Streamflow Statistics for Unregulated and Regulated Conditions for Selected Locations on the Upper Yellowstone and Bighorn Rivers, Montana and Wyoming, 1928–2002

Prepared in cooperation with the Yellowstone River Conservation District Council and the U.S. Army Corps of Engineers

Scientific Investigations Report 2014–5115

U.S. Department of the Interior U.S. Geological Survey Front cover. Yellowstone River downstream from Highway 89 Bridge, Montana. Photograph by Katherine Chase, U.S. Geological Survey (USGS) , May 14, 2014.

Back cover. Looking west at the Yellowstone River and Crazy Mountains, near Big Timber, Montana. Photograph by Katherine Chase, USGS, May 14, 2014. Streamflow Statistics for Unregulated and Regulated Conditions for Selected Locations on the Upper Yellowstone and Bighorn Rivers, Montana and Wyoming, 1928–2002

By Katherine J. Chase

Prepared in cooperation with the Yellowstone River Conservation District Council and the U.S. Army Corps of Engineers

Scientific Investigations Report 2014–5115

U.S. Department of the Interior U.S. Geological Survey U.S. Department of the Interior SALLY JEWELL, Secretary U.S. Geological Survey Suzette M. Kimball, Acting Director

U.S. Geological Survey, Reston, Virginia: 2014

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Suggested citation: Chase, K.J., 2014, Streamflow statistics for unregulated and regulated conditions for selected locations on the Upper Yellowstone and Bighorn Rivers, Montana and Wyoming, 1928–2002: U.S. Geological Survey Scientific Investigations Report 2014–5115, 117 p., http://dx.doi.org/10.3133/sir20145115.

ISSN 2328-0328 (online) iii

Acknowledgments

The author appreciates the assistance of Douglas J. Clemetson and Roger L. Kay, both of the U.S. Army Corps of Engineers.

Special thanks are given to Steven K. Sando of the U.S. Geological Survey Wyoming-Montana Water Science Center and Daniel G. Driscoll of the U.S. Geological Survey South Dakota Water Science Center. iv

Contents

Acknowledgments...... iii Abstract...... 1 Introduction...... 1 Purpose and Scope...... 4 Description of Study Area...... 4 Methods for Calculating Streamflow Statistics for Unregulated and Regulated Conditions...... 4 Streamflow Conditions Analyzed...... 5 Depletion Estimates...... 6 Low-Flow Frequency Analysis...... 6 Monthly and Annual Streamflow Characteristics...... 7 Interpolation of Low-Flow Statistics for Locations Between Streamflow-Gaging Stations...... 7 Streamflow Statistics for Unregulated and Regulated Conditions for Selected Locations on the Upper Yellowstone and Bighorn Rivers...... 7 Summary...... 9 References Cited...... 9 Glossary...... 11 Appendixes...... 13 Appendix 1. Statistics for Unregulated and Regulated Streamflow Conditions for Selected Streamflow-Gaging Stations on the Upper Yellowstone and Bighorn Rivers, Montana and Wyoming, 1928–2002...... 14 Appendix 1–1. Statistics for streamflow-gaging station 06186500 (Yellowstone River at Yellowstone Lake Outlet, Yellowstone National Park, Wyoming)...... 15 Appendix 1–2. Statistics for streamflow-gaging station 06191500 (Yellowstone River at Corwin Springs, Montana)...... 26 Appendix 1–3. Statistics for streamflow-gaging station 06192500 (Yellowstone River near Livingston, Montana)...... 37 Appendix 1–4. Statistics for streamflow-gaging station 06214500 (Yellowstone River at Billings, Montana)...... 57 Appendix 1–5. Statistics for streamflow-gaging station 06294500 (Bighorn River above Tullock Creek, near Bighorn, Montana)...... 77 Appendix 1–6. Statistics for streamflow-gaging station 06295000 (Yellowstone River at Forsyth, Montana)...... 97 Appendix 2. Locations, Drainage Areas, and Annual n-day Low-Flow Frequency Data for Unregulated and Regulated Streamflow Conditions at Selected Locations on the Yellowstone River, Montana and Wyoming, 1928–2002...... 117 v

Figures

1. Map showing location of the Yellowstone River Basin in Montana, Wyoming, and North Dakota...... 2 2. Map showing location of study subbasins in Montana, Wyoming, and North Dakota, and Bureau of Reclamation depletion node basins and streamflow-gaging stations in Montana and Wyoming...... 3 3. Map showing location of selected reaches along the Yellowstone River, Montana...... 8

Appendix Figures

1–1–1. Graph showing annual n-day low-flow frequency data for streamflow-gaging station 06186500 (Yellowstone River at Yellowstone Lake Outlet, Yellowstone National Park, Wyoming) for unregulated streamflow conditions, 1928–2002...... 17 1–1–2. Graph showing winter (January–March) n-day low-flow frequency data for streamflow-gaging station 06186500 (Yellowstone River at Yellowstone Lake Outlet, Yellowstone National Park, Wyoming) for unregulated streamflow conditions, 1928–2002...... 17 1–1–3. Graph showing spring (April–June) n-day low-flow frequency data for streamflow-gaging station 06186500 (Yellowstone River at Yellowstone Lake Outlet, Yellowstone National Park, Wyoming) for unregulated streamflow conditions, 1928–2002...... 18 1–1–4. Graph showing summer (July–September) n-day low-flow frequency data for streamflow-gaging station 06186500 (Yellowstone River at Yellowstone Lake Outlet, Yellowstone National Park, Wyoming) for unregulated streamflow conditions, 1928–2002...... 18 1–1–5. Graph showing fall (October–December) n-day low-flow frequency data for streamflow-gaging station 06186500 (Yellowstone River at Yellowstone Lake Outlet, Yellowstone National Park, Wyoming) for unregulated streamflow conditions, 1928–2002...... 19 1–1–6. Graph showing January 7-day low-flow frequency data for streamflow-gaging station 06186500 (Yellowstone River at Yellowstone Lake Outlet, Yellowstone National Park, Wyoming) for unregulated streamflow conditions, 1928–2002...... 19 1–1–7. Graph showing February 7-day low-flow frequency data for streamflow-gaging station 06186500 (Yellowstone River at Yellowstone Lake Outlet, Yellowstone National Park, Wyoming) for unregulated streamflow conditions, 1928–2002...... 20 1–1–8. Graph showing March 7-day low-flow frequency data for streamflow-gaging station 06186500 (Yellowstone River at Yellowstone Lake Outlet, Yellowstone National Park, Wyoming) for unregulated streamflow conditions, 1928–2002...... 20 1–1–9. Graph showing April 7-day low-flow frequency data for streamflow-gaging station 06186500 (Yellowstone River at Yellowstone Lake Outlet, Yellowstone National Park, Wyoming) for unregulated streamflow conditions, 1928–2002...... 21 1–1–10. Graph showing May 7-day low-flow frequency data for streamflow-gaging station 06186500 (Yellowstone River at Yellowstone Lake Outlet, Yellowstone National Park, Wyoming) for unregulated streamflow conditions, 1928–2002...... 21 1–1–11. June 7-day low-flow frequency data for streamflow-gaging station 06186500 (Yellowstone River at Yellowstone Lake Outlet, Yellowstone National Park, Wyoming) for unregulated streamflow conditions, 1928–2002...... 22 vi

1–1–12. Graph showing July 7-day low-flow frequency data for streamflow-gaging station 06186500 (Yellowstone River at Yellowstone Lake Outlet, Yellowstone National Park, Wyoming) for unregulated streamflow conditions, 1928–2002...... 22 1–1–13. Graph showing August 7-day low-flow frequency data for streamflow-gaging station 06186500 (Yellowstone River at Yellowstone Lake Outlet, Yellowstone National Park, Wyoming) for unregulated streamflow conditions, 1928–2002...... 23 1–1–14. Graph showing September 7-day low-flow frequency data for streamflow-gaging station 06186500 (Yellowstone River at Yellowstone Lake Outlet, Yellowstone National Park, Wyoming) for unregulated streamflow conditions, 1928–2002...... 23 1–1–15. Graph showing October 7-day low-flow frequency data for streamflow-gaging station 06186500 (Yellowstone River at Yellowstone Lake Outlet, Yellowstone National Park, Wyoming) for unregulated streamflow conditions, 1928–2002...... 24 1–1–16. Graph showing November 7-day low-flow frequency data for streamflow-gaging station 06186500 (Yellowstone River at Yellowstone Lake Outlet, Yellowstone National Park, Wyoming) for unregulated streamflow conditions, 1928–2002...... 24 1–1–17. Graph showing December 7-day low-flow frequency data for streamflow-gaging station 06186500 (Yellowstone River at Yellowstone Lake Outlet, Yellowstone National Park, Wyoming) for unregulated streamflow conditions, 1928–2002...... 25 1–2–1. Graph showing annual n-day low-flow frequency data for streamflow-gaging station 06191500 (Yellowstone River at Corwin Springs, Montana) for unregulated streamflow conditions, 1928–2002...... 28 1–2–2. Graph showing winter (January–March) n-day low-flow frequency data for streamflow-gaging station 06191500 (Yellowstone River at Corwin Springs, Montana) for unregulated streamflow conditions, 1928–2002...... 28 1–2–3. Graph showing spring (April–June) n-day low-flow frequency data for streamflow-gaging station 06191500 (Yellowstone River at Corwin Springs, Montana) for unregulated streamflow conditions, 1928–2002...... 29 1–2–4. Graph showing summer (July–September) n-day low-flow frequency data for streamflow-gaging station 06191500 (Yellowstone River at Corwin Springs, Montana) for unregulated streamflow conditions, 1928–2002...... 29 1–2–5. Graph showing fall (October–December) 7-day low-flow frequency data for streamflow-gaging station 06191500 (Yellowstone River at Corwin Springs, Montana) for unregulated streamflow conditions, 1928–2002...... 30 1–2–6. Graph showing January 7-day low-flow frequency data for streamflow-gaging station 06191500 (Yellowstone River at Corwin Springs, Montana) for unregulated streamflow conditions, 1928–2002...... 30 1–2–7. Graph showing February 7-day low-flow frequency data for streamflow-gaging station 06191500 (Yellowstone River at Corwin Springs, Montana) for unregulated streamflow conditions, 1928–2002...... 31 1–2–8. Graph showing March 7-day low-flow frequency data for streamflow-gaging station 06191500 (Yellowstone River at Corwin Springs, Montana) for unregulated streamflow conditions, 1928–2002...... 31 1–2–9. Graph showing April 7-day low-flow frequency data for streamflow-gaging station 06191500 (Yellowstone River at Corwin Springs, Montana) for unregulated streamflow conditions, 1928–2002...... 32 1–2–10. Graph showing May 7-day low-flow frequency data for streamflow-gaging station 06191500 (Yellowstone River at Corwin Springs, Montana) for unregulated streamflow conditions, 1928–2002...... 32 vii

1–2–11. Graph showing June 7-day low-flow frequency data for streamflow-gaging station 06191500 (Yellowstone River at Corwin Springs, Montana) for unregulated streamflow conditions, 1928–2002...... 33 1–2–12. Graph showing July 7-day low-flow frequency data for streamflow-gaging station 06191500 (Yellowstone River at Corwin Springs, Montana) for unregulated streamflow conditions, 1928–2002...... 33 1–2–13. Graph showing August 7-day low-flow frequency data for streamflow-gaging station 06191500 (Yellowstone River at Corwin Springs, Montana) for unregulated streamflow conditions, 1928–2002...... 34 1–2–14. Graph showing September 7-day low-flow frequency data for streamflow-gaging station 06191500 (Yellowstone River at Corwin Springs, Montana) for unregulated streamflow conditions, 1928–2002...... 34 1–2–15. Graph showing October 7-day low-flow frequency data for streamflow-gaging station 06191500 (Yellowstone River at Corwin Springs, Montana) for unregulated streamflow conditions, 1928–2002...... 35 1–2–16. Graph showing November 7-day low-flow frequency data for streamflow-gaging station 06191500 (Yellowstone River at Corwin Springs, Montana) for unregulated streamflow conditions, 1928–2002...... 35 1–2–17. Graph showing December 7-day low-flow frequency data for streamflow-gaging station 06191500 (Yellowstone River at Corwin Springs, Montana) for unregulated streamflow conditions, 1928–2002...... 36 1–3–1. Graph showing annual n-day low-flow frequency data for streamflow-gaging station 06192500 (Yellowstone River near Livingston, Montana) for unregulated and regulated streamflow conditions, 1928–2002...... 40 1–3–2. Graph showing winter (January–March) n-day low-flow frequency data for streamflow-gaging station 06192500 (Yellowstone River near Livingston, Montana) for unregulated and regulated streamflow conditions, 1928–2002...... 41 1–3–3. Graph showing spring (April–June) n-day low-flow frequency data for streamflow-gaging station 06192500 (Yellowstone River near Livingston, Montana) for unregulated and regulated streamflow conditions, 1928–2002...... 42 1–3–4. Graph showing summer (July–September) n-day low-flow frequency data for streamflow-gaging station 06192500 (Yellowstone River near Livingston, Montana) for unregulated and regulated streamflow conditions, 1928–2002...... 43 1–3–5. Graph showing fall (October–December) n-day low-flow frequency data for streamflow-gaging station 06192500 (Yellowstone River near Livingston, Montana) for unregulated and regulated streamflow conditions, 1928–2002...... 44 1–3–6. Graph showing January 7-day low-flow frequency data for streamflow-gaging station 06192500 (Yellowstone River near Livingston, Montana) for unregulated and regulated streamflow conditions, 1928–2002...... 45 1–3–7. Graph showing February 7-day low-flow frequency data for streamflow-gaging station 06192500 (Yellowstone River near Livingston, Montana) for unregulated and regulated streamflow conditions, 1928–2002...... 46 1–3–8. Graph showing March 7-day low-flow frequency data for streamflow-gaging station 06192500 (Yellowstone River near Livingston, Montana) for unregulated and regulated streamflow conditions, 1928–2002...... 47 1–3–9. Graph showing April 7-day low-flow frequency data for streamflow-gaging station 06192500 (Yellowstone River near Livingston, Montana) for unregulated and regulated streamflow conditions, 1928–2002...... 48 viii

1–3–10. Graph showing May 7-day low-flow frequency data for streamflow-gaging station 06192500 (Yellowstone River near Livingston, Montana) for unregulated and regulated streamflow conditions, 1928–2002...... 49 1–3–11. Graph showing June 7-day low-flow frequency data for streamflow-gaging station 06192500 (Yellowstone River near Livingston, Montana) for unregulated and regulated streamflow conditions, 1928–2002...... 50 1–3–12. Graph showing July 7-day low-flow frequency data for streamflow-gaging station 06192500 (Yellowstone River near Livingston, Montana) for unregulated and regulated streamflow conditions, 1928–2002...... 51 1–3–13. Graph showing August 7-day low-flow frequency data for streamflow-gaging station 06192500 (Yellowstone River near Livingston, Montana) for unregulated and regulated streamflow conditions, 1928–2002...... 52 1–3–14. Graph showing September 7-day low-flow frequency data for streamflow-gaging station 06192500 (Yellowstone River near Livingston, Montana) for unregulated and regulated streamflow conditions, 1928–2002...... 53 1–3–15. Graph showing October 7-day low-flow frequency data for streamflow-gaging station 06192500 (Yellowstone River near Livingston, Montana) for unregulated and regulated streamflow conditions, 1928–2002...... 54 1–3–16. Graph showing November 7-day low-flow frequency data for streamflow-gaging station 06192500 (Yellowstone River near Livingston, Montana) for unregulated and regulated streamflow conditions, 1928–2002...... 55 1–3–17. Graph showing December 7-day low-flow frequency data for streamflow-gaging station 06192500 (Yellowstone River near Livingston, Montana) for unregulated and regulated streamflow conditions, 1928–2002...... 56 1–4–1. Graph showing annual n-day low-flow frequency data for streamflow-gaging station 06214500 (Yellowstone River at Billings, Montana) for unregulated and regulated streamflow conditions, 1928–2002...... 60 1–4–2. Graph showing winter (January–March) n-day low-flow frequency data for streamflow-gaging station 06214500 (Yellowstone River at Billings, Montana) for unregulated and regulated streamflow conditions, 1928–2002...... 61 1–4–3. Graph showing spring (April–June) n-day low-flow frequency data for streamflow-gaging station 06214500 (Yellowstone River at Billings, Montana) for unregulated and regulated streamflow conditions, 1928–2002...... 62 1–4–4. Graph showing summer (July–September) n-day low-flow frequency data for streamflow-gaging station 06214500 (Yellowstone River at Billings, Montana) for unregulated and regulated streamflow conditions, 1928–2002...... 63 1–4–5. Graph showing fall (October–December) n-day low-flow frequency data for streamflow-gaging station 06214500 (Yellowstone River at Billings, Montana) for unregulated and regulated streamflow conditions, 1928–2002...... 64 1–4–6. Graph showing January 7-day low-flow frequency data for streamflow-gaging station 06214500 (Yellowstone River at Billings, Montana) for unregulated and regulated streamflow conditions, 1928–2002...... 65 1–4–7. Graph showing February 7-day low-flow frequency data for streamflow-gaging station 06214500 (Yellowstone River at Billings, Montana) for unregulated and regulated streamflow conditions, 1928–2002...... 66 1–4–8. Graph showing March 7-day low-flow frequency data for streamflow-gaging station 06214500 (Yellowstone River at Billings, Montana) for unregulated and regulated streamflow conditions, 1928–2002...... 67 ix

1–4–9. Graph showing April 7-day low-flow frequency data for streamflow-gaging station 06214500 (Yellowstone River at Billings, Montana) for unregulated and regulated streamflow conditions, 1928–2002...... 68 1–4–10. Graph showing May 7-day low-flow frequency data for streamflow-gaging station 06214500 (Yellowstone River at Billings, Montana) for unregulated and regulated streamflow conditions, 1928–2002...... 69 1–4–11. Graphs showing June 7-day low-flow frequency data for streamflow-gaging station 06214500 (Yellowstone River at Billings, Montana) for unregulated and regulated streamflow conditions, 1928–2002...... 70 1–4–12. Graphs showing July 7-day low-flow frequency data for streamflow-gaging station 06214500 (Yellowstone River at Billings, Montana) for unregulated and regulated streamflow conditions, 1928–2002...... 71 1–4–13. Graphs showing August 7-day low-flow frequency data for streamflow-gaging station 06214500 (Yellowstone River at Billings, Montana) for unregulated and regulated streamflow conditions, 1928–2002...... 72 1–4–14. Graphs showing September 7-day low-flow frequency data for streamflow-gaging station 06214500 (Yellowstone River at Billings, Montana) for unregulated and regulated streamflow conditions, 1928–2002...... 73 1–4–15. Graphs showing October 7-day low-flow frequency data for streamflow-gaging station 06214500 (Yellowstone River at Billings, Montana) for unregulated and regulated streamflow conditions, 1928–2002...... 74 1–4–16. Graphs showing November 7-day low-flow frequency data for streamflow-gaging station 06214500 (Yellowstone River at Billings, Montana) for unregulated and regulated streamflow conditions, 1928–2002...... 75 1–4–17. Graphs showing December 7-day low-flow frequency data for streamflow-gaging station 06214500 (Yellowstone River at Billings, Montana) for unregulated and regulated streamflow conditions, 1928–2002...... 76 1–5–1. Graphs showing annual n-day low-flow frequency data for streamflow-gaging station 06294500 (Bighorn River above Tullock Creek, near Bighorn, Montana) for unregulated and regulated streamflow conditions, 1928–2002...... 80 1–5–2. Graphs showing winter (January–March) n-day low-flow frequency data for streamflow-gaging station 06294500 (Bighorn River above Tullock Creek, near Bighorn, Montana) for unregulated and regulated streamflow conditions, 1928–2002...81 1–5–3. Graphs showing spring (April–June) n-day low-flow frequency data for streamflow-gaging station 06294500 (Bighorn River above Tullock Creek, near Bighorn, Montana) for unregulated and regulated streamflow conditions, 1928–2002...82 1–5–4. Graphs showing summer (July–September) n-day low-flow frequency data for streamflow-gaging station 06294500 (Bighorn River above Tullock Creek, near Bighorn, Montana) for unregulated and regulated streamflow conditions, 1928–2002...83 1–5–5. Graphs showing fall (October–December) n-day low-flow frequency data for streamflow-gaging station 06294500 (Bighorn River above Tullock Creek, near Bighorn, Montana) for unregulated and regulated streamflow conditions, 1928–2002...84 1–5–6. Graphs showing January 7-day low-flow frequency data for streamflow-gaging station 06294500 (Bighorn River above Tullock Creek, near Bighorn, Montana) for unregulated and regulated streamflow conditions, 1928–2002...... 85 1–5–7. Graphs showing February 7-day low-flow frequency data for streamflow-gaging station 06294500 (Bighorn River above Tullock Creek, near Bighorn, Montana) for unregulated and regulated streamflow conditions, 1928–2002...... 86 x

1–5–8. Graphs showing March 7-day low-flow frequency data for streamflow-gaging station 06294500 (Bighorn River above Tullock Creek, near Bighorn, Montana) for unregulated and regulated streamflow conditions, 1928–2002...... 87 1–5–9. Graphs showing April 7-day low-flow frequency data for streamflow-gaging station 06294500 (Bighorn River above Tullock Creek, near Bighorn, Montana) for unregulated and regulated streamflow conditions, 1928–2002...... 88 1–5–10. Graphs showing May 7-day low-flow frequency data for streamflow-gaging station 06294500 (Bighorn River above Tullock Creek, near Bighorn, Montana) for unregulated and regulated streamflow conditions, 1928–2002...... 89 1–5–11. Graphs showing June 7-day low-flow frequency data for streamflow-gaging station 06294500 (Bighorn River above Tullock Creek, near Bighorn, Montana) for unregulated and regulated streamflow conditions, 1928–2002...... 90 1–5–12. Graphs showing July 7-day low-flow frequency data for streamflow-gaging station 06294500 (Bighorn River above Tullock Creek, near Bighorn, Montana) for unregulated and regulated streamflow conditions, 1928–2002...... 91 1–5–13. Graphs showing August 7-day low-flow frequency data for streamflow-gaging station 06294500 (Bighorn River above Tullock Creek, near Bighorn, Montana) for unregulated and regulated streamflow conditions, 1928–2002...... 92 1–5–14. Graphs showing September 7-day low-flow frequency data for streamflow-gaging station 06294500 (Bighorn River above Tullock Creek, near Bighorn, Montana) for unregulated and regulated streamflow conditions, 1928–2002...... 93 1–5–15. Graphs showing October 7-day low-flow frequency data for streamflow-gaging station 06294500 (Bighorn River above Tullock Creek, near Bighorn, Montana) for unregulated and regulated streamflow conditions, 1928–2002...... 94 1–5–16. Graphs showing November 7-day low-flow frequency data for streamflow-gaging station 06294500 (Bighorn River above Tullock Creek, near Bighorn, Montana) for unregulated and regulated streamflow conditions, 1928–2002...... 95 1–5–17. Graphs showing December 7-day low-flow frequency data for streamflow-gaging station 06294500 (Bighorn River above Tullock Creek, near Bighorn, Montana) for unregulated and regulated streamflow conditions, 1928–2002...... 96 1–6–1. Graphs showing annual n-day low-flow frequency data for streamflow-gaging station 06295000 (Yellowstone River at Forsyth, Montana) for unregulated and regulated streamflow conditions, 1928–2002...... 100 1–6–2. Graphs showing winter (January–March) n-day low-flow frequency data for streamflow-gaging station 06295000 (Yellowstone River at Forsyth, Montana) for unregulated and regulated streamflow conditions, 1928–2002...... 101 1–6–3. Graphs showing spring (April–June) n-day low-flow frequency data for streamflow-gaging station 06295000 (Yellowstone River at Forsyth, Montana) for unregulated and regulated streamflow conditions, 1928–2002...... 102 1–6–4. Graphs showing summer (July–September) n-day low-flow frequency data for streamflow-gaging station 06295000 (Yellowstone River at Forsyth, Montana) for unregulated and regulated streamflow conditions, 1928–2002...... 103 1–6–5. Graphs showing fall (October–December) n-day low-flow frequency data for streamflow-gaging station 06295000 (Yellowstone River at Forsyth, Montana) for unregulated and regulated streamflow conditions, 1928–2002...... 104 1–6–6. Graphs showing January 7-day low-flow frequency data for streamflow-gaging station 06295000 (Yellowstone River at Forsyth, Montana) for unregulated and regulated streamflow conditions, 1928–2002...... 105 xi

1–6–7. Graphs showing February 7-day low-flow frequency data for streamflow-gaging station 06295000 (Yellowstone River at Forsyth, Montana) for unregulated and regulated streamflow conditions, 1928–2002...... 106 1–6–8. Graphs showing March 7-day low-flow frequency data for streamflow-gaging station 06295000 (Yellowstone River at Forsyth, Montana) for unregulated and regulated streamflow conditions, 1928–2002...... 107 1–6–9. Graphs showing April 7-day low-flow frequency data for streamflow-gaging station 06295000 (Yellowstone River at Forsyth, Montana) for unregulated and regulated streamflow conditions, 1928–2002...... 108 1–6–10. Graphs showing May 7-day low-flow frequency data for streamflow-gaging station 06295000 (Yellowstone River at Forsyth, Montana) for unregulated and regulated streamflow conditions, 1928–2002...... 109 1–6–11. Graphs showing June 7-day low-flow frequency data for streamflow-gaging station 06295000 (Yellowstone River at Forsyth, Montana) for unregulated and regulated streamflow conditions, 1928–2002...... 110 1–6–12. Graphs showing July 7-day low-flow frequency data for streamflow-gaging station 06295000 (Yellowstone River at Forsyth, Montana) for unregulated and regulated streamflow conditions, 1928–2002...... 111 1–6–13. Graphs showing August 7-day low-flow frequency data for streamflow-gaging station 06295000 (Yellowstone River at Forsyth, Montana) for unregulated and regulated streamflow conditions, 1928–2002...... 112 1–6–14. Graphs showing September 7-day low-flow frequency data for streamflow-gaging station 06295000 (Yellowstone River at Forsyth, Montana) for unregulated and regulated streamflow conditions, 1928–2002...... 113 1–6–15. Graphs showing October 7-day low-flow frequency data for streamflow-gaging station 06295000 (Yellowstone River at Forsyth, Montana) for unregulated and regulated streamflow conditions, 1928–2002...... 114 1–6–16. Graphs showing November 7-day low-flow frequency data for streamflow-gaging station 06295000 (Yellowstone River at Forsyth, Montana) for unregulated and regulated streamflow conditions, 1928–2002...... 115 1–6–17. Graphs showing December 7-day low-flow frequency data for streamflow-gaging station 06295000 (Yellowstone River at Forsyth, Montana) for unregulated and regulated streamflow conditions, 1928–2002...... 116

Tables

1. Information for selected streamflow-gaging stations in the Yellowstone River Basin, Montana and Wyoming...... 5 xii

Appendix Tables

1–1–1. Annual, seasonal, and monthly n-day low-flow frequency data for streamflow-gaging station 06186500 (Yellowstone River at Yellowstone Lake Outlet, Yellowstone National Park, Wyoming) for unregulated streamflow conditions, 1928–2002...... 15 1–1–2. Monthly and annual streamflow characteristics for streamflow-gaging station 06186500 (Yellowstone River at Yellowstone Lake Outlet, Yellowstone National Park, Wyoming) for unregulated streamflow conditions, 1928–2002...... 16 1–2–1. Annual, seasonal, and monthly n-day low-flow frequency data for streamflow-gaging station 06191500 (Yellowstone River at Corwin Springs, Montana) for unregulated streamflow conditions, 1928–2002...... 26 1–2–2. Monthly and annual streamflow characteristics for streamflow-gaging station 06191500 (Yellowstone River at Corwin Springs, Montana) for unregulated streamflow conditions, 1928–2002...... 27 1–3–1. Annual, seasonal, and monthly n-day low-flow frequency data for streamflow-gaging station 06192500 (Yellowstone River near Livingston, Montana) for unregulated and regulated streamflow conditions, 1928–2002...... 37 1–3–2. Monthly and annual streamflow characteristics for streamflow-gaging station 06192500 (Yellowstone River near Livingston, Montana) for unregulated and regulated streamflow conditions, 1928–2002...... 39 1–4–1. Annual, seasonal, and monthly n-day low-flow frequency data for streamflow-gaging station 06214500 (Yellowstone River at Billings, Montana) for unregulated and regulated streamflow conditions, 1928–2002 ...... 57 1–4–2. Monthly and annual streamflow characteristics for streamflow-gaging station 06214500 (Yellowstone River at Billings, Montana) for unregulated and regulated streamflow conditions, 1928–2002...... 59 1–5–1. Annual, seasonal, and monthly n-day low-flow frequency data for streamflow-gaging station 06294500 (Bighorn River above Tullock Creek, near Bighorn, Montana) for unregulated and regulated streamflow conditions, 1928–2002...... 77 1–5–2. Monthly and annual streamflow characteristics for streamflow-gaging station 06294500 (Bighorn River above Tullock Creek, near Bighorn, Montana) for unregulated and regulated streamflow conditions, 1928–2002...... 79 1–6–1. Annual, seasonal, and monthly n-day low-flow frequency data for streamflow-gaging station 06295000 (Yellowstone River at Forsyth, Montana) for unregulated and regulated streamflow conditions, 1928–2002...... 97 1–6–2. Monthly and annual streamflow characteristics for streamflow-gaging station 06295000 (Yellowstone River at Forsyth, Montana) for unregulated and regulated streamflow conditions, 1928–2002...... 99 xiii

Conversion Factors

Inch/Pound to SI

Multiply By To obtain Length inch (in.) 2.54 centimeter (cm) inch (in.) 25.4 millimeter (mm) foot (ft) 0.3048 meter (m) mile (mi) 1.609 kilometer (km) Area acre 4,047 square meter (m2) acre 0.4047 hectare (ha) acre 0.4047 square hectometer (hm2) acre 0.004047 square kilometer (km2) square mile (mi2) 259.0 hectare (ha) square mile (mi2) 2.590 square kilometer (km2) acre-foot (acre-ft) 1,233 cubic meter (m3) Flow rate cubic foot per second (ft3/s) 0.02832 cubic meter per second (m3/s)

Temperature in degrees Fahrenheit (°F) may be converted to degrees Celsius (°C) as follows: °C = (°F-32)/1.8 Vertical coordinate information is referenced to the North American Vertical Datum of 1988 (NAVD 88). Horizontal coordinate information is referenced to the North American Datum of 1983 (NAD 83).

Abbreviations

CES cumulative effects study NAVD 88 North American Vertical Datum of 1988 Reclamation Bureau of Reclamation USACE U.S. Army Corps of Engineers USGS U.S. Geological Survey YRCDC Yellowstone River Conservation District Council

Streamflow Statistics for Unregulated and Regulated Streamflow Conditions for Selected Locations on the Upper Yellowstone and Bighorn Rivers, Montana and Wyoming, 1928–2002

By Katherine J. Chase

Abstract variety of agricultural, domestic, industrial, and recreational uses. Major floods in 1996 and 1997 intensified public debate Major floods in 1996 and 1997 intensified public debate about the effects of human activities on the Yellowstone River. about the effects of human activities on the Yellowstone River, In 1999, the Yellowstone River Conservation District Council and led to multidisciplinary efforts to understand the river’s was formed to address conservation issues on the river. The response to flood control, channel stabilization, and other con- Yellowstone River Conservation District Council partnered struction along the Yellowstone River corridor. In 1999, the with the U.S. Army Corps of Engineers to carry out a cumula- Yellowstone River Conservation District Council (YRCDC) tive effects study on the main stem of the Yellowstone River. was formed to address conservation issues on the river. The The cumulative effects study is intended to provide a basis for YRCDC partnered with the U.S. Army Corps of Engineers future management decisions within the watershed. Stream- (USACE) to carry out a cumulative effects study (CES) on flow statistics, such as flow-frequency data calculated for the Yellowstone River main stem. The CES is intended to unregulated and regulated streamflow conditions, are a neces- provide a scientific basis for future management decisions on sary component of the cumulative effects study. the Yellowstone. Streamflow statistics for unregulated and The U.S. Geological Survey, in cooperation with the regulated streamflow conditions along the Yellowstone River Yellowstone River Conservation District Council and the main stem are a necessary component of the CES. To facilitate U.S. Army Corps of Engineers, calculated low-flow frequency the data analyses for this study, the Yellowstone River Basin data and general monthly and annual statistics for unregulated was divided into five subbasins (fig. 2): (1) Upper Yellow- stone River subbasin, (2) Bighorn River subbasin, (3) Lower and regulated streamflow conditions for the Upper Yellow- Yellowstone River subbasin, (4) Tongue River subbasin, and stone and Bighorn Rivers for the 1928–2002 study period; (5) Powder River subbasin. For the purposes of this report, the these data are presented in this report. Unregulated streamflow Upper Yellowstone River is defined as the main stem Yel- represents flow conditions during the 1928–2002 study period lowstone River within the Upper Yellowstone River subbasin, if there had been no water-resources development in the Yel- and the Lower Yellowstone River is defined as the main stem lowstone River Basin. Regulated streamflow represents esti- Yellowstone River in the Lower Yellowstone River subbasin. mates of flow conditions during the 1928–2002 study period if Some streamflow statistics for unregulated and regu- the level of water-resources development existing in 2002 was lated conditions for selected locations in the Yellowstone in place during the entire study period. River Basin have been calculated by the USACE and by the U.S. Geological Survey (USGS). The USACE calculated peak-flow data, high-flow frequency data, and flow-duration Introduction data for unregulated and regulated streamflow conditions for the Yellowstone River main stem in the Upper Yellowstone The Yellowstone River is one of the longest free-flowing River subbasin and for the Bighorn River (fig. 2; U.S. Army rivers in the lower 48 states, draining about 70,000 square Corps of Engineers, 2011a, b). The USGS calculated peak- miles (mi2) as it flows more than 600 miles (mi) from its origin flow data, high-flow frequency data, low-flow frequency data, east of Yellowstone National Park, Wyoming (Wyo.), through and flow-duration data for unregulated and regulated stream- Montana (Mont.) to the confluence with the Missouri River flow conditions for the Yellowstone River main stem in the in North Dakota (Jean and Crispin, 2001; U.S. Geological Lower Yellowstone River subbasin and for the Tongue and Survey, 2010; fig. 1). The Yellowstone River supports a wide Powder Rivers (Chase, 2013). 2 Streamflow Statistics for the Upper Yellowstone and Bighorn Rivers, Montana and Wyoming, 1928–2002

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Figure 1. Location of the Yellowstone River Basin in Montana, Wyoming, and North Dakota. Introduction 3

111º 110º 109º 108º 107º 106º 105º 104º

EXPLANATION

Bureau of Reclamation node basin names and numbers

Yellowstone River at Billings, Mont. (35) Subbasin boundary ri River Missou Yellowstone River at Corwin Springs, Mont. (36) 48º Bureau of Reclamation Bighorn River at Bighorn, Mont. (37) depletion node Bighorn River at St. Xavier, Mont. (38) 06192500 U.S. Geological Survey streamflow-gaging 06329500 Wind River below Boysen Dam, Wyo. (39) station and number (table 1; station Bighorn River at Kane, Wyo. (40) numbers in italics from U.S. Army Corps Shoshone River below Buffalo Bill Dam, Wyo. (41) of Engineers (2011a, b) and Chase (2013) Tongue River at Miles City, Mont. (42) and are not shown in table 1) River Tongue River at Wyo.−Mont. Stateline (43) Powder River at Locate, Mont. (44) NORTH DAKOTA 47º Powder River at Moorhead, Mont. (45) MONTANA Yellowstone River at Sidney, Mont. (46) River subbasin Yellowstone06327500 Area not included in Bureau of Reclamation node basin for this study 06309000 Lower Yellowstone 06294700 06295000 River 06294500

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Figure 2. Location of study subbasins in Montana, Wyoming, and North Dakota, and Bureau of Reclamation depletion node basins and streamflow-gaging stations in Montana and Wyoming. Depletion node basins from U.S. Department of the Interior, Bureau of Reclamation (2005). 4 Streamflow Statistics for the Upper Yellowstone and Bighorn Rivers, Montana and Wyoming, 1928–2002

The U.S. Geological Survey, in cooperation with the River in North Dakota (fig. 1). Elevations in the drainage basin Yellowstone River Conservation District Council and the range from about 13,780 feet (ft) above the North American U.S. Army Corps of Engineers, calculated low-flow frequency Vertical Datum of 1988 (NAVD 88) in the mountains south of data and general monthly and annual statistics for unregulated Yellowstone National Park, to about 2,700 ft at the Yellow- and regulated streamflow conditions for the Upper Yellow- stone and Bighorn River confluence, to 1,850 ft at the Mis- stone and Bighorn Rivers for the 1928–2002 study period. souri River confluence (Zelt and others, 1999; U.S. Geological These data and statistics supplement the previous work by Survey, 2010). Major tributaries to the Yellowstone River USACE and USGS. include the Bighorn, Tongue, and Powder Rivers (fig. 1). Generally, the climate is semiarid with cold winters and warm summers. Based on climatic data for 1971–2000, Purpose and Scope monthly mean temperatures at Yellowstone Lake, Wyo. (fig. 1; elevation 7,870 ft above NAVD 88) ranged from -3.1 degrees The primary purpose of this report is to supplement the Fahrenheit (°F) in January to 70.4 °F in July. Monthly mean previous streamflow statistical summaries (U.S. Army Corps temperatures at Billings, Mont. (elevation 3,097 ft) ranged of Engineers, 2011a, b; Chase, 2013) by presenting low-flow from 13.3 °F in January to 88.4 °F in July. The mean annual frequency data and monthly and annual streamflow character- precipitation of 20.40 inches (in.) at Yellowstone Lake, Wyo., istics for four streamflow-gaging stations on the Upper Yel- lowstone River and for one streamflow-gaging station on the was distributed fairly evenly throughout the year, whereas Bighorn River for the 1928–2002 (calendar year) study period. about 46 percent of the mean annual precipitation (13.96 in.) These low-flow frequency data also were interpolated for 48 at Billings, Mont., fell from May to August (National Oceanic ungaged locations on the Upper Yellowstone River between and Atmospheric Administration, 2002). streamflow-gaging stations. For two of the four streamflow- The typical annual flow pattern for the Yellowstone River gaging stations on the Upper Yellowstone River, and for the upstream from Livingston, Mont., consists of a peak during streamflow-gaging station on the Bighorn River, data were the late spring/early summer mountain snowmelt (Zelt and calculated for two streamflow conditions: unregulated, where others, 1999). For the Yellowstone River downstream from effects of streamflow regulation and water use have been Billings, Mont., the typical annual flow pattern consists of a removed, and regulated, where streamflows are adjusted to lowland snowmelt peak during the late winter/early spring fol- represent near-present-day (based on 2002 data) levels of lowed by a peak from the mountain snowmelt during the late development. For two of the four streamflow-gaging stations spring/early summer (Zelt and others, 1999). Several short- to on the Upper Yellowstone River, data were calculated only for moderate-duration rainstorm peaks typically augment the unregulated conditions. spring/summer snowmelt peaks and the summer base flows. Additionally, low-flow frequency data and monthly and annual streamflow characteristics are presented for nine ungaged locations on the Lower Yellowstone River, between Methods for Calculating Streamflow the Bighorn River confluence and streamflow-gaging station 06295000 (Yellowstone River at Forsyth, Mont.) for unregu- Statistics for Unregulated and lated and regulated conditions. Low-flow frequency data and Regulated Conditions monthly and annual streamflow characteristics for streamflow- gaging station 06295000 (Yellowstone River at Forsyth, Observed daily streamflow records from USGS stream- Mont.) were presented in Chase (2013) and also are presented flow-gaging stations served as the basis for calculating the in this report. streamflow statistics. Daily mean streamflows (referred to Information for selected streamflow-gaging stations on herein as “daily streamflows”) for the Upper Yellowstone the Yellowstone and Bighorn Rivers is summarized in table 1; River and the Bighorn River were retrieved and analyzed locations of selected streamflow-gaging stations in the Yellow- using methods developed by the USACE and the USGS. stone River Basin are shown in figure 2. Selected streamflow- The USACE retrieved daily streamflows for selected USGS gaging stations outside of the Upper Yellowstone River streamflow-gaging stations (U.S. Geological Survey, 2010) subbasin also are included in figure 2 to facilitate association and organized the data into a USACE Hydrologic Engineering of this report with U.S. Army Corps of Engineers (2011a, b) Center Data Storage System database using the computer pro- and Chase (2013). gram HEC-DSSvue (U.S. Army Corps of Engineers, 2009a; Douglas J. Clemetson, U.S. Army Corps of Engineers, written Description of Study Area commun., 2011). The USACE also synthesized missing daily streamflows to develop a complete set of daily streamflows for The headwaters of the Yellowstone River are in northern the Upper Yellowstone River and Bighorn River streamflow- Wyoming, east of Yellowstone National Park. The river enters gaging stations for the 1928–2002 study period (U.S. Army Montana near the town of Gardiner and flows north and east Corps of Engineers, 2011a, b). The 1928–2002 study period across 500 mi of Montana to its confluence with the Missouri was chosen for this investigation because the USACE desired Methods for Calculating Streamflow Statistics for Unregulated and Regulated Conditions 5

Table 1. Information for selected streamflow-gaging stations in the Yellowstone River Basin, Montana and Wyoming (U.S. Geological Survey, 2010).

[--, no data]

Contributing Station Drainage area Period of record Streamflow condition(s) Station name drainage area number (square miles) (through 2010) analyzed (square miles)1 06186500 Yellowstone River at Yellowstone 991 -- 1922–82, 1983–86, 1988–2010 Unregulated2 -- Lake Outlet, Yellowstone National Park, Wyo. 06191500 Yellowstone River at Corwin 2,619 -- 1889–93, 1910–2010 Unregulated -- Springs, Mont. 06192500 Yellowstone River near Livings- 3,551 -- 1897–1905, 1928–32, 1937–2010 Unregulated Regulated3 ton, Mont. 06214500 Yellowstone River at Billings, 11,805 11,408 1904–05, 1928–2010 Unregulated Regulated Mont. 06294500 Bighorn River above Tullock 22,414 -- 1945–55, 1956–2010 Unregulated Regulated Creek near Bighorn, Mont. 06295000 Yellowstone River at Forsyth, 40,146 39,455 1921–23, 1977–2010 Unregulated Regulated Mont. 1Contributing area only specified for selected streamflow-gaging stations in U.S. Geological Survey (2010). 2Unregulated streamflow represents flow conditions that might have occurred during the 1928–2002 study period if there had been no water-resources development in the Yellowstone River Basin. 3Regulated streamflow represents estimates of flow conditions during the 1928–2002 study period if the level of water-resources development existing in 2002 was in place during the entire study period.

a 75-year study period, and Bureau of Reclamation (Reclama- removed (for the unregulated dataset) or modified to be uni- tion) depletions data (necessary to estimate unregulated and form through the study period (for the regulated dataset). Data regulated streamflows) only were available until 2002. Finally, homogeneity is an important criterion for the procedures used the USACE modified the daily streamflows to represent in the statistical analyses (U.S. Interagency Advisory Council unregulated and regulated streamflow conditions (U.S. Army on Water Data, 1982). Corps of Engineers, 2011a, b). Unregulated conditions represent estimates of stream- The USGS then used the USACE datasets to calculate flows during the 1928–2002 study period assuming there was low-flow frequency statistics for unregulated and regulated no water-resources development in the basin. Water-resources daily streamflows for 1928–2002 for this report. Low-flow development includes irrigation operations, reservoir opera- frequency statistics included annual n-day low-flow frequency tions, and other human-caused changes to the amount and tim- data, seasonal n-day low-flow frequency data, and monthly ing of streamflow. Historic depletions estimated by Reclama- 7-day low-flow frequency data, as discussed in the “Low-Flow tion (U.S. Department of the Interior Bureau of Reclamation, Frequency Analysis” section. 1999, 2005) and described in the section “Depletion Esti- mates,” account for changes to streamflow caused by water- Streamflow Conditions Analyzed resources development throughout the Yellowstone River Basin. Unregulated streamflows were estimated by adding the For three Yellowstone River streamflow-gaging sta- historic depletions estimated by Reclamation to the observed tions; 06192500 (Yellowstone River near Livingston, Mont.), streamflows. 06214500 (Yellowstone River at Billings, Mont.), and Regulated streamflows represent estimates of streamflows 06295000 (Yellowstone River at Forsyth, Mont.), and for the during the 1928–2002 study period assuming a uniform level Bighorn River streamflow gaging station 06294500 (Bighorn of water-resources development existing in 2002 and applied River above Tullock Creek near Bighorn, Mont.), streamflow throughout the entire study period. Regulated streamflows datasets were synthesized for two hypothetical streamflow were estimated by subtracting the “2002-level depletions” conditions: unregulated and regulated (table 1, figs.1 and (described in the section “Depletion Estimates”) from the 2). These datasets are more homogenous than the observed unregulated streamflows. streamflow datasets at sites affected by water-use develop- Because of minimal effects from regulation and deple- ment, because effects of changing water-use practices were tion, only unregulated streamflows were analyzed for 6 Streamflow Statistics for the Upper Yellowstone and Bighorn Rivers, Montana and Wyoming, 1928–2002 streamflow-gaging station 06186500 (Yellowstone River at that existed in 2002, which then were applied to each year Yellowstone Lake Outlet, Yellowstone National Park, Wyo.) during 1929–2002. Applying the 2002-level depletions to each and streamflow-gaging station 06191500 (Yellowstone River year accounts for effects of interannual climatic variability on at Corwin Springs, Mont.), which are the two most upstream water demand and consumptive use. Because Reclamation did sites on the Yellowstone River (table 1 and fig. 2). For both not develop depletion estimates for 1928, monthly depletions streamflow-gaging stations, the maximum difference between for 1928 (this study) were estimated from the monthly aver- unregulated and regulated flows was less than 2 cubic feet ages for the years 1929–1933 for the historic and 2002-level per second (ft3/s), which is less than 1 percent of the lowest depletions. The Reclamation 1929–2002 depletion data and unregulated flow during the study period (380 ft3/s). 1928 estimates are presented in appendix 1 in Chase (2013). As reported in Chase (2013), the U.S. Army Corps of Engi- Depletion Estimates neers (2011b) modified the monthly depletions calculated by Reclamation for the Bighorn River subbasin. These modified The U.S. Department of the Interior, Bureau of Reclama- depletions were used to calculate streamflows for unregulated tion (2005) developed estimates of historic and 2002-level and regulated streamflow conditions for this report. depletions for the entire Missouri River Basin for water years 1929–2002. Depletion estimates were developed for 118 node Low-Flow Frequency Analysis basins in the Missouri River Basin, which included 12 node basins (fig. 2) in the Yellowstone River Basin. The node basin Annual n-day low-flow frequency data were developed boundaries do not necessarily correspond with the subbasin from an annual series of the lowest daily streamflows for boundaries (fig. 2). For example, the Yellowstone River at n-day consecutive periods within each climatic year, from Sidney node basin includes the Lower Yellowstone River April 1 to March 31 (Riggs, 1972). For example, an annual subbasin and a part of the Upper Yellowstone River subbasin. series of 7-day low flows consists of the lowest mean flow Also, a small part of the Upper Yellowstone River subbasin that occurred during any 7-day consecutive period during each northwest of streamflow-gaging station 06214500 (Yellow- year of record. In addition, seasonal low-flow frequency data stone River at Billings, Mont.) was not included in any node were developed from the annual series of the lowest daily basins within the Yellowstone River Basin; this area corre- streamflows for 7- and 30-day consecutive periods for the sponds with the noncontributing drainage area of 691 mi2 at winter (January–March), spring (April–June), summer (July– streamflow-gaging station 06295000 (Yellowstone River at September) and fall (October–December) seasons. Monthly Forsyth, Mont.) (table 1; difference between drainage area and low-flow frequency data also were developed from the annual noncontributing drainage area). series of the lowest daily streamflows for7 -day consecutive The term “depletion” refers to changes to natural stream- periods for each month. flows that result from water-resources development. In almost The computer program HEC-SSP (U.S. Army Corps of all cases, water-resources development results in net decreases Engineers, 2010) was used to calculate the low-flow frequency in streamflow during periods of 1 or more years; however, some water-resources development (for example, reservoir relations for n-day datasets for unregulated and regulated and irrigation operations) can result in decreases in stream- streamflow conditions. The log-Pearson III distribution flow (relative to natural conditions) during specific times of (U.S. Interagency Advisory Council on Water Data, 1982) the year and increases in streamflow during other times of was used to estimate low-flow frequency data for consecutive the year. Thus, the term “depletion” as used in this report and periods of 7 and 30 days for recurrence intervals of 2, 5, 10, by Reclamation (U.S. Department of the Interior, Bureau of 25, 50, and 100 years. The 200- and 500-year low-flow fre- Reclamation, 2005) does not imply a decrease in streamflow, quency data were not estimated because the study period only especially on a seasonal basis. Positive depletions indicate includes 75 years of data, and USGS guidelines recommend decreases in streamflow relative to natural conditions, and limiting analyses to twice the period of record (Parrett, 1997; conversely, negative depletions indicate increases in stream- Walter Hofmann, U.S. Geological Survey, written commun., flow relative to natural conditions. 1973). Nonexceedance probabilities were calculated using The historic depletions determined by Reclamation only nonzero flows, then a conditional adjustment probability (U.S. Department of the Interior, Bureau of Reclamation, was used to adjust the non-exceedance probability for the zero 2005) included monthly estimates of irrigation operations, flows in the record. If the log-Pearson III distribution did not reservoir operations, and other water uses that existed each fit the data, then a Pearson III distribution (U.S. Interagency year during 1929–2002. Those estimates were based on Advisory Council on Water Data, 1982) was applied. If neither climatological records, the irrigation methods in use and the log-Pearson III nor the Pearson III distribution fit the data, number of irrigated acres, and municipal and industrial water a graphical curve was fit through the data. Where applicable, a uses for each year. The 2002-level depletions determined by graphical curve was determined by visually examining the pat- Reclamation were based on estimates of irrigation operations, tern of plotted points and estimating streamflow magnitudes reservoir operations, and municipal and industrial water uses at intersections of perceived uniform-fit lines and reported Streamflow Statistics for Unregulated and Regulated Conditions for Selected Locations 7 probability levels. Straight-line fits were applied between was largely focused on calculation of streamflow statistics at reported probability levels. gaging stations, and because streamflow data to improve interpolation are unavailable, the interpolated data are presented with those unrealistic decreases. Monthly and Annual Streamflow Characteristics Drainage areas for locations at the downstream end of each study reach were estimated using digital elevation Maxima, minima, and mean monthly and annual stream- models (cell size 689 square meters) provided by the USACE flows were calculated for unregulated and regulated conditions (Douglas J. Clemetson, U.S. Army Corps of Engineers, written using HEC-DSSvue (U.S. Army Corps of Engineers, 2009a). commun., 2009). For study reach A12, which includes the The standard deviations of the mean monthly streamflows and Stillwater River confluence, and for reach A17, which includes the mean annual streamflows also were calculated. the Clarks Fork Yellowstone confluence, the drainage areas were estimated for a location just upstream from each conflu- Interpolation of Low-Flow Statistics for ence. In some instances, the drainage areas estimated for the Locations Between Streamflow-Gaging Stations streamflow-gaging stations using the digital elevation models were different (by as much as 1 percent of total contribut- The Yellowstone River was divided into study reaches for ing drainage area) than the drainage areas reported by the the CES (fig. 3). For study reaches PC2, PC12, B2 and C10, U.S. Geological Survey (2010), probably because of differ- the statistics calculated at the streamflow-gaging station that is ences in the resolution of the elevation data and methods used located within or at the end of each reach represent the study- to delineate the drainage area boundaries. reach statistics. For the ungaged reaches on the Upper Yel- lowstone River main stem (48 reaches), low-flow frequency statistics were linearly interpolated between streamflow- Streamflow Statistics for Unregulated gaging stations. Low-flow frequency statistics interpolation was extended downstream, from streamflow-gaging station and Regulated Conditions for Selected 06214500 (Yellowstone River at Billings, Mont.) to stream- Locations on the Upper Yellowstone flow-gaging station 06295000 (Yellowstone River at Forsyth, Mont.) to supplement the results of Chase (2013). The Yel- and Bighorn Rivers lowstone River between Billings and Forsyth extends into the Lower Yellowstone River subbasin (fig. 2) and includes nine Streamflow statistics for 1928–2002 were calculated only ungaged reaches in the Lower Yellowstone River subbasin. for unregulated conditions for two streamflow-gaging sta- Monthly and annual streamflow characteristics are reported tions on the Upper Yellowstone River main stem; 06186500 for the streamflow-gaging stations but are not reported for the (Yellowstone River at Yellowstone Lake Outlet, Yellowstone ungaged reaches because some of these statistics (including National Park, Wyo.) and 06191500 (Yellowstone River at maximum and minimum values with associated months of Corwin Springs, Mont.). Streamflow statistics were calculated occurrence) cannot be accurately determined by interpolation. for unregulated and regulated conditions for the two other To be consistent with Chase (2013), streamflow statis- streamflow-gaging stations on the Upper Yellowstone River tics for ungaged reaches were linearly interpolated on the main stem; 06192500 (Yellowstone River near Livingston, basis of approximate drainage area at the downstream end Mont.), and 06214500 (Yellowstone River at Billings, Mont.), of each ungaged reach relative to the drainage areas of the and for the Bighorn River streamflow gaging station 06294500 bracketing streamflow-gaging stations. In many cases, such (Bighorn River above Tullock Creek near Bighorn, Mont.) as downstream from a relatively large tributary, changes in in the Upper Yellowstone River subbasin. Additionally, to streamflow statistics between different locations on a river provide information relating to calculation of interpolated channel do not vary linearly with proportional changes in estimates at ungaged locations and supplement the results of drainage area. Therefore, the interpolated statistics for reaches Chase (2013), streamflow statistics were calculated for one A18 and B1, [Clarks Fork Yellowstone River confluence to streamflow-gaging station on the Lower Yellowstone River streamflow-gaging station 06214500 (Yellowstone River at main stem; 06295000 (Yellowstone River at Forsyth, Mont.). Billings, Mont.)] and C1 through C9 [Bighorn River conflu- Streamflow statistics for the six streamflow-gaging stations are ence to streamflow-gaging station 06295000 (Yellowstone presented in tables and figures contained in appendix 1. The River at Forsyth, Mont.)], might not be as representative tables and graphs summarize annual, seasonal, and monthly of actual conditions as for the rest of the reaches. In fact, at n-day low-flow frequency data; and maxima, minima, and some locations a given streamflow statistic decreased between mean monthly and annual streamflow data. one streamflow-gaging station and the next downstream In addition, low-flow frequency data were interpolated streamflow-gaging station. In those locations, interpolation for 48 ungaged locations between streamflow-gaging sta- on the basis of drainage areas resulted in unrealistically large tions on the Upper Yellowstone River main stem, and for nine decreases in the streamflow statistic in reaches containing a ungaged locations on the Lower Yellowstone River to supple- large tributary (such as the Bighorn River). Because this study ment the results of Chase (2013). Interpolated annual n-day 8 Streamflow Statistics for the Upper Yellowstone and Bighorn Rivers, Montana and Wyoming, 1928–2002

111° 110° 109° 108° 107°

EXPLANATION 47° Yellowstone National Park

Upper Yellowstone River subbasin

Lower Yellowstone River subbasin PC17 Yellowstone River reach and reach number—Yellow and orange highlighting is alternated to distinguish adjacent reaches, for illustration purposes only Interpolation location 06214500 U.S. Geological Survey streamflow-gaging station and number C6 C5 C7 C8 C10 C4 C9 C2 B12 C3 River 06295000

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Base modified from U.S. Geological Survey Digital Line Graph (DLG), 1973, 1:2,000,000 0 25 50 MILES Lambert Conformal Conic projection Standard parallels 45°00' and 49°00' Central meridian –109°30' 0 25 50 KILOMETERS North American Datum of 1983 (NAD 83)

Figure 3. Location of selected reaches along the Yellowstone River, Montana (modified from Bryan Swindell, DTM Consulting, Inc., written commun., 2011). References Cited 9 low-flow frequency data for the 57 ungaged locations between water-resources development. Data homogeneity is an impor- streamflow-gaging stations, as well as calculated data for the tant criterion for the procedures used in the statistical analyses. 5 Yellowstone River streamflow-gaging stations used in the Because of minimal effects from regulation and deple- interpolations, are presented in appendix 2. tion, only unregulated streamflows were analyzed for streamflow-gaging station 06186500 (Yellowstone River at Yellowstone Lake Outlet, Yellowstone National Park, Wyo.) Summary and streamflow-gaging station 06191500 (Yellowstone River at Corwin Springs, Mont.), which are the two most upstream The Yellowstone River is one of the longest free-flowing sites on the Yellowstone River. For both streamflow-gaging rivers in the lower 48 states. The river supports a wide variety stations, the maximum difference between unregulated and of agricultural, domestic, industrial, and recreational uses. regulated flows was less than 2 cubic feet per second, which is Major floods in 1996 and 1997 intensified public debate about less than 1 percent of the lowest unregulated flow during the the effects of human activities on the Yellowstone River. In study period (380 cubic feet per second). 1999, the Yellowstone River Conservation District Council Low-flow frequency data were developed from an annual (YRCDC) was formed to address conservation issues on the series of lowest daily streamflows for specifiedn -day consecu- river. The YRCDC partnered with the U.S. Army Corps of tive periods within the calendar year. Monthly and annual Engineers (USACE) to carry out a cumulative effects study streamflow characteristics also were calculated for the unregu- (CES) on the main stem of the Yellowstone River. The CES is lated and regulated streamflows. intended to provide a basis for future management decisions in the watershed. Streamflow statistics, such as flow-frequency data calculated for unregulated and regulated streamflow conditions, are a necessary component of the cumulative References Cited effects study. Streamflow statistics for unregulated and regulated condi- Chase, K.J., 2013, Streamflow statistics for unregulated and tions for the Yellowstone River Basin have been calculated regulated streamflow conditions for selected locations on by the U.S. Geological Survey (USGS) and by the USACE. the Yellowstone, Tongue, and Powder and Bighorn Rivers, The USACE calculated peak-flow data, high-flow frequency Montana, 1928–2002: U.S. Geological Survey Scientific data, and flow-duration data for unregulated and regulated Investigations Report 2013–5173, 182 p. plus appendixes. streamflow conditions for the Yellowstone River main stem in the Upper Yellowstone River subbasin and for the Bighorn Jean, C., and Crispin, S., 2001, Inventory of important biologi- River. The USGS calculated peak-flow data, high-flow fre- cal resources in the Upper Yellowstone River Watershed: quency data, low-flow frequency data, and flow-duration data Report to the Environmental Protection Agency, Montana for unregulated and regulated streamflow conditions for the Natural Heritage Program, Helena Mont., 26 p. plus appen- Yellowstone River main stem in the Lower Yellowstone River dixes. subbasin and for the Tongue and Powder Rivers. National Oceanic and Atmospheric Administration, 2002, To supplement the previous statistical summaries, the Monthly station normals of temperature, precipitation, USGS, in cooperation with the YRCDC and the USACE, and heating and cooling degree days, 1971–2000, Mon- calculated low-flow frequency data and monthly and annual statistics for the Upper Yellowstone and Bighorn Rivers for tana: Asheville, N.C., National Environmental Satellite, the 1928–2002 study period; these data are presented in this Data, and Information Service, National Climatic Data report. Also included in this report are low-flow frequency Center, Climatography of the United States, no. 81, 51 p., data, interpolated for 48 ungaged locations between stream- accessed May 10, 2011, at http://hurricane.ncdc.noaa.gov/ flow-gaging stations on the Upper Yellowstone River, and for climatenormals/clim81/MTnorm.pdf. 9 ungaged locations on the Lower Yellowstone River. Parrett, Charles, 1997, Regional analyses of annual precipita- For the Bighorn River and for the three Yellowstone tion maxima in Montana: U.S. Geological Survey Water- River sites downstream from Corwin Springs, streamflow Resources Investigations Report 97–4004, 51 p. datasets were synthesized for two hypothetical streamflow conditions: unregulated and regulated. Unregulated stream- Riggs, H.C., 1972, Low-flow investigations: Techniques of flows were estimated by adding historic depletions estimated Water-Resources Investigations of the United States Geo- by the Bureau of Reclamation to the observed streamflows (or logical Survey, book 4, chap. B1, 18 p. (Reprinted 1982.) to the synthesized streamflows for periods of missing records). Regulated streamflows were estimated by subtracting the U.S. Army Corps of Engineers, 2009, Hydrologic Engineer- 2002-level depletions from the unregulated streamflows. These ing Center data storage system HEC-DSSVue visual utility datasets are more homogenous than the observed stream- engine user’s manual: Davis, Calif., U.S. Army Corps of flow datasets for the sites where streamflows are affected by Engineers Hydrologic Engineering Center, 490 p. 10 Streamflow Statistics for the Upper Yellowstone and Bighorn Rivers, Montana and Wyoming, 1928–2002

U.S. Army Corps of Engineers, 2010, Hydrologic Engineering U.S. Department of the Interior, Bureau of Reclamation, 2005, Center statistical software package HEC-SSP, version 2.0: A study to determine the historic and present-level stream- Davis, Calif., U.S. Army Corps of Engineers Hydrologic flow depletions in the Missouri River basin for the period Engineering Center, 313 p. 1929 to 2002: Billings, Mont., U.S. Department of the Interior, Bureau of Reclamation, Water Resources Service U.S. Army Corps of Engineers, 2011a, Yellowstone River Group, Great Plains Regional Office, variously paged. corridor study, Lower Bighorn River hydrology: Omaha, Nebr., U.S. Army Corps of Engineers Engineering Division, U.S. Geological Survey, 2010, Water data for the nation, Hydrologic Engineering Branch, Hydrology Section, Final surface water: U.S. Geological Survey database, accessed Report, 22 p. November 4, 2010, at http://waterdata.usgs.gov. U.S. Army Corps of Engineers, 2011b, Yellowstone River cor- U.S. Interagency Advisory Council on Water Data, 1982, ridor study, Upper Yellowstone River hydrology: Omaha, Guidelines for determining flood flow frequency—Bulletin Nebr., U.S. Army Corps of Engineers Engineering Division, 17B of the Hydrology Subcommittee: U.S. Geological Sur- Hydrologic Engineering Branch, Hydrology Section, Final vey, Office of Water Data Coordination, 183 p. Report, 63 p. Zelt, R.B., Boughton, G.K., Miller, K.A., Mason, J.P., and U.S. Department of the Interior, Bureau of Reclamation, 1999, Gianakos, L.M., 1999, Environmental setting of the Yellow- A study to determine the historic and present-level stream- stone River basin, Montana, North Dakota, and Wyoming: flow depletions in the Missouri River basin above Hermann, U.S. Geological Survey Water-Resources Investigations Missouri, Appendix F–C of Upper Mississippi River system Report 98–4269, 112 p. flow frequency study: Billings, Mont., U.S. Department of the Interior, Bureau of Reclamation, Water Resources Ser- vice Group, Great Plains Regional Office, variously paged. Glossary 11

Glossary annual mean streamflow Arithmetic mean of all daily mean streamflows for a single specified year. annual precipitation Total precipitation for a single specified year. daily mean streamflow Arithmetic mean streamflow for a single specified day. mean annual streamflow Arithmetic mean of all annual mean streamflows for the period of record or a specific period of multiple years. mean annual precipitation Arithmetic mean of all annual precipitation amounts for the period of record or a specific period of multiple years. mean monthly streamflow Arithmetic mean of all monthly mean streamflows for a specified month for the period of record or for a specific period of multiple years. monthly mean streamflow Arithmetic mean of all daily mean streamflows for a single specified month in a single specified year. monthly mean temperature Arithmetic mean of all daily mean temperatures for a single specified month in a single specified year.

Appendixes

Streamflow statistics for selected streamflow-gaging stations (appendix 1) are included as part of this report. Appendix 2, presented in Excel spreadsheets, contains information about locations and drainage areas for selected streamflow-gaging stations and reach locations on the Yellow- stone River, Montana and Wyoming. Appendix 2 also contains annual n-day low-flow frequency data for unregulated and regulated streamflow conditions for selected streamflow-gaging stations and reach locations on the Yellowstone River, Montana and Wyoming. The excel files are named sir2014-5155_APP_2.1_loc_and_da.xlsx and sir2014-5155_APP_2.2_lowflowfreq.xlsx. Locations of the streamflow-gaging stations and reach locations are shown on figures 2 and 3 (main report). 14 Streamflow Statistics for the Upper Yellowstone and Bighorn Rivers, Montana and Wyoming, 1928–2002

Appendix 1. Statistics for Unregulated and Regulated Streamflow Conditions for Selected Streamflow-Gaging Stations on the Upper Yellowstone and Bighorn Rivers, Montana and Wyoming, 1928–2002

Appendix 1 contains tables and figures showing statistics for six selected streamflow-gaging stations. Locations of the streamflow-gaging stations are shown in figure 2 (main report). Data in tables 1-6-1 and 1-6-2 and figures 1-6-1 through 1-6-17 are from Chase (2013). Appendixes 15

Appendix 1–1. Statistics for streamflow-gaging station 06186500 (Yellowstone River at Yellowstone Lake Outlet, Yellowstone National Park, Wyoming)

Table 1–1–1. Annual, seasonal, and monthly n-day low-flow frequency data for streamflow-gaging station 06186500 (Yellowstone River at Yellowstone Lake Outlet, Yellowstone National Park, Wyoming) for unregulated streamflow conditions, 1928–2002.

[ft3/s, cubic feet per second; %, percent]

Unregulated n, period of consecutive Streamflow, in ft3/s, for indicated recurrence interval, in years, and exceedance probability, in percent days (month, for monthly 2 5 10 20 25 50 100 frequency data) 50% 20% 10% 5% 4% 2% 1% Annual 7 325 227 184 152 143 121 103 30 348 247 200 165 156 131 111 Winter (January–March) 7 342 238 192 158 149 126 107 30 355 249 201 167 157 132 113 Spring (April–June) 7 516 389 318 261 245 202 167 30 552 439 376 324 310 269 235 Summer (July–September) 7 985 769 665 586 564 504 453 30 1,190 912 783 685 658 584 522 Fall (October–December) 7 412 317 274 242 234 210 191 30 458 355 307 272 262 235 212 Monthly 7 (January) 360 259 214 182 173 150 132 7 (February) 352 245 197 163 153 129 109 7 (March) 409 285 226 181 170 138 113 7 (April) 516 389 318 261 245 202 167 7 (May) 654 538 488 452 442 415 393 7 (June) 2,430 1,780 1,510 1,310 1,260 1,120 1,010 7 (July) 3,180 2,290 1,890 1,590 1,510 1,300 1,130 7 (August) 1,630 1,220 1,040 898 860 758 674 7 (September) 985 769 665 586 564 504 453 7 (October) 691 541 471 417 402 362 328 7 (November) 532 416 363 322 311 280 255 7 (December) 412 317 274 242 234 210 191 16 Streamflow Statistics for the Upper Yellowstone and Bighorn Rivers, Montana and Wyoming, 1928–2002

Table 1–1–2. Monthly and annual streamflow characteristics for streamflow-gaging station 06186500 (Yellowstone River at Yellowstone Lake Outlet, Yellowstone National Park, Wyoming) for unregulated streamflow conditions, 1928–2002.

[ft3/s, cubic feet per second]

Unregulated Streamflow, in ft3/s, or year, for indicated streamflow characteristic Maximum Year of maximum Year of minimum Standard Minimum monthly monthly mean monthly mean monthly mean Mean monthly deviation of Period mean and and maximum and maximum and minimum and mean annual mean monthly minimum annual annual mean annual mean annual mean streamflow and mean annual mean streamflow streamflow streamflow streamflow streamflow January 778 1951 243 1989 481 136 February 699 1998 165 1937 420 131 March 736 1986 140 1935 456 130 April 874 1972 200 1937 563 122 May 3,200 1928 692 1953 1,410 485 June 7,470 1997 1,580 1977 3,480 1,060 July 9,140 1997 1,650 1934 4,770 1,560 August 6,750 1982 1,290 1934 3,890 1,270 September 4,240 1982 838 1934 2,280 738 October 1,950 1951 559 1934 1,240 343 November 1,260 1950 335 1988 804 210 December 1,000 1950 280 1988 607 160

Annual 2,290 1997 659 1934 1,330 324 Appendixes 17

06186500 Yellowstone River at Yellowstone Lake Outlet, Yellowstone National Park, Wyo. Annual n-day low-flow frequency data Recurrence interval, in years 1.0 1.1 2 5 10 50 100 200 500 1,000 10,000 1,000

100

EXPLANATION Streamflow, in cubic feet per second Streamflow, 7-Day data 30-Day data Estimated n-day values Estimated n-day values n-day frequency curve n-day frequency curve

10 0.9999 0.999 0.99 0.9 0.5 0.2 0.1 0.02 0.01 0.005 0.002 0.001 0.0001 Probability

Figure 1–1–1. Annual n-day low-flow frequency data for streamflow-gaging station 06186500 (Yellowstone River at Yellowstone Lake Outlet, Yellowstone National Park, Wyoming) for unregulated streamflow conditions, 1928–2002.

06186500 Yellowstone River at Yellowstone Lake Outlet, Yellowstone National Park, Wyo. Winter (January–March) n-day low-flow frequency data Recurrence interval, in years 1.0 1.1 2 5 10 50 100 200 500 1,000 10,000 1,000

100

EXPLANATION Streamflow, in cubic feet per second Streamflow, 7-Day data 30-Day data Estimated n-day values Estimated n-day values n-day frequency curve n-day frequency curve

10 0.9999 0.999 0.99 0.9 0.5 0.2 0.1 0.02 0.01 0.005 0.002 0.001 0.0001 Probability

Figure 1–1–2. Winter (January–March) n-day low-flow frequency data for streamflow-gaging station 06186500 (Yellowstone River at Yellowstone Lake Outlet, Yellowstone National Park, Wyoming) for unregulated streamflow conditions, 1928–2002. 18 Streamflow Statistics for the Upper Yellowstone and Bighorn Rivers, Montana and Wyoming, 1928–2002

06186500 Yellowstone River at Yellowstone Lake Outlet, Yellowstone National Park, Wyo. Spring (April–June) n-day low-flow frequency data Recurrence interval, in years 1.0 1.1 2 5 10 50 100 200 500 1,000 10,000 1,000

EXPLANATION Streamflow, in cubic feet per second Streamflow, 7-Day data 30-Day data Estimated n-day values Estimated n-day values n-day frequency curve n-day frequency curve Outlier Outlier

100 0.9999 0.999 0.99 0.9 0.5 0.2 0.1 0.02 0.01 0.005 0.002 0.001 0.0001 Probability

Figure 1–1–3. Spring (April–June) n-day low-flow frequency data for streamflow-gaging station 06186500 (Yellowstone River at Yellowstone Lake Outlet, Yellowstone National Park, Wyoming) for unregulated streamflow conditions, 1928–2002.

06186500 Yellowstone River at Yellowstone Lake Outlet, Yellowstone National Park, Wyo. Summer (July–September) n-day low-flow frequency data Recurrence interval, in years 1.0 1.1 2 5 10 50 100 200 500 1,000 10,000 10,000

1,000 Streamflow, in cubic feet per second Streamflow,

EXPLANATION 7-Day data 30-Day data Estimated n-day values Estimated n-day values n-day frequency curve n-day frequency curve

100 0.9999 0.999 0.99 0.9 0.5 0.2 0.1 0.02 0.01 0.005 0.002 0.001 0.0001 Probability

Figure 1–1–4. Summer (July–September) n-day low-flow frequency data for streamflow-gaging station 06186500 (Yellowstone River at Yellowstone Lake Outlet, Yellowstone National Park, Wyoming) for unregulated streamflow conditions, 1928–2002. Appendixes 19

06186500 Yellowstone River at Yellowstone Lake Outlet, Yellowstone National Park, Wyo. Fall (October–December) n-day low-flow frequency data Recurrence interval, in years 1.0 1.1 2 5 10 50 100 200 500 1,000 10,000 1,000 Streamflow, in cubic feet per second Streamflow, EXPLANATION 7-Day data 30-Day data Estimated n-day values Estimated n-day values n-day frequency curve n-day frequency curve

100 0.9999 0.999 0.99 0.9 0.5 0.2 0.1 0.02 0.01 0.005 0.002 0.001 0.0001 Probability Figure 1–1–5. Fall (October–December) n-day low-flow frequency data for streamflow-gaging station 06186500 (Yellowstone River at Yellowstone Lake Outlet, Yellowstone National Park, Wyoming) for unregulated streamflow conditions, 1928–2002.

06186500 Yellowstone River at Yellowstone Lake Outlet, Yellowstone National Park, Wyo. January 7-day low-flow frequency data Recurrence interval, in years 1.0 1.1 2 5 10 50 100 200 500 1,000 10,000 1,000 Streamflow, in cubic feet per second Streamflow, EXPLANATION 7-Day data Estimated n-day values n-day frequency curve

100 0.9999 0.999 0.99 0.9 0.5 0.2 0.1 0.02 0.01 0.005 0.002 0.001 0.0001 Probability

Figure 1–1–6. January 7-day low-flow frequency data for streamflow-gaging station 06186500 (Yellowstone River at Yellowstone Lake Outlet, Yellowstone National Park, Wyoming) for unregulated streamflow conditions, 1928–2002. 20 Streamflow Statistics for the Upper Yellowstone and Bighorn Rivers, Montana and Wyoming, 1928–2002

06186500 Yellowstone River at Yellowstone Lake Outlet, Yellowstone National Park, Wyo. February 7-day low-flow frequency data Recurrence interval, in years 1.0 1.1 2 5 10 50 100 200 500 1,000 10,000 1,000

100 Streamflow, in cubic feet per second Streamflow, EXPLANATION 7-Day data Estimated n-day values n-day frequency curve

10 0.9999 0.999 0.99 0.9 0.5 0.2 0.1 0.02 0.01 0.005 0.002 0.001 0.0001 Probability

Figure 1–1–7. February 7-day low-flow frequency data for streamflow-gaging station 06186500 (Yellowstone River at Yellowstone Lake Outlet, Yellowstone National Park, Wyoming) for unregulated streamflow conditions, 1928–2002.

06186500 Yellowstone River at Yellowstone Lake Outlet, Yellowstone National Park, Wyo. March 7-day low-flow frequency data Recurrence interval, in years 1.0 1.1 2 5 10 50 100 200 500 1,000 10,000 1,000

100 Streamflow, in cubic feet per second Streamflow, EXPLANATION 7-Day data Estimated n-day values n-day frequency curve

10 0.9999 0.999 0.99 0.9 0.5 0.2 0.1 0.02 0.01 0.005 0.002 0.001 0.0001 Probability

Figure 1–1–8. March 7-day low-flow frequency data for streamflow-gaging station 06186500 (Yellowstone River at Yellowstone Lake Outlet, Yellowstone National Park, Wyoming) for unregulated streamflow conditions, 1928–2002. Appendixes 21

06186500 Yellowstone River at Yellowstone Lake Outlet, Yellowstone National Park, Wyo. April 7-day low-flow frequency data Recurrence interval, in years 1.0 1.1 2 5 10 50 100 200 500 1,000 10,000 1,000

EXPLANATION Streamflow, in cubic feet per second Streamflow, 7-Day data Estimated n-day values n-day frequency curve Outlier

100 0.9999 0.999 0.99 0.9 0.5 0.2 0.1 0.02 0.01 0.005 0.002 0.001 0.0001 Probability

Figure 1–1–9. April 7-day low-flow frequency data for streamflow-gaging station 06186500 (Yellowstone River at Yellowstone Lake Outlet, Yellowstone National Park, Wyoming) for unregulated streamflow conditions, 1928–2002.

06186500 Yellowstone River at Yellowstone Lake Outlet, Yellowstone National Park, Wyo. May 7-day low-flow frequency data Recurrence interval, in years 1.0 1.1 2 5 10 50 100 200 500 1,000 10,000 10,000

1,000 Streamflow, in cubic feet per second Streamflow,

EXPLANATION 7-Day data Estimated n-day values n-day frequency curve

100 0.9999 0.999 0.99 0.9 0.5 0.2 0.1 0.02 0.01 0.005 0.002 0.001 0.0001 Probability

Figure 1–1–10. May 7-day low-flow frequency data for streamflow-gaging station 06186500 (Yellowstone River at Yellowstone Lake Outlet, Yellowstone National Park, Wyoming) for unregulated streamflow conditions, 1928–2002. 22 Streamflow Statistics for the Upper Yellowstone and Bighorn Rivers, Montana and Wyoming, 1928–2002

06186500 Yellowstone River at Yellowstone Lake Outlet, Yellowstone National Park, Wyo. June 7-day low-flow frequency data Recurrence interval, in years 1.0 1.1 2 5 10 50 100 200 500 1,000 10,000 10,000

1,000 Streamflow, in cubic feet per second Streamflow, EXPLANATION 7-Day data Estimated n-day values n-day frequency curve

100 0.9999 0.999 0.99 0.9 0.5 0.2 0.1 0.02 0.01 0.005 0.002 0.001 0.0001 Probability

Figure 1–1–11. June 7-day low-flow frequency data for streamflow-gaging station 06186500 (Yellowstone River at Yellowstone Lake Outlet, Yellowstone National Park, Wyoming) for unregulated streamflow conditions, 1928–2002.

06186500 Yellowstone River at Yellowstone Lake Outlet, Yellowstone National Park, Wyo. July 7-day low-flow frequency data Recurrence interval, in years 1.0 1.1 2 5 10 50 100 200 500 1,000 10,000 10,000

1,000 Streamflow, in cubic feet per second Streamflow, EXPLANATION 7-Day data Estimated n-day values n-day frequency curve

100 0.9999 0.999 0.99 0.9 0.5 0.2 0.1 0.02 0.01 0.005 0.002 0.001 0.0001 Probability

Figure 1–1–12. July 7-day low-flow frequency data for streamflow-gaging station 06186500 (Yellowstone River at Yellowstone Lake Outlet, Yellowstone National Park, Wyoming) for unregulated streamflow conditions, 1928–2002. Appendixes 23

06186500 Yellowstone River at Yellowstone Lake Outlet, Yellowstone National Park, Wyo. August 7-day low-flow frequency data Recurrence interval, in years 1.0 1.1 2 5 10 50 100 200 500 1,000 10,000 10,000

1,000 Streamflow, in cubic feet per second Streamflow, EXPLANATION 7-Day data Estimated n-day values n-day frequency curve

100 0.9999 0.999 0.99 0.9 0.5 0.2 0.1 0.02 0.01 0.005 0.002 0.001 0.0001 Probability

Figure 1–1–13. August 7-day low-flow frequency data for streamflow-gaging station 06186500 (Yellowstone River at Yellowstone Lake Outlet, Yellowstone National Park, Wyoming) for unregulated streamflow conditions, 1928–2002.

06186500 Yellowstone River at Yellowstone Lake Outlet, Yellowstone National Park, Wyo. September 7-day low-flow frequency data Recurrence interval, in years 1.0 1.1 2 5 10 50 100 200 500 1,000 10,000 10,000

1,000 Streamflow, in cubic feet per second Streamflow, EXPLANATION 7-Day data Estimated n-day values n-day frequency curve

100 0.9999 0.999 0.99 0.9 0.5 0.2 0.1 0.02 0.01 0.005 0.002 0.001 0.0001 Probability

Figure 1–1–14. September 7-day low-flow frequency data for streamflow-gaging station 06186500 (Yellowstone River at Yellowstone Lake Outlet, Yellowstone National Park, Wyoming) for unregulated streamflow conditions, 1928–2002. 24 Streamflow Statistics for the Upper Yellowstone and Bighorn Rivers, Montana and Wyoming, 1928–2002

06186500 Yellowstone River at Yellowstone Lake Outlet, Yellowstone National Park, Wyo. October 7-day low-flow frequency data Recurrence interval, in years 1.0 1.1 2 5 10 50 100 200 500 1,000 10,000 10,000

1,000 Streamflow, in cubic feet per second Streamflow, EXPLANATION 7-Day data Estimated n-day values n-day frequency curve

100 0.9999 0.999 0.99 0.9 0.5 0.2 0.1 0.02 0.01 0.005 0.002 0.001 0.0001 Probability

Figure 1–1–15. October 7-day low-flow frequency data for streamflow-gaging station 06186500 (Yellowstone River at Yellowstone Lake Outlet, Yellowstone National Park, Wyoming) for unregulated streamflow conditions, 1928–2002.

06186500 Yellowstone River at Yellowstone Lake Outlet, Yellowstone National Park, Wyo. November 7-day low-flow frequency data Recurrence interval, in years 1.0 1.1 2 5 10 50 100 200 500 1,000 10,000 1,000 Streamflow, in cubic feet per second Streamflow, EXPLANATION 7-Day data Estimated n-day values n-day frequency curve

100 0.9999 0.999 0.99 0.9 0.5 0.2 0.1 0.02 0.01 0.005 0.002 0.001 0.0001 Probability

Figure 1–1–16. November 7-day low-flow frequency data for streamflow-gaging station 06186500 (Yellowstone River at Yellowstone Lake Outlet, Yellowstone National Park, Wyoming) for unregulated streamflow conditions, 1928–2002. Appendixes 25

06186500 Yellowstone River at Yellowstone Lake Outlet, Yellowstone National Park, Wyo. December 7-day low-flow frequency data Recurrence interval, in years 1.0 1.1 2 5 10 50 100 200 500 1,000 10,000 1,000 Streamflow, in cubic feet per second Streamflow, EXPLANATION 7-Day data Estimated n-day values n-day frequency curve

100 0.9999 0.999 0.99 0.9 0.5 0.2 0.1 0.02 0.01 0.005 0.002 0.001 0.0001 Probability

Figure 1–1–17. December 7-day low-flow frequency data for streamflow-gaging station 06186500 (Yellowstone River at Yellowstone Lake Outlet, Yellowstone National Park, Wyoming) for unregulated streamflow conditions, 1928–2002. 26 Streamflow Statistics for the Upper Yellowstone and Bighorn Rivers, Montana and Wyoming, 1928–2002

Appendix 1–2. Statistics for streamflow-gaging station 06191500 (Yellowstone River at Corwin Springs, Montana)

Table 1–2–1. Annual, seasonal, and monthly n-day low-flow frequency data for streamflow-gaging station 06191500 (Yellowstone River at Corwin Springs, Montana) for unregulated streamflow conditions, 1928–2002.

[ft3/s, cubic feet per second; %, percent]

Unregulated n, period of consecutive Streamflow, in ft3/s, for indicated recurrence interval, in years, and exceedance probability, in percent days (month, for monthly 2 5 10 20 25 50 100 frequency data) 50% 20% 10% 5% 4% 2% 1% Annual 7 675 553 497 454 442 409 381 30 739 607 545 497 484 448 417 Winter (January–March) 7 695 563 504 459 447 414 386 30 742 605 543 496 483 447 418 Spring (April–June) 7 1,030 829 733 657 636 578 528 30 1,440 1,090 947 847 821 751 694 Summer (July–September) 7 1,610 1,290 1,140 1,030 1,000 916 845 30 1,860 1,470 1,290 1,150 1,120 1,010 925 Fall (October–December) 7 799 672 613 567 555 520 490 30 899 759 694 645 632 594 562 Monthly 7 (January) 727 589 526 479 466 431 401 7 (February) 738 597 532 482 469 431 400 7 (March) 803 654 581 524 508 464 426 7 (April) 1,030 829 733 657 636 578 528 7 (May) 2,600 1,740 1,430 1,230 1,180 1,050 942 7 (June) 8,480 6,250 5,260 4,520 4,310 3,770 3,330 7 (July) 4,420 3,190 2,660 2,270 2,170 1,890 1,670 7 (August) 2,360 1,810 1,560 1,380 1,330 1,190 1,080 7 (September) 1,610 1,290 1,140 1,030 1,000 916 845 7 (October) 1,280 1,040 932 851 829 768 717 7 (November) 1,010 833 756 699 683 640 604 7 (December) 802 674 614 568 555 519 489 Appendixes 27

Table 1–2–2. Monthly and annual streamflow characteristics for streamflow-gaging station 06191500 (Yellowstone River at Corwin Springs, Montana) for unregulated streamflow conditions, 1928–2002.

[ft3/s, cubic feet per second]

Unregulated Streamflow, in ft3/s, or year, for indicated streamflow characteristic Maximum Year of maximum Year of minimum Standard Minimum monthly monthly mean monthly mean monthly mean Mean monthly deviation of Period mean and and maximum and maximum and minimum and mean annual mean monthly minimum annual annual mean annual mean annual mean streamflow and mean annual mean streamflow streamflow streamflow streamflow streamflow January 1,360 1997 448 1937 814 196 February 1,340 1997 411 1937 806 194 March 1,380 1997 412 1937 889 184 April 3,540 1990 576 1937 1,550 570 May 13,600 1928 2,570 1975 6,320 2,060 June 22,500 1997 4,250 1934 11,400 3,580 July 13,300 1982 2,100 1934 6,630 2,600 August 5,690 1982 1,390 1934 3,110 970 September 3,210 1968 938 1988 1,900 493 October 2,430 1972 781 1988 1,460 370 November 1,960 1983 702 1988 1,150 263 December 1,420 1983 551 1936 922 187

Annual 5,250 1997 1,872 1934 3,080 698 28 Streamflow Statistics for the Upper Yellowstone and Bighorn Rivers, Montana and Wyoming, 1928–2002

06191500 Yellowstone River at Corwin Springs, Mont. Annual n-day low-flow frequency data Recurrence interval, in years 1.0 1.1 2 5 10 50 100 200 500 1,000 10,000 10,000

1,000

Streamflow, in cubic feet per second Streamflow, EXPLANATION 7-Day data 30-Day data Estimated n-day values Estimated n-day values n-day frequency curve n-day frequency curve

100 0.9999 0.999 0.99 0.9 0.5 0.2 0.1 0.02 0.01 0.005 0.002 0.001 0.0001 Probability

Figure 1–2–1. Annual n-day low-flow frequency data for streamflow-gaging station 06191500 (Yellowstone River at Corwin Springs, Montana) for unregulated streamflow conditions, 1928–2002.

06191500 Yellowstone River at Corwin Springs, Mont. Winter (January–March) n-day low-flow frequency data Recurrence interval, in years 1.0 1.1 2 5 10 50 100 200 500 1,000 10,000 10,000

1,000 Streamflow, in cubic feet per second Streamflow, EXPLANATION 7-Day data 30-Day data Estimated n-day values Estimated n-day values n-day frequency curve n-day frequency curve

100 0.9999 0.999 0.99 0.9 0.5 0.2 0.1 0.02 0.01 0.005 0.002 0.001 0.0001 Probability

Figure 1–2–2. Winter (January–March) n-day low-flow frequency data for streamflow-gaging station 06191500 (Yellowstone River at Corwin Springs, Montana) for unregulated streamflow conditions, 1928–2002. Appendixes 29

06191500 Yellowstone River at Corwin Springs, Mont. Spring (April–June) n-day low-flow frequency data Recurrence interval, in years 1.0 1.1 2 5 10 50 100 200 500 1,000 10,000 10,000

1,000

Streamflow, in cubic feet per second Streamflow, EXPLANATION 7-Day data 30-Day data Estimated n-day values Estimated n-day values n-day frequency curve n-day frequency curve Outlier

100 0.9999 0.999 0.99 0.9 0.5 0.2 0.1 0.02 0.01 0.005 0.002 0.001 0.0001 Probability

Figure 1–2–3. Spring (April–June) n-day low-flow frequency data for streamflow-gaging station 06191500 (Yellowstone River at Corwin Springs, Montana) for unregulated streamflow conditions, 1928–2002.

06191500 Yellowstone River at Corwin Springs, Mont. Summer (July–September) n-day low-flow frequency data Recurrence interval, in years 1.0 1.1 2 5 10 50 100 200 500 1,000 10,000 10,000

1,000 Streamflow, in cubic feet per second Streamflow,

EXPLANATION 7-Day data 30-Day data Estimated n-day values Estimated n-day values n-day frequency curve n-day frequency curve

100 0.9999 0.999 0.99 0.9 0.5 0.2 0.1 0.02 0.01 0.005 0.002 0.001 0.0001 Probability

Figure 1–2–4. Summer (July–September) n-day low-flow frequency data for streamflow-gaging station 06191500 (Yellowstone River at Corwin Springs, Montana) for unregulated streamflow conditions, 1928–2002. 30 Streamflow Statistics for the Upper Yellowstone and Bighorn Rivers, Montana and Wyoming, 1928–2002

06191500 Yellowstone River at Corwin Springs, Mont. Fall (October–December) n-day low-flow frequency data Recurrence interval, in years 1.0 1.1 2 5 10 50 100 200 500 1,000 10,000 10,000

1,000 Streamflow, in cubic feet per second Streamflow, EXPLANATION 7-Day data 30-Day data Estimated n-day values Estimated n-day values n-day frequency curve n-day frequency curve

100 0.9999 0.999 0.99 0.9 0.5 0.2 0.1 0.02 0.01 0.005 0.002 0.001 0.0001 Probability

Figure 1–2–5. Fall (October–December) 7-day low-flow frequency data for streamflow-gaging station 06191500 (Yellowstone River at Corwin Springs, Montana) for unregulated streamflow conditions, 1928–2002.

06191500 Yellowstone River at Corwin Springs, Mont. January 7-day low-flow frequency data Recurrence interval, in years 1.0 1.1 2 5 10 50 100 200 500 1,000 10,000 10,000

1,000 Streamflow, in cubic feet per second Streamflow, EXPLANATION 7-Day data Estimated n-day values n-day frequency curve

100 0.9999 0.999 0.99 0.9 0.5 0.2 0.1 0.02 0.01 0.005 0.002 0.001 0.0001 Probability

Figure 1–2–6. January 7-day low-flow frequency data for streamflow-gaging station 06191500 (Yellowstone River at Corwin Springs, Montana) for unregulated streamflow conditions, 1928–2002. Appendixes 31

06191500 Yellowstone River at Corwin Springs, Mont. February 7-day low-flow frequency data Recurrence interval, in years 1.0 1.1 2 5 10 50 100 200 500 1,000 10,000 10,000

1,000 Streamflow, in cubic feet per second Streamflow, EXPLANATION 7-Day data Estimated n-day values n-day frequency curve

100 0.9999 0.999 0.99 0.9 0.5 0.2 0.1 0.02 0.01 0.005 0.002 0.001 0.0001 Probability

Figure 1–2–7. February 7-day low-flow frequency data for streamflow-gaging station 06191500 (Yellowstone River at Corwin Springs, Montana) for unregulated streamflow conditions, 1928–2002.

06191500 Yellowstone River at Corwin Springs, Mont. March 7-day low-flow frequency data Recurrence interval, in years 1.0 1.1 2 5 10 50 100 200 500 1,000 10,000 10,000

1,000

Streamflow, in cubic feet per second Streamflow, EXPLANATION 7-Day data Estimated n-day values n-day frequency curve Outlier

100 0.9999 0.999 0.99 0.9 0.5 0.2 0.1 0.02 0.01 0.005 0.002 0.001 0.0001 Probability

Figure 1–2–8. March 7-day low-flow frequency data for streamflow-gaging station 06191500 (Yellowstone River at Corwin Springs, Montana) for unregulated streamflow conditions, 1928–2002. 32 Streamflow Statistics for the Upper Yellowstone and Bighorn Rivers, Montana and Wyoming, 1928–2002

06191500 Yellowstone River at Corwin Springs, Mont. April 7-day low-flow frequency data Recurrence interval, in years 1.0 1.1 2 5 10 50 100 200 500 1,000 10,000 10,000

1,000

Streamflow, in cubic feet per second Streamflow, EXPLANATION 7-Day data Estimated n-day values n-day frequency curve Outlier

100 0.9999 0.999 0.99 0.9 0.5 0.2 0.1 0.02 0.01 0.005 0.002 0.001 0.0001 Probability

Figure 1–2–9. April 7-day low-flow frequency data for streamflow-gaging station 06191500 (Yellowstone River at Corwin Springs, Montana) for unregulated streamflow conditions, 1928–2002.

06191500 Yellowstone River at Corwin Springs, Mont. May 7-day low-flow frequency data Recurrence interval, in years 1.0 1.1 2 5 10 50 100 200 500 1,000 10,000 100,000

10,000

1,000 Streamflow, in cubic feet per second Streamflow,

EXPLANATION 7-Day data Estimated n-day values n-day frequency curve

100 0.9999 0.999 0.99 0.9 0.5 0.2 0.1 0.02 0.01 0.005 0.002 0.001 0.0001 Probability

Figure 1–2–10. May 7-day low-flow frequency data for streamflow-gaging station 06191500 (Yellowstone River at Corwin Springs, Montana) for unregulated streamflow conditions, 1928–2002. Appendixes 33

06191500 Yellowstone River at Corwin Springs, Mont. June 7-day low-flow frequency data Recurrence interval, in years 1.0 1.1 2 5 10 50 100 200 500 1,000 10,000 100,000

10,000 Streamflow, in cubic feet per second Streamflow, EXPLANATION 7-Day data Estimated n-day values n-day frequency curve

1,000 0.9999 0.999 0.99 0.9 0.5 0.2 0.1 0.02 0.01 0.005 0.002 0.001 0.0001 Probability

Figure 1–2–11. June 7-day low-flow frequency data for streamflow-gaging station 06191500 (Yellowstone River at Corwin Springs, Montana) for unregulated streamflow conditions, 1928–2002.

06191500 Yellowstone River at Corwin Springs, Mont. July 7-day low-flow frequency data Recurrence interval, in years 1.0 1.1 2 5 10 50 100 200 500 1,000 10,000 10,000 Streamflow, in cubic feet per second Streamflow, EXPLANATION 7-Day data Estimated n-day values n-day frequency curve

1,000 0.9999 0.999 0.99 0.9 0.5 0.2 0.1 0.02 0.01 0.005 0.002 0.001 0.0001 Probability

Figure 1–2–12. July 7-day low-flow frequency data for streamflow-gaging station 06191500 (Yellowstone River at Corwin Springs, Montana) for unregulated streamflow conditions, 1928–2002. 34 Streamflow Statistics for the Upper Yellowstone and Bighorn Rivers, Montana and Wyoming, 1928–2002

06191500 Yellowstone River at Corwin Springs, Mont. August 7-day low-flow frequency data Recurrence interval, in years 1.0 1.1 2 5 10 50 100 200 500 1,000 10,000 10,000

1,000 Streamflow, in cubic feet per second Streamflow, EXPLANATION 7-Day data Estimated n-day values n-day frequency curve

100 0.9999 0.999 0.99 0.9 0.5 0.2 0.1 0.02 0.01 0.005 0.002 0.001 0.0001 Probability

Figure 1–2–13. August 7-day low-flow frequency data for streamflow-gaging station 06191500 (Yellowstone River at Corwin Springs, Montana) for unregulated streamflow conditions, 1928–2002.

06191500 Yellowstone River at Corwin Springs, Mont. September 7-day low-flow frequency data Recurrence interval, in years 1.0 1.1 2 5 10 50 100 200 500 1,000 10,000 10,000

1,000 Streamflow, in cubic feet per second Streamflow, EXPLANATION 7-Day data Estimated n-day values n-day frequency curve

100 0.9999 0.999 0.99 0.9 0.5 0.2 0.1 0.02 0.01 0.005 0.002 0.001 0.0001 Probability

Figure 1–2–14. September 7-day low-flow frequency data for streamflow-gaging station 06191500 (Yellowstone River at Corwin Springs, Montana) for unregulated streamflow conditions, 1928–2002. Appendixes 35

06191500 Yellowstone River at Corwin Springs, Mont. October 7-day low-flow frequency data Recurrence interval, in years 1.0 1.1 2 5 10 50 100 200 500 1,000 10,000 10,000

1,000 Streamflow, in cubic feet per second Streamflow, EXPLANATION 7-Day data Estimated n-day values n-day frequency curve

100 0.9999 0.999 0.99 0.9 0.5 0.2 0.1 0.02 0.01 0.005 0.002 0.001 0.0001 Probability

Figure 1–2–15. October 7-day low-flow frequency data for streamflow-gaging station 06191500 (Yellowstone River at Corwin Springs, Montana) for unregulated streamflow conditions, 1928–2002.

06191500 Yellowstone River at Corwin Springs, Mont. November 7-day low-flow frequency data Recurrence interval, in years 1.0 1.1 2 5 10 50 100 200 500 1,000 10,000 10,000

1,000 Streamflow, in cubic feet per second Streamflow, EXPLANATION 7-Day data Estimated n-day values n-day frequency curve

100 0.9999 0.999 0.99 0.9 0.5 0.2 0.1 0.02 0.01 0.005 0.002 0.001 0.0001 Probability

Figure 1–2–16. November 7-day low-flow frequency data for streamflow-gaging station 06191500 (Yellowstone River at Corwin Springs, Montana) for unregulated streamflow conditions, 1928–2002. 36 Streamflow Statistics for the Upper Yellowstone and Bighorn Rivers, Montana and Wyoming, 1928–2002

06191500 Yellowstone River at Corwin Springs, Mont. December 7-day low-flow frequency data Recurrence interval, in years 1.0 1.1 2 5 10 50 100 200 500 1,000 10,000 10,000

1,000 Streamflow, in cubic feet per second Streamflow, EXPLANATION 7-Day data Estimated n-day values n-day frequency curve

100 0.9999 0.999 0.99 0.9 0.5 0.2 0.1 0.02 0.01 0.005 0.002 0.001 0.0001 Probability

Figure 1–2–17. December 7-day low-flow frequency data for streamflow-gaging station 06191500 (Yellowstone River at Corwin Springs, Montana) for unregulated streamflow conditions, 1928–2002. Appendixes 37

Appendix 1–3. Statistics for streamflow-gaging station 06192500 (Yellowstone River near Livingston, Montana)

Table 1–3–1. Annual, seasonal, and monthly n-day low-flow frequency data for streamflow-gaging station 06192500 (Yellowstone River near Livingston, Montana) for unregulated and regulated streamflow conditions, 1928–2002.

[ft3/s, cubic feet per second; %, percent]

Unregulated n, period of consecutive Streamflow, in ft3/s, for indicated recurrence interval, in years, and exceedance probability, in percent days (month, for monthly 2 5 10 20 25 50 100 frequency data) 50% 20% 10% 5% 4% 2% 1% Annual 7 991 833 756 695 678 630 589 30 1,110 937 853 787 768 716 671 Winter (January–March) 7 1,012 844 764 701 684 635 594 30 1,110 937 852 785 766 714 669 Spring (April–June) 7 1,420 1,190 1,080 992 967 897 837 30 1,880 1,470 1,300 1,190 1,150 1,070 1,000 Summer (July–September) 7 2,140 1,730 1,550 1,400 1,360 1,250 1,160 30 2,390 1,930 1,710 1,540 1,490 1,370 1,260 Fall (October–December) 7 1,171 996 911 844 826 773 728 30 1,330 1,140 1,060 985 966 911 864 Monthly 7 (January) 1,060 881 796 729 710 658 614 7 (February) 1,090 909 821 752 732 678 632 7 (March) 1,170 988 898 827 807 750 700 7 (April) 1,420 1,190 1,080 992 967 897 837 7 (May) 3,090 2,140 1,800 1,580 1,520 1,370 1,260 7 (June) 9,700 7,210 6,120 5,310 5,090 4,500 4,020 7 (July) 5,130 3,780 3,200 2,770 2,650 2,340 2,090 7 (August) 2,910 2,290 2,010 1,790 1,730 1,560 1,420 7 (September) 2,140 1,730 1,550 1,400 1,360 1,250 1,160 7 (October) 1,790 1,480 1,340 1,230 1,200 1,110 1,040 7 (November) 1,470 1,230 1,130 1,040 1,020 955 901 7 (December) 1,170 999 914 846 827 774 729 38 Streamflow Statistics for the Upper Yellowstone and Bighorn Rivers, Montana and Wyoming, 1928–2002

[ft3/s, cubic feet per second; %, percent]

Regulated n, period of consecutive Streamflow, in ft3/s, for indicated recurrence interval, in years, and exceedance probability, in percent days (month, for monthly 2 5 10 20 25 50 100 frequency data) 50% 20% 10% 5% 4% 2% 1% Annual 7 1,000 840 762 701 684 635 594 30 1,110 940 860 790 780 720 680 Winter (January–March) 7 1,020 850 770 710 691 642 601 30 1,120 940 860 790 770 720 680 Spring (April–June) 7 1,400 1,180 1,070 980 960 890 830 30 1,840 1,450 1,280 1,170 1,140 1,060 990 Summer (July–September) 7 2,090 1,680 1,500 1,360 1,320 1,210 1,120 30 2,320 1,860 1,640 1,480 1,430 1,310 1,200 Fall (October–December) 7 1,180 1,010 920 857 838 785 739 30 1,350 1,160 1,070 1,000 980 920 880 Monthly 7 (January) 1,070 889 804 737 718 666 621 7 (February) 1,100 916 827 758 739 685 639 7 (March) 1,170 993 903 832 812 755 706 7 (April) 1,400 1,180 1,070 980 956 888 829 7 (May) 2,990 2,080 1,750 1,540 1,480 1,340 1,230 7 (June) 9,530 7,030 5,930 5,120 4,900 4,320 3,830 7 (July) 4,950 3,610 3,030 2,600 2,490 2,190 1,900 7 (August) 2,800 2,180 1,890 1,670 1,610 1,450 1,320 7 (September) 2,090 1,680 1,500 1,360 1,320 1,210 1,120 7 (October) 1,810 1,490 1,350 1,240 1,210 1,120 1,050 7 (November) 1,490 1,250 1,150 1,060 1,040 974 919 7 (December) 1,190 1,010 926 858 839 786 740 Appendixes 39

Table 1–3–2. Monthly and annual streamflow characteristics for streamflow-gaging station 06192500 (Yellowstone River near Livingston, Montana) for unregulated and regulated streamflow conditions, 1928–2002.

[ft3/s, cubic feet per second]

Unregulated Streamflow, in ft3/s, or year, for indicated streamflow characteristic Maximum Year of maximum Year of minimum Standard Minimum monthly monthly mean monthly mean monthly mean Mean monthly deviation of Period mean and and maximum and maximum and minimum and mean annual mean monthly minimum annual annual mean annual mean annual mean streamflow and mean annual mean streamflow streamflow streamflow streamflow streamflow January 1,750 1984 721 1989 1,195 235 February 1,722 1997 691 1937 1,186 230 March 1,800 1997 696 1937 1,268 212 April 3,880 1990 926 1937 2,000 632 May 15,700 1928 3,360 1953 7,170 2,320 June 27,300 1997 5,210 1934 13,300 4,270 July 15,200 1975 2,810 1934 7,760 3,010 August 5,890 1982 1,860 1988 3,710 1,060 September 3,860 1968 1,342 1988 2,430 574 October 3,100 1972 1,123 1988 1,980 454 November 2,580 1983 1,013 1936 1,640 329 December 1,970 1983 842 1936 1,354 238

Annual 6,290 1997 2,341 1931 3,740 807

Regulated Streamflow, in ft3/s, or year, for indicated streamflow characteristic Maximum Year of maximum Year of minimum Standard Minimum monthly monthly mean monthly mean monthly mean Mean monthly deviation of Period mean and and maximum and maximum and minimum and mean annual mean monthly minimum annual annual mean annual mean annual mean streamflow and mean annual mean streamflow streamflow streamflow streamflow streamflow January 1,760 1984 727 1989 1,200 235 February 1,730 1997 697 1937 1,190 230 March 1,800 1997 698 1937 1,270 211 April 3,850 1990 889 1937 1,960 614 May 15,500 1928 3,270 1953 7,000 2,300 June 27,100 1997 4,990 1987 13,100 4,300 July 15,000 1975 2,630 1934 7,500 3,010 August 5,720 1982 1,710 1988 3,560 1,050 September 3,810 1968 1,280 2001 2,370 583 October 3,120 1972 1,130 1988 1,990 454 November 2,600 1983 1,030 1936 1,660 329 December 1,990 1983 853 1936 1,370 238

Annual 6,230 1997 2,270 1931 3,670 811 40 Streamflow Statistics for the Upper Yellowstone and Bighorn Rivers, Montana and Wyoming, 1928–2002

06192500 Yellowstone River near Livingston, Mont. Annual n-day low-flow frequency data Recurrence interval, in years 1.0 1.1 2 5 10 50 100 200 5001,000 10,000 10,000 5

UNREGULATED

1,000

Streamflow, in cubic feet per second Streamflow, EXPLANATION 7-Day data 30-Day data Estimated n-day values Estimated n-day values n-day frequency curve n-day frequency curve

A 100 0.9999 0.999 0.99 0.9 0.5 0.2 0.1 0.02 0.01 0.005 0.002 0.001 0.0001 Probability 06192500 Yellowstone River near Livingston, Mont. Annual n-day low-flow frequency data Recurrence interval, in years 1.0 1.1 2 5 10 50 100 200 5001,000 10,000 10,000

REGULATED

1,000

Streamflow, in cubic feet per second Streamflow, EXPLANATION 7-Day data 30-Day data Estimated n-day values Estimated n-day values n-day frequency curve n-day frequency curve

B 100 0.9999 0.999 0.99 0.9 0.5 0.2 0.1 0.02 0.01 0.005 0.002 0.001 0.0001 Probability

Figure 1–3–1. Annual n-day low-flow frequency data for streamflow-gaging station 06192500 (Yellowstone River near Livingston, Montana) for A, unregulated and B, regulated streamflow conditions, 1928–2002. Appendixes 41

06192500 Yellowstone River near Livingston, Mont. Winter (January–March) n-day low-flow frequency data Recurrence interval, in years 1.0 1.1 2 5 10 50 100 200 5001,000 10,000 10,000

UNREGULATED

1,000

Streamflow, in cubic feet per second Streamflow, EXPLANATION 7-Day data 30-Day data Estimated n-day values Estimated n-day values n-day frequency curve n-day frequency curve

A 100 0.9999 0.999 0.99 0.9 0.5 0.2 0.1 0.02 0.01 0.005 0.002 0.001 0.0001 Probability 06192500 Yellowstone River near Livingston, Mont. Winter (January–March) n-day low-flow frequency data Recurrence interval, in years 1.0 1.1 2 5 10 50 100 200 5001,000 10,000 10,000

REGULATED

1,000

Streamflow, in cubic feet per second Streamflow, EXPLANATION 7-Day data 30-Day data Estimated n-day values Estimated n-day values n-day frequency curve n-day frequency curve

B 100 0.9999 0.999 0.99 0.9 0.5 0.2 0.1 0.02 0.01 0.005 0.002 0.001 0.0001 Probability

Figure 1–3–2. Winter (January–March) n-day low-flow frequency data for streamflow-gaging station 06192500 (Yellowstone River near Livingston, Montana) for A, unregulated and B, regulated streamflow conditions, 1928–2002. 42 Streamflow Statistics for the Upper Yellowstone and Bighorn Rivers, Montana and Wyoming, 1928–2002

06192500 Yellowstone River near Livingston, Mont. Spring (April–June) n-day low-flow frequency data Recurrence interval, in years 1.0 1.1 2 5 10 50 100 200 5001,000 10,000 10,000

UNREGULATED 1,000

EXPLANATION

Streamflow, in cubic feet per second Streamflow, 7-Day data 30-Day data Estimated n-day values Estimated n-day values n-day frequency curve n-day frequency curve Outlier

A 100 0.9999 0.999 0.99 0.9 0.5 0.2 0.1 0.02 0.01 0.005 0.002 0.001 0.0001 Probability 06192500 Yellowstone River near Livingston, Mont. Spring (April–June) n-day low-flow frequency data Recurrence interval, in years 1.0 1.1 2 5 10 50 100 200 5001,000 10,000 10,000

REGULATED 1,000

EXPLANATION

Streamflow, in cubic feet per second Streamflow, 7-Day data 30-Day data Estimated n-day values Estimated n-day values n-day frequency curve n-day frequency curve Outlier

B 100 0.9999 0.999 0.99 0.9 0.5 0.2 0.1 0.02 0.01 0.005 0.002 0.001 0.0001 Probability

Figure 1–3–3. Spring (April–June) n-day low-flow frequency data for streamflow-gaging station 06192500 (Yellowstone River near Livingston, Montana) for A, unregulated and B, regulated streamflow conditions, 1928–2002. Appendixes 43

06192500 Yellowstone River near Livingston, Mont. Summer (July–September) n-day low-flow frequency data Recurrence interval, in years 1.0 1.1 2 5 10 50 100 200 5001,000 10,000 10,000

EXPLANATION 7-Day data 30-Day data Estimated n-day values Estimated n-day values n-day frequency curve n-day frequency curve

UNREGULATED Streamflow, in cubic feet per second Streamflow,

A 1,000 0.9999 0.999 0.99 0.9 0.5 0.2 0.1 0.02 0.01 0.005 0.002 0.001 0.0001 Probability 06192500 Yellowstone River near Livingston, Mont. Summer (July–September) n-day low-flow frequency data Recurrence interval, in years 1.0 1.1 2 5 10 50 100 200 5001,000 10,000 10,000

EXPLANATION 7-Day data 30-Day data Estimated n-day values Estimated n-day values n-day frequency curve n-day frequency curve

REGULATED Streamflow, in cubic feet per second Streamflow,

B 1,000 0.9999 0.999 0.99 0.9 0.5 0.2 0.1 0.02 0.01 0.005 0.002 0.001 0.0001 Probability

Figure 1–3–4. Summer (July–September) n-day low-flow frequency data for streamflow-gaging station 06192500 (Yellowstone River near Livingston, Montana) for A, unregulated and B, regulated streamflow conditions, 1928–2002. 44 Streamflow Statistics for the Upper Yellowstone and Bighorn Rivers, Montana and Wyoming, 1928–2002

06192500 Yellowstone River near Livingston, Mont. Fall (October–December) n-day low-flow frequency data Recurrence interval, in years 1.0 1.1 2 5 10 50 100 200 5001,000 10,000 10,000

UNREGULATED

1,000

Streamflow, in cubic feet per second Streamflow, EXPLANATION 7-Day data 30-Day data Estimated n-day values Estimated n-day values n-day frequency curve n-day frequency curve

A 100 0.9999 0.999 0.99 0.9 0.5 0.2 0.1 0.02 0.01 0.005 0.002 0.001 0.0001 Probability 06192500 Yellowstone River near Livingston, Mont. Fall (October–December) n-day low-flow frequency data Recurrence interval, in years 1.0 1.1 2 5 10 50 100 200 5001,000 10,000 10,000

REGULATED

1,000

Streamflow, in cubic feet per second Streamflow, EXPLANATION 7-Day data 30-Day data Estimated n-day values Estimated n-day values n-day frequency curve n-day frequency curve

B 100 0.9999 0.999 0.99 0.9 0.5 0.2 0.1 0.02 0.01 0.005 0.002 0.001 0.0001 Probability

Figure 1–3–5. Fall (October–December) n-day low-flow frequency data for streamflow-gaging station 06192500 (Yellowstone River near Livingston, Montana) for A, unregulated and B, regulated streamflow conditions, 1928–2002. Appendixes 45

06192500 Yellowstone River near Livingston, Mont. January 7-day low-flow frequency data Recurrence interval, in years 1.0 1.1 2 5 10 50 100 200 5001,000 10,000 10,000

UNREGULATED

1,000

Streamflow, in cubic feet per second Streamflow, EXPLANATION 7-Day data Estimated n-day values n-day frequency curve

A 100 0.9999 0.999 0.99 0.9 0.5 0.2 0.1 0.02 0.01 0.005 0.002 0.001 0.0001 Probability 06192500 Yellowstone River near Livingston, Mont. January 7-day low-flow frequency data Recurrence interval, in years 1.0 1.1 2 5 10 50 100 200 5001,000 10,000 10,000

REGULATED

1,000

Streamflow, in cubic feet per second Streamflow, EXPLANATION 7-Day data Estimated n-day values n-day frequency curve

B 100 0.9999 0.999 0.99 0.9 0.5 0.2 0.1 0.02 0.01 0.005 0.002 0.001 0.0001 Probability

Figure 1–3–6. January 7-day low-flow frequency data for streamflow-gaging station 06192500 (Yellowstone River near Livingston, Montana) for A, unregulated and B, regulated streamflow conditions, 1928–2002. 46 Streamflow Statistics for the Upper Yellowstone and Bighorn Rivers, Montana and Wyoming, 1928–2002

06192500 Yellowstone River near Livingston, Mont. February 7-day low-flow frequency data Recurrence interval, in years 1.0 1.1 2 5 10 50 100 200 5001,000 10,000 10,000

UNREGULATED

1,000

EXPLANATION Streamflow, in cubic feet per second Streamflow, 7-Day data Estimated n-day values n-day frequency curve Outlier

A 100 0.9999 0.999 0.99 0.9 0.5 0.2 0.1 0.02 0.01 0.005 0.002 0.001 0.0001 Probability 06192500 Yellowstone River near Livingston, Mont. February 7-day low-flow frequency data Recurrence interval, in years 1.0 1.1 2 5 10 50 100 200 5001,000 10,000 10,000

REGULATED

1,000

EXPLANATION Streamflow, in cubic feet per second Streamflow, 7-Day data Estimated n-day values n-day frequency curve Outlier

B 100 0.9999 0.999 0.99 0.9 0.5 0.2 0.1 0.02 0.01 0.005 0.002 0.001 0.0001 Probability

Figure 1–3–7. February 7-day low-flow frequency data for streamflow-gaging station 06192500 (Yellowstone River near Livingston, Montana) for A, unregulated and B, regulated streamflow conditions, 1928–2002. Appendixes 47

06192500 Yellowstone River near Livingston, Mont. March 7-day low-flow frequency data Recurrence interval, in years 1.0 1.1 2 5 10 50 100 200 5001,000 10,000 10,000

UNREGULATED

1,000

Streamflow, in cubic feet per second Streamflow, EXPLANATION 7-Day data Estimated n-day values n-day frequency curve

A 100 0.9999 0.999 0.99 0.9 0.5 0.2 0.1 0.02 0.01 0.005 0.002 0.001 0.0001 Probability 06192500 Yellowstone River near Livingston, Mont. March 7-day low-flow frequency data Recurrence interval, in years 1.0 1.1 2 5 10 50 100 200 5001,000 10,000 10,000

REGULATED

1,000

Streamflow, in cubic feet per second Streamflow, EXPLANATION 7-Day data Estimated n-day values n-day frequency curve

B 100 0.9999 0.999 0.99 0.9 0.5 0.2 0.1 0.02 0.01 0.005 0.002 0.001 0.0001 Probability

Figure 1–3–8. March 7-day low-flow frequency data for streamflow-gaging station 06192500 (Yellowstone River near Livingston, Montana) for A, unregulated and B, regulated streamflow conditions, 1928–2002. 48 Streamflow Statistics for the Upper Yellowstone and Bighorn Rivers, Montana and Wyoming, 1928–2002

06192500 Yellowstone River near Livingston, Mont. April 7-day low-flow frequency data Recurrence interval, in years 1.0 1.1 2 5 10 50 100 200 5001,000 10,000 10,000

UNREGULATED

1,000

EXPLANATION Streamflow, in cubic feet per second Streamflow, 7-Day data Estimated n-day values n-day frequency curve Outlier

A 100 0.9999 0.999 0.99 0.9 0.5 0.2 0.1 0.02 0.01 0.005 0.002 0.001 0.0001 Probability 06192500 Yellowstone River near Livingston, Mont. April 7-day low-flow frequency data Recurrence interval, in years 1.0 1.1 2 5 10 50 100 200 5001,000 10,000 10,000

REGULATED

1,000

EXPLANATION Streamflow, in cubic feet per second Streamflow, 7-Day data Estimated n-day values n-day frequency curve Outlier

B 100 0.9999 0.999 0.99 0.9 0.5 0.2 0.1 0.02 0.01 0.005 0.002 0.001 0.0001 Probability

Figure 1–3–9. April 7-day low-flow frequency data for streamflow-gaging station 06192500 (Yellowstone River near Livingston, Montana) for A, unregulated and B, regulated streamflow conditions, 1928–2002. Appendixes 49

06192500 Yellowstone River near Livingston, Mont. May 7-day low-flow frequency data Recurrence interval, in years 1.0 1.1 2 5 10 50 100 200 5001,000 10,000 100,000

UNREGULATED

10,000

Streamflow, in cubic feet per second Streamflow, EXPLANATION 7-Day data Estimated n-day values n-day frequency curve

A 1,000 0.9999 0.999 0.99 0.9 0.5 0.2 0.1 0.02 0.01 0.005 0.002 0.001 0.0001 Probability 06192500 Yellowstone River near Livingston, Mont. May 7-day low-flow frequency data Recurrence interval, in years 1.0 1.1 2 5 10 50 100 200 5001,000 10,000 100,000

REGULATED

10,000

Streamflow, in cubic feet per second Streamflow, EXPLANATION 7-Day data Estimated n-day values n-day frequency curve

B 1,000 0.9999 0.999 0.99 0.9 0.5 0.2 0.1 0.02 0.01 0.005 0.002 0.001 0.0001 Probability

Figure 1–3–10. May 7-day low-flow frequency data for streamflow-gaging station 06192500 (Yellowstone River near Livingston, Montana) for A, unregulated and B, regulated streamflow conditions, 1928–2002. 50 Streamflow Statistics for the Upper Yellowstone and Bighorn Rivers, Montana and Wyoming, 1928–2002

06192500 Yellowstone River near Livingston, Mont. June 7-day low-flow frequency data Recurrence interval, in years 1.0 1.1 2 5 10 50 100 200 5001,000 10,000 100,000

UNREGULATED

10,000

Streamflow, in cubic feet per second Streamflow, EXPLANATION 7-Day data Estimated n-day values n-day frequency curve

A 1,000 0.9999 0.999 0.99 0.9 0.5 0.2 0.1 0.02 0.01 0.005 0.002 0.001 0.0001 Probability 06192500 Yellowstone River near Livingston, Mont. June 7-day low-flow frequency data Recurrence interval, in years 1.0 1.1 2 5 10 50 100 200 5001,000 10,000 100,000

REGULATED

10,000

Streamflow, in cubic feet per second Streamflow, EXPLANATION 7-Day data Estimated n-day values n-day frequency curve

B 1,000 0.9999 0.999 0.99 0.9 0.5 0.2 0.1 0.02 0.01 0.005 0.002 0.001 0.0001 Probability

Figure 1–3–11. June 7-day low-flow frequency data for streamflow-gaging station 06192500 (Yellowstone River near Livingston, Montana) for A, unregulated and B, regulated streamflow conditions, 1928–2002. Appendixes 51

06192500 Yellowstone River near Livingston, Mont. July 7-day low-flow frequency data Recurrence interval, in years 1.0 1.1 2 5 10 50 100 200 5001,000 10,000 100,000

UNREGULATED

10,000

Streamflow, in cubic feet per second Streamflow, EXPLANATION 7-Day data Estimated n-day values n-day frequency curve

A 1,000 0.9999 0.999 0.99 0.9 0.5 0.2 0.1 0.02 0.01 0.005 0.002 0.001 0.0001 Probability 06192500 Yellowstone River near Livingston, Mont. July 7-day low-flow frequency data Recurrence interval, in years 1.0 1.1 2 5 10 50 100 200 5001,000 10,000 100,000

REGULATED

10,000

Streamflow, in cubic feet per second Streamflow, EXPLANATION 7-Day data Estimated n-day values n-day frequency curve

B 1,000 0.9999 0.999 0.99 0.9 0.5 0.2 0.1 0.02 0.01 0.005 0.002 0.001 0.0001 Probability

Figure 1–3–12. July 7-day low-flow frequency data for streamflow-gaging station 06192500 (Yellowstone River near Livingston, Montana) for A, unregulated and B, regulated streamflow conditions, 1928–2002. 52 Streamflow Statistics for the Upper Yellowstone and Bighorn Rivers, Montana and Wyoming, 1928–2002

06192500 Yellowstone River near Livingston, Mont. August 7-day low-flow frequency data Recurrence interval, in years 1.0 1.1 2 5 10 50 100 200 5001,000 10,000 10,000

UNREGULATED

Streamflow, in cubic feet per second Streamflow, EXPLANATION 7-Day data Estimated n-day values n-day frequency curve

A 1,000 0.9999 0.999 0.99 0.9 0.5 0.2 0.1 0.02 0.01 0.005 0.002 0.001 0.0001 Probability 06192500 Yellowstone River near Livingston, Mont. August 7-day low-flow frequency data Recurrence interval, in years 1.0 1.1 2 5 10 50 100 200 5001,000 10,000 10,000

REGULATED

Streamflow, in cubic feet per second Streamflow, EXPLANATION 7-Day data Estimated n-day values n-day frequency curve

B 1,000 0.9999 0.999 0.99 0.9 0.5 0.2 0.1 0.02 0.01 0.005 0.002 0.001 0.0001 Probability

Figure 1–3–13. August 7-day low-flow frequency data for streamflow-gaging station 06192500 (Yellowstone River near Livingston, Montana) for A, unregulated and B, regulated streamflow conditions, 1928–2002. Appendixes 53

06192500 Yellowstone River near Livingston, Mont. September 7-day low-flow frequency data Recurrence interval, in years 1.0 1.1 2 5 10 50 100 200 5001,000 10,000 10,000

UNREGULATED

Streamflow, in cubic feet per second Streamflow, EXPLANATION 7-Day data Estimated n-day values n-day frequency curve

A 1,000 0.9999 0.999 0.99 0.9 0.5 0.2 0.1 0.02 0.01 0.005 0.002 0.001 0.0001 Probability 06192500 Yellowstone River near Livingston, Mont. September 7-day low-flow frequency data Recurrence interval, in years 1.0 1.1 2 5 10 50 100 200 5001,000 10,000 10,000

REGULATED

Streamflow, in cubic feet per second Streamflow, EXPLANATION 7-Day data Estimated n-day values n-day frequency curve

B 1,000 0.9999 0.999 0.99 0.9 0.5 0.2 0.1 0.02 0.01 0.005 0.002 0.001 0.0001 Probability

Figure 1–3–14. September 7-day low-flow frequency data for streamflow-gaging station 06192500 (Yellowstone River near Livingston, Montana) for A, unregulated and B, regulated streamflow conditions, 1928–2002. 54 Streamflow Statistics for the Upper Yellowstone and Bighorn Rivers, Montana and Wyoming, 1928–2002

06192500 Yellowstone River near Livingston, Mont. October 7-day low-flow frequency data Recurrence interval, in years 1.0 1.1 2 5 10 50 100 200 5001,000 10,000 10,000

UNREGULATED

1,000

Streamflow, in cubic feet per second Streamflow, EXPLANATION 7-Day data Estimated n-day values n-day frequency curve

A 100 0.9999 0.999 0.99 0.9 0.5 0.2 0.1 0.02 0.01 0.005 0.002 0.001 0.0001 Probability 06192500 Yellowstone River near Livingston, Mont. October 7-day low-flow frequency data Recurrence interval, in years 1.0 1.1 2 5 10 50 100 200 5001,000 10,000 10,000

REGULATED

1,000

Streamflow, in cubic feet per second Streamflow, EXPLANATION 7-Day data Estimated n-day values n-day frequency curve

B 100 0.9999 0.999 0.99 0.9 0.5 0.2 0.1 0.02 0.01 0.005 0.002 0.001 0.0001 Probability

Figure 1–3–15. October 7-day low-flow frequency data for streamflow-gaging station 06192500 (Yellowstone River near Livingston, Montana) for A, unregulated and B, regulated streamflow conditions, 1928–2002. Appendixes 55

06192500 Yellowstone River near Livingston, Mont. November 7-day low-flow frequency data Recurrence interval, in years 1.0 1.1 2 5 10 50 100 200 5001,000 10,000 10,000

UNREGULATED

1,000

Streamflow, in cubic feet per second Streamflow, EXPLANATION 7-Day data Estimated n-day values n-day frequency curve

A 100 0.9999 0.999 0.99 0.9 0.5 0.2 0.1 0.02 0.01 0.005 0.002 0.001 0.0001 Probability 06192500 Yellowstone River near Livingston, Mont. November 7-day low-flow frequency data Recurrence interval, in years 1.0 1.1 2 5 10 50 100 200 5001,000 10,000 10,000

REGULATED

1,000

Streamflow, in cubic feet per second Streamflow, EXPLANATION 7-Day data Estimated n-day values n-day frequency curve

B 100 0.9999 0.999 0.99 0.9 0.5 0.2 0.1 0.02 0.01 0.005 0.002 0.001 0.0001 Probability

Figure 1–3–16. November 7-day low-flow frequency data for streamflow-gaging station 06192500 (Yellowstone River near Livingston, Montana) for A, unregulated and B, regulated streamflow conditions, 1928–2002. 56 Streamflow Statistics for the Upper Yellowstone and Bighorn Rivers, Montana and Wyoming, 1928–2002

06192500 Yellowstone River near Livingston, Mont. December 7-day low-flow frequency data Recurrence interval, in years 1.0 1.1 2 5 10 50 100 200 5001,000 10,000 10,000

UNREGULATED

1,000

Streamflow, in cubic feet per second Streamflow, EXPLANATION 7-Day data Estimated n-day values n-day frequency curve

A 100 0.9999 0.999 0.99 0.9 0.5 0.2 0.1 0.02 0.01 0.005 0.002 0.001 0.0001 Probability 06192500 Yellowstone River near Livingston, Mont. December 7-day low-flow frequency data Recurrence interval, in years 1.0 1.1 2 5 10 50 100 200 5001,000 10,000 10,000

REGULATED

1,000

Streamflow, in cubic feet per second Streamflow, EXPLANATION 7-Day data Estimated n-day values n-day frequency curve

B 100 0.9999 0.999 0.99 0.9 0.5 0.2 0.1 0.02 0.01 0.005 0.002 0.001 0.0001 Probability

Figure 1–3–17. December 7-day low-flow frequency data for streamflow-gaging station 06192500 (Yellowstone River near Livingston, Montana) for A, unregulated and B, regulated streamflow conditions, 1928–2002. Appendixes 57

Appendix 1–4. Statistics for streamflow-gaging station 06214500 (Yellowstone River at Billings, Montana)

Table 1–4–1. Annual, seasonal, and monthly n-day low-flow frequency data for streamflow-gaging station 06214500 (Yellowstone River at Billings, Montana) for unregulated and regulated streamflow conditions, 1928–2002.

[ft3/s, cubic feet per second; %, percent]

Unregulated n, period of consecutive Streamflow, in ft3/s, for indicated recurrence interval, in years, and exceedance probability, in percent days (month, for monthly 2 5 10 20 25 50 100 frequency data) 50% 20% 10% 5% 4% 2% 1% Annual 7 1,460 1,140 995 883 852 767 696 30 2,070 1,690 1,500 1,350 1,310 1,190 1,090 Winter (January–March) 7 1,590 1,240 1,080 950 916 821 741 30 2,120 1,750 1,580 1,440 1,400 1,300 1,200 Spring (April–June) 7 3,290 2,540 2,190 1,920 1,850 1,650 1,480 30 4,460 3,370 2,900 2,550 2,460 2,210 2,010 Summer (July–September) 7 4,110 3,290 2,910 2,630 2,540 2,330 2,140 30 4,890 3,920 3,460 3,100 3,000 2,720 2,480 Fall (October–December) 7 1,880 1,400 1,190 1,020 979 859 760 30 2,520 2,070 1,860 1,690 1,640 1,520 1,410 Monthly 7 (January) 1,800 1,390 1,180 1,020 978 856 755 7 (February) 1,980 1,530 1,320 1,160 1,120 1,000 901 7 (March) 2,350 1,940 1,740 1,600 1,560 1,450 1,350 7 (April) 3,290 2,540 2,190 1,920 1,850 1,650 1,480 7 (May) 7,270 5,140 4,250 3,610 3,440 2,990 2,630 7 (June) 19,900 15,000 12,800 11,100 10,700 9,440 8,420 7 (July) 10,260 7,400 6,170 5,290 5,050 4,420 3,910 7 (August) 5,510 4,330 3,800 3,390 3,280 2,980 2,730 7 (September) 4,140 3,310 2,930 2,640 2,550 2,330 2,140 7 (October) 3,400 2,680 2,360 2,110 2,050 1,860 1,710 7 (November) 2,830 2,150 1,820 1,550 1,480 1,280 1,110 7 (December) 1,940 1,450 1,220 1,050 1,010 879 774 58 Streamflow Statistics for the Upper Yellowstone and Bighorn Rivers, Montana and Wyoming, 1928–2002

[ft3/s, cubic feet per second; %, percent]

Regulated n, period of consecutive Streamflow, in ft3/s, for indicated recurrence interval, in years, and exceedance probability, in percent days (month, for monthly 2 5 10 20 25 50 100 frequency data) 50% 20% 10% 5% 4% 2% 1% Annual 7 1,570 1,250 1,100 991 959 874 801 30 2,180 1,780 1,580 1,420 1,380 1,260 1,150 Winter (January–March) 7 1,690 1,340 1,180 1,050 1,020 920 839 30 2,230 1,860 1,690 1,560 1,520 1,410 1,320 Spring (April–June) 7 3,010 2,330 2,000 1,740 1,670 1,480 1,320 30 3,980 3,040 2,620 2,310 2,220 1,990 1,800 Summer (July–September) 7 3,200 2,370 2,000 1,730 1,660 1,460 1,300 30 3,700 2,700 2,260 1,940 1,850 1,620 1,420 Fall (October–December) 7 2,060 1,580 1,360 1,190 1,150 1,020 914 30 2,730 2,280 2,060 1,890 1,840 1,700 1,580 Monthly 7 (January) 1,920 1,500 1,300 1,140 1,090 968 863 7 (February) 2,080 1,620 1,410 1,250 1,200 1,080 977 7 (March) 2,400 1,990 1,800 1,660 1,620 1,500 1,410 7 (April) 3,010 2,330 2,000 1,750 1,680 1,480 1,320 7 (May) 5,830 4,290 3,730 3,350 3,250 2,990 2,790 7 (June) 17,300 12,400 10,200 8,650 8,220 7,080 6,150 7 (July) 7,750 4,950 3,820 3,050 2,850 2,330 1,900 7 (August) 3,770 2,650 2,170 1,830 1,740 1,500 1,310 7 (September) 3,330 2,450 2,060 1,770 1,700 1,490 1,320 7 (October) 3,540 2,760 2,410 2,140 2,070 1,870 1,700 7 (November) 3,120 2,450 2,110 1,850 1,770 1,560 1,390 7 (December) 2,110 1,620 1,390 1,210 1,160 1,020 912 Appendixes 59

Table 1–4–2. Monthly and annual streamflow characteristics for streamflow-gaging station 06214500 (Yellowstone River at Billings, Montana) for unregulated and regulated streamflow conditions, 1928–2002.

[ft3/s, cubic feet per second]

Unregulated Streamflow, in ft3/s, or year, for indicated streamflow characteristic Maximum Year of maximum Year of minimum Standard Minimum monthly monthly mean monthly mean monthly mean Mean monthly deviation of Period mean and and maximum and maximum and minimum and mean annual mean monthly minimum annual annual mean annual mean annual mean streamflow and mean annual mean streamflow streamflow streamflow streamflow streamflow January 3,720 1984 1,200 1940 2,350 513 February 4,281 1997 1,440 1932 2,550 655 March 5,450 1979 1,700 2002 2,970 728 April 9,600 1943 1,650 1961 4,640 1,520 May 32,300 1928 7,020 1953 15,280 4,630 June 56,300 1997 12,900 2001 28,600 8,350 July 39,900 1975 6,650 1934 17,050 6,620 August 11,960 1997 3,940 1988 7,500 2,100 September 8,130 1968 2,400 1988 5,010 1,180 October 6,600 1941 2,080 2001 3,900 1,060 November 4,890 1983 1,890 1931 3,230 720 December 4,290 1975 1,380 1932 2,580 547

Annual 13,100 1997 4,690 2001 7,980 1,695

Regulated Streamflow, in ft3/s, or year, for indicated streamflow characteristic Maximum Year of maximum Year of minimum Standard Minimum monthly monthly mean monthly mean monthly mean Mean monthly deviation of Period mean and and maximum and maximum and minimum and mean annual mean monthly minimum annual annual mean annual mean annual mean streamflow and mean annual mean streamflow streamflow streamflow streamflow streamflow January 3,840 1984 1,340 1940 2,480 512 February 4,380 1997 1,540 1932 2,650 652 March 5,480 1979 1,770 2002 3,020 722 April 8,880 1943 1,440 1961 4,140 1,290 May 29,800 1928 5,680 1953 13,000 4,370 June 53,900 1997 9,860 1987 25,400 8,400 July 37,100 1975 3,400 1988 13,800 6,560 August 9,810 1997 1,470 2001 5,300 2,100 September 7,300 1968 1,530 2001 4,110 1,340 October 6,780 1941 2,130 2001 4,000 1,060 November 5,180 1983 2,210 1931 3,540 707 December 4,460 1975 1,550 1932 2,780 542

Annual 12,250 1997 3,610 2001 7,020 1,750 60 Streamflow Statistics for the Upper Yellowstone and Bighorn Rivers, Montana and Wyoming, 1928–2002

06214500 Yellowstone River at Billings, Mont. Annual n-day low-flow frequency data Recurrence interval, in years 1.0 1.1 2 5 10 50 100 200 5001,000 10,000 10,000

UNREGULATED

1,000

EXPLANATION Streamflow, in cubic feet per second Streamflow, 7-Day data 30-Day data Estimated n-day values Estimated n-day values n-day frequency curve n-day frequency curve Outlier

A 100 0.9999 0.999 0.99 0.9 0.5 0.2 0.1 0.02 0.01 0.005 0.002 0.001 0.0001 Probability 06214500 Yellowstone River at Billings, Mont. Annual n-day low-flow frequency data Recurrence interval, in years 1.0 1.1 2 5 10 50 100 200 5001,000 10,000 10,000

REGULATED

1,000 Streamflow, in cubic feet per second Streamflow, EXPLANATION 7-Day data 30-Day data Estimated n-day values Estimated n-day values n-day frequency curve n-day frequency curve

B 100 0.9999 0.999 0.99 0.9 0.5 0.2 0.1 0.02 0.01 0.005 0.002 0.001 0.0001 Probability

Figure 1–4–1. Annual n-day low-flow frequency data for streamflow-gaging station 06214500 (Yellowstone River at Billings, Montana) for A, unregulated and B, regulated streamflow conditions, 1928–2002. Appendixes 61

06214500 Yellowstone River at Billings, Mont. Winter (January–March) n-day low-flow frequency data Recurrence interval, in years 1.0 1.1 2 5 10 50 100 200 5001,000 10,000 10,000

UNREGULATED

1,000

Streamflow, in cubic feet per second Streamflow, EXPLANATION 7-Day data 30-Day data Estimated n-day values Estimated n-day values n-day frequency curve n-day frequency curve

A 100 0.9999 0.999 0.99 0.9 0.5 0.2 0.1 0.02 0.01 0.005 0.002 0.001 0.0001 Probability 06214500 Yellowstone River at Billings, Mont. Winter (January–March) n-day low-flow frequency data Recurrence interval, in years 1.0 1.1 2 5 10 50 100 200 5001,000 10,000 10,000

REGULATED

1,000

Streamflow, in cubic feet per second Streamflow, EXPLANATION 7-Day data 30-Day data Estimated n-day values Estimated n-day values n-day frequency curve n-day frequency curve

B 100 0.9999 0.999 0.99 0.9 0.5 0.2 0.1 0.02 0.01 0.005 0.002 0.001 0.0001 Probability

Figure 1–4–2. Winter (January–March) n-day low-flow frequency data for streamflow-gaging station 06214500 (Yellowstone River at Billings, Montana) for A, unregulated and B, regulated streamflow conditions, 1928–2002. 62 Streamflow Statistics for the Upper Yellowstone and Bighorn Rivers, Montana and Wyoming, 1928–2002

06214500 Yellowstone River at Billings, Mont. Spring (April–June) n-day low-flow frequency data Recurrence interval, in years 1.0 1.1 2 5 10 50 100 200 5001,000 10,000 10,000

UNREGULATED

EXPLANATION

Streamflow, in cubic feet per second Streamflow, 7-Day data 30-Day data Estimated n-day values Estimated n-day values n-day frequency curve n-day frequency curve Outlier Outlier

A 1,000 0.9999 0.999 0.99 0.9 0.5 0.2 0.1 0.02 0.01 0.005 0.002 0.001 0.0001 Probability 06214500 Yellowstone River at Billings, Mont. Spring (April–June) n-day low-flow frequency data Recurrence interval, in years 1.0 1.1 2 5 10 50 100 200 5001,000 10,000 10,000

REGULATED

EXPLANATION

Streamflow, in cubic feet per second Streamflow, 7-Day data 30-Day data Estimated n-day values Estimated n-day values n-day frequency curve n-day frequency curve Outlier Outlier

B 1,000 0.9999 0.999 0.99 0.9 0.5 0.2 0.1 0.02 0.01 0.005 0.002 0.001 0.0001 Probability

Figure 1–4–3. Spring (April–June) n-day low-flow frequency data for streamflow-gaging station 06214500 (Yellowstone River at Billings, Montana) for A, unregulated and B, regulated streamflow conditions, 1928–2002. Appendixes 63

06214500 Yellowstone River at Billings, Mont. Summer (July–September) n-day low-flow frequency data Recurrence interval, in years 1.0 1.1 2 5 10 50 100 200 5001,000 10,000 10,000

UNREGULATED Streamflow, in cubic feet per second Streamflow, EXPLANATION 7-Day data 30-Day data Estimated n-day values Estimated n-day values n-day frequency curve n-day frequency curve

A 1,000 0.9999 0.999 0.99 0.9 0.5 0.2 0.1 0.02 0.01 0.005 0.002 0.001 0.0001 Probability 06214500 Yellowstone River at Billings, Mont. Summer (July–September) n-day low-flow frequency data Recurrence interval, in years 1.0 1.1 2 5 10 50 100 200 5001,000 10,000 10,000

REGULATED

EXPLANATION Streamflow, in cubic feet per second Streamflow, 7-Day data 30-Day data Estimated n-day values Estimated n-day values n-day frequency curve n-day frequency curve Outlier

B 1,000 0.9999 0.999 0.99 0.9 0.5 0.2 0.1 0.02 0.01 0.005 0.002 0.001 0.0001 Probability

Figure 1–4–4. Summer (July–September) n-day low-flow frequency data for streamflow-gaging station 06214500 (Yellowstone River at Billings, Montana) for A, unregulated and B, regulated streamflow conditions, 1928–2002. 64 Streamflow Statistics for the Upper Yellowstone and Bighorn Rivers, Montana and Wyoming, 1928–2002

06214500 Yellowstone River at Billings, Mont. Fall (October–December) n-day low-flow frequency data Recurrence interval, in years 1.0 1.1 2 5 10 50 100 200 5001,000 10,000 10,000

UNREGULATED

1,000

EXPLANATION Streamflow, in cubic feet per second Streamflow, 7-Day data 30-Day data Estimated n-day values Estimated n-day values n-day frequency curve n-day frequency curve Outlier

A 100 0.9999 0.999 0.99 0.9 0.5 0.2 0.1 0.02 0.01 0.005 0.002 0.001 0.0001 Probability 06214500 Yellowstone River at Billings, Mont. Fall (October–December) n-day low-flow frequency data Recurrence interval, in years 1.0 1.1 2 5 10 50 100 200 5001,000 10,000 10,000

REGULATED 1,000

EXPLANATION Streamflow, in cubic feet per second Streamflow, 7-Day data 30-Day data Estimated n-day values Estimated n-day values n-day frequency curve n-day frequency curve Outlier

B 100 0.9999 0.999 0.99 0.9 0.5 0.2 0.1 0.02 0.01 0.005 0.002 0.001 0.0001 Probability

Figure 1–4–5. Fall (October–December) n-day low-flow frequency data for streamflow-gaging station 06214500 (Yellowstone River at Billings, Montana) for A, unregulated and B, regulated streamflow conditions, 1928–2002. Appendixes 65

06214500 Yellowstone River at Billings, Mont. January 7-day low-flow frequency data Recurrence interval, in years 1.0 1.1 2 5 10 50 100 200 5001,000 10,000 10,000

UNREGULATED

1,000

Streamflow, in cubic feet per second Streamflow, EXPLANATION 7-Day data Estimated n-day values n-day frequency curve

A 100 0.9999 0.999 0.99 0.9 0.5 0.2 0.1 0.02 0.01 0.005 0.002 0.001 0.0001 Probability 06214500 Yellowstone River at Billings, Mont. January 7-day low-flow frequency data Recurrence interval, in years 1.0 1.1 2 5 10 50 100 200 5001,000 10,000 10,000

REGULATED 1,000

Streamflow, in cubic feet per second Streamflow, EXPLANATION 7-Day data Estimated n-day values n-day frequency curve

B 100 0.9999 0.999 0.99 0.9 0.5 0.2 0.1 0.02 0.01 0.005 0.002 0.001 0.0001 Probability

Figure 1–4–6. January 7-day low-flow frequency data for streamflow-gaging station 06214500 (Yellowstone River at Billings, Montana) for A, unregulated and B, regulated streamflow conditions, 1928–2002. 66 Streamflow Statistics for the Upper Yellowstone and Bighorn Rivers, Montana and Wyoming, 1928–2002

06214500 Yellowstone River at Billings, Mont. February 7-day low-flow frequency data Recurrence interval, in years 1.0 1.1 2 5 10 50 100 200 5001,000 10,000 10,000

UNREGULATED

1,000

Streamflow, in cubic feet per second Streamflow, EXPLANATION 7-Day data Estimated n-day values n-day frequency curve

A 100 0.9999 0.999 0.99 0.9 0.5 0.2 0.1 0.02 0.01 0.005 0.002 0.001 0.0001 Probability 06214500 Yellowstone River at Billings, Mont. February 7-day low-flow frequency data Recurrence interval, in years 1.0 1.1 2 5 10 50 100 200 5001,000 10,000 10,000

REGULATED 1,000

Streamflow, in cubic feet per second Streamflow, EXPLANATION 7-Day data Estimated n-day values n-day frequency curve

B 100 0.9999 0.999 0.99 0.9 0.5 0.2 0.1 0.02 0.01 0.005 0.002 0.001 0.0001 Probability

Figure 1–4–7. February 7-day low-flow frequency data for streamflow-gaging station 06214500 (Yellowstone River at Billings, Montana) for A, unregulated and B, regulated streamflow conditions, 1928–2002. Appendixes 67

06214500 Yellowstone River at Billings, Mont. March 7-day low-flow frequency data Recurrence interval, in years 1.0 1.1 2 5 10 50 100 200 5001,000 10,000 10,000

UNREGULATED

Streamflow, in cubic feet per second Streamflow, EXPLANATION 7-Day data Estimated n-day values n-day frequency curve

A 1,000 0.9999 0.999 0.99 0.9 0.5 0.2 0.1 0.02 0.01 0.005 0.002 0.001 0.0001 Probability 06214500 Yellowstone River at Billings, Mont. March 7-day low-flow frequency data Recurrence interval, in years 1.0 1.1 2 5 10 50 100 200 5001,000 10,000 10,000

REGULATED

Streamflow, in cubic feet per second Streamflow, EXPLANATION 7-Day data Estimated n-day values n-day frequency curve

B 1,000 0.9999 0.999 0.99 0.9 0.5 0.2 0.1 0.02 0.01 0.005 0.002 0.001 0.0001 Probability

Figure 1–4–8. March 7-day low-flow frequency data for streamflow-gaging station 06214500 (Yellowstone River at Billings, Montana) for A, unregulated and B, regulated streamflow conditions, 1928–2002. 68 Streamflow Statistics for the Upper Yellowstone and Bighorn Rivers, Montana and Wyoming, 1928–2002

06214500 Yellowstone River at Billings, Mont. April 7-day low-flow frequency data Recurrence interval, in years 1.0 1.1 2 5 10 50 100 200 5001,000 10,000 10,000

UNREGULATED

EXPLANATION Streamflow, in cubic feet per second Streamflow, 7-Day data Estimated n-day values n-day frequency curve Outlier

A 1,000 0.9999 0.999 0.99 0.9 0.5 0.2 0.1 0.02 0.01 0.005 0.002 0.001 0.0001 Probability 06214500 Yellowstone River at Billings, Mont. April 7-day low-flow frequency data Recurrence interval, in years 1.0 1.1 2 5 10 50 100 200 5001,000 10,000 10,000

REGULATED

EXPLANATION Streamflow, in cubic feet per second Streamflow, 7-Day data Estimated n-day values n-day frequency curve Outlier

B 1,000 0.9999 0.999 0.99 0.9 0.5 0.2 0.1 0.02 0.01 0.005 0.002 0.001 0.0001 Probability

Figure 1–4–9. April 7-day low-flow frequency data for streamflow-gaging station 06214500 (Yellowstone River at Billings, Montana) for A, unregulated and B, regulated streamflow conditions, 1928–2002. Appendixes 69

06214500 Yellowstone River at Billings, Mont. May 7-day low-flow frequency data Recurrence interval, in years 1.0 1.1 2 5 10 50 100 200 5001,000 10,000 100,000

UNREGULATED

10,000

EXPLANATION Streamflow, in cubic feet per second Streamflow, 7-Day data Estimated n-day values n-day frequency curve Outlier

A 1,000 0.9999 0.999 0.99 0.9 0.5 0.2 0.1 0.02 0.01 0.005 0.002 0.001 0.0001 Probability 06214500 Yellowstone River at Billings, Mont. May 7-day low-flow frequency data Recurrence interval, in years 1.0 1.1 2 5 10 50 100 200 5001,000 10,000 100,000

REGULATED

10,000

EXPLANATION Streamflow, in cubic feet per second Streamflow, 7-Day data Estimated n-day values n-day frequency curve Outlier

B 1,000 0.9999 0.999 0.99 0.9 0.5 0.2 0.1 0.02 0.01 0.005 0.002 0.001 0.0001 Probability

Figure 1–4–10. May 7-day low-flow frequency data for streamflow-gaging station 06214500 (Yellowstone River at Billings, Montana) for A, unregulated and B, regulated streamflow conditions, 1928–2002. 70 Streamflow Statistics for the Upper Yellowstone and Bighorn Rivers, Montana and Wyoming, 1928–2002

06214500 Yellowstone River at Billings, Mont. June 7-day low-flow frequency data Recurrence interval, in years 1.0 1.1 2 5 10 50 100 200 5001,000 10,000 100,000

UNREGULATED

10,000 Streamflow, in cubic feet per second Streamflow, EXPLANATION 7-Day data Estimated n-day values n-day frequency curve

A 1,000 0.9999 0.999 0.99 0.9 0.5 0.2 0.1 0.02 0.01 0.005 0.002 0.001 0.0001 Probability 06214500 Yellowstone River at Billings, Mont. June 7-day low-flow frequency data Recurrence interval, in years 1.0 1.1 2 5 10 50 100 200 5001,000 10,000 100,000

REGULATED 10,000

EXPLANATION Streamflow, in cubic feet per second Streamflow, 7-Day data Estimated n-day values n-day frequency curve Outlier

B 1,000 0.9999 0.999 0.99 0.9 0.5 0.2 0.1 0.02 0.01 0.005 0.002 0.001 0.0001 Probability

Figure 1–4–11. June 7-day low-flow frequency data for streamflow-gaging station 06214500 (Yellowstone River at Billings, Montana) for A, unregulated and B, regulated streamflow conditions, 1928–2002. Appendixes 71

06214500 Yellowstone River at Billings, Mont. July 7-day low-flow frequency data Recurrence interval, in years 1.0 1.1 2 5 10 50 100 200 5001,000 10,000 100,000

UNREGULATED

10,000

Streamflow, in cubic feet per second Streamflow, EXPLANATION 7-Day data Estimated n-day values n-day frequency curve

A 1,000 0.9999 0.999 0.99 0.9 0.5 0.2 0.1 0.02 0.01 0.005 0.002 0.001 0.0001 Probability 06214500 Yellowstone River at Billings, Mont. July 7-day low-flow frequency data Recurrence interval, in years 1.0 1.1 2 5 10 50 100 200 5001,000 10,000 100,000

REGULATED

10,000

Streamflow, in cubic feet per second Streamflow, EXPLANATION 7-Day data Estimated n-day values n-day frequency curve

B 1,000 0.9999 0.999 0.99 0.9 0.5 0.2 0.1 0.02 0.01 0.005 0.002 0.001 0.0001 Probability

Figure 1–4–12. July 7-day low-flow frequency data for streamflow-gaging station 06214500 (Yellowstone River at Billings, Montana) for A, unregulated and B, regulated streamflow conditions, 1928–2002. 72 Streamflow Statistics for the Upper Yellowstone and Bighorn Rivers, Montana and Wyoming, 1928–2002

06214500 Yellowstone River at Billings, Mont. August 7-day low-flow frequency data Recurrence interval, in years 1.0 1.1 2 5 10 50 100 200 5001,000 10,000 10,000

UNREGULATED

Streamflow, in cubic feet per second Streamflow, EXPLANATION 7-Day data Estimated n-day values n-day frequency curve

A 1,000 0.9999 0.999 0.99 0.9 0.5 0.2 0.1 0.02 0.01 0.005 0.002 0.001 0.0001 Probability 06214500 Yellowstone River at Billings, Mont. August 7-day low-flow frequency data Recurrence interval, in years 1.0 1.1 2 5 10 50 100 200 5001,000 10,000 10,000

REGULATED

Streamflow, in cubic feet per second Streamflow, EXPLANATION 7-Day data Estimated n-day values n-day frequency curve

B 1,000 0.9999 0.999 0.99 0.9 0.5 0.2 0.1 0.02 0.01 0.005 0.002 0.001 0.0001 Probability

Figure 1–4–13. August 7-day low-flow frequency data for streamflow-gaging station 06214500 (Yellowstone River at Billings, Montana) for A, unregulated and B, regulated streamflow conditions, 1928–2002. Appendixes 73

06214500 Yellowstone River at Billings, Mont. September 7-day low-flow frequency data Recurrence interval, in years 1.0 1.1 2 5 10 50 100 200 5001,000 10,000 10,000

UNREGULATED

Streamflow, in cubic feet per second Streamflow, EXPLANATION 7-Day data Estimated n-day values n-day frequency curve

A 1,000 0.9999 0.999 0.99 0.9 0.5 0.2 0.1 0.02 0.01 0.005 0.002 0.001 0.0001 Probability 06214500 Yellowstone River at Billings, Mont. September 7-day low-flow frequency data Recurrence interval, in years 1.0 1.1 2 5 10 50 100 200 5001,000 10,000 10,000

REGULATED

Streamflow, in cubic feet per second Streamflow, EXPLANATION 7-Day data Estimated n-day values n-day frequency curve

B 1,000 0.9999 0.999 0.99 0.9 0.5 0.2 0.1 0.02 0.01 0.005 0.002 0.001 0.0001 Probability

EXPLANATION 7-Day Data Estimated n-day values n-day frequency curve

Figure 1–4–14. September 7-day low-flow frequency data for streamflow-gaging station 06214500 (Yellowstone River at Billings, Montana) for A, unregulated and B, regulated streamflow conditions, 1928–2002. 74 Streamflow Statistics for the Upper Yellowstone and Bighorn Rivers, Montana and Wyoming, 1928–2002

06214500 Yellowstone River at Billings, Mont. October 7-day low-flow frequency data Recurrence interval, in years 1.0 1.1 2 5 10 50 100 200 5001,000 10,000 10,000

UNREGULATED

Streamflow, in cubic feet per second Streamflow, EXPLANATION 7-Day data Estimated n-day values n-day frequency curve

A 1,000 0.9999 0.999 0.99 0.9 0.5 0.2 0.1 0.02 0.01 0.005 0.002 0.001 0.0001 Probability 06214500 Yellowstone River at Billings, Mont. October 7-day low-flow frequency data Recurrence interval, in years 1.0 1.1 2 5 10 50 100 200 5001,000 10,000 10,000

REGULATED

Streamflow, in cubic feet per second Streamflow, EXPLANATION 7-Day data Estimated n-day values n-day frequency curve

B 1,000 0.9999 0.999 0.99 0.9 0.5 0.2 0.1 0.02 0.01 0.005 0.002 0.001 0.0001 Probability

Figure 1–4–15. October 7-day low-flow frequency data for streamflow-gaging station 06214500 (Yellowstone River at Billings, Montana) for A, unregulated and B, regulated streamflow conditions, 1928–2002. Appendixes 75

06214500 Yellowstone River at Billings, Mont. November 7-day low-flow frequency data Recurrence interval, in years 1.0 1.1 2 5 10 50 100 200 5001,000 10,000 10,000

UNREGULATED

1,000

EXPLANATION Streamflow, in cubic feet per second Streamflow, 7-Day data Estimated n-day values n-day frequency curve Outlier

A 100 0.9999 0.999 0.99 0.9 0.5 0.2 0.1 0.02 0.01 0.005 0.002 0.001 0.0001 Probability 06214500 Yellowstone River at Billings, Mont. November 7-day low-flow frequency data Recurrence interval, in years 1.0 1.1 2 5 10 50 100 200 5001,000 10,000 10,000

REGULATED

1,000

EXPLANATION Streamflow, in cubic feet per second Streamflow, 7-Day data Estimated n-day values n-day frequency curve Outlier

B 100 0.9999 0.999 0.99 0.9 0.5 0.2 0.1 0.02 0.01 0.005 0.002 0.001 0.0001 Probability

Figure 1–4–16. November 7-day low-flow frequency data for streamflow-gaging station 06214500 (Yellowstone River at Billings, Montana) for A, unregulated and B, regulated streamflow conditions, 1928–2002. 76 Streamflow Statistics for the Upper Yellowstone and Bighorn Rivers, Montana and Wyoming, 1928–2002

06214500 Yellowstone River at Billings, Mont. December 7-day low-flow frequency data Recurrence interval, in years 1.0 1.1 2 5 10 50 100 200 5001,000 10,000 10,000

UNREGULATED

1,000

EXPLANATION Streamflow, in cubic feet per second Streamflow, 7-Day data Estimated n-day values n-day frequency curve Outlier

A 100 0.9999 0.999 0.99 0.9 0.5 0.2 0.1 0.02 0.01 0.005 0.002 0.001 0.0001 Probability 06214500 Yellowstone River at Billings, Mont. December 7-day low-flow frequency data Recurrence interval, in years 1.0 1.1 2 5 10 50 100 200 5001,000 10,000 10,000

REGULATED 1,000

EXPLANATION Streamflow, in cubic feet per second Streamflow, 7-Day data Estimated n-day values n-day frequency curve Outlier

B 100 0.9999 0.999 0.99 0.9 0.5 0.2 0.1 0.02 0.01 0.005 0.002 0.001 0.0001 Probability

Figure 1–4–17. December 7-day low-flow frequency data for streamflow-gaging station 06214500 (Yellowstone River at Billings, Montana) for A, unregulated and B, regulated streamflow conditions, 1928–2002. Appendixes 77

Appendix 1–5. Statistics for streamflow-gaging station 06294500 (Bighorn River above Tullock Creek, near Bighorn, Montana)

Table 1–5–1. Annual, seasonal, and monthly n-day low-flow frequency data for streamflow-gaging station 06294500 (Bighorn River above Tullock Creek, near Bighorn, Montana) for unregulated and regulated streamflow conditions, 1928–2002.

[ft3/s, cubic feet per second; %, percent]

Unregulated n, period of consecutive Streamflow, in ft3/s, for indicated recurrence interval, in years, and exceedance probability, in percent days (month, for monthly 2 5 10 20 25 50 100 frequency data) 50% 20% 10% 5% 4% 2% 1% Annual 7 1,000 300 1 0 0 0 0 30 1,600 875 550 344 296 184 115 Winter (January–March) 7 1,350 658 386 228 192 113 67 30 1,940 1,100 679 410 347 206 121 Spring (April–June) 7 3,210 2,350 1,990 1,740 1,670 1,490 1,340 30 3,930 2,900 2,460 2,140 2,050 1,820 1,630 Summer (July–September) 7 2,810 1,980 1,580 1,270 1,190 970 796 30 3,510 2,730 2,340 2,040 1,950 1,720 1,520 Fall (October–December) 7 1,110 425 124 28 16 3 1 30 1,860 1,140 787 543 482 332 229 Monthly 7 (January) 1,450 712 421 250 212 126 76 7 (February) 1,720 1,050 699 450 403 220 67 7 (March) 2,110 1,420 1,130 935 883 746 639 7 (April) 3,210 2,350 1,990 1,740 1,670 1,490 1,340 7 (May) 7,640 5,920 5,110 4,490 4,310 3,840 3,450 7 (June) 11,100 8,600 7,500 6,700 6,500 5,890 5,400 7 (July) 7,700 6,140 5,510 5,050 4,930 4,610 4,340 7 (August) 4,720 3,990 3,640 3,370 3,290 3,080 2,890 7 (September) 2,860 2,000 1,580 1,270 1,190 965 790 7 (October) 2,060 1,340 1,020 788 728 574 456 7 (November) 1,810 961 446 180 131 47 16 7 (December) 1,240 721 271 72 44 9 2 78 Streamflow Statistics for the Upper Yellowstone and Bighorn Rivers, Montana and Wyoming, 1928–2002

[ft3/s, cubic feet per second; %, percent]

Regulated n, period of consecutive Streamflow, in ft3/s, for indicated recurrence interval, in years, and exceedance probability, in percent days (month, for monthly 2 5 10 20 25 50 100 frequency data) 50% 20% 10% 5% 4% 2% 1% Annual 7 1,200 300 90 30 20 7 2 30 1,580 802 504 323 281 183 120 Winter (January–March) 7 2,400 1,620 1,240 970 897 708 563 30 2,840 2,080 1,690 1,380 1,290 1,060 879 Spring (April–June) 7 1,430 496 110 30 26 7 2 30 2,190 1,070 664 422 366 238 156 Summer (July–September) 7 1,480 590 294 146 117 58 29 30 2,080 1,120 728 483 425 286 194 Fall (October–December) 7 2,160 1,420 1,110 886 828 679 562 30 2,790 2,030 1,660 1,380 1,310 1,110 940 Monthly 7 (January) 2,560 1,790 1,430 1,170 1,100 907 756 7 (February) 2,780 2,050 1,640 1,290 1,190 888 612 7 (March) 3,050 2,040 1,550 1,190 1,100 852 665 7 (April) 2,120 1,100 670 407 347 211 128 7 (May) 1,770 616 231 80 56 18 6 7 (June) 4,100 1,900 1,200 723 623 398 257 7 (July) 2,810 969 433 193 149 67 30 7 (August) 1,920 1,000 659 446 395 273 191 7 (September) 2,300 1,420 1,040 767 698 525 397 7 (October) 2,770 1,980 1,620 1,350 1,280 1,090 930 7 (November) 2,810 1,820 1,390 1,080 1,000 796 638 7 (December) 2,590 1,750 1,380 1,100 1,030 839 689 Appendixes 79

Table 1–5–2. Monthly and annual streamflow characteristics for streamflow-gaging station 06294500 (Bighorn River above Tullock Creek, near Bighorn, Montana) for unregulated and regulated streamflow conditions, 1928–2002.

[ft3/s, cubic feet per second]

Unregulated Streamflow, in ft3/s, or year, for indicated streamflow characteristic Maximum Year of maximum Year of minimum Standard Minimum monthly monthly mean monthly mean monthly mean Mean monthly deviation of Period mean and and maximum and maximum and minimum and mean annual mean monthly minimum annual annual mean annual mean annual mean streamflow and mean annual mean streamflow streamflow streamflow streamflow streamflow January 3,510 1983 51 1937 1,970 740 February 5,050 1971 246 1936 2,340 1,020 March 9,670 1929 1,090 1931 3,330 1,440 April 7,790 1996 1,670 1935 4,090 1,370 May 15,500 1978 4,300 1935 9,620 2,280 June 28,700 1944 7,150 1985 14,600 4,610 July 22,700 1967 4,980 1934 10,950 4,260 August 11,000 1930 3,600 1966 5,610 1,280 September 5,720 1998 1,290 1934 3,510 895 October 4,740 1982 566 2002 2,500 922 November 3,960 1978 555 1960 2,200 837 December 3,440 1982 626 1936 2,030 709

Annual 7,340 1997 3,190 2002 5,240 1,035

Regulated Streamflow, in ft3/s, or year, for indicated streamflow characteristic Maximum Year of maximum Year of minimum Standard Minimum monthly monthly mean monthly mean monthly mean Mean monthly deviation of mean and Period and maximum and maximum and minimum and mean annual mean monthly minimum annual annual mean annual mean annual mean streamflow and mean annual mean streamflow streamflow streamflow streamflow streamflow January 5,260 1968 1,140 1937 3,120 790 February 5,350 1971 1,270 1936 3,260 970 March 10,590 1929 697 1966 3,970 1,483 April 7,920 1997 882 1934 2,830 1,550 May 8,900 1978 76 1934 3,300 1,950 June 20,200 1944 502 1961 6,600 3,800 July 18,600 1967 169 1931 5,500 4,310 August 7,780 1930 668 1934 2,830 1,570 September 6,170 1941 605 1940 2,820 1,076 October 5,750 1971 1,160 2002 3,340 1,083 November 5,700 1973 1,090 1960 3,300 1,086 December 4,900 1982 1,400 2002 3,200 823

Annual 5,850 1997 1,310 1966 3,680 1,130 80 Streamflow Statistics for the Upper Yellowstone and Bighorn Rivers, Montana and Wyoming, 1928–2002

06294500 Bighorn River above Tullock Creek, near Bighorn, Mont. Annual n-day low-flow frequency data Recurrence interval, in years 1.0 1.1 2 5 10 50 100 200 5001,000 10,000 10,000

1,000

UNREGULATED 100

EXPLANATION Streamflow, in cubic feet per second Streamflow, 10 7-Day data 30-Day data Estimated n-day values Estimated n-day values n-day frequency curve n-day frequency curve Outlier Outlier

A 1.0 0.9999 0.999 0.99 0.9 0.5 0.2 0.1 0.02 0.01 0.005 0.002 0.001 0.0001 Probability 06294500 Bighorn River above Tullock Creek, near Bighorn, Mont. Annual n-day low-flow frequency data Recurrence interval, in years 1.0 1.1 2 5 10 50 100 200 5001,000 10,000 10,000

1,000

REGULATED 100

EXPLANATION

Streamflow, in cubic feet per second Streamflow, 10 7-Day data 30-Day data Estimated n-day values Estimated n-day values n-day frequency curve n-day frequency curve Outlier

B 1.0 0.9999 0.999 0.99 0.9 0.5 0.2 0.1 0.02 0.01 0.005 0.002 0.001 0.0001 Probability

Figure 1–5–1. Annual n-day low-flow frequency data for streamflow-gaging station 06294500 (Bighorn River above Tullock Creek, near Bighorn, Montana) for A, unregulated and B, regulated streamflow conditions, 1928–2002.. Appendixes 81

06294500 Bighorn River above Tullock Creek, near Bighorn, Mont. Winter (January−March) n-day low-flow frequency data Recurrence interval, in years 1.0 1.1 2 5 10 50 100 200 5001,000 10,000 10,000

UNREGULATED 1,000

100 EXPLANATION Streamflow, in cubic feet per second Streamflow, 7-Day data 30-Day data Estimated n-day values Estimated n-day values n-day frequency curve n-day frequency curve Outlier Outlier

A 10 0.9999 0.999 0.99 0.9 0.5 0.2 0.1 0.02 0.01 0.005 0.002 0.001 0.0001 Probability 06294500 Bighorn River above Tullock Creek, near Bighorn, Mont. Winter (January−March) n-day low-flow frequency data Recurrence interval, in years 1.0 1.1 2 5 10 50 100 200 5001,000 10,000 10,000

REGULATED 1,000

100 EXPLANATION Streamflow, in cubic feet per second Streamflow, 7-Day data 30-Day data Estimated n-day values Estimated n-day values n-day frequency curve n-day frequency curve Outlier Outlier

B 10 0.9999 0.999 0.99 0.9 0.5 0.2 0.1 0.02 0.01 0.005 0.002 0.001 0.0001 Probability

Figure 1–5–2. Winter (January–March) n-day low-flow frequency data for streamflow-gaging station 06294500 (Bighorn River above Tullock Creek, near Bighorn, Montana) for A, unregulated and B, regulated streamflow conditions, 1928–2002. 82 Streamflow Statistics for the Upper Yellowstone and Bighorn Rivers, Montana and Wyoming, 1928–2002

06294500 Bighorn River above Tullock Creek, near Bighorn, Mont. Spring (April−June) n-day low-flow frequency data Recurrence interval, in years 1.0 1.1 2 5 10 50 100 200 5001,000 10,000 10,000

UNREGULATED 1,000

100 Streamflow, in cubic feet per second Streamflow, 10 EXPLANATION 7-Day data 30-Day data Estimated n-day values Estimated n-day values n-day frequency curve n-day frequency curve

A 1.0 0.9999 0.999 0.99 0.9 0.5 0.2 0.1 0.02 0.01 0.005 0.002 0.001 0.0001 Probability 06294500 Bighorn River above Tullock Creek, near Bighorn, Mont. Spring (April−June) n-day low-flow frequency data Recurrence interval, in years 1.0 1.1 2 5 10 50 100 200 5001,000 10,000 10,000

REGULATED 1,000

100

EXPLANATION Streamflow, in cubic feet per second Streamflow, 10 7-Day data 30-Day data Estimated n-day values Estimated n-day values n-day frequency curve n-day frequency curve Outlier Outlier

B 1.0 0.9999 0.999 0.99 0.9 0.5 0.2 0.1 0.02 0.01 0.005 0.002 0.001 0.0001 Probability

Figure 1–5–3. Spring (April–June) n-day low-flow frequency data for streamflow-gaging station 06294500 (Bighorn River above Tullock Creek, near Bighorn, Montana) for A, unregulated and B, regulated streamflow conditions, 1928–2002. Appendixes 83

06294500 Bighorn River above Tullock Creek, near Bighorn, Mont. Summer (July−September) n-day low-flow frequency data Recurrence interval, in years 1.0 1.1 2 5 10 50 100 200 5001,000 10,000 10,000

UNREGULATED 1,000

100 EXPLANATION Streamflow, in cubic feet per second Streamflow, 7-Day data 30-Day data Estimated n-day values Estimated n-day values n-day frequency curve n-day frequency curve Outlier Outlier

A 10 0.9999 0.999 0.99 0.9 0.5 0.2 0.1 0.02 0.01 0.005 0.002 0.001 0.0001 Probability 06294500 Bighorn River above Tullock Creek, near Bighorn, Mont. Summer (July−September) n-day low-flow frequency data Recurrence interval, in years 1.0 1.1 2 5 10 50 100 200 5001,000 10,000 10,000

REGULATED 1,000

100 EXPLANATION Streamflow, in cubic feet per second Streamflow, 7-Day data 30-Day data Estimated n-day values Estimated n-day values n-day frequency curve n-day frequency curve Outlier Outlier

B 10 0.9999 0.999 0.99 0.9 0.5 0.2 0.1 0.02 0.01 0.005 0.002 0.001 0.0001 Probability

Figure 1–5–4. Summer (July–September) n-day low-flow frequency data for streamflow-gaging station 06294500 (Bighorn River above Tullock Creek, near Bighorn, Montana) for A, unregulated and B, regulated streamflow conditions, 1928–2002. 84 Streamflow Statistics for the Upper Yellowstone and Bighorn Rivers, Montana and Wyoming, 1928–2002

06294500 Bighorn River above Tullock Creek, near Bighorn, Mont. Fall (October−December) n-day low-flow frequency data Recurrence interval, in years 1.0 1.1 2 5 10 50 100 200 5001,000 10,000 10,000

UNREGULATED 1,000

100

EXPLANATION Streamflow, in cubic feet per second Streamflow, 10 7-Day data 30-Day data Estimated n-day values Estimated n-day values n-day frequency curve n-day frequency curve Outlier Outlier

A 1.0 0.9999 0.999 0.99 0.9 0.5 0.2 0.1 0.02 0.01 0.005 0.002 0.001 0.0001 Probability 06294500 Bighorn River above Tullock Creek, near Bighorn, Mont. Fall (October−December) n-day low-flow frequency data Recurrence interval, in years 1.0 1.1 2 5 10 50 100 200 5001,000 10,000 10,000

REGULATED 1,000

100

EXPLANATION Streamflow, in cubic feet per second Streamflow, 10 7-Day data 30-Day data Estimated n-day values Estimated n-day values n-day frequency curve n-day frequency curve Outlier Outlier

B 1.0 0.9999 0.999 0.99 0.9 0.5 0.2 0.1 0.02 0.01 0.005 0.002 0.001 0.0001 Probability

Figure 1–5–5. Fall (October–December) n-day low-flow frequency data for streamflow-gaging station 06294500 (Bighorn River above Tullock Creek, near Bighorn, Montana) for A, unregulated and B, regulated streamflow conditions, 1928–2002. Appendixes 85

06294500 Bighorn River above Tullock Creek, near Bighorn, Mont. Janaury 7-day low-flow frequency data Recurrence interval, in years 1.0 1.1 2 5 10 50 100 200 5001,000 10,000 10,000

UNREGULATED 1,000

100

Streamflow, in cubic feet per second Streamflow, EXPLANATION 7-Day data Estimated n-day values n-day frequency curve Outlier

A 10 0.9999 0.999 0.99 0.9 0.5 0.2 0.1 0.02 0.01 0.005 0.002 0.001 0.0001 Probability 06294500 Bighorn River above Tullock Creek, near Bighorn, Mont. Janaury 7-day low-flow frequency data Recurrence interval, in years 1.0 1.1 2 5 10 50 100 200 5001,000 10,000 10,000

REGULATED 1,000

100 EXPLANATION Streamflow, in cubic feet per second Streamflow, 7-Day data Estimated n-day values n-day frequency curve Outlier

B 10 0.9999 0.999 0.99 0.9 0.5 0.2 0.1 0.02 0.01 0.005 0.002 0.001 0.0001 Probability

Figure 1–5–6. January 7-day low-flow frequency data for streamflow-gaging station 06294500 (Bighorn River above Tullock Creek, near Bighorn, Montana) for A, unregulated and B, regulated streamflow conditions, 1928–2002. 86 Streamflow Statistics for the Upper Yellowstone and Bighorn Rivers, Montana and Wyoming, 1928–2002

06294500 Bighorn River above Tullock Creek, near Bighorn, Mont. Februry 7-day low-flow frequency data Recurrence interval, in years 1.0 1.1 2 5 10 50 100 200 5001,000 10,000 5,000

4,500

4,000

3,500

3,000

2,500 UNREGULATED 2,000

1,500 Streamflow, in cubic feet per second Streamflow, EXPLANATION 1,000 7-Day data Estimated n-day values 500 n-day frequency curve A 0 0.9999 0.999 0.99 0.9 0.5 0.2 0.1 0.02 0.01 0.005 0.002 0.001 0.0001 Probability 06294500 Bighorn River above Tullock Creek, near Bighorn, Mont. February 7-day low-flow frequency data Recurrence interval, in years 1.0 1.1 2 5 10 50 100 200 5001,000 10,000 5,000

4,500

4,000

3,500

3,000

2,500 REGULATED 2,000

1,500 Streamflow, in cubic feet per second Streamflow, EXPLANATION 1,000 7-Day data Estimated n-day values 500 n-day frequency curve B 0 0.9999 0.999 0.99 0.9 0.5 0.2 0.1 0.02 0.01 0.005 0.002 0.001 0.0001 Probability

Figure 1–5–7. February 7-day low-flow frequency data for streamflow-gaging station 06294500 (Bighorn River above Tullock Creek, near Bighorn, Montana) for A, unregulated and B, regulated streamflow conditions, 1928–2002. Appendixes 87

06294500 Bighorn River above Tullock Creek, near Bighorn, Mont. March 7-day low-flow frequency data Recurrence interval, in years 1.0 1.1 2 5 10 50 100 200 5001,000 10,000 10,000

UNREGULATED

1,000 Streamflow, in cubic feet per second Streamflow, EXPLANATION 7-Day data Estimated n-day values n-day frequency curve

A 100 0.9999 0.999 0.99 0.9 0.5 0.2 0.1 0.02 0.01 0.005 0.002 0.001 0.0001 Probability 06294500 Bighorn River above Tullock Creek, near Bighorn, Mont. March 7-day low-flow frequency data Recurrence interval, in years 1.0 1.1 2 5 10 50 100 200 5001,000 10,000 10,000

REGULATED

1,000

EXPLANATION Streamflow, in cubic feet per second Streamflow, 7-Day data Estimated n-day values n-day frequency curve Outlier

B 100 0.9999 0.999 0.99 0.9 0.5 0.2 0.1 0.02 0.01 0.005 0.002 0.001 0.0001 Probability

Figure 1–5–8. March 7-day low-flow frequency data for streamflow-gaging station 06294500 (Bighorn River above Tullock Creek, near Bighorn, Montana) for A, unregulated and B, regulated streamflow conditions, 1928–2002. 88 Streamflow Statistics for the Upper Yellowstone and Bighorn Rivers, Montana and Wyoming, 1928–2002

06294500 Bighorn River above Tullock Creek, near Bighorn, Mont. April 7-day low-flow frequency data Recurrence interval, in years 1.0 1.1 2 5 10 50 100 200 5001,000 10,000 10,000

UNREGULATED

1,000 Streamflow, in cubic feet per second Streamflow, EXPLANATION 7-Day data Estimated n-day values n-day frequency curve

A 100 0.9999 0.999 0.99 0.9 0.5 0.2 0.1 0.02 0.01 0.005 0.002 0.001 0.0001 Probability 06294500 Bighorn River above Tullock Creek, near Bighorn, Mont. April 7-day low-flow frequency data Recurrence interval, in years 1.0 1.1 2 5 10 50 100 200 5001,000 10,000 10,000

REGULATED

1,000

EXPLANATION Streamflow, in cubic feet per second Streamflow, 7-Day data Estimated n-day values n-day frequency curve Outlier

B 100 0.9999 0.999 0.99 0.9 0.5 0.2 0.1 0.02 0.01 0.005 0.002 0.001 0.0001 Probability

Figure 1–5–9. April 7-day low-flow frequency data for streamflow-gaging station 06294500 (Bighorn River above Tullock Creek, near Bighorn, Montana) for A, unregulated and B, regulated streamflow conditions, 1928–2002. Appendixes 89

06294500 Bighorn River above Tullock Creek, near Bighorn, Mont. May 7-day low-flow frequency data Recurrence interval, in years 1.0 1.1 2 5 10 50 100 200 5001,000 10,000 100,000

10,000

UNREGULATED 1,000

100

Streamflow, in cubic feet per second Streamflow, EXPLANATION 7-Day data 10 Estimated n-day values n-day frequency curve Outlier

A 1.0 0.9999 0.999 0.99 0.9 0.5 0.2 0.1 0.02 0.01 0.005 0.002 0.001 0.0001 Probability 06294500 Bighorn River above Tullock Creek, near Bighorn, Mont. May 7-day low-flow frequency data Recurrence interval, in years 1.0 1.1 2 5 10 50 100 200 5001,000 10,000 100,000

10,000

REGULATED 1,000

100

EXPLANATION Streamflow, in cubic feet per second Streamflow, 7-Day data 10 Estimated n-day values n-day frequency curve Outlier

B 1.0 0.9999 0.999 0.99 0.9 0.5 0.2 0.1 0.02 0.01 0.005 0.002 0.001 0.0001 Probability

Figure 1–5–10. May 7-day low-flow frequency data for streamflow-gaging station 06294500 (Bighorn River above Tullock Creek, near Bighorn, Montana) for A, unregulated and B, regulated streamflow conditions, 1928–2002. 90 Streamflow Statistics for the Upper Yellowstone and Bighorn Rivers, Montana and Wyoming, 1928–2002

06294500 Bighorn River above Tullock Creek, near Bighorn, Mont. June 7-day low-flow frequency data Recurrence interval, in years 1.0 1.1 2 5 10 50 100 200 5001,000 10,000 100,000

10,000

UNREGULATED

1,000 Streamflow, in cubic feet per second Streamflow, EXPLANATION 7-Day data Estimated n-day values n-day frequency curve

A 100 0.9999 0.999 0.99 0.9 0.5 0.2 0.1 0.02 0.01 0.005 0.002 0.001 0.0001 Probability 06294500 Bighorn River above Tullock Creek, near Bighorn, Mont. June 7-day low-flow frequency data Recurrence interval, in years 1.0 1.1 2 5 10 50 100 200 5001,000 10,000 100,000

10,000

REGULATED

1,000 EXPLANATION Streamflow, in cubic feet per second Streamflow, 7-Day data Estimated n-day values n-day frequency curve Outlier

B 100 0.9999 0.999 0.99 0.9 0.5 0.2 0.1 0.02 0.01 0.005 0.002 0.001 0.0001 Probability

Figure 1–5–11. June 7-day low-flow frequency data for streamflow-gaging station 06294500 (Bighorn River above Tullock Creek, near Bighorn, Montana) for A, unregulated and B, regulated streamflow conditions, 1928–2002. Appendixes 91

06294500 Bighorn River above Tullock Creek, near Bighorn, Mont. July 7-day low-flow frequency data Recurrence interval, in years 1.0 1.1 2 5 10 50 100 200 5001,000 10,000 100,000

10,000

UNREGULATED

1,000

Streamflow, in cubic feet per second Streamflow, 100 EXPLANATION 7-Day data Estimated n-day values n-day frequency curve

A 10 0.9999 0.999 0.99 0.9 0.5 0.2 0.1 0.02 0.01 0.005 0.002 0.001 0.0001 Probability 06294500 Bighorn River above Tullock Creek, near Bighorn, Mont. July 7-day low-flow frequency data Recurrence interval, in years 1.0 1.1 2 5 10 50 100 200 5001,000 10,000 100,000

10,000

REGULATED

1,000

EXPLANATION Streamflow, in cubic feet per second Streamflow, 100 7-Day data Estimated n-day values n-day frequency curve Outlier

B 10 0.9999 0.999 0.99 0.9 0.5 0.2 0.1 0.02 0.01 0.005 0.002 0.001 0.0001 Probability

Figure 1–5–12. July 7-day low-flow frequency data for streamflow-gaging station 06294500 (Bighorn River above Tullock Creek, near Bighorn, Montana) for A, unregulated and B, regulated streamflow conditions, 1928–2002. 92 Streamflow Statistics for the Upper Yellowstone and Bighorn Rivers, Montana and Wyoming, 1928–2002

06294500 Bighorn River above Tullock Creek, near Bighorn, Mont. August 7-day low-flow frequency data Recurrence interval, in years 1.0 1.1 2 5 10 50 100 200 5001,000 10,000 10,000

UNREGULATED

1,000 Streamflow, in cubic feet per second Streamflow, EXPLANATION 7-Day data Estimated n-day values n-day frequency curve

A 100 0.9999 0.999 0.99 0.9 0.5 0.2 0.1 0.02 0.01 0.005 0.002 0.001 0.0001 Probability 06294500 Bighorn River above Tullock Creek, near Bighorn, Mont. August 7-day low-flow frequency data Recurrence interval, in years 1.0 1.1 2 5 10 50 100 200 5001,000 10,000 10,000

REGULATED

1,000

EXPLANATION Streamflow, in cubic feet per second Streamflow, 7-Day data Estimated n-day values n-day frequency curve Outlier

B 100 0.9999 0.999 0.99 0.9 0.5 0.2 0.1 0.02 0.01 0.005 0.002 0.001 0.0001 Probability

Figure 1–5–13. August 7-day low-flow frequency data for streamflow-gaging station 06294500 (Bighorn River above Tullock Creek, near Bighorn, Montana) for A, unregulated and B, regulated streamflow conditions, 1928–2002. Appendixes 93

06294500 Bighorn River above Tullock Creek, near Bighorn, Mont. September 7-day low-flow frequency data Recurrence interval, in years 1.0 1.1 2 5 10 50 100 200 5001,000 10,000 10,000

UNREGULATED

1,000

Streamflow, in cubic feet per second Streamflow, EXPLANATION 7-Day data Estimated n-day values n-day frequency curve Outlier

A 100 0.9999 0.999 0.99 0.9 0.5 0.2 0.1 0.02 0.01 0.005 0.002 0.001 0.0001 Probability 06294500 Bighorn River above Tullock Creek, near Bighorn, Mont. September 7-day low-flow frequency data Recurrence interval, in years 1.0 1.1 2 5 10 50 100 200 5001,000 10,000 10,000

REGULATED

1,000

EXPLANATION Streamflow, in cubic feet per second Streamflow, 7-Day data Estimated n-day values n-day frequency curve Outlier

B 100 0.9999 0.999 0.99 0.9 0.5 0.2 0.1 0.02 0.01 0.005 0.002 0.001 0.0001 Probability

Figure 1–5–14. September 7-day low-flow frequency data for streamflow-gaging station 06294500 (Bighorn River above Tullock Creek, near Bighorn, Montana) for A, unregulated and B, regulated streamflow conditions, 1928–2002. 94 Streamflow Statistics for the Upper Yellowstone and Bighorn Rivers, Montana and Wyoming, 1928–2002

06294500 Bighorn River above Tullock Creek, near Bighorn, Mont. October 7-day low-flow frequency data Recurrence interval, in years 1.0 1.1 2 5 10 50 100 200 5001,000 10,000 10,000

UNREGULATED

1,000

Streamflow, in cubic feet per second Streamflow, EXPLANATION 7-Day data Estimated n-day values n-day frequency curve Outlier

A 100 0.9999 0.999 0.99 0.9 0.5 0.2 0.1 0.02 0.01 0.005 0.002 0.001 0.0001 Probability 06294500 Bighorn River above Tullock Creek, near Bighorn, Mont. October 7-day low-flow frequency data Recurrence interval, in years 1.0 1.1 2 5 10 50 100 200 5001,000 10,000 10,000

REGULATED

1,000 Streamflow, in cubic feet per second Streamflow, EXPLANATION 7-Day data Estimated n-day values n-day frequency curve

B 100 0.9999 0.999 0.99 0.9 0.5 0.2 0.1 0.02 0.01 0.005 0.002 0.001 0.0001 Probability

Figure 1–5–15. October 7-day low-flow frequency data for streamflow-gaging station 06294500 (Bighorn River above Tullock Creek, near Bighorn, Montana) for A, unregulated and B, regulated streamflow conditions, 1928–2002. Appendixes 95

06294500 Bighorn River above Tullock Creek, near Bighorn, Mont. November 7-day low-flow frequency data Recurrence interval, in years 1.0 1.1 2 5 10 50 100 200 5001,000 10,000 10,000

UNREGULATED 1,000

100

Streamflow, in cubic feet per second Streamflow, EXPLANATION 7-Day data Estimated n-day values n-day frequency curve Outlier

A 10 0.9999 0.999 0.99 0.9 0.5 0.2 0.1 0.02 0.01 0.005 0.002 0.001 0.0001 Probability 06294500 Bighorn River above Tullock Creek, near Bighorn, Mont. November 7-day low-flow frequency data Recurrence interval, in years 1.0 1.1 2 5 10 50 100 200 5001,000 10,000 10,000

REGULATED 1,000

100

Streamflow, in cubic feet per second Streamflow, EXPLANATION 7-Day data Estimated n-day values n-day frequency curve

B 10 0.9999 0.999 0.99 0.9 0.5 0.2 0.1 0.02 0.01 0.005 0.002 0.001 0.0001 Probability

Figure 1–5–16. November 7-day low-flow frequency data for streamflow-gaging station 06294500 (Bighorn River above Tullock Creek, near Bighorn, Montana) for A, unregulated and B, regulated streamflow conditions, 1928–2002. 96 Streamflow Statistics for the Upper Yellowstone and Bighorn Rivers, Montana and Wyoming, 1928–2002

06294500 Bighorn River above Tullock Creek, near Bighorn, Mont. December 7-day low-flow frequency data Recurrence interval, in years 1.0 1.1 2 5 10 50 100 200 5001,000 10,000 10,000

1,000

UNREGULATED

100

Streamflow, in cubic feet per second Streamflow, 10 EXPLANATION 7-Day data Estimated n-day values n-day frequency curve Outlier

A 1.0 0.9999 0.999 0.99 0.9 0.5 0.2 0.1 0.02 0.01 0.005 0.002 0.001 0.0001 Probability 06294500 Bighorn River above Tullock Creek, near Bighorn, Mont. December 7-day low-flow frequency data Recurrence interval, in years 1.0 1.1 2 5 10 50 100 200 5001,000 10,000 10,000

1,000

REGULATED

100

Streamflow, in cubic feet per second Streamflow, 10 EXPLANATION 7-Day data Estimated n-day values n-day frequency curve

B 1.0 0.9999 0.999 0.99 0.9 0.5 0.2 0.1 0.02 0.01 0.005 0.002 0.001 0.0001 Probability

Figure 1–5–17. December 7-day low-flow frequency data for streamflow-gaging station 06294500 (Bighorn River above Tullock Creek, near Bighorn, Montana) for A, unregulated and B, regulated streamflow conditions, 1928–2002. Appendixes 97

Appendix 1–6. Statistics for streamflow-gaging station 06295000 (Yellowstone River at Forsyth, Montana)

Table 1–6–1. Annual, seasonal, and monthly n-day low-flow frequency data for streamflow-gaging station 06295000 (Yellowstone River at Forsyth, Montana) for unregulated and regulated streamflow conditions, 1928–2002.

[ft3/s, cubic feet per second; %, percent]

Unregulated n, period of consecutive Streamflow, in ft3/s, for indicated recurrence interval, in years, and exceedance probability, in percent days (month, for monthly 2 5 10 20 25 50 100 frequency data) 50% 20% 10% 5% 4% 2% 1% Annual 7 1,920 1,210 927 732 681 551 452 30 3,410 2,620 2,250 1,960 1,880 1,660 1,480 Winter (January–March) 7 2,560 1,690 1,320 1,060 994 815 676 30 3,820 2,840 2,380 2,040 1,950 1,700 1,490 Spring (April–June) 7 7,280 5,510 4,700 4,100 3,940 3,500 3,130 30 8,620 6,610 5,720 5,060 4,880 4,400 3,990 Summer (July–September) 7 7,600 5,710 4,730 3,960 3,750 3,170 2,690 30 8,750 7,010 6,140 5,450 5,260 4,720 4,260 Fall (October–December) 7 2,490 1,470 1,080 826 760 596 474 30 4,190 3,260 2,830 2,500 2,400 2,150 1,940 Monthly 7 (January) 2,840 1,830 1,400 1,100 1,020 820 664 7 (February) 3,650 2,570 2,100 1,760 1,670 1,430 1,240 7 (March) 4,770 3,520 2,990 2,600 2,490 2,210 1,980 7 (April) 7,280 5,510 4,700 4,100 3,940 3,500 3,130 7 (May) 17,500 14,100 12,500 11,300 10,900 10,000 9,220 7 (June) 33,100 26,000 22,700 20,400 19,700 17,900 16,400 7 (July) 20,000 15,700 13,900 12,500 12,100 11,100 10,200 7 (August) 11,400 9,630 8,820 8,210 8,040 7,570 7,170 7 (September) 7,600 5,710 4,730 3,960 3,750 3,170 2,690 7 (October) 5,700 4,230 3,550 3,040 2,900 2,530 2,220 7 (November) 4,820 3,110 2,270 1,670 1,520 1,120 835 7 (December) 2,750 1,650 1,210 914 838 648 508 98 Streamflow Statistics for the Upper Yellowstone and Bighorn Rivers, Montana and Wyoming, 1928–2002

[ft3/s, cubic feet per second; %, percent]

Regulated

n, period of consecutive Streamflow, in ft3/s, for indicated recurrence interval, in years, and exceedance probability, in percent days (month, for monthly 2 5 10 20 25 50 100 frequency data) 50% 20% 10% 5% 4% 2% 1% Annual 7 3,350 2,650 2,340 2,110 2,050 1,880 1,740 30 4,480 3,550 3,090 2,730 2,630 2,360 2,130 Winter (January–March) 7 3,900 3,100 2,750 2,480 2,405 2,207 2,041 30 5,000 4,050 3,610 3,270 3,180 2,920 2,710 Spring (April–June) 7 5,400 4,040 3,460 3,040 2,920 2,620 2,370 30 6,620 4,980 4,280 3,770 3,640 3,270 2,970 Summer (July–September) 7 5,130 3,660 3,020 2,560 2,440 2,110 1,840 30 5,890 4,160 3,420 2,890 2,740 2,360 2,060 Fall (October–December) 7 4,050 3,040 2,630 2,330 2,250 2,036 1,863 30 5,550 4,490 3,970 3,570 3,460 3,140 2,880 Monthly 7 (January) 4,240 3,320 2,910 2,600 2,510 2,275 2,080 7 (February) 4,820 3,750 3,270 2,900 2,800 2,530 2,300 7 (March) 5,630 4,370 3,820 3,410 3,310 3,010 2,760 7 (April) 5,410 4,050 3,470 3,050 2,930 2,630 2,380 7 (May) 8,730 6,260 5,200 4,440 4,230 3,690 3,240 7 (June) 22,700 15,900 13,000 10,900 10,400 8,900 7,730 7 (July) 10,700 6,550 4,980 3,950 3,680 3,010 2,500 7 (August) 5,500 3,790 3,110 2,630 2,510 2,180 1,920 7 (September) 5,570 4,000 3,320 2,820 2,690 2,340 2,050 7 (October) 6,780 5,220 4,480 3,910 3,750 3,320 2,960 7 (November) 6,180 4,580 3,790 3,190 3,020 2,570 2,200 7 (December) 4,270 3,230 2,780 2,450 2,360 2,130 1,930 Appendixes 99

Table 1–6–2. Monthly and annual streamflow characteristics for streamflow-gaging station 06295000 (Yellowstone River at Forsyth, Montana) for unregulated and regulated streamflow conditions, 1928–2002.

[ft3/s, cubic feet per second]

Unregulated Streamflow, in ft3/s, or year, for indicated streamflow characteristic Maximum Year of maximum Year of minimum Minimum monthly Standard deviation monthly mean monthly mean monthly mean Mean monthly Period mean and of mean monthly and maximum and maximum and minimum and mean annual minimum annual and mean annual annual mean annual mean annual mean streamflow mean streamflow streamflow streamflow streamflow streamflow January 7,090 1983 1,570 1937 4,210 1,206 February 15,100 1971 1,850 1932 5,180 2,098 March 17,600 1929 2,850 2002 7,270 2,853 April 16,400 1943 3,410 1961 8,970 2,687 May 44,300 1928 13,660 1953 25,580 5,807 June 78,100 1997 20,389 1934 43,760 11,650 July 55,900 1975 12,101 1934 29,010 10,040 August 22,100 1997 8,120 1934 13,631 3,137 September 13,500 1968 4,010 1934 8,760 2,007 October 11,500 1941 2,860 2001 6,570 2,000 November 8,520 1982 2,900 1931 5,510 1,400 December 7,310 1982 2,240 1932 4,440 1,151

Annual 20,800 1997 8,750 2001 13,500 2,549 Regulated Streamflow, in ft3/s, or year, for indicated streamflow characteristic Maximum Year of maximum Year of minimum Minimum monthly Standard deviation monthly mean monthly mean monthly mean Mean monthly Period mean and of mean monthly and maximum and maximum and minimum and mean annual minimum annual and mean annual annual mean annual mean annual mean streamflow mean streamflow streamflow streamflow streamflow streamflow January 8,340 1968 2,800 1937 5,520 1,210 February 15,600 1971 3,040 1932 6,220 2,020 March 18,600 1929 3,220 2002 8,010 2,820 April 13,300 1997 2,450 1961 7,070 2,360 May 35,300 1928 7,040 1961 16,300 4,970 June 64,100 1997 11,700 1934 32,200 10,600 July 43,700 1967 3,820 1934 19,400 9,720 August 17,800 1997 2,540 1934 7,910 3,450 September 13,400 1941 2,740 2001 6,960 2,380 October 12,800 1941 3,570 2001 7,620 2,050 November 10,600 1982 4,030 1934 7,020 1,610 December 8,970 1982 3,430 1934 5,850 1,220

Annual 18,200 1997 5,680 1934 10,800 2,720 100 Streamflow Statistics for the Upper Yellowstone and Bighorn Rivers, Montana and Wyoming, 1928–2002

06295000 Yellowstone River at Forsyth, Mont. Annual n-day low-flow frequency data Recurrence interval, in years 1.0 1.1 2 5 10 50 100 200 5001,000 10,000 10,000

UNREGULATED

1,000

EXPLANATION Streamflow, in cubic feet per second Streamflow, 7-Day data 30-Day data Estimated n-day values Estimated n-day values n-day frequency curve n-day frequency curve Outlier

A 100 0.9999 0.999 0.99 0.9 0.5 0.2 0.1 0.02 0.01 0.005 0.002 0.001 0.0001 Probability 06295000 Yellowstone River at Forsyth, Mont. Annual n-day low-flow frequency data Recurrence interval, in years 1.0 1.1 2 5 10 50 100 200 5001,000 10,000 10,000

REGULATED

1,000

Streamflow, in cubic feet per second Streamflow, EXPLANATION 7-Day data 30-Day data Estimated n-day values Estimated n-day values n-day frequency curve n-day frequency curve

B 100 0.9999 0.999 0.99 0.9 0.5 0.2 0.1 0.02 0.01 0.005 0.002 0.001 0.0001 Probability

Figure 1–6–1. Annual n-day low-flow frequency data for streamflow-gaging station 06295000 (Yellowstone River at Forsyth, Montana) for A, unregulated and B, regulated streamflow conditions, 1928–2002. Appendixes 101

06295000 Yellowstone River at Forsyth, Mont. Winter (January–March) n-day low-flow frequency data Recurrence interval, in years 1.0 1.1 2 5 10 50 100 200 5001,000 10,000 10,000

UNREGULATED

1,000

EXPLANATION Streamflow, in cubic feet per second Streamflow, 7-Day data 30-Day data Estimated n-day values Estimated n-day values n-day frequency curve n-day frequency curve Outlier

A 100 0.9999 0.999 0.99 0.9 0.5 0.2 0.1 0.02 0.01 0.005 0.002 0.001 0.0001 Probability 06295000 Yellowstone River at Forsyth, Mont. Winter (January–March) n-day low-flow frequency data Recurrence interval, in years 1.0 1.1 2 5 10 50 100 200 5001,000 10,000 10,000

REGULATED

1,000

Streamflow, in cubic feet per second Streamflow, EXPLANATION 7-Day data 30-Day data Estimated n-day values Estimated n-day values n-day frequency curve n-day frequency curve

B 100 0.9999 0.999 0.99 0.9 0.5 0.2 0.1 0.02 0.01 0.005 0.002 0.001 0.0001 Probability

Figure 1–6–2. Winter (January–March) n-day low-flow frequency data for streamflow-gaging station 06295000 (Yellowstone River at Forsyth, Montana) for A, unregulated and B, regulated streamflow conditions, 1928–2002. 102 Streamflow Statistics for the Upper Yellowstone and Bighorn Rivers, Montana and Wyoming, 1928–2002

06295000 Yellowstone River at Forsyth, Mont. Spring (April–June) n-day low-flow frequency data Recurrence interval, in years 1.0 1.1 2 5 10 50 100 200 5001,000 10,000 100,000

UNREGULATED

10,000

EXPLANATION Streamflow, in cubic feet per second Streamflow, 7-Day data 30-Day data Estimated n-day values Estimated n-day values n-day frequency curve n-day frequency curve Outlier Outlier

A 1,000 0.9999 0.999 0.99 0.9 0.5 0.2 0.1 0.02 0.01 0.005 0.002 0.001 0.0001 Probability

06295000 Yellowstone River at Forsyth, Mont. Spring (April–June) n-day low-flow frequency data Recurrence interval, in years 1.0 1.1 2 5 10 50 100 200 5001,000 10,000 100,000

REGULATED

10,000

EXPLANATION Streamflow, in cubic feet per second Streamflow, 7-Day data 30-Day data Estimated n-day values Estimated n-day values n-day frequency curve n-day frequency curve Outlier Outlier

B 1,000 0.9999 0.999 0.99 0.9 0.5 0.2 0.1 0.02 0.01 0.005 0.002 0.001 0.0001 Probability

Figure 1–6–3. Spring (April–June) n-day low-flow frequency data for streamflow-gaging station 06295000 (Yellowstone River at Forsyth, Montana) for A, unregulated and B, regulated streamflow conditions, 1928–2002. Appendixes 103

06295000 Yellowstone River at Forsyth, Mont. Summer (July–September) n-day low-flow frequency data Recurrence interval, in years 1.0 1.1 2 5 10 50 100 200 500 1,000 10,000 100,000

UNREGULATED

10,000

EXPLANATION Streamflow, in cubic feet per second Streamflow, 7-Day data 30-Day data Estimated n-day values Estimated n-day values n-day frequency curve n-day frequency curve Outlier Outlier

A 1,000 0.9999 0.999 0.99 0.9 0.5 0.2 0.1 0.02 0.01 0.005 0.002 0.001 0.0001 Probability 06295000 Yellowstone River at Forsyth, Mont. Summer (July–September) n-day low-flow frequency data Recurrence interval, in years 1.0 1.1 2 5 10 50 100 200 5001,000 10,000 100,000

REGULATED

10,000 Streamflow, in cubic feet per second Streamflow, EXPLANATION 7-Day data 30-Day data Estimated n-day values Estimated n-day values n-day frequency curve n-day frequency curve

B 1,000 0.9999 0.999 0.99 0.9 0.5 0.2 0.1 0.02 0.01 0.005 0.002 0.001 0.0001 Probability

Figure 1–6–4. Summer (July–September) n-day low-flow frequency data for streamflow-gaging station 06295000 (Yellowstone River at Forsyth, Montana) for A, unregulated and B, regulated streamflow conditions, 1928–2002. 104 Streamflow Statistics for the Upper Yellowstone and Bighorn Rivers, Montana and Wyoming, 1928–2002

06295000 Yellowstone River at Forsyth, Mont. Fall (October–December) n-day low-flow frequency data Recurrence interval, in years 1.0 1.1 2 5 10 50 100 200 500 1,000 10,000 10,000

UNREGULATED

1,000

EXPLANATION Streamflow, in cubic feet per second Streamflow, 7-Day data 30-Day data Estimated n-day values Estimated n-day values n-day frequency curve n-day frequency curve Outlier

A 100 0.9999 0.999 0.99 0.9 0.5 0.2 0.1 0.02 0.01 0.005 0.002 0.001 0.0001 Probability 06295000 Yellowstone River at Forsyth, Mont. Fall (October–December) n-day low-flow frequency data Recurrence interval, in years 1.0 1.1 2 5 10 50 100 200 5001,000 10,000 10,000

REGULATED

1,000

Streamflow, in cubic feet per second Streamflow, EXPLANATION 7-Day data 30-Day data Estimated n-day values Estimated n-day values n-day frequency curve n-day frequency curve

B 100 0.9999 0.999 0.99 0.9 0.5 0.2 0.1 0.02 0.01 0.005 0.002 0.001 0.0001 Probability

Figure 1–6–5. Fall (October–December) n-day low-flow frequency data for streamflow-gaging station 06295000 (Yellowstone River at Forsyth, Montana) for A, unregulated and B, regulated streamflow conditions, 1928–2002. Appendixes 105

06295000 Yellowstone River at Forsyth, Mont. January 7-day low-flow frequency data Recurrence interval, in years 1.0 1.1 2 5 10 50 100 200 500 1,000 10,000 10,000

UNREGULATED

1,000

Streamflow, in cubic feet per second Streamflow, EXPLANATION 7-Day data Estimated n-day values n-day frequency curve Outlier

A 100 0.9999 0.999 0.99 0.9 0.5 0.2 0.1 0.02 0.01 0.005 0.002 0.001 0.0001 Probability 06295000 Yellowstone River at Forsyth, Mont. January 7-day low-flow frequency data Recurrence interval, in years 1.0 1.1 2 5 10 50 100 200 5001,000 10,000 10,000

REGULATED

1,000 Streamflow, in cubic feet per second Streamflow, EXPLANATION 7-Day data Estimated n-day values n-day frequency curve

B 100 0.9999 0.999 0.99 0.9 0.5 0.2 0.1 0.02 0.01 0.005 0.002 0.001 0.0001 Probability

Figure 1–6–6. January 7-day low-flow frequency data for streamflow-gaging station 06295000 (Yellowstone River at Forsyth, Montana) for A, unregulated and B, regulated streamflow conditions, 1928–2002. 106 Streamflow Statistics for the Upper Yellowstone and Bighorn Rivers, Montana and Wyoming, 1928–2002

06295000 Yellowstone River at Forsyth, Mont. February 7-day low-flow frequency data Recurrence interval, in years 1.0 1.1 2 5 10 50 100 200 500 1,000 10,000 10,000

UNREGULATED

1,000 Streamflow, in cubic feet per second Streamflow, EXPLANATION 7-Day data Estimated n-day values n-day frequency curve

A 100 0.9999 0.999 0.99 0.9 0.5 0.2 0.1 0.02 0.01 0.005 0.002 0.001 0.0001 Probability 06295000 Yellowstone River at Forsyth, Mont. February 7-day low-flow frequency data Recurrence interval, in years 1.0 1.1 2 5 10 50 100 200 5001,000 10,000 10,000

REGULATED

1,000 Streamflow, in cubic feet per second Streamflow, EXPLANATION 7-Day data Estimated n-day values n-day frequency curve

B 100 0.9999 0.999 0.99 0.9 0.5 0.2 0.1 0.02 0.01 0.005 0.002 0.001 0.0001 Probability

Figure 1–6–7. February 7-day low-flow frequency data for streamflow-gaging station 06295000 (Yellowstone River at Forsyth, Montana) for A, unregulated and B, regulated streamflow conditions, 1928–2002. Appendixes 107

06295000 Yellowstone River at Forsyth, Mont. March 7-day low-flow frequency data Recurrence interval, in years 1.0 1.1 2 5 10 50 100 200 500 1,000 10,000 100,000

UNREGULATED

10,000 Streamflow, in cubic feet per second Streamflow, EXPLANATION 7-Day data Estimated n-day values n-day frequency curve A 1,000 0.9999 0.999 0.99 0.9 0.5 0.2 0.1 0.02 0.01 0.005 0.002 0.001 0.0001 Probability 06295000 Yellowstone River at Forsyth, Mont. March 7-day low-flow frequency data Recurrence interval, in years 1.0 1.1 2 5 10 50 100 200 5001,000 10,000 100,000

REGULATED

10,000 Streamflow, in cubic feet per second Streamflow, EXPLANATION 7-Day data Estimated n-day values n-day frequency curve

B 1,000 0.9999 0.999 0.99 0.9 0.5 0.2 0.1 0.02 0.01 0.005 0.002 0.001 0.0001 Probability

Figure 1–6–8. March 7-day low-flow frequency data for streamflow-gaging station 06295000 (Yellowstone River at Forsyth, Montana) for A, unregulated and B, regulated streamflow conditions, 1928–2002. 108 Streamflow Statistics for the Upper Yellowstone and Bighorn Rivers, Montana and Wyoming, 1928–2002

06295000 Yellowstone River at Forsyth, Mont. April 7-day low-flow frequency data Recurrence interval, in years 1.0 1.1 2 5 10 50 100 200 500 1,000 10,000 100,000

UNREGULATED

10,000

Streamflow, in cubic feet per second Streamflow, EXPLANATION 7-Day data Estimated n-day values n-day frequency curve Outlier A 1,000 0.9999 0.999 0.99 0.9 0.5 0.2 0.1 0.02 0.01 0.005 0.002 0.001 0.0001 Probability 06295000 Yellowstone River at Forsyth, Mont. April 7-day low-flow frequency data Recurrence interval, in years 1.0 1.1 2 5 10 50 100 200 5001,000 10,000 100,000

REGULATED

10,000

Streamflow, in cubic feet per second Streamflow, EXPLANATION 7-Day data Estimated n-day values n-day frequency curve Outlier

B 1,000 0.9999 0.999 0.99 0.9 0.5 0.2 0.1 0.02 0.01 0.005 0.002 0.001 0.0001 Probability

Figure 1–6–9. April 7-day low-flow frequency data for streamflow-gaging station 06295000 (Yellowstone River at Forsyth, Montana) for A, unregulated and B, regulated streamflow conditions, 1928–2002. Appendixes 109

06295000 Yellowstone River at Forsyth, Mont. May 7-day low-flow frequency data Recurrence interval, in years 1.0 1.1 2 5 10 50 100 200 500 1,000 10,000 100,000

UNREGULATED

10,000

Streamflow, in cubic feet per second Streamflow, EXPLANATION 7-Day data Estimated n-day values n-day frequency curve

A 1,000 0.9999 0.999 0.99 0.9 0.5 0.2 0.1 0.02 0.01 0.005 0.002 0.001 0.0001 Probability 06295000 Yellowstone River at Forsyth, Mont. May 7-day low-flow frequency data Recurrence interval, in years 1.0 1.1 2 5 10 50 100 200 5001,000 10,000 100,000

REGULATED

10,000

EXPLANATION Streamflow, in cubic feet per second Streamflow, 7-Day data Estimated n-day values n-day frequency curve Outlier

B 1,000 0.9999 0.999 0.99 0.9 0.5 0.2 0.1 0.02 0.01 0.005 0.002 0.001 0.0001 Probability

Figure 1–6–10. May 7-day low-flow frequency data for streamflow-gaging station 06295000 (Yellowstone River at Forsyth, Montana) for A, unregulated and B, regulated streamflow conditions, 1928–2002. 110 Streamflow Statistics for the Upper Yellowstone and Bighorn Rivers, Montana and Wyoming, 1928–2002

06295000 Yellowstone River at Forsyth, Mont. June 7-day low-flow frequency data Recurrence interval, in years 1.0 1.1 2 5 10 50 100 200 500 1,000 10,000 100,000

UNREGULATED

10,000 Streamflow, in cubic feet per second Streamflow, EXPLANATION 7-Day data Estimated n-day values n-day frequency curve

A 1,000 0.9999 0.999 0.99 0.9 0.5 0.2 0.1 0.02 0.01 0.005 0.002 0.001 0.0001 Probability 06295000 Yellowstone River at Forsyth, Mont. June 7-day low-flow frequency data Recurrence interval, in years 1.0 1.1 2 5 10 50 100 200 5001,000 10,000 100,000

REGULATED

10,000 Streamflow, in cubic feet per second Streamflow, EXPLANATION 7-Day data Estimated n-day values n-day frequency curve

B 1,000 0.9999 0.999 0.99 0.9 0.5 0.2 0.1 0.02 0.01 0.005 0.002 0.001 0.0001 Probability

Figure 1–6–11. June 7-day low-flow frequency data for streamflow-gaging station 06295000 (Yellowstone River at Forsyth, Montana) for A, unregulated and B, regulated streamflow conditions, 1928–2002. Appendixes 111

06295000 Yellowstone River at Forsyth, Mont. July 7-day low-flow frequency data Recurrence interval, in years 1.0 1.1 2 5 10 50 100 200 500 1,000 10,000 100,000

UNREGULATED

10,000

Streamflow, in cubic feet per second Streamflow, EXPLANATION 7-Day data Estimated n-day values n-day frequency curve

A 1,000 0.9999 0.999 0.99 0.9 0.5 0.2 0.1 0.02 0.01 0.005 0.002 0.001 0.0001 Probability 06295000 Yellowstone River at Forsyth, Mont. July 7-day low-flow frequency data Recurrence interval, in years 1.0 1.1 2 5 10 50 100 200 5001,000 10,000 100,000

REGULATED

10,000

Streamflow, in cubic feet per second Streamflow, EXPLANATION 7-Day data Estimated n-day values n-day frequency curve

B 1,000 0.9999 0.999 0.99 0.9 0.5 0.2 0.1 0.02 0.01 0.005 0.002 0.001 0.0001 Probability

Figure 1–6–12. July 7-day low-flow frequency data for streamflow-gaging station 06295000 (Yellowstone River at Forsyth, Montana) for A, unregulated and B, regulated streamflow conditions, 1928–2002. 112 Streamflow Statistics for the Upper Yellowstone and Bighorn Rivers, Montana and Wyoming, 1928–2002

06295000 Yellowstone River at Forsyth, Mont. August 7-day low-flow frequency data Recurrence interval, in years 1.0 1.1 2 5 10 50 100 200 500 1,000 10,000 100,000

UNREGULATED

10,000

Streamflow, in cubic feet per second Streamflow, EXPLANATION 7-Day data Estimated n-day values n-day frequency curve

A 1,000 0.9999 0.999 0.99 0.9 0.5 0.2 0.1 0.02 0.01 0.005 0.002 0.001 0.0001 Probability 06295000 Yellowstone River at Forsyth, Mont. August 7-day low-flow frequency data Recurrence interval, in years 1.0 1.1 2 5 10 50 100 200 5001,000 10,000 100,000

REGULATED

10,000

Streamflow, in cubic feet per second Streamflow, EXPLANATION 7-Day data Estimated n-day values n-day frequency curve

B 1,000 0.9999 0.999 0.99 0.9 0.5 0.2 0.1 0.02 0.01 0.005 0.002 0.001 0.0001 Probability

Figure 1–6–13. August 7-day low-flow frequency data for streamflow-gaging station 06295000 (Yellowstone River at Forsyth, Montana) for A, unregulated and B, regulated streamflow conditions, 1928–2002. Appendixes 113

06295000 Yellowstone River at Forsyth, Mont. September 7-day low-flow frequency data Recurrence interval, in years 1.0 1.1 2 5 10 50 100 200 500 1,000 10,000 100,000

UNREGULATED

10,000

Streamflow, in cubic feet per second Streamflow, EXPLANATION 7-Day data Estimated n-day values n-day frequency curve Outlier

A 1,000 0.9999 0.999 0.99 0.9 0.5 0.2 0.1 0.02 0.01 0.005 0.002 0.001 0.0001 Probability 06295000 Yellowstone River at Forsyth, Mont. September 7-day low-flow frequency data Recurrence interval, in years 1.0 1.1 2 5 10 50 100 200 5001,000 10,000 100,000

REGULATED

10,000 Streamflow, in cubic feet per second Streamflow, EXPLANATION 7-Day data Estimated n-day values n-day frequency curve

B 1,000 0.9999 0.999 0.99 0.9 0.5 0.2 0.1 0.02 0.01 0.005 0.002 0.001 0.0001 Probability

Figure 1–6–14. September 7-day low-flow frequency data for streamflow-gaging station 06295000 (Yellowstone River at Forsyth, Montana) for A, unregulated and B, regulated streamflow conditions, 1928–2002. 114 Streamflow Statistics for the Upper Yellowstone and Bighorn Rivers, Montana and Wyoming, 1928–2002

06295000 Yellowstone River at Forsyth, Mont. October 7-day low-flow frequency data Recurrence interval, in years 1.0 1.1 2 5 10 50 100 200 500 1,000 10,000 10,000

UNREGULATED

1,000

Streamflow, in cubic feet per second Streamflow, EXPLANATION 7-Day data Estimated n-day values n-day frequency curve Outlier A 100 0.9999 0.999 0.99 0.9 0.5 0.2 0.1 0.02 0.01 0.005 0.002 0.001 0.0001 Probability 06295000 Yellowstone River at Forsyth, Mont. October 7-day low-flow frequency data Recurrence interval, in years 1.0 1.1 2 5 10 50 100 200 5001,000 10,000 100,000

REGULATED

10,000

Streamflow, in cubic feet per second Streamflow, EXPLANATION 7-Day data Estimated n-day values n-day frequency curve Outlier B 1,000 0.9999 0.999 0.99 0.9 0.5 0.2 0.1 0.02 0.01 0.005 0.002 0.001 0.0001 Probability

Figure 1–6–15. October 7-day low-flow frequency data for streamflow-gaging station 06295000 (Yellowstone River at Forsyth, Montana) for A, unregulated and B, regulated streamflow conditions, 1928–2002. Appendixes 115

06295000 Yellowstone River at Forsyth, Mont. November 7-day low-flow frequency data Recurrence interval, in years 1.0 1.1 2 5 10 50 100 200 500 1,000 10,000 10,000

UNREGULATED

1,000

Streamflow, in cubic feet per second Streamflow, EXPLANATION 7-Day data Estimated n-day values n-day frequency curve Outlier

A 100 0.9999 0.999 0.99 0.9 0.5 0.2 0.1 0.02 0.01 0.005 0.002 0.001 0.0001 Probability 06295000 Yellowstone River at Forsyth, Mont. November 7-day low-flow frequency data Recurrence interval, in years 1.0 1.1 2 5 10 50 100 200 5001,000 10,000 10,000

REGULATED

1,000 Streamflow, in cubic feet per second Streamflow, EXPLANATION 7-Day data Estimated n-day values n-day frequency curve

B 100 0.9999 0.999 0.99 0.9 0.5 0.2 0.1 0.02 0.01 0.005 0.002 0.001 0.0001 Probability

Figure 1–6–16. November 7-day low-flow frequency data for streamflow-gaging station 06295000 (Yellowstone River at Forsyth, Montana) for A, unregulated and B, regulated streamflow conditions, 1928–2002. 116 Streamflow Statistics for the Upper Yellowstone and Bighorn Rivers, Montana and Wyoming, 1928–2002

06295000 Yellowstone River at Forsyth, Mont. December 7-day low-flow frequency data Recurrence interval, in years 1.0 1.1 2 5 10 50 100 200 500 1,000 10,000 10,000

UNREGULATED

1,000

Streamflow, in cubic feet per second Streamflow, EXPLANATION 7-Day data Estimated n-day values n-day frequency curve Outlier

A 100 0.9999 0.999 0.99 0.9 0.5 0.2 0.1 0.02 0.01 0.005 0.002 0.001 0.0001 Probability 06295000 Yellowstone River at Forsyth, Mont. December 7-day low-flow frequency data Recurrence interval, in years 1.0 1.1 2 5 10 50 100 200 5001,000 10,000 10,000

REGULATED

1,000 Streamflow, in cubic feet per second Streamflow, EXPLANATION 7-Day data Estimated n-day values n-day frequency curve

B 100 0.9999 0.999 0.99 0.9 0.5 0.2 0.1 0.02 0.01 0.005 0.002 0.001 0.0001 Probability

Figure 1–6–17. December 7-day low-flow frequency data for streamflow-gaging station 06295000 (Yellowstone River at Forsyth, Montana) for A, unregulated and B, regulated streamflow conditions, 1928–2002. Appendixes 117

Appendix 2. Locations, Drainage Areas, and Annual n-day Low-Flow Frequency Data for Unregulated and Regulated Streamflow Conditions at Selected Locations on the Yellowstone River, Montana and Wyoming, 1928–2002

Appendix 2, presented in Microsoft® Excel spread- are named sir2014-5155_APP_2.1_loc_and_da.xlsx and sheets, contains information about locations and drainage sir2014-5155_APP_2.2_lowflowfreq.xlsx. Locations of the areas for selected streamflow-gaging stations and reach streamflow-gaging stations and reach locations are shown on locations on the Yellowstone River. Appendix 2 also contains figures 2 and 3 (main report). annual n-day low-flow frequency data at selected Yellow- stone River streamflow-gaging stations; these data also were Appendix 2–1. Locations and drainage areas for selected interpolated for selected locations on the Yellowstone River. streamflow-gaging station and reach locations on the Yellowstone For streamflow-gaging stations 06186500 and 06191500 River (http://pubs.usgs.gov/sir/2014/5115/downloads/sir2014-5155_ (Yellowstone River at Yellowstone Lake Outlet Yellowstone APP_2.1_loc_and_da.xlsx). National Park, Wyoming, and Yellowstone River at Corwin Springs, Montana) and for the reaches between those two Appendix 2–2. Annual, seasonal, and monthly n-day low-flow streamflow-gaging stations, only data for unregulated con- frequency data at selected locations on the Yellowstone River, ditions are included. For the remaining streamflow-gaging Montana and Wyoming, for unregulated and regulated streamflow stations and reaches, data for unregulated and regulated conditions, 1928–2002 (http://pubs.usgs.gov/sir/2014/5115/ streamflow conditions are included. The Excel spreadsheets downloads/sir2014-5155_APP_2.2_lowflowfreq.xlsx). Publishing support provided by: Rolla Publishing Service Center

For more information concerning this publication, contact: Director, Wyoming-Montana Water Science Center U.S. Geological Survey 3162 Bozeman Ave. Helena, MT 59601 (406) 457–5900

Or visit the Wyoming-Montana Water Science Center Web site at: http://wy-mt.water.usgs.gov/

Chase—Streamflow Statistics for the Upper Yellowstone and Bighorn Rivers, Montana and Wyoming, 1928–2002—SIR 2014–5115 ISSN 2328-0328 (online) http://dx.doi.org/110.3133/sir20145115