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Regression Equations NDOR Research Project Number SPR-1(2) P541 Transportation Research Studies REGRESSION EQUATIONS Branden J. Strahm and David M. Admiraal University of Nebraska – Lincoln W355 Nebraska Hall Lincoln, NE 68588-0531 Telephone (402) 472-8568 FAX (402) 472-8934 Sponsored by The Nebraska Department of Roads 1500 Nebraska Highway 2 Lincoln, Nebraska 68509-4567 Telephone (402) 479-4337 FAX (402) 479-3975 August 2005 Technical Report Documentation Page 1. Report No. 2. Government Accession No. 3. Recipient’s Catalog No. SPR-1(2) P541 4. Title and Subtitle 5. Report Date Regression Equations August 2005 6. Performing Organization Code 7. Author/s 8. Performing Organization Report No. Branden J. Strahm and David M. Admiraal 9. Performing Organization Name and Address 10. Work Unit No. (TRAIS) Department of Civil Engineering University of Nebraska – Lincoln 11. Contract or Grant No. W348 Nebraska Hall SPR-1(2) P541 Lincoln, NE 68588-0531 12. Sponsoring Organization Name and Address 13. Type of Report and Period Covered U.S. Department of Transportation Final Report Research and Special Programs Administration 400 7th Street, SW Washington, DC 20590-0001 14. Sponsoring Agency Code 15. Supplementary Notes 16. Abstract Regional regression equations were developed to estimate peak-flow magnitudes using Geographic Information systems (GIS). Peak discharges were estimated at return intervals ranging from 2- to 500-years in Nebraska. Flow data from gaging stations located in or within 50 miles of Nebraska were collected. Regional regression analysis, using weighted-least squares (WLS) regression and data from 273 gaging stations, were used to develop equations for seven hydrologic regions. The WLS regression accounted for the differences in record lengths of the annual peak streamflows between sites. Contributing drainage areas ranged from 0.42 to 6,230 mi2. The equations can be used to estimate peak discharges for selected return periods at sites without flow data. Digital Elevation Models (DEMs) were the primary data used to extract basin characteristics. The DEMs used in this project are based on 30 m by 30 m data spacing intervals with a Universal Transverse Mercator projection, and are commercially available from the USGS. Morphometric basin characteristics were extracted using ArcInfo software. The DEMs reduced processing time and improved the accuracy of the physical basin characteristics. Soil characteristics were used to improve the accuracy of the regression equations while precipitation data were found to be of lower statistical importance than other characteristics. Regression equations were developed for seven hydrologic regions in Nebraska. Two sets of regression equations were developed for each region: one representative of basins with drainage areas of less than 10 mi2 and one for the complete range of drainage areas. The standard error of estimate for the 10- and 25-year frequency equations ranged from 24 to 93 percent for the complete range of drainage areas. The equations for basins with areas of less than 10 mi2 had a standard error of estimate for the 10- and 25-year return period of 22 to 75 percent. Based on standard error estimates and comparison with other methods, the regression equations worked best for regions located in eastern Nebraska. The equations for western Nebraska regions do not estimate peak flows as accurately because of insufficient peak flow data and high spatial variability of basin attributes. 17. Key Words 18. Distribution Statement Nebraska regression equations, No Restrictions. This document is available to the public peak stream flow prediction, from the sponsoring agency. small watersheds, GIS 19. Security Classification (of this report) 20. Security Classification (of this page) 21. No. Of Pages 22. Price Unclassified Unclassified 145 Form DOT F 1700.7 (8-72) Reproduction of form and completed page is authorized. ii ABSTRACT Regional regression equations were developed to estimate peak-flow magnitudes using Geographic Information systems (GIS). Peak discharges were estimated at return intervals ranging from 2- to 500-years in Nebraska. Flow data from gaging stations located in or within 50 miles of Nebraska were collected. Regional regression analysis, using weighted-least squares (WLS) regression and data from 273 gaging stations, were used to develop equations for seven hydrologic regions. The WLS regression accounted for the differences in record lengths of the annual peak streamflows between sites. Contributing drainage areas ranged from 0.42 to 6,230 mi2. The equations can be used to estimate peak discharges for selected return periods at sites without flow data. Digital Elevation Models (DEMs) were the primary data used to extract basin characteristics. The DEMs used in this project are based on 30 m by 30 m data spacing intervals with a Universal Transverse Mercator projection, and are commercially available from the USGS. Morphometric basin characteristics were extracted using ArcInfo software. The DEMs reduced processing time and improved the accuracy of the physical basin characteristics. Soil characteristics were used to improve the accuracy of the regression equations while precipitation data were found to be of lower statistical importance than other characteristics. Regression equations were developed for seven hydrologic regions in Nebraska. Two sets of regression equations were developed for each region: one representative of basins with drainage areas of less than 10 mi2 and one for the complete range of drainage areas. The standard error of estimate for the 10- and 25-year frequency equations ranged from 24 to 93 percent for the complete range of drainage areas. The equations for basins with areas of less than 10 mi2 had a standard error of estimate for the 10- and 25-year return period of 22 to 75 percent. Based on standard error estimates and comparison with other methods, the regression equations worked best for regions located in eastern Nebraska. The equations for western Nebraska regions do not estimate peak flows as accurately because of insufficient peak flow data and high spatial variability of basin attributes. iii DISCLAIMER The contents of this report reflect the views of the authors who are responsible for the facts and the accuracy of the data presented herein. The contents do not necessarily reflect the official views or policies of the Nebraska Department of Roads, the Federal Highway Administration, or the University of Nebraska-Lincoln. This report does not constitute a standard, specification, or regulation. Trade or manufacturers’ names, which may appear in this report, are cited only because they are considered essential to the objectives of the report. The U.S. government and the State of Nebraska do not endorse products or manufacturers. iv ACKNOWLEDGMENTS This research project would not have been possible without the funding provided by the Nebraska Department of Roads. We would also like to thank the engineers at the Department of Roads for their assistance with this project, and especially Kevin Donahoo and Robert Carnazzo for providing us with project data and administrative advice. We also appreciate the assistance of the Department of Natural Resources of the State of Nebraska and The Conservation and Survey Division of the University of Nebraska, who provided us with much of the electronic data and technical advice that we needed to complete this project. v TABLE OF CONTENTS ABSTRACT...................................................................................................................................iii DISCLAIMER ............................................................................................................................... iv ACKNOWLEDGMENTS .............................................................................................................. v TABLE OF CONTENTS...............................................................................................................vi LIST OF FIGURES ....................................................................................................................... ix LIST OF TABLES......................................................................................................................... xi 1. INTRODUCTION ...................................................................................................................... 1 1.1 Background........................................................................................................................... 1 1.2 Regression Analysis.............................................................................................................. 2 1.3 Purpose.................................................................................................................................. 2 1.4 Outline of Other Chapters..................................................................................................... 3 2. LITERATURE REVIEW ........................................................................................................... 4 2.1 Regionalization ..................................................................................................................... 4 2.1.1 Nebraska Regions ..........................................................................................................4 2.1.2 Data Splitting ................................................................................................................. 5 2.1.3 Regionalization Methods ..............................................................................................
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