CMG Collaborative Research: Envirodynamics on River Networks

在过去的几十年里，人们利用霍顿、斯特拉勒、施里夫和德永的开创性著作中开发的一套定量方法，对河网的拓扑结构进行了广泛的研究。因此，河流排序方案和统计自相似概念在水文学和地貌学中得到了相当程度的探索，并已渗透到自然科学的其他领域。与此同时，有关河网的静态拓扑如何影响在该网络上运行的动态过程的问题已被研究到相当小的程度，而这些过程的影响从环境，经济和社会的角度来看是最感兴趣的。本项目持续进行研究工作，重点是河网沿线的环境运输，特别是等级分支结构的动态过程。主要目标是开发一个理论和建模框架，以促进对网络几何形状和在其上运行的动态过程之间关系的预测性理解。该项目中将要开发和应用的分析方法来自于层次聚合和复杂网络的理论。提出的传输建模是基于布尔延迟方程（BDEs）的数学理论，这是一个专门为表现阈值、多重反馈和不同时间延迟的系统的数学建模而量身定制的框架。BDE模型将为初步评估土地利用和气候变化对河流系统资源属性的影响提供一个灵活的基础，包括沉积物粒度分布、藻类生产和运输、营养负荷和鱼类种群。它也将构成一个简单的平台。用于检验假设和指导进一步的数据收集工作，以改进不确定性下的预测。该项目将采用其他学科的概念和工具，主要是动力和复杂系统，用于地球表面研究。该研究为研究河网的环境运输开辟了一个新的方向。这个项目的智力价值在于新颖的数学、建模和数据探索方法，由一个跨学科团队提出，旨在预测河流网络的环境动态。网络动态问题的关键社会和经济重要性？在地球科学和其他物理和生命科学领域？对提案有实质性的补充吗？我的智力价值。该项目将有助于更好地预测环境通量，包括降水、泥沙、营养物质、污染物等，并为河流提供新的认识。栖息地结构和食物网。该项目将影响其他涉及网络动态和等级聚合的科学领域，包括基因相互作用、社会网络、疾病传播和互联网安全。新的结果将通过进一步发展动态网络的新理论概念，将这一概念整合到具体应用中，并开发相应的数值模型来实现。项目pi积极参与促进数学家、物理学家和地球科学研究人员之间的互动，并将在本项目中进一步加强这种互动。该项目的协作和跨学科方法使其成为研究生，博士后和年轻科学家的理想培训基地。

The topology of river networks has been extensively studied over the past decades using the suite of quantitative methods developed in the pioneering works of Horton, Strahler, Shreve, and Tokunaga. As a result, stream-ordering schemes and statistical self-similarity concepts have been explored to a considerable extent in hydrologic and geomorphologic sciences and have penetrated other areas of natural sciences. At the same time, questions related to how the static topology of a river network affects the dynamical processes operating on this network have been studied to a considerably lesser degree, while the impact of such processes is of the greatest interest from environmental, economic, and societal points of view. This project maintains a sustained research effort focused on environmental transport along river networks, in particular, and dynamic processes on hierarchical branching structures, in general. The main goal is to develop a theoretical and modeling framework that will facilitate predictive understanding of the relationships between the geometry of a network and dynamic processes that operate on it. The analytic methods to be developed and applied in the project arise from the theories of hierarchical aggregation and complex networks. The proposed transport modeling is based on the mathematical theory of Boolean delay equations (BDEs), a framework especially tailored for the mathematical modeling of systems that exhibit thresholds, multiple feedbacks and distinct time delays. The BDE modeling will provide a flexible basis for a preliminary assessment of land-use and climate change effects on resource attributes of a river system, including sediment grain size distribution, algae production and transport, nutrient loading, and fish population. It will also constitute a simple ?platform? for testing hypotheses and guiding further data collection efforts for improved prediction under uncertainty. The project will adapt concepts and tools from other disciplines, mainly dynamical and complex systems, to earth-surface research. The proposed study opens a new direction in earth-surface modeling, focused on environmental transport on river networks. The intellectual merit of this project resides in the novel mathematical, modeling, and data exploration approaches, put forward by an interdisciplinary team toward predictive understanding of environmental dynamics on river networks. The critical societal and economic importance of network dynamic problems? in the geosciences and other areas of the physical and life sciences?adds substantially to the proposal?s intellectual merit. The project will result in better predictive understanding of environmental fluxes including precipitation, sediment bedload, nutrients, pollutants, etc., and provide new insight into rivers? habitat structure and food webs. The project will impact other science areas that involve network dynamics and hierarchical aggregation, including gene interactions, social networks, spread of diseases, and Internet security. The new results will be achieved by further developing a novel theoretical concept of dynamic networks, integrating this concept into concrete applications, and developing corresponding numerical models. The project PIs are actively involved in promoting interactions between mathematicians, physicists and researchers in geosciences and will further strengthen such interactions within this project. The collaborative and cross-disciplinary approach of this project makes it an ideal training ground for graduate students, post-docs and young scientists.