A Discontinuous Galerkin-based Forecasting Tool for the Ohio River A Thesis Presented in Partial Fulfillment of the Requirements for the Degree Master of Science in the Graduate School of The Ohio State University By Mariah B. Yaufman, B.S. Graduate Program in Civil Engineering The Ohio State University 2016 Master's Examination Committee: Ethan J. Kubatko, Advisor Gil Bohrer Gajan Sivandran © Copyright by Mariah B. Yaufman 2016 ABSTRACT This thesis presents the development and application of a multidimensional (2- D & 1-D) river flow model in the discontinuous Galerkin framework for simulating overland flow and runoff due to rain events within the Ohio River watershed. The purpose of this work is to improve on the forecasting of stage height and discharge on the Ohio River | the largest tributary, by volume, of the Mississippi River in the United States. This forecasting tool makes use of the 2-D kinematic wave equations for overland flow caused by the rainfall events occurring over the Ohio River watershed and the 1-D kinematic wave equation for approximating stage height and discharge in the Ohio River. We highlight some of the challenges involved in modeling the various rainfall-runoff processes. Furthermore, we discuss the various data sets incorporated into the model, such as detailed cross-sectional data for the Ohio River obtained from the US Army Corps of Engineers, topographic data generated from NASA's Shuttle Radar Topography Mission (SRTM), and land use/land cover data from the US Geologic Survey. The model is verified against a set of analytic test cases and validated in a series of hindcasts that make use of historical rainfall and river gauge data. ii To my family for their love and support, and to Stephen for making ice cream runs with me and filling my life with laughter. iii ACKNOWLEDGMENTS I would like to thank my advisor, Ethan Kubatko, for captaining this river project and never giving up on it, or me. Thank you to the two C.H.I.L. members who helped us repair this sinking ship...while other members never fully got on board, fell off the boat, or jumped ship, you two hopped aboard and helped save the day. You two are awesome and I am forever grateful for the help you've provided me. iv VITA 2010 ::::::::::::::::::::: Bellbrook High School, Bellbrook, OH 2014 ::::::::::::::::::::: B.S. Civil Engineering, Cum Laude, The Ohio State University 2014 − 2016 : : : : : : : : : : : : ::Graduate Teaching Associate, Civil, Environmental, and Geodetic Engineering, The Ohio State University 2015 to Present ::::::::::Graduate Research Associate, Civil, Environmental, and Geodetic Engineering, The Ohio State University FIELDS OF STUDY Major Field: Civil Engineering Area of Specialization: Environmental Engineering and Water Resources v TABLE OF CONTENTS Page Abstract . ii Dedication . iii Acknowledgments . iv Vita......................................... v List of Tables . viii List of Figures . ix 1. Introduction . 1 1.1 Background . 1 1.2 Motivation and Objectives . 5 1.3 Thesis Organization . 6 2. Model Background . 8 2.1 Governing equations . 8 2.1.1 Overland flow . 8 2.1.2 Open-channel flow . 9 2.1.3 The kinematic wave approximation . 10 2.2 Domain discretization . 12 2.2.1 The discontinuous Galerkin spatial discretizations . 13 2.2.2 Multidimensional Coupling . 17 2.3 Mesh Generation . 18 2.3.1 Admesh+: Generating a constrained mesh and the accom- panying data structure . 19 vi 3. Data Inputs . 25 3.1 DEMs and Cross Sections . 25 3.1.1 Cross section modifications . 26 3.1.2 DEM modifications . 29 3.1.3 Combination . 30 3.2 U.S. Geological Survey Inputs . 30 3.2.1 River Inputs . 33 4. Forecasting . 35 4.1 Forecast data . 35 4.2 Unit hydrographs . 40 4.2.1 Historic Rainfall Data . 42 4.2.2 Historic discharge and baseflow separation . 43 4.2.3 Unit hydrograph implementation with forecast data . 45 5. Testing and Validation . 51 5.1 Graphical User Interface . 51 5.2 Model initialization . 56 5.2.1 Tributary initialization . 56 5.2.2 Ohio River pool initialization . 60 5.2.3 Running the Model . 61 5.3 Results . 64 6. Conclusions and Future Work . 68 6.1 Findings and Conclusions . 68 6.2 Future Work . 68 Appendices A. Model Inputs . 70 Bibliography . 91 vii LIST OF TABLES Table Page 1.1 Ohio River Navigational Dams. 2 1.2 The hydroelectric dams that are owned by AMP with their production specifications. 5 3.1 Land-use/ Land-cover description, Manning's n coefficient, and inter- ception depth provided by the USGS. 32 3.2 Soil infiltration parameters provided by the USGS. 32 A.1 List of the tributary rivers in the Pittsburgh USACE Engineering dis- trict being fed into the Ohio River model. Tributaries with an * next to the description have forecast discharge data provided by the National Weather Service AHPS. 70 A.2 List of the tributary rivers in the Huntington USACE Engineering district being fed into the Ohio River model. Tributaries with an * next to the description have forecast discharge data provided by the National Weather Service AHPS. 71 A.3 List of the tributary rivers in the Louisville USACE Engineering dis- trict being fed into the Ohio River model. Tributaries with an * next to the description have forecast discharge data provided by the National Weather Service AHPS. 72 A.4 Stage height gauges along the Ohio River used to initialize the model. 73 viii LIST OF FIGURES Figure Page 1.1 A map of the U.S. Army Corps of Engineers operated locks and dams along the Ohio River courtesy of the U.S. Army Corps of Engineers. 3 2.1 Simple schematic of a watershed of horizontal extent Ω, with boundary @Ω indicated by the thick black line. In hydrologic modeling, the watershed's drainage network (the set of dashed blue lines denoted by !) is typically represented as a set of connected line segments !i. The inset (right) shows a simple example of how junctions are handled in the numerical model; see discussion in Section 2.2.1. 12 2.2 An illustration of the multidimensional coupling that is accomplished by simply setting qL = q · n at the common 1D and 2D (edge) Gauss{ Lobatto integration points. 17 b 2.3 The channel network (blue lines) and watershed boundary (black lines) extracted from a sample DEM using TopoToolbox. 19 2.4 Insets showing the original representations of the channel network (left, blue line) and watershed boundary (right, black line) obtained from the DEM and the spline approximations (red lines) used in Admesh+. 21 2.5 Example of a finite element mesh generated automatically by Admesh+, where the red lines indicate the constrained channel network. 22 2.6 A three-dimensional profile view of a finite element mesh produced by Admesh+ for a sample watershed, where blue lines indicate edges that are part of the original constrained channel network, red lines indicate one-dimensional overland flow routing edges and large open arrows indicate flow direction over each element face. The sketch to the right illustrates a converging edge. 24 ix 3.1 A typical UTM map projection around the world. 28 3.2 An example of a Digital Elevation Model (green line) being combined with the raw cross section (blue line) to produce a complete river cross section. 31 3.3 The stage height interpolation from a known tailwater to a known headwater. 34 4.1 A comparison of threat scores of the leading forecasting products over the last year using 6-hour temporal resolution for volumes of rainfall of 0.25 inches [4]. 39 4.2 A comparison of threat scores of the leading forecasting products over the last year using 6-hour temporal resolution for volumes of rainfall of 0.5 inches [4]. 40 4.3 A typical unit hydrograph with an instantaneous precipitation event at time t = 0. 41 4.4 An example of the average hydrographs that are produced as depicted by the red asterisk line on top of the rainfall-runoff events in a given volume theshold. 45 4.5 The rainfall that falls within the watershed of USGS tributary station # 03159540 Shade River near Chester, Ohio are depicted as black circles. The tributary boundary is the black surrounding polygon and the outlet is the orange dot. 47 4.6 A hydrograph created for input to the USGS tributary station # 03159540 Shade River near Chester, Ohio. This hydrograph depicts a single storm event. 49 4.7 A hydrograph created for input to the USGS tributary station # 03612000 Cache River at Froman, Illinois. This hydrograph depicts two combined storm events separated by about one full day of no rain- fall. 50 5.1 The Graphical User Interface that will be provided to AMP, on Eleva- tion view. 52 x 5.2 The mesh from the GUI on Land-Cover view. 53 5.3 The mesh from the GUI on Soil Data view. 54 5.4 The complete Ohio River watershed boundary is represented by the bold red line. The stream networks are displayed as well, with the streamline magnitudes defined on the left. The boundary and stream- lines were provided by the USGS Elevation Derivatives for National Applications (EDNA). 55 5.5 Example of the rectangular channel cross section geometry. 57 5.6 A sample dQ vs. Qin correction fit. 63 5.7 The headwater and tailwater results at Montgomery Island Lock and Dam. Observed stage height is represented by the orange line, the DG model results by the blue line, and the gray shaded region is a ±0.5 foot envelope around the observed data. 65 5.8 The headwater and tailwater results at New Cumberland Lock and Dam.