Hydrologic Hazard Curve 

Methods for Dam Safety

15 Years of Progress, 

Development and Applications

John England, Ph.D. , P.E., P.H., Flood Hydrology Technical Specialist
Some Key HHA Concepts

• Hierarchy and Risk Process – Agency Specific

• Probability Estimates and Full Distributions 

needed, with Uncertainty

• PMF and Single (Point) Deterministic Flood 

Estimate No Longer Adequate – more 

information required

• Hydrologic Hazard Curves are the Load Input to 

Risk

– Peak Flow and Volume Frequency Curves

– 1/1,000 AEP to 1/10,000 AEP (typical for failure 

probability)

– less than 1/10,000 AEP extrapolation!

• Hydrographs; Maximum Reservoir Levels

• HHA Methods vary; depend on study level

• Multiple HHA Methods Used and Combined
15-Year History of Estimating 

Hydrologic Hazards for Dam Safety

Pre 1997 Interpolation of the PMF probability (Much debate)

1997 to Present - Method Development/Applications

 Paleoflood Studies

 Stochastic Flood Modeling Studies, Meteorology

June 1997 - Logan Flood Workshop

 Blueprint for the Future – Characterizing Extreme Floods

July 2001 – Flood Hydrology and Paleoflood Cadre

June 2004 – Hydrologic Hazard Research Report

June 2006 – Hydrologic Hazard Guidelines

Ongoing – improvements to HHA tools, data sets, 

applications
Reclamation Extreme Flood Workshop

Logan, Utah June 16-20, 1997

NRC PFHA Workshop Participants

Jery Stedinger, Mel Schaefer

John England, David Bowles
Hydrologic Hazard Curve Principles

Reclamation Flood Workshop

• Do Not Assign AEP to the PMF

• No Single Approach Describing Flood 

Hazards Over the Range of AEP 

Needed

• Greatest Gains From Incorporating 

Regional Precipitation, Streamflow, 

Paleoflood Data

• Honestly Represent Uncertainty

• Research and Development -

Data/Methods

ftp://ftp.usbr.gov/jengland/Dam_Safety/LoganWorkshop.pdf
Development of New Flood Methods 

and Hydrologic Hazard Curves

•Paleoflood Studies

 Bradbury Dam Investigations (1993-1996)

 A.R. Bowman Dam Investigations (1995-1999)

•Stochastic Flood Modeling Studies

 PMF Variability estimates at Bumping Lake Dam, WA (1995-

1997)

 Hydrologic Hazard estimates for Bowman Dam (1996-1998)

 Hydrologic Hazard estimates at Seminoe and Glendo dams 

(1997-2000)

 Many other studies completed 2001 – 2012 and ongoing
Hydrologic Hazard Guidelines

Guidelines Report 

provides details on the 

HHA methods and 

overall framework

Reclamation technical 

reports for specific 

facilities describe 

advances in data and 

methods June 2006 guidelines report

ftp://ftp.usbr.gov/jengland/Dam_Safety/Hydrologic_Hazard_Guidelines_final.pdf
Hydrologic Hazard Guidelines

Methods (as of 2006) developed and used by 

Reclamation for flood loadings

• Substantial Investment in Data, Tools, 

Software, Applications over past 15 

years

• Methods applied on Reclamation, BIA, 

NPS, USACE watersheds

– available in various technical reports

• Multiple Methods used – combine results

• Paleoflood and Stochastic Rainfall-Runoff 

model based methods
Hydrologic Hazard Curve Definition

• A Hydrologic Hazard Curve is defined as a 

graph of peak flow and/or volume (for specified 

duration) versus Annual Exceedance Probability 

(AEP) (< 1 in 10,000 for Reclamation)

• Hydrologic Hazard Curves may also depict 

Maximum Reservoir Elevation versus AEP

• AEP estimates are made for peak flows, runoff 

volumes and reservoir elevations to cover the 

range of values needed for risk-based dam 

safety decision making at specific facility

• Evaluate specific Potential Failure Modes 

(overtopping, gates, spillway chute, etc)
Hydrologic Hazard Curve

Portrays Flood Magnitude: Peak and Volume, and Exceedance 

Probabilities. Full distributions in the range of interest

1.00E+05

1.00E+06

1.00E+07

1.00E+04

1.00E+05

1.00E+06

Volume (acre ft)

Peak Discharge (ft3/s)

Annual Exceedance Probability

 

0.990.95

0.84

0.7

0.5

0.3

0.160.05

0.1

0.01

0.003

0.001

0.0001

1 (10-5)

1 (10-6)

1 (10-8)1 (10-7)

0.025

Peak Discharge

1-Day Volume 

3-Day Volume

5-Day Volume

7-Day Volume

15-Day Volume
Example Extreme Flood Hydrographs
Hydrologic Hazard Reservoir Frequency 

Curve with Uncertainty

evaluate reservoir restriction, Trinity Dam
Hydrologic Hazard Data

Some key sources and types

• Extreme Storm Rainfall

– point gages – NCDC

– Depth-Area Duration storm catalog from USACE, Reclamation, NWS

– MPE and MPR gridded precip (NWS)

• Extreme Flood Data

– USGS stream gages: peaks, hydrographs

– Historical information

– Paleoflood data

Further Details: Panels 3 and 6
Hydrologic Hazard Data

Types, Combinations, Extrapolation

USBR - USU (1999), Swain et al. (2006)

Also in: Australian Rainfall-Runoff Book VI Extreme Floods (2001)
Paleoflood Methods

House et al. (2002) AGU Paleoflood Monograph
South Fork American near Lotus
Hydrologic Hazard Curve Principles

•Data - focus on past (paleoflood) and 

present (recent) data –Future climate projections assessed/used project by project – study 

and decision dependent

•Flood Hazards Estimated using 

Interdisciplinary Teams

•Flood Models, Relationships and Tools 

developed in-house by Reclamation and 

collaborators

•Uncertainty of Estimates is Quantified
HHA Principles: Integrated Teams

HHA requires interdisciplinary load specialist teams:

• Geologists/Geomorphologists – expertise in soils, stratigraphy, paleofloods

• Hydraulic Engineers – 2D river flow modeling for paleofloods

• Meteorologists – storm rainfall data, analyses, temporal and spatial patterns, statistics, extreme precipitation for 

runoff modeling

• Hydrologists and Hydraulic Engineers – flood frequency, flood statistics, rainfall-runoff modeling
HHA Principles: Multiple Methods

Development of Hydrologic Hazard Curves requires multiple methods, typically at least:

• Streamflow-based peak-flow frequency with historical and paleoflood data (EMA, FLDFRQ3)

• Stochastic rainfall-runoff modeling, such as SEFM using Monte-Carlo methods

• Data, information and models on peak flows, 

geomorphology, hydrometeorology, and flood hydrology 

can be integrated

• Because estimation of Hydrologic Hazard Curves 

involves substantial extrapolations, use of multiple 

methods and independent data sets provides more 

reliable results 
HHA Principles

Expand Data and Information in the Hydrologic Hazard analysis and Hydrologic Hazard Curve

• Temporal Information: expand data in time

• Spatial Information: expand data in space

• Causal Information: utilize hydrological understanding of flood-producing factors

• We need to be more deliberate to include each concept, 

and include more information on hydrological processes 

and hydrological reasoning

• extreme flood and storm data representative of extreme 

process we’re trying to predict?

• combine data evidence from each piece to do this

Merz and Bloschl (2008), 

WRR
Principles for Improving estimation with annual 

exceedance probabilities on the order of 10-3 or 

smaller

1. Substitution of space for time (e.g. regional precip 

frequency)

2. Introduction of more ‘structure’ into models 

(e.g. antecedent soil moisture seasonal dependence)

3. Focus of extremes or ‘tails’ as opposed to or 

even to the exclusion of central 

characteristics (e.g. topfitting flood distributions)

Hydrologic Hazard Curves: Extreme 

Flood Probability Estimation Methods

NRC (1988) Estimating Probabilities of 

Extreme Floods
Hydrologic Hazard Methods

Class Method of Analysis and 

Modeling Level of Effort2

Streamflow-based statistics Graphical Flood Frequency Low

Streamflow-based statistics EMA Low/Moderate

Streamflow-based statistics FLDFRQ3 Low/Moderate

Streamflow-based statistics Hydrograph Scaling Low

Rainfall-based statistics and 

Runoff Transfer GRADEX Moderate

Rainfall-based statistics and 

Rainfall-Runoff Australian Rainfall-Runoff Moderate

Rainfall-based statistics and 

Rainfall-Runoff NWS SAC-SMA Moderate

Rainfall-based statistics and 

Rainfall-Runoff SEFM High

Rainfall-based statistics and 

Rainfall-Runoff TREX High

2Low: 10-20 staff days; Moderate: 21-100 staff days; High: more than 100 staff days
Hydrologic Hazard Methods

Method Data Inputs Assumptions

Graphical Flood 

Frequency

peak flow, reconnaissance paleofloods, 

PMF hydrograph

logNormal flood frequency; PMF hydrograph 

represents volume 

EMA peak flow, detailed paleofloods LP3 flood frequency distribution with moments

FLDFRQ3 peak flow, detailed paleofloods various flood frequency distributions with likelihood

Hydrograph Scaling hydrographs and volumes hydrographs represent extreme flood response; 

requires FFA for scaling

GRADEX rainfall gages/regional statistics; 

streamflow volumes

flood frequency same shape as rainfall frequency with 

exponential tail; saturated basin

Australian RainfallRunoffPMP design storm; rainfall frequency; 

watershed parameters

Exceedance Probability of PMP; average watershed 

parameter values; runoff frequency same as 

rainfall frequency

NWS SAC-SMA

Precipitation frequency, 6-hr P,T, soil 

parameters, snow parameters, 

hourly and 6-hr streamflow 

(calibration)

existing RFC calibration acceptable; runoff frequency 

approximated by rainfall frequency; calibrated 

parameters apply to extremes

SEFM

rainfall gages/detailed regional rainfall 

frequency, watershed parameters, 

snowpack, reservoir data

main inputs defined by distributions; unit hydrograph; 

rainfall frequency using GEV/lmoments

TREX regional extreme storm DAD data, 

watershed parameters, snowpack

diffusive wave runoff; stochastic storm transposition 

rainfall frequency
Hydrologic Hazard Methods

Streamflow-Based Statistics

FLDFRQ3 Overview

• At-site peak-flow frequency

• Uses lots of different types of historical and 

paleoflood information, as well as uncertainties 

of each data type 

• Bayesian Maximum Likelihood used for 

parameter estimation, with confidence intervals 

estimated by numerical grid integration

• user can choose a 3-parameter frequency distribution: LP3, P3, GEV, GLO, GPA, GNO

• statistically efficient

references/details in O’Connell (1999); 

O’Connell et al. (2002)


Hydrologic Hazard Methods

Rainfall-Runoff

 construct a space-time extreme rainfall

model (rainfall probability biggest factor) 

 generate several large storms from model 

 model “deterministic” rainfall-runoff 

transformation

 produce approximate probability 

statements for resultant large flood peaks 

and hydrographs.

 can use similar rainfall and runoff tools as 

PMF techniques

after NRC (1988)
Australian Rainfall-Runoff Method

Use ARR rainfall/PMP probability concepts

Customize ARR concepts on spatial/temporal patterns, 

runoff models, loss rates and sensitivity by Reclamation

• Estimate rainfall distribution to 1/100 (NOAA 2) or 

1/1000 (NOAA 14, state studies)

• Assume rainfall distribution from this AEP to PMP using 

ARR shape factors.

• Assign AEP to point PMP from drainage area

• Develop rainfall point to area relationship, temporal 

pattern, and spatial pattern

• Use runoff model (e.g. unit hydrograph) with AEP 

neutral parameters for losses, lag time, antecedent 

floods, initial reservoir level
Australian Rainfall-Runoff

Example 

combining 

L-Moments 

regional 

precip 

frequency 

(Kappa 

distribution) 

with AEP of 

PMP (10-7)
Australian Rainfall-Runoff

Example 

varying 

temporal 

pattern
Australian Rainfall-Runoff

Example 

with HEC-1 

and 

varying:

-loss rate

-lag 

coefficient

-temporal 

pattern

-upper and 

lower 

rainfall 

estimates
Stochastic Event-Based Rainfall-Runoff Model 

(SEFM) Key Elements

• Regional Rainfall Frequency using L-Moments

• Hydrometeorological parameters treated as 

random variables (snowpack , infiltration..)

• Utilize Storm Patterns and Sequence of Storms

• Runoff Computed using HRU Approach with Unit 

Hydrograph

• Perform Monte Carlo Simulations - Frequency 

Analysis on output; examine combinations that 

cause largest floods

Details/Application: Panel 6
SEFM Simulation
Hydrologic Hazard Reservoir Frequency 

Curve with Uncertainty (SEFM)

evaluate reservoir restriction, Trinity Dam, CA

538 ft high (structural height) embankment
Multiple Methods and Weighting

• For detailed IE/CAS and design studies, 

Reclamation uses multiple methods

• Methods typically include:

– peak-flow frequency using EMA or FLDFRQ3 with detailed paleoflood data

– SEFM or equivalent stochastic rainfall-runoff model

• Results are combined and weighted by a team 

of hydrologists

• Weights are subjective and case-specific

• Typical goal is to ensure rainfall-runoff model is 

consistent with field observations, causal 

information, streamflow and paleoflood data
Reclamation HHA Ongoing R&D

• Paleoflood data collection

• Extreme storm data collection

• Gridded spatial and temporal extreme storms - orographics

• Extreme storm ingredients and NWP models (NCAR and 

NOAA-ESRL)

• Physics of extreme storms (WRF) with NOAA-ESRL

• Monte-Carlo reservoir routing

• NWS SAC-SMA stochastic runoff modeling framework

• Gridded SNODAS data assimilation

• NWS-RFS gridded, continuous models (NWS NWRFC, 

NCAR) (also considering NCAR WRF-Hydro)

• Climate change and flood extremes (statistics, rainfall-runoff)
Questions/Comments?

ftp://ftp.usbr.gov/jengland; jengland@usbr.gov

Sacramento

Folsom JFP

Reclamation

USACE

~$1.3B

HHA: 

Paleofloods, 

FLDFRQ3

SEFM

PMF