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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
50000
60000
70000
80000
90000
100000
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 [email protected]
Keil J. Neff, P.E., Ph.D.Hydrologic [email protected]
U.S. Bureau of ReclamationTechnical Service CenterFlood Hydrology & Meteorology
U.S. Nuclear Regulatory CommissionOffice of Nuclear Regulatory Research
Joseph Kanney, [email protected]
mailto:[email protected]:[email protected]:[email protected]
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