Evaluation of Recommended Revisions

to Bulletin 17B

99.5 99 95 90 80 65 50 35 20 10 4 2 1 0.5

1

0.1

10

100

1,000

10,000

Annual peak discharge, in cubic feet per second

Annual exceedance probability, in percent

1932 to 2013; 82 years

18 years of PILFs

12 zero floods

Flow range of interest:

 4,000 to 15,000 ft3/s

Systematic (gage) peak flow

Potentially influential low flood (PILF)

 (less than 782 ft3/s) from

 systematic record

Zero flow (12 years; plotted at 0.1 ft3/s)

 from systematic record

EXPLANATION

Open-File Report 2017–1064

U.S. Department of the Interior

U.S. Geological Survey
Cover. Graph showing an example empirical frequency distribution and potentially influential low

floods (PILFs) at U.S. Geological Survey station 11274500, Orestimba Creek near Newman,

California.
Evaluation of Recommended Revisions

to Bulletin 17B

By Timothy A. Cohn, U.S. Geological Survey (deceased)

Nancy A. Barth, U.S. Geological Survey

John F. England, Jr., U.S. Army Corps of Engineers

Beth A. Faber, U.S. Army Corps of Engineers

Robert R. Mason, Jr., U.S. Geological Survey

Jery R. Stedinger, Cornell University

Open-File Report 2017–1064

U.S. Department of the Interior

U.S. Geological Survey
U.S. Department of the Interior

DAVID BERNHARDT, Acting Secretary

U.S. Geological Survey

James F. Reilly II, Director

U.S. Geological Survey, Reston, Virginia: 2019

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Suggested citation:

Cohn, T.A., Barth, N.A., England, J.F., Jr., Faber, B.A., Mason, R.R., Jr., and Stedinger, J.R., 2019, Evaluation of recommended revisions to Bulletin 17B: U.S. Geological Survey Open-File Report 2017–1064, 141 p.,

https://doi.org/10.3133/ofr20171064.

ISSN 2331-1258 (online)
iii

Acknowledgments

The work in this report was conceived by the Hydrologic Frequency Analysis Work Group (HFAWG) under the Subcommitee

on Hydrology (SOH), Advisory Committee on Water Data. The HFAWG is currently chaired by Wilbert Thomas. A data subgroup and a testing subgroup were formed under HFAWG to examine potential changes to Bulletin 17B. The data subgroup

consisted of Wilbert Thomas, Martin Becker, Don Woodward, Beth Faber, and Jerry Coffey. The HFAWG data subgroup

provided a set of peak-flow datasets and suggested tests to perform in comparing Bulletin 17B and the Expected Moments

Algorithm.

Lastly, our colleague and friend, Dr. Timothy A. Cohn, performed much of the work presented in this report. He wrote

software that was critical to implementing these testing results and shared it with others. He gave freely of his time in

teaching and instructing others in flood frequency and statistics. Tim was also instrumental in building support amongst

HFAWG, SOH, and many Federal agencies. He will be missed.

Timothy A. Cohn

February 26, 1957–February 20, 2017
iv

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v

Contents

Abstract .................................................................................................................................................................................... 1

Introduction .............................................................................................................................................................................. 2

Literature Sources: The History of Flooding and Flood Risk Estimation ..................................................................... 4

Metrics for Evaluating Flood-Frequency Estimators ....................................................................................................... 4

Estimation ................................................................................................................................................................................. 5

Parameter Estimation ................................................................................................................................................... 5

Identification of Outliers and Potentially Influential Low Floods ........................................................................ 6

The MGB Test Algorithm for Identifying Potentially Influential Low Floods ..................................................... 6

Would Identification of Fewer PILFs Yield Better Fits? ......................................................................................... 7

Treatment of Floods Identified as Potentially Influential Low Floods: Conditional Probability Adjustment and Expected Moments Algorithm .................................................................................................................. 9

Estimation Methods Considered in this Publication .............................................................................................. 11

Software .......................................................................................................................................................................... 11

Comparisons of Methods ...................................................................................................................................................... 12

Understanding the Graphical Presentation of Results .......................................................................................... 12

Studies with LP3 Distribution ...................................................................................................................................... 13

Studies with LP3 Distribution and Regional Skew ................................................................................................. 16

Robustness Studies ....................................................................................................................................................... 16

Robustness with Respect to Pearson Type 3 Population ............................................................................. 16

Robustness with Respect to Mixed Population Constructed from Two LP3 Distributions .................... 18

Robustness with Respect to Population Constructed from Two LP3 Distributions ................................ 18

Robustness with Respect to Population Constructed from Two Generalized Extreme Value

Distributions ............................................................................................................................................................ 18

Examples Based on Real Data at Selected Test Sites .................................................................................................... 22

Eighty-two Example Test Sites .................................................................................................................................... 22

Sites With Systematic Gage Data and No PILFs or Historical Information ...................................................... 22

Sites with Historical Information ................................................................................................................................ 25

Sites with Systematic Gage Data and Potentially Influential Low Floods ........................................................ 28

Sites With Potentially Influential Low Floods, Historical Information, and (or) High Outliers ...................... 34

Resampling Studies ....................................................................................................................................................... 34

Summary .......................................................................................................................................................................... 43

Conclusions .............................................................................................................................................................................. 43

References Cited .................................................................................................................................................................... 44

Appendix 1. Characteristics of 82 Test Sites ................................................................................................................. 47

Appendix 2. Graphical Comparisons Between the EMA and B17B at 82 Test Sites ............................................ 53

Systematic Data Sites ................................................................................................................................................... 54

Sites With Historical Information ............................................................................................................................... 80

Sites With Potentially Influential Low Floods .......................................................................................................... 99
vi

Sites With a Combination of Data Types .................................................................................................................. 119

Studies With log-Pearson Type III (LP3) Distribution and Regional Skew ........................................................ 136

Additional Studies With Specific Frequency Curves ............................................................................................. 136

Figures

1. One-day peak floods from 1932 to 2008; discharge measured in cubic feet per second at

Sacramento River at Shasta Dam ....................................................................................................................... 10

2. Monte Carlo results based on 10,000 replicate samples using systematic record, NS=40, and

historical record, NH=100, drawn from a log-Pearson Type III (LP3) distribution with skew of

0.0 ................................................................................................................................................................................ 14

3. Monte Carlo results based on 10,000 replicate samples using systematic record, NS=40, and

historical record, NH=100, drawn from a log-Pearson Type III (LP3) distribution with skew of

0.5 ............................................................................................................................................................................ 15

4. Monte Carlo results based on 10,000 replicate samples using systematic record, NS=40, and

historical record, NH=100, drawn from a log-Pearson Type III (LP3) distribution with skew of

0.5 ................................................................................................................................................................................ 17

5. Monte Carlo results based on 10,000 replicate samples using systematic record, NS=40, and

historical record, NH=100, drawn from robustness test curve 3 ................................................................ 19

6. Monte Carlo results based on 10,000 replicate samples using systematic record, NS=40, and

historical record, NH=100, drawn from a mixed population based on robustness test curve 4 .......... 20

7. Monte Carlo results based on 10,000 replicate samples using systematic record, NS=40, and

historical record, NH=100, drawn from robustness test curve 5 ................................................................ 21

8. Monte Carlo results based on 10,000 replicate samples using systematic record, NS=40, and

historical record, NH=100, drawn from robustness test curve 6 ................................................................ 23

9. Relative percent difference (RPD) for Bulletin 17B/Grubbs-Beck (B17B/GB) and Expected

Moments Algorithm/multiple Grubbs-Beck (EMA/MGB) estimators for 10-percent (%), 1-%,

and 0.2-% exceedance probabilities (Qp). Includes 26 sites without historical flood information

where no potentially influential low floods were identified by either test ................................................. 24

10. Relative percent difference (RPD) for Bulletin 17B/Grubbs-Beck (B17B/GB) and Expected

Moments Algorithm/multiple Grubbs-Beck (EMA/MGB) estimators for 10-percent (%), 1-%,

and 0.2-% exceedance probabilities (Qp). Figure represents 19 sites with historical information where no potentially influential low floods were identified by either GB test ................................ 26

11. Pryor Creek near Billings, Montana (06216500) .............................................................................................. 27

12. Relative percent difference (RPD) for Bulletin 17B/Grubbs-Beck (B17B/GB), Bulletin

17B/multiple Grubbs Beck (B17B/MGB), and Expected Moments Algorithm/multiple GrubbsBeck (EMA/MGB) estimators for 10-percent (%), 1-%, and 0.2-% exceedance probabilities

(Qp). The figure represents 20 sites where potentially influential low floods were identified by

GB or MGB tests, and with no historical information ................................................................................... 29

13. Number of floods identified as potentially influential low floods or below gage base using

the standard Grubbs-Beck (GB) and multiple Grubbs-Beck (MGB) tests. Figure represents 20

sites without historical information .................................................................................................................. 30
vii

14. Percent potentially influential low floods identified using the multiple Grubbs-Beck test.

Figure represents 20 sites without historical information ........................................................................... 31

15. Orestimba Creek near Newman, California (11274500), fit after application of the multiple

Grubbs-Beck (MGB) test to identify potentially influential low floods ...................................................... 32

16. Santa Cruz River near Lochiel, Arizona (09480000) ........................................................................................ 33

17. Relative percent difference (RPD) for Bulletin 17B/Grubbs Beck (B17B/GB), Bulletin

17B/multiple Grubbs Beck (B17B/MGB), and Expected Moments Algorithm/multiple Grubbs

Beck (EMA/MGB) estimators for 10-percent (%), 1-%, and 0.2-% exceedance probabilities

(Qp). Represents 17 sites with historical flood information where potentially influential low

floods were identified by the GB or MGB test ................................................................................................ 35

18. Arroyo Mocho near Livermore, California (11176000) ................................................................................... 36

19. Tenmile Creek near Rimini, Montana (06062500) ............................................................................................ 37

20. Results based on resampled data using systematic record, NS=40, and historical record,

NH=100, drawn from observed discharges at “Historical” category site 03011020 ............................. 38

21. Results based on resampled data using systematic record, NS=40, and historical record,

NH=100, drawn from observed discharges at “potentially influential low flood” category site

11152000 .................................................................................................................................................................. 39

22. Results based on resampled data using systematic record, NS=40, and historical record,

NH=100, drawn from observed discharges at “Gage Only” category site 14048000 ............................ 40

23. Results based on resampled data using systematic record, NS=40, and historical record,

NH=100, drawn from observed discharges at “potentially influential low flood” category site

14321000 .................................................................................................................................................................. 41

24. Results based on resampled data using systematic record, NS=40, and historical record,

NH=100, drawn from observed discharges at “Combination” category site 13185000 ........................ 42

2–1. Site 01076500–Pemigewasset River at Plymouth, New Hampshire (NH) with systematic data

only ......................................................................................................................................................................... 54

2–2. Site 01439500–Bush Kill at Shoemakers, Pennsylvania (PA) with systematic data only .................... 55

2–3. Site 01555500–East Mahantango Creek near Dalmatia, Pennsylvania (PA) with systematic

data only ............................................................................................................................................................... 56

2–4. Site 01635500–Passage Creek near Buckton, Virginia (VA) with systematic data only ...................... 57

2–5. Site 02037500–James River near Richmond, Virginia (VA) with systematic data only ........................ 58

2–6. Site 02256500–Fisheating Creek at Palmdale, Florida (FL) with systematic data only ......................... 59

2–7. Site 03183500–Greenbrier River at Alderson, West Virginia (WV) with systematic data only ........... 60

2–8. Site 05586500–Hurricane Creek near Roodhouse, Illinois (IL) with systematic data only .................. 61

2–9. Site 06406000–Battle Creek at Hermosa, South Dakota (SD) with systematic data only ................... 62

2–10. Site 06710500–Bear Creek at Morrison, Colorado (CO) with systematic data only ........................... 63

2–11. Site 07208500–Rayado Creek near Cimarron, New Mexico (NM) with systematic data only ......... 64

2–12. Site 07382000–Bayou Cocodrie near Clearwater, Louisiana (LA) with systematic data only .......... 65

2–13. Site 08380500–Gallinas Creek near Montezuma, New Mexico (NM) with systematic data

only ....................................................................................................................................................................... 66

2–14. Site 08387000–Rio Ruidoso at Hollywood, New Mexico (NM) with systematic data only ............... 67

2–15. Site 10128500–Weber River near Oakley, Utah (UT) with systematic data only ................................. 68
viii

2–16. Site 11266500–Merced River at Pohono Bridge near Yosemite, California (CA) with systematic data only ..................................................................................................................................................... 69

2–17. Site 12134500–Skykomish River near Gold Bar, Washington (WA) with systematic data only ....... 70

2–18. Site 12414500–St. Joe River at Calder, Idaho (ID) with systematic data only ..................................... 71

2–19. Site 12437950–East Fork Foster Creek tributary near Bridgeport, Washington (WA) with

systematic data only ........................................................................................................................................ 72

2–20. Site 12451000–Stehekin River at Stehekin, Washington (WA) with systematic data only ............... 73

2–21. Site 14021000–Umatilla River at Pendleton, Oregon (OR) with systematic data only ........................ 74

2–22. Site 14048000–John Day River at McDonald Ferry, Oregon (OR) with systematic data only ........... 75

2–23. Site 14137000–Sandy River near Marmot, Oregon (OR) with systematic data only ........................... 76

2–24. Site 15072000–Fish Creek near Ketchikan, Alaska (AK) with systematic data only ........................... 77

2–25. Site 16518000–West Wailuaiki Stream near Keanae, Hawaii (HI) with systematic data only ......... 78

2–26. Site 16587000–Honopou Stream near Huelo Maui, Hawaii (HI) with systematic data only ............. 79

2–27. Site 01350000–Schoharie Creek at Prattsville, New York (NY) with systematic and historical

data ...................................................................................................................................................................... 80

2–28. Site 01562000–Raystown Branch Juniata River at Saxton, Pennsylvania (PA) with systematic and historical data .................................................................................................................................... 81

2–29. Site 01636500–Shenandoah River at Millville, West Virginia (WV) with systematic and

historical data .................................................................................................................................................... 82

2–30. Site 02138500–Linville River near Nebo, North Carolina (NC) with systematic and historical

data ...................................................................................................................................................................... 83

2–31. Site 03011020–Allegheny River at Salamanca, New York (NY) with systematic and historical

data ...................................................................................................................................................................... 84

2–32. Site 03051000–Tygart Valley River at Belington, West Virginia (WV) with systematic and

historical data .................................................................................................................................................... 85

2–33. Site 03159500–Hocking River at Athens, Ohio (OH) with systematic and historical data ................. 86

2–34. Site 03550000–Valley River at Tomotla, North Carolina (NC) with systematic and historical

data ...................................................................................................................................................................... 87

2–35. Site 03558000–Toccoa River near Dial, Georgia (GA) with systematic and historical data ............. 88

2–36. Site 03606500–Big Sandy River at Bruceton, Tennessee (TN) with systematic and historical

data ...................................................................................................................................................................... 89

2–37. Site 04293500–Missisquoi River near East Berkshire, Vermont (VT) with systematic and

historical data .................................................................................................................................................... 90

2–38. Site 06216500–Pryor Creek near Billings, Montana (MT) with systematic and historical data ....... 91

2–39. Site 06600500–Floyd River at James, Iowa (IA) with systematic and historical data ........................ 92

2–40. Site 06898000–Thompson River at Davis City, Iowa (IA) with systematic and historical data ......... 93

2–41. Site 07067000–Current River at Van Buren, Missouri (MO) with systematic and historical

data ...................................................................................................................................................................... 94

2–42. Site 08167000–Guadalupe River at Comfort, Texas (TX) with systematic and historical data ......... 95

2–43. Site 08378500–Pecos Rivert near Pecos, New Mexico (NM) with systematic and historical

data ...................................................................................................................................................................... 96

2–44. Site 09482500–Santa Cruz River at Tucson, Arizona (AZ) with systematic and historical data ....... 97
ix

2–45. Site 12413000–North Fork (NF) Coeur D’Alene River at Enaville, Idaho (ID) with systematic

and historical data ............................................................................................................................................ 98

2–46. Site 01668000–Rappahannock River near Fredericksburg, Virginia (VA) with potentially

influential low floods and no historical information .................................................................................. 99

2–47. Site 03345500–Embarras River at Ste. Marie, Illinois (IL) with potentially influential low

floods and no historical information ............................................................................................................. 100

2–48. Site 05572000–Sangamon River at Monticello, Illinois (IL) with potentially influential low

floods and no historical information ............................................................................................................. 101

2–49. Site 06176500–Wolf Creek near Wolf Point, Montana (MT) with potentially influential low

floods and no historical information ............................................................................................................. 102

2–50. Site 07203000–Vermejo River near Dawson, New Mexico (NM) ........................................................... 103

2–51. Site 08133500–North Concho River at Sterling City, Texas (TX) with potentially influential low floods and no historical information. EMA, Expected Moments Algorithm; B17B,

Bulletin 17B ........................................................................................................................................................ 104

2–52. Site 08150000–Llano River near Junction, Texas (TX) with potentially influential low floods

and no historical information ......................................................................................................................... 105

2–53. Site 08189500–Mission River at Refugio, Texas (TX) with potentially influential low floods

and no historical information ......................................................................................................................... 106

2–54. Site 09241000–Elk River at Clark, Colorado (CO) with potentially influential low floods and

no historical information ................................................................................................................................. 107

2–55. Site 09480000–Santa Cruz River near Lochiel, Arizona (AZ) with potentially influential low

floods and no historical information ............................................................................................................. 108

2–56. Site 10234500–Beaver River near Beaver, Utah (UT) with potentially influential low floods

and no historical information ......................................................................................................................... 109

2–57. Site 11028500–Santa Maria Creek near Ramona, California (CA) with potentially influential

low floods and no historical information ..................................................................................................... 110

2–58. Site 11152000–Arroyo Seco near Soledad, California (CA) with potentially influential low

floods and no historical information ............................................................................................................. 111

2–59. Site 11274500–Orestimba Creek near Newman, California (CA) with potentially influential

low floods and no historical information ..................................................................................................... 112

2–60. Site 11383500–Deer Creek near Vina, California (CA) with potentially influential low floods

and no historical information ......................................................................................................................... 113

2–61. Site 12307500–Moyie River at Eileen, Idaho (ID) with potentially influential low floods and

no historical information ................................................................................................................................. 114

2–62. Site 13302500–Salmon River at Salmon, Idaho (ID) with potentially influential low floods and

no historical information ................................................................................................................................. 115

2–63. Site 13343660–Smith Gulch tributary near Pataha, Washington (WA) with potentially influential low floods and no historical information .......................................................................................... 116

2–64. Site 14321000–Umpqua River near Elkton, Oregon (OR) with potentially influential low

floods and no historical information ............................................................................................................. 117

2–65. Site 16068000–East Branch (EB) of North Fork (NF) Wailua River near Lihue, Hawaii (HI)

with potentially influential low floods and no historical information .................................................... 118

2–66. Site 03289500–Elkhorn Creek near Frankfort, Kentucky (KY) with a combination of potentially influential low floods, historical, and (or) high outliers in the data .............................................. 119
x

2–67. Site 05270500–Sauk River near St. Cloud, Minnesota (MN) with a combination of potentially

influential low floods, historical, and (or) high outliers in the data ....................................................... 120

2–68. Site 05291000–Whetstone River near Big Stone City, South Dakota (SD) with a combination

of potentially influential low floods, historical, and (or) high outliers in the data .............................. 121

2–69. Site 05464500–Cedar River at Cedar Rapids, Iowa (IA) with a combination of potentially

influential low floods, historical, and (or) high outliers in the data ....................................................... 122

2–70. Site 06062500–Tenmile Creek near Rimini, Montana (MT) with a combination of potentially

influential low floods, historical, and (or) high outliers in the data ....................................................... 123

2–71. Site 06897000–East Fork Big Creek near Bethany, Missouri (MO) with a combination of

potentially influential low floods, historical, and (or) high outliers in the data ................................... 124

2–72. Site 06933500–Gasconade River at Jerome, Missouri (MO) with a combination of potentially influential low floods, historical, and (or) high outliers in the data. EMA, Expected

Moments Algorithm; B17B, Bulletin 17B ...................................................................................................... 125

2–73. Site 07138600–White Woman Creek tributary near Selkirk, Kansas (KS) with a combination

of potentially influential low floods, historical, and (or) high outliers in the data .............................. 126

2–74. Site 08164000–Lavaca River near Edna, Texas (TX) with a combination of potentially influential low floods, historical, and (or) high outliers in the data ............................................................... 127

2–75. Site 08171000–Blanco River at Wimberley, Texas (TX) with a combination of potentially

influential low floods, historical, and (or) high outliers in the data ....................................................... 128

2–76. Site 09361500–Animas River at Durango, Colorado (CO) with a combination of potentially

influential low floods, historical, and (or) high outliers in the data ....................................................... 129

2–77. Site 09471000–San Pedro River at Charleston, Arizona (AZ) with a combination of potentially influential low floods, historical, and (or) high outliers in the data .............................................. 130

2–78. Site 11176000–Arroyo Mocho near Livermore, California (CA) with a combination of potentially influential low floods, historical, and (or) high outliers in the data .............................................. 131

2–79. Site 11464500–Dry Creek near Cloverdale, California (CA) with a combination of potentially

influential low floods, historical, and (or) high outliers in the data. EMA, Expected Moments

Algorithm; B17B, Bulletin 17B ........................................................................................................................ 132

2–80. Site 11522500–Salmon River at Somes Bar, California (CA) with a combination of potentially

influential low floods, historical, and (or) high outliers in the data ....................................................... 133

2–81. Site 12039500–Quinault River at Quinault Lake, Washington (WA) with a combination of

potentially influential low floods, historical, and (or) high outliers in the data ................................... 134

2–82. Site 13185000–Boise River near Twin Springs, Idaho (ID) with a combination of potentially

influential low floods, historical, and (or) high outliers in the data ....................................................... 135

2–83. Results are based on 10,000 replicate samples with systematic record, NS=40, and historical record, NH=100, drawn from a log-Pearson type III distribution with skew, γ=0.0.

Regional skew is assumed to be 0.0 with mean square error of 0.15 ................................................... 137

2–84. Results are based on 10,000 replicate samples with systematic record, NS=40, and historical record, NH=100, drawn from a log-Pearson type III distribution with skew, γ=0.5.

Regional skew is assumed to be 0.5 with mean square error of 0.15 ................................................ 138

2–85. Results are based on 10,000 replicate samples with systematic record, NS=40, and historical record, NH=100, drawn from a log-Pearson type III distribution with skew, γ=0.5.

Regional skew is assumed to be 0.5 with mean square error of 0.15 ................................................... 139
xi

2–86. Results are based on 10,000 replicate samples with systematic record, NS=40, and historical record, NH=100, drawn from robustness test curve 1 ...................................................................... 140

2–87. Results are based on 10,000 replicate samples with systematic record, NS=40, and historical record, NH=100, drawn from robustness test curve 2 ...................................................................... 141

Tables

1. Impact of restricting search for potentially influential low floods to the bottom quartile of

sample at the 13 sites where more than 25 percent of the observations had been identified as

PILFs using the standard multiple Grubbs-Beck test ...................................................................................... 8

1–1. Characteristics of at-site streamflow records used in comparing Bulletin 17B and the

Expected Moments Algorithm estimators ..................................................................................................... 48
xii

Conversion Factors

U.S. customary units to International System of Units

Multiply By To obtain

foot (ft) 0.3048 meter (m)

mile (mi) 1.609 kilometer (km)

square mile (mi2) 2.590 square kilometer (km2)

cubic foot per second (ft3/s) 0.02832 cubic meter per second (m3/s)

Datum

Horizontal coordinate information is referenced to the North American Datum of 1983 (NAD 83).

Vertical coordinate information is referenced to the National Geodetic Vertical Datum of 1929 (NGVD 29).

Abbreviations

ACWI Advisory Committee on Water Information

AEP annual exceedance probability

AG average gain

AMS annual maximum series

B17B Bulletin 17B

CDF cumulative distribution function

CPA conditional probability adjustment

EMA Expected Moments Algorithm

ERL effective record length

GB Grubbs-Beck

HFAWG Hydrologic Frequency Analysis Work Group

IAWCD Interagency Committee on Water Data

LP3 log-Pearson Type III distribution

MGB Multiple Grubbs-Beck

MGBT Multiple Grubbs-Beck Test

MSE mean square error

NWIS USGS National Water Information System

P3 Pearson Type III distribution

PILF Potentially Influential Low Flood

RPD relative percent difference

SOH Subcommittee on Hydrology

USGS U.S. Geological Survey

USWRC U.S. Water Resources Council
Evaluation of Recommended Revisions

to Bulletin 17B

By Timothy A. Cohn, Nancy A. Barth, John F. England, Jr., Beth A. Faber, Robert R. Mason, Jr., and Jery R.

Stedinger

Abstract

For the past 36 years, Bulletin 17B, published by the Interagency Committee on Water Data in 1982, has

guided flood-frequency analyses in the United States. During this period, much has been learned about both

hydrology and statistical methods. In keeping with the tradition of periodically updating the Bulletin 17B

guidelines in light of advances in our understanding and methods, the Hydrologic Frequency Analysis Work

Group (HFAWG) was charged by the Subcommittee on Hydrology (SOH) of the Advisory Committee on

Water Information (ACWI) to consider possible updates to Bulletin 17B.

The purpose of this report is to consider the statistical performance of possible revisions to Bulletin 17B

procedures. Of particular interest are procedures designed to accommodate more general forms of flood information. The concern is how the proposed procedures would affect the precision, accuracy and robustness of

flood-frequency estimates. The investigations reported here focus on techniques for the following:


 incorporating information related to historical flooding that occurred outside the period of systematic

streamgaging; and


 identification of potentially influential low floods (PILFs).

The proposed changes, which mostly involve generalizing Bulletin 17B’s method-of-moments procedures by

using the Expected Moments Algorithm (EMA), are relatively modest, at least in the sense that they would not

affect the main features of Bulletin 17B. The proposed methods include the following:










continued use of the log-Pearson Type 3 (LP3) distribution;

continued use of the Method-of-Moments fitting method applied to the logarithms of annual-peak-flow

data; and

a generalization of the Grubbs-Beck test used in Bulletin 17B to identify low outliers. The new multiple

Grubbs-Beck test is sensitive to multiple PILFs.

The hydrological literature already provides extensive support for the theory behind the proposed changes.

The remaining question is practical: How well do the proposed methods perform under typical and realistic

conditions and, specifically, with difficult records occasionally encountered in practice? In order to answer

these questions, the HFAWG commissioned the work reported here. The following four major sets of results

are provided:


 Monte Carlo simulations of fitting procedures employing data drawn from simulated LP3 populations;
2 Evaluation of Recommended Revisions to Bulletin 17B


 Monte Carlo simulations of fitting procedures employing data drawn from non-LP3 populations that were

selected to reflect likely deviations of flood series from LP3 distributions, based on the experience of

HFAWG members;


 a direct comparison of the fitted LP3 distributions for 82 real “test sites” identified by an independent data

group as both “typical” and “challenging” for flood-frequency estimation; and


 simulations of fitting procedures using records obtained by resampling with replacement from the longest

of the 82 test-site records.

Collectively, these studies provide a reasonably comprehensive, valid, and robust assessment of the properties

of the Bulletin 17B methods and proposed alternatives. The experiments and analysis indicate that the flood

quantile estimators, proposed as a revision of Bulletin 17B, do the following:


 perform generally as well as, and in some cases much better than, Bulletin 17B estimators in terms of the

mean square error of flood quantiles estimates;


 allow for incorporation and efficient statistical treatment of broader classes of flood-frequency data and

information, including historical information, binomial data and interval data; and


 generally confirm studies and the theoretical findings reported in the hydrological literature that would

support use of updated estimation procedures that have been developed since Bulletin 17B was published.

Introduction

Flooding is the costliest natural hazard facing the United States in terms of loss of both life and property

(Mileti, 1999; ACWI, 2011). While policymakers and planners have an array of tools to reduce flood losses

through structural and nonstructural mitigation, doing so in practice requires a quantitative, uniform, and consistent approach for estimating flood risk (Tasker and Thomas, 1978; Thomas, 1985; Griffis and Stedinger,

2007). Recognizing this, the Federal Government has developed standard guidelines for performing floodfrequency analyses, and published these guidelines in a document known as “Bulletin 17B” by the Interagency

Advisory Committee on Water Data (IACWD, 1982). The methods defined in Bulletin 17B (B17B) inform literally millions of decisions about land use and construction, emergency response and recovery, and countless

other governmental and private-sector activities in the United States. The practical value of Federal guidelines

is not in dispute.

Nonetheless, Bulletin 17B (IACWD, 1982) has its limitations. The document itself recognized that additional work was needed to improve some of its procedures (IACWD, 1982, p. 27, “Future Studies”). In light

of additional research conducted to address these concerns, both researchers and practicing hydrologists have

recently called for updates to the Bulletin 17B Guidelines. The purpose of this report is to evaluate some proposed modifications to the flood-frequency methods specified in Bulletin 17B.

In November of 2005, the Hydrologic Frequency Analysis Workgroup (HFAWG) proposed the following

(Hydrologic Frequency Analysis Work Group, 2006):

Based on recently completed research, the HFAWG proposes to investigate the following possible improvements in Bulletin 17B:

1. Evaluate and compare the performance of the Expected Moments Algorithm (EMA) (Cohn and

others, 1997) to the weighted-moments approach of Bulletin 17B (appendix 6) for analyzing

datasets with historic information and paleoflood data.
Literature Sources: The History of Flooding and Flood Risk Estimation 3




historic data and those that do not. Develop criteria for determining if EMA provides more

accurate and consistent flood estimates.


 Review and evaluate the published literature for comparisons of EMA to conventional

Bulletin 17B procedures.


 Recommend improved plotting position formula when historic data are available.

2. Evaluate and compare the performance of EMA to the conditional probability adjustment of

Bulletin 17B for analyzing datasets with potentially influential low floods (PILFs) and zero

flows.


 Apply EMA and Bulletin 17B to gaging station data that include low and high outliers

and historic data and those that do not (same dataset as noted above). Develop criteria for

determining if EMA provides more accurate and consistent flood estimates.

3. Describe improved procedures for estimating generalized/regional skew.


 Evaluate revisions needed in Bulletin 17B to describe improved procedures for estimating

generalized/regional skew based on recently completed research.

4. Describe improved procedures for defining confidence limits.


 Evaluate revisions needed in Bulletin 17B to describe new procedures for defining confidence limits that include the uncertainty in the skew coefficient.


 Describe confidence limit procedures for EMA (if adopted).

This report presents results of analyses that focus on items 1 and 2. Items 3 and 4 are addressed in previous literature. Advances in regional skew analyses are described in a series of U.S. Geological Survey (USGS) 

reports (Lamontagne and others, 2012; Veilleux and Stedinger, 2010; Veilleux and others, 2012). Confidence

interval issues have been discussed in Cohn and others (2001) and earlier in Chowdhury and Stedinger (1991);

see also Cohn and others (2013).

Note that none of the proposed changes to Bulletin 17B methods address issues that arise when fitting

flood-frequency curves to nonstationary conditions that may arise due to land use change, changes to watermanagement practices, or climate variability or change. This is left to future work.

This report is organized in the following manner: Section Literature Sources: The History of Flooding and

Flood Risk Estimation provides a brief review of literature on the topic addressed herein and, through references, a more general review of the larger field of flood frequency analysis. Section Metrics for Evaluating

Flood-Frequency Estimators discusses criteria for judging estimator performance, including statistical, practical, and operational concerns. Section Estimation reviews the statistical methods that are considered in this

report, primarily the existing Bulletin 17B recommendations and the proposed EMA. Section Comparisons

of Methods presents a set of Monte Carlo results based on synthetic samples from a variety of assumed and

alternative distributional families, as well as based on resampling at long-record sites. Section Examples Based

on Real Data at Selected Test Sites reviews the performance of the Bulletin 17B and the EMA procedures at

82 real sites that were selected to represent conditions that exist at sites throughout the United States. Section

Conclusions presents conclusions—a summary of the main findings of the research as reported in the earlier

sections. Two appendixes are included that provide metadata on the real-world sites employed in this study

and additional figures illustrating estimator performance.

Apply EMA and Bulletin 17B to gaging station data that include low and high outliers and
4 Evaluation of Recommended Revisions to Bulletin 17B

Literature Sources: The History of Flooding and Flood Risk Estimation

Bulletin 17B (IACWD, 1982) defines the current method for conducting peak-flow frequency analyses in

the United States. It descends from a series of studies and guidelines beginning with Bulletins 13 (Interagency

Committee on Water Resources, 1966), 15 (U.S. Water Resources Council, 1967), 17 (U.S. Water Resources

Council, 1976), and 17A (U.S. Water Resources Council, 1977). Each of these reports includes a list of relevant citations. The history of these bulletins and a discussion of the methods recommended in Bulletin 17B

appear in Thomas (1985), Stedinger and others (1993), and Griffis and Stedinger (2007). There is also a vast

amount of literature on methods for flood-frequency estimation, and an extensive list of citations can be found

in Stedinger and others (1993), Griffis and Stedinger (2007), and Dawdy and others (2012). American Institutes for Research (2005) provides a comprehensive chronology of the history of flood-risk estimation, as well

as a comprehensive bibliography of the flood-frequency literature prior to 2000. Stedinger and others (1993)

provides a bibliography of statistical techniques employed in flood-frequency analyses.

Metrics for Evaluating Flood-Frequency Estimators

In practice, the benefits of more accurate flood information depend on many factors that are site specific.

In particular, benefits depend on the physical, geological, social, and other characteristics of the site. However,

in trying to assess the performance of flood-risk estimation techniques, one typically simplifies the problem

by considering a small number of generally accepted criteria that are believed to characterize adequately an

estimator’s performance.

The criteria employed in this study can be divided into several groups.


 Operational

1. Ease of Application—Methods should be relatively easy to implement.

2. Applicability to Available Data—Methods should be able to make efficient use of the data types

available for flood investigations.

3. Uniformity of Methods—Where possible, standardized methods and software should be used to

ensure that different people performing the same analysis will obtain the same risk estimates. This

will also ensure that frequency estimates are fully reproducible.


 Statistical

1. Bias and consistency—On average, risk estimates should approximately equal the true risk; as

more information becomes available, risk estimates should converge to the true risk.

2. Efficiency—Estimators should extract as much information from the data as possible so as to minimize the mean square error of estimated statistics.

3. Quantified uncertainty—Estimates should be accompanied by quantitative assessments of their

uncertainty.


 Political, Legal, and Institutional Criteria Standard methods should be consistent, uniform, and easily explained. They should satisfy legal requirements and should serve institutional requirements of the

Federal Government and its National Flood Insurance Program, among others.

In this report, the following set of metrics is used to quantify the differences among different parameter estimation procedures:
Estimation 5

BIAS The expected difference between the estimate and true value of the parameter of interest.

MSE Mean square error (MSE) is defined as the expected squared difference between the estimate and true

value of the parameter of interest. This is sometimes expressed as the sum of the variance plus the bias

squared.

ERL The efficiency of estimators that employ historical flood information is quantified in terms of effective

record length (ERL), the amount of equivalent systematic record that, by itself, would provide the precision achieved with the combination of both systematic and historical information.

AG A more general measure of estimator efficiency is the average gain (AG), which expresses the benefit of

each year of historical information in terms of the information in a year of systematic data.

RPD The relative percent difference (RPD) statistic is used to quantify differences among estimators.

Taken as a whole, these metrics provide the quantitative foundation for characterizing the performance of

Bulletin 17B flood-frequency methods and proposed alternatives.

Estimation

For most of this study, flood quantile estimates were computed using two parameter estimation methods

(B17B and EMA) and two PILF identification procedures (Grubbs-Beck [GB] and multiple Grubbs-Beck

[MGB]). Section Identification of Outliers and Potentially Influential Low Floods discusses the motivation

of the GB procedure in Bulletin 17B and of a proposed replacement, MGB. The characteristics of the MGB

method are discussed in section The MGB Test Algorithm for Identifying Potentially Influential Low Floods.

Section Treatment of Floods Identified as Potentially Influential Low Floods: Conditional Probability Adjustment and Expected Moments Algorithm provides a discussion of the conditional probability adjustment (CPA)

used by Bulletin 17B and the proposed EMA approach to analyze records containing zero flows, PILFs, and

other events described as being less than a specified threshold. Section Estimation Methods Considered in this

Publication discusses three specific combinations of parameter estimators and PILF identification procedures

considered in this publication. Section Software identifies the software used in the studies.

Parameter Estimation

Bulletin 17B (IACWD, 1982) recommends use of the method of moments to estimate the first three sample moments, although a number of additional procedures are employed for dealing with special situations.

All of the procedures are documented in the Bulletin, and additional information on the procedures is found in

Thomas (1985), Stedinger and others (1993), and Griffis and Stedinger (2007).

The EMA is a straightforward generalization of the method of moments that is designed to accommodate

both the point data envisioned in Bulletin 17B (IACWD, 1982), as well as various forms of nonstandard interval data. The details of EMA are discussed in Cohn and others (1997), Cohn and others (2001), and Griffis

and others (2004). At most sites across the United States, where only systematic annual peak flow data are

currently available, the B17B and EMA frequency estimates are essentially identical. However, where nonstandard data are present, the two estimates will differ. In some cases, the differences can be substantial (see

section Examples Based on Real Data at Selected Test Sites).
6 Evaluation of Recommended Revisions to Bulletin 17B

Identification of Outliers and Potentially Influential Low Floods

Among the proposed improvements to Bulletin 17B is a new MGB test (MGBT) for PILFs. The MGBT

is a natural generalization of the Bulletin 17B Grubbs-Beck test, and addresses item 3 in the Bulletin 17B list

of needed future work (IACWD, 1982): “The treatment of outliers both as to identification and computational

procedures.”

PILF identification and treatment are important issues in flood-frequency analysis guidelines because

unusually small observations, which often result from physical processes that are of little relevance to the

estimation of large floods, can nevertheless have a large influence on statistical estimates of extreme flood

quantiles. In arid regions, for example, channel losses often result in annual flood peaks that are zero. As a

result, an LP3 distribution cannot fit the entire flood record. Moreover, samples from an LP3 distribution with

substantial negative log-space skew (γ  ̈ 0.5) often contain very low flood values and, using log-space

moments, those unusually small values have undue influence and can result in poor estimates of the large flood

quantiles of interest in flood risk management. Unusually small values are, therefore, a real concern because

it is imperative that the estimators defined in a Bulletin 17C analysis, in addition to being efficient, possess the

characteristic of robustness, meaning that they perform reasonably well, even when underlying assumptions

are violated.

Robustness is sometimes achieved in statistical analyses through explicit adaptation: The analyst looks for

problems and then addresses the critical issues. In frequency analyses, for example, one often uses a probability plot to examine if sample data are consistent with a fitted curve (Stedinger and others, 1993). The authors

of Bulletin 17B dealt with the robustness issue by explicitly identifying low outliers that “depart significantly

from the trend of the remaining data.” They note that “The retention, modification and deletion of these outliers can significantly affect the statistical parameters computed from the data.” Thus, the authors of Bulletin

17B explicitly recognized that we do not want small flood values distorting the model that describes the distribution of large floods (the “trend of the remaining data”). They explicitly note that failure to address this issue

would “significantly affect the [computed] statistical parameters.”

Barnett and Lewis (1994, p. 7–9) discuss this idea of using outlier tests to identify unusual observations

that otherwise might have undue influence in an analysis. Low-outlier identification tests provide an objective

and standard method for identifying PILFs, ensuring that different hydrologists analyzing the same data will

arrive at the same conclusions.

The purpose of using the Bulletin 17B GB test, and the MGB extension considered here, is to identify

potentially influential low floods, or PILFs. The defining characteristic of PILFs is that they potentially have

a large influence on the upper tail of the fitted frequency curve. For example, when datasets are highly negatively skewed, the smallest observations can be very influential in determining the estimated skewness coefficient, and, as a result, the estimated value of the 1 percent exceedance probability flood (100-year flood).

The MGB Test Algorithm for Identifying Potentially Influential Low Floods

The Bulletin 17B GB test provides an objective method for identifying values that should be treated as

“low outliers,” in the terminology employed in that report. However, the Bulletin 17B GB test “low-outlier”

threshold is based on the assumption that only the smallest observation in the sample might be a PILF. As

a result, even though multiple PILFs in flood data are common, the GB test rarely identifies more than one

(Lamontagne and others, 2013). To provide an objective criterion for identification of multiple PILFs, a multiple Grubbs-Beck test was developed that employs the actual distribution of the i

th smallest observation in a

sample of n independent LP3 variates with zero skew (Cohn and others, 2013).
Estimation 7

Cohn and others (2013) provides the probability p(i;n) that the i

th smallest observation in a normal sample

of size n might be as small or smaller than the value observed. If p(i;n) is small enough, then the i

th smallest observation is considered unusual, and all values equal to and less than the i

th smallest observation are

recoded as censored values. Rosner (1975) explains the advantages of this generalization of the GB statistic in the context of an analogous two-sided multiple outlier test. The specialized test adopted here considers

only outliers in the lower tail. Spencer and McCuen (1996) and McCuen (2003) also discuss outlier tests based

upon a generalized GB statistic.

The procedure for actually identifying PILFs includes the two following steps:

1. Starting at the median and sweeping outward towards the smallest observation, each observation is tested

and is identified as a PILF if p(i;n)  ̈ 0.5%. If the k

th observation is identified as a PILF, the outward

sweep stops and the k

th and all smaller observations are also identified as PILFs.

2. Then, as with the current GB procedure in Bulletin 17B, an inward sweep starts at the pk  1q

st smallest

observation, where the observation is identified as a PILF if p(k+1;n)  ̈ 10%. This is repeated, sweeping

towards the median, until an observation m fails to be identified as a PILF by the inward sweep, at which

point the inward sweep stops.

The number of PILFs identified by the procedure is then the larger of k and m  1.

Bulletin 17B also used a 10 percent significance test but employed only a single inward sweep. A second

critical difference is that the new inward sweep uses the p(i;n) function, which correctly describes whether the

i

th largest observation is unusual in a sample of size n. The MGB’s first outward sweep seeks to determine

if there is some break in the lower half of the data that would suggest the sample is best treated as if it had

a number of PILFs. The second sweep using a less severe significance level, p(i;n)  ̈ 10%, mimics Bulletin

17B’s willingness to identify one or more of the smallest observations as PILFs so that the analysis is more

robust.

If a record has, for example, five zero flows, then the smallest nonzero flow is considered to be the sixth

smallest observation in the record. This correctly reflects the fact that the flood record included five smaller

values. The GB test in Bulletin 17B includes no mechanism for correcting its threshold when testing the smallest nonzero flood value in a record containing one or more zeros, or below-threshold discharges at sites with

crest-stage gages. This is particularly problematic because sites with zero flows are likely to include one or

more small or near-zero flood values that should be identified as PILFs. The MGB test (MGBT) solves this

problem.

Would Identification of Fewer PILFs Yield Better Fits?

The MGBT was defined to search for PILFs—potentially influential low floods—in the bottom 50 percent of the sample. Citing various reasons, some practicing hydrologists have expressed concern about declaring half of a sample to be PILFs. In part, this reflects concern about the number of PILFs; however, the focus

should be on achieving robustness in estimating large floods, not to utilize as many point observations as possible.

In any case, one can determine the consequence of limiting the number of identified PILFs to, for example, one quarter of the sample rather than half. This question is addressed here through consideration of the 82

test sites. One immediate observation is that the question is relevant to only a handful of cases; the MGBT

identifies fewer than 25 percent of PILFs at 69 of the 82 test sites. The 25-percent constraint would not be

binding at these sites, and the results at these sites are not affected by limiting the number of PILFs to 25 percent.
8 Evaluation of Recommended Revisions to Bulletin 17B

Table 1. Impact of restricting search for potentially influential low floods to the bottom quartile of sample at the 13 sites where

more than 25 percent (%) of the observations had been identified as PILFs using the standard multiple Grubbs-Beck test. The

change in the 1%-exceedance event appears in the right-most column, and ranged from -20% (0.20) to +58% (0.58), with a

median increase of +6% and average increase of +9%. Here, Qˆ0.01,r50s and Nr50s refer to the estimated 1%-exceedance flood

with the 50% limit and the corresponding number of identified PILFs; Qˆ0.01,r25s and Nr25s refer to the corresponding statistics

for the 25% limit.

 	 ˆ ˆ Q0.01,r25sQ0.01,r50s Site USGS ID Q0.01,r50s Nr50s Q0.01,r25s Nr25s Q0.01,r50s

17 03345500 49,700 34 54,100 1 0.09

23 05291000 16,000 29 12,800 20 -0.20

37 07138600 1,110 12 983 5 -0.12

41 08133500 26,800 23 34,900 0 0.30

45 08171000 113,000 27 110,000 19 -0.02

50 09241000 4,810 22 4,550 17 -0.05

56 10234500 1,110 45 1,360 0 0.22

58 11152000 30,800 46 32,100 18 0.04

59 11176000 2,440 19 3,860 1 0.58

61 11274500 13,600 29 14,500 19 0.06

63 11464500 21,600 15 25,400 5 0.18

65 12039500 50,400 47 56,500 0 0.12

73 13302500 18,000 42 18,500 16 0.03

Table 1 reports the impact of the 25-percent (25%) limit at the remaining 13 test sites. At these sites, limiting the number of PILFs to 25% of the sample will affect estimates of the 1-percent exceedance event, which

appears in the right-most column. The changes ranged from -20 percent to +58 percent with a median difference of +6 percent and average increase of +9 percent.

On average, use of the lower quartile (25 percent limit) resulted in a modest increase in the 100-year-flood

estimate. The question then becomes essentially subjective: Are the fitted frequency curves “better” with the

25-percent limit or the 50-percent limit? In the three cases where the absolute value of the change exceeded 20

percent, the 100-year flood increased by 22 percent, 30 percent, and 50 percent. If the MGBT has been censoring too heavily, we would expect to see no consistent increase or decrease from censoring less. To see an

average increase of 9 percent, with such consistently positive increases when large differences occur, suggests

that the 25-percent constraint leads to admitting small peaks that unduly affect the 1-percent exceedance flood

estimate.

Appendix 2 includes figures showing flood magnitude plotted against annual exceedance probability

(AEP) for these three cases. Visual examination of the plots suggests that the algorithm that was started

searching at the median resulted in reasonable decisions, as can be seen in the following three figures:

08133500 MGBT [50] identifies 23 PILFS while MGBT[25] identifies none. Note the sharp break in the data

just above the lower quartile that MGBT[50] catches and MGBT[25] would not (fig. 2–51).

11176000 Note a weak break in the data just above the lower quartile. Using the MGBT[50] identifies this

discontinuity and results in a fit that is much more consistent with the eight largest observations.

B17B/GB with one “low outlier” seems to overestimate the 1-percent exceedance flood when compared with the data (fig. 2–78).

10234500 Note kink visible just below the median that MGBT[50] identifies, with the result that the MGBT
Estimation 9

recommends censoring almost half the data. Given the shape of the data, that seems reasonable.

Which approach provided the best fit? With the more extreme censoring, less weight is placed on

the smallest observations and the B17B/MGB and EMA/MGB fits are much more consistent with

the seven largest observations in the sample. In short, the MGB as defined seems to achieve the goal

of matching the trend in the largest observations (fig. 2–56).

In 10 of 13 cases, the differences were small. In three cases, the differences were greater than 20 percent

and all were positive. In at least two of the three cases, better fits were obtained with the more aggressive

censoring, and it is arguable that this is the case in all three. Thus, MGBT[50] is arguably a good choice for

identifying PILFs.

Treatment of Floods Identified as Potentially Influential Low Floods: Conditional Probability

Adjustment and Expected Moments Algorithm

The logarithm of zero is minus infinity, so zero flows cannot be employed in a standard method-ofmoments fit using the logarithms of the flood magnitudes. As discussed here, the two estimation methods—

B17B and EMA—deal with zeros and PILFs in different ways.

To deal with such zeros and PILFs, B17B employs the conditional probability adjustment (CPA) developed by Jennings and Benson (1969). If the r smallest floods in a record of length n are identified as outliers

less than some threshold, qT , then the CPA fits a LP3 distribution to the retained pn  rq largest values. Then

for any large flood value, q ¡ qT , its nonexceedance probability is estimated as r{n plus p1  r{nq times

the probability it would not be exceeded given the distribution fit to the pn  rq retained observations. Then

for convenience and computation of confidence intervals, the 50, 90, and 99 percentiles of that “probabilityadjusted” distribution are computed and used to compute the three parameters of a “synthetic” LP3 distribution

that is used to represent flood risk at the site. This procedure is relatively robust, and has been shown to work

well with zeros and PILFs (Griffis and others, 2004).

The EMA uses ranges and thresholds to describe historical flood information, floods measured with limited precision, and PILFs. In particular, PILFs can be represented as being less than the smallest retained

observation when the LP3 distribution parameters are estimated. This allows the EMA to address a large range

of circumstances, while appropriately representing all of the available information. Censoring several of the

smallest observations in a sample results in almost no decrease of precision in flood quantile estimates with

the EMA or with the CPA (Griffis and others, 2004). However, the EMA can be much more sensitive than the

CPA to PILFs that are not afforded special treatment. Suppose a record had three PILFs, and we identified

two. Then using the CPA, the value of the smallest two observations are completely ignored, and the frequency

adjustment (CPA) corrects for omitting two observations in the curve fitting step. Thus, 66.7 percent of the

PILFs have been dropped, greatly reducing their impact. With the EMA, if there are three PILFs and two are

identified, the EMA represents the two smallest observations as being less than the third. This can make things

worse.

Consider, for example, the Sacramento River 1-day-flood record discussed in

Cohn and others (2013, fig. 3) (reproduced here as fig. 1), which has three small values that are each at

least a factor of two smaller than the other observations. The GBT identifies one PILF in this case; MGBT

correctly identifies all three, which can be seen immediately to be the most reasonable decision. Because

EMA in some sense takes the data seriously, one needs to identify all of the PILFs to reliably avoid potential

problems. Grubbs-Beck frequently fails to identify obvious PILFs, other than the smallest flow.

Given the well understood sensitivity of the EMA method to PILFs, no EMA/GB combination is considered in this report. The EMA does not perform reliably when paired with GB. As will be shown, the MGB

criterion identifies obvious outliers and PILFs in the lower half of troublesome datasets. As a result, as will be
10 Evaluation of Recommended Revisions to Bulletin 17B

–2 –1 0 1 2

Z−score

Discharge, in cubic feet per second

10,000

20,000

50,000

100,000

200,000

Figure 1. One-day peak floods from 1932 to 2008; discharge measured in cubic feet per second at Sacramento River at Shasta

Dam, California (Cohn and others, 2013, fig. 3). (Z-score, distance from the mean as measured by standard deviations).
Comparisons of Methods 11

shown here, both B17B and the EMA, when used with the MGB PILF identification procedure, are reliable

flood-quantile estimators in terms of their ability to avoid problems caused by unusually small peaks.

Estimation Methods Considered in this Publication

Bulletin 17B (IACWD, 1982) procedures include a GB outlier identification procedure, a weighted

moment computation if a historical record period is included with a perception threshold that was exceeded

at least once, use of CPA if a record contains zero flows, low outliers, or peaks below gage base, and, finally,

computation of a weighted skewness coefficient (Griffis and Stedinger, 2007, fig. 2); (IACWD, 1982, p. 12–2

through 12–3). All four of those steps, as needed, are components of the flood-frequency method denoted here

as B17B.

The proposal under consideration is to replace those procedures with the MGB test for identification of

PILFs (Cohn and others, 2013), and the EMA for the estimation of the parameters of an LP3 distribution

simultaneously considering zeros and PILFs as censored data, one or more periods with different perception

thresholds for historical floods, and a regional skewness coefficient with specified MSE (Cohn and others,

1997; Griffis and others, 2004). An advantage of the EMA approach is that all of the data is treated consistently in a single parameter estimation step, rather than as a sequence of procedures that first address historical

information, then zeros and PILFs, and finally, regional skew information (or the opposite ordering of PILFs

and historical adjustments when the skew coefficient is less than 0.4). Uncertainty analysis of the B17B

sequence of steps is more difficult than that of the unified EMA procedure, and the EMA is more efficient

because it allows simultaneous use of all of the data. For example, an informative regional skew should be

used to inform the interpretation of historical and interval information, rather than being introduced as a separate and independent final adjustment of just the skewness coefficient as recommended by B17B. The EMA

also allows for different thresholds to describe historical information from different periods, and the use of

interval estimates of flood peaks to represent measurement uncertainty, which is often appropriate when representing the magnitude of historical flood information.

The studies that follow consider three estimation combinations:

1. The EMA (Cohn and others, 1997), with a generalized MGBT (Cohn and others, 2013) for detecting multiple PILFs in a flood series (EMA/MGB);

2. B17B (IACWD, 1982), with the standard GB method for identifying low outliers followed by the CPA to

address zeros, low outliers, and peaks below gage base (B17B/GB); and

3. B17B, where the new MGBT was employed to identify multiple PILFs, followed by the CPA (IACWD,

1982) to address zeros, PILFs, and peaks below gage base (denoted by “B17B/MGB”).

Software

The USGS PEAKFQ version 7.0 program was used to create the comparisons between B17B and the

EMA estimates. PeakfqSA version 0.995, a development version of PEAKFQ written by Tim Cohn, was used

to check the EMA results generated in PEAKFQ 7.0.

The Monte Carlo and resampling results reported in section Comparisons of Methods are based on the

underlying code employed in PEAKFQ, with analysis routines prepared by Tim Cohn, and a front-end “driver”

routine developed by Jery Stedinger called “monte.f.”

Results based on the Bulletin 17B Guidelines are referred to as “B17B” or “PEAKFQ/B17B”. Results

based on the proposed EMA methods are denoted by “EMA” or “PeakfqSA”. Additional letters are appended,

yielding names of the form “B17B/GB,” “B17B/MGB,” and “EMA/MGB,” to specify explicitly which PILF

test procedure was used.
12 Evaluation of Recommended Revisions to Bulletin 17B

Comparisons of Methods

Hundreds of distinct Monte Carlo and resampling experiments were conducted, each involving 10, 000

replicate samples, in order to determine how well the B17B/GB, B17B/MGB, and EMA/MGB estimators satisfy the criteria listed in the section Metrics for Evaluating Flood-Frequency Estimators. These Monte Carlo

experiments are described in this section.

Understanding the Graphical Presentation of Results

In order to simplify the discussion, comparisons between estimators for cases with different historical

information are presented concisely using a single graphical format. Each figure considers the performance of

the estimators when data are drawn from a specific population. Figure 2, for example, corresponds to an LP3

distribution with a log-skew γ=0.0; later graphs consider estimator performance when data are drawn from

other populations.

Each graphic has two parts. The top panel contains 12 boxplots (Tukey, 1977), divided into four groups

of three, showing the distribution of three estimators for Q1%, the 1-percent exceedance event (that is, the

“100-year flood”). The central colored rectangle spans the 25th to 75th percentiles of the estimators’ distributions. The central line indicates the median. Additional information about the distribution of the estimations

is shown by the whiskers and hinges. The whisker length is 1.5 times the interquartile range. Observations

beyond the whiskers are plotted as individual circles. For those cases where the population mean is known, an

additional symbol is present on each box—a circle with a cross—indicating the location of the mean.

The three estimators are defined below and in IACWD (1982), Cohn and others (1997), Griffis and others

(2004), and Cohn and others (2013). Although flood quantiles other than the 1-percent exceedance were investigated, the results were found to be insensitive as to which quantile was considered. Because Q1% is the flood

of interest for many Federal activities, this case is reported.

Each of the four groups corresponds to NS=40 years of systematic data. The first group involves no historical information (ErHs=0). The other three have a historical period with NH=100 years, during which different perception thresholds are set so that, in expectation, 1, 2 or 10, historic floods would have been recorded.

The red-dashed line indicates the true value of Q1%, where it is known; in some later plots, where Q1% is estimated by interpolation between real observations, a purple line is used to indicate an estimate of Q1% because

the true value of Q1% is unknown.

The colored dots appearing in the lower panel in each graph indicate the effective record length (ERL) of

each estimator. ERL is defined in this case, where NS=40 and NH=100, as the ratio:

ERL  NS

#

MSErlogpQˆ

1%pNS  40, NH  0qqs

MSErlogpQˆ

1%pNS  40, NH  100qqs+

(1)

where NS is the length of the systematic record, NH is the length of the historical period, and

MSErlogpQˆ

1%pNS, NHqqs  pBiasrlogpQˆ1%pNS, NHqqsq2 

VarrlogpQˆ

1%pNS, NHqqs. (2)

ERL expresses, in a rough way, how well an estimator exploits historical information by expressing its effect

in terms of an equivalent number of years of exclusively systematic data. Note that the estimator variance,

denoted by “Var” in equation 2, is simply the variance of the 10,000 replicate estimates of Qˆ

1%. The bias,

however, is not always so easily defined. Where the flood distribution is known, the bias is defined in the conventional manner as the average difference between Qˆ

1% and the true mean. When dealing with real data (for
Comparisons of Methods 13

example, in section Examples Based on Real Data at Selected Test Sites), however, the true value Q1% is not

known. In these cases, for want of a better assumption, the bias is assumed to be zero for all estimators. Thus,

the ERL is computed using only the estimated variance.

The bottom left-most box contains three numbers in lavender. These are, respectively, the percentage of

observations identified as PILFs by the GB test with Bulletin 17B (B17B/GB), the MGB test with Bulletin

17B (B17B/MGB), and the MGB test with the EMA (EMA/MGB). The number of PILFs with B17B/MGB

and EMA/MGB are in fact always identical because the tests do not depend on the fitting procedure.

The triplets of black numbers in the three boxes to the right indicate the average gain (AG), in percent,

associated with each year of historical flood information, for B17B/GB, B17B/MGB, and EMA/MGB, respectively. The AG quantifies the relative value of an additional year of historical information to an additional year

of systematic gage record, and is defined as the following:

AG  100 

ERL  NS

NH




(3)

where AG is the percentage increase of ERL for each year in the historical period.

Where the expected number of historic floods is high (on the right side of the graph) the AG is typically

also high. Where no historic floods can be expected (the group on the left) the average gain is zero. Note that

the AG results are based on 10,000 replicate samples, and have a corresponding uncertainty of about 1 percent.

The three colored circles in the bottom box represent the ERL corresponding to each estimator and censoring

threshold.

Studies with LP3 Distribution

Figures 2 through 4 correspond to the case where we are fitting the LP3 distribution to LP3 data assuming

we have no regional information. In these cases, we expect good results for all the estimators because we are

applying the correct model for the population from which the data are drawn. The distribution of the Monte

Carlo population, depicted as a frequency plot and as a probability density function of the logarithm of Q,

appears below the main plot. Cases with regional skew information are addressed in Section Studies with LP3

Distribution and Regional Skew.

Figure 2 depicts the case when the population skew γ is zero and PILFs are rare. The figure shows that the

three estimators are identical when there is no historical information (the left-most three boxplots). If historical information is present with a perception threshold at approximately the 1-percent exceedance flood level

(Stedinger and Cohn, 1986), the EMA/MGB (AG=39) method performs substantially better than B17B/GB

(AG=27) or B17B/MGB (AG=29). The same conclusion applies when the threshold is at the 2-percent

exceedance level, where the average gains are 42, 44, and 53 for B17B/GB, B17B/MGB, and EMA/MGB,

respectively. When the threshold is at the 10-percent exceedance level, which corresponds to a rare situation,

all of the estimators perform extremely well, with average gains of 77, 80, and 72.

Figure 3 depicts the case when the population skew is γ=-0.5. In this case, many PILFs are to be expected.

Figure 3 reveals several interesting properties of the estimators. First, the center of the boxplots are substantially above the hashed line (the true 1-percent exceedance level), indicating that all of the estimators are

biased upward when only systematic data are employed. This phenomenon is actually well known (Kirby,

1974; Stedinger and others, 1993). The method-of-moments estimator for the skew coefficient is biased toward

zero and, thus, method-of-moments quantile estimators are biased upwards for populations with negative

skews and downwards for populations with positive skews (see fig. 4). When historical information is present,

the EMA/MGB method performs substantially better than B17B/GB or B17B/MGB.
14 Evaluation of Recommended Revisions to Bulletin 17B

Discharge, in cubic feet per second

10

0

40

80

120

100

1,000

10,000

100,000

B17B/GB

B17B/MGB

EMA/MGB

Q[0.01]

Expected number of historic floods (H)

27 29 39 42 44 53

77 80 72 0.11 0.96 0.96

None (H=0) 1 2 10

EXPLANATION

A

Effective record

length

Outlier

Outlier

25th percentile

75th percentile

50th percentile

(median)

Frequency distribution

LP3 distribution G = 0

Percent exceedance probability

99 90 50 10 1

0.001

0.1

1,000

B

10

Q, in cubic feet per second

Probability density function

LP3 distribution G = 0

Log (Q)

0

0.1

0.2

0.4

0.3

C

Density

–4 –2 0 2 4

Figure 2. Monte Carlo results based on 10,000 replicate samples using systematic record, NS=40, and historical record,

NH=100, drawn from a log-Pearson Type III (LP3) distribution with skew of 0.0. Terms within graph are defined as follows:

B17B/GB, Bulletin 17B/Grubbs-Beck; B17B/MGB, Bulletin 17B/multiple Grubbs-Beck; EMA/MGB, Expected Moments Algorithm/multiple Grubbs-Beck; G, skew; and Q[0.01], discharge for annual exceedance probability of 0.01.
Comparisons of Methods 15

Discharge, in cubic feet per second

10

0

40

80

120

100

1,000

0.32 2.8 2.8

None (H=0) 1 2 10

18 21

51

27 33

64 60

74

86

B17B/GB

B17B/MGB

EMA/MGB

Q[0.01]

Expected number of historic floods (H)

EXPLANATION

A

Frequency distribution

LP3 distribution G = –0.5

Probability density function

LP3 distribution G = –0.5

Percent exceedance probability Log (Q)

99 90 50 10 1

0.001

0

0.1

0.2

0.5

0.4

0.3

0.1

B C

10

Q, in cubic feet per second

Density

–6 –4 –2 0 2

Effective record

length

Outlier

Outlier

25th percentile

75th percentile

50th percentile

(median)

Figure 3. Monte Carlo results based on 10,000 replicate samples using systematic record, NS=40, and historical record,

NH=100, drawn from a log-Pearson Type III (LP3) distribution with skew of 0.5. Terms within graph are defined as follows:

B17B/GB, Bulletin 17B/Grubbs-Beck; B17B/MGB, Bulletin 17B/multiple Grubbs-Beck; EMA/MGB, Expected Moments Algorithm/multiple Grubbs-Beck; G, skew; and Q[0.01], discharge for annual exceedance probability of 0.01.
16 Evaluation of Recommended Revisions to Bulletin 17B

Figure 4 depicts the case when the population skew is γ=0.5 and no PILFs are to be expected. This case

reveals the opposite bias seen in figure 3. However, in this case, all of the estimators make good use of the

historical information because, for positively skewed populations, the smaller values in the dataset have little impact on the sample moments and, therefore, do not influence the results, regardless of which estimator

is employed. In figures 2 and 4 with H=10 expected floods, both B17B estimators do a little better than the

EMA, though visually the boxplots are indistinguishable. In all other cases, the EMA did essentially as well as

the B17B estimators.

Studies with LP3 Distribution and Regional Skew

Figures 2–83 through 2–85 show the same cases as figures 2 through 4, except that regional skew information has been added. Synthetic regional skews are modeled and generated as normal variate with a mean of

the observed skew and a variance of 0.15—a typical value consistent with Bayesian Generalized Least Squares

(GLS) skew maps (Lamontagne and others, 2012; Parrett and others, 2011; Gotvald and others, 2009). The

addition of regional skew information improves all of the estimators, including EMA/MGB and B17B/GB.

The impact is essentially the same for all of the estimators and most pronounced for the negative skew example.

In conclusion, while accurate regional skew is a valuable addition to frequency analyses, it does not need

to be considered as an important factor in determining the relative performance of the three estimators. For

the cases with historical information where one or two historical floods are expected, the EMA again provides more precise quantile estimators than the B17B estimators. For the case where 10 historical floods are

expected and γ=0.5, there is a virtual tie; when γ=0.5 and γ=0 (figs. 2–83 and 2–84), B17B/MGB does a little

better than EMA, while B17B/GB does slightly better only when γ=0 (fig. 2–83). However, it is noteworthy

that the value of historical information, when carefully employed with the EMA (see fig. 2), ranges from an

average gain of 39 percent when one historical flood is expected, to 72 percent when when ten historical floods

are expected.

Robustness Studies

To test their robustness to data with different distributions, the three estimators—B17B/GB, B17B/MGB,

and EMA/MGB—were applied to six test curves. These are referred to as “robustness test curves 1–6.” The

first two of these test curves are based on LP3 data with different skew values, and are similar to those discussed in section Studies with LP3 Distribution. Figures 2–86 and 2–87 in the appendix also depict these

two test curves. The remaining four test curves are used to test the performance of the three estimators—

B17B/GB, B17B/MGB, and EMA/MGB—when applied to non-LP3 data.

There are an infinite number of distribution “curves” that could be used to test robustness. While these

curves represent only a tiny portion of the non-LP3 universe, they were chosen because it is believed they

reflect at least some of the non-LP3 populations that have been observed in practice. For example, mixed populations may arise due to the existence of multiple peak-flow-generating processes in a watershed.

Robustness with Respect to Pearson Type 3 Population

Figure 5 depicts the performance of the estimators when data are drawn from a Pearson Type 3 (P3) population, not the LP3 (robustness test curve 3). As can be seen in the figure, the P3 has a substantially different shape than the LP3. All of the estimators are biased when fitting this population, as is expected because it

is not the assumed population. However, the EMA/MGB estimator does perform slightly better than the two
Comparisons of Methods 17

Discharge, in cubic feet per second

10

0

40

80

120

100

1,000

10,000

100,000

1,000,000

10,000,000

0.01 0.18 0.18

None (H=0) 1 2 10

33 34 36

50 50 49

81 80

67

B17B/GB

B17B/MGB

EMA/MGB

Q[0.01]

Expected number of historic floods (H)

EXPLANATION

A

Frequency distribution

LP3 distribution G = 0.5

Probability density function

LP3 distribution G = 0.5

Percent exceedance probability Log (Q)

99 90 50 10 1

0.01

0

0.1

0.2

0.5

0.4

0.3

1

B C

100

Q, in cubic feet per second

Density

–2 0 2 4 6

Effective record

length

Outlier

Outlier

25th percentile

75th percentile

50th percentile

(median)

Figure 4. Monte Carlo results based on 10,000 replicate samples using systematic record, NS=40, and historical record,

NH=100, drawn from a log-Pearson Type III (LP3) distribution with skew of 0.5. Terms within graph are defined as follows:

B17B/GB, Bulletin 17B/Grubbs-Beck; B17B/MGB, Bulletin 17B/multiple Grubbs-Beck; EMA/MGB, Expected Moments Algorithm/multiple Grubbs-Beck; G, skew; and Q[0.01], discharge for annual exceedance probability of 0.01.
18 Evaluation of Recommended Revisions to Bulletin 17B

other estimators when historical information is present. In the absence of historical information, differences

arise only due to outliers.

Robustness with Respect to Mixed Population Constructed from Two LP3 Distributions

Figure 6 depicts the performance of the estimators when data are drawn from robustness test curve 4, a

mixed population created by choosing the maximum of observations drawn from two different LP3 distributions, the first with parameters

tM, S2, Gu  t4.1212, 0.292, 1.00u

and the second with parameters

tM, S2, Gu  t4.0900, 0.132, 0.15u.

Without historical information, all three estimators are nearly identical. When historical information is present,

the estimators are no longer identical, with EMA/MGB performing slightly better.

Robustness with Respect to Population Constructed from Two LP3 Distributions

Figure 7 depicts the performance of the estimators when data are drawn from robustness test curve 5, a

constructed population based on two LP3 distributions, the first with parameters

tM, S2, Gu  t4.3438, 0.412

, 1.00u

and the second with parameters

tM, S2, Gu  t4.3936, 0.502, 0.20u.

The lower half of the distribution function employs the first parameters, and the upper half is based on the second parameters. The two parent distributions are spliced together at their shared median. Fitting data from

this population again tests the robustness of the estimators with a misspecified population, but this time when

PILFs are present. Without historical information, EMA/MGB and B17B/MGB are nearly identical, and both

perform better than B17B/GB. When historical information is present, EMA/MGB performs much better than

the other estimators.

Robustness with Respect to Population Constructed from Two Generalized Extreme Value

Distributions

Figure 8 depicts the performance of the estimators when data are drawn from robustness test curve 6, a

constructed population based on two Generalized Extreme Value (GEV) distributions, the first with location,

scale, and shape parameters

tκ, α, ξu  t0.08, 24326, 6378u

and the second with parameters

tκ, α, ξu  t0.55, 10000, 17330u.
Comparisons of Methods 19

Discharge, in cubic feet per second

0

40

80

120

100,000

0 0.19 0.19

None (H=0) 1 2 10

18 19

38 36 37 48

89 88 86

B17B/GB

B17B/MGB

EMA/MGB

Q[0.01]

Expected number of historic floods (H)

EXPLANATION

A

Frequency distribution

robustness test curve 3

Probability density function

robustness test curve 3

Percent exceedance probability Log (Q)

99 90 50 10 1

20,000

0

50,000

B C

100,000

Q, in cubic feet per second

Density

4.5 5.0 5.5

6

8

2

4

14

12

10

Effective record

length

Outlier

Outlier

25th percentile

75th percentile

50th percentile

(median)

Figure 5. Monte Carlo results based on 10,000 replicate samples using systematic record, NS=40, and historical record,

NH=100, drawn from robustness test curve 3. Terms within graph are defined as follows: B17B/GB, Bulletin 17B/Grubbs-Beck;

B17B/MGB, Bulletin 17B/multiple Grubbs-Beck; EMA/MGB, Expected Moments Algorithm/multiple Grubbs-Beck; G, skew; and

Q[0.01], discharge for annual exceedance probability of 0.01.
20 Evaluation of Recommended Revisions to Bulletin 17B

Discharge, in cubic feet per second

0

40

80

120

100,000

1,000,000

0 0 0

None (H=0) 1 2 10

34 34 36

47 47 53

71 72 68

B17B/GB

B17B/MGB

EMA/MGB

Q[0.01]

Expected number of historic floods (H)

EXPLANATION

A

Frequency distribution

robustness test curve 4

Probability density function

robustness test curve 4

Percent exceedance probability Log (Q)

99 90 50 10 1

20,000

10,000

0

0.5

1.0

2.5

2.0

50,000 1.5

B C

100,000

200,000

Q, in cubic feet per second

Density

4.0 4.5 5.0 5.5 5.5 5.5

Effective record

length

Outlier

Outlier

25th percentile

75th percentile

50th percentile

(median)

Figure 6. Monte Carlo results based on 10,000 replicate samples using systematic record, NS=40, and historical record,

NH=100, drawn from a mixed population based on robustness test curve 4. Terms within graph are defined as follows: B17B/GB,

Bulletin 17B/Grubbs-Beck; B17B/MGB, Bulletin 17B/multiple Grubbs-Beck; EMA/MGB, Expected Moments Algorithm/multiple

Grubbs-Beck; G, skew; and Q[0.01], discharge for annual exceedance probability of 0.01.
Comparisons of Methods 21

Discharge, in cubic feet per second

0

40

80

120

100,000

0.41 8.5 8.5

None (H=0) 1 2 10

7 12

77

12 19

83

27 37

92

B17B/GB

B17B/MGB

EMA/MGB

Q[0.01]

Expected number of historic floods (H)

EXPLANATION

● ●

●

● ●

●

● ●

●

A

Frequency distribution

Robustness test curve 5

Probability density function

Robustness test curve 5

Percent exceedance probability Log (Q)

99 90 50 10 1

5,000

1,000

0

0.2

0.4

1.0

0.8

0.6

20,000

B C

100,000

Q, in cubic feet per second

Density

1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0

Effective record

length

Outlier

Outlier

25th percentile

75th percentile

50th percentile

(median)

Figure 7. Monte Carlo results based on 10,000 replicate samples using systematic record, NS=40, and historical record,

NH=100, drawn from robustness test curve 5. Terms within graph are defined as follows: B17B/GB, Bulletin 17B/Grubbs-Beck;

B17B/MGB, Bulletin 17B/multiple Grubbs-Beck; EMA/MGB, Expected Moments Algorithm/multiple Grubbs-Beck; G, skew; and

Q[0.01], discharge for annual exceedance probability of 0.01.
22 Evaluation of Recommended Revisions to Bulletin 17B

The lower three quarters of the distribution function employs the second parameters, and the upper quarter is

based on the first parameters. The distributions have the same upper quartile, which is where they join. As was

seen in figure 7 and many other examples, when historical information is present, EMA/MGB performs much

better than the other estimators.

Examples Based on Real Data at Selected Test Sites

Eighty-two Example Test Sites

Eighty-two USGS streamflow-gaging (streamgages) stations (listed in appendix 1) were selected by a subset of the HFAWG named the “Data Group.” The types of data found at these sites are organized into four categories in this publication:

1. Systematic gage data, no historical data or PILFs (26 sites);

2. Historical data, possibly including high outliers (19 sites);

3. PILFs; no historical information (20 sites); and

4. PILFs, historical and (or) high outliers (17 sites).

These 82 sites include all of the sites used as examples in Bulletin 17B (B17B), which were also included in

this study. Clearly, 82 sites is a limited sample of the many thousands of streamgage records throughout the

Nation. However, the set is believed to cover the range of situations, and particularly the most difficult situations, that arise in practice.

The respective estimated frequency curves for the sites are presented graphically in appendix 2. Because

we do not know the true frequency curve, judgments about the various estimates are necessarily subjective;

graphs provide a convenient way to visualize the differences. The magnitude of observed differences, however,

can be summarized in terms of a statistic, the RPD, defined as

RP D  100 

QˆEMA{MGB

p  QˆB17B{p

QˆB17B{

p



(4)

where p corresponds to the quantile of interest and B17B{ refers to B17B{GB or B17B{MGB, respectively, depending on which estimators are being compared. Although the RP D does not tell us which estimator is better, it does quantify the magnitude of observed differences between the estimators.

Sites With Systematic Gage Data and No PILFs or Historical Information

The first category, “Gage Only” data, included 26 sites. The sites have systematic data with no historical information, no below-gage-base floods, and no PILFs identified by either using the GB or MGB tests.

Almost all RPDs were zero, as expected. In this case all of the estimators are, in theory, identical. Apparent differences between PEAKFQ/B17B and PeakfqSA results of less than 1 percent in RPD occur because

PEAKFQ/B17B rounds quantile estimates to between two and three significant digits; PeakfqSA does no

rounding. The estimated moments, which are not rounded, are identical in these cases. As can be seen in figure 9, however, there were two sites where, in fact, the RPD was not zero.

At site 02037500, James River near Richmond (fig. 2–5), the RPD ranged between 3 to 5 percent for the

three quantiles. This was because the 1937 peak discharge was recorded with a qualification code indicating

the discharge was greater than the reported 152,000 cubic feet per second (cfs) value. PEAKFQ/B17B, the

USGS software that implements Bulletin 17B, by default omitted the 1937 peak. A user-supplied point discharge value of 152,000 cfs was instead used to characterize the 1937 peak. This is a “known problem” with
Examples Based on Real Data at Selected Test Sites 23

Discharge, in cubic feet per second

0

40

80

120

100,000

0 0.27 0.27

None (H=0) 1 2 10

16 17

46

29 30

56

80 79

98

B17B/GB

B17B/MGB

EMA/MGB

Q[0.01]

Expected number of historic floods (H)

EXPLANATION

A

Frequency distribution

robustness test curve 6

Probability density function

robustness test curve 6

Percent exceedance probability Log (Q)

99 90 50 10 1

20,000

10,000

0

1.5

1.0

0.5

50,000

B C

100,000

Q, in cubic feet per second

Density

3.5 4.0 4.5 5.0

Effective record

length

Outlier

Outlier

25th percentile

75th percentile

50th percentile

(median)

Figure 8. Monte Carlo results based on 10,000 replicate samples using systematic record, NS=40, and historical record,

NH=100, drawn from robustness test curve 6. Terms within graph are defined as follows: B17B/GB, Bulletin 17B/Grubbs-Beck;

B17B/MGB, Bulletin 17B/multiple Grubbs-Beck; EMA/MGB, Expected Moments Algorithm/multiple Grubbs-Beck; G, skew; and

Q[0.01], discharge for annual exceedance probability of 0.01.
24 Evaluation of Recommended Revisions to Bulletin 17B

Annual exceedence probability, in percent

Q10% Q0.2% Q1%

EXPLANATION

Outlier

Outlier

25th percentile

75th percentile

50th percentile

(median)

5

0

–5

–10

–15

RPD = 100 *(Q

–20

p

^EMA/MGB – Qp^B17B/*) / (Qp^B17B/*)

Figure 9. Relative percent difference (RPD) for Bulletin 17B/Grubbs-Beck (B17B/GB) and Expected Moments Algorithm/multiple Grubbs-Beck (EMA/MGB) estimators for 10-percent (%), 1-%, and 0.2-% exceedance probabilities (Qp). Includes

26 sites without historical flood information where no potentially influential low floods were identified by either test.
Examples Based on Real Data at Selected Test Sites 25

B17B, but it bears repeating: PEAKFQ/B17B is not well adapted to incorporating nonstandard discharge values; in some cases, the way it handles them is to ignore them altogether. As a result, the PEAKFQ/B17B estimates, which reflect B17B methods, do not properly employ the data.

The EMA, the alternative method, does accommodate interval data. Thus, the 1937 peak could be correctly described as inside an interval from 152,000 cfs to infinity. This was used in the EMA analysis to capture the additional information associated with the 1937 peak. Because the EMA employs an interval range

greater than 152,000 cfs for the large 1937 peak, the EMA estimated higher values for the upper portion of the

frequency curve.

Site 05586500, Hurricane Creek near Roodhouse (fig. 2–8), had a similar problem. It showed a RPD

range from 4 to 20 percent. The sixth lowest recorded discharge had a qualification code indicating the

recorded value was less than 70 cfs. PEAKFQ/B17B employed a gage base at 70 cfs, consequently omitting

five additional recorded point discharge values below 70 cfs. No PILFs were identified by either the GB or

MGB test. Thus, PEAKFQ/B17B unnecessarily truncated a portion of the left hand tail due to the qualification code of one observation. A user-supplied interval discharge range from 0 to 70 cfs was properly set in

the EMA for that single water year, and the five recorded point discharges below 70 cfs were included in the

flood-frequency analysis. Because the EMA used all recorded discharges and the 0 to 70 cfs censored data,

the EMA’s estimates were lower particularly at the upper end of the curve. In both cases where the estimates

differed, it was because EMA can accommodate data properly that PEAKFQ/B17B cannot accommodate.

Sites with Historical Information

The testing for the “Historical Data” category included 19 sites, some of which included high outliers.

The historical data sites illustrate a fundamental difference between the EMA and B17B (Stedinger and Cohn,

1986; England and others, 2003).

The EMA estimates and, therefore, the RPDs, are sensitive to the historic threshold and historical period

employed. All attempts were made to manually enter the same values into both software programs. However,

some adjustments were made to accommodate PEAKFQ/B17B’s inability to use interval discharge ranges.

Many sites had one to three recorded historic peaks that exceeded the historic threshold. A few sites had

recorded gage heights at or near the record value with missing discharges. Interval discharge values were set

in the EMA to accommodate these observations. As PEAKFQ/B17B has no corresponding capability, point

discharge values were estimated by relating log-space discharge to log-space gage height for those years and

these were entered into PEAKFQ/B17B with the use of similar historic thresholds. Additionally, as a default,

PEAKFQ/B17B sets an historic threshold at the lowest recorded historic value for a user-specified historic

period. Thus, all missing years of information in the historic record are effectively set to the lowest historic

threshold. If a systematic record is missing any discharges (a broken systematic record) in a historical period,

the missing data is set to the same historic threshold. This is not the case if there is missing data in a purely

systematic record. PEAKFQ/B17B will operate under the assumption that no information is known about

those missing years of systematic record.

Overall, the majority of sites with historical information showed a positive RPD in the flood estimates

(fig. 10). The interquartile distances ranged from approximately 0 to 10 percent for Qˆ

1%. Three sites had

higher RPD for Qˆ

1%, ranging from 11 to 37 percent. The EMA and B17B provide substantially different estimates for these three sites, all of which include historical information and high outliers. Site 06216500, Pryor

Creek near Billings, Montana, had one large flood that was the largest in an extended historical period of 99

years. Figure 11 shows the frequency plots for both B17B and the EMA. Based on visual inspection of the frequency curves, the EMA seems to provide a better fit to the data, most clearly to the high outlier in the righthand tail.
26 Evaluation of Recommended Revisions to Bulletin 17B

EXPLANATION

Outlier

Outlier

25th percentile

75th percentile

50th percentile

(median)

70

60

50

40

30

20

10

0

RPD = 100 *(Qp^EMA/MGB – Qp^B17B/*) / (Qp^B17B/*)

Annual exceedence probability, in percent

Q10% Q0.2% Q1%

Figure 10. Relative percent difference (RPD) for Bulletin 17B/Grubbs-Beck (B17B/GB) and Expected Moments Algorithm/multiple Grubbs-Beck (EMA/MGB) estimators for 10-percent (%), 1-%, and 0.2-% exceedance probabilities (Qp). Figure

represents 19 sites with historical information where no potentially influential low floods were identified by either GB test.
Examples Based on Real Data at Selected Test Sites 27

10,000

100,000

100

1,000

Peak discharge, in cubic feet per second

99 98 95 90 80 70 50 30 20 10 5 2 1 0.5 0.2

Annual exceedance probability, in percent

Bulletin 17B/Grubbs-Beck

Expected Moments Algorithm/

multiple Grubbs-Beck

Systematic data

Historical data

EXPLANATION

Figure 11. Pryor Creek near Billings, Montana (06216500).
28 Evaluation of Recommended Revisions to Bulletin 17B

Sites with Systematic Gage Data and Potentially Influential Low Floods

The testing for the PILFs category utilized 20 sites with PILFs identified using either the standard GB test

recommended by B17B or the MGBT (Cohn and others, 2013). These sites did not include historic data. Two

sets of comparisons were made between the results of EMA/MGB as follows:

1. B17B using the GB test followed by the CPA (B17B/GB); and

2. B17B using the MGB PILF threshold followed by the CPA (B17B/MGB).

Current PEAKFQ/B17B software does not include a MGB test option, so, where needed, the MGB threshold

was computed independently and then entered into PEAKFQ as a user-supplied threshold.

The systematic flood series for site 08133500, North Concho River at Sterling City, Texas (fig. 2–51),

included three peaks with a qualification code indicating the discharge was less than the reported value of

300 cfs. As discussed in the systematic “Gage Only” section (Sites With Systematic Gage Data and No PILFs

or Historical Information), PEAKFQ/B17B arbitrarily set a gage base for the entire record, in this case omitting an additional 17 systematic point discharges less than 300 cfs that did not have remark codes. In the

EMA, the three peaks were recoded as between 0 and 300 cfs. However, the MGB test identified a PILF

threshold of 634 cfs. Thus, EMA/MGB identified 23 PILFs and B17B/GB (with a default-set gage base of

300 cfs) identified 20 PILFs. The result is that the estimated flood quantiles do not differ by very much.

Flood estimate comparisons between EMA/MGB and B17B/GB for figure 12 show the median RPD is

essentially zero. However, the RPD has substantial variability, indicating that the B17B/GB and EMA/MGB

estimators behave differently when PILFs are present. This increased variability in RPD is attributed to the

very different number of PILFs identified in the flood series and the methods used to handle PILFs in the frequency analysis (that is, the EMA’s PILF censoring versus B17B’s CPA). Of the 20 sites in this PILF category,

the GB test found only 0 to 2 low outliers per site above gage base, while the MGB test found 1 to 46 PILFs

(fig. 13). At some sites, the MGB identified nearly 50 percent of the recorded floods (fig. 14) as PILFs. This is

the upper bound on the percentage of peaks that MGB will test and designate as PILFs.

The observed RPDs were both positive and negative, a result of complex interactions between different

PILF tests and different fitting procedures. However, use of the EMA/MGB method seems to produce a better

fit to the upper portion of the frequency curve than is obtained with B17B/GB.

Orestimba Creek near Newman, California (site 11274500, fig. 15), which is also presented in B17B, represents an extreme case of PILFs—a flood series of 79 years, including 11 zero floods. The LP3 distribution

cannot describe the full range of observed flood flows at this site because the support for the LP3 distribution

vanishes for Q  ̈ 0 (Cohn and others, 2013). PEAKFQ/B17B treats all zero flows as below gage base, while

the EMA regards them as PILFs.

The Grubbs-Beck (GB) test yields a low-outlier threshold of 10.8 cfs and identification of a single additional low outlier. The MGB test, in contrast, yields a PILF threshold of 782 cfs, identifying 29 peaks, or

37 percent of the data, as PILFs. The RPD between EMA/MGB and B17B/GB ranges from 9 percent to

21 percent for the 1-percent and 0.2-percent exceedance probability estimates, respectively (fig. 15).

It is interesting to note that B17B/MGB, while close to EMA/MGB in this case, provides a different

and much poorer fit to the data, as can be seen in figure 15. The B17B/MGB curve lies above the data for

exceedance probabilities between 40 and 50 percent, and below the data for exceedance probabilities between

10 and 40 percent. Above the 10-percent level, the B17B/MGB curve rises more sharply than the EMA/MGB

curve, which appears to match the concave downward trend in the data.

The pattern seen at Orestimba is also observed at other sites with multiple PILFs. For example, at Santa

Cruz River near Lochiel, Arizona (09480000, fig. 16), one sees that EMA/MGB, by treating the influential

small peaks as PILFs, results in a reasonably close fit in the right-hand tail. On the other hand, the B17B/GB

estimator generates a frequency curve that is greatly exceeded by two of the sample values.
Examples Based on Real Data at Selected Test Sites 29

Bulletin 17B/Grubbs-Beck

Bulletin 17B/multiple Grubbs-Beck

EXPLANATION

Outlier

Outlier

25th percentile

75th percentile

50th percentile

(median)

RPD = 100 *(Qp^EMA/MGB – Qp^B17B/*) / (Qp^B17B/*)

Annual exceedence probability, in percent

Q10% Q0.2% Q1%

125

100

75

5 0

25

0

–25

–50

–75

Figure 12. Relative percent difference (RPD) for Bulletin 17B/Grubbs-Beck (B17B/GB), Bulletin 17B/multiple Grubbs Beck

(B17B/MGB), and Expected Moments Algorithm/multiple Grubbs-Beck (EMA/MGB) estimators for 10-percent (%), 1-%, and 0.2-

% exceedance probabilities (Qp). The figure represents 20 sites where potentially influential low floods were identified by GB or

MGB tests, and with no historical information.
30 Evaluation of Recommended Revisions to Bulletin 17B

EXPLANATION

Number of low outliers (MGB)

Number of low outliers and below

 gage base (pkfq and GB)

01668000

03345500

05572000

06176500

07203000

08133500

08150000

08189500

09241000

09480000

10234500

11028500

11152000

11274500

11383500

12307500

13302500

13343660

14321000

16068000

Sites in low outlier category

Number of low outliers in systematic record

50

40

30

20

10

0

Figure 13. Number of floods identified as potentially influential low floods or below gage base using the standard Grubbs-Beck

(GB) and multiple Grubbs-Beck (MGB) tests. Figure represents 20 sites without historical information.
Examples Based on Real Data at Selected Test Sites 31

Percent censored flood data (per site)

Number of sites

7

6

5

4

3

2

1

0

<10 10–20 20–30 30–40 40–50

Figure 14. Percent potentially influential low floods identified using the multiple Grubbs-Beck test. Figure represents 20 sites

without historical information.
32 Evaluation of Recommended Revisions to Bulletin 17B

10,000

100,000

100

10

1

1,000

Peak discharge, in cubic feet per second

99 98 95 90 80 70 50 30 20 10 5 2 1 0.5 0.2

Annual exceedance probability, in percent

Bulletin 17B/Grubbs-Beck

Expected Moments Algorithm/

multiple Grubbs-Beck

Bulletin 17B/multiple Grubbs-Beck

Systematic data 

Systematic data identified as

low outlier (MGB)

EXPLANATION

Figure 15. Orestimba Creek near Newman, California (11274500), fit after application of the multiple Grubbs-Beck (MGB) test to

identify potentially influential low floods.
Examples Based on Real Data at Selected Test Sites 33

10,000

100,000

1,000,000

100

10

1

0.1

1,000

Peak discharge, in cubic feet per second

99 98 95 90 80 70 50 30 20 10 5 2 1 0.5 0.2

Annual exceedance probability, in percent

Bulletin 17B/Grubbs-Beck

Expected Moments Algorithm/

multiple Grubbs-Beck

Bulletin 17B/multiple Grubbs-Beck

Systematic data 

Systematic data identified as

low outlier (MGB)

EXPLANATION

Figure 16. Santa Cruz River near Lochiel, Arizona (09480000).
34 Evaluation of Recommended Revisions to Bulletin 17B

Sites With Potentially Influential Low Floods, Historical Information, and (or) High Outliers

Seventeen of the 82 sites included the combination “PILFs, historical information and (or) high outlier.”

This category contains sites whose flood series have PILFs and also the following:

1. High outliers in a systematic record, or

2. High outliers in a historical period.

Nothing fundamentally new appeared in these cases. The RPD between EMA/MGB and B17B/GB are similar to those found in both the “PILF” and “Historical” categories. The median RPD for the Qˆ

10% estimates

remained near zero, while the median RPD were slightly positive for the Qˆ

1% and Qˆ0.2% estimates (fig. 17).

About one-third of the sites in this category showed a RPD greater than 15 percent for the 0.2-percent estimates and three sites were less than 18 percent. The largest RPD between EMA/MGB and B17B/GB was

found at site 11176000, Arroyo Mocho near Livermore, California. The RPDs for the estimates were between

48 and 68 percent, for the Qˆ

1% and Qˆ0.2% , respectively. EMA/MGB found 19 PILFs in the systematic

record (fig. 18) while B17B/GB found only one PILF above gage base. Additionally, one historic peak was

recorded in the flood series. By censoring multiple PILFs, EMA/MGB more accurately fit the right-hand tail.

A large positive RPD between EMA/MGB and B17B/GB was found at site 06062500, Tenmile Creek

near Rimini, Montana. A 10-percent and 19-percent RPD difference was found for the Qˆ

1% and the Qˆ0.2%

estimates, respectively. EMA/MGB found two PILFs, while B17B/GB found none (fig. 19). Here, the EMA

seems to provide a fit that is more consistent with the trends exhibited by the largest seven observations.

Figures 18 and 19 illustrate an important point—both B17B/GB and EMA/MGB often provide a good fit

to the data they employ. However, B17B/GB can be highly influenced by PILFs with the result being a poor

fit at the high end of the distribution. EMA/MGB, on the other hand, avoids this problem by identifying and

recoding PILFs so that their exact magnitudes do not distort the fit in the right-hand tail.

The RPD between EMA/MGB and B17B/MGB, when a flood series has both PILFs and high outlier data,

is similar to that found when only PILFs are present. The median value and interquartile range for the estimates in the “combination category” were slightly positive, while the median values and interquartile ranges

for the estimates in the “PILF” category were slightly negative. As expected, the variance in the RPD was minimized for all estimates when the same PILF threshold was used. The higher estimate from B17B/MGB is

illustrated by figure 18 (site 11176000, Arroyo Mocho near Livermore, California) where a 21-percent RPD

difference for the Qˆ

1% was found. The MGB PILF threshold of 106 cfs was used in B17B/MGB. The MGB

test identified almost 33 percent of the peaks as PILFs. Using the same MGB test, based on visual inspection,

EMA/MGB and B17B/MGB both show an improved fit versus B17B/GB.

Resampling Studies

Figures 20–24 depict results from applying the three estimators—B17B/GB, B17B/MGB, and

EMA/MGB—to resampled data from five of the longest-record (¡100 observations) sites among the 82

“test” sites considered in section Eighty-two Example Test Sites. In these cases, we do not know what the true

value of the 1-percent exceedance event is, so the figures instead employ an interpolated value based on the

two largest observations in the dataset. However, this is an unreliable estimator; as noted in the section Summary, many of the “test” sites were selected specifically because they contained high outliers. In reviewing

figures 20–24, it is likely best to use one’s judgment about the reasonableness of the results, possibly referring back to the test-site results, rather than trying to conjure up a strict quantitative assessment. However, it is

noteworthy that, when historical information is present, the EMA/MGB estimator generally outperforms the

other estimators in terms of ERL, with site 03011020 in figure 20 being an exception.
Examples Based on Real Data at Selected Test Sites 35

Bulletin 17B/Grubbs-Beck

Bulletin 17B/multiple Grubbs-Beck

EXPLANATION

Outlier

Outlier

25th percentile

75th percentile

50th percentile

(median)

RPD = 100 *(Qp^EMA/MGB – Qp^B17B/*) / (Qp^B17B/*)

Annual exceedence probability, in percent

Q10% Q0.2% Q1%

125

100

75

5 0

25

0

–25

–50

–75

Figure 17. Relative percent difference (RPD) for Bulletin 17B/Grubbs Beck (B17B/GB), Bulletin 17B/multiple Grubbs Beck

(B17B/MGB), and Expected Moments Algorithm/multiple Grubbs Beck (EMA/MGB) estimators for 10-percent (%), 1-%, and 0.2-

% exceedance probabilities (Qp). Represents 17 sites with historical flood information where potentially influential low floods

were identified by the GB or MGB test.
36 Evaluation of Recommended Revisions to Bulletin 17B

10,000

100,000

100

10

1

0.1

1,000

Peak discharge, in cubic feet per second

99 98 95 90 80 70 50 30 20 10 5 2 1 0.5 0.2

Annual exceedance probability, in percent

Bulletin 17B/Grubbs-Beck

Expected Moments Algorithm/

multiple Grubbs-Beck

Bulletin 17B/multiple Grubbs-Beck

Systematic data 

Systematic data identified as

low outlier (MGB)

Historical data

EXPLANATION

Figure 18. Arroyo Mocho near Livermore, California (11176000).
Examples Based on Real Data at Selected Test Sites 37

10,000

100

10

1,000

Peak discharge, in cubic feet per second

99 98 95 90 80 70 50 30 20 10 5 2 1 0.5 0.2

Annual exceedance probability, in percent

Bulletin 17B/Grubbs-Beck

Expected Moments Algorithm/

multiple Grubbs-Beck

Bulletin 17B/multiple Grubbs-Beck

Systematic data 

Systematic data identified as

low outlier (MGB)

EXPLANATION

Figure 19. Tenmile Creek near Rimini, Montana (06062500).
38 Evaluation of Recommended Revisions to Bulletin 17B

Discharge, in cubic feet per second

0

40

80

120

100,000

Expected number of historic floods (H)

0.3 1.1 1.1

None (H=0) 1 2 10

B17B/GB

B17B/MGB

EMA/MGB

Q[0.01]

EXPLANATION

58 60

42

65 66

46

75 69

57

Effective record

length

Outlier

Outlier

25th percentile

75th percentile

50th percentile

(median)

Figure 20. Results based on resampled data using systematic record, NS=40, and historical record, NH=100, drawn from

observed discharges at “Historical” category site 03011020. Terms within graph are defined as follows: B17B/GB, Bulletin

17B/Grubbs-Beck; B17B/MGB, Bulletin 17B/multiple Grubbs-Beck; EMA/MGB, Expected Moments Algorithm/multiple GrubbsBeck; G, skew; and Q[0.01], discharge for annual exceedance probability of 0.01.
Examples Based on Real Data at Selected Test Sites 39

Discharge, in cubic feet per second

0

50

100

150

100,000

Expected number of historic floods (H)

0.22 6.5 6.5

None (H=0) 1 2 10

11 14

106

11 14

106

28 32

98

B17B/GB

B17B/MGB

EMA/MGB

Q[0.01]

EXPLANATION

Effective record

length

Outlier

Outlier

25th percentile

75th percentile

50th percentile

(median)

Figure 21. Results based on resampled data using systematic record, NS=40, and historical record, NH=100, drawn from

observed discharges at “potentially influential low flood” category site 11152000. Terms within graph are defined as follows:

B17B/GB, Bulletin 17B/Grubbs-Beck; B17B/MGB, Bulletin 17B/multiple Grubbs-Beck; EMA/MGB, Expected Moments Algorithm/multiple Grubbs-Beck; G, skew; Q[0.01], discharge for annual exceedance probability of 0.01) .
40 Evaluation of Recommended Revisions to Bulletin 17B

Discharge, in cubic feet per second

0

40

80

120

Expected number of historic floods (H)

0.05 1.4 1.4

None (H=0) 1 2 10

31 34

55

38 42

64 64 65

92

B17B/GB

B17B/MGB

EMA/MGB

Q[0.01]

EXPLANATION

Effective record

length

Outlier

Outlier

25th percentile

75th percentile

50th percentile

(median)

Figure 22. Results based on resampled data using systematic record, NS=40, and historical record, NH=100, drawn from

observed discharges at “Gage Only” category site 14048000. Terms within graph are defined as follows: B17B/GB, Bulletin

17B/Grubbs-Beck; B17B/MGB, Bulletin 17B/multiple Grubbs-Beck; EMA/MGB, Expected Moments Algorithm/multiple GrubbsBeck; G, skew; and Q[0.01], discharge for annual exceedance probability of 0.01.
Examples Based on Real Data at Selected Test Sites 41

Discharge, in cubic feet per second

0

50

100

150

Expected number of historic floods (H)

Effective record

length

0.87 2.1 2.1

None (H=0) 1 2 10

17 23

56

23 31

65

51 60

109 0.87 2.1

B17B/GB

B17B/MGB

EMA/MGB

Q[0.01]

EXPLANATION

Outlier

Outlier

25th percentile

75th percentile

50th percentile

(median)

Figure 23. Results based on resampled data using systematic record, NS=40, and historical record, NH=100, drawn from

observed discharges at “potentially influential low flood” category site 14321000. Terms within graph are defined as follows:

B17B/GB, Bulletin 17B/Grubbs-Beck; B17B/MGB, Bulletin 17B/multiple Grubbs-Beck; EMA/MGB, Expected Moments Algorithm/multiple Grubbs-Beck; G, skew; and Q[0.01], discharge for annual exceedance probability of 0.01.
42 Evaluation of Recommended Revisions to Bulletin 17B

Discharge, in cubic feet per second

0

40

80

120

10,000

Expected number of historic floods (H)

Effective record

length

0.37 3.9 3.9

None (H=0) 1 2 10

44

57 60

78

98 92 82 89 77

B17B/GB

B17B/MGB

EMA/MGB

Q[0.01]

EXPLANATION

A

Outlier

25th percentile

75th percentile

50th percentile

(median)

Figure 24. Results based on resampled data using systematic record, NS=40, and historical record, NH=100, drawn from

observed discharges at “Combination” category site 13185000. Terms within graph are defined as follows: B17B/GB, Bulletin

17B/Grubbs-Beck; B17B/MGB, Bulletin 17B/multiple Grubbs-Beck; EMA/MGB, Expected Moments Algorithm/multiple GrubbsBeck; G, skew; and Q[0.01], discharge for annual exceedance probability of 0.01.
Conclusions 43

Summary

Eighty-two streamflow-gaging stations were chosen as a representative sample of long-term sites, where

flood series include a variety of situations and problems that are believed to be found throughout the United

States. The flood data were divided into four categories:

1. Systematic gage data, and no PILFs or historical information,

2. Historical and (or) high outliers,

3. PILFs, and

4. PILFs with historical and (or) high outliers.

The performances of EMA/MGB, B17B/GB, and B17B/MGB methods were compared visually for each of the

sites, and a RPD statistic was calculated corresponding to each of three exceedance probabilities to compare

the EMA and B17B estimates.

When only systematic flood data were present, identical flood estimates (RPD equal to zero) were

obtained, except for those cases where B17B cannot accommodate nonstandard data correctly. When historical and (or) high outliers were present, observed RPDs were positive more than half of the time. This is at

least in part due to the 82 sites that were selected for testing, many of which included historical “high outliers.”

The EMA tends to attach more “weight” to historical flood information than does B17B (Stedinger and Cohn,

1987), so where the historical period includes an unusually high peak, the EMA/MGB estimate will tend to be

higher than the B17B/GB estimate.

Flood series that contain multiple PILFs exhibited a range of results, primarily due to the very different

number of PILFs identified by the GB and MGB tests and the methods used to handle PILFs in the frequency

analysis (that is, EMA’s censoring versus B17B’s CPA). When the same PILF threshold was used for the EMA

and B17B’s CPA fitting procedure, the RPDs were usually smaller and negative. For those sites with PILFs

and historical and (or) high-outlier data, similar RPDs were found to those in the historical and PILF categories. This combination group included both PILFs and high outliers. The RPDs were notably more positive

for these estimates. EMA/MGB generally identified more PILFs when PILFs were present. In these cases,

based on subjective assessment, EMA/MGB always provided a closer fit to the largest peaks in the dataset.

Additional studies were conducted that involved resampling data from sites with the longest records.

Although the true value of the 1-percent exceedance event is not known for these sites, the resampling experiments confirmed that the EMA/MGB estimator performed reasonably well in all cases and generally provided

higher average gains than the alternative estimators.

Conclusions

The study reported here was designed to determine how well proposed changes to Bulletin 17B (B17B)

would perform in practice compared to the current recommendations in Bulletin 17B. In particular, the investigations focused on techniques for the following:


 incorporating information related to historical flooding that occurred outside the period of systematic

streamgaging, and


 addressing the identification and treatment of PILFs.
44 Evaluation of Recommended Revisions to Bulletin 17B

In order to answer these questions, Monte Carlo studies were conducted by resampling from real records,

or by drawing random samples from specified LP3 and non-LP3 distributions. In addition, problematic

datasets from across the country were selected to serve as test cases for comparing the estimators. To summarize, results are presented for the following:


 Monte Carlo simulations employing data drawn from specific LP3 populations;


 Monte Carlo simulations employing data drawn from non-LP3 populations that were selected to reflect

likely deviations, based on the experience of the Data Group, from the hypothesized LP3 distribution;


 a direct subjective comparison of results at 82 real “test sites” identified by an independent Data Group as

both “typical” and “challenging” for flood-frequency estimation; and


 resampling with replacement of the data at the 82 sites.

It is believed that, taken together, these studies provide a reasonably comprehensive, valid, and robust assessment of the properties of the Bulletin 17B procedures and proposed extensions and improvements. The results

demonstrate that the proposed alternative method, denoted by “EMA/MGB,” is as follows:


 generally performs at least as well as, and in some cases much better than, Bulletin 17B procedures, in

terms of the mean square error of flood quantile estimates; and


 allows for incorporation of more general types of flood-frequency information, thereby avoiding some

annoying problems that arise when applying Bulletin 17B in practice with datasets containing nonstandard flood data (exceedances of thresholds, and “less-than” values).

In summary, the results here generally confirmed other studies published in the hydrological literature that

have found that the EMA generally provides improved flood-frequency estimates.

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2096.
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Dawdy, D.R., Griffis, V.W., and Gupta, V.K., 2012, Regional flood-frequency analysis: How we got here and

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Stedinger, J.R., and Cohn, T.A., 1986, Flood frequency analysis with historical and paleoflood information:

Water Resources Research, v. 22, no. 5, p. 785–793.

Stedinger, J.R., and Cohn, T.A., 1987, Historical flood-frequency data: Its value and use, in Singh, V.P., ed.,

Regional flood frequency analysis: D. Reidel Publishing Company, p. 273–286.

Stedinger, J.R., Vogel, R.M., and Foufoula-Georgiou, Efi, 1993, Frequency analysis of extreme events, in

Maidment, D.R., ed., Handbook of hydrology: McGraw Hill, Inc., p. 18.1–18.66.

Tasker, G.D., and Thomas, W.O., 1978, Flood frequency analysis with pre-record information: ASCE Journal

of the Hydraulics Division (HY2), v. 104, no. 2, p. 249–259.

Thomas, W.O., 1985, A uniform technique for flood frequency analysis: Journal of Water Resources Planning

and Management, v. 111, no. 3, p. 321–337.

Tukey, J.W., 1977, Exploratory data analysis: Reading, MA, Addison-Wesley, 712 p.

U.S. Water Resources Council, 1967, A uniform technique for determining flood flow frequencies, Bulletin

No. 15: U.S. Water Resources Council, Subcommittee on Hydrology, Washington, D.C.

U.S. Water Resources Council, 1976, Guidelines for determining flood flow frequency, Bulletin No. 17: U.S.

Water Resources Council, Subcommittee on Hydrology, Washington, D.C.

U.S. Water Resources Council, 1977, Guidelines for determining flood flow frequency, Bulletin No. 17A: U.S.

Water Resources Council, Subcommittee on Hydrology, Washington, D.C.

Veilleux, A.G., and Stedinger, J.R., 2010, Bayesian GLS analysis of california regional skew, in World Environmental and Water Resources Congress 2010: Challenges of Change, ASCE, p. 2422–2431.

Veilleux, A.G., Stedinger, J.R., and Eash, D.A., 2012, Bayesian WLS/GLS regression for regional skewness

analysis for regions with large crest stage gage networks, in World Environmental and Water Resources

Congress 2012: Crossing Boundaries, ASCE, p. 2253–2263.
Appendix 1. Characteristics of 82 Test Sites 47

Appendix 1. Characteristics of 82 Test Sites
48 Evaluation of Recommended Revisions to Bulletin 17B Table 1–1. Characteristics of at-site streamflow records used in comparing Bulletin 17B and Expected Moments Algorithm estimators. DA drainage area in square miles;

NP k number of peaks;NS number of systematic peaks;N0 number of zero peaks;NH length of historical period;NZ number of historic peaks;

Qgd gage base discharge, cubic feet per second (cfs);N

 gd number of point discharge values below gage base;

QGB Grubbs-Beck critical value (cfs)–low-outlier criterion;NGB number of low outliers identified using Grubbs-Beck test;NMGB number of potentially influential low floods identified using multiple

Grubbs-Beck test.

.

Site USGS ID Station Name DA

NP k

NS N0 NH

NZ

Qgd

N gd

QGB

NGB

NMGB

1 01076500 Pemigewasset River at

Plymouth, NH

622 106 106 0 106 0 0 0 6,316.7 0 0

2 01350000 Schoharie Creek at Prattsville,

NY

237 100 99 0 106 1 0 0 2,064 0 0

3 01439500 Bush Kill at Shoemakers, PA 117 102 102 0 102 0 0 0 427.5 0 04 01555500 East Mahantango Creek near

Dalmatia, PA

162 81 81 0 81 0 0 0 784.9 0 0

5 01562000 Raystown Branch Juniata River

at Saxton, PA

756 99 98 0 122 1 0 0 2,977 0 0

6 01635500 Passage Creek near Buckton,

VA

86.5 78 78 0 78 0 0 0 267.5 0 0

7 01636500 Shenandoah River at Millville,

WV

3,041 97 95 0 141 2 0 0 4,178.7 0 0

8 01668000 Rappahannock River near

Fredericksburg, VA

1,595 100 100 0 103 0 0 0 5,209.8 1 2

9 02037500 James River near Richmond,

VA

6,753 76 76 0 76 0 0 0 14,965.1 0 0

10 02138500 Linville River near Nebo, NC 66.7 89 88 0 95 1 0 0 461.7 0 011 02256500 Fisheating Creek at Palmdale,

FL

311 79 79 0 79 0 0 0 227.9 0 0
Appendix 1. Characteristics of 82 Test Sites 49

Table 1–1. Characteristics of at-site streamflow records used in comparing Bulletin 17B and Expected Moments Algorithm estimators.—Continued

Site USGS ID Station Name DA NP k NS N0 NH NZ Qgd N gd QGB NGB NMGB12 03011020 Allegheny River at Salamanca,

NY

1,608 107 107 0 146 0 0 0 8,502.9 0 0

13 03051000 Tygart Valley River at

Belington, WV

406 104 103 0 123 1 0 0 3,992.9 0 0

14 03159500 Hocking River at Athens, OH 943 78 77 0 137 1 0 0 3,655.4 0 015 03183500 Greenbrier River at Alderson,

WV

1,364 115 115 0 115 0 0 0 10,190.8 0 0

16 03289500 Elkhorn Creek near Frankfort,

KY

473 72 70 0 94 2 0 0 3,050.9 1 6

17 03345500 Embarras River at Ste. Marie,

IL

1,516 99 99 0 101 0 0 0 1,698.2 1 34

18 03550000 Valley River at Tomotla, NC 104 101 100 0 113 1 0 0 862.1 0 019 03558000 Toccoa River near Dial, GA 177 85 84 0 157 1 0 0 1,022.6 0 020 03606500 Big Sandy River at Bruceton,

TN

205 70 67 0 114 3 0 0 704.3 0 0

21 04293500 Missisquoi River near East

Berkshire, VT

479 92 91 0 180 1 0 0 4,328.8 0 0

22 05270500 Sauk River near St. Cloud, MN 1,030 75 75 0 101 0 0 0 152.1 1 123 05291000 Whetstone River near Big Stone

City, SD

398 83 83 0 101 0 0 0 23.4 0 29

24 05464500 Cedar River at Cedar Rapids,

IA

6,510 109 108 0 311 1 0 0 3,187.3 0 5

25 05572000 Sangamon River at Monticello,

IL

550 101 101 0 103 0 0 0 755.6 1 1

26 05586500 Hurricane Creek near

Roodhouse, IL

2.3 45 44 0 45 1 70 6 38 0 0

27 06062500 Tenmile Creek near Rimini, MT 30.9 94 94 0 103 0 0 0 28.1 0 228 06176500 Wolf Creek near Wolf Point,

MT

251 37 37 0 84 0 0 0 0.5 0 7

29 06216500 Pryor Creek near Billings, MT 440 49 48 0 99 1 0 0 101.6 0 030 06406000 Battle Cr at Hermosa, SD 178 61 61 0 61 0 0 0 1.8 0 031 06600500 Floyd River at James, IA 886 76 76 0 119 0 0 0 282.2 0 0
50 Evaluation of Recommended Revisions to Bulletin 17B Table 1–1. Characteristics of at-site streamflow records used in comparing Bulletin 17B and Expected Moments Algorithm estimators.—Continued Site USGS ID Station Name DA

NP k

NS N0 NH

NZ

Qgd

N gd

QGB

NGB

NMGB

32 06710500 Bear Creek at Morrison, CO 164 98 98 0 120 0 0 0 19.3 0 033 06897000 East Fork Big Creek near

Bethany, MO

95 53 52 0 77 1 0 0 376.2 1 6

34 06898000 Thompson River at Davis City,

IA

701 80 79 0 126 1 0 0 1,171.9 0 0

35 06933500 Gasconade River at Jerome,

MO

2,840 92 88 0 114 4 4,320 1 4369.7 0 18

36 07067000 Current River at Van Buren,

MO

1667 99 98 0 107 1 0 0 2,536.9 0 0

37 07138600 White Woman C Tr near

Selkirk, KS

38 39 39 4 54 0 0 0 2.5 0 12

38 07203000 Vermejo River near Dawson,

NM

301 76 76 0 81 0 0 0 59.7 1 6

39 07208500 Rayado Creek near Cimarron,

NM

65 86 86 0 96 0 0 0 7 0 0

40 07382000 Bayou Cocodrie near

Clearwater, LA

240 72 72 0 88 0 0 0 272.6 0 0

41 08133500 N Concho Rv at Sterling City,

TX

588 65 65 0 68 0 300 20 130.7 0 23

42 08150000 Llano Rv near Junction, TX 1,854 91 91 0 95 0 0 0 34.4 0 1643 08164000 Lavaca Rv near Edna, TX 817 73 72 0 75 1 0 0 734.7 1 144 08167000 Guadalupe Rv at Comfort, TX 839 76 72 0 163 4 0 0 104.9 0 045 08171000 Blanco Rv at Wimberley, TX 355 87 86 0 142 1 0 0 57.6 1 2746 08189500 Mission Rv at Refugio, TX 690 71 71 0 71 0 0 0 65.9 1 1247 08378500 Pecos River near Pecos, NM 189 87 85 0 90 2 0 0 70.3 0 048 08380500 Gallinas Creek near

Montezuma, NM

84 93 93 0 95 0 0 0 16.2 0 0

49 08387000 Rio Ruidoso at Hollywood, NM 56 120 56 57 0 0 0 0 19.1 0 050 09241000 Elk River at Clark, CO 216 78 78 0 93 0 0 0 1,025.5 0 2251 09361500 Animas River at Durango, CO 692 102 102 0 113 0 0 0 1,374.4 1 252 09471000 San Pedro River at Charleston,

AZ

1,234 95 95 0 105 0 0 0 490.9 1 3
Appendix 1. Characteristics of 82 Test Sites 51

Table 1–1. Characteristics of at-site streamflow records used in comparing Bulletin 17B and Expected Moments Algorithm estimators.—Continued

Site USGS ID Station Name DA NP k NS N0 NH NZ Qgd N gd QGB NGB NMGB53 09480000 Santa Cruz River near Lochiel,

AZ

82.2 62 62 0 62 0 0 0 10.1 2 8

54 09482500 Santa Cruz River at Tucson, AZ 2,222 94 93 0 119 1 0 0 559.6 0 055 10128500 Weber River near Oakley, UT 162 105 105 0 106 0 0 0 579.8 0 056 10234500 Beaver River near Beaver, UT 91 97 97 0 97 0 0 0 40.4 0 4557 11028500 Santa Maria C near Ramona,

CA

57.6 71 71 11 97 0 0 0 0 1 13

58 11152000 Arroyo Seco near Soledad, CA 244 105 105 0 105 0 0 0 447.9 0 4659 11176000 Arroyo Mocho near Livermore,

CA

38.2 57 56 1 89 1 0 0 2.4 1 19

60 11266500 Merced R at Pohono Bridge

near Yosemite, CA

321 94 94 0 94 0 0 0 819.6 0 0

61 11274500 Orestimba C near Newman, CA 134 79 79 11 79 0 0 0 10.8 1 2962 11383500 Deer C near Vina, CA 208 94 94 0 99 0 0 0 521.4 1 163 11464500 Dry C near Cloverdale, CA 87.8 40 39 0 43 1 0 0 693.5 1 1564 11522500 Salmon R A Somes Bar, CA 751 86 86 0 99 0 0 0 1,923.5 1 165 12039500 Quinault River at Quinault

Lake, WA

264 97 96 0 101 1 0 0 9,162.2 0 47

66 12134500 Skykomish River near Gold

Bar, WA

535 82 82 0 82 0 0 0 2,227.9 1 0

67 12307500 Moyie River at Eileen, ID 755 53 53 0 53 0 0 0 6,220.4 0 1268 12413000 N Fork Coeur D’Alene River at

Enaville, ID

895 74 71 0 99 3 0 0 3,271.3 0 0

69 12414500 St Joe River at Calder, ID 1,030 92 92 0 100 0 0 0 4,310.5 0 070 12437950 East Fork Foster Creek

Tributary near Bridgeport, WA

4.75 21 21 0 21 0 0 0 0.8 0 0

71 12451000 Stehekin River at Stehekin, WA 321 89 89 0 100 0 0 0 3,396.8 0 072 13185000 Boise River near Twin Springs,

ID

830 102 100 0 140 2 0 0 1,840.6 1 25

73 13302500 Salmon River at Salmon, ID 3,760 96 96 0 99 0 0 0 2,039.2 0 4274 13343660 Smith Gulch Tributary near

Pataha, WA

1.85 20 20 0 20 0 0 0 0.7 1 3
52 Evaluation of Recommended Revisions to Bulletin 17B Table 1–1. Characteristics of at-site streamflow records used in comparing Bulletin 17B and Expected Moments Algorithm estimators.—Continued Site USGS ID Station Name DA

NP k

NS N0 NH

NZ

Qgd

N gd

QGB

NGB

NMGB

75 14021000 Umatilla River at Pendleton,

OR

637 57 57 0 86 0 0 0 1,066.7 0 0

76 14048000 John Day River at Mcdonald

Ferry, OR

7,580 105 105 0 117 0 0 0 2,549.2 0 0

77 14137000 Sandy River near Marmot, OR 263 99 99 0 99 0 0 0 2,894.4 0 078 14321000 Umpqua River near Elkton, OR 3,683 104 104 0 105 0 0 0 18,022.5 2 979 15072000 Fish C near Ketchikan, AK 32.1 91 91 0 95 0 0 0 1,352.2 0 080 16068000 E Branch of N Fork Wailua

River near Lihue, Kauai, HI

6.27 95 95 0 95 0 0 0 418.8 0 5

81 16518000 West Wailuaiki Stream near

Keanae, Maui, HI

3.66 90 90 0 96 0 0 0 926.2 0 0

82 16587000 Honopou Stream near Huelo,

Maui, HI

0.64 98 98 0 100 0 0 0 36.7 0 0
Appendix 2. Graphical Comparisons Between the EMA and B17B at 82 Test Sites 53

Appendix 2. Graphical Comparisons Between the EMA

and B17B at 82 Test Sites
54 Evaluation of Recommended Revisions to Bulletin 17B

Systematic Data Sites

NS= number of systematic peaks

NH= length of the historical period

NZ= number of historic peaks

NGB= number of low outliers identified using Grubbs-Beck test

NMGB= number of potentially influential low floods

1,000

10,000

100,000

1,000,000

Peak discharge, in cubic feet per second

99 98 95 90 80 70 50

Annual exceedance probabilty, in percent

30 20 10 5 2 1 0.5 0.2

EXPLANATION

Pemigewassett River at Plymouth, NH (station 01076500)

Bulletin 17B/Grubbs-Beck

Expected Moments Algorithm/

multiple Grubbs-Beck

Systematic data

Figure 2–1. Site 01076500–Pemigewasset River at Plymouth, New Hampshire (NH) with systematic data only.
Appendix 2. Graphical Comparisons Between the EMA and B17B at 82 Test Sites 55

100

1,000

10,000

100,000

Peak discharge, in cubic feet per second

99 98 95 90 80 70 50

Annual exceedance probabilty, in percent

30 20 10 5 2 1 0.5 0.2

EXPLANATION

Bush Kill at Shoemakers, PA (station 01439500)

Bulletin 17B/Grubbs-Beck

Expected Moments Algorithm/

multiple Grubbs-Beck

Systematic data

Figure 2–2. Site 01439500–Bush Kill at Shoemakers, Pennsylvania (PA) with systematic data only.
56 Evaluation of Recommended Revisions to Bulletin 17B

100

1,000

10,000

100,000

Peak discharge, in cubic feet per second

99 98 95 90 80 70 50

Annual exceedance probabilty, in percent

East Mahantango Creek near Dalmatia, PA (station 01555500)

30 20 10 5 2 1 0.5 0.2

EXPLANATION

Bulletin 17B/Grubbs-Beck

Expected Moments Algorithm/

multiple Grubbs-Beck

Systematic data

Figure 2–3. Site 01555500–East Mahantango Creek near Dalmatia, Pennsylvania (PA) with systematic data only.
Appendix 2. Graphical Comparisons Between the EMA and B17B at 82 Test Sites 57

100

1,000

10,000

100,000

Peak discharge, in cubic feet per second

99 98 95 90 80 70 50

Annual exceedance probabilty, in percent

Passage Creek near Buckton, VA (station 01635500)

30 20 10 5 2 1 0.5 0.2

EXPLANATION

Bulletin 17B/Grubbs-Beck

Expected Moments Algorithm/

multiple Grubbs-Beck

Systematic data

Figure 2–4. Site 01635500–Passage Creek near Buckton, Virginia (VA) with systematic data only.
58 Evaluation of Recommended Revisions to Bulletin 17B

1,000,000

10,000

100,000

Peak discharge, in cubic feet per second

99 98 95 90 80 70 50

Annual exceedance probabilty, in percent

James River near Richmond, VA (station 02037500)

30 20 10 5 2 1 0.5 0.2

1

Peak flow record indicates 1937 peak greater than 152,000 cubic feet

per second. Interval discharge range set in Expected Moments

Algorithm (EMA) from 152,000 cubic feet per second to infinity for

1937 peak, while a point discharge value of 152,000 cubic feet per

second was used in the Bulletin 17B analysis.

EXPLANATION

Bulletin 17B/Grubbs-Beck

Expected Moments Algorithm/

multiple Grubbs-Beck

Systematic data

Figure 2–5. Site 02037500–James River near Richmond, Virginia (VA) with systematic data only.
Appendix 2. Graphical Comparisons Between the EMA and B17B at 82 Test Sites 59

100,000

100

10,000

1,000

Peak discharge, in cubic feet per second

99 98 95 90 80 70 50

Annual exceedance probabilty, in percent

Fisheating Creek at Palmdale, FL (station 02256500)

30 20 10 5 2 1 0.5 0.2

EXPLANATION

Bulletin 17B/Grubbs-Beck

Expected Moments Algorithm/

multiple Grubbs-Beck

Systematic data

Figure 2–6. Site 02256500–Fisheating Creek at Palmdale, Florida (FL) with systematic data only.
60 Evaluation of Recommended Revisions to Bulletin 17B

100,000

10,000

1,000,000

Peak discharge, in cubic feet per second

99 98 95 90 80 70 50

Annual exceedance probabilty, in percent

Greenbrier River at Alderson, WV (station 03183500)

30 20 10 5 2 1 0.5 0.2

EXPLANATION

Bulletin 17B/Grubbs-Beck

Expected Moments Algorithm/

multiple Grubbs-Beck

Systematic data

Figure 2–7. Site 03183500–Greenbrier River at Alderson, West Virginia (WV) with systematic data only.
Appendix 2. Graphical Comparisons Between the EMA and B17B at 82 Test Sites 61

1,000

100

10

10,000

Peak discharge, in cubic feet per second

99 98 95 90 80 70 50

Annual exceedance probabilty, in percent

Hurricane Creek near Roodhouse, IL (station 05586500)

30 20 10 5 2 1 0.5 0.2

1

Peak flow record indicates one year with a below gage-base flow.

Interval discharge range set in Expected Moments Algorithm from

0 to 70 cubic feet per second for year with below gage-base flow.

Six systematic peaks were dropped in Bulletin 17B analysis because

flows below gage-base were omitted.

EXPLANATION

Bulletin 17B/Grubbs-Beck

Expected Moments Algorithm/

multiple Grubbs-Beck

Systematic data

Figure 2–8. Site 05586500–Hurricane Creek near Roodhouse, Illinois (IL) with systematic data only.
62 Evaluation of Recommended Revisions to Bulletin 17B

1,000

100

10

0

10,000

100,000

Peak discharge, in cubic feet per second

99 98 95 90 80 70 50

Annual exceedance probabilty, in percent

Battle Creek at Hermosa, SD (station 06406000)

30 20 10 5 2 1 0.5 0.2

EXPLANATION

Bulletin 17B/Grubbs-Beck

Expected Moments Algorithm/

multiple Grubbs-Beck

Systematic data

Figure 2–9. Site 06406000–Battle Creek at Hermosa, South Dakota (SD) with systematic data only.
Appendix 2. Graphical Comparisons Between the EMA and B17B at 82 Test Sites 63

1,000

100

10

10,000

100,000

Peak discharge, in cubic feet per second

99 98 95 90 80 70 50

Annual exceedance probabilty, in percent

Bear Creek at Morrison, CO (station 06710500)

30 20 10 5 2 1 0.5 0.2

EXPLANATION

Bulletin 17B/Grubbs-Beck

Expected Moments Algorithm/

multiple Grubbs-Beck

Systematic data

Figure 2–10. Site 06710500–Bear Creek at Morrison, Colorado (CO) with systematic data only.
64 Evaluation of Recommended Revisions to Bulletin 17B

1,000

100

10

1

10,000

100,000

Peak discharge, in cubic feet per second

99 98 95 90 80 70 50

Annual exceedance probabilty, in percent

Rayado Creek near Cimarron, NM (station 07208500)

30 20 10 5 2 1 0.5 0.2

EXPLANATION

Bulletin 17B/Grubbs-Beck

Expected Moments Algorithm/

multiple Grubbs-Beck

Systematic data

Figure 2–11. Site 07208500–Rayado Creek near Cimarron, New Mexico (NM) with systematic data only.
Appendix 2. Graphical Comparisons Between the EMA and B17B at 82 Test Sites 65

1,000

100

10,000

100,000

Peak discharge, in cubic feet per second

99 98 95 90 80 70 50

Annual exceedance probabilty, in percent

Bayou Cocodrie near Clearwater, LA (station 07382000)

30 20 10 5 2 1 0.5 0.2

EXPLANATION

Bulletin 17B/Grubbs-Beck

Expected Moments Algorithm/

multiple Grubbs-Beck

Systematic data

Figure 2–12. Site 07382000–Bayou Cocodrie near Clearwater, Louisiana (LA) with systematic data only.
66 Evaluation of Recommended Revisions to Bulletin 17B

1,000

100

10

10,000

100,000

Peak discharge, in cubic feet per second

99 98 95 90 80 70 50

Annual exceedance probabilty, in percent

Gallinas Creek near Montezuma, NM (station 08380500)

30 20 10 5 2 1 0.5 0.2

EXPLANATION

Bulletin 17B/Grubbs-Beck

Expected Moments Algorithm/

multiple Grubbs-Beck

Systematic data

Figure 2–13. Site 08380500–Gallinas Creek near Montezuma, New Mexico (NM) with systematic data only.
Appendix 2. Graphical Comparisons Between the EMA and B17B at 82 Test Sites 67

1,000

100

10

10,000

100,000

Peak discharge, in cubic feet per second

99 98 95 90 80 70 50

Annual exceedance probabilty, in percent

Rio Ruidoso at Hollywood, NM (station 08387000)

30 20 10 5 2 1 0.5 0.2

EXPLANATION

Bulletin 17B/Grubbs-Beck

Expected Moments Algorithm/

multiple Grubbs-Beck

Systematic data

Figure 2–14. Site 08387000–Rio Ruidoso at Hollywood, New Mexico (NM) with systematic data only.
68 Evaluation of Recommended Revisions to Bulletin 17B

1,000

100

10,000

100,000

Peak discharge, in cubic feet per second

99 98 95 90 80 70 50

Annual exceedance probabilty, in percent

Weber River near Oakley, UT (station 10128500)

30 20 10 5 2 1 0.5 0.2

EXPLANATION

Bulletin 17B/Grubbs-Beck

Expected Moments Algorithm/

multiple Grubbs-Beck

Systematic data

Figure 2–15. Site 10128500–Weber River near Oakley, Utah (UT) with systematic data only.
Appendix 2. Graphical Comparisons Between the EMA and B17B at 82 Test Sites 69

1,000

10,000

100,000

Peak discharge, in cubic feet per second

99 98 95 90 80 70 50

Annual exceedance probabilty, in percent

Merced River at Pohono Bridge near Yosemite, CA (station 11266500)

30 20 10 5 2 1 0.5 0.2

EXPLANATION

Bulletin 17B/Grubbs-Beck

Expected Moments Algorithm/

multiple Grubbs-Beck

Systematic data

Figure 2–16. Site 11266500–Merced River at Pohono Bridge near Yosemite, California (CA) with systematic data only.
70 Evaluation of Recommended Revisions to Bulletin 17B

1,000

10,000

1,000,000

100,000

Peak discharge, in cubic feet per second

99 98 95 90 80 70 50

Annual exceedance probabilty, in percent

Skykomish River near Gold Bar, WA (station 12134500)

30 20 10 5 2 1 0.5 0.2

EXPLANATION

Bulletin 17B/Grubbs-Beck

Expected Moments Algorithm/

multiple Grubbs-Beck

Systematic data

Figure 2–17. Site 12134500–Skykomish River near Gold Bar, Washington (WA) with systematic data only.
Appendix 2. Graphical Comparisons Between the EMA and B17B at 82 Test Sites 71

1,000

10,000

100,000

Peak discharge, in cubic feet per second

99 98 95 90 80 70 50

Annual exceedance probabilty, in percent

St. Joe River at Calder, ID (station 12414500)

30 20 10 5 2 1 0.5 0.2

EXPLANATION

Bulletin 17B/Grubbs-Beck

Expected Moments Algorithm/

multiple Grubbs-Beck

Systematic data

Figure 2–18. Site 12414500–St. Joe River at Calder, Idaho (ID) with systematic data only.
72 Evaluation of Recommended Revisions to Bulletin 17B

0.1

1

10

100

1,000

10,000

Peak discharge, in cubic feet per second

99 98 95 90 80 70 50

Annual exceedance probabilty, in percent

East Fork Foster Creek tributary near Bridgeport, WA (station 12437950)

30 20 10 5 2 1 0.5 0.2

EXPLANATION

Bulletin 17B/Grubbs-Beck

Expected Moments Algorithm/

multiple Grubbs-Beck

Systematic data

Figure 2–19. Site 12437950–East Fork Foster Creek tributary near Bridgeport, Washington (WA) with systematic data only.
Appendix 2. Graphical Comparisons Between the EMA and B17B at 82 Test Sites 73

10,000

1,000

100,000

Peak discharge, in cubic feet per second

99 98 95 90 80 70 50

Annual exceedance probabilty, in percent

Stehekin River at Stehekin, WA (station 12451000)

30 20 10 5 2 1 0.5 0.2

EXPLANATION

Bulletin 17B/Grubbs-Beck

Expected Moments Algorithm/

multiple Grubbs-Beck

Systematic data

Figure 2–20. Site 12451000–Stehekin River at Stehekin, Washington (WA) with systematic data only.
74 Evaluation of Recommended Revisions to Bulletin 17B

10,000

1,000

100,000

Peak discharge, in cubic feet per second

99 98 95 90 80 70 50

Annual exceedance probabilty, in percent

Umatilla River at Pendleton, OR (station 14021000)

30 20 10 5 2 1 0.5 0.2

EXPLANATION

Bulletin 17B/Grubbs-Beck

Expected Moments Algorithm/

multiple Grubbs-Beck

Systematic data

Figure 2–21. Site 14021000–Umatilla River at Pendleton, Oregon (OR) with systematic data only.
Appendix 2. Graphical Comparisons Between the EMA and B17B at 82 Test Sites 75

10,000

1,000

100,000

Peak discharge, in cubic feet per second

99 98 95 90 80 70 50

Annual exceedance probabilty, in percent

John Day River at McDonald Ferry, OR (station 14048000)

30 20 10 5 2 1 0.5 0.2

EXPLANATION

Bulletin 17B/Grubbs-Beck

Expected Moments Algorithm/

multiple Grubbs-Beck

Systematic data

Figure 2–22. Site 14048000–John Day River at McDonald Ferry, Oregon (OR) with systematic data only.
76 Evaluation of Recommended Revisions to Bulletin 17B

10,000

1,000

100,000

Peak discharge, in cubic feet per second

99 98 95 90 80 70 50

Annual exceedance probabilty, in percent

Sandy River near Marmot, OR (station 14137000)

30 20 10 5 2 1 0.5 0.2

EXPLANATION

Bulletin 17B/Grubbs-Beck

Expected Moments Algorithm/

multiple Grubbs-Beck

Systematic data

Figure 2–23. Site 14137000–Sandy River near Marmot, Oregon (OR) with systematic data only.
Appendix 2. Graphical Comparisons Between the EMA and B17B at 82 Test Sites 77

10,000

1,000

Peak discharge, in cubic feet per second

99 98 95 90 80 70 50

Annual exceedance probabilty, in percent

Fish Creek near Ketchikan, AK (station 15072000)

30 20 10 5 2 1 0.5 0.2

EXPLANATION

Bulletin 17B/Grubbs-Beck

Expected Moments Algorithm/

multiple Grubbs-Beck

Systematic data

Figure 2–24. Site 15072000–Fish Creek near Ketchikan, Alaska (AK) with systematic data only.
78 Evaluation of Recommended Revisions to Bulletin 17B

100,000

10,000

1,000

100

Peak discharge, in cubic feet per second

99 98 95 90 80 70 50

Annual exceedance probabilty, in percent

West Wailuaiki Stream near Keanae, HI (station 16518000)

30 20 10 5 2 1 0.5 0.2

EXPLANATION

Bulletin 17B/Grubbs-Beck

Expected Moments Algorithm/

multiple Grubbs-Beck

Systematic data

Figure 2–25. Site 16518000–West Wailuaiki Stream near Keanae, Hawaii (HI) with systematic data only.
Appendix 2. Graphical Comparisons Between the EMA and B17B at 82 Test Sites 79

100,000

10,000

1,000

100

10

Peak discharge, in cubic feet per second

99 98 95 90 80 70 50

Annual exceedance probabilty, in percent

Honopou Stream near Huelo Maui, HI (station 16587000)

30 20 10 5 2 1 0.5 0.2

EXPLANATION

Bulletin 17B/Grubbs-Beck

Expected Moments Algorithm/

multiple Grubbs-Beck

Systematic data

Figure 2–26. Site 16587000–Honopou Stream near Huelo Maui, Hawaii (HI) with systematic data only.
80 Evaluation of Recommended Revisions to Bulletin 17B

Sites With Historical Information

100,000

1,000,000

10,000

1,000

Peak discharge, in cubic feet per second

99 98 95 90 80 70 50

Annual exceedance probabilty, in percent

Schoharie Creek at Prattsville, NY (station 01350000)

30 20 10 5 2 1 0.5 0.2

EXPLANATION

Bulletin 17B/Grubbs-Beck

Expected Moments Algorithm/

multiple Grubbs-Beck

Systematic data

Historical data

Figure 2–27. Site 01350000–Schoharie Creek at Prattsville, New York (NY) with systematic and historical data.
Appendix 2. Graphical Comparisons Between the EMA and B17B at 82 Test Sites 81

100,000

10,000

1,000

Peak discharge, in cubic feet per second

99 98 95 90 80 70 50

Annual exceedance probabilty, in percent

Raystown Branch Juniata River at Saxton, PA (station 01562000)

30 20 10 5 2 1 0.5 0.2

EXPLANATION

Bulletin 17B/Grubbs-Beck

Expected Moments Algorithm/

multiple Grubbs-Beck

Systematic data

Historical data

Figure 2–28. Site 01562000–Raystown Branch Juniata River at Saxton, Pennsylvania (PA) with systematic and historical data.
82 Evaluation of Recommended Revisions to Bulletin 17B

100,000

1,000,000

10,000

1,000

Peak discharge, in cubic feet per second

99 98 95 90 80 70 50

Annual exceedance probabilty, in percent

Shenandoah River at Millville, WV (station 01636500)

30 20 10 5 2 1 0.5 0.2

EXPLANATION

Bulletin 17B/Grubbs-Beck

Expected Moments Algorithm/

multiple Grubbs-Beck

Systematic data

Historical data

Figure 2–29. Site 01636500–Shenandoah River at Millville, West Virginia (WV) with systematic and historical data.
Appendix 2. Graphical Comparisons Between the EMA and B17B at 82 Test Sites 83

100,000

10,000

1,000

100

Peak discharge, in cubic feet per second

99 98 95 90 80 70 50

Annual exceedance probabilty, in percent

30 20 10 5 2 1 0.5 0.2

EXPLANATION

Bulletin 17B/Grubbs-Beck

Expected Moments Algorithm/

multiple Grubbs-Beck

Systematic data

Historical data

Linville River near Nebo, NC (station 02138500)

Figure 2–30. Site 02138500–Linville River near Nebo, North Carolina (NC) with systematic and historical data.
84 Evaluation of Recommended Revisions to Bulletin 17B

1,000,000

100,000

10,000

1,000

Peak discharge, in cubic feet per second

99 98 95 90 80 70 50

Annual exceedance probabilty, in percent

Allegheny River at Salamanca, NY (station 03011020)

30 20 10 5 2 1 0.5 0.2

EXPLANATION

Bulletin 17B/Grubbs-Beck

Expected Moments Algorithm/

multiple Grubbs-Beck

Systematic data

Figure 2–31. Site 03011020–Allegheny River at Salamanca, New York (NY) with systematic and historical data.
Appendix 2. Graphical Comparisons Between the EMA and B17B at 82 Test Sites 85

100,000

10,000

1,000

Peak discharge, in cubic feet per second

99 98 95 90 80 70 50

Annual exceedance probabilty, in percent

Tygart Valley River at Belington, WV (station 03051000)

30 20 10 5 2 1 0.5 0.2

EXPLANATION

Bulletin 17B/Grubbs-Beck

Expected Moments Algorithm/

multiple Grubbs-Beck

Systematic data

Historical data

Figure 2–32. Site 03051000–Tygart Valley River at Belington, West Virginia (WV) with systematic and historical data.
86 Evaluation of Recommended Revisions to Bulletin 17B

100,000

10,000

1,000

Peak discharge, in cubic feet per second

99 98 95 90 80 70 50

Annual exceedance probabilty, in percent

Hocking River at Athens, OH (station 03159500)

30 20 10 5 2 1 0.5 0.2

EXPLANATION

Bulletin 17B/Grubbs-Beck

Expected Moments Algorithm/

multiple Grubbs-Beck

Systematic data

Historical data

Figure 2–33. Site 03159500–Hocking River at Athens, Ohio (OH) with systematic and historical data.
Appendix 2. Graphical Comparisons Between the EMA and B17B at 82 Test Sites 87

100,000

10,000

1,000

100

Peak discharge, in cubic feet per second

99 98 95 90 80 70 50

Annual exceedance probabilty, in percent

Valley River at Tomotla, NC (station 03550000)

30 20 10 5 2 1 0.5 0.2

EXPLANATION

Bulletin 17B/Grubbs-Beck

Expected Moments Algorithm/

multiple Grubbs-Beck

Systematic data

Historical data

Figure 2–34. Site 03550000–Valley River at Tomotla, North Carolina (NC) with systematic and historical data.
88 Evaluation of Recommended Revisions to Bulletin 17B

100,000

10,000

1,000

Peak discharge, in cubic feet per second

99 98 95 90 80 70 50

Annual exceedance probabilty, in percent

Toccoa River near Dial, GA (station 03558000)

30 20 10 5 2 1 0.5 0.2

EXPLANATION

Bulletin 17B/Grubbs-Beck

Expected Moments Algorithm/

multiple Grubbs-Beck

Systematic data

Historical data

Figure 2–35. Site 03558000–Toccoa River near Dial, Georgia (GA) with systematic and historical data.
Appendix 2. Graphical Comparisons Between the EMA and B17B at 82 Test Sites 89

100,000

10,000

1,000

100

Peak discharge, in cubic feet per second

99 98 95 90 80 70 50

Annual exceedance probabilty, in percent

Big Sandy River at Bruceton, TN (station 03606500)

30 20 10 5 2 1 0.5 0.2

1

2010 systematic peak missing, yet highest gage height on record was

recorded. Interval discharge range set in Expected Moments Algorithm from

18,500 to infinity for 2010 peak, while an estimated point discharge value

of 30,600 cubic feet per second was used in Bulletin 17B analysis. 

EXPLANATION

Bulletin 17B/Grubbs-Beck

Expected Moments Algorithm/

multiple Grubbs-Beck

Systematic data

Historical data

Figure 2–36. Site 03606500–Big Sandy River at Bruceton, Tennessee (TN) with systematic and historical data.
90 Evaluation of Recommended Revisions to Bulletin 17B

100,000

10,000

1,000

Peak discharge, in cubic feet per second

99 98 95 90 80 70 50

Annual exceedance probabilty, in percent

Missisquoi River near East Berkshire, VT (station 04293500)

30 20 10 5 2 1 0.5 0.2

EXPLANATION

Bulletin 17B/Grubbs-Beck

Expected Moments Algorithm/

multiple Grubbs-Beck

Systematic data

Historical data

Figure 2–37. Site 04293500–Missisquoi River near East Berkshire, Vermont (VT) with systematic and historical data.
Appendix 2. Graphical Comparisons Between the EMA and B17B at 82 Test Sites 91

100,000

10,000

1,000

100

Peak discharge, in cubic feet per second

99 98 95 90 80 70 50

Annual exceedance probabilty, in percent

Pryor Creek near Billings, MT (station 06216500)

30 20 10 5 2 1 0.5 0.2

EXPLANATION

Bulletin 17B/Grubbs-Beck

Expected Moments Algorithm/

multiple Grubbs-Beck

Systematic data

Historical data

Figure 2–38. Site 06216500–Pryor Creek near Billings, Montana (MT) with systematic and historical data.
92 Evaluation of Recommended Revisions to Bulletin 17B

100,000

10,000

1,000

100

Peak discharge, in cubic feet per second

99 98 95 90 80 70 50

Annual exceedance probabilty, in percent

Floyd River at James, IA (station 06600500)

30 20 10 5 2 1 0.5 0.2

EXPLANATION

Bulletin 17B/Grubbs-Beck

Expected Moments Algorithm/

multiple Grubbs-Beck

Systematic data

Historical data

Figure 2–39. Site 06600500–Floyd River at James, Iowa (IA) with systematic and historical data.
Appendix 2. Graphical Comparisons Between the EMA and B17B at 82 Test Sites 93

100,000

10,000

1,000

100

Peak discharge, in cubic feet per second

99 98 95 90 80 70 50

Annual exceedance probabilty, in percent

Thompson River at Davis City, IA (station 06898000)

30 20 10 5 2 1 0.5 0.2

EXPLANATION

Bulletin 17B/Grubbs-Beck

Expected Moments Algorithm/

multiple Grubbs-Beck

Systematic data

Historical data

Figure 2–40. Site 06898000–Thompson River at Davis City, Iowa (IA) with systematic and historical data.
94 Evaluation of Recommended Revisions to Bulletin 17B

100,000

1,000,000

10,000

1,000

Peak discharge, in cubic feet per second

99 98 95 90 80 70 50

Annual exceedance probabilty, in percent

Current River at Van Buren, MO (station 07067000)

30 20 10 5 2 1 0.5 0.2

EXPLANATION

Bulletin 17B/Grubbs-Beck

Expected Moments Algorithm/

multiple Grubbs-Beck

Systematic data

Historical data

Figure 2–41. Site 07067000–Current River at Van Buren, Missouri (MO) with systematic and historical data.
Appendix 2. Graphical Comparisons Between the EMA and B17B at 82 Test Sites 95

1

Four historic peaks used in Expected Moments Algorithm (EMA)

analysis; multiple perception thresholds set for historical period. Four 

historic peaks not used in Bulletin 17B analysis. User-supplied

high-outlier threshold of 240,000 cfs set for extended historical period.

100,000

1,000,000

10,000

1,000

100

10

Peak discharge, in cubic feet per second

99 98 95 90 80 70 50

Annual exceedance probabilty, in percent

Guadalupe River at Comfort, TX (station 08167000)

30 20 10 5 2 1 0.5 0.2

EXPLANATION

Bulletin 17B/Grubbs-Beck

Expected Moments Algorithm/

multiple Grubbs-Beck

Systematic data

Historical data

Figure 2–42. Site 08167000–Guadalupe River at Comfort, Texas (TX) with systematic and historical data.
96 Evaluation of Recommended Revisions to Bulletin 17B

10

100

10,000

1,000

Peak discharge, in cubic feet per second

99 98 95 90 80 70 50

Annual exceedance probabilty, in percent

Pecos River near Pecos, NM (station 08378500)

30 20 10 5 2 1 0.5 0.2

EXPLANATION

Bulletin 17B/Grubbs-Beck

Expected Moments Algorithm/

multiple Grubbs-Beck

Systematic data

Historical data

Figure 2–43. Site 08378500–Pecos Rivert near Pecos, New Mexico (NM) with systematic and historical data.
Appendix 2. Graphical Comparisons Between the EMA and B17B at 82 Test Sites 97

100,000

93

26

1

100

10,000

1,000

Peak discharge, in cubic feet per second

99 98 95 90 80 70 50

Annual exceedance probabilty, in percent

Santa Cruz River at Tucson, AZ (station 09482500)

30 20 10 5 2 1 0.5 0.2

EXPLANATION

Bulletin 17B/Grubbs-Beck

Expected Moments Algorithm/

multiple Grubbs-Beck

Systematic data

Historical data

Figure 2–44. Site 09482500–Santa Cruz River at Tucson, Arizona (AZ) with systematic and historical data.
98 Evaluation of Recommended Revisions to Bulletin 17B

1,000,000

1,000

100,000

10,000

Peak discharge, in cubic feet per second

99 98 95 90 80 70 50

Annual exceedance probabilty, in percent

NF Coeur D’Alene River at Enaville, ID (station 12413000)

30 20 10 5 2 1 0.5 0.2

EXPLANATION

Bulletin 17B/Grubbs-Beck

Expected Moments Algorithm/

multiple Grubbs-Beck

Systematic data

Historical data

Figure 2–45. Site 12413000–North Fork (NF) Coeur D’Alene River at Enaville, Idaho (ID) with systematic and historical data.
Appendix 2. Graphical Comparisons Between the EMA and B17B at 82 Test Sites 99

Sites With Potentially Influential Low Floods

1,000,000

1,000

100,000

10,000

Peak discharge, in cubic feet per second

99 98 95 90 80 70 50

Annual exceedance probabilty, in percent

Rappahannock River near Fredericksburg, VA (station 01668000)

30 20 10 5 2 1 0.5 0.2

EXPLANATION

Bulletin 17B/Grubbs-Beck

Expected Moments Algorithm/

multiple Grubbs-Beck

Bulletin 17B/multiple Grubbs-Beck

Systematic data

Systematic data identified as

low outlier (MGB)

Figure 2–46. Site 01668000–Rappahannock River near Fredericksburg, Virginia (VA) with potentially influential low floods and

no historical information.
100 Evaluation of Recommended Revisions to Bulletin 17B

1,000,000

1,000

100

100,000

10,000

Peak discharge, in cubic feet per second

99 98 95 90 80 70 50

Annual exceedance probabilty, in percent

Embarras River at Ste. Marie, IL (station 03345500)

30 20 10 5 2 1 0.5 0.2

EXPLANATION

Bulletin 17B/Grubbs-Beck

Expected Moments Algorithm/

multiple Grubbs-Beck

Bulletin 17B/multiple Grubbs-Beck

Systematic data

Systematic data identified as

low outlier (MGB)

Figure 2–47. Site 03345500–Embarras River at Ste. Marie, Illinois (IL) with potentially influential low floods and no historical

information.
Appendix 2. Graphical Comparisons Between the EMA and B17B at 82 Test Sites 101

1,000

100

100,000

10,000

Peak discharge, in cubic feet per second

99 98 95 90 80 70 50

Annual exceedance probabilty, in percent

Sangamon River at Monticello, IL (station 05572000)

30 20 10 5 2 1 0.5 0.2

EXPLANATION

Bulletin 17B/Grubbs-Beck

Expected Moments Algorithm/

multiple Grubbs-Beck

Bulletin 17B/multiple Grubbs-Beck

Systematic data

Systematic data identified as

low outlier (MGB)

Figure 2–48. Site 05572000–Sangamon River at Monticello, Illinois (IL) with potentially influential low floods and no historical

information.
102 Evaluation of Recommended Revisions to Bulletin 17B

1,000

100

10

1

0.1

100,000

1,000,000

10,000

Peak discharge, in cubic feet per second

99 98 95 90 80 70 50

Annual exceedance probabilty, in percent

Wolf Creek near Wolf Point, MT (station 06176500)

30 20 10 5 2 1 0.5 0.2

EXPLANATION

Bulletin 17B/Grubbs-Beck

Expected Moments Algorithm/

multiple Grubbs-Beck

Bulletin 17B/multiple Grubbs-Beck

Systematic data

Systematic data identified as

low outlier (MGB)

Figure 2–49. Site 06176500–Wolf Creek near Wolf Point, Montana (MT) with potentially influential low floods and no historical

information.
Appendix 2. Graphical Comparisons Between the EMA and B17B at 82 Test Sites 103

1,000

100

10

100,000

10,000

Peak discharge, in cubic feet per second

99 98 95 90 80 70 50

Annual exceedance probabilty, in percent

Vermejo River near Dawson, NM (station 07203000)

30 20 10 5 2 1 0.5 0.2

EXPLANATION

Bulletin 17B/Grubbs-Beck

Expected Moments Algorithm/

multiple Grubbs-Beck

Bulletin 17B/multiple Grubbs-Beck

Systematic data

Systematic data identified as

low outlier (MGB)

Figure 2–50. Site 07203000–Vermejo River near Dawson, New Mexico (NM).
104 Evaluation of Recommended Revisions to Bulletin 17B

1

Peak flow record indicates 3 years below gage-base flows. Interval

discharge range set in EMA from 0 to 300 cubic feet per second for

years with below gage-base flows. Twenty systematic peaks were

dropped in B17B analysis because below gage base are omitted.

1,000

100

10

100,000

10,000

Peak discharge, in cubic feet per second

99 98 95 90 80 70 50

Annual exceedance probabilty, in percent

North Concho River at Sterling City, TX (station 08133500)

30 20 10 5 2 1 0.5 0.2

EXPLANATION

Bulletin 17B/Grubbs-Beck

Expected Moments Algorithm/

multiple Grubbs-Beck

Bulletin 17B/multiple Grubbs-Beck

Systematic data

Systematic data identified as

low outlier (MGB)

Figure 2–51. Site 08133500–North Concho River at Sterling City, Texas (TX) with potentially influential low floods and no historical information. EMA, Expected Moments Algorithm; B17B, Bulletin 17B.
Appendix 2. Graphical Comparisons Between the EMA and B17B at 82 Test Sites 105

1,000

100

10

10,000,000

1,000,000

100,000

10,000

Peak discharge, in cubic feet per second

99 98 95 90 80 70 50

Annual exceedance probabilty, in percent

Llano River near Junction, TX (station 08150000)

30 20 10 5 2 1 0.5 0.2

EXPLANATION

Bulletin 17B/Grubbs-Beck

Expected Moments Algorithm/

multiple Grubbs-Beck

Bulletin 17B/multiple Grubbs-Beck

Systematic data

Systematic data identified as

low outlier (MGB)

Figure 2–52. Site 08150000–Llano River near Junction, Texas (TX) with potentially influential low floods and no historical information.
106 Evaluation of Recommended Revisions to Bulletin 17B

1,000

100

10

1,000,000

100,000

10,000

Peak discharge, in cubic feet per second

99 98 95 90 80 70 50

Annual exceedance probabilty, in percent

Mission River at Refugio, TX (station 08189500)

30 20 10 5 2 1 0.5 0.2

EXPLANATION

Bulletin 17B/Grubbs-Beck

Expected Moments Algorithm/

multiple Grubbs-Beck

Bulletin 17B/multiple Grubbs-Beck

Systematic data

Systematic data identified as

low outlier (MGB)

Figure 2–53. Site 08189500–Mission River at Refugio, Texas (TX) with potentially influential low floods and no historical information.
Appendix 2. Graphical Comparisons Between the EMA and B17B at 82 Test Sites 107

1,000

100

100,000

10,000

Peak discharge, in cubic feet per second

99 98 95 90 80 70 50

Annual exceedance probabilty, in percent

Elk River at Clark, CO (station 09241000)

30 20 10 5 2 1 0.5 0.2

EXPLANATION

Bulletin 17B/Grubbs-Beck

Expected Moments Algorithm/

multiple Grubbs-Beck

Bulletin 17B/multiple Grubbs-Beck

Systematic data

Systematic data identified as

low outlier (MGB)

Figure 2–54. Site 09241000–Elk River at Clark, Colorado (CO) with potentially influential low floods and no historical information.
108 Evaluation of Recommended Revisions to Bulletin 17B

1,000

100

10

1

0.1

100,000

1,000,000

10,000

Peak discharge, in cubic feet per second

99 98 95 90 80 70 50

Annual exceedance probabilty, in percent

Santa Cruz River near Lochiel, AZ (station 09480000)

30 20 10 5 2 1 0.5 0.2

EXPLANATION

Bulletin 17B/Grubbs-Beck

Expected Moments Algorithm/

multiple Grubbs-Beck

Bulletin 17B/multiple Grubbs-Beck

Systematic data

Systematic data identified as

low outlier (MGB)

Figure 2–55. Site 09480000–Santa Cruz River near Lochiel, Arizona (AZ) with potentially influential low floods and no historical

information.
Appendix 2. Graphical Comparisons Between the EMA and B17B at 82 Test Sites 109

1,000

100

10

10,000

Peak discharge, in cubic feet per second

99 98 95 90 80 70 50

Annual exceedance probabilty, in percent

Beaver River near Beaver, UT (station 10234500)

30 20 10 5 2 1 0.5 0.2

EXPLANATION

Bulletin 17B/Grubbs-Beck

Expected Moments Algorithm/

multiple Grubbs-Beck

Bulletin 17B/multiple Grubbs-Beck

Systematic data

Systematic data identified as

low outlier (MGB)

Figure 2–56. Site 10234500–Beaver River near Beaver, Utah (UT) with potentially influential low floods and no historical information.
110 Evaluation of Recommended Revisions to Bulletin 17B

1,000

100

10

10,000

0.1

0.01

0.001

1

100,000

1,000,000

Peak discharge, in cubic feet per second

99 98 95 90 80 70 50

Annual exceedance probabilty, in percent

Santa Maria Creek near Ramona, CA (station 11028500)

30 20 10 5 2 1 0.5 0.2

EXPLANATION

Bulletin 17B/Grubbs-Beck

Expected Moments Algorithm/

multiple Grubbs-Beck

Bulletin 17B/multiple Grubbs-Beck

Systematic data

Systematic data identified as

low outlier (MGB)

Figure 2–57. Site 11028500–Santa Maria Creek near Ramona, California (CA) with potentially influential low floods and no historical information.
Appendix 2. Graphical Comparisons Between the EMA and B17B at 82 Test Sites 111

1,000

100

10,000

100,000

1,000,000

Peak discharge, in cubic feet per second

99 98 95 90 80 70 50

Annual exceedance probabilty, in percent

Arroyo Seco near Soledad, CA (station 11152000)

30 20 10 5 2 1 0.5 0.2

EXPLANATION

Bulletin 17B/Grubbs-Beck

Expected Moments Algorithm/

multiple Grubbs-Beck

Bulletin 17B/multiple Grubbs-Beck

Systematic data

Systematic data identified as

low outlier (MGB)

Figure 2–58. Site 11152000–Arroyo Seco near Soledad, California (CA) with potentially influential low floods and no historical

information.
112 Evaluation of Recommended Revisions to Bulletin 17B

1,000

100

10

1

10,000

100,000

Peak discharge, in cubic feet per second

99 98 95 90 80 70 50

Annual exceedance probabilty, in percent

Orestimba Creek near Newman, CA (station 11274500)

30 20 10 5 2 1 0.5 0.2

EXPLANATION

Bulletin 17B/Grubbs-Beck

Expected Moments Algorithm/

multiple Grubbs-Beck

Bulletin 17B/multiple Grubbs-Beck

Systematic data

Systematic data identified as

low outlier (MGB)

Figure 2–59. Site 11274500–Orestimba Creek near Newman, California (CA) with potentially influential low floods and no historical information.
Appendix 2. Graphical Comparisons Between the EMA and B17B at 82 Test Sites 113

1,000

100

10,000

100,000

Peak discharge, in cubic feet per second

99 98 95 90 80 70 50

Annual exceedance probabilty, in percent

Deer Creek near Vina, CA (station 11383500)

30 20 10 5 2 1 0.5 0.2

EXPLANATION

Bulletin 17B/Grubbs-Beck

Expected Moments Algorithm/

multiple Grubbs-Beck

Bulletin 17B/multiple Grubbs-Beck

Systematic data

Systematic data identified as

low outlier (MGB)

Figure 2–60. Site 11383500–Deer Creek near Vina, California (CA) with potentially influential low floods and no historical information.
114 Evaluation of Recommended Revisions to Bulletin 17B

1,000

10,000

100,000

Peak discharge, in cubic feet per second

99 98 95 90 80 70 50

Annual exceedance probabilty, in percent

30 20 10 5 2 1 0.5 0.2

Moyie River at Eileen, ID (station 12307500)

EXPLANATION

Bulletin 17B/Grubbs-Beck

Expected Moments Algorithm/

multiple Grubbs-Beck

Bulletin 17B/multiple Grubbs-Beck

Systematic data

Systematic data identified as

low outlier (MGB)

Figure 2–61. Site 12307500–Moyie River at Eileen, Idaho (ID) with potentially influential low floods and no historical information.
Appendix 2. Graphical Comparisons Between the EMA and B17B at 82 Test Sites 115

1,000

10,000

100,000

Peak discharge, in cubic feet per second

99 98 95 90 80 70 50

Annual exceedance probabilty, in percent

Salmon River at Salmon, ID (station 13302500)

30 20 10 5 2 1 0.5 0.2

EXPLANATION

Bulletin 17B/Grubbs-Beck

Expected Moments Algorithm/

multiple Grubbs-Beck

Bulletin 17B/multiple Grubbs-Beck

Systematic data

Systematic data identified as

low outlier (MGB)

Figure 2–62. Site 13302500–Salmon River at Salmon, Idaho (ID) with potentially influential low floods and no historical information.
116 Evaluation of Recommended Revisions to Bulletin 17B

1,000

10,000

0.1

1

10

100

Peak discharge, in cubic feet per second

99 98 95 90 80 70 50

Annual exceedance probabilty, in percent

Smith Gulch tributary near Pataha, WA (station 13343660)

30 20 10 5 2 1 0.5 0.2

EXPLANATION

Bulletin 17B/Grubbs-Beck

Expected Moments Algorithm/

multiple Grubbs-Beck

Bulletin 17B/multiple Grubbs-Beck

Systematic data

Systematic data identified as

low outlier (MGB)

Figure 2–63. Site 13343660–Smith Gulch tributary near Pataha, Washington (WA) with potentially influential low floods and no

historical information.
Appendix 2. Graphical Comparisons Between the EMA and B17B at 82 Test Sites 117

100,000

1,000,000

10,000

Peak discharge, in cubic feet per second

99 98 95 90 80 70 50

Annual exceedance probabilty, in percent

Umpqua River near Elkton, OR (station 14321000)

30 20 10 5 2 1 0.5 0.2

EXPLANATION

Bulletin 17B/Grubbs-Beck

Expected Moments Algorithm/

multiple Grubbs-Beck

Bulletin 17B/multiple Grubbs-Beck

Systematic data

Systematic data identified as

low outlier (MGB)

Figure 2–64. Site 14321000–Umpqua River near Elkton, Oregon (OR) with potentially influential low floods and no historical

information.
118 Evaluation of Recommended Revisions to Bulletin 17B

100,000

10,000

1,000

100

Peak discharge, in cubic feet per second

99 98 95 90 80 70 50

Annual exceedance probabilty, in percent

EB of NF Wailua River near Lihue, HI (station 16068000)

30 20 10 5 2 1 0.5 0.2

EXPLANATION

Bulletin 17B/Grubbs-Beck

Expected Moments Algorithm/

multiple Grubbs-Beck

Bulletin 17B/multiple Grubbs-Beck

Systematic data

Systematic data identified as

low outlier (MGB)

Figure 2–65. Site 16068000–East Branch (EB) of North Fork (NF) Wailua River near Lihue, Hawaii (HI) with potentially influential

low floods and no historical information.
Appendix 2. Graphical Comparisons Between the EMA and B17B at 82 Test Sites 119

Sites With a Combination of Data Types

100,000

10,000

1,000

Peak discharge, in cubic feet per second

99 98 95 90 80 70 50

Annual exceedance probabilty, in percent

Elkhorn Creek near Frankfort, KY (station 03289500)

30 20 10 5 2 1 0.5 0.2

EXPLANATION

Bulletin 17B/Grubbs-Beck

Expected Moments Algorithm/

multiple Grubbs-Beck

Bulletin 17B/multiple Grubbs-Beck

Systematic data

Systematic data identified as

low outlier (MGB)

Historical data

Figure 2–66. Site 03289500–Elkhorn Creek near Frankfort, Kentucky (KY) with a combination of potentially influential low floods,

historical, and (or) high outliers in the data.
120 Evaluation of Recommended Revisions to Bulletin 17B

100,000

10,000

1,000

100

10

Peak discharge, in cubic feet per second

99 98 95 90 80 70 50

Annual exceedance probabilty, in percent

Sauk River near St. Cloud, MN (station 05270500)

30 20 10 5 2 1 0.5 0.2

EXPLANATION

Bulletin 17B/Grubbs-Beck

Expected Moments Algorithm/

multiple Grubbs-Beck

Bulletin 17B/multiple Grubbs-Beck

Systematic data

Systematic data identified as

low outlier (MGB)

Figure 2–67. Site 05270500–Sauk River near St. Cloud, Minnesota (MN) with a combination of potentially influential low floods,

historical, and (or) high outliers in the data.
Appendix 2. Graphical Comparisons Between the EMA and B17B at 82 Test Sites 121

100,000

10,000

1,000

100

10

Peak discharge, in cubic feet per second

99 98 95 90 80 70 50

Annual exceedance probabilty, in percent

Whetstone River near Big Stone City, SD (station 05291000)

30 20 10 5 2 1 0.5 0.2

EXPLANATION

Bulletin 17B/Grubbs-Beck

Expected Moments Algorithm/

multiple Grubbs-Beck

Bulletin 17B/multiple Grubbs-Beck

Systematic data

Systematic data identified as

low outlier (MGB)

Figure 2–68. Site 05291000–Whetstone River near Big Stone City, South Dakota (SD) with a combination of potentially influential low floods, historical, and (or) high outliers in the data.
122 Evaluation of Recommended Revisions to Bulletin 17B

100,000

10,000

1,000

1,000,000

Peak discharge, in cubic feet per second

99 98 95 90 80 70 50

Annual exceedance probabilty, in percent

Cedar River at Cedar Rapids, IA (station 05464500)

30 20 10 5 2 1 0.5 0.2

EXPLANATION

Bulletin 17B/Grubbs-Beck

Expected Moments Algorithm/

multiple Grubbs-Beck

Bulletin 17B/multiple Grubbs-Beck

Systematic data

Systematic data identified as

low outlier (MGB)

Historical data

Figure 2–69. Site 05464500–Cedar River at Cedar Rapids, Iowa (IA) with a combination of potentially influential low floods,

historical, and (or) high outliers in the data.
Appendix 2. Graphical Comparisons Between the EMA and B17B at 82 Test Sites 123

10,000

1,000

100

10

Peak discharge, in cubic feet per second

99 98 95 90 80 70 50

Annual exceedance probabilty, in percent

Tenmile Creek near Rimini, MT (station 06062500)

30 20 10 5 2 1 0.5 0.2

EXPLANATION

Bulletin 17B/Grubbs-Beck

Expected Moments Algorithm/

multiple Grubbs-Beck

Bulletin 17B/multiple Grubbs-Beck

Systematic data

Systematic data identified as

low outlier (MGB)

Figure 2–70. Site 06062500–Tenmile Creek near Rimini, Montana (MT) with a combination of potentially influential low floods,

historical, and (or) high outliers in the data.
124 Evaluation of Recommended Revisions to Bulletin 17B

100,000

10,000

1,000

100

Peak discharge, in cubic feet per second

99 98 95 90 80 70 50

Annual exceedance probabilty, in percent

East Fork Big Creek near Bethany, MO (station 06897000)

30 20 10 5 2 1 0.5 0.2

EXPLANATION

Bulletin 17B/Grubbs-Beck

Expected Moments Algorithm/

multiple Grubbs-Beck

Bulletin 17B/multiple Grubbs-Beck

Systematic data

Systematic data identified as

low outlier (MGB)

Historical data

Figure 2–71. Site 06897000–East Fork Big Creek near Bethany, Missouri (MO) with a combination of potentially influential low

floods, historical, and (or) high outliers in the data.
Appendix 2. Graphical Comparisons Between the EMA and B17B at 82 Test Sites 125

1,000,000

100,000

10,000

1,000

Peak discharge, in cubic feet per second

99 98 95 90 80 70 50

Annual exceedance probabilty, in percent

30 20 10 5 2 1 0.5 0.2

1

Peak flow record indicates 1 year with below gage-base flow.

Interval discharge range set in EMA from 0 to 4,320 cubic feet per second

for year with below gage-base flow. One systematic peak was dropped

in B17B analysis because flows below gage-base are omitted.

Gasconade River at Jerome, MO (station 06933500)

EXPLANATION

Bulletin 17B/Grubbs-Beck

Expected Moments Algorithm/

multiple Grubbs-Beck

Bulletin 17B/multiple Grubbs-Beck

Systematic data

Systematic data identified as

low outlier (MGB)

Historical data

Figure 2–72. Site 06933500–Gasconade River at Jerome, Missouri (MO) with a combination of potentially influential low floods,

historical, and (or) high outliers in the data. EMA, Expected Moments Algorithm; B17B, Bulletin 17B.
126 Evaluation of Recommended Revisions to Bulletin 17B

10,000

1,000

100

10

1

Peak discharge, in cubic feet per second

99 98 95 90 80 70 50

Annual exceedance probabilty, in percent

White Woman Creek tributary near Selkirk, KS (station 07138600)

30 20 10 5 2 1 0.5 0.2

EXPLANATION

Bulletin 17B/Grubbs-Beck

Expected Moments Algorithm/

multiple Grubbs-Beck

Bulletin 17B/multiple Grubbs-Beck

Systematic data

Systematic data identified as

low outlier (MGB)

Figure 2–73. Site 07138600–White Woman Creek tributary near Selkirk, Kansas (KS) with a combination of potentially influential

low floods, historical, and (or) high outliers in the data.
Appendix 2. Graphical Comparisons Between the EMA and B17B at 82 Test Sites 127

10,000

1,000

100

10

1

Peak discharge, in cubic feet per second

99 98 95 90 80 70 50

Annual exceedance probabilty, in percent

Lavaca River near Edna, TX (station 08164000)

30 20 10 5 2 1 0.5 0.2

EXPLANATION

Bulletin 17B/Grubbs-Beck

Expected Moments Algorithm/

multiple Grubbs-Beck

Bulletin 17B/multiple Grubbs-Beck

Systematic data

Systematic data identified as

low outlier (MGB)

Historical data

Figure 2–74. Site 08164000–Lavaca River near Edna, Texas (TX) with a combination of potentially influential low floods, historical, and (or) high outliers in the data.
128 Evaluation of Recommended Revisions to Bulletin 17B

1,000,000

100,000

10,000

1,000

10

Peak discharge, in cubic feet per second

100

99 98 95 90 80 70 50

Annual exceedance probabilty, in percent

Blanco River at Wimberley, TX (station 08171000)

30 20 10 25 1 0.20.5

1

1869 historic peak missing, yet highest gage height on record was

recorded. Interval discharge range set in EMA from 37,000 to infinity

for 1869 peak, while an estimated point discharge value of

63,900 cubic feet per second was used in the B17B analysis.

EXPLANATION

Bulletin 17B/Grubbs-Beck

Expected Moments Algorithm/

multiple Grubbs-Beck

Bulletin 17B/multiple Grubbs-Beck

Systematic data

Systematic data identified as

low outlier (MGB)

Historical data

Figure 2–75. Site 08171000–Blanco River at Wimberley, Texas (TX) with a combination of potentially influential low floods,

historical, and (or) high outliers in the data. EMA, Expected Moments Algorithm; B17B, Bulletin 17B.
Appendix 2. Graphical Comparisons Between the EMA and B17B at 82 Test Sites 129

100,000

10,000

1,000

100

Peak discharge, in cubic feet per second

99 98 95 90 80 70 50

Annual exceedance probabilty, in percent

Animas River at Durango, CO (station 093615000)

30 20 10 5 2 1 0.5 0.2

EXPLANATION

Bulletin 17B/Grubbs-Beck

Expected Moments Algorithm/

multiple Grubbs-Beck

Bulletin 17B/multiple Grubbs-Beck

Systematic data

Systematic data identified as

low outlier (MGB)

Historical data

Figure 2–76. Site 09361500–Animas River at Durango, Colorado (CO) with a combination of potentially influential low floods,

historical, and (or) high outliers in the data.
130 Evaluation of Recommended Revisions to Bulletin 17B

100,000

1,000,000

10,000

1,000

100

Peak discharge, in cubic feet per second

99 98 95 90 80 70 50

Annual exceedance probabilty, in percent

San Pedro River at Charleston, AZ (station 09471000)

30 20 10 5 2 1 0.5 0.2

EXPLANATION

Bulletin 17B/Grubbs-Beck

Expected Moments Algorithm/

multiple Grubbs-Beck

Bulletin 17B/multiple Grubbs-Beck

Systematic data

Systematic data identified as

low outlier (MGB)

Figure 2–77. Site 09471000–San Pedro River at Charleston, Arizona (AZ) with a combination of potentially influential low floods,

historical, and (or) high outliers in the data.
Appendix 2. Graphical Comparisons Between the EMA and B17B at 82 Test Sites 131

100,000

10,000

1,000

100

10

1

0.1

Peak discharge, in cubic feet per second

99 98 95 90 80 70 50

Annual exceedance probabilty, in percent

30 20 10 5 2 1 0.5 0.2

Arroyo Mocho near Livermore, CA (station 11176000)

EXPLANATION

Bulletin 17B/Grubbs-Beck

Expected Moments Algorithm/

multiple Grubbs-Beck

Bulletin 17B/multiple Grubbs-Beck

Systematic data

Systematic data identified as

low outlier (MGB)

Historical data

Figure 2–78. Site 11176000–Arroyo Mocho near Livermore, California (CA) with a combination of potentially influential low

floods, historical, and (or) high outliers in the data.
132 Evaluation of Recommended Revisions to Bulletin 17B

100,000

1,000,000

10,000

1,000

100

Peak discharge, in cubic feet per second

99 98 95 90 80 70 50

Annual exceedance probabilty, in percent

Dry Creek near Cloverdale, CA (station 11464500)

30 20 10 5 2 1 0.5 0.2

1

1938 historic peak missing, yet second highest gage height on record

was recorded. Internal discharge range set in EMA from 15,600 to infinity

for 1938 peak, while an estimated point discharge value of 18,100 cubic feet

per second was used in the B17B analysis.

EXPLANATION

Bulletin 17B/Grubbs-Beck

Expected Moments Algorithm/

multiple Grubbs-Beck

Bulletin 17B/multiple Grubbs-Beck

Systematic data

Systematic data identified as

low outlier (MGB)

Figure 2–79. Site 11464500–Dry Creek near Cloverdale, California (CA) with a combination of potentially influential low floods,

historical, and (or) high outliers in the data. EMA, Expected Moments Algorithm; B17B, Bulletin 17B.
Appendix 2. Graphical Comparisons Between the EMA and B17B at 82 Test Sites 133

100,000

1,000,000

10,000

1,000

Peak discharge, in cubic feet per second

99 98 95 90 80 70 50

Annual exceedance probabilty, in percent

30 20 10 5 2 1 0.5 0.2

Salmon River at Somes Bar, CA (station 11522500)

EXPLANATION

Bulletin 17B/Grubbs-Beck

Expected Moments Algorithm/

multiple Grubbs-Beck

Bulletin 17B/multiple Grubbs-Beck

Systematic data

Systematic data identified as

low outlier (MGB)

Figure 2–80. Site 11522500–Salmon River at Somes Bar, California (CA) with a combination of potentially influential low floods,

historical, and (or) high outliers in the data.
134 Evaluation of Recommended Revisions to Bulletin 17B

100,000

1,000,000

10,000

1,000

Peak discharge, in cubic feet per second

99 98 95 90 80 70 50

Annual exceedance probabilty, in percent

Quinault River at Quinault Lake, WA (station 12039500)

30 20 10 5 2 1 0.5 0.2

EXPLANATION

Bulletin 17B/Grubbs-Beck

Expected Moments Algorithm/

multiple Grubbs-Beck

Bulletin 17B/multiple Grubbs-Beck

Systematic data

Systematic data identified as

low outlier (MGB)

Historical data

Figure 2–81. Site 12039500–Quinault River at Quinault Lake, Washington (WA) with a combination of potentially influential low

floods, historical, and (or) high outliers in the data.
Appendix 2. Graphical Comparisons Between the EMA and B17B at 82 Test Sites 135

100,000

10,000

1,000

Peak discharge, in cubic feet per second

99 98 95 90 80 70 50

Annual exceedance probabilty, in percent

Boise River near Twin Springs, ID (station 13185000)

30 20 10 5 2 1 0.5 0.2

EXPLANATION

Bulletin 17B/Grubbs-Beck

Expected Moments Algorithm/

multiple Grubbs-Beck

Bulletin 17B/multiple Grubbs-Beck

Systematic data

Systematic data identified as

low outlier (MGB)

Historical data

Figure 2–82. Site 13185000–Boise River near Twin Springs, Idaho (ID) with a combination of potentially influential low floods,

historical, and (or) high outliers in the data.
136 Evaluation of Recommended Revisions to Bulletin 17B

Studies With log-Pearson Type III (LP3) Distribution and Regional Skew

Figures 2–83 through 2–85 show the same cases as figures 2–4, except that regional skew information has

been added with a mean square error (MSE) of 0.15—a typical value consistent with Bayesian/GLS skew

maps (Lamontagne and others, 2012; Parrett and others, 2011; Gotvald and others, 2009). As expected, all

of the estimators perform better with regional information. Aside from that, however, there is little difference

between the corresponding figures.

Additional Studies With Specific Frequency Curves

Figures 5-8 and 2–86 through 2–87 apply the three estimators—EMA/MGB, B17B/GB, and

B17B/MGB—to data drawn from specific populations selected to test the estimators’ performance. The cases

are labeled “robustness test curve 1 through 6” in recognition of their origins. Figures 5-8 are presented in the

main body of this report. Figures 2–86 and 2–87 are presented here in the appendix because they do not actually deal with robustness but rather with specific log-Pearson Type III (LP3) populations. In fact, because the

estimators are all invariant with respect to location and scale, these two cases duplicate cases already considered in the report. Figure 2–86 depicts essentially the same case as figure 4 with a population skew of γ=0.5.

Figure 2–87 depicts essentially the same case as figure 3 with a population skew of γ=0.5.
Appendix 2. Graphical Comparisons Between the EMA and B17B at 82 Test Sites 137

B17B/GB

B17B/MGB

EMA/MGB

Q[0.01]

Expected number of historic floods (H)

EXPLANATION

Discharge, in cubic feet per second

0

40

80

120

100

1,000

10,000

0.11 0.96 0.96

None (H=0) 1 2 10

18 19 28 30 31 39

64 68 59

Frequency distribution

LP3 distribution G = 0

Probability density function

LP3 distribution G = 0

Percent exceedance probability Log (Q)

99 90 50 10 1

0.001 0

0.1

0.2

0.4

0.3

0.1

1,000

B

A

C

10

Q, in cubic feet per second

Density

–4 –2 0 2 4

Effective record

length

Outlier

Outlier

25th percentile

75th percentile

50th percentile

(median)

Figure 2–83. Results are based on 10,000 replicate samples with systematic record, NS=40, and historical record, NH=100,

drawn from a log-Pearson type III distribution with skew, γ=0.0. Regional skew is assumed to be 0.0 with mean square error of

0.15.
138 Evaluation of Recommended Revisions to Bulletin 17B

Discharge, in cubic feet per second

10

0

40

80

120

100

1,000

0.32 2.8 2.8

None (H=0) 1 2 10

● ●

● ● ●

●

● ● ●

14 15

33 24 28

44

58

68 59

B17B/GB

B17B/MGB

EMA/MGB

Q[0.01]

Expected number of historic floods (H)

EXPLANATION

A

Frequency distribution

LP3 distribution G = –0.5

Probability density function

LP3 distribution G = –0.5

Percent exceedance probability Log (Q)

99 90 50 10 1

0.001

0

0.1

0.2

0.5

0.4

0.3

0.1

B C

10

Q, in cubic feet per second

Density

–6 –4 –2 0 2

Effective record

length

Outlier

Outlier

25th percentile

75th percentile

50th percentile

(median)

Figure 2–84. Results are based on 10,000 replicate samples with systematic record, NS=40, and historical record, NH=100,

drawn from a log-Pearson type III distribution with skew, γ=0.5. Regional skew is assumed to be 0.5 with mean square error

of 0.15.
Appendix 2. Graphical Comparisons Between the EMA and B17B at 82 Test Sites 139

Discharge, in cubic feet per second

0

40

80

120

100

1,000

10,000

100,000

0.01 0.18 0.18

None (H=0) 1 2 10

B17B/GB

B17B/MGB

EMA/MGB

Q[0.01]

Expected number of historic floods (H)

EXPLANATION

18 18

28 31 31 38

62 60 60

A

Frequency distribution

LP3 distribution G = 0.5

Probability density function

LP3 distribution G = 0.5

Percent exceedance probability Log (Q)

99 90 50 10 1

0.01

0

0.1

0.2

0.5

0.4

0.3

1

B C

100

Q, in cubic feet per second

Density

–2 0 2 4 6

Effective record

length

Outlier

Outlier

25th percentile

75th percentile

50th percentile

(median)

Figure 2–85. Results are based on 10,000 replicate samples with systematic record, NS=40, and historical record, NH=100,

drawn from a log-Pearson type III distribution with skew, γ=0.5. Regional skew is assumed to be 0.5 with mean square error of

0.15.
140 Evaluation of Recommended Revisions to Bulletin 17B

Discharge, in cubic feet per second

0

40

80

120

100,000

0.01 0.18 0.18

None (H=0) 1 2 10

B17B/GB

B17B/MGB

EMA/MGB

Q[0.01]

Expected number of historic floods (H)

EXPLANATION

33 34 36

50 51 50

81 80

67

A

Frequency distribution

robustness test curve 1

Probability density function

robustness test curve 1

Percent exceedance probability Log (Q)

99 90 50 10 1

5,000

20,000

50,000

0

0.6

0.8

0.2

0.4

1.4

1.2

1.0

B C

Q, in cubic feet per second

Density

3.5 4.0 4.5 5.0 5.5 6.0

Effective record

length

Outlier

Outlier

25th percentile

75th percentile

50th percentile

(median)

Figure 2–86. Results are based on 10,000 replicate samples with systematic record, NS=40, and historical record, NH=100,

drawn from robustness test curve 1.
Appendix 2. Graphical Comparisons Between the EMA and B17B at 82 Test Sites 141

Discharge, in cubic feet per second

0

40

80

120

100,000

0.32 2.8 2.8

None (H=0) 1 2 10

B17B/GB

B17B/MGB

EMA/MGB

Q[0.01]

Expected number of historic floods (H)

EXPLANATION

● ● ●

● ● ●

● ●

A

Frequency distribution

robustness test curve 2

Probability density function

robustness test curve 2

Percent exceedance probability Log (Q)

99 90 50 10 1

5,000

20,000

50,000

0

0.6

0.8

0.2

0.4

1.4

1.2

1.0

B C

Q, in cubic feet per second

Density

2.5 3.0 3.5 4.0 4.5 5.0

Effective record

length

●

18 21 52

27 33 65

60 74

87

0 0.02

Outlier

Outlier

25th percentile

75th percentile

50th percentile

(median)

Figure 2–87. Results are based on 10,000 replicate samples with systematic record, NS=40, and historical record, NH=100,

drawn from robustness test curve 2.

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Science Publishing Network, Reston Publishing Service Center

For information concerning this publication, please contact:

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https://water.usgs.gov/
ISSN 2331-1258 (online)

https://doi.org/10.3133/ofr20171064

Cohn and others—Evaluation of Recommended Revisions to Bulletin 17B—Open-File Report 2017–1064