Extending Flood Frequency Curves Beyond Current Consensus Limits

Joseph Wright, Keil NeffFlood Hydrology and Meteorology GroupTechnical Service Center

IntroductionThis project provides information the NRC can use to

develop guidance for extending frequency analysis methods beyond current consensus limits for both rainfall and riverine flooding applications.

The focus is describing methods used by Reclamation to estimate flood loadings, which have been developed over the past 20 years. Case studies exemplifying these approaches are also included.

Uncertainty characterization and quantification is also a focus of this project.

Flood Loadings to Support Reclamation Dam Safety Risk Activities

From a hydrologic perspective, risk estimates require an evaluation of a full range of hydrologic loading conditions and possible failure mechanisms tied to consequences of failure.

Hydrologic hazard curves combine peak flow, water surface elevation, duration thresholds, and volume probability relationships plotted with respect to their AEPs.

Flood loadings and associated flow and stage frequency hydrographs are used to assess the risk of potential hydrologic-related failure modes.

Reclamation primarily focuses on medium to large catchments in the Western U.S.

99 95 80 60 40 20 5 1 0.1 1E-3100

1,000

10,000

Historic Event2100 - 2500 ft3/s580 - 690 years

Observation EMA Model Results 90% Confidence Interval Paleoflood Event

Disc

harg

e (ft3

/s)

AEP (%)

Non-Exceedance3800 - 5000 ft3/s1020 - 1240 years

Flood Frequency Extrapolation

Credible ExtrapolationType of Analysis Typical Range Range (Best)

At-Site Stream Gage 1 in 100 1 in 200

Regional Stream Gages 1 in 500 1 in 1,000

At-Site Stream Gage combined with Paleoflood Data

1 in 4,000 1 in 10,000

Regional Precipitation Data 1 in 2,000 1 in 10,000

Regional Streamflow and Regional Paleoflood Data

1 in 15,000 1 in 40,000

Combinations of regional Datasets and Extrapolation

1 in 40,000 1 in 100,000

Reclamation & Utah State University (1999), Reclamation (2006)

Level of EffortThe goal of any hydrologic analysis is to provide hydrologic information to

the necessary level to make effective dam safety decisions. The available data, possible analysis techniques, resources available, and needs of the decision influence the selection of method(s) used.

Method Level of Effort Benefits LimitationsGraphical Flood

FrequencyLow

(CR, IE, CAS, FD)Conservative, incorporates paleoflood

informationEstimates far beyond credible

extrapolation, conservative

EMA/FLDFRQ3 Low(CR, IE, CAS, FD)Better estimate of uncertainty,

incorporates paleoflood informationEstimates often extended beyond

credible extrapolation

Australian Rainfall-Runoff

Low(CR, IE)

Rarer events, very conservative (pragmatic)

Primarily intended for largely deterministic design use, very conservative

GRADEX Moderate(CR, IE) Rarer events, conservativeAssumption of all rainfall to runoff,

little physically-based modeling

Regional Precipitation Frequency

Moderate(IE, CAS, FD)

Better estimated of uncertainty, still conservative

Improved estimate of precipitation frequency, limited by AEP neutrality

Stochastic Rainfall-Runoff Modeling

High(IE, CAS, FD)

Currently the best estimate of uncertainty, uses information from statistical frequency methods, physical understanding of driving factors/ processes

Extremely rare extrapolation is still uncertain and full range of aleatory variability and epistemic uncertainty is not understood, difficulties calibrating to extreme events

Data SourcesThe sources of information used for flood hazard analyses

include streamflow, precipitation, and paleoflood data.

Data Source Level of Effort(Cost) Analyses

Public Data Sources - Precipitation (e.g. NOAA, PRISM, NCEI)

Low(generally free)

Precipitation frequency (L-moments, Bayesian); storm templates

Public Data Sources – Gaging Stations (e.g USGS, Reclamation)

Low(generally free)

EMA, FLDFRQ3, rainfall-runoff modeling, graphical approach

Public Data Sources – GIS (e.g USGS, NRCS, states)

Low(generally free) Rainfall runoff-modeling

Regional Paleoflood Information Moderate(generally free)EMA, FLDFRQ3, graphical approach

Site-Specific Paleoflood Stratigraphy Moderate(moderate)EMA, FLDFRQ3, graphical approach

Detailed Paleoflood Information High (high) EMA, FLDFRQ3, graphical approach

LiDAR Collection High (high) Paleoflood information, H&H modeling

Incorporating Paleoflood Data

-1200-1000-800 -600 -400 -200 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 20100

2,000

4,000

6,000

2100 to 2500 ft3/s occurred during the past 580 - 690 years

Paleohydrologic Non-Exceedance Bound

Years Before Present

Peak

Disc

harg

e (ft3

/s)

Water Year

Paleoflood data can be combined with stream gage data to extend the time series well before the historic record. This allowsfor credible extrapolationto rare events having anAEP less than .01 %

Low Level AnalysesReclamation will typically spend 5-10 days for some preliminary analyses (CRs, feasibility

level, etc). This often includes EMA with regional paleoflood information. ARR (frequency PMF) is often used to deal conservatively estimate beyond credible extrapolation.

99 95 80 60 40 20 5 1 0.1 1E-3100

1,000

10,000

Historic Event2100 - 2500 ft3/s580 - 690 years

Observation EMA Model Results 90% Confidence Interval Paleoflood Event

Disc

harg

e (ft3

/s)

AEP (%)

Non-Exceedance3800 - 5000 ft3/s1020 - 1240 years

Moderate Level Analyses15-45 day efforts are often applied to Issue Evaluation, Corrective Action, and Final

Design studies (and some high level Comprehensive Reviews). 99

.5 99 98 95 90 80 70 60 50 40 30 20 10 5 2 1 0.5

0.1

0.01

1E-3

1E-4

1E-5

1E-6

10

100

1000

10000

Two non-exceedance boundsQ=7,070-14,120 ft3/sn = 9,000-11,000 yearsQ=3,530-7,060 ft3/sn = 950-1,400 years

May 1957 1.00 in. initial loss and 0.135 in/hr infiltration May 1985 2.35 in. initial loss and 0.180 in/hr infiltration

LP-III EMA Model 90% Confidence Interval Observed and Estimated PeaksP

eak

Dis

char

ge (f

t3 /s)

Annual Exceedance Probability (%)

One paleofloodQ=3,000-6,000 ft3/swith a time context of 125 - 355 years

High Level AnalysesWhen the hydrologic risk at a facility may require expensive mitigation (i.e. operations,

mechanical, construction risk reduction measure alternatives), studies often require extensive time, effort, and cost to produce flood estimates.

5 2 1 0.5 0.1 0.01 1E-3 1E-4 1E-5

10000

100000

1000000

SEFM Median SEFM 90% Confidence

1957 IDF = 212,000 ft3/s

1983 PMF = 369,000 ft3/s

Peak

Disc

harg

e (ft

3 /s)

% AEP

1988 PMF = 574,000 ft3/s

Case Study – Friant Dam HHAThis study provided a detailed probabilistic flood loading analysis used to quantify risks

associated with various failure modes. This was accomplished by developing flood frequency hydrographs using a stochastic rainfall-runoff model (SEFM).

• Structural Height of 319 feet• One 100x18 ft Drum Gate• Two 100x18 ft Obermeyer Gates• Spillway Capacity is 83,000 ft3/s• Combined Outlet Work Capacity is

17,000 ft3/s

• Controls 1,660 ft3

• 11 Upstream facilities (six of which are large dams)

Stochastic Rainfall-Runoff Model

1. Develop physical based 1-dimensional rainfall-runoff using hydrologic runoff units (HRU’s)

2. Estimate a precipitation frequency curve using the L-Moments method of regional statistics

3. Randomly sample the frequency precipitation curve as well as a storm pattern to determine an annual maximum storm event

4. Randomly determine the initial model conditions5. Repeat steps 3 and 4 to develop a simulate time-series of maximum

flood events6. Fit a statistical distribution to the time series of annual maximum

events

Regional Precipitation Analysis

Spatial and Temporal Storm PatternsStorm 72-hr Precipitation Use

November 13-22, 1950 10.58 Calibration/ProductionDecember 18-27, 1955 15.09 Calibration/ProductionFebruary 3-17, 1962 9.56 ProductionJanuary 29 - February 7, 1963 14.91 Calibration/ProductionDecember 17-31, 1964 5.69 ProductionDecember 1-11, 1966 9.56 ProductionJanuary 18-22, 1969 10.86 ProductionJanuary 23-29, 1969 7.56 ProductionSeptember 1-10, 1972 1.67 Calibration September 1-10, 1978 3.63 Calibration/ProductionJanuary 9-19, 1980 8.97 ProductionSepetember 23 - October 2, 1982 4.28 Calibration/ProductionFebruary 12-21, 1986 8.78 ProductionMarch 8-18, 1995 9.84 ProductionDec 29, 1996 - Jan 7, 1997 7.29 Calibration/ProductionNovember 6-16, 2002 7.15 Calibration/ProductionDec 26, 2005 - Jan 9, 2006 7.88 ProductionDecember 15-24, 2010 11.2 Production

Stochastic Storm Template

0

0.2

0.4

0.6

0.8

1

1.2

0 20 40 60 80 100 120 140 160 180Per

cent

Pre

cipi

tatio

n

Time (hr)

Cummulative Precip

-12000

-10000

-8000

-6000

-4000

-2000

0

2000

-30

-25

-20

-15

-10

-5

0

5

0 50 100 150 200 250 300 350

Free

ze L

evel

Inde

x

Tem

pera

ture

Inde

x

Time (hr)

Temperature and Freeze Level Index

1000 mb Temperature Index

Freeze Level Index

Physical Based Model8 soil zones5 MAP zones9 elevation zones360 HRUs per sub-basin8,280 HRU’s total!

Calibration8 Historic Flood Events were used in CalibrationFriant is a mixed population (rain and snowmelt)

system – the maximum annual rainfall didn’t always yield the maximum annual flood

Fall events were used to calibrate high elevation basins because they represented snow-free ground

Runoff calibration was performed from the upstream basins to the downstream basins

Adjustments were made to the routing parameters and freeze level offsets to better fit the peak-discharge frequency

Calibration

0

10000

20000

30000

40000

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90000

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0 100 200 300

Dis

char

ge (f

t3/s

)

Time (hr)

Recorded

Simulated

05000

100001500020000250003000035000400004500050000

12/29/1996 0:0012/30/1996 0:0012/31/1996 0:001/1/1997 0:001/2/1997 0:001/3/1997 0:001/4/1997 0:001/5/1997 0:001/6/1997 0:001/7/1997 0:001/8/1997 0:001/9/1997 0:001/10/1997 0:001/11/1997 0:001/12/1997 0:00

Dis

char

ge (c

fs)

Date

Recorded

Simulated

Peak-Discharge Frequency Calibration

50 40 30 20 10 5 2 1 0.5 0.1 0.01 1E-3 1E-4 1E-5 1E-6

10000

100000

EMA Median Estimate EMA 90% Confidence Paleoflood SEFM Calibration

Peak

Disc

harg

e (ft

3 /s)

% AEP

Peak-Discharge Frequency

50 40 30 20 10 5 2 1 0.5 0.1 0.01 1E-3 1E-4 1E-5 1E-6 1E-7 1E-8

10000

100000

1000000

1957 IDF = 212,000 ft3/s

1983 PMF = 369,000 ft3/s

R4560 R45600 R456000 R4560000

Peak

Disc

harg

e (ft

3/s)

% AEP

1988 PMF = 574,000 ft3/s

Overall Probability Fit

Friant Inflow Hydrographs that result in 1,000-yr RWSEL

0

20000

40000

60000

80000

100000

120000

140000

160000

180000

200000

0 50 100 150 200 250 300 350

Dis

char

ge (f

t3/s

)

Time (hr)

Rank AEP (%) Simulation Number

Init WSEL

(ft)

Peak Discharge

(ft3/s)

Total Volume (ac-ft)

Peak Discharge

Rank

Total Volume

Rank

454 0.0995 5735 531.2 153,396 684,560 644 399

455 0.0997 7021 550.4 172,089 502,242 424 1178

456 0.0999 2540 504.1 142,907 730,048 814 306

457 0.1001 659 563.3 160,704 460,092 540 1531

458 0.1003 3094 485.0 175,883 711,248 387 338

459 0.1006 5992 557.6 135,378 673,066 980 428

460 0.1008 10596 537.0 138,460 661,433 919 454

Friant Hydrologic Loading

5 2 1 0.5 0.1 0.01 0.001 1E-4 1E-5

560

580

600

90% LHS Uncertainty Median Maximum WSEL

Elev

atio

n (ft

)

% AEP

Top of Parapet Wall

Joseph M Wright, P.E.Hydraulic Engineer303-445-2463jmwright@usbr.gov

Keil J. Neff, P.E., Ph.D.Hydrologic Engineer303-445-2541kneff@usbr.gov

U.S. Bureau of ReclamationTechnical Service CenterFlood Hydrology & Meteorology

U.S. Nuclear Regulatory CommissionOffice of Nuclear Regulatory Research

Joseph Kanney, Ph.D.Hydrologist301-415-1920joseph.kanney@nrc.gov

mailto:jmwright@usbr.govmailto:kneff@usbr.govmailto:joseph.kanney@nrc.gov

Slide Number 1IntroductionFlood Loadings to Support Reclamation Dam Safety Risk ActivitiesFlood Frequency ExtrapolationCredible ExtrapolationLevel of EffortData SourcesIncorporating Paleoflood DataLow Level AnalysesModerate Level AnalysesHigh Level AnalysesCase Study – Friant Dam HHAStochastic Rainfall-Runoff Model Regional Precipitation AnalysisSpatial and Temporal Storm PatternsStochastic Storm TemplatePhysical Based ModelCalibrationCalibrationPeak-Discharge Frequency CalibrationPeak-Discharge FrequencyFriant Inflow Hydrographs that result in 1,000-yr RWSELFriant Hydrologic LoadingSlide Number 24