Probabilistic Flood Hazard Assessment Workshop

Sponsored by the Nuclear Regulatory Commission

Rockville, Maryland

Overview and History of Flood Frequency in the United States

January 29-31, 2013

Will Thomas

Michael Baker, Jr.
Objective of Presentation

 Provide an overview and brief history of 

statistical flood frequency analysis in the US

 Describe the evolution of statistical 

procedures for analyzing gaged streams with 

observed flood data (at-site analysis)
Beginnings of Flood Frequency in US

 Statistical flood frequency analysis started in US 

with Fuller’s (1914) paper on Flood Flows, ASCE 

Transactions Volume 77, Paper No. 1293:

 used plotting positions to get at-site estimates

 developed first equation relating discharge for a given 

return period to drainage area (regional analysis)

 in discussion of Fuller’s (1914) paper, Hazen presented 

for the first time the concept of probability paper and 

argued for the use of the lognormal distribution as a 

model for peak flows
Flood Frequency - The Early Years

 In 1921, Hazen suggested the use of a three 

parameter distribution that included skew and 

developed an approach for adjusting the logarithms 

of peak flows for skew

 In 1924, Foster introduced the Pearson system of 

frequency distributions and recommended use of 

the Pearson Type III for flood flows

 In 1930, Hazen documented in Flood Flows

 his plotting position (2m-1/2N) where m=1 for the 

largest event and N is the sample size and

 his method for adjusting for skew 
World Engineering Congress in Japan (1929)

 Allen Hazen attended the 

World Engineering 

Congress in Tokyo, Japan in 

the fall of 1929 as a 

representative of ASCE. 

See picture of Mr. and Mrs. 

Hazen on the steamer 

(Hazen’s scrapbook of trip). 

He passed away in 1930. 
Flood Frequency - The Early Years

 In 1943, Beard developed the median plotting 

position which is (m-0.30/N+0.4), where m=1 for 

the largest event and N is the sample size

 In the 1940s, the USGS adopted the Weibull

plotting position (m/N+1) and plotted annual 

peak flows on Gumbel probability paper 

(Dalrymple, 1960; Benson, 1962)

 For the 1940s and 1950s, plotting positions were 

the prevalent approach for at-site frequency 

analysis
Flood Frequency - The Early Years

 Leo Beard contributed significantly to statistical 

hydrology in the early years and established 

procedures used by USACE as evidenced by:

 Beard (1952) – Statistical Methods in Hydrology

 Beard (1962 – Statistical Methods in Hydrology

 Beard (1962) described the application of the 

Pearson Type III distribution to the logarithms of 

annual peak flows, implying USACE was using the 

LPIII method by 1962
Bulletin 13

 Bulletin 13:

 April 1966 - First Federal 

interagency effort to 

describe procedures for 

flood frequency analysis 

by Subcommittee on 

Hydrology, Inter-Agency 

Committee on Water 

Resources – no testing or 

evaluation of procedures
House Document No. 465

 House Document No. 465 (August 1966), passed by the 

89th Congress, recommended the establishment of a 

panel of the Hydrology Committee of the U.S. Water 

Resources Council (WRC) to “present a set of techniques 

for frequency analysis that are based on the best of 

known hydrological and statistical procedures.”

 House Document No. 465 “A Unified National Program for 

Managing Flood Losses” - motivation for uniform flood 

frequency procedures was to reduce flood losses 

(recommended national flood insurance program that 

was established in 1968).
Bulletin 15

 Bulletin 15: 

Published in December 

1967 by the U.S. Water 

Resources Council (WRC), 

recommended fitting the 

Pearson Type III 

distribution to the 

logarithms of annual peak 

flows by the method of 

moments (LPIII). Testing 

of 6 different methods at 

10 long-term gaging 

stations (details provided 

by Benson (1968)).
Bulletin 17

 Bulletin 17:

Published in March 1976 

by WRC, continued use of 

LPIII, included the use of 

low-outlier test, 

generalized skew, and 

adjustment for historic 

information. 

 Testing by Beard (1974) of 

8 different methods at 300 

gaging stations indicated 

that LPIII with regional 

skew was best method. 
Bulletin 17A

 Bulletin 17A:

Published in June 1977 by WRC, clarified that the 

adjustment for historic data was to occur before the 

weighting of station and generalized skew. A few 

editorial changes were also made.
Bulletin 17B

 Bulletin 17B:

Published in September 

1981 by WRC, included 

revised guidelines for 

(Thomas, 1985): 

 Estimating generalized 

skew 

 Weighting of generalized 

and station skew

 Detection of low- and highoutliers

 Application of conditional 

probability adjustment
WRC Transition to IACWD

 In 1982 fiscal year - Hydrology Committee of WRC became 

Hydrology Subcommittee of the Interagency Advisory 

Committee on Water Data (IACWD)

 IACWD was comprised of Federal agencies involved in 

water resources analyses

 WRC was terminated on October 31, 1982

 Bulletin 17B - Re-issued in March 1982 by IACWD, 

corrected typographical errors in 1981 version, no 

technical changes 
Existing Guidelines - Bulletin 17B

Published in March 1982, 

includes guidelines for:

 Fitting the Pearson Type III 

distribution to logs of annual 

peak flows

 Estimating generalized skew 

 Weighting generalized skew with 

station skew

 Low- and high-outlier detection 

tests

 Conditional probability 

adjustment for low outliers

 Adjustments for historical flood 

information
Transition of Procedures

 The early years of flood frequency analysis 

focused on plotting positions – Hazen, Median 

and Weibull

 The use of the Pearson Type III distribution and 

logarithms of annual peak flows was prevalent 

before Bulletin 15 in 1967

 The emphasis starting with Bulletin 15 was on a 

uniform and consistent approach for all Federal 

agencies to reduce flood losses

 The effort leading to the development of Bulletin 

17B, existing guidelines, was by Federal agencies
 Established December 1999 under the Subcommittee on 

Hydrology of the Advisory Committee on Water 

Information 

 Representatives from Federal agencies, private 

consultants, academia, water management agencies

 Minutes of meetings from January 2000 to September 

2012 are on the following web site:

 http://acwi.gov/hydrology/Frequency/ 

 Bulletin 17B is located at:

 http://water.usgs.gov/osw/bulletin17b/bulletin_17B.html

Hydrologic Frequency Analysis WG
HFAWG Scope 

 The overall goal of the HFAWG is to recommend 

procedures to increase the usefulness of the 

current guidelines (Bulletin 17B)

 HFAWG plans are confined to research that can be 

accomplished with limited resources

 Maintain the “spirit” of Bulletin 17B through fitting 

the Pearson Type III distribution to the logs of 

annual peak flows with the method of moments
HFAWG Current Activities

 Evaluate the Expected Moments Algorithm (EMA) 

for analyzing data sets with historical information

 Evaluate EMA for analyzing data sets with low 

outliers and zero flows

 Describe improved procedures for estimating 

generalized skew

 Develop improved procedures for defining 

confidence limits
HFAWG Current Activities

 Considerable progress has been achieved in 2012 

with testing EMA versus current Bulletin 17B 

procedures

 A March 2012 report on the HFAWG web site 

(http://acwi.gov/hydrology/Frequency) describes this 

testing process

 It is anticipated that a revised draft of Bulletin 

17B will be developed in 2013
Papers on Evolution of Flood Frequency

 Thomas, W.O., Jr., 1985, A Uniform Technique For Flood 

Frequency Analysis: ASCE Journal of Water Resources 

Planning and Management, Vol. 111. No. 3, 321-337.

 Griffis, V.W., and Stedinger, J.R., 2007, Evolution of Flood 

Frequency Analysis with Bulletin 17B: ASCE Journal of 

Hydrologic Engineering, Vol. 12, No. 3, 283-297.

 Dawdy, D.R., Griffis, V.W., and Gupta, V.K., 2012, 

Regional Flood-Frequency Analysis: How We Got Here and 

Where We Are Going: ASCE Journal of Hydrologic 

Engineering, Vol. 17, 953-959.