力学。 该理论的核心假设是，在大流域的限制下，自相似网络拓扑结构和几何形状中的质量和动量守恒方程的解产生了洪峰径流事件的缩放，正在进行的研究是建立在诊断的基础上的，与广泛使用的将模型与数据拟合以使误差最小化的实践相反。诊断的目的是了解数据，理论和计算机模拟之间的关系，而无需拟合。基于诊断结果，可以引入新的假设，可以修改假设并重复诊断。研究人员在诊断降雨，渗透和径流产生的作用，在事件时间尺度上的洪水在密西西比的古德温溪实验流域（GCEW）的斜坡和拦截的空间尺度关系的经验。这个项目是建立在他们公布的结果，并将其扩展到一个年度的时间尺度。他们正在使用概率（集合）框架诊断GCEW中的峰值流量缩放关系。一个集合被定义为不同的过程线的集合，这些过程线是从相同的降雨场产生的，但从不同的初始山坡入渗和产流条件。这一定义是因为发表的研究表明，山坡径流条件大大影响的时间和缩放功能的小流域，如GCEW的径流。两个关键问题正在解决的是，“如何敏感的空间尺度的峰值流量的空间变异性在山坡渗透和径流产生？年最大洪峰流量的换算与年径流事件中洪峰流量的换算有何关系？《科学》杂志（2008年第319期）最近的一篇文章指出，“鉴于目前显然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亡，不应再作为水资源风险评估和规划的核心默认假设。找到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不大。因此，无论气候平稳性是否成立，新兴的基于网络自相似性的洪峰流量标度理论都适用。如果我们能够更好地理解流域的物理运作以及如何使用物理过程和条件来预测观测到的峰值径流的空间尺度，那么该理论可以用于预测非平稳气候变化下的洪水。这项研究的结果也为国际水文科学协会长达十年的研究计划（2003-2013年）“无资料流域预测”（PUB）做出了重要贡献。

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.