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Flow Routing Techniques for Environmental Modeling

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Flow Routing Techniques for Environmental Modeling EPA/600/B-18/256 | August 2018 | www.epa.gov/research Flow Routing Techniques for Environmental Modeling photo 0 EPA/600/B-18/256 August 2018 Flow Routing Techniques for Environmental Modeling by Jan Sitterson1 , Chris Knightes2 , Brian Avant3 1 Oak Ridge Associated Universities 2 U.S. Environmental Protection Agency, Office of Research and Development 3 Oak Ridge Institute for Science and Education Chris Knightes - Project Officer Office of Research and Development National Exposure Research Laboratory Athens, GA, 30605 1 Notice The U.S. Environmental Protection Agency (EPA) through its Office of Research and Development funded and managed the research described here. The research described herein was conducted at the Computational Exposure Division of the U.S. Environmental Protection Agency National Exposure Research Laboratory in Athens, GA. Any mention of trade names, products, or services does not imply an endorsement by the U.S. Government or the U.S. Environmental Protection Agency. The EPA does not endorse any commercial products, services, or enterprises. This document has been reviewed by the U.S. Environmental Protection Agency, Office of Research and Development, and approved for publication. 2 Abstract This report describes a few ways to simulate the movement of water through a network of streams. Flow routing connects excess water from precipitation and runoff to the stream to other surface water as part of the hydrological cycle. Simulating flow helps elucidate the transportation of nutrients through a stream system, predict flood events, inform decision makers, and regulate water quality and quantity issues. Three flow routing techniques are presented and discussed in this paper. Constant volume and changing volume techniques use the continuity equation, while the third technique, the kinematic wave approximation, uses the continuity and momentum equations. Inputs and outputs differ for each flow routing technique, with kinematic wave being the most complex model. Each option has a set of applications it is best suited for. Numerical errors such as distortion and instability are potential errors that can affect the accuracy of model outputs. Routing methods should be chosen based on input data availability and scope of the problem being addressed. This report informs modelers of algorithms, input data needed, and the applicability of a few flow routing techniques used in environmental modeling. 3 Foreword The U.S. Environmental Protection Agency (EPA) is charged by Congress with protecting the Nation's land, air, and water resources. Under a mandate of national environmental laws, the Agency strives to formulate and implement actions leading to a compatible balance between human activities and the ability of natural systems to support and nurture life. To meet this mandate, EPA's research program is providing data and technical support for solving environmental problems today and building a science knowledge base necessary to manage our ecological resources wisely, understand how pollutants affect our health, and prevent or reduce environmental risks in the future. The National Exposure Research Laboratory (NERL) Computational Exposure Division (CED) develops and evaluates data, decision-support tools, and models to be applied to media-specific or receptor-specific problem areas. CED uses modeling-based approaches to characterize exposures, evaluate fate and transport, and support environmental diagnostics/forensics with input from multiple data sources. It also develops media- and receptor-specific models, process models, and decision support tools for use both within and outside of EPA. The goal of the Hydrologic Micro Services (HMS) project is to develop an ecosystem of inter- operable water quantity and quality modeling components. Components are light-weight and can be integrated to rapidly compose work flows to address water quantity and quality related questions. Each component may have multiple implementations ranging from macro (coarse) to micro (detailed) levels of modeling the physical processes. The components leverage existing internet-based data sources and sensors. They can be integrated into a work flow in two ways: calling a web service or downloading component libraries. For light-weight components, it is generally more efficient to call a web service, however, it is more efficient to have local copies of components if the component requires large amounts of input/output data. Tom Pierce, Acting Division Director for CED 4 Table of Contents Notice .............................................................................................................................................. 2 Abstract ........................................................................................................................................... 3 Foreword ......................................................................................................................................... 4 List of Figures ................................................................................................................................. 5 List of Tables .................................................................................................................................. 6 List of Equations ............................................................................................................................. 6 Introduction ..................................................................................................................................... 7 Stream Routing Options .................................................................................................................. 9 Constant Volume Routing......................................................................................................... 11 Changing Volume Routing ....................................................................................................... 12 Kinematic Wave Routing .......................................................................................................... 13 Channel Geometry ........................................................................................................................ 17 Potential Errors ............................................................................................................................. 19 Discussion ..................................................................................................................................... 20 References ..................................................................................................................................... 20 Appendix A ................................................................................................................................... 22 List of Figures Figure 1: A simplified diagram of the water cycle within a watershed. ......................................... 7 Figure 2: The momentum terms and equation used for each model. .............................................. 9 Figure 3: Graphs of flow moving through instantaneous and non- instantaneous models. .......... 11 Figure 4: Instantaneous flow schematic. ....................................................................................... 12 Figure 5: The flow-depth regression graph ................................................................................... 13 Figure 6: The computational grid for solving the finite difference numerical approximation ..... 15 Figure 7: Stream location visualization. ....................................................................................... 16 Figure 8: Channel Cross Sectional Geometry Descriptions ......................................................... 18 Figure 9: Outputs from models that show numerical errors. ........................................................ 19 5 List of Tables Table 1: Input parameters for flow routing schemes. ................................................................... 10 Table 2: Outputs for flow routing schemes................................................................................... 10 Table 3: Table of formulas for channel shapes ............................................................................. 18 List of Equations Equation (1) .................................................................................................................................... 8 Equation (2) .................................................................................................................................... 8 Equation (3) .................................................................................................................................. 11 Equation (4) .................................................................................................................................. 11 Equation (5) .................................................................................................................................. 12 Equation (6) .................................................................................................................................. 12 Equation (7) .................................................................................................................................. 13 Equation (8) .................................................................................................................................. 13 Equation (9) .................................................................................................................................
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