FLOOD FREQUENCY ANALYSIS IN THE UNITED STATES: TIME FOR AN UPDATE

1
FLOOD FREQUENCY ANALYSISIN THE UNITED
STATESTIME FOR AN UPDATE

• Veronica Webster Griffis
• March 12, 2009

2
Outline Flood Frequency Analysis in U.S.

• Need for flood frequency analysis
• Development of Bulletin 17B
• Areas of Bulletin 17B to be updated
• Regional skew information
• Historical flood information
• Low Outliers
• Effects of nonstationarity in flood records

3
Flooding in the U.S.

• Large portion of U.S. population, industry, and
  infrastructure in flood prone areas
• Floods cause an average of 140 deaths and cost
  6 billion annually
• Excludes flooding caused by Hurricane Katrina
  which cost 200 billion alone
• 1993 flooding along the Mississippi and Missouri
  Rivers caused 20 billion in damages
• Neglects real costs ? emotional costs
• Over 75 of declared Federal disasters are
  related to floods

4
Guernsey County, Ohio August 2004
http//www.guernseycounty.org/Floods/frances.htm
5
Guernsey County, Ohio August 2004
http//www.guernseycounty.org/Floods/frances.htm
6
Guernsey County, Ohio September 2004
http//www.guernseycounty.org/Floods/frances.htm
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Mid-Atlantic Region June 2006
http//www.nytimes.com/imagepages/2006/06/29/nyreg
ion/20060629_FLOOD_MAP.html
8
Livingston Manor, NY June 2006
http//www.nytimes.com/slideshow/2006/06/28/nyregi
on/20060629_FLOOD_SLIDESHOW_2.html
9
Sidney, NY June 2006
http//www.nytimes.com/slideshow/2006/06/28/nyregi
on/20060629_FLOOD_SLIDESHOW_2.html
10
Rt. 209 Pennsylvania July 2006
http//home.nps.gov/applications/digest/headline.c
fm?typeIncidentsid2681
11
Kingsland, Texas Summer 2007
http//www.kxan.com/Global/Link.asp?L252150
12
Marble Falls, Texas Summer 2007
http//www.kxan.com/Global/Link.asp?L252150
13
Marble Falls, Texas Summer 2007
http//www.kxan.com/Global/Link.asp?L252150
14
Midwest Floods June 2008
http//www.weather.gov/ahps/index.php
15
Waterloo, Iowa June 2008
http//www.usgs.gov/hazards/floods/images.asp?CurP
age1
16
Cedar Rapids, Iowa June 2008
http//www.usgs.gov/hazards/floods/images.asp?CurP
age1
17
Cedar Rapids, Iowa June 2008
http//www.usgs.gov/hazards/floods/images.asp?CurP
age1
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Flood Frequency Analysis

• Engineers cannot stop floods from happening, but
  should seek structural and nonstructural
  strategies to reduce flood risk
• Need to estimate flows for use in
• floodplain management
• design of dams, culverts, bridges and roads
• water management (dam / reservoir operation)
• Need to reduce risk of economic loss,
  environmental damage, and loss of life

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Flood Frequency Analysis

• How can we estimate design flows when we dont
  really know what is happening?
• Randomness
• driving variables (precipitation evaporation)
• hydrologic system (aquifer soil
  characteristics)
• Sampling error (limited data)
• Prediction errors due to imperfect models
• limited knowledge of system properties

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Flood Frequency Analysis

• Flood frequency analysis (FFA) is used to
  estimate large events such as 100-year flood
• Flood flow expected to occur once every 100
  years equivalent to the 99th percentile
• Design flow used in floodplain management and by
  FEMA to define the regulated floodplain
• Estimate using annual maximum flood series
• ?Typically requires extrapolation beyond the data
  (record lengths generally 30 to 40 years)

21
Current set of uniform flood frequency techniques
for U.S. Federal agencies described by Bulletin
17B
22
Bulletin 17B Methods

• Fit log-Pearson type 3 (LP3) distribution to
  annual maximum flood series by fitting Pearson
  type 3 (P3) distribution to logs of flood peaks
  using method of moments (MOM)
• P3 distribution is defined by
• mean µ
• standard deviation s
• skew ?
• Moments computed for the logs of the data using
  traditional estimators

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Frequency Curve

• For annual maximum flood series, create frequency
  curve by fitting probability distribution to data
  to reflect likelihood these data values would
  have been observed
• Use fitted distribution to estimate design events
  (100 year flow)

N 36 years
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Frequency Curve

• Estimation of 100-year event requires
  extrapolation
• To improve estimate
• Increase effective record length using regional
  skew and historical flood information
• Adjust for low outliers

N 36 years
25
Flood Frequency Analysis

• Bulletin 17B describes uniform flood frequency
  techniques for U.S. Federal agencies
• Need for uniform techniques recognized in
  mid-1960s
• development of national flood insurance program
• interaction between levels of government
• Series of updates / revisions published beginning
  with Bulletin 13 (1966)
• last updated to Bulletin 17B (1982)

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Development of Bulletin 17B

• Bulletin 13 published April 1966
• summary of FFA techniques commonly employed by
  Federal agencies
• Congressional mandate in 1966 to
• present a set of techniques for frequency
  analyses that are based on the best of known
  hydrological and statistical procedures
• House Document No. 465, August 1966, p. 22

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Development of Bulletin 17B

• Bulletin 13 published April 1966
• summary of FFA techniques commonly employed by
  Federal agencies
• Congressional mandate August 1966
• Bulletin 15 published December 1967
• recommended use of log-Pearson type 3 (LP3)
  distribution with regional skew information

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Development of Bulletin 17B

• Bulletin 17 published January 1976
• recommendations for handling low outliers,
• use of historical information
• provided regional skew map
• Bulletin 17A published June 1977
• revised method for historical information
• Bulletin 17B published March 1982
• revised method for incorporation of
• regional skew information
• revised test for low outliers

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Bulletin 17B

• This present revision is adopted with the
  knowledge and understanding that review of these
  procedures will continue. When warranted by
  experience and by examination and testing of new
  techniques, other revisions will be published.
• (Bulletin 17B, IACWD, 1982)

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Bulletin 17B

• Bulletin not updated in over 25 years
• despite significant amount of research
• additional 30 years of data for skew map
• better statistical procedures for spatial and
  censored data
• Push by USGS, USBR, and USACE to update Bulletin
  17B
• HFAWG established to develop
• updated guidelines ? Bulletin 17C

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HFAWG Membership/Reporting Structure

• HFAWG Members
• Representatives of government agencies - FEMA,
  USGS, USBR, USACE, NWS, FHA
• Faculty from universities throughout U.S.

Congress, Office of Management and Budget
Department of the Interior
U.S. Geological Survey
Advisory Committee on Water Information
Subcommittee on Hydrology
Hydrologic Frequency Analysis Work Group (HFAWG)
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Bulletin 17B

• Major areas to be updated
• estimation of regional skew
• use of historical information
• low outlier adjustments
• Also need to consider possible nonstationarity in
  flood records

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Use of Regional Skew Information

• Sample skew is sensitive to extreme events
• estimate of third moment ?x (population skew)
• most inaccurate moment estimate
• Use regional skew information to improve accuracy
  of skewness estimator, and thus quantile (flood
  risk) estimators

34
Bulletin 17B Weighted Skew

• Regional skew information is used to improve
  accuracy of skewness estimator by weighting
• -- sample skew (Gs)
• with
• -- regional skew (Gg)

Mean Square Error MSE Variance Bias2
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Regional Skew Estimation

• Obtain regional skew Gg
• from Bulletins skew map (published in 1976)
• -0.5 Gg 0.6
• Map SE 0.55
• ? MSEGg 0.302
• (Effective record length of 17 years)

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Regional Skew Estimation

• Tasker Stedinger (1986)
• MSE mostly sampling error
• Separate sampling error and model error using
  weighted least squares (WLS) regression
• In Illinois, MSEGg 0.100
• (Effective record length 60 years)
• Values on order of 0.01 to 0.10 obtained in
  several other studies using WLS and
• generalized least squares (GLS) regression

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Monte Carlo Analysis

• MC study demonstrated value of regional skew
  information (Griffis et al., 2004)
• Data generated from P3 populations with
• N 10, 25, 50, 100
• Gg -1.0 to 1.0
• MSEGg 0.010, 0.100, 0.302
• 5,000 replicates were generated for all
  combinations of N and Gg and MSEGg

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Method of Moments Estimators

• Method 1 MOMn
• No regional skew information
• Method 2 MOM
• Sample skew is combined with a regional skew to
  obtain weighted skew as recommended by Bulletin
  17B
• Performance Measure
• Mean square error of 99th quantile estimates
• ? Smaller MSE indicated improved performance

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MSE of 99th Quantile Estimates (Gg0)
MSE(Gg) 0.100
MSE(Gg) 0.010
MSE(Gg) 0.302
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Regional Skew Estimation

• More accurate estimators of regional skew can be
  obtained using WLS or GLS regression
• Use of more accurate skewness estimators shown to
  yield more accurate estimates of design events
• HFAWG recommendation
• Use GLS regression procedures to
• develop new skew map

41
Bulletin 17B

• Major areas to be updated
• estimation of regional skew
• use of historical information
• low outlier adjustments
• Also need to consider possible nonstationarity in
  flood records

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Historical and Gauged Record

Threshold for h-year historical record
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Historic Flood Information Wheeling, Ohio 1907
Flood
...The worst flood since the memorable 1884
flood now holds sway in the Ohio valley. A new
high water record has been established in
Pittsburg, and though the mark of '84 was not
passed at Wheeling the second flood stage to that
destructive water will be attained here this
morning. .. --The Intelligencer, March 15,
1907, p. 1
44
Paleoflood Data
(Source Jarrett 1991, modified from Baker 1987)
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Expected Moments Algorithm (EMA)

• Proposed by Cohn et al. (1997) for incorporation
  of historical information into flood frequency
  analyses with LP3 distribution
• Shown to be as efficient as MLEs and more
  efficient than Bulletin 17B method
• HFAWG recommendation
• Use EMA in place of Bulletin 17B method to
  incorporate historical flood information

46
Bulletin 17B

• Major areas to be updated
• estimation of regional skew
• use of historical information
• low outlier adjustments
• Also need to consider possible nonstationarity in
  flood records

47
Expected Moments Algorithm (EMA)

• Proposed by Griffis et al. (2004) as an
  alternative to Bulletin 17Bs Conditional
  Probability Adjustment (CPA) for low outliers
• Extended EMA for use with low outliers and to
  incorporate regional skew information
• Performed MC study to illustrate likely value of
  low outlier adjustment procedures in real flood
  records using contaminated samples

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From Bulletin 17B
49
Contaminated Samples

• Data generated from P3 populations for sample
  sizes N 25, 50, 100
• Smallest k observations in each sample
  contaminated in log space by subtracting log(5)
  equivalent to dividing by factor of 5 in real
  space
• k 1 in N 25
• k 2 in N 50
• k 3 in N 100

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MSE of 99th Quantile Estimates (Gg0,
MSEGg0.100)
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MSE of 99th Quantile Estimates (Gg0,
MSEGg0.100)

• Significant reduction in MSE when low outlier
• adjustments are employed
• Minor differences in performance of EMA and CPA

52
Expected Moments Algorithm

• ? Minor difference in performance of EMA and CPA
  for low outlier adjustments
• BUT -- EMA provides simple and consistent
  framework to simultaneously
• (a) incorporate historical flood information
• (b) incorporate regional skew information
• (c) adjust for low outliers
• whereas Bulletin 17B requires three separate
  procedures

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Recommendations for Change
54
Recommendations

• After 25 years, it is time to update Bulletin 17B
• New techniques are now available that correct
  known problems with Bulletin 17B
• GLS regional regression should be used for
  computation of regional skew and its precision
• EMA should be used to simultaneously
• (a) incorporate historical flood information
• (b) incorporate regional skew information
• (c) adjust for low outliers

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Bulletin 17B

• Major areas to be updated
• estimation of regional skew
• use of historical information
• low outlier adjustments
• Also need to consider possible nonstationarity in
  flood records

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Problem

• Bulletin 17B procedures assume annual maximum
  flood series are stationary
• Distribution is not significantly affected by
  climatic trends or longer-term cycles
• Historical flood behavior is representative of
  future events
• Is assumption of stationarity valid?
• Trends in flood series?
• Possible impacts from climate variability?

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Problem

• Climatic changes are evident in streamflow
• Several studies have identified trends in U.S.
  streamflow records
• Links have been identified between average
  annual/monthly streamflow and oceanic-atmospheric
  patterns such as
• Pacific Decadal Oscillation (PDO)
• Northern Atlantic Oscillation (NAO)
• El Niño-Southern Oscillation (ENSO)

58
Trend in Flood Flows at Momence, IL (lt0.1
Significance Level)
Source Kashelikar Griffis (2008) EWRI
Proceedings
59
396 Unimpaired Gauging Stationswith period of
record 1941 - 2005
Source Kashelikar Griffis (2008) EWRI
Proceedings
60
Trends in Annual Maximum Flood Series(5
significance level)
Upward Trend Downward Trend
Source Kashelikar Griffis (2008) EWRI
Proceedings
61
Significant Relationships Between ENSO Indices
and Annual Maximum Flood Series (5-month lag)

• 5 significance level
• 10 significance level

Source Ashwini Kashelikar, Masters Student
62
Significant Relationships Between PDO Indices and
Annual Maximum Flood Series (1-month lag)

• 5 significance level
• 10 significance level

Source Ashwini Kashelikar, Masters Student
63
Significant Relationships Between NAO Indices and
Annual Maximum Flood Series (7-month lag)

• 5 significance level
• 10 significance level

Source Ashwini Kashelikar, Masters Student
64
Modification of Bulletin 17B

• Proposal Relate nonstationarity in flood series
  to climate indices representing patterns such as
  PDO, NAO, or ENSO
• Goals
• Produce forecasts of flood risk which reflect
  intensity/phase of ENSO, PDO, etc.
• Improve one-year ahead (or short-term) forecasts
  of flood risk

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Incorporation of ENSO Effects

• Method Forecast flood risk as function of
  forecasted climate index (i.e. SST anomaly)
• Incorporate effects of ENSO by relating P3
  parameters to 3-month average of SST anomalies
  observed each year
• Consider three models of logs of flood peaks
• 1. Xt P3 µ(SST), s(SST), ?(SST)
• 2. Xt P3 µ(SST), s(SST), ?
• 3. Xt P3 µ(SST), s, ?

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Incorporation of ENSO Effects

• A model for the mean (of logs) is
• µt mean computed using all floods in the
• observed record available through time t
• a, ß regression parameters
• ct climate index (SST anomaly)
• observed in time t
• et independent model error

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Incorporation of ENSO Effects

• One-year ahead forecast of the mean
• µt1 a b ct1
• ct1 forecasted value of SST anomaly
• Forecast flood risk for the next year using
  updated (forecasted) mean
• Requires estimation of only two additional
  parameters beyond Bulletin 17B methods
• Flood risk estimate will reflect phase and
  intensity of ENSO/PDO event

68
One-Year Ahead Forecast of Flood Risk(New River,
VA)
Forecasted SST 0.23 (Neutral ENSO
event) Difference for 100-year event 6,000 cfs
Source Ashwini Kashelikar, Masters Student
69
One-Year Ahead Forecast of Flood Risk(New River,
VA)
Forecasted SST 1.2 (Strong El Nino
Event) Difference for 100-year event 13,400 cfs
Source Ashwini Kashelikar, Masters Student
70
Incorporation of ENSO Effects

• Effects of short-term climatic cycles (i.e. ENSO)
  are averaged into Bulletin 17B estimates
• If intensity/frequency of events does not change
  over time, flood frequency analysis naturally
  accounts for variability associated with these
  events
• Proposed modification to incorporate ENSO effects
  can yield improved year-specific forecasts for
  reservoir operation and management
• Flood risk estimate related to phase and
  intensity of ENSO event

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The Future of Bulletin 17B

• HFAWG currently working to update flood frequency
  guidelines with intent to publish Bulletin 17C
• New guidelines will include updated procedures
  for
• Estimation and incorporation of regional skew
• Incorporation of historical flood information
• Low outlier adjustments
• Bulletin 17B guidelines should also be adapted to
  deal with nonstationarity in flood records

72
The Future of Bulletin 17B

• Revisions of guidelines and publication of
• Bulletin 17C slow to be realized
• Need to thoroughly evaluate current procedures
  and proposed modifications
• Need approval from various levels of government
  and government agencies
• Number of consequences beyond future flood
  control and water management projects
• ? Revisions of FEMA floodplain hazard maps and
  changes related to National Flood Insurance
  Program