Collaborative Research: Scaling Theories of 3-D Geometry and Flows of River Networks

9421445河道是河流地貌学和流域水文学的经典问题之一，它是对无量测流域流量的预测。这是一个非常困难的问题，因为它不仅涉及通过守恒方程的动力学概念，而且还涉及通过河流网络分支的几何概念，以及由于河流流量和河流网络中存在的MF涨落而产生的概率概念。由于这些概念在广泛的空间尺度上重复出现，我们建议的研究的重点是发展和实证检验尺度不变性的思想和理论。在过去的几年里，两个私人投资机构都广泛参与探索一个尺度框架，以研究空间降雨量、被视为形成河道的流量的峰值河流流量，以及河网的三维结构。在过去的三年中，这一研究领域的一些意想不到的重大进展表明，尺度不变性的思想为解决这一问题提供了一个非常丰富的框架。在这个提案中，我们的目标是：(1)发展河网的几何-统计尺度理论，(2)发展被视为河道形成流量的河流径流的统计-动态尺度理论，(3)发展几何-统计-动态尺度理论，将河网和水流的三维几何形状联系起来，以及(4)通过空间数据分析和模拟对目标1、2和3中的理论进行测试。这项拟议的研究解决了如何将不同的尺度概念，即几何、动态和统计概念交织在一起，形成一个单一的、连贯的理论框架，以理解这个问题的物理和解释时空水文数据。它可以应用于跨越各种空间和时间尺度的各种水文问题。

9421445 Waymire One of the classic problems in fluvial geomorphology and river basin hydrology is prediction of flows from ungauged river basins. This is a very difficult problem because not only does it involve notions of dynamics via the conservation equations, but also that of geometry via branching of river networks, and of probability due to the presence mf fluctuations in river flows and river networks. Since these notions recur across a broad range of spatial scales, the focus of our proposed research is on developing and empirically testing scaling invariance ideas and theories. For the past several years, both the PIs have been extensively involved in exploring a scaling framework to study spatial rainfall, peak river flows viewed as channel forming discharges, and the 3-D structure of river networks. Several unexpected and significant developments in this line of research within the last three years show that the scaling invariance ideas provide a very rich framework to tackle this problem. In this proposal our objectives are: (1) to develop a geometric-statistical scaling theory of river networks, (2) to develop a statistical-dynamic scaling theory of river runoff, which are viewed as channel-forming discharges, (3) to develop a geometric-statistical-dynamic scaling theory to connect the 3-D geometry of river networks and flows and (4) to carry out tests of the theories in Objectives 1,2, and 3 via spatial data analysis and simulations. This proposed research addresses how different notions of scaling, namely, geometric, dynamic, and statistical, can be woven together into a single, coherent theoretical framework to understand the physics of this problem and interpret space-time hydrologic data. It has applications to a variety of hydrologic problems spanning a broad range of space and time scales.