U.S. Department of Interior
Bureau of Reclamation March 2010
Design Standards No. 14
Appurtenant Structures for Dams
(Spillway and Outlet Works)
Design Standards
Chapter 1: Introduction
Draft: Phase 3 (Public and Stakeholders Review)
MISSION STATEMENTS
The mission of the Department of the Interior is to protect and provide
access to our Nation's natural and cultural heritage and honor our trust
responsibilities to Indian tribes and our commitments to island
communities.
The mission of the Bureau of Reclamation is to manage, develop, and
protect water and related resources in an environmentally and
economically sound manner in the interest of the American public.
Design Standards Signature Sheet
Design Standards No. 14
Appurtenant Structures for Dams
(Spillways and Outlet Works)
Design Standards
DS-14(1)-2: Draft: Phase 3 (Public and Stakeholders Review)
March 2010
Chapter 1: Introduction
Approved:
Deputy Commissioner, Operations Date
DS-14(1)-2 March 2010 1-iii
Chapter Signature Sheet
Bureau of Reclamation
Technical Service Center
Design Standards No. 14
Appurtenant Structures for
Dams (Spillways and Outlet
Works) Design Standards
Chapter 1: Introduction
DS-14(1)-2:1 Draft: Phase 3 (Public and Stakeholders Review)
March 2010
Design Standard 14 is a new document. Chapter 1 of this Design Standard was
developed to provide:
An overview of how the Bureau of Reclamation analyzes/designs
spillways and outlet works appurtenant for dams and/or dikes.
An outline of the following chapters for this design standard that provides
details for spillway and outlet works analyses/designs.
A list of key technical references used for each major task involved with
spillway and outlet works analyses/designs.
1 DS-14(1)-2 refers to Design Standard No. 14, chapter 1, revision 2.
DS-14(1)-2 March 2010 1-v
Contents
Page
Chapter 1: Introduction ......................................................................... 1-1
1.1 Purpose .......................................................................................... 1-1
1.2 Application of Design Standards .................................................. 1-1
1.3 Deviations and Proposed Revisions .............................................. 1-1
1.4 Scope ............................................................................................. 1-2
1.5 Definitions........................................................................................... 1-2
1.5.1 Spillway ............................................................................... 1-2
1.5.1.1 Service Spillway .......................................................... 1-3
1.5.1.2 Auxiliary Spillway ....................................................... 1-3
1.5.1.3 Emergency Spillway .................................................... 1-3
1.5.2 Outlet Works ........................................................................ 1-3
1.6 Configurations............................................................................... 1-4
1.6.1 Spillway ............................................................................... 1-4
1.6.2 Outlet Works ........................................................................ 1-5
1.7 Design Procedures/Considerations ............................................... 1-7
1.7.1 Spillway Design/Analysis .................................................... 1-7
1.7.1.1 Location, Type and Size. ............................................. 1-7
1.7.1.2 Hydraulic Analysis/Design ......................................... 1-8
1.7.1.3 Foundation Analysis/Design ....................................... 1-10
1.7.1.4 Structural Analysis/Design ......................................... 1-11
1.7.1.5 Mechanical/Electrical Design ..................................... 1-13
1.7.1.6 Risk Analysis (only for significant and high hazard
dams/dikes) .................................................................... 1-15
1.7.2 Outlet Works Design/Analysis ............................................ 1-17
1.7.2.1 Location, Type and Size. ............................................. 1-17
1.7.2.2 Hydraulic Analysis/Design ......................................... 1-19
1.7.2.3 Foundation Analysis/Design ....................................... 1-21
1.7.2.4 Structural Analysis/Design ......................................... 1-22
1.7.2.5 Mechanical/Electrical Design. .................................... 1-23
1.7.2.6 Risk Analysis (only for significant and high hazard
dams/dikes) .................................................................... 1-25
References .................................................................................................. 1-39
1-vi DS-14(1)-2 March 2010
Figures
Page
1.5.1.1-1 Example: Service spillway (gated) Jackson Lake Dam,
Wyoming............................................................................. 1-28
1.5.1.1-2 Example: Service spillway (ogee crest) Crystal Dam,
Colorado .............................................................................. 1-28
1.5.1.2-3 Example: Auxiliary spillway (gated) in foreground, service
spillway (gated) in background Stewart Mountain
Dam, Arizona ...................................................................... 1-29
1.5.1.2-4 Example: Auxiliary spillway (grade control sill) Heart
Butte Dam, North Dakota ................................................... 1-29
1.5.1.3-5 Example: Emergency spillway (fuseplug) in foreground,
auxiliary spillway (ogee crest) in background New
Waddell Dam, Arizona ....................................................... 1-30
1.5.1.3-6 Example: Emergency spillway San Justo Dam, California . 1-30
1.5.2-7 Example: Combination tunnel outlet work and power
penstock, highlighting a number of features such as
the upstream intake structure and the downstream
control structures. Theodore Roosevelt Dam, Arizona. ..... 1-31
1.6.1-8 Common features of spillway .................................................. 1-32
1.6.1-9 Ogee crest (uncontrolled) spillway Bumping Lake Dam,
Washington ......................................................................... 1-33
1.6.1-10 Double side-channel (bathtub) crest (uncontrolled)
spillway Fontenelle Dam, Wyoming ............................... 1-33
1.6.1.-11 Side-channel crest (uncontrolled) spillway Big Sandy
Dam, Wyoming .................................................................. 1-34
1.6.1-12 Morning glory (glory hole) crest (uncontrolled)
spillway Whiskeytown Dam, California .......................... 1-34
1.6.1-13 Labyrinth crest (uncontrolled) spillway Ute Dam,
New Mexico ........................................................................ 1-35
1.6.1-14 Radial gated (controlled) spillway Stewart Mountain
Dam, Arizona ...................................................................... 1-35
1.6.1-15 Crest (Obermeyer type) gated (controlled) spillway
Friant Dam, California ........................................................ 1-35
1.6.1-16 Drum gated (controlled) spillway Hoover Dam,
Arizona-Nevada .................................................................. 1-35
1.6.1-17 Fuseplug crest (controlled) spillway (reservoir rim)
Horseshoe Dam, Arizona .................................................... 1-36
1.6.1-18 Fusegate (controlled) spillway Terminus Dam, California ... 1-36
1.6.2-19 Common features of outlet works ............................................ 1-37
1.6.2-20 Preferred outlet works configuration: hydraulic control
at upstream intake with free flow conditions
downstream of the regulating gate/valve ............................ 1-38
DS-14(1)-2 March 2010 1-vii
Figures
Page
1.6.2-21 Preferred outlet works configuration: hydraulic control
at downstream control structure, with guard/emergency
gate/valve at/near centerline of dam/dike, and downstream
pressurized pipe (between dam/dike centerline
and control structure inside larger access conduit) ............. 1-38
1.6.2-22 Acceptable outlet works configuration: hydraulic control
at/near centerline of dam/dike with free flow conditions
downstream of the regulating gate/valve ............................ 1-38
1.6.2-23 Least acceptable outlet works configuration: hydraulic
control at downstream control structure (i.e., pressurized
flow conditions upstream of the regulating gate/valve
along most of the outlet works) .......................................... 1-38
DS-14(1)-2 March 2010 1-1
Chapter 1
Introduction
1.1 Purpose
The design standards present clear and concise technical requirements and
processes to enable design professionals to prepare design documents and reports
necessary to manage, develop, and protect water and related resources in an
environmentally and economically sound manner in the interest of the American
public. Compliance with these design standards assists in the development and
improvement of Bureau of Reclamation (Reclamation) facilities in a way that
protects the public's health, safety, and welfare; recognizes all stakeholder needs;
and achieves the lasting value and functionality necessary for Reclamation
facilities. The responsible designer(s) accomplishes this through processes that
enable compliance with these design standards and all other applicable technical
codes, as well as incorporation of the stakeholders vision and values, that are
then reflected in the construction project.
1.2 Application of Design Standards
All Reclamation design work, whether performed by the Technical Service Center
(TSC), the regional offices, or an architectural/engineering (A&E) firm, will
conform to the design standards.
Reclamations use of its design standards requires designers to also integrate
sound engineering judgment with applicable national standards, site-specific
technical considerations, and project-specific considerations to ensure suitable
designs and protect public safety.
The design standards are not intended to provide cookbook solutions to complex
engineering problems. Strict adherence to a handbook procedure is not a
substitute for sound engineering judgment. The designer should be aware of and
use state-of-the-art procedures. Designers are responsible for using the most
current edition of referenced codes and standards and to be aware that
Reclamation design standards may include exceptions to requirements of these
codes and standards.
1.3 Deviations and Proposed Revisions
Design activities must be performed in accordance with established Reclamation
design criteria, Reclamation engineering, architectural, or technical standards, and
approved national design standards. Exceptions to this requirement will be
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1-2 DS-14(1)-2 March 2010
pursued in accordance with provisions of Reclamation Manual Policy, Performing
Designs and Construction Activities, FAC P03.
Reclamation designers should inform the TSC, via the Web site notification
procedure, of any recommended updates or changes for the design standards to
meet current design practices.
1.4 Scope
Design Standard No. 14 provides technical guidance concerning Reclamations
procedures/considerations for analyzing/designing two key appurtenant structures
associated with dams and/or dikes. These appurtenant structures are spillways
and outlet works. Chapter 1 provides an overview for the analysis/design of
spillways and outlet works, while the following chapters provide detailed
procedures/considerations that should be followed by Reclamation staff and
others involved with analyzing/designing modifications to and/or new spillways
and outlet works. It should be stressed that this design standard will not duplicate
other existing technical references but, wherever possible, it will reference
existing procedures/considerations that should be used for the analysis/design of
spillways and outlet works.
1.5 Definitions
The following definitions are provided to clarify the terminology used in Design
Standard No. 14. These definitions are consistent with other technical references
used by Reclamation.
1.5.1 Spillway
A spillway is a hydraulic structure that passes normal (operational) and/or flood
flows in a manner that protects the structural integrity of the dam and/or dikes
(reservoir impoundment structures). Spillways are hydraulically sized to safely
pass the Inflow Design Flood (IDF).2 The IDF will be equal to, or less than, the
Probable Maximum Flood (PMF).3 For more details and guidance about floods,
refer to Chapter 2, Hydrologic Considerations.
2 For significant and high hazard dams and/or dikes and their appurtenant structures, selection of the IDF will
be based on a quantitative risk analysis. The IDF will be less than, or equal to, the PMF.
3 The largest flood that may reasonably be expected to occur at a given maximum runoff condition resulting
from the most severe combination of meteorological and hydrologic conditions that are considered
reasonably possible for the drainage basin under study.
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DS-14(1)-2 March 2010 1-3
There are three types or classifications of spillways typically employed by
Reclamation, which are based on frequency of use. They are explained in more
detail below.
1.5.1.1 Service Spillway
A service spillway provides continuous or frequent regulated (controlled) or
unregulated (uncontrolled) releases from a reservoir without significant damage to
the dam, dike, or appurtenant structures due to releases up to and including the
design discharge. Service spillways are illustrated in figures 1.5.1.1-1 and
1.5.1.1-2.
1.5.1.2 Auxiliary Spillway
An auxiliary spillway is infrequently used and may be a secondary spillway which
is operated sparingly. During operation there could be some degree of structural
damage or erosion to the auxiliary spillway due to releases up to and including the
design discharge. Auxiliary spillways are illustrated in figures 1.5.1.2-3 and
1.5.1.2-4.
1.5.1.3 Emergency Spillway
An emergency spillway is designed to provide additional protection against
overtopping of a dam and/or dike and is intended for use under extreme
conditions such as misoperation or malfunction of the service spillway or other
emergency conditions or during very large, remote floods (such as the PMF). As
with auxiliary spillways, some degree of structural damage and/or erosion would
be expected due to releases up to and including the design discharge. Emergency
spillways are illustrated in figures 1.5.1.3-5 and 1.5.1.3-6.
1.5.2 Outlet Works
Outlet works consist of a combination of features (i.e., intake structure,
conveyance features such as conduits, control structure, etc.) and operating
equipment (electrical and mechanical) required for the safe operation and control
of water released from a reservoir to meet downstream needs. The outlet works
serves various purposes such as regulating streamflow and water quality;
releasing floodwater; power generation; emergency evacuation; and providing
irrigation, municipal, and/or industrial water. Features of outlet works are
illustrated in figure 1.5.2-7.
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1.6 Configurations
There are some common/typical and unique configurations (features) associated
with spillways and outlet works. These features are further discussed in the
following sections.
1.6.1 Spillway
Generally speaking, features common to most spillways are illustrated in
figure 1.6.1-8 and include:
Approach channel and safety/debris/log boom.
Control structure, such as crest structure or grade sill, and gates,
bulkheads, stoplogs, along with associated operating equipment.
Conveyance features, such as chute floor and walls and/or
conduit(s)/tunnel(s).
Terminal structure, such as hydraulic jump stilling basin, flip bucket,
plunge pool, etc.
Downstream channel.
Another consideration of the spillway configuration relates to the type of
hydraulic control. With some exceptions,4 the two types are uncontrolled or freeflow
spillways and controlled or gated spillways. The hydraulic control is usually
based on whether the spillway crest structure has gates or not. Finally, with some
exceptions, the spillway is typically referred to by the type of crest structure, such
as:
For uncontrolled spillways:
o Ogee crest (figure 1.6.1-9) and grade control sill spillway
(figures 1.5.1.2-4 and 1.5.1.3-6).
o Bathtub (or double side-channel) (figure 1.6.1-10) and side-channel
ogee crest spillway (figure 1.6.1-11).
o Morning glory (or glory hole) spillway (figure1.6.1-12).
o Labyrinth weir spillway (figure 1.6.1-13).
4 There are exceptions, such as the morning glory spillway, that could experience hydraulic control shifts
with increasing hydraulic head: crest or free flow control to throat or orifice control to pipe or pressure
control.
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DS-14(1)-2 March 2010 1-5
For controlled spillways:
o Gated spillway (figures 1.6.1-14 through 1.6.1-16).
o Fuseplug spillway (figure 1.6.1-17).
o Fusegate spillway (figure 1.6.1-18).
Consideration should also be given to the location of the spillway, which should
not be on or through an embankment dam/dike unless there is justification to
deviate. The preferred locations would be on the dam abutments or through the
reservoir rim.
For more detailed guidance, refer to Chapter 3, General Spillway Design
Considerations.
1.6.2 Outlet Works
Features common to most outlet works are illustrated in figure 1.6.2-19 and
include:
Intake structures, trashracks, gates/valves, and bulkheads (if appropriate).
Conveyance features, such as conduit(s)/tunnel(s).
Control structure, such as gate chamber, gates/valves, access
shaft/adit/conduit, along with operating equipment.
Terminal structure, such as hydraulic jump stilling basin, impact structure,
plunge pool, etc.
Downstream channel.
Considerations that should be used, unless there is justification to deviate,
include:
Two gates or valves in series should be installed and operated in
Reclamation outlet works. The downstream gate or valve provides
regulating capabilities, while the upstream gate or valve provides
emergency closure capabilities under unbalanced head (flow) conditions,
or routine closure capabilities under balanced head (nonflow) conditions.
Although common throughout the water resource engineering industry,
constructing an outlet works through/beneath an embankment dam and/or
dike should be viewed as a second choice (i.e., avoid/limit
contact/interface between the conduit and embankment). A preferred
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alternative to minimize internal erosion potential is to construct a tunnel
outlet works through the dam and/or dike abutment or through the
reservoir rim.
Another aspect of outlet works configuration relates to the location of
hydraulic control (i.e., the location of the regulating gate or valve). The four
configurations [1]5 typically used by Reclamation are illustrated in
figures 1.6.2-20 through 1.6.2-23 and include the following:6
,
7
Preferred configuration. Hydraulic control at intake with free flow
conditions downstream of the regulating gate or valve. Most often used
for low head applications in embankment dams where pressurized flow is
not required at the downstream end of the outlet works. When the outlet
works is not being operated, there is access for inspection and
maintenance through the entire length of the conduit (figure 1.6.2-20).
Preferred configuration. Hydraulic control at downstream control
structure, with guard/emergency gate/valve at/near centerline of dam/dike,
and downstream pressurized pipe (between dam/dike centerline and
control structure) inside larger access conduit. Applicable for power
generation or pressurized downstream flow. During both operation and
nonoperation of the outlet works, there is excellent access for inspection
and maintenance through downstream conduit (figure 1.6.2-21).
Acceptable configuration. Hydraulic control at/near the dam/dike
centerline with free flow conditions downstream of the regulating gate or
valve. When the outlet works is not being operated, there is access for
inspection and maintenance through the downstream conduit
(figure 1.6.2-22).
Least acceptable configuration. Hydraulic control at the downstream
end of the outlet works, which may be near the downstream toe or face of
the dam/dike (i.e., pressure flow conditions upstream of the regulating
gate or valve along most of the outlet works). Commonly used in concrete
5 Numbers in brackets indicate a reference listed at the end of this chapter.
6 Outlet works configurations are listed in order of increasing potential of pressurizing surrounding dam,
dike, and/or foundation materials, which could lead to an incident or failure.
7 Although the figures associated with following outlet works configurations illustrate an outlet works
through/beneath an embankment dam/dike (which should be a second choice to a tunnel through the
dam/dike abutment or reservoir rim), the focus is on the hydraulic control configuration, which would be
applicable regardless of the location of the outlet works.
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DS-14(1)-2 March 2010 1-7
dams. Accessibility for inspection and maintenance is limited (underwater
inspection) without bulkheading upstream intake structure or draining the
reservoir (figure 1.6.2-23).
For more detailed guidance, refer to Chapter 4, General Outlet Works and
Diversion Design Considerations.
1.7 Design Procedures/Considerations
Details of analysis/design procedures/considerations will be provided in the
following chapters of Design Standard No. 14. An overview is provided in the
following text of this chapter. Analysis and/or design (including both new and
modification) for a spillway and/or outlet works will typically follow a number of
key procedural guidelines including:
Design data collection guidelines [2].
Feasibility design guidelines [3].
Final design process [4].
Cost estimating [5].
Safety of Dams project management guidelines [6].
1.7.1 Spillway Design/Analysis
Tasks for analyzing/designing spillways are summarized in the following
sections.
1.7.1.1 Location, Type, and Size
Selection of the location, type, and size of a spillway will be dependent on the
evaluation of a number of factors including:
Site conditions (geology/topography).
Dam and/or dike type.
Hydrologic considerations.
Hydraulic considerations.
Seismic considerations.
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Construction/constructability considerations.
Project objectives.
Robustness of design.
Risks associated with Plausible Potential Failure Modes (PFMs),
which must be tolerably below Reclamations public protection guidelines
[7].
Operation and maintenance considerations.
Economics.
These factors are further discussed in the following chapters of this design
standard and some of the following sections. Two factors that should be
highlighted, which are somewhat unique to Reclamation facilities, are the
robustness of design and the risks associated with PFMs. Because many of the
spillways are associated with significant and high hazard dams/dikes, it is
important that any new or modified appurtenant structure designs protect the
public to levels consistent with Reclamations public protection guidelines [7]
(i.e., maintain and/or reduce risks to acceptable levels). This could mean some
redundant features/equipment and designing to stricter requirements than
commonly called for by professional codes, standards, and/or guidelines.
For more detailed guidance associated with locating, along with selecting, a type
and size of a spillway, refer to Chapter 3, General Spillway Design
Considerations.
1.7.1.2 Hydraulic Analysis/Design
The hydraulic analysis/design will be concurrent with the previous task of
locating and selecting a type and size of spillway. The following chapters of this
design standard explain the steps of hydraulic analysis/design, including:
Develop/verify discharge curves.
Prepare initial flood routings of frequency floods up to the PMF to verify
the appropriateness of the spillway type and size, and to select the IDF.
Refine spillway control (crest) structure layout and associated discharge
curves based on results from previous steps.
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DS-14(1)-2 March 2010 1-9
Prepare final flood routings to estimate maximum reservoir water surfaces
(RWS) and discharge ranges for various floods and operational conditions
(part of the final flood routings will include a freeboard assessment, which
is sometimes referred to as a robustness study).
Prepare initial water surface profiles to lay out the spillway conveyance
features and terminal structure size and type.
Refine spillway conveyance features and terminal structure based on
results from previous step.
Prepare final water surface profiles to finalize size and type of the spillway
conveyance features and terminal structure.
For more detailed guidance associated with hydrologic and hydraulic
analysis/design for a spillway, refer to Chapter 2, Hydrologic Considerations,
and Chapter 5, Hydraulic Considerations.
Technical references associated with the hydraulic analysis/design of spillways
include:
Design of Small Dams, third edition [8].
Engineering Monograph (EM) No. 9 Discharge Coefficients for
Irregular Overfall Spillways [9].
EM No. 25 Hydraulic Design of Stilling Basins and Energy Dissipators
[10].
EM No. 42 Cavitation in Chutes and Spillways [11].
Reclamation Engineering and Research Center (REC-ERC)-73-5
Hydraulic Model Studies of Chute Offsets, Air Slots, and Deflectors for
High-Velocity Jets [12].
REC-ERC-78-8 Low Froude Number Stilling Basin Design [13].
REC-ERC-85-7 Hydraulic Model Studies of Fuseplug Embankments
[14].
REC-ERC-88-3 Overtopping Flow on Low Embankment Dams
Summary Report of Model Test [15].
Dam Safety Office (DSO)-07-07 Uplift and Crack Flow Resulting from
High Velocity Discharges Over Offset Joints [16].
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Assistant Commissioner Engineering and Research (ACER) Technical
Memorandum (TM) No. 10 Guidelines for Using Fuseplug
Embankments in Auxiliary Spillways [17].
Hydraulic and Excavation Tables, 11th edition [18].
Computing Degradation and Local Scour [19].
Guide for Computing Water Surface Profiles [20].
Design of Labyrinth Spillways [50].
Research State-of-the-Art and Needs for Hydraulic Design of Stepped
Spillways [51].
Plastic Pipe Used In Embankment Dams: Best Practices for Design,
Construction, Identification and Evaluation, Inspection, Maintenance,
Renovation, and Repair [52].
Outlet Works Energy Dissipators: Best Practices for Design,
Construction, Identification and Evaluation, Inspection, Maintenance,
Renovation, and Repair [53].
1.7.1.3 Foundation Analysis/Design
The foundation analysis/design will start when a tentative type and size of
spillway is located and selected, and it parallels the structural analysis/design
efforts. The following chapters of this design standard explain the steps of
foundation analysis/design, including:
Define site-specific foundation material and strength properties.
Assist in identifying suitable sites based on site-specific foundation needs
for a spillway.
Define and analyze ground water conditions.
Develop appropriate foundation designs which include:
o Drainage features such as underdrains, slope drainage, and filters
(NOTE: Identify and evaluate drainage features/systems that will be
accessible for inspection using closed circuit television (CCTV)
equipment).
o Adequate support for the spillway, which could range from excavating
to competent rock to driving piles or placing piers in a soil foundation.
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DS-14(1)-2 March 2010 1-11
o Accommodating loading conditions on the spillway that could include
static (hydrostatic, rock/soil, ice and frost heave), hydrologic (floods),
and seismic (hydrodynamic, dynamic soil/rock) loads.
For more detailed guidance associated with foundation analysis/design for a
spillway, refer to Chapter 6, Foundation Considerations.
Technical references associated with the foundation analysis/design of spillways
include:
Design of Small Dams, third edition [8].
EM No. 13 Estimating Foundation Settlement by One-Dimensional
Consolidation Tests [21].
REC-ERC-74-10 Rock Mechanics Properties of Typical Foundation
Rock Types [22].
REC-ERC-82-17 Frost Action in Soil Foundations and Control of
Surface Structure Heaving [23].
ACER TM No. 9 Guidelines for Controlling Seepage Along Conduits
Through Embankments [24].
Drainage for Dams and Associated Structures [25].
Guidelines, Foundation and Geotechnical Studies for Existing Concrete
Dams [41].
1.7.1.4 Structural Analysis/Design
The structural analysis/design of the spillway typically follows the hydraulic
analysis/design. The following chapters of this design standard explain the steps
of structural analysis/design, including:
Identify which features are considered critical8 and noncritical.9 [26]
8 A critical feature is one in which its failure or damage could lead to failure and/or damage of the
dam/dike or other appurtenant structures, which, in turn, may lead to the uncontrolled release of
part or the entire reservoir or leave the appurtenant structure inoperable, preventing releases
needed to protect the dam/dike.
9 A noncritical structure is one in which failure or damage would not lead to failure of and/or
damage to the dam/dike, nor would it inhibit operations of the structure to protect the dam/dike.
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Identify and define loading conditions for both critical and noncritical
features, which will typically fall into four categories, including:
o Construction.
o Operational (normal or static).
o Flood (hydrologic).
o Earthquake (seismic).10
Identify, evaluate, and select material types and associated properties.
Materials could include concrete (reinforced, conventional mass, roller
compacted, and precast), steel, and plastic such as high-density
polyethylene (HDPE).
Apply appropriate structural analysis/design methods, which are based on
the crawl, walk, and run philosophy (i.e., using the simplest approach that
is technically adequate to prepare the analysis/design). These include:
o For analyses. Pseudo-static, linear elastic finite element modeling
(FEM), using response spectra, and nonlinear elastic FEM, using time
histories, are employed to analyze a structure.
o For designs. Design methods are typically based on Reclamation
technical references, such as Design of Small Dams [8], and industry
codes are used, such as the American Concrete Institute (ACI)
manuals.
For more detailed guidance associated with structural analysis/design for a
spillway, refer to Chapter 7, Structural Considerations.
Technical references associated with the structural analysis/design of spillways
include:
Design of Small Dams, third edition [8].
EM No. 14 Beggs Deformeter-Stress Analysis of Single-Barrel
Conduits [27].
EM No. 14 Supplement Beggs Deformeter-Analysis of Additional
Shapes [28].
10 For significant and high hazard dams and/or dikes and their appurtenant structures which have been
identified as critical, selection of the seismic design load will be based on a quantitative risk analysis. For
noncritical structures, a minimum earthquake loading will be used which approximates a design basis
earthquake (DBE) or about a 500-year event.
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DS-14(1)-2 March 2010 1-13
EM No. 27 Moments and Reactions for Rectangular Plates [29].
EM No. 34 Control of Cracking in Mass Concrete Structures [30].
Concrete Manual, eighth edition [31].
Current ACI 318 and ACI 350 building codes.
EM 1110-2-2104 Strength Design for Reinforced Concrete Hydraulic
Structures, U.S. Army Corps of Engineers [32].
ACI SP-3 Reinforced Concrete Design Handbook (Working Stress
Method), third edition [33].
Design Criteria for Retaining Walls [34].
Roller-Compacted Concrete: Design and Construction Considerations for
Hydraulic Structures [35].
1.7.1.5 Mechanical/Electrical Design
The mechanical/electrical design takes place concurrently with the structural
analysis/design. The following chapters of this design standard explain the steps
of mechanical/electrical design, including:
Select, size, and design gates/valves, if applicable.
Select, size, and design trashracks, stoplogs, and/or bulkhead gates, if
applicable.
Select, size, and design gate/valve operators and generators, if applicable.
Select, size, and design heating, ventilation, and cooling (HVAC) systems,
if applicable.
Select, size, and design hoists and/or cranes, if applicable.
Design lighting and electrical control systems for gate/valve operations,
HVAC systems, and supervisory control and data acquisition (SCADA)
systems.
Address life safety considerations as note in the National Fire Protection
Association (NFPA) 100, Life Safety Code Handbook, 2009 edition.
For more detailed guidance associated with mechanical/electrical design for a
spillway, refer to Chapter 7, Mechanical/Electrical Considerations.
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Selection of type and size of a spillway gate and operating system will be
dependent on the evaluation of a number of factors including:
Site conditions.
Spillway configuration.
Access.
Available power.
Hydraulic considerations.
Seismic considerations.
Construction/constructability considerations.
Ice loading.
Navigation needs.
Sediment and debris loading.
Operation and maintenance considerations.
Economics.
These factors are further discussed in the following chapters of this design
standard and some of the following sections. Because many of the spillways are
associated with significant and high hazard dams/dikes, and failure of
gates/valves may result in uncontrolled release of large flows, some redundant
features/equipment might be required. Therefore, it may be advisable to design to
stricter requirements than commonly called for by professional codes, standards,
and/or guidelines.
Technical references associated with the mechanical/electrical design of spillways
include:
American Institute of Steel Construction (AISC) Manual of Steel
Construction, thirteenth edition - refer to American National Standards
Institute (ANSI)/AISC 360-05, Specifications for Structural Steel
Buildings).
DRAFT - Chapter 1 - Introduction
DS-14(1)-2 March 2010 1-15
American Welding Society (AWS) AWS D1.1/D1.1M Structural Welding
Code Steel; AWS D1.6 Structural Welding Code - Stainless Steel.
1.7.1.6 Risk Analysis (Only for Significant and High Hazard
Dams/Dikes)
Probabilistic (in the form of a quantitative risk analysis), rather than deterministic,
considerations will be part of any analysis/design for significant and high hazard
dams and/or dikes, along with associated appurtenant structures (such as
spillways) or critical components of associated appurtenant structures. The steps
will be integrated with the previous design/analysis and include:
Identify and define credible PFMs for the existing, modified, and/or new
spillway. Although each spillway may have some unique PFMs, common
PFMs include:
o Flood-induced overtopping of dam and/or dike.
o Flood-induced spillway operations which exceed the
original/maximum design discharge, leading to overtopping of the
chute wall and/or terminal structure walls, pressurizing the conduit
and/or tunnel, or sweepout of the terminal structure, and leading to
erosional headcutting of the spillway foundation or erosion of the dam
and/or dam foundation.
o Flood-induced spillway operations which result in cavitation damage
of the chute and/or conduit, leading to erosion of the foundation.
o Flood-induced operations which result in stagnation pressure
(hydraulic jacking) and/or structural collapse of the chute and/or
terminal structure, leading to erosion of the foundation.
o Seismic-induced structural collapse of the spillway crest structure or
features (such as piers, walls, and/or gates).
Based on Reclamations public protection guidelines [7], estimate the sum
of the baseline (existing) annual probability of failure (APF) for all
credible PFMs, and annualized loss of life (ALL) for all credible PFMs for
a given loading condition, associated with existing and/or new dams,
dikes, and all appurtenant structures such as spillways and outlet works.
If an existing spillway is to be modified, estimate the sum of the modified
APF for all credible PMFs and the sum of ALL for all credible PMFs
associated with a given loading condition.
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For the modified or new spillway, if estimated sum of APF for all credible
PFMs, and the sum of ALL for all credible PFMs associated with a given
loading condition are tolerably11 below Reclamation guidelines (1E-4 or
a 1 in 10,000 chance during a given year for APF; and 1E-3 or a 1 in
1,000 chance during a given year for ALL), designs may be acceptable;
however, if not tolerably below Reclamation guidelines, additional design
considerations/features will be necessary to lower the estimated APF and
ALL for the modified or new spillway.
To address the uncertainties associated with using quantitative risk
analysis to select an IDF, a robustness study is done to evaluate plausible
operational and hydrologic/hydraulic scenarios that could increase the
maximum RWS above the IDF-induced RWS. Typical scenarios that are
evaluated include:
o Misoperation.
o Change in hydrology.
o Debris blockage.
o Change in downstream consequences.
o Wind-generated waves.
For more detailed guidance associated with risk analysis/design for a spillway,
refer to Chapter 2, Hydrologic Considerations and Chapter 3, General
Spillway Design Considerations.
Technical references associated with the risk analysis/design of spillways include:
Guidelines for Achieving Public Protection in Dam Safety
Decisionmaking [7].
REC-ERC-88-3 Overtopping Flow on Low Embankment Dams
Summary Report of Model Test [15].
DSO-07-07 Uplift and Crack Flow Resulting from High Velocity
Discharges Over Offset Joints [16].
DSO-99-06 A Procedure for Estimating Loss of Life Caused by Dam
Failure [36].
11 Tolerably below Reclamation guidelines will be unique to each condition/situation and will be mutually
agreed to by the designer of record and Reclamations Dam Safety Office, along with concurrence by
Reclamation management. Consideration will include the level of uncertainty associated with estimates, and
future conditions that could increase the estimates (such as changes in downstream consequences).
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DS-14(1)-2 March 2010 1-17
Final Technical Report No. 99DG81029 Considerations for Estimating
Structural Response Probabilities in Dam Safety Risk Analysis [37].
Appendix D Toolbox for Handling Loads by Upstream Dams and
Incorporating Consequences for Failure of Downstream Dams [38].
DSO-98-004 Prediction of Embankment Dam Breach Parameters: A
Literature Review and Needs Assessment [39].
Interim Guidelines for Addressing the Risk of Extreme Hydrologic Events
[40].
Risk Analysis Facilitators Notebook [42].
Dam Safety Risk Analysis Best Practices Training Manual [43].
1.7.2 Outlet Works Design/Analysis
Tasks for analyzing/designing outlet works are summarized in the following
sections.
1.7.2.1 Location, Type and Size
Similar to the spillway, selection of the location, type, and size of an outlet works
will be dependent on the evaluation of a number of factors including:
Site conditions (geology/topography).
Dam and/or dike type.
Hydrologic considerations.
Hydraulic considerations.
Seismic considerations.
Construction/constructability considerations.
Project objectives.
Robustness of design.
Risks associated with credible PFMs, which must be tolerably below
Reclamations public protection guidelines [7].
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Operation and maintenance considerations.
Economics.
These factors are further discussed in the following chapters of this design
standard and some of the following sections. Also, the two factors that were
highlighted for the spillway are also highlighted for the outlet works, which are
the robustness of design and the risks associated with PFMs. It is worth restating
that because many of the outlet works are associated with significant and high
hazard dams/dikes, it is important that any new or modified appurtenant structure
designs protect the public to levels consistent with Reclamations public
protection guidelines [7]. This could mean some redundant features/equipment
and designing to stricter requirements than commonly called for by professional
codes, standards, and/or guidelines. Additionally, it should be restated that, as a
starting point, an outlet works should include:
Two gates or valves in series (one guard or emergency valve and one
regulating gate/valve) that can be operated under unbalanced head
conditions.
Hydraulic control at or upstream of the projected centerline of the
dam/dike with either a pressurized pipe inside a larger access conduit
and/or tunnel or a free flow conduit and/or tunnel downstream of
hydraulic control, particularly when associated with embankment
dams/dikes.
Stoplogs or bulkhead and slots provided near the intake structure.
For embankment and/or rockfill dams/dikes, isolate the outlet works from
the dam/dike (i.e., consider tunnel through the dam/dike abutments or
reservoir rim, rather than a cut-and-cover outlet works through or beneath
the dam/dike).
There will be cases where deviation from the above considerations will occur.
However, there should be strong justification to not incorporate these
considerations.
For more detailed guidance associated with locating, along with selecting, a type
and size of an outlet works, refer to Chapter 4, General Outlet Works and
Diversion Design Considerations.
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1.7.2.2 Hydraulic Analysis/Design
Similar to the spillway, the hydraulic analysis/design will be concurrent with the
previous task of locating and selecting a type and size of outlet works. The
following chapters of the design standard explain the following steps of hydraulic
analysis/design:
Develop/verify discharge curves.
Evaluate intake structure and conveyance features (such as conduit) sizes,
along with gate/valve types/sizes based on:
o Diversion. If outlet works will be used for diversion during
construction, initial flood routings of diversion floods (sometimes
referred to as construction floods) should be done to size conveyance
features and temporary cofferdams.
o Normal operations. Evaluate conveyance features size and
gate/valve type/size for passing operational flows.
o Emergency evacuation. Evaluate ability of outlet works to lower the
reservoir in a timely fashion pursuant to guidelines noted in Criteria
and Guidelines for Evacuating Storage Reservoirs and Sizing
Low-Level Outlet Works [45].
o Floods. Although not typical, some outlet works are used in passing
floods. If this is the case, flood routing steps similar to those noted for
the spillway should be employed.
Refine discharge curves based on results from previous steps and finalize
intake structure and conveyance features sizes, along with gate/valve
types/sizes.
Depending on type/configuration of the outlet works, initial water surface
profiles to layout conveyance features (such as chute/conduit) and
terminal structure size and type.
Final water surface profiles to finalize size and type of outlet works
conveyance features and terminal structure.
For more detailed guidance associated with hydraulic analysis/design for an outlet
works, refer to Chapter 2, Hydrologic Considerations, and Chapter 5,
Hydraulic Considerations.
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Technical references associated with the hydraulic analysis/design of outlet works
include:
Conduits through Embankment Dams: Best Practices for Design,
Construction, Problems Identification and Evaluation, Inspection,
Maintenance, Renovation, and Repair [1].
Design of Small Dams, third edition [8].
EM No. 25 Hydraulic Design of Stilling Basins and Energy Dissipators
[10].
REC-ERC-73-5 Hydraulic Model Studies of Chute Offsets, Air Slots,
and Deflectors for High-Velocity Jets [12].
REC-ERC-78-8 Low Froude Number Stilling Basin Design [13].
DSO-07-07 Uplift and Crack Flow Resulting from High Velocity
Discharges Over Offset Joints [16].
Hydraulic and Excavation Tables, 11th edition [18].
Computing Degradation and Local Scour [19].
Guide for Computing Water Surface Profiles [20].
ACER TM No. 3 Criteria and Guidelines for Evacuating Storage
Reservoirs and Sizing Low-Level Outlet Works [44].
EM No. 7 Friction Factors for Large Conduits Flowing Full [45].
REC-ERC-78-24 Hydraulic Design of Stilling Basin for Pipe or Channel
Outlets [46].
EM No. 41 Air-Water Flow in Hydraulic Structures [47].
ACER TM No. 4 Criteria for Bulkheading Outlet Works Intakes for
Storage Dams [48].
Plastic Pipe Used In Embankment Dams: Best Practices for Design,
Construction, Identification and Evaluation, Inspection, Maintenance,
Renovation, and Repair [52].
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DS-14(1)-2 March 2010 1-21
Outlet Works Energy Dissipators: Best Practices for Design,
Construction, Identification and Evaluation, Inspection, Maintenance,
Renovation, and Repair [53].
1.7.2.3 Foundation Analysis/Design
The foundation analysis/design will start when locating and selecting a type and
size of outlet works and parallels the structural analysis/design efforts. The
following chapters of this design standard explain the steps of foundation
analysis/design, including:
Define site-specific foundation material and strength of properties.
Assist in identifying suitable sites based on site-specific foundation needs
for an outlet works.
Define and analyze ground water conditions.
Develop appropriate foundation designs which include:
o Drainage features, which in many cases are the key foundation design
feature. (NOTE: Identify and evaluate drainage features/systems that
will be accessible for inspection using CCTV equipment).
o Adequate support for the outlet, which could range from excavating to
competent rock to driving piles, placing piers in a soil foundation, or
supporting excavated tunnels with rock bolts, shotcrete, etc.
Accommodating loading conditions loads on the outlet works that could
include static (hydrostatic, rock/soil, ice, and frost heave), hydrologic
(floods), and seismic (hydrodynamic, dynamic soil/rock) loads, etc.
For more detailed guidance associated with foundation analysis/design for an
outlet works, refer to Chapter 6, Foundation Considerations.
Technical references associated with the foundation analysis/design of outlet
works include:
Conduits through Embankment Dams: Best Practices for Design,
Construction, Problems Identification and Evaluation, Inspection,
Maintenance, Renovation, and Repair [1].
Design of Small Dams, third edition [8].
EM No. 13 Estimating Foundation Settlement by One-Dimensional
Consolidation Tests [21].
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REC-ERC-74-10 Rock Mechanics Properties of Typical Foundation
Rock Types [22].
REC-ERC-82-17 Frost Action in Soil Foundations and Control of
Surface Structure Heaving [23].
ACER TM No. 9 Guidelines for Controlling Seepage Along Conduits
Through Embankments [24].
Drainage for Dams and Associated Structures [25].
1.7.2.4 Structural Analysis/Design
Similar to the spillway, the structural analysis/design of the outlet works typically
follows the hydraulic analysis/design. The following chapters of this design
standard explain the steps of structural analysis/design, including:
Identify which features are considered critical7 and noncritical8 [26].
Identify and define loading conditions for both critical and noncritical
features, which will typically fall into four categories, including:
o Construction.
o Operational (normal or static).
o Flood (hydrologic).
o Earthquake (seismic).
Identify, evaluate, and select material types and associated properties.
Materials could include concrete (reinforced, conventional mass, roller
compacted, and precast), steel, and plastic such as HDPE.
Apply appropriate structural analysis/design methods which are based on
the crawl, walk, and run philosophy (i.e., using the simplest approach that
is technically adequate to prepare the analysis/design). These include:
o For analyses. Pseudo-static, linear elastic FEM using response
spectra and nonlinear elastic FEM using time histories.
o For designs. Design methods are typically based on Reclamation
technical references such as Design of Small Dams [8], and industry
codes are used such as the ACI manuals.
For more detailed guidance associated with structural analysis/design for an outlet
works, refer to Chapter 7, Structural Considerations.
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DS-14(1)-2 March 2010 1-23
Technical references associated with the structural analysis/design of outlet works
include:
Conduits through Embankment Dams: Best Practices for Design,
Construction, Problems Identification and Evaluation, Inspection,
Maintenance, Renovation, and Repair [1].
Design of Small Dams, third edition [8].
EM No. 14 Beggs Deformeter-Stress Analysis of Single-Barrel
Conduits [27].
EM No. 14 Supplement Beggs Deformeter-Analysis of Additional
Shapes [28].
EM No. 27 Moments and Reactions for Rectangular Plates [29].
EM No. 34 Control of Cracking in Mass Concrete Structures [30].
Concrete Manual, eighth edition [31].
Current ACI 318 and ACI 350 building codes.
EM 1110-2-2104 Strength Design for Reinforced-Concrete Design of
Hydraulic Structures [32].
ACI SP-3 Reinforced Concrete Design Handbook (Working Stress
Method), third edition [33].
Design Criteria for Retaining Walls [34].
Roller-Compacted Concrete: Design and Construction Considerations for
Hydraulic Structures [35].
1.7.2.5 Mechanical/Electrical Design.
The mechanical/electrical design takes place concurrently with the structural
analysis/design. The following chapters of this design standard explain the steps
of mechanical/electrical design, including:
Select, size, and design gates/valves.
Select, size, and design bulkhead gates, if applicable.
Select, size, and design trashracks.
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Select, size, and design steel pipe.
Select, size, and design gate/valve operators and generators.
Select, size and design HVAC systems.
Select, size, and design hoists and/or cranes, if applicable.
Design lighting and electrical control systems for gate/valve operations,
HVAC systems, and SCADA systems.
Address life safety considerations as noted in NFPA 100, Life Safety Code
Handbook, 2009 edition.
For more detailed guidance associated with mechanical/electrical design for an
outlet works, refer to Chapter 7, Mechanical/Electrical Considerations.
Selection of type and size of an outlet gate or valve and operating system will be
dependent on the evaluation of a number of factors including:
Site conditions.
Outlet works configuration.
Access.
Available power.
Hydraulic considerations.
Seismic considerations.
Construction/constructability considerations.
Ice loading.
Sedimentation and debris loading.
Operation and maintenance considerations.
Economics.
These factors are further discussed in the following chapters of this design
standard and in some of the following sections. Because reliable operation of
outlet works may be critical in maintaining the safety of dams, some redundant
DRAFT - Chapter 1 - Introduction
DS-14(1)-2 March 2010 1-25
features/equipment might be required, and it may be advisable to design to stricter
requirements than commonly called for by professional codes, standards, and/or
guidelines. Of special note, gate and/or valve controls should be located outside
of flooded area, should a failure occur, to ensure that emergency/guard gates
and/or valves can be operated.
Technical references associated with the mechanical/electrical design of outlet
works include:
AISC Manual of Steel Construction, thirteenth edition (refer to
ANSC/AISC 360-05, Specifications for Structural Steel Buildings).
AWS D1.1/D1.1M Structural Welding Code Steel; AWS D1.6
Structural Welding Code - Stainless Steel.
Hydraulic Downpull Forces on Large Gates, Research Report No. 4 [49].
1.7.2.6 Risk Analysis (Only for Significant and High Hazard
Dams/Dikes)
Similar to the spillway, probabilistic (in the form of a quantitative risk analysis),
rather than deterministic, considerations will be part of any analysis/design for
significant and high hazard dams and/or dikes, along with appurtenant structures
such as outlet works. The steps will be integrated with the previous
design/analysis and include:
Identify and define credible PFMs for the existing, modified, and/or new
outlet works. Although each outlet works may have some unique credible
PFMs, common PFMs have included:
o Flood-induced overtopping of dam and/or dike (if outlet works are
used to help pass floods).
o Flood-induced outlet works operations which exceed the
original/maximum design discharge, leading to overtopping of the
chute wall and/or terminal structure walls, or sweepout of the terminal
structure, and leading to erosional headcutting of the outlet works
foundation or erosion of the dam and/or dam foundation, overstressing
the conduits and/or tunnels, introducing pressurized seepage through
cracks/joints in the conduit and/or tunnels into surrounding
embankment or foundation materials.
o Operational- and/or flood-induced cavitation damage typically
downstream of gates/valves in the chute and/or conduit, leading to
erosion of the foundation.
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o Stagnation pressure (hydraulic jacking) and/or structural collapse of
the chute and/or terminal structure, leading to erosion of the
foundation.
Based on Reclamations public protection guidelines [7], estimate the sum
of the baseline (existing) APF for all credible PFMs and ALL for all
credible PFM for a given loading condition, associated with existing
and/or new dams, dikes, and appurtenant structures such as spillways and
outlet works.
If an existing spillway is to be modified, estimate the sum of the modified
APF for all credible PMFs and the sum of ALL for all credible PMF
associated with a given loading condition.
For the modified or new spillway, if estimated sum of APF for all credible
PFMs, and the sum of ALL for all credible PFMs associated with a given
loading condition are tolerably below Reclamation guidelines (1E-4 or a
1 in 10,000 chance during a given year for APF; and 1E-3 or a 1 in
1,000 chance during a given year for ALL), designs may be acceptable;
however, if not tolerably below Reclamation guidelines, additional design
considerations/features will be necessary to lower the estimated APF and
ALL for the modified or new outlet works.
For more detailed guidance associated with risk analysis/design for an outlet
works, refer to Chapter 2, Hydrologic Considerations and Chapter 4, General
Outlet Works and Diversion Design Considerations.
Technical references associated with the risk analysis/design of spillways include:
Guidelines for Achieving Public Protection in Dam Safety Decisionmaking
[7].
REC-ERC-88-3 Overtopping Flow on Low Embankment Dams
Summary Report of Model Test [15].
DSO-07-07 Uplift and Crack Flow Resulting from High Velocity
Discharges Over Offset Joints [16].
DSO-99-06 A Procedure for Estimating Loss of Life Caused by Dam
Failure [36].
Final Technical Report No. 99DG81029 Considerations for Estimating
Structural Response Probabilities in Dam Safety Risk Analysis [37].
DRAFT - Chapter 1 - Introduction
DS-14(1)-2 March 2010 1-27
Appendix D Toolbox for Handling Loads by Upstream Dams and
Incorporating Consequences for Failure of Downstream Dams [38].
DSO-98-004 Prediction of Embankment Dam Breach Parameters: A
Literature Review and Needs Assessment [39].
Interim Guidelines for Addressing the Risk of Extreme Hydrologic
Events [40].
Risk Analysis Facilitators Notebook [42].
Dam Safety Risk Analysis Best Practices Training Manual [43].
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Figure 1.5.1.1-1. Example: Service spillway (gated), Jackson Lake Dam,
Wyoming.
Figure 1.5.1.1-2. Example: Service
spillway (ogee crest), Crystal Dam,
Colorado.
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Figure 1.5.1.2-3. Example: Auxiliary spillway (gated) in foreground and
service spillway (gated) in background, Stewart Mountain Dam, Arizona.
Figure 1.5.1.2-4. Example:
Auxiliary spillway (grade control
sill), Heart Butte Dam, North
Dakota.
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Figures 1.5.1.3-5. Example: Emergency spillway (fuseplug) in foreground
and auxiliary spillway (ogee crest) in background, New Waddell Dam,
Arizona.
Figure 1.5.1.3-6. Example: Emergency
spillway (grade control sill), San Justo
Dam, California.
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Figure 1.5.2-7. Example: Combination Tunnel outlet work and power penstock, highlighting a number of features such as the upstream
intake structure and the downstream structures. Theodore Roosevelt Dam, Arizona.
Modified Theodore
Roosevelt Dam
Steel liner for
lake tap shaft
Downstream
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Figure 1.5.2-8. Common features of spillways.
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Figure 1.6.1-9. Ogee crest (uncontrolled) spillway, Bumping Lake Dam,
Washington.
Figure 1.6.1-10. Double side-channel (bathtub) crest (uncontrolled) spillway,
Fontenelle Dam, Wyoming.
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Figure 1.6.1-11. Side-channel crest (uncontrolled) spillway, Big Sandy Dam,
Wyoming.
Figure 1.6.1-12. Morning glory (glory hole) crest (uncontrolled) spillway,
Whiskeytown Dam, California.
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Figure 1.6.2-13. Labyrinth crest (uncontrolled) spillway, Ute Dam, New Mexico.
Figure 1.6.1-14. Radial gated (controlled) spillway,
Bradbury Dam, California.
Figure 1.6.1-15. Crest (Obermeyer type) gated
(controlled) spillway, Friant Dam, California.
Figure 1.6.1-16. Drum gated
(controlled) spillway, Hoover Dam,
Arizona-Nevada.
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Figure 1.6.1-17. Fuseplug crest (controlled) spillway (reservoir rim), Horseshoe Dam, Arizona.
Figures 1.6.1-18. Fusegate crest (controlled) spillway, Terminus
Dam, California (courtesy of the U.S. Army Corps of Engineers,
Sacramento District, Rick Poeppelman).
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Figure 1.6.2-19. Common features of outlet works.
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Figure 1.6.2-20. Preferred outlet works configuration for low-head embankment dams: hydraulic
control at upstream intake with free flow conditions downstream of the regulating gate/valve [1].
Figure 1.6.2-21. Preferred outlet works configuration for high-head embankment dams: hydraulic
control at downstream control structure, with guard/emergency gate/valve at/near centerline of
dam/dike, and downstream pressurized pipe (between dam/dike centerline and control structure
inside larger access conduit) [1].
Figure 1.6.2-22. Acceptable outlet works configuration for embankment dams: hydraulic control
at/near centerline of dam/dike, with free flow conditions downstream of the regulating
gate/valve [1].
Figure 1.6.2-23. Least acceptable outlet works configuration for embankment dams: hydraulic
control at downstream control structure (i.e., pressurized flow conditions upstream of the
regulating gate/valve along most of the outlet works) [1].
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References
[1] Conduits through Embankment Dams Best Practices for Design,
Construction, Problem Identification and Evaluation, Inspection,
Maintenance, Renovation, and Repair, technical manual, Federal
Emergency Management Agency, September 2005.
[2] Reclamation Manual Design Data Collection Guidelines, Bureau of
Reclamation, September 2007.
[3] Feasibility Design Guidelines, Bureau of Reclamation, July 2008.
[4] Final Design Process, Bureau of Reclamation, April 2008.
[5] Reclamation Manual Cost Estimating, Bureau of Reclamation,
October 2007.
[6] Safety of Dams Project Management Guidelines, Bureau of Reclamation,
March 2003.
[7] Guidelines for Achieving Public Protection in Dam Safety Decisionmaking,
Bureau of Reclamation, June 2003.
[8] Design of Small Dams, third edition, Bureau of Reclamation, 1987.
[9] EM No. 9 Discharge Coefficient for Irregular Overfall Spillways, Bureau
of Reclamation, March 1952.
[10] EM No. 25 Hydraulic Design of Stilling Basins and Energy Dissipators,
Bureau of Reclamation, March 1984.
[11] EM No. 42 Cavitation in Chutes and Spillways, Bureau of Reclamation,
April 1990.
[12] REC-ERC-73-5 Hydraulic Model Studies of Chute Offsets, Air Slots, and
Deflectors for High-Velocity Jets, Bureau of Reclamation, March 1973.
[13] REC-ERC-78-8 Low Froude Number Stilling Basin Design, Bureau of
Reclamation, August 1978.
[14] REC-ERC-85-7 Hydraulic Model Studies of Fuseplug Embankments,
Bureau of Reclamation, December 1985.
[15] REC-ERC-88-3 Overtopping Flow on Low Embankment Dams, Bureau of
Reclamation, August 1988.
DRAFT - Design Standards No. 14 - Appurtenant Structures for Dams
(Spillways and Outlet Works) Design Standards
1-40 DS-14(1)-2 March 2010
[16] DSO-07-07 Uplift and Crack Flow Resulting from High Velocity
Discharge Over Offset Joints, Bureau of Reclamation, December 2007.
[17] ACER TM No. 10 Guidelines for Using Fuseplug Embankments in
Auxiliary Spillways, Bureau of Reclamation, July 1987.
[18] Hydraulic and Excavation Tables, 11th edition, Bureau of Reclamation,
1957.
[19] Computing Degradation and Local Scour, Bureau of Reclamation,
January 1984.
[20] Guide for Computing Water Surface Profiles, Bureau of Reclamation,
undated.
[21] EM No. 13 Estimating Foundation Settlement by One-Dimensional
Consolidation Tests, Bureau of Reclamation, March 1953.
[22] REC-ERC-74-10 Rock Mechanics Properties of Typical Foundation Rock
Types, Bureau of Reclamation, July 1974.
[23] REC-ERC-82-17 Frost Action in Soil Foundations and Control of Surface
Structure Heaving, Bureau of Reclamation, June 1982.
[24] ACER TM No. 9 Guidelines for Controlling Seepage Along Conduits
Through Embankments, Bureau of Reclamation, April 1987.
[25] Drainage for Dams and Associated Structures, technical manual, Bureau of
Reclamation, 2004.
[26] Guidelines for Earthquake Design and Evaluation of Structures
Appurtenant to Dams, United States Committee on Large Dams,
May 1995.
[27] EM No. 14 Beggs Deformeter-Stress Analysis of Single-Barrel Conduits,
Bureau of Reclamation, 1968.
[28] EM No. 14 Supplement Beggs Deformeter-Stress Analysis of Single-
Barrel Conduits, Bureau of Reclamation, 1971.
[29] EM No. 27 Moments and Reactions for Rectangular Plates, Bureau of
Reclamation, 1963.
[30] EM No. 34 Control of Cracking in Mass Concrete Structures, Bureau of
Reclamation, May 1981.
DRAFT - Chapter 1 - Introduction
DS-14(1)-2 March 2010 1-41
[31] Concrete Manual, eighth edition, Bureau of Reclamation, 1981.
[32] EM No. 1110-2-2104, Strength Design for Reinforced-Concrete Hydraulic
Structures, U.S. Army Corps of Engineers, June 30, 1992.
[33] ACI SP-3 Reinforced Concrete Design Handbook (Working Stress
Method), third edition, ACI Committee 317, 1977.
[34] Design Criteria of Retaining Walls, Report of the Task Committee of
Design Criteria of Retaining Walls, Bureau of Reclamation, August 1971.
[35] Roller-Compacted Concrete: Design and Construction Considerations for
Hydraulic Structures, technical manual, Bureau of Reclamation, 2005.
[36] DSO-99-06 A Procedure for Estimating Loss of Life Caused by Dam
Failure, Bureau of Reclamation, September 1999.
[37] Final Technical Report No. 99DG81029 Considerations for Estimating
Structural Response Probabilities in Dam Safety Risk Analysis, Bureau of
Reclamation, September 1999.
[38] Appendix D Toolbox for Handling Loads by Upstream Dams and
Incorporating Consequences for Failure of Downstream Dams, Bureau of
Reclamation, March 2000.
[39] DSO-98-004 Prediction of Embankment Dam Breach Parameters: A
Literature Review and Needs Assessment, Bureau of Reclamation,
July 1998.
[40] Interim Guidelines for Addressing the Risk of Extreme Hydrologic Events,
Bureau of Reclamation, August 2002.
[41] Guidelines, Foundation and Geotechnical Studies for Existing Concrete
Dams, Bureau of Reclamation, September 1999.
[42] Risk Analysis Facilitators Notebook, Bureau of Reclamation, 2008.
[43] Dam Safety Risk Analysis Best Practices Training Manual, Version 1.1,
Bureau of Reclamation, May 2009.
[44] ACER TM No. 3 Criteria and Guidelines for Evacuating Storage
Reservoirs and Sizing Low-Level Outlet Works, Bureau of Reclamation,
1990.
[45] EM No. 7 Friction Factors for Large Conduits Flowing Full, Bureau of
Reclamation, 1977.
DRAFT - Design Standards No. 14 - Appurtenant Structures for Dams
(Spillways and Outlet Works) Design Standards
1-42 DS-14(1)-2 March 2010
[46] Research Report No. 24 Hydraulic Design of Stilling Basin for Pipe or
Channel Outlets, Bureau of Reclamation, 1978.
[47] EM No. 41 Air-Water Flow in Hydraulic Structures, Bureau of
Reclamation, December 1980.
[48] ACER TM No. 4 Criteria for Bulkheading Outlet Works Intakes for
Storage Dams, Bureau of Reclamation, February 1982.
[49] Research Report No. 4 Hydraulic Downpull Forces on Large Gates,
Bureau of Reclamation, 1966.
[50] American Society of Civil Engineers Journal of Hydraulic Engineering
Design of Labyrinth Spillways, by J. Paul Tullis, Nasratollah Amanian,
and David Waldron, March 1995.
[51] Hydraulic Laboratory Report HL-2005-06 Research State-of-the-Art and
Needs for Hydraulic Design of Stepped Spillways, Bureau of Reclamation,
June 2006.
[52] Plastic Pipe Used in Embankment Dams: Best Practices for Design,
Construction, Problem Identification and Evaluation, Inspection,
Maintenance, Renovation, and Repair, technical manual, Federal
Emergency Management Agency, November 2007.
[53] Outlet Works Energy Dissipators: Best Practices for Design, Construction,
Problem Identification and Evaluation, Inspection, Maintenance,
Renovation, and Repair, technical manual, Federal Emergency
Management Agency (to be published in 2010).
Guidelines for Evaluating
Hydrologic Hazards
U.S. Department of the Interior
Bureau of Reclamation June 2006
MISSION STATEMENTS
The mission of the Department of the Interior is to protect and provide access to
our Nations natural and cultural heritage and honor our trust responsibilities to
Indian tribes and our commitments to island communities.
The mission of the Bureau of Reclamation is to manage, develop, and protect water
and related resources in an environmentally and economically sound manner
in the interest of the American public.
Guidelines for Evaluating
Hydrologic Hazards
By
Robert E. Swain
John F. England, Jr.
Kenneth L. Bullard
David A. Raff
U.S. Department of the Interior
Bureau of Reclamation
June 2006
Contents
Page
Executive Summary...................................................................................................................S-1
1. Introduction..............................................................................................................................1
2. Background ...............................................................................................................................1
2.1 General .......................................................................................................................................... 1
2.2 Public Protection Guidelines .......................................................................................................... 2
Dam Safety Program Processes.............................................................................................................. 2
3. Process.......................................................................................................................................3
3.1 Data Sources.................................................................................................................................. 4
3.2 Flood Frequency Extrapolation ...................................................................................................... 4
3.3 Flood Peak and Volume Relationships........................................................................................... 7
4. Analysis Techniques..................................................................................................................8
4.1 Flood Frequency Analysis with Historical/Paleoflood Data .......................................................... 9
4.1.1 Historical and Paleoflood Data ............................................................................................ 9
4.1.2 Mixed-Population Graphical Approach............................................................................ 11
4.1.3 Expected Moments Algorithm.......................................................................................... 12
4.1.4 FLDFRQ3........................................................................................................................ 13
4.2 Hydrograph Scaling and Volumes................................................................................................ 15
4.3 GRADEX Method........................................................................................................................ 17
4.4 Australian Rainfall-Runoff Method ............................................................................................. 25
4.4.1 Approach........................................................................................................................... 26
4.4.2 Calibration ........................................................................................................................ 28
4.4.3 Strengths and Limitations ................................................................................................. 29
4.5 Stochastic Event-Based Precipitation Runoff Modeling with the SEFM..................................... 29
4.6 Stochastic Rainfall-Runoff Modeling With CASC2D ................................................................. 35
4.7 PMF Analysis Technique ............................................................................................................. 36
5. Characterization of Hydrologic Hazards..............................................................................45
5.1 Integration of the PMF into Hydrologic Hazard Evaluations....................................................... 46
5.2 Characterization of Hydrologic Risk for the CFR........................................................................ 46
5.3 Detailed Hydrologic Studies......................................................................................................... 50
6. Case Studies............................................................................................................................52
6.1 Los Banos Dam ............................................................................................................................ 52
6.1.1 Los Banos Hydrologic Hazard Curves Using Flood Frequency Analysis and
Hydrograph Scaling .......................................................................................................... 53
6.2 A.R. Bowman Dam ...................................................................................................................... 54
6.2.1 A.R. Bowman Hydrologic Hazard Curves Using Flood Frequency Analysis and
Hydrograph Scaling .......................................................................................................... 56
6.2.2 A.R. Bowman Hydrologic Hazard Estimates Based on a Stochastic Event Flood Model 57
6.2.3 A.R. Bowman Hydrologic Hazard Estimates Using Bayesian Statistical Estimation ....... 60
6.2.4 Combined Hydrologic Hazard Estimates for Risk Analysis and Dam Safety
Implications ..................................................................................................................... 62
6.3 Fresno Dam ................................................................................................................................. 64
6.3.1 Fresno Dam Hydrologic Hazard Curves Using Flood Frequency Analysis and
Hydrograph Scaling .......................................................................................................... 64
6.3.2 Fresno Dam Hydrologic Hazard Analysis Using the GRADEX Method......................... 66
7. Summary.................................................................................................................................72
8. Bibliography ............................................................................................................................74
Executive Summary
The purpose of this document is to establish guidelines for generating hydrologic hazard
information for use in evaluating hydrologic risk at dams. This information is intended to be
used for risk analysis and prioritization of further work at Bureau of Reclamation (Reclamation)
dams and other U.S. Department of the Interior facilities. Hydrologic hazard information
consists of a flood frequency analysis and frequency flood hydrographs for a full range of
Annual Exceedance Probabilities (AEP) necessary for decision making.
Reclamation has developed an approach toward developing hydrologic hazard curves for use in
evaluating dam safety issues. The procedure relies on extracting information from existing
studies to the fullest extent possible. The procedures and analysis techniques defined in these
guidelines allow for the possibility, and even plausibility, that peak discharge and volume
estimates may exceed the probable maximum flood (PMF). This is a function of the uncertainty
and inconsistency among and between analysis techniques. Therefore, in these cases, the PMF is
believed to represent the upper limit to hydrologic risk.
The procedure for developing hydrologic hazard curves considers the dam safety decision
criteria, potential dam failure mode and dam characteristics, available hydrologic data, possible
analysis techniques, resources available for analysis, and tolerable level of uncertainty. Dam
safety decision criteria determine the probabilistic range of floods needed to address hydrologic
issues. The potential dam failure mode and dam characteristics impact the type of hydrologic
information needed to assess the problem. The specific elements selected to be incorporated in
an analysis of hydrologic hazards should consider the tolerable level of uncertainty. To reduce
the uncertainty in the estimates, additional data collection and use of more sophisticated solution
techniques may be required.
Reclamation currently uses a combination of seven hydrologic methods to develop hydrologic
hazard curves. These general techniques include:
Flood frequency analysis with historical/paleoflood data
Hydrograph scaling and volumes
The GRADEX Method
The Australian Rainfall-Runoff Method
Stochastic event-based precipitation runoff modeling with stochastic event flood model
Stochastic rainfall-runoff modeling with CASC2D
The PMF
It is believed that increasing the level of effort and sophistication of analysis technique increases
the level of confidence associated with the results.
The amount of effort expended on analyzing a hydrologic hazard depends on the nature of the
problem and the potential cost of the solution. A staged approach toward evaluating a
hydrologic safety issue is recommended. Initially, very little effort is expended to determine the
magnitude of the hydrologic hazard. Reclamation attempts to make use of all the available
studies for the site of interest. Often, the PMF and initial flood frequency studies are the only
hydrologic studies available before the start of a probabilistic investigation. When other
hydrologic studies have been performed, available data will be used to decrease uncertainty in
results as well as provide an overall assessment of hydrologic risk.
Dam safety evaluations usually begin by characterizing hydrologic risk for the Comprehensive
Facility Review (CFR) process. If detailed studies have been conducted for the site of interest,
they are summarized, consolidated, and presented to the risk assessment team. About two-thirds
of Reclamations dams can safely accommodate the PMF; when the PMF is selected as the
inflow design flood, no additional work may be required unless other hydraulic issues need
evaluation. Additional hydrologic work begins with a flood frequency analysis developed for
peak flows and volumes and hydrograph scaling. It is believed that this type of information is
sufficient to address hydrologic issues and make dam safety decisions at about 80 percent of the
remaining dams. For the sites that still have potential safety problems, more sophisticated
solution techniques than the initial flood frequency analysis and hydrograph scaling may be
required.
When planning more detailed studies, the goal is to achieve a balance between the amount of
hydrologic analysis needed to address the issues and the level of effort required to conduct the
study. As the studies get more detailed, the results should become more precise and contain less
uncertainty.
When multiple methods are used, alternative hazard curves are developed by weighting results
from the individual analyses. A team of hydrologists evaluates the alternatives and selects the
one most representative for the site for use in the risk assessment. Selection of the final
hydrologic hazard curve depends on the experience of the hydrologists and the assumptions that
went into each analysis.
Three case studies, Los Banos, Fresno, and A.R. Bowman Dams, are presented in these
guidelines to illustrate the variety of methods available. These sites were chosen to demonstrate
the use of flood frequency analysis and hydrograph scaling to characterize the flood hazard and
more detailed followup studies, where available. The A.R. Bowman example shows how
multiple studies were combined into a single flood hazard curve for use in risk assessment.
1. Introduction
The purpose of these guidelines is to develop hydrologic hazard curves and flood hydrographs
for use in evaluating and prioritizing the need for dam safety modifications at Reclamation and
other U.S. Department of the Interior (Interior) facilities. Hydrologic hazard curves are defined
as graphs of peak flow and volume (for specified durations) versus Annual Exceedance
Probability (AEP). The range of AEPs that is displayed on these graphs is to be sufficient to
support the decision making needs of the organization. The intent of these guidelines is to
provide a procedure for developing hydrologic hazard information that will allow decision
makers to determine appropriate courses of action to assure the safety of the dam while
minimizing study costs. Hydrologic hazard information is intended to support Reclamations
risk-based Dam Safety Program.
These guidelines are based on the Dam Safety Research Report DSO-04-08, Hydrologic Hazard
Curve Estimating Procedures (Swain et al., 2004). The research project used information
developed at the Logan, Utah Workshop held in 1999 to provide a framework for Reclamation to
assess flood hazards. The workshop produced the report, A Framework for Characterizing
Extreme Floods for Dam Safety Risk Assessment (Bureau of Reclamation, 1999). Hydrologic
research has led to advances in flood estimation procedures that allow improvements to the
framework. These guidelines describe current approaches used by Reclamation to determine
flood loadings for its dams. New techniques for developing hydrologic hazard information can
be added to these guidelines as they are developed by the hydrology community.
2. Background
2.1 General
Reclamations Dam Safety Program mission is To ensure that Reclamation dams do not present
unacceptable risks to people, property, and the environment (Bureau of Reclamation, 1993). As
the owner of over 350 high- or significant-hazard storage dams in the western U.S., Reclamation
is committed to providing the public and the environment with adequate protection from the risks
that are inherent in collecting and storing large volumes of water. Traditional design and
analysis methods have focused on selecting a level of protection based on spillway evaluation
flood loadings, which were usually based on the probable maximum flood (PMF) (Bureau of
Reclamation, 1999).
Since 1995, Reclamation has used a risk assessment process to determine an appropriate level of
public protection by evaluating a full range of loading conditions and possible dam failure
consequences. This is in contrast to the traditional approach of using upper bound events
without regard to their likelihood of occurrence and without assessment of their incremental
consequences. As a water resources management agency, Reclamation strives to provide
decisionmakers with risk-based information founded upon current or emerging water resources
management and public safety practices (Bureau of Reclamation, 1999).
Risk assessment methods provide techniques to organize and plan the data collection and
technical studies necessary to evaluate dam safety issues at a site. The risk assessment process
allows the risk assessment team to consider the possible adverse outcomes to a given loading
condition and compute the risk associated with each possible outcome. The process involves
identifying all of the possible loading conditions, dam responses, exposure conditions, and
consequences. The overall risk from the dam is the accumulation of the risks associated with
each of these factors (Bureau of Reclamation, 1999).
When evaluating hydrologic hazards, a systematic means of developing flood hazard
relationships is needed for risk-based assessments to determine hydrologic adequacy for
Reclamation dams. The nature of the potential failure mode and characteristics of the dam and
reservoir dictate the type of hydrologic information needed. For some sites, only a peakdischarge
frequency analysis may be required, while at other sites, flood volumes and
hydrographs may be required. The goal of any hydrologic analysis is to provide the hydrologic
information needed to make dam safety decisions at the least possible cost.
2.2 Public Protection Guidelines
Guidance for providing adequate and consistent levels of public protection in the evaluation and
modification of existing dams and the design of new structures are described in the Guidelines
for Achieving Public Protection in Dam Safety Decisionmaking, (Bureau of Reclamation,
2003a). The reader may refer to the guidelines for a complete description of the assessment
measures used by Reclamation in making dam safety decisions.
Determining an appropriate level of public protection involves assessing the existing risks,
determining the need for risk reduction, and, where needed, evaluating specific alternatives to
reduce risk. Because the total needs for the agencys financial and human resources generally
exceed the available resources, the Public Protection Guidelines were prepared to assist
Reclamation staff in presenting public safety information to decisionmakers for prioritizing
among projects and allocating limited resources.
Reclamations Public Protection Guidelines consist of two assessment measures of risk that are
considered in the decision process for a dam: (1) the probability of dam failure and (2) the life
loss consequences resulting from unintentional reservoir release. The annual probability of
failure guideline considers the accumulation of risks from Reclamations total inventory of dams.
The life loss guideline deals with agency public trust responsibilities.
Dam Safety Program Processes
Hydrologic hazard information is generally required during four stages of the dam safety
program process. These four stages include the Comprehensive Facility Review (CFR), Issue
Evaluation (IE), Corrective Action Study (CAS), and Final Design (FD). Most projects do not
progress through each stage of the process because the process is intended to address dam safety
deficiencies, and many projects either have no deficiencies or the safety issues can be resolved
without a need for structural modifications. The remainder of this section of the guidelines will
briefly describe the four stages of the dam safety program process that require hydrologic hazard
information. For more detailed information about the dam safety process, the reader should
review the references cited.
The CFR provides a mechanism for early detection of developing and/or existing dam safety
issues. The CFR is performed every 6 years and consists of a state-of-the-art review of the dam
and its performance, previous studies/analyses (including hydrology), construction practices,
downstream consequences, risk, and dam safety decisions (Bureau of Reclamation, 1998). The
CFR is used to identify risks at individual dams and to prioritize further work. Once hydrologic
hazard information is developed for the CFR, the Dam Safety Office determines whether or not
additional hydrologic studies are required to make decisions during subsequent stages of the
process.
The IE stage is used to confirm problems identified previously. Data collection and/or analysis
activities are focused on addressing specific dam safety issues and updating risk estimates. At
the conclusion of the IE, the decision makers determine whether or not actions are required to
reduce risk at the dam (Bureau of Reclamation, 2003b).
A CAS formulates and evaluates risk reduction alternatives. Data is collected and analyzed to
the extent necessary to develop the details of identified alternatives, to estimate project costs, and
to provide sufficient information to allow decision makers to select and justify the proper course
of action. The baseline risk analysis is updated to show the risk reduction potential of each of
the developed alternatives (Bureau of Reclamation, 2003b).
During the FD stage, the conceptual design is transformed into the final design. Additional data
collection and analysis are used to improve the design, reduce and refine project costs, and
finalize design drawings and specifications (Bureau of Reclamation, 2003b).
3. Process
The elements selected for incorporation in an analysis of hydrologic hazards must consider the
potential dam failure mode and dam characteristics, available hydrologic data, possible analysis
techniques, resources available for analysis, and tolerable level of uncertainty. The potential
dam failure mode and dam characteristics impact the type of hydrologic information needed to
assess the problem. Some problems may require only a peak-discharge frequency curve, while
others may need complete hydrographs. The available data, possible analysis techniques,
resources available, and needs of the decision makers influence the selection of elements to be
included in developing hydrologic hazard curves.
The process that follows provides a systematic approach for estimating hydrologic hazard curves
that can be used for dam safety decisionmaking. It recognizes that additional studies do not
always lead to better decisions. Therefore, the process relies on using existing data and previous
analyses as much as possible to produce hydrologic information suitable for dam safety
decisionmaking at the least possible cost.
3.1 Data Sources
Developing hydrologic hazard curves for risk assessment uses the length of record and type of
data to determine the extrapolation limits for flood frequency analysis. Extrapolation beyond the
data is often necessary to provide information needed for dam safety risk assessments. The
sources of information used for flood hazard analyses include streamflow and precipitation
records and paleoflood data.
Streamflow records consist of data collected at established gaging stations and indirect
measurements of streamflow at other sites. Streamflow data can include estimates of peak
discharge as well as average or mean discharge for various time periods. Most streamflow
measurements on U.S. streams began after 1900, with only a few records dating back that far.
Most often, streamflow records at a single site range in length from about 20 to 60 years. In
some cases these records can be extended to about 150 years using historical information, which
include human observations and recordings prior to the development of systematic streamflow
measurement.
Precipitation and weather data used in hydrologic models can include rainfall, snowfall, snow
water equivalent, temperature, solar radiation, and wind speed and direction. These data are
available from various sources and vary greatly in record length and quality throughout the
United States. Some of these types of data (i.e., snowfall, snow water equivalent, solar radiation,
and wind) are limited to record lengths of less than about 30 years; rainfall and temperature data
are available for some stations for up to 150 years, but in most cases are limited to less than
100 years.
Paleoflood hydrology is the study of past or ancient flood events which occurred before the time
of human observation or direct measurement by modern hydrological procedures (Baker, 1987).
Unlike historical data, paleoflood data do not involve direct human observation of the flood
events. Instead, the paleoflood investigator studies geomorphic and stratigraphic records
(various indicators) of past floods, as well as the evidence of past floods and streamflow derived
from historical, archeological, dendrochronologic, or other sources. The advantage of paleoflood
data is that it is often possible to develop records that are 10 to 100 times longer than
conventional or historical records from other data sources in the western United States.
Paleoflood data generally include records of the largest floods, or commonly, the limits on
the stages of the largest floods over long time periods.
3.2 Flood Frequency Extrapolation
The type of data and the record length used in the analysis form the primary basis for
establishing a range on credible extrapolation of flood estimates. The objective of flood
frequency analysis and extrapolation is to provide reliable flood estimates for a full range of
AEPs necessary for dam safety decisionmaking. In order to develop reliable flood estimates,
flood frequency relationships should include an estimate of the uncertainty around the median
values. The data used in the analysis provide the only basis for verification of the analysis or
modeling results, and as such, extensions beyond the data cannot be verified. The greatest gains
to be made in providing credible estimates of extreme floods can be achieved by combining
regional data from multiple sources. Thus, analysis approaches that pool data and information
from regional precipitation, regional streamflow, and regional paleoflood sources should provide
the highest assurance of credible characterization of low AEP floods. The information that
follows was developed in a workshop sponsored by Reclamation and documented in Bureau of
Reclamation, 1999.
For Reclamation dam safety risk assessments, flood estimates are needed for AEPs of 1 in
10,000 and possibly ranging down to as low as 1 in 100,000,000. Developing credible estimates
at these low AEPs generally requires combining data from multiple sources and a regional
approach. Table 3-1 lists the different types of data that can be used as a basis for flood
frequency estimates and the typical and optimal ranges of credible extrapolation for AEP
(Bureau of Reclamation, 1999). In general, the optimal ranges are based on the best
combination(s) of data envisioned in the western U.S. in the foreseeable future. Typical ranges
are based on the combination(s) of data that are commonly available and analyzed for most sites.
Table 3-1.Data types and extrapolation ranges for flood frequency analysis
(Bureau of Reclamation, 1999)
Type of data used for flood frequency analysis
Range of credible extrapolation for annual
exceedance probability
Typical
Optimal
At-site streamflow data
1 in 100
1 in 200
Regional streamflow data
1 in 500
1 in 1,000
At-site streamflow and at-site 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 data sets and extrapolation
1 in 40,000
1 in 100,000
Many factors can affect the equivalent independent record length for the optimal case. For
example, gaged streamflow records in the western United States only rarely exceed 100 years,
and extrapolation beyond twice the length of record, or to about 1 in 200 AEP, is generally not
recommended (Interagency Advisory Committee on Water Data [IACWD], 1982). Likewise,
for regional streamflow data the optimal range of credible extrapolation is established at up to 1
in 1,000 AEP by considering the number of stations in the region, lengths of record, and degree
of independence of these data (Hosking and Wallis, 1997). For paleoflood data, only in the
Holocene epoch (or the past 10,000 years) is climate judged to be sufficiently like that of the
present climate for these types of records to have meaning in estimating extreme floods for dam
safety risk assessment. This climatic constraint indicates that an optimal range for extrapolation
from paleoflood data, when combined with at-site gaged data, for a single stream should be up to
about 1 in 10,000 AEP. For regional precipitation data, a similar range is imposed because of the
difficulty in collecting sufficient station-years of clearly independent precipitation records in the
orographically complex regions of the western United States. Combined data sets of regional
gaged and regional paleoflood data can be extended to smaller AEPs, perhaps to about 1 in
40,000, in regions with abundant paleoflood data. Analysis approaches that combine all types
of data are judged to be capable of providing credible estimates for an AEP range up to about 1
in 100,000 under optimal conditions.
In many situations, credible extrapolation ranges may be less than optimal. Typical ranges
would need to reflect the practical constraints on the equivalent independent record length that
apply for a particular location. For example, many at-site streamflow record lengths are shorter
than 100 years. If in a typical situation the record length is only 50 years, then the range of
credible extrapolation might be up to an AEP of about 1 in 100. Similarly, many paleoflood
records do not extend to 10,000 years, and extensive regional paleoflood data sets do not
currently exist. Using a record length of about 4,000 years, a typical range of credible
extrapolation might be up to an AEP of 1 in 15,000 based on regional streamflow and regional
paleoflood data.
The information presented in table 3-1 is intended as a guide; each situation is different and
should be assessed individually. The ranges of extrapolation should be determined by evaluating
the lengths of records, number of stations in a hydrologically homogeneous region, degree of
correlation between stations, and other data characteristics that may affect the accuracy of the
data.
Ideally, one would like to construct the flood frequency distribution for all floods that could
conceivably occur. However, the amount of data and flood experience for any site or region
constrain the range of the floods to which AEPs can be assigned based solely on data. In
general, the scientific range to which the flood frequency relationship can be credibly extended,
based upon any characteristics of the data and the record length, will fall short of the PMF for a
site. However, there is a need in dam safety risk assessment to determine the probability of
occurrence of very large floods with very small AEPs. The lack of an ideal data set does not
absolve the hydrologist from extending the flood frequency relationship to cover the full range of
AEPs needed for risk assessment. Therefore, a systematic approach is provided for estimating
hydrologic hazard curves that can be used for dam safety decisionmaking.
Floods can be categorized, according to the Australian Rainfall and Runoff: A Guide to Flood
Estimation (Nathan and Weinmann, 2001), as large, rare, and extreme. These flood categories
are shown in figure 3-1. Large floods generally encompass events for which direct observations
and measurements are available. Rare floods represent events located in the region between
direct observations and the credible range of extrapolation from the data. Extreme floods
generally have very small AEPs, which are beyond the credible range of extrapolation but are
still needed for dam safety risk assessments. Occasionally, Reclamation has an interest in floods
with an AEP as low as 1 in 108.
Extreme floods border on the unknowable. Uncertainty is very large and unquantifiable. Since
data cannot support flood estimates in this AEP range, hydrologists and engineers must rely on
our knowledge and understanding of hydrologic processes to estimate extreme floods.
Oftentimes, these floods may result from unforeseen and unusual combinations of hydrologic
parameters generally not represented in the flood history at a particular location. One potential
upper bound to the largest flood at a particular site of interest is the PMF.
Figure 3-1.Characteristics of notional floods (Nathan and Weinmann, 2001).
Reclamation uses the PMF as the upper limit of flood potential at a site for storm durations
defined by the probable maximum precipitation (PMP). If peak flows or volumes calculated
using probability or statistically based hydrology methods exceed those of the PMF, then the
PMF is used in evaluating the hydrologic risk and as a theoretical and practical upper limit to
statistical extrapolations. The PMF is defined as the maximum runoff condition resulting from
the most severe combination of hydrologic and meteorological conditions that are considered
reasonably possible for the drainage basin under study (Cudworth, 1989). If the PMF has been
properly developed, it represents the upper limit to runoff that can physically occur at a particular
site. Various storm types, sequences, and durations are taken together with the most severe
hydrologic parameters in its development. Extrapolation of statistical analyses can become
unbounded for flood distributions that exhibit positive skewness; therefore, Reclamation uses the
PMF to limit extrapolation to flood discharges that are physically possible.
Oftentimes, reliable flood frequency estimates are needed for very low AEPs for use in dam
safety decisionmaking. Considerable judgment may be required to extrapolate out to the low
AEPs required for risk assessment. Even though the flood frequency estimates become less
reliable as they are extended beyond the optimal ranges, a systematic way of doing this provides
a useful decision making tool.
3.3 Flood Peak and Volume Relationships
Hydrologic hazard relationships display peak flow and flood volumes for various durations
versus AEP. Figure 3-2 is a hypothetical example of the type of relationship needed to address
hydrologic dam safety issues. Floods with AEPs as low as 1 in 108 are desired to encompass the
full range of events needed for dam safety risk assessment. The next section of this report
describes the available approaches for developing the flood peak and volume relationship. Some
of the approaches will also produce flood hydrographs, which can be routed through the
reservoir.
1.00E+03
1.00E+04
1.00E+05
1.00E+06
Annual Exceedance Probability (%)
Peak Discharge (ft3/s)
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Volume (acre ft)
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1 (10-6)
1 (10-5)
2.5
Peak Discharge
1-Day Volume
3-Day Volume
5-Day Volume
7-Day Volume
15-Day Volume
Figure 3-2.Example hydrologic hazard curve.
4. Analysis Techniques
The main probabilistic and engineering hydrology methods that are currently being used,
applied, and under investigation by the Flood Hydrology Group are summarized in this section
of the report. There are seven general techniques:
Flood frequency analysis with historical/paleoflood data
Hydrograph scaling and volumes
The GRADEX Method
The Australian Rainfall-Runoff Method
Stochastic event-based precipitation runoff modeling with the stochastic event flood
model (SEFM)
Stochastic rainfall-runoff modeling with CASC2D
The PMF
Other models and approaches are briefly noted by reference in each section. General sources of
models and approaches for estimating extreme floods are listed in Maidment (1993), Singh
(1995), and Bureau of Reclamation (1999). Methods to calculate extreme floods and associated
probabilities have recently been revised and published in the United Kingdom (Institute of
Hydrology, 1999) and Australia (Nathan and Weinmann, 2001).
4.1 Flood Frequency Analysis with Historical/Paleoflood Data
There are three main techniques that Reclamation currently uses to develop a peak-flow
frequency curve and integrate streamflow (gage) data, historical data, and paleoflood data. The
first is a mixed-population graphical approach (England et al., 2001). The two other techniques
are statistical models that use gage, historical, and paleoflood data. The Expected Moments
Algorithm (EMA) (England, 1999) uses moments to estimate the parameters of a log-Pearson
Type III (LP-III) distribution and is consistent with Bulletin 17B (IACWD, 1982). A Bayesian
maximum likelihood approach is used by FLDFRQ3 (OConnell, 1999) to estimate a peak-flow
frequency curve with historical and paleoflood data and uncertainties. All three techniques have
been used for estimating flood peaks at various Reclamation dams.
4.1.1 Historical and Paleoflood Data
Many different kinds of historical and paleoflood data can be used for flood frequency analysis.
Historical flood data are typically extreme floods that have occurred and were described in some
qualitative or quantitative fashion before establishing a stream gaging station. The typical
information that is available for historical floods is the date of occurrence and the height of the
water surface (Thomson et al., 1964). In many cases, people physically mark, on a relatively
permanent surface, the approximate high-water mark of a flood (Thomson et al., 1964; Leese,
1973; Natural Environment Research Council, 1975; Sutcliffe, 1987; Fanok and Wohl, 1997).
Paleoflood hydrology is the study of past or ancient floods that occurred before the time of
human observation or direct measurement by modern hydrologic procedures (Baker, 1987). The
basic types of paleoflood indicators that are useful for flood frequency analysis are paleostage
indicators and botanical evidence (Wohl and Enzel, 1995; Baker, 2000). Recent investigations,
techniques, and analyses for collecting and using paleoflood data are discussed in House et al.
(2002). Fluvial geomorphic evidence includes erosional and/or depositional features that are
used to infer paleostages or non-inundation levels. The fluvial geomorphic evidence used in
paleoflood and flood frequency studies that represents paleostage indicators includes: silt lines,
scour lines, slackwater deposits, boulder and gravel bars, and modified geomorphic surfaces
(Costa, 1978; Baker, 1987; Kochel and Ritter, 1987; Jarrett and Costa, 1988; Salas et al., 1994;
Jarrett and England, 2002; Levish, 2002). Botanical evidence consists of vegetation that records
evidence of a flood (or several floods) or indicates stability of a geomorphic surface for some
time period. Botanical evidence of floods includes: corrosion scars, adventitious sprouts, tree
age, and tree-ring anomalies (Hupp, 1987).
The historical and paleoflood data can generally be represented with four major data classes
(Stedinger et al., 1988): floods of known magnitude, floods of unknown magnitude that are less
than some level, floods of unknown magnitude that exceed some level, and floods with
magnitudes described by a range. Historical and paleoflood data generally are described in terms
of exceedance or non-exceedance of a discharge threshold (Qo). To correctly interpret the data,
one needs to understand the mechanisms by which historical and paleoflood records document
the magnitudes of floods that either did, or did not, occur (Stedinger et al., 1993). In many
situations, one knows the magnitude of each flood. Annual (gage) peak discharge estimates,
historical floods, and paleofloods whose magnitudes are known are described by floods of
known magnitude class. For example, the solid bars depicted in figure 4-1 describe known
floods in the gage and historical period.
The most common situation for using historical and paleoflood data in flood frequency analysis
is that a peak discharge Q is known to be smaller than some threshold Qo, but the magnitude of
Q is unknown. The shaded region in figure 4-1 represents these unknown floods that are below a
threshold Qo. The total record length (n) is the sum of the systematic (s) and historical/
paleoflood (h) record lengths (n=s+h). We define the number of observations that exceed the
threshold in the systematic record (s) as e, which is equal to 1 in figure 4-1. The number of
known observations in the historical period (h) is designated e (equal to 3 in figure 4-1); it is
also known that the values are greater than Qo. We define k as a random variable equal to the
number of observations greater than Qo in the entire record n, where k = e + e. The number of
observed floods is denoted g, where g = s + k - e.
In some cases, one may know that no floods exceeded the discharge threshold, or k=0. Data in
this case have been termed a non-exceedance bound (Levish et al., 1994; Levish, 2002), where
one has knowledge that no flood has exceeded a designated threshold or geomorphic surface in
some time period. An example of a non-exceedance bound is knowledge that a river has not
inundated Main Street, a bridge deck spanning a river, or a geomorphic surface in some time
period. Knowledge that k = 0 is valuable information that can be used in flood frequency
analysis.
Historical and paleoflood information may be described in terms of a flood that exceeded a
threshold, with no upper bound. In some cases, one knows only that a flood was larger than
some level and does not know the magnitude of the flood. One knows the number of floods that
exceeded the discharge threshold. Stedinger and Cohn (1986) have termed this category as
binomial censoring, in which the exact magnitude of a value is unknown except that it
exceeded a lower threshold (see also Russell, 1982). This situation is common for some types of
botanical investigations where one can, at present, determine only the minimum stage for plant
damage (Hupp, 1988).
There are many situations in which one does not know the exact magnitude of a flood, but that it
lies within a range or interval. Interval censoring is used when the exact magnitude of a flood is
unknown, but is known to be between some upper and lower amount (Stedinger et al., 1988;
Cohn et al., 1997). This class can be used to describe floods with measurement uncertainty. In
some cases, the upper threshold, Qu, can vary for each observation, depending on the data source.
e' = 3 e = 1
k = number of floods exceeding Qo = e + e' = 4
historical period h systematic (gage) record s
Qt
t
total record length n = h + s
Peak Discharge
Water Year
discharge threshold Qo
Figure 4-1.Example of peak discharge time series with historical period and discharge
threshold Qo. The shaded area represents floods of unknown magnitude less than Qo.
4.1.2 Mixed-Population Graphical Approach
A mixed-population graphical peak-discharge frequency approach has been developed by
Reclamation (England et al., 2001). The graphical approach is an at-site frequency method and
the frequency curve is constructed in two distinct parts: (1) standard hydrologic statistical
methods are used to define a frequency curve for return periods less than and including the
100-year return period (e.g., IACWD, 1982; Ries and Crouse, 2002) and (2) graphical methods
are used for estimates greater than the 100-year return period. Peak discharge estimates from
gaging stations are used to define the first part of the curve and at-site paleoflood data are used to
define the second part of the curve. The first part is estimated assuming an LP-III distribution.
One of three at-site techniques and associated computer programs is typically used to estimate
the parameters of the LP-III distribution, calculate quantiles, and estimate confidence intervals:
(1) the Bulletin 17B Method (IACWD, 1982) and FREQY (Carson, 1989); (2) expected
moments methods (Cohn et al., 1997) and EMA (England, 1999); or (3) Bayesian maximum
likelihood and FLDFRQ3 (OConnell, 1999). Historical information is included in the at-site
frequency analysis when it is available. Historical data can be used to adjust a so-called high
outlier using FREQY, EMA, or FLDFRQ3. Low outliers can be adjusted using IACWD (1982)
methods. The second portion of the frequency curve is estimated assuming a 2-parameter log-
Normal (LN-2) distribution. It is defined between the 100-year and the available paleoflood data
return periods, and extrapolated beyond the paleoflood data using this LN-2 distribution. Two
points are typically used to estimate this portion of the flood-frequency curve: (1) the LP-III
model 100-year peak discharge estimate and (2) the midpoint in time and discharge of the
paleoflood data. Logarithms (base 10) of the peak flows and standard Normal variates of return
periods are used to estimate the LN-2 parameters using least squares (England, 2000). The LN-2
distribution was found to reasonably represent daily standardized precipitation in the western
United States (Lane, 1997).
The mixed-population graphical approach is used to estimate flood hazard curves. The approach
has been developed so that one can estimate an extreme flood frequency curve at any location in
the western United States with a minimal amount of effort using existing streamflow data and
some site-specific paleoflood data. There are two main assumptions of this graphical approach
for estimating extreme flood probabilities: the upper portion of the frequency curve is
appropriately defined by the 100-year peak discharge and paleoflood data and the extrapolation
of this portion of the curve using a LN-2 model is appropriate. An example peak-flow frequency
curve using the graphical approach is shown in figure 4-2. The approach has been reviewed by
Kuczera (2000). Kuczera pointed out the major weaknesses were the use of an envelope curve,
lack of confidence intervals, and extrapolation. Kuczera recommended that regional growth
curves be used to compliment the use of envelope curves.
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General Storm PMF Peak Discharge 233,700 ft3/s
Spillway capacity 53,000 ft3/s at El. 3565 (top of dam)
This flood frequency relationship is based on available streamflow data
and preliminary paleoflood data. This information presented is only
suitable for use in a CFR Baseline Risk Analysis. These curves should not
be extrapolated. Refer to the report for a discussion of uncertainties.
Preliminary Regional Paleoflood Estimates
70,000 - 165,000 ft3/s in 200 to 10,000 years
Preliminary Range of Regional Peak Discharge Observations
70,000 - 165,000 ft3/s
Observed Peaks
middle estimate
upper and lower estimates
Peak Discharge (ft3/s)
Return Period (years)
Figure 4-2.Example application of mixed-population graphical flood frequency curve
using peak discharges on the South Fork Flathead River near Hungry Horse, Montana.
4.1.3 Expected Moments Algorithm
The EMA (Lane, 1995; Lane and Cohn, 1996; Cohn et al., 1997, 2001) is a new moments-based
parameter estimation procedure that was designed to incorporate many different types of
systematic, historical, and paleoflood data into flood frequency analysis. EMA assumes the
LP-III distribution is the true distribution for floods. EMA was designed to handle the four
different classes of historical and paleoflood data beyond the applicability of the Bulletin 17B
historical weighting procedure (IAWCD, 1982). As noted by Cohn et al. (1997, 2001) and
England (1998), EMA is philosophically consistent with, and is an improvement to, the Bulletin
17B method of moments procedure when one has historical or paleoflood information. EMA is
specifically designed to use historical and paleoflood data, in addition to annual peak flows from
gaging stations, in a manner similar to Maximum Likelihood Estimators (Lane and Cohn, 1996).
It is a more logical and efficient way to use historical and paleoflood data than the current
Bulletin 17B historical method, and it is a natural extension to the moments-based framework
of Bulletin 17B.
The five basic steps of EMA are:
(1) Estimate an initial set of the three sample statistics (΅,s 2 ,.), from the floods with known
magnitudes. These floods are typically observations from the gaging station record and
possibly some historical or paleofloods. At this step, floods with unknown magnitudes
and magnitudes described by a range are not included.
(2) Based on the initial sample statistics from step (1), estimate a set of the LP-III
distribution parameters (t,a,ί ).
(3) From the set of LP-III parameters from step (2), estimate a new set of sample moments
based on the complete data set: known-magnitude floods, floods less than some
threshold(s), unknown magnitude floods that exceed some threshold(s), and floods
described by a range.
(4) From this new set of moments, estimate a new set of LP-III parameters.
(5) Compare the parameters from step (4) to those computed from step (2). Repeat steps (3)
and (4) until the parameter estimates converge. The main equations used by EMA are
listed in Cohn et al. (1997), England (1999), and England et al. (2003).
EMA has been rigorously peer reviewed in the literature (Cohn et al., 1997, 2001; England et al.,
2003a, 2003b) and provides a suitable flood frequency model. EMA has been applied at many
sites for peak-flow frequency (England et al., 2003b). The National Research Council applied
EMA for 3-day annual maximum mean floodflows on the American River (NRC, 1999). An
example peak-flow frequency curve with EMA is shown in figure 4-3. There are several
limitations with the current version of EMA: (1) the program assumes that the distribution is
LP-III, (2) software has not been fully developed to implement the confidence interval technique
of Cohn et al. (2001), and (3) low outlier and regional skew methods with EMA have been
recently developed (Griffis et al., 2003), but not tested with actual data.
4.1.4 FLDFRQ3
FLDFRQ3 (OConnell, 1999; OConnell et al. 2002) uses a Bayesian maximum likelihood
procedure to estimate parameters of various distributions. The Bayesian approach includes
Figure 4-3.Example application of EMA for American River annual maximum
3-day mean discharge frequency analysis.
measurement uncertainty in the parameter estimation procedure. This approach uses a global
parameter integration grid in order to identify ranges of probability distributions that are
consistent with the data (OConnell, 1999). Two measurement error sources are included: peak
discharge measurement errors and errors in paleohydrologic bound ages. Bayesian methods
(Tarantola, 1987) and likelihood functions modified from Stedinger and Cohn (1986) are used to
incorporate data and parameter uncertainties. Two options can be used to find the global
maximum likelihood estimate in FLDFRQ3 (OConnell, 1999): simulated annealing and the
downhill simplex method. In FLDFRQ3, one is able to choose among five main three-parameter
probability distributions to assume a peak discharge parent distribution. These distributions are
the Generalized Extreme Value, Generalized Logistic, Generalized Normal, Generalized Pareto,
and Pearson Type III (P-III) (Hosking and Wallis, 1997). These distributions include two
logarithmic transform options for P-III models to include the LP-III. OConnell (1999) provides
details of the numerical approach used for estimating distribution parameters and uncertainty
using grid integration.
There are generally three main steps in running FLDFRQ3 (OConnell, 1999): input and data
check, parameter estimation for a particular distribution, and generating parameter uncertainties
for a particular model (e.g., LP-III) using grid integration. The data are grouped into two broad
classes: data with normal uncertainties, such as peak discharge, and values in a range with
potentially variable probability density and skew within the range, such as paleohydrologic
bound discharges and ages and discrete paleofloods. After entering and checking data, the
parameter estimates are obtained from the data and assumed model. The user then checks the
appropriateness of the model and estimated parameters. There can be several steps here to
99 98 95 90 80 70 60 50 40 30 20 10 5 2 1 0.5
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1848-1997, n=149, s=93, h=56,
Qo=4,160 m3/s, 1862 flood= 4,160 m3/s
Observed Flows
LP-III model
90% Confidence Intervals
Discharge (m3/s)
Annual Exceedance Probability (%)
determine the best models (there can be more than one) that fit the data and the model
parameters. Finally, the user estimates the parameter uncertainty given the chosen model and
parameter combination. OConnell et al. (2002) demonstrate how to combine results of several
models and their parameter uncertainties using a likelihood criterion.
FLDFRQ3 has been rigorously peer reviewed in the literature (OConnell et al., 2002) and
contains suitable flood frequency models for all levels of analysis. It has been used at many sites
for peak-flow frequency, such as Folsom Dam (Bureau of Reclamation, 2002), Seminoe and
Glendo Dams (Levish et al., 2003), and Pathfinder Dam (England, 2003). An example peakdischarge
frequency curve using FLDFRQ3 is shown in figure 4-4.
Figure 4-4Annual peak-discharge frequency inflows to Pathfinder Dam, Wyoming,
from best-fitting LP-III distribution using FLDFRQ3 (England, April 2003).
4.2 Hydrograph Scaling and Volumes
Practical tools have been developed for estimating probabilistic hydrographs that can be used in
risk analyses for dam safety. These tools are presented in England (2003a) and are summarized
below. The key feature of the approach is to use peak-discharge frequency curves that include
paleoflood data as a basis to develop hydrographs and volume frequency curves. The methods
are relatively flexible and can be tailored to different types of investigations. The methods need
to be adjusted depending on the available data at the site and region of interest. For example, if
a peak-discharge frequency curve developed using the graphical approach is available, one
could use less detailed methods to develop hydrographs because the data might not warrant
sophisticated techniques. In contrast, if detailed, high-quality peak discharge and paleoflood
60 50 40 30 20 10 5 2 1 0.5 0.1 0.01
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9,000
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Results show best-fitting LP-III Distribution
Observed_D
LP-III Median (50%)
LP-III 2.5 and 97.5 Cofidence Limits
5 Paleofloods
Transferred from Glendo Dam
Reservoir Inflow Peak Discharge (ft3/s)
Annual Exceedance Probability (%)
Paleohydrologic Bounds
Transferred from Glendo Dam
data are available, one could use more refined methods such as the SEFM (MGS Engineering
Consultants, Inc. [MGS], 2001) discussed below.
Probabilistic hydrographs can be constructed based on streamflow estimates from gaging
stations, historical data, and paleoflood data. Four components are used: (1) a peak dischargeprobability
relationship, (2) an extreme storm duration probability relationship, (3) relationships
between peak discharge and maximum mean daily flow volumes, and (4) observed hourly flow
hydrographs that have regulation effects removed. The key idea is calibration or scaling of
hydrographs to match peak discharge for a given probability. The approach relies completely on
the specification of a peak-flow frequency curve that describes the probabilities of interest, based
on paleoflood data.
There are four major assumptions for developing the hydrographs: (1) the probability of peak
discharge represents a probability of the composite hydrograph, (2) unit hydrograph assumptions
apply to the basin, (3) direct runoff volumes can be estimated from daily flow hydrographs, and
(4) the recorded streamflow observations, historical information, and paleoflood data in the river
basin of interest provide an adequate sample so one can extrapolate peak discharge probabilities,
peak-volume relationships, and hydrographs for extreme floods. Maximum mean discharge
( d Q ) for n-day periods is related to peak discharge (Qp) by a power function:
(1)
The assumed known variable is peak discharge (Qp), with an associated exceedance probability
estimate from the frequency curve. The quality of the regression relationship expressed in
equation (1) depends principally on the data from the site of interest and the flow duration (n).
Mixed-population flood data (e.g., from thunderstorms, snowmelt, or rain-on-snow) can lead to
difficulties in obtaining statistically significant relationships. Good regression fits are typically
found for shorter duration (1- to 7-day) flow volumes; the relationships become progressively
worse for longer durations. The maximum n-day hydrograph ordinates are linearly scaled, based
on the selected n-day volume.
An alternate approach to using streamflow data is to use hydrographs from rainfall-runoff
models as a basis for scaling. In these cases, there are typically no flood hydrograph data at the
site of interest. A design flood hydrograph, a PMF hydrograph, or other suitable hydrograph for
the basin is obtained. The hydrograph can then be scaled in some linear fashion to match peak
flows from a peak-flow frequency curve. The analyst needs to be careful to ensure that flood
volumes do not exceed physical limits when applying this scaling procedure.
Probabilistic hydrographs, developed from scaling streamflow observations or from rainfallrunoff
models, are combined with recommendations for initial reservoir levels for hydrograph
routing. Reservoir routing issues and selection of varying initial levels are discussed in England
(2003a). One can then determine a maximum reservoir level by routing the given hydrograph
and initial reservoir level. Initial reservoir levels can sometimes have a large effect on maximum
reservoir level estimates for extreme floods. Maximum reservoir elevation probability estimates
depend on the inflow hydrograph peak, volume, shape, and probability estimate. The initial
reservoir level can also be a major factor. The selection of an appropriate initial reservoir level is
of considerable importance in determination of spillway adequacy (Nathan and Weinmann,
d p logQ = a+ blogQ
1999, p. 57). For estimating maximum reservoir levels for design floods such as the PMF,
Reclamation uses a fixed initial reservoir level. This initial reservoir level is usually set at the
top of active conservation or bottom of the flood control pool. This assumption has been
criticized as being unduly conservative. Newton (1983, p. 914) notes that current practice for
most agencies is to assume conservatively high initial pool levels for routing PMFs. Instead of
using a fixed initial reservoir level for routing hydrographs, variable initial reservoir levels are
needed for risk analysis. Initial reservoir levels and associated exceedance probabilities should
be estimated from daily reservoir elevation estimates for the period of record at the site of
interest.
4.3 GRADEX Method
Much of this description of the GRADEX Method is paraphrased from the Ph.D. dissertation,
Methodology for Estimating the Upper Tail of Flood-Peak Frequency Distributions Using
Hydrometeorological Information, by Mauro Da Chunha Naghettini, completed in partial
fulfillment of the requirements for the Ph.D. degree at the University of Colorado, Department of
Civil, Environmental, and Architectural Engineering, 1994. Naghettini, Potter, and Illangasekare
later described the same method in the Water Resources Research publication in 1996. Some
additional comments related to Reclamation dam safety needs are inserted when appropriate.
In its 1988 report, the National Research Council Committee on Estimating the Probabilities
of Extreme Floods identified principles for improving the estimation of floods with AEPs
on the order of 10-3 or smaller. These principles are: (1) substitution of space for time;
(2) introduction of more structure into the models; and (3) focus on extremes or tails as
opposed to or even to the exclusion of central characteristics (NRC, 1988). The methodology
proposed in Naghettinis Ph.D. dissertation (1994) presents techniques for the estimation of
extreme flood peaks and volumes that make strong use of these principles. The main objective
is to develop a peak-flow frequency curve for the extremely rare probabilities. To do so, the
method involves a peak to volume relationship and the derivation of a frequency curve of
extreme flood volumes based on extreme regional rainfall statistics. The method is useful to
current Reclamation dam safety needs in that it provides a means to produce frequency curves
for rare flood volumes and also some apparatus to define peak flows for the extreme flood
volumes. It can also be used to create hydrographs based on the flood volumes and peaks, if
needed.
The method relies on extrapolating a conventionally estimated probability distribution of flood
volumes. To strengthen this step, the GRADEX Method, originally developed by Guillot and
Duband (1967), is incorporated. The GRADEX Method has been used extensively in France
since about 1967 for various improvements and hydrologic safety investigations and spillway
renovations at numerous hydroelectric dams and facilities. The French Committee on Large
Dams has prepared the publication, Small Dams (undated), which outlines the very basic steps
that can be used to perform such calculations in France. The main GRADEX Method is based
on two assumptions:
(1) That, asymptotically, the upper tail of the flood volume distribution is exponential
with the same scale parameter as that which describes the upper tail of the
distribution of rainfall volumes for the basin. Figure 4-5 graphically displays this
assumption.
(2) That any increase in total precipitation during a severe rain event, falling on already
saturated ground, will produce a corresponding increase in volume of the resulting
flood.
The estimation of the rainfall scale parameter has been enhanced in this application from the
original French methodology by incorporating the work of Smith (1989), who developed a
regional model for estimating the upper tail of a frequency distribution based on extreme order
statistics. Figure 4-5 depicts the GRADEX Method.
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RETURN PERIOD (YEARS)
5 - DAY PRECIPITATION TOTALS
BASED ON REGIONAL ANALYSIS AND
EXPONENTIAL DISTRIBUTION
CONVERTED TO A VOLUME OVER
THE BASIN
EXPRESSED AS CFS-DAYS
5 DAY FLOOD VOLUMES FREQUENCY CURVE
FOR THE BASIN BASED ON GRADEX METHOD AND CALIBRATED
TO AVAILABLE STREAM GAUGE
RECORD FLOW VOLUME DATA
EXPRESSED AS CFS-DAYS
5-DAY VOLUMES FROM 54 YEARS OF STREAM GAUGE RECORD
WEIBUL PLOTTING POSITIONS - CFS-DAYS
Figure 4-5.GRADEX Method of volume frequency curve calculation.
The location where the extrapolated flood volume curve takes over from a more conventional
analysis of stream gage volume data, such as using LP-III, is not fixed, but must be assumed. In
the literature from France, this return period ranges from about 10 years, for very impermeable
basins, to 50 years for very permeable basins.
The first assumption of the GRADEX Method given above refers to the upper tail of the rainfall
volume distribution, which is assumed to be a generalized Pareto density function of the form:
gp(p|s,K) = 1/a [1- ((Kp)/a)]1/K - 1 if K . 0 (2)
This will reduce to a simple exponential density function of the form:
gp(p|s,K) = (1/a)exp(-p/a) if K = 0 (3)
Where the positive constants K and a are the location and scale parameters, respectively. The
scale parameter a is a function of various physical components of the available rain gage data
sets such as elevation and mean annual precipitation (MAP). If K > 0 then the distribution of
rainfall for all sites has an upper bound; if K < 0 it is unbounded. If K = 0 the upper tail of the
distribution is exponential with a scale parameter a. The parameter estimates are found by fitting
a distribution that asymptotically exhibits an exponential upper tail (e.g., Exponential, Gumbel,
Gamma, or log-Normal) to rainfall maxima. Combining the two GRADEX assumptions causes
the upper tail of the flood volume distribution to also be exponential with the same scale
parameter a (the GRADEX parameter) as the one estimated for the upper tail of the distribution
of rainfall volumes, except for a necessary conversion to units of volume instead of precipitation
depth.
The first step in the GRADEX Method involves selecting a critical duration. This begins with an
examination of the time series of unregulated daily flows for a stream gage record deemed to be
hydrologically similar to the basin being studied or a record of reservoir daily inflows. What is
required is a series of independent flood events (hydrographs) that have occurred over the entire
length of the unregulated streamflow record. These flood events should be rain-generated, as
opposed to floods derived from snowmelt. Also, the rain-generated flood events should all be of
the same storm type. For these reasons, the stream gage record analysis should be limited to a
season when the rain floods of the same type are most likely to occur based on historic
experience. Once the season is selected, the daily streamflows for each year within that season
are examined. A threshold discharge, Q threshold, is set. The number of daily flows above this
threshold value is observed. Multi-day events with several days of flow above the threshold are
observed. The number of and the duration of each of these multi-day events are then calculated.
It is desired to obtain a set of independent flood events with nearly the same number of events as
the number of years in the length of record. If the number of events calculated is too large or
small, then the threshold Q value is raised or lowered until approximately the number of events
equals the number of years in the stream gage record. The average duration for the entire set of
events is then calculated. This average duration, generally raised to the next highest number of
days, will become the critical duration d used for the rest of the study. Once the critical duration
d is determined, the average flow discharge of all of these events can be calculated. A second
flow value, termed the reference discharge, is also determined such that 90 percent of the
selected flood events will have average d-day flow values less than this discharge value. An
approximate return period is also placed on this reference discharge value by the inverse of the
Gringorten plotting position formula.
Reference return period = 1/((i - 0.44) /(N + 0.12)) (4)
Where N is the total number of years of record and i is the rank of the selected reference
discharge. This part of the analysis can require much hydrologic judgment. Often, a set of daily
flows will show a pattern that is above the selected threshold Q for 1, 2, or 3 or more days, then
drop just below the threshold for 1, 2, or 3 days, and then continue for a few more days above the
threshold. Decisions have to be made as to whether this should all be considered one flood event
or separated into two or more events. Rainfall records from the area may help with this decision,
but, generally, it is left to the analyst to make the decision. Independence of the events is
generally assumed if the time from the end of the first event to the beginning of the next event is
longer than the critical duration that is calculated for this set of events.
In hydrology, this process is often referred to as a marked point process. Much literature is
available dealing with statistical assumptions related to events derived by the marked point
process. By its nature, the set of floods derived by this process may include several events in any
one year, and no events for several years. This is what is desired because the data will be used to
help calibrate the GRADEX-derived flood volume information from rainfall totals for the critical
duration. It is often the case that several large rainfall events can occur in any one year.
Cautions that are given for the selection of the critical duration are: (1) that selection of too short
a duration might result in non-exponential, probably heavier-than-exponential, upper tails for
the rainfall volumes and (2) adoption of too long a duration might result in poor peak-volume
relationships. Since the goal of the application of the GRADEX Method to Reclamation dam
safety investigations is to create a good volume relationship, it is advised to raise the computed
critical duration value to the next higher full day.
In conventional applications of the GRADEX Method, the parameter a can be estimated by
fitting an exponentially tailed distribution to seasonal or annual rainfall maxima. The simplest
estimation procedure of the GRADEX parameter is to fit a Gumbel distribution to a series of
annual maximum rainfall events for a duration d that is equal to the watershed critical duration,
or some other measure based on time of concentration calculations. However, the most
frequently used estimation procedure is to fit an exponentially tailed distribution to seasonal
(sometimes monthly) rainfall maxima and then combine the seasonal (monthly) distributions to
obtain the annual distribution. What can be shown is that the annual frequency curve, which
would no longer be a strictly exponential curve, will tend to have the same shape or slope
(GRADEX) as that of the month that produces the largest rainfall amounts, especially at the
extreme upper end. A slightly more conservative approach is to use smaller durations of
seasonal maxima rainfall totals for even smaller durations, even 24 or 48 hours.
Estimation of the GRADEX parameter of flood volumes requires that different units for
expressing the rainfall be used. If the drainage area and critical duration d are expressed as mi2
and days, respectively, and the GRADEX parameters are to be expressed in English units, then:
Flood Volume GRADEX = [(26.89 * DA)/d] * Rainfall GRADEX (5)
Similar expressions exist for computations done in metric units.
Usually, following the French examples, the extrapolation of the flood volume distribution
according to the GRADEX parameter starts at the 10-year flood for small and relatively
impervious basins, or at the 20-year flood for larger basins, or possibly the 50-year flood for
watersheds showing very little topographical relief or high infiltration capacity.
The current application of the GRADEX Method applies a new methodology to estimate the
slope of the rainfall durations for a critical duration d within a specified season. This new
approach combines deterministic constraints with contemporary statistical techniques, extracting
the maximum information from the available data. The regional rainfall frequency model
described in this section is based on the premise that meteorological processes affecting large
rainfall events may be different from those affecting smaller rainfall events. The model is an
adaptation of a regional flood frequency model developed by Smith (1989) and is based on
results from extreme value theory. In this model, the parameters a and K in the Pareto or
exponential distribution functions (equations 2 or 3) are determined based on a regional analysis
of the largest d-day rainfall totals for several daily rainfall stations that are shown to be or
believed to be homogeneous and to represent the meteorological conditions of the basin under
study. The parameter a is further allowed to be a function of the basin mean annual precipitation
and the basin mean elevation.
a = Si = exp(c + b1Wi1 + b2Wi2) (6)
Where Wi1 and Wi2 are the natural logarithms of the set of rain gage elevations and mean annual
precipitation values for each gage site i, respectively. The constants b1, b2, and c are determined
as part of the parameter estimation process. This is an improvement over the French general
cases where only one rain gage or set of regional information reduced to one point for any basin
may be used. Further, no consideration of elevation or mean annual precipitation is given in the
standard GRADEX analysis.
The mathematical process to estimate the parameters K, c, b1, and b2 from the data set of rainfall
totals proceeds as a maximum likelihood parameter estimation process. A log-likelihood
function is then formed.
L K b b c =S S g Zg K b b c + C n p ( , , , ) ln[ ( / , , , )] 1 2 1 2 (7)
Zg is the set of random variables of d-day rainfall totals above the threshold precipitation value
at each gage site. The double sum is for all of precipitation values above the threshold value at
each site and then summed over all sites.
Partial derivatives of the log-likelihood function with respect to the four parameters to be
estimated (K, b1, b2, and c) are derived. In taking the partial derivatives, the additional constant
C in the log-likelihood function is eliminated. These partial derivative functions are then set
equal to zero, and a series of four non-linear equations with four unknowns (if K 0) or three
non-linear equations with three unknowns (if K = 0 is assumed) are formed. As part of the
parameter estimation process, statistical tests are performed to see if the three-parameter
exponential distribution form is equally valid for the data set as is the four-parameter Pareto
distribution. In almost all cases, this is true. The assumption that the extreme rainfall totals can
follow an exponential distribution is validated, and the rest of the GRADEX Method follows.
The three parameters are then used to form the single scale parameter a (equation 5) for a single
parameter exponential distribution form. In cases where the statistical test does not prove the
validity of the three-parameter exponential distribution form, the rainfall total data sets need to
be further investigated as to homogeneity.
.
Software to solve the complex sets of non-linear equations was adopted from the MINPACK
software package originally developed in 1980 at the Argonne National Laboratory. This
software is now free and in the public domain. Only the most extreme rainfall totals for the
critical durations d at each daily rainfall stations are used as data. Once the equations are solved,
the scale parameter a is estimated. Readers who are interested in the complete theoretical and
mathematical background are referred to Naghettini (1994, chapter 4). The remainder of this
discussion deals with the hydrological and meteorological details of this method.
The method requires that all stations selected have a common period of record that is as long as
possible. Daily rainfall totals for all official rainfall gage stations in the United States are
available on compact disks from Hydrosphere Corp. (2002). Several stations near the basin
being studied need to be selected and their periods of record noted. These rain gage records
should represent climate and meteorological conditions similar to conditions in the basin being
studied. Stations too far from the study area or too high or low in elevation should not be used.
The same continuous period of record should be available for each rain gage selected. It is also
advisable to avoid selecting too many stations in any one area, which would then overly weight
the climate and rainfall records in that localized area compared to the rest of the surrounding
areas for the basin being studied.
The method relies on data from the rainfall gage records that cover the same continuous period
of time for each gage. If large gaps in the gage record are found (even though the beginning and
ending dates may cover the continuous period needed), the record should be discarded.
Recorded rainfall data is subject to many errors, omissions, and other anomalies. Within each
rain gage record, missing days, days with accumulated rainfall from several previous days, and
days with only a trace of precipitation or other notations are noted. Analyzing the daily rainfall
totals involves summing the total rainfalls for the number of days previously defined as the
critical duration d for this basin based on analysis of the appropriate stream gage records. The
process is complicated by the need to eliminate all the days with missing data or with special
notes, such as when the recorded value was already an accumulated value. Any multi-day total
rainfall that includes such data is then set to zero and eliminated from further consideration.
Trace values are set to zero for the day that they were reported and then they are allowed in the
summation process. Any extremely large daily rainfall totals need to be further checked against
official hardcopy records, and the correct daily values for these dates are inserted in the analysis
if changes are needed. In the process, independence of the rainfall total events also needs to be
ensured. The start dates of any two multi-day events must be more than the critical duration d
apart.
The method requires selection of a number of multi-day total rain events at each gage equal to
the number of common years of record for all selected gages. A threshold d-day total rainfall for
each gage is selected such that exactly the same number of independent d-day rain totals is above
this value as are in the continuous period of record covered by all the rain gages in the analysis.
Further, a reference total precipitation value for each rain gage is also selected such that
90 percent of the previously selected events are below this reference precipitation value. The
threshold and reference precipitation values are used later in the statistical analysis. Only the top
10 percent of the d-day rainfall totals are used in the regional analysis. This amounts to a form
of top-end fitting for the precipitation totals.
To further facilitate the computations, the rainfall multi-day totals are reduced by subtraction of
the reference precipitation amount for each rain gage. This step is necessary to eliminate very
large numbers in the calculations that follow. This is a form of indexing and is common in
many regional flood methodologies.
The upper order statistical method calculates the slope (or GRADEX parameter) of the best-fit
decaying exponential distribution of the top 10 percent of the d-day total indexed precipitation
amounts for each selected rain gage site. The selected station elevations and mean annual
precipitations help weight the slope parameter. Knowing the basins mean elevation and MAP, a
GRADEX parameter fit specifically to the drainage basin being studied can be calculated. The
result is the slope of the decaying exponential distribution of the most extreme precipitation
amounts that the selected precipitation data suggest can occur over the drainage basin. The
distribution of d-day total index precipitation values can then be used with knowledge of the
contributing drainage area for the basin to create associated d-day volumes as shown in
equation 5, above. This distribution of d-day volumes now has a slope, but it must also be fit to
the actual reservoir d-day inflow volumes at the lower return periods. This is done through a
statistical procedure. The fitted curve will match the experienced stream gage d-day volumes
near the computed reference Q value previously computed. The resulting curve can be extended
to very high return periods based on the second basic assumption of the method, that all large
flood volumes will occur from rain falling on already thoroughly saturated conditions in the
contributing areas of the basin, and any increase in a d-day rainfall will result in a corresponding
increase in d-day inflow volume to the reservoir.
Since the GRADEX parameter a is calculated using a maximum likelihood estimate, it is further
possible to place a confidence bound on this parameter. Note that for one-parameter
distributions such as the exponential, the natural logarithm ratio between the estimated likelihood
function and a true likelihood function for the one parameter can be proportional to a chi-square
distribution with one degree of freedom. This process is displayed on the Web page,
.
By a trial and error process, the upper and lower confidence bounds associated with the a
parameter estimate can be determined for some set confidence level.
Once the slope and location of the flood volume curve for the d-day durations have been
established, the question of what is the probability that a particular volume of flooding will be
equaled or exceeded in any year can be answered. The more common question is what is the
volume of flooding that will be exceeded on average only once in a stated return period,
Tc = number of years. To answer that question, the calculated exponential distribution and
associated confidence bounds, need to be inversed. The inverse of the distribution has the form:
(8) ( ) .. .
.. .
=ί + +ί
1 2
Tc ln Tc x a
Where:
(Tc) x is the d-day flow value for any required return period, in ft3/s-days, Tc is the
return period (in years) for which a d-day flow estimate is required, is the previously
estimated GRADEX slope factors converted to volume units, and and are
constants that can be estimated from a system of simultaneous equations that are
formed knowing the mean of the sample of d-day flood discharges and the reference
d-day discharge with an approximate return period. Both of these discharge values and
the reference discharge return periods are previously computed from the daily inflow
record for the location of the study. The *
a
ί
1 ί
2
(Tc) x value can then be further converted to
more common volume units such as acre-feet for a specified number of days.
The original goal of the method, as presented in Naghettini (1994), was to produce a peak-flow
frequency curve. In this procedure, a known set of peak flows associated with d-day volumes
can be determined from the stream or reservoir inflows, assuming peak flows have been
recorded. This set of paired data for the period of the streamflow record can be further extended
by the use of various rainfall-runoff models. Calibrated rainfall-runoff models can be created for
some of the largest events in the stream gage record if appropriate rainfall data are also available.
In the original presentation of the method, it is suggested that several large storms, all of the
same type and from meteorologically similar areas, could be transposed into the basin. For each
of these large storms, the calibrated rainfall-runoff models can then be rerun with the transposed
storm precipitation data and a new peak flow and hydrograph can be generated. Additional
sensitivity analysis runs can be made by varying certain parameters in the rainfall-runoff model
that affect the peak, such as the lag time or other parameters related to unit hydrograph
development. The peaks and d-day volumes from all of the additional transposed storms can
then be added to the original set of peak and volume data. Regressions on this extended set of
peaks and volumes can provide the necessary information to help determine a peak flow for a
selected volume at some rare return period that has been calculated by the GRADEX Method.
In both the French and American literature for the GRADEX Method, it is suggested that the
regression between volume and peak data should not be linear. The French literature states that
the ratio of peaks to a d-day volume will increase with increasing return periods. A regression
procedure known as LOWESS (Locally Weighted Regression and Smoothing of Scatter Plots)
(Cleveland, 1979) can be used to perform the non-linear curve fitting required for this procedure.
Reclamations practice with the method has not involved multiple storm transpositions. For each
application, some attempt has been made to create a calibrated rainfall-runoff model using HECHMS
(U.S. Army Corps of Engineers, 2002). The largest one or two floods from the stream
gage record and the best available rainfall data are used to create the calibrated runoff model.
The model is calibrated to match as nearly as possible the peak and the entire volume of
flooding, which may be longer than the d-day critical duration determined earlier. Once the
calibrated rainfall-runoff model is completed, the historic rainfall information, with both
temporal and spatial distribution, is increased by a constant ratio at each time period. The
resulting peak and d-day volume of the hydrograph is recorded. Additional runs are made and
the lag times are reduced by 10 or 20 percent to account for the fact that the historic flood may
not have resulted from such intense rainfall as the desired higher return period floods might
produce. With more intense rainfalls, it may be that the basin lag times should be reduced to
allow for quicker formation of the flood peaks. The extended peak and d-day volume set is then
fit with the LOWESS procedure. Using this non-linear regression, peak flows associated with
the various volumes for different return periods by the GRADEX Method can be estimated. This
method will also allow for production of the entire hydrograph with exactly the required d-day
volume estimated by the GRADEX Method. Examples of the results of this computation can be
seen in the Fresno Dam example at the end of this report.
In the publication, Small Dams, (French Committee on Large Dams, undated), an empirical
equation is given that will produce an entire hydrograph with a specified peak, time to peak, and
the desired time step. One of the parameters in that equation can be varied by trial and error until
the desired volume of the hydrograph over any period of time, such as d-days, is achieved. This
represents another strictly empirical method to derive a hydrograph once a peak and volume for
the desired return period are known.
Some other concerns have become apparent in the application of the GRADEX Method to some
dams in the Reclamation inventory. The first concern is with the possible additional volume of
flooding that may result from snowmelt that may not be explicitly considered in the GRADEX
Method. The available literature indicates that a separate snowmelt volume analysis should be
undertaken. For each year of stream gage record, the maximum snowmelt volume for some time
period larger than d-days should be estimated. A separate LP-III (or any other distribution)
analysis of the snowmelt volumes can be constructed and extrapolated to rare return periods.
This frequency curve of snowmelt flood volumes can be used with a combined probability
analysis of the rain flood GRADEX d-day volumes. The resulting frequency curve will display
the probability of getting a flood volume composed of both snowmelt and rain flood volumes.
What becomes apparent for the large return periods is that the GRADEX rain flood curve will
dominate the combined probability volumes. The combined probability curve is almost identical
to the GRADEX curve at the large return periods. For a large return period, the probability of
getting a flood with X acre-feet composed of Y acre-feet of snowmelt, plus Z acre-feet of rain
generated flood volume (X = Y + Z), is nearly identical to getting the rain flood alone with X
acre-feet of volume. An example of this type of combined probability analysis is given in the
Fresno Dam example later in this report. It is recommended that in all future applications of the
GRADEX Method to Reclamation dams some attempt be made to create a separate snowmelt
flood volume frequency curve and a combined probability analysis with the GRADEX rain-flood
curve be made to ensure that the rain floods dominate at the rare return periods.
A second concern is with drainage area size. The GRADEX Method is based on assumed basin
average rainfall. Because of this, there is a clear question as to its applicability to large basins.
The original French literature limits the size of the drainage basins where the GRADEX Method
can be applied to about 104 square kilometers, or about 3,800 square miles. It is noted that few
storms with greater aerial coverage exist in the rain gage data. The application of the method to
such larger drainage sizes would not produce defendable results. To approach this problem, the
suggestion is that the larger basin be broken into smaller parts along logical lines, such as at
major tributary confluences, such that each part is no larger than 3,000 square miles. The
GRADEX Method could be applied to each separate part, and a combined probability analysis
could then be performed with the resulting curves for each part. The resulting frequency curve
would show the volume of flooding that could occur resulting from contributions from each
separate part of the basin. This approach has not yet been tried for any Reclamation dams.
For the full application of the method for a detailed hydrologic study, additional effort should be
made to determine a homogeneous set of rain gages for use in the GRADEX Method. Naghettini
(1994) provides some useful suggestions and examples along these lines. Due to time and
money constraints, this has not been done in any Reclamation studies to date.
4.4 Australian Rainfall-Runoff Method
The Australian Institution of Engineers developed and published an approach for estimating
large to extreme floods in 1999 and revised the method in 2001 (Nathan and Weinmann, 2001).
The focus of this work is on estimating floods with very low probabilities of occurrence. The
floods developed using this technique usually have AEPs ranging between 1 in 50 and 1 in
10 million. Uncertainties involved in estimating floods increase with increasing sizes of floods.
The following discussion describes Reclamations experience with estimating rare and extreme
floods using the Australian approach.
Three categories of floods are considered large, rare, and extreme. Large floods typically have
probabilities of occurrence ranging from 1 in 50 to 1 in 100. Rare floods include floods with
AEPs extending from 1 in 100 to the credible limit of extrapolation, generally around 1 in
2,000. Extreme floods involve estimating floods for the AEPs beyond the limit of credible
extrapolation. For risk analysis purposes, rare and extreme floods are of most interest.
Rare floods include events between the largest observed flood and the credible limit of
extrapolation. The creditable limit of extrapolation depends on the type and amount of data used
for flood frequency analysis. Generally, regional flood and precipitation data, and the inclusion
of paleoflood data, allow extrapolation out to around 1 in 2,000 or 1 in 5,000. It is important to
note that floods in this category contain considerable uncertainty because estimates are outside
the range of observations.
Extreme floods extend beyond the credible limit of extrapolation from the data to AEPs out to
1 in 10 million. Estimating these floods requires prescriptive measures, which do not allow the
hydrologist to quantify the uncertainty of the estimates even though it is known to be very large.
Extreme floods determined by these methods are intended to be consistent and as reasonable as
possible given the state of current knowledge.
4.4.1 Approach
The procedures involved in the Australian Rainfall-Runoff Method are based on flood frequency
analysis and rainfall-runoff modeling. Any of the flood frequency analysis techniques
previously discussed in previous sections of this report are applicable to the Australian Rainfall-
Runoff Method. The unique concept in this approach is the use of AEP-neutral parameters in
the rainfall-runoff modeling process. This involves selecting model parameters such that the
AEP of the 1 in Y rainfall amount produces a flood with a 1 in Y AEP.
Reclamation has used an event-based deterministic rainfall-runoff model to convert a 1 in Y AEP
design rainfall into a 1 in Y AEP flood. A single set of hydrometeorological parameters and
watershed characteristics are used to produce a flood event. No soil moisture or surface storage
recovery is provided. Therefore, the deterministic model always produces the same output.
The major inputs to the deterministic rainfall-runoff model are: (1) precipitation (rainfall and
snowfall), (2) losses (infiltration/interception), (3) physical watershed characteristics for runoff
and routing simulations (drainage areas, watershed and channel slopes, lag times, antecedent
moisture, etc.), (4) precipitation-runoff transformation function, and (5) runoff conveyance and
routing mechanisms. Model output includes runoff hydrographs at user-specified locations,
maximum peak discharges, and total runoff volumes.
Deterministic event-based precipitation-runoff modeling applies design rainfall distributions and
volumes to watersheds for which runoff response is characterized by unit hydrographs and
generalized loss-rate functions. Calculations proceed from upstream to downstream in the
watershed. Subbasin hydrographs are routed and combined at the points of interest.
A design storm (rainfall and basin snow cover) is the primary model input. Typically, a time
series of basin-average rainfall for a preselected duration and frequency is input to the model. A
1-hour to 72-hour duration storm event is typically simulated. Appropriate duration storm events
should be derived from local and regional rainfall records. In the process of developing extreme
floods, the Australian Rainfall-Runoff Method assigns an AEP to the PMP, and is solely a
function of drainage area size. Reclamation assigns an AEP to the PMP on an as-needed basis
and does not endorse the drainage area relationship used by the Australians. Reclamation
considers the proximity to moisture sources, areal coverage of the storm, and other factors in
assigning an AEP to the PMP.
Excess precipitation is estimated by subtracting losses typically due to infiltration and
interception. A variety of infiltration models are available and range from constant uniform loss
rates to approximate theory-based functions (Green and Ampt, Philips equation). Antecedent
storm assumptions can have a severe impact on basin infiltration estimates. Since the
deterministic rainfall-runoff model is based on a single event, soil moisture storage and recovery
during and between storms is not considered.
The amount of watershed information required is a function of the type of precipitation-runoff
model used. Two classes of models are currently usedlumped and distributed parameter
models. Lumped parameter models consider the system as being spatially averaged. In contrast,
a distributed system considers hydrologic processes at various points in space and defines model
variables as functions of the space dimensions. Some lumped parameter models that are widely
in use are HEC-1 (HEC, 1990), FHAR (Bureau of Reclamation, 1990), and RORB (Laurenson
and Mein, 1995). Some distributed models that can handle single events include DR3M (Dawdy
et. al, 1978), PRMS (Leavesley et. al, 1983), HEC-HMS, and WMS. Additional surface water
models are discussed in DeVries and Hromadka (1993).
Transformation of rainfall excess to a direct runoff hydrograph is completed via a convolution
integral using (1) unit hydrograph techniques or (2) kinematic wave routing for overland flow.
The unit hydrograph has been used extensively for flood runoff estimation. Kinematic wave and
distributed modeling approaches may be more appropriate for modeling non-linear systems. A
good discussion about rainfall-runoff processes and floods, including practical issues comparing
design floods and actual storms, is presented in Pilgrim and Cordery (1993). Beard (1990)
presents a methodology for simulating floods of a given probability from hypothetical design
storms derived from point rainfall.
Streamflow routing may be classified as either lumped/hydrologic (linear reservoirs, level-pool,
Muskingum, etc.) or distributed/hydraulic (diffusive wave, kinematic wave, etc.). In lumped
flow routing, streamflows are computed as a function of time at one location; however, in
distributed flow routing, streamflows are computed as a function of time at several locations
along the stream. Most precipitation-runoff models have adequate routing mechanisms. A
detailed discussion of routing options is presented in Chow et al. (1988).
For risk-based dam safety studies, it is necessary to adopt an AEP-neutral approach, where the
objective is to derive a 1 in Y AEP flood with an AEP equivalent to its 1 in Y rainfall. The
factors that influence the transfer between rainfall and runoff can be characterized by probability
distributions. Thus, ideally, the design hydrograph should be determined by considering the joint
probabilities of all the input factors. Stochastic methods are ideally suited to the AEP-neutral
objective because they accommodate the observed variability of the inputs while still preserving
the interdependencies between parameters. However, for the least important parameters, it may
be appropriate to adopt a single representative value instead of the full distribution. Since the
relationship between rainfall and runoff is non-linear, it is important to note that adoption of a
single representative value for the major inputs will introduce bias into the rainfall-runoff
transformation. Therefore, more important model inputs may require use of a joint probability
approach.
The simplest approach to deriving AEP-neutral inputs is to use the correlation relationship
between the two variables. For example, if it is necessary to derive a temporal relationship to
use with the design rainfall magnitude, an appropriate relationship may be derived from the
correlation between the largest observed storms and their temporal characteristics during the
largest storms on record. When applying relationships based on a limited historical sample to
large flood events, the inputs should be conditioned by physical reasoning. For instance, large
snowmelt events may require large snowpacks and high temperatures, but the meteorological
conditions required to sustain an extreme rainfall event may preclude the joint occurrence of
extreme wind speeds. The concurrent wind speeds used in the transformation of snow into
runoff must be bounded by a reasonable upper limit.
The selection loss parameters are required inputs common to all event-based rainfall-runoff
models. With loss rates, there is evidence to suggest that loss rates are independent of flood
magnitude for design floods up to 1 in 100 AEP, though, for more extreme events, it is possible
that the loss rates depend on both the AEP and the duration of the design rainfall. When
considering snowmelt design floods, it may be necessary to vary loss rates with snowpack extent
(Nathan and Bowles, 1997).
The most appropriate approach required to achieve AEP-neutrality depends on the complexity of
the system being modelled, the nature of the available data, and the requirements of the flood
model. In many cases, it may be expedient to adopt model input parameters derived using
regional data, and it will be necessary to supplement empirical evidence by physical reasoning.
Calibration of the design flood estimates to flood frequency quantiles will help reduce the
uncertainty in extreme flood estimates.
4.4.2 Calibration
Calibration of a flood event model for application to design flood estimation is traditionally
restricted to the selection of model parameters to achieve a fit between observed and estimated
hydrographs. Attention is focused on collecting streamflow and rainfall data corresponding to
the largest events on record. Considerable effort is required to ensure that the temporal and
spatial distribution of the rainfall data is representative of the actual event. The ability of a
model to reproduce historic events certainly gives some confidence to the validity of subsequent
flood estimates. However, the available historic information for floods is usually much smaller
than the extreme floods of interest. In most watersheds, the AEPs of the calibration floods are
likely to range between 1 in 10 and 1 in 25. While it would be expected that floods of this
magnitude would activate some floodplain storage, the non-linear nature of the out-of-bank flood
response is such that the streamflow routing characteristics of larger events may be considerably
different. Therefore, while calibration of the model provides valuable information on the flood
routing parameters for small floods, caution is needed when using the model to estimate extreme
floods of much larger magnitude.
Calibration of rainfall-runoff model results to flood frequency quantiles can provide important
information on flood response characteristics for extreme flood events. With this approach,
rainfall data are prepared for a specified AEP and then used with a given set of model parameters
and input assumptions to derive a flood hydrograph. The peak (or volume) of the flood
hydrograph can then be compared to the corresponding quantile obtained from flood frequency
analyses. The model inputs associated with the greatest uncertainty can be varied within
appropriate limits to ensure agreement between the selected flood quantile. It is recommended
that model calibration be undertaken for a range of exceedance probabilities to ensure a
consistent variation of parameters with flood magnitude. The approach is suited to ungaged
watersheds using regional flood frequency methods as well as sites with limited information.
The approach is considered to be particularly useful when combined with flood frequency
information that uses paleoflood data.
4.4.3 Strengths and Limitations
Event-based deterministic rainfall-runoff modeling has a long track record in the engineering
and hydrologic community and is a proven technique for generating design hydrographs.
Reclamation uses deterministic precipitation-runoff modeling. From a technical standpoint, the
approach is flexible and requires less effort than most of the more complex approaches. Model
choice should be a function of the hydrometeorological and physical data available. For
example, a distributed model could be applied in cases where detailed information was available;
however, a simplified lumped-parameter model would be appropriate in less data-rich locations.
Output from either model would be similar.
Limitations to this method arise from the need to calibrate model results to known historical
flood events or to flood frequency analyses so that the AEP of the storm is the same as the
resulting flood. Calibration can be difficult if the model is sensitive to many input parameters.
A lack of good meteorological data can prove troublesome in developing design storms with
appropriate temporal and special characteristics. Rainfall-runoff modeling in data-sparse
locations may require a high level of regional data gathering and analyses to obtain the necessary
hydrometeorological inputs.
4.5 Stochastic Event-Based Precipitation Runoff Modeling with the
SEFM
The SEFM has been developed by MGS Engineering Consultants, Inc., in conjunction with
Reclamation personnel. The SEFM was developed for analysis of extreme floods resulting from
72-hour general storms and to provide magnitude-frequency estimates for flood peak discharge,
runoff volume, and maximum reservoir levels for use in hydrologic risk assessments at dams
(Schaefer and Barker, 2002). The SEFM is fully described in MGS Engineering Consultants,
Inc. (March 2001) and summarized in Schaefer and Barker (2002).
The basic concept of the SEFM is to employ a deterministic flood computation model and treat
the input parameters as variables instead of fixed values. Monte Carlo sampling procedures are
used to allow the hydrometeorological input parameters to vary in accordance with those
observed in nature, while preserving the natural dependencies that exist between some climatic
and hydrologic parameters. Example outputs from the SEFM are shown in figures 4-6, 4-7, and
4-8 (MGS, March 2001).
ANNUAL EXCEEDANCE PROBABILITY
PEAK DISCHARGE (cfs)
10-1 10 10 10-4 10-5 -2 -3
Figure 4-6.Example of magnitude-frequency curve for peak discharge.
ANNUAL EXCEEDANCE PROBABILITY
RUNOFF VOLUME ( acre-feet )
10-1 10-5 10-4 10 10 -2 -3
Figure 4-7.Example of magnitude-frequency curve for runoff volume.
ANNUAL EXCEEDANCE PROBABILITY
RESERVOIR LEVEL (Feet)
Dam Crest Elevation
10-1 10 10 10 -4 10-5 -2 -3
Figure 4-8.Example of magnitude-frequency curve for maximum reservoir level.
A general flowchart for stochastic modeling with the SEFM is shown in figure 4-9. Thousands
of computer simulations are conducted where each simulation contains a set of input parameters
that were selected based on the historical record and, collectively, the simulations preserve the
dependencies between parameters. The simulated floods constitute elements of an annual
maxima flood series that can be analyzed by standard flood-frequency methods. The resultant
flood magnitude-frequency estimates reflect the likelihood of occurrence of the various
combinations of hydrometeorological factors that affect flood magnitude. The use of the
stochastic approach allows the development of separate magnitude-frequency curves for flood
peak discharge, flood runoff volume, and maximum reservoir level. Frequency information
about maximum reservoir levels is particularly important for use in hydrologic risk assessments
because it accounts for flood peak discharge, runoff volume, hydrograph shape, initial reservoir
level, and reservoir operations. The precipitation estimates used in the SEFM are typically
developed using regional precipitation frequency analysis with L-Moments (Hosking and Wallis,
1997). This approach uses a space-time substitution principle and assumes that there is sufficient
precipitation data in a region to combine for subsequent model extrapolation to the probabilities
of interest.
The general storm SEFM is composed of seven software components: data entry, input data preprocessor,
multiple sample parameter test workbook, HEC-1 template file, stochastic inputs
generator, HEC-1 rainfall-runoff flood computation model, and an output data post-processor.
The flowchart shown below (figure 4-10) depicts the sequence of actions required for conducting
the computer simulations using the software components. Each of these components is described
in the SEFM Technical Support Manual (MGS, March 2001). The software (MGS, April 2001)
helps the user input data, run the model, and visualize results.
Select Month of Storm Occurrence
Select Storm Characteristics
Assemble 72-hour General Storm
Repeat
Select All Hydrometeorological, Hydrologic,
n
and Hydraulic Parameters that are
Times
Dependent Upon Month of Occurrence
Select Remaining Parameters that are
Independent of Other Parameters
Select Remaining Parameters that are
Dependent Upon Other Parameters
Do Flood Modeling and Reservoir Routing
Rank All Events in Descending Order of Magnitude
and Develop Magnitude-Frequency Curves
Figure 4-9.General flowchart for the SEFM simulations (after MGS, 2001).
DATA ENTRY
Enter Input Parameters Into Excel Workbook
With Filename Input.xls
INPUT DATA PRE-PROCESSOR
Conduct Separate Monte Carlo Simulations
For Each Hydrometeorological Component
Optionally Write Output to Multiple Sample Test Workbook TestParms.xls
MULTIPLE PARAMETER SAMPLE WORKBOOK MODULE
Compute Statistics and Plot Graphs to Confirm That
Sampled Components Match Input Probability Distributions
and Validate Relationships With Other Parameters
(Performed in TestParms.xls Workbook)
HEC-1 TEMPLATE FILE
Create HEC-1 Template File for Watershed
MONTE CARLO GENERATION OF HYDROMETEOROLOGICAL INPUTS
Conduct Monte Carlo Simulation of Hydrometeorological Inputs
Initiate Execution From Simulate Worksheet in Input.xls Workbook
EXECUTE HEC-1 MODEL
Conduct HEC-1 Modeling for each Simulation
Initiate by Executing MCRun.bat
OUTPUT DATABASE AND POST-PROCESSOR
List All Simulation Inputs and Outputs
Construct Magnitude-Frequency Curves for
Peak Discharge, Runoff Volume, and Maximum Reservoir Level
(SEFMSimDat.mdb and SimOutput.xls)
Figure 4-10.General flowchart for the sequence of actions required for conducting
the computer simulations using the SEFM.
The input processor to the SEFM is an Excel workbook. The workbook includes different
spreadsheet screens for input (figure 4-11), for model execution, and for output (figure 4-12).
The improvements are contained in software version 1.8 of the SEFM.
Figure 4-11.The SEFM input screen.
Figure 4-12.The SEFM output simulation options.
The basic concept behind the SEFM was first used to explore PMF variability and extreme flood
probability issues at Bumping Lake Dam for Reclamation (Barker et al., 1996; 1997). The
prototype of the SEFM was developed for application to the A.R. Bowman watershed (Schaefer
and Barker, 1997; 1998). The SEFM was subsequently generalized for use by Reclamation on
other projects and applied at Keechelus and Cle Elum Dams (Bullard and Schaefer, 1999). A
sensitivity analysis has been performed for A.R. Bowman Dam (MGS, January 2001) to
determine the dominant features that affect model results. A brief review of the model (Singh,
1999) indicated that the model is a sound package for extreme flood modeling, and there could
be some eventual improvements.
There are some current limitations to the SEFM and the applicability to certain Reclamation
sites. The SEFM is currently configured for simulation of 72-hour general storms. There is no
computational limit to the size of the watershed to which it can be applied. However, implicit in
the development of the model is the condition that some hydrometeorological parameters are
highly correlated spatially. As the watershed size increases, the requirement for high spatial
correlation of multi-month precipitation and snowpack becomes more difficult to satisfy. This
consideration suggests that the stochastic model is applicable to watersheds up to a nominal size
of about 500 mi2. For larger watersheds, the spatial variability of some hydrometeorological
parameters may warrant that site-specific modules be developed to address the site-specific
characteristics of the watershed under study (Schaefer and Barker, 2002, p. 732). Currently, the
model does not handle thunderstorm events. Additional routines would need to be added to
simulate any storms with durations that differ from 72 hours. These limitations may be relaxed
as improvements are made to the model.
4.6 Stochastic Rainfall-Runoff Modeling With CASC2D
CASC2D is a fully unsteady, physically based, distributed-parameter, raster (square-grid), twodimensional,
infiltration-excess (Hortonian) hydrologic model for simulating the runoff response
of a watershed subject to an input rainfall field for a particular storm event (Julien and Saghafian,
1991; Julien et al., 1995; Ogden and Julien, 2002). Major components of the model include
rainfall interception, infiltration, surface and channel runoff routing using the diffusive wave
method, soil erosion, and sediment transport. CASC2D is appropriate for simulating extreme
floods and physically based extrapolations of frequency relationships combined with a derived
distribution approach. The main differences between CASC2D and the SEFM are that CASC2D
is a fully distributed model and uses hydraulic principles for runoff generation and routing
precipitation excess. The SEFM is essentially a lumped model and uses the unit hydrograph as
the basis for runoff and routing precipitation excess. Other differences are the infiltration models
and routing mechanisms for river channels. CASC2D is also a somewhat experimental model
that has not been used in extreme flood applications for dam safety, or for many applications
outside academic research.
The idea and basis to use CASC2D for extreme flood modeling and prediction is centered on two
concepts: (1) a derived distribution approach (e.g., Eagleson, 1972) can be used to estimate the
extreme flood peak and volume probability distributions and (2) physically-based methods for
flood runoff and routing provide a suitable and improved physical basis for the extrapolations of
derived flood probability distributions. Ramirez (2000) summarizes the theory behind the
derived distribution approach. In the disciplines of science and engineering, relationships that
predict the value of a dependent variable in terms of one or many basic (independent) variables
are commonly developed. Physical systems are naturally complex. The functional form of the
relationship between independent and dependent quantities or the values of the independent
variables (or both) is not usually known with certainty. Techniques based on probabilistic
assumptions can be used to account for this uncertainty. When the uncertainty derives from
uncertainty in the independent variables, but not from uncertainty in the functional dependence, a
derived distribution approach leads to the probability density function of the dependent variable.
In this case, the functional form relating independent and dependent variables is assumed known
with certainty. In such instances, it is possible to derive the probability density function of the
dependent variable(s) from that of the independent variable(s) (Ang and Tang, 1975).
Several research applications use the derived distribution approach to estimate flood frequency
curves; these show much promise. The pioneering study for flood frequency is Eagleson (1972).
Bras (1990) discusses some of the potential applications of derived distributions in hydrology.
4.7 PMF Analysis Technique
The PMF is defined by Reclamation as the maximum runoff condition resulting from the most
severe combination of hydrologic and meteorologic conditions that are considered reasonably
possible for the drainage basin under study (Cudworth, 1989). Other agencies have developed
somewhat different definitions, but all consider the PMF to be a maximum runoff condition
that is reasonably possible.
In Reclamation practice, the basic model to convert PMP to runoff is the unit hydrograph. It is
recognized that many other techniques, including sophisticated computerized models, are
available for making this conversion. The unit hydrograph concept represents the modeling of
the rainfall-runoff process as a linear system. The fact that the rainfall-runoff process is actually
non-linear is one of the acknowledged shortcomings of the concept. However, if properly
applied, the concept provides entirely satisfactory results for developing flood hydrographs
resulting from extreme rainfall events.
During the period from the mid-1940s to the late 1990s Reclamation engineers designed and
built most of the large storage dams currently in Reclamations inventory. During this period,
Reclamation published three editions of the Design of Small Dams. That publication has served
as a textbook and as a technical guide for numerous States and many foreign countries. Many
States, consultants, and other agencies still use the methods and PMF philosophies expressed in
the recent editions of those publications. The basic PMF methodologies described in those
publications have served as the basis for thousands of dams in the U.S. and other countries
designed by both Reclamation and non-Reclamation engineers. These publications are still in
widespread use. Reclamation engineers often employed somewhat different techniques and
nomenclature for deriving design floods, but the intent was nearly always to design for the PMF
determined by the then current techniques. Some exceptions were made for small dams and
diversion structures where it was believed that failure of the structure caused by overtopping
would not produce any loss of life or major economic damages.
The steps involved in deriving the PMF hydrograph for a single basin have been described in
many sources. The following steps are modified from the list given by the National Research
Council (NRC, 1988). This list briefly summarizes the PMF calculation process currently
followed by Reclamation and many other dam building agencies:
1. Divide the drainage area into subbasins, if necessary, and determine the appropriate
drainage areas.
2. Derive a runoff model (unit hydrographs for Reclamation studies).
3. Determine the PMP using criteria contained in NOAA Hydrometeorological Report
(HMR) series.
4. Arrange the PMP increments into a logical storm rainfall pattern.
5. Estimate for each time interval the losses from rainfall, due to such actions as
surface detention and infiltration within the watershed.
6. Deduct the losses from rainfall to estimate rainfall excess values for each time
interval.
7. Apply rainfall excess values to the runoff model for each subbasin.
8. Add to the storm runoff hydrograph allowances for stream base flow, runoff from
prior storms, etc., to obtain the synthesized flood hydrograph for each subbasin.
9. Route the flood from each subbasin to a point of interest.
10. Compare the computed PMF peak and volume to the applicable envelope curve of
peak and volume flows, if available.
11. Route the resulting inflow hydrograph through the reservoir storage, outlets, and
spillways to obtain estimates of maximum storage, elevations and discharges, and
durations at the dam.
Many factors influence the ultimate magnitude of the PMF hydrograph, but the intensity and
duration of the rainfall are the most important. Considerable analysis and discussion of the
derivation and application of PMP estimates has taken place in the past. The original definition
of PMP dates back to the late 1930s. In 1981, Reclamation, the National Weather Service, and
the U.S. Corps of Engineers adopted a mutually acceptable, uniform definition of the widely
used term PMP. The PMP, as defined by these three agencies at that time, is theoretically, the
greatest depth of precipitation for a given duration that is physically possible over a given size
storm area at a particular geographical location at a certain time of the year. PMP must always
be termed as an estimate because there is no direct means of computing and evaluating the
accuracy of the results. Since the mid-1980s, Reclamation has considered that the series of
HMRs prepared and updated by the National Weather Service provide the best estimates of PMP
potential within the limits of each report. Figure 4-13 displays the current coverage of the
continental United States by this series of reports.
Figure 4-13.Regions covered by generalized PMP studies.
Other aspects of the PMP to PMF conversion that are unique to Reclamation are discussed in the
following paragraphs.
After determining the total PMP depths for specific time intervals from the appropriate HMR, a
smooth depth-duration curve is created. This curve is then read at time intervals equal to the
desired computation interval for the PMF hydrograph. Each individual precipitation total for
each time increment is subtracted from the preceding time increment total PMP. The result is the
incremental values of PMP to be used in the computation of the PMF hydrograph. Figure 4-14
displays a typical depth-duration curve from which incremental PMP can be determined.
The temporal rainfall pattern most commonly used with Reclamation PMF studies places the
maximum increment of rainfall at the 2/3 point of the storm and arranges the remaining
increments of precipitation in descending order about this point. This distribution is applied
throughout the United States and results from an examination of individual drainage area
regionalized storm criteria combined with various hydrological tests. This arrangement, when
combined with the unit hydrograph procedures, will produce a maximum runoff condition for the
basin being studied that is still reasonable based on meteorological experience. Figure 4-15
displays this temporal distribution.
Depth Duration Curves based on HMR 49
0
2
4
6
8
10
12
14
0 10 20 30 40 50 60 70 8
Time (hours)
Accumulated Precipitation (inches)
General Storm PMP - DAD Curve
Local Storm PMP - DAD Curve
Figure 4-14.Typical PMP depth duration curves.
PMP arrangement at 1-hour increments
0
0.5
1
1.5
2
2.5
3
3.5
4
1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70
One-hour time Increments for a 72-hour general storm PMP Incremental Precipitation Amount (inches)
Figure 4-15.Typical PMP temporal arrangement for a 72-hour storm.
In Reclamation PMF studies for large basins with many subbasins, consideration is given to
centering of the PMF by allowing the spatial distribution of the PMP to vary across the entire
basin. The storm is centered over a single subbasin, and the PMP for that subbasin is calculated
along with the PMP for the total basin. PMP amounts over the other subbasins are calculated in
a manner that preserves the total basin volume of the PMP but allows for heavier amounts over
the subbasins nearest the assumed center of the storm. This calculation is termed successive
subtraction.
Another unique feature of some PMF studies is the use of an elliptical storm pattern as specified
in the appropriate HMR. The use of this pattern allows the PMP to vary within a large area in a
manner that does not depend on subbasin sizes or shapes but, rather, on historic observations of
large storms. This type of PMP calculation is most common for large general storms in the
HMR 51-52 area. Local storm PMPs can also use a theoretical elliptical shape in the HMR 49
and HMR 59 areas. For these types of studies, the PMP storm is usually centered over the basin.
Volume centerings will center the entire PMP storm over the subbasin nearest to the center of the
entire basin. Peak centerings will allow the PMP to be centered over the subbasin nearest to the
dam. Volume centerings will typically produce a PMF hydrograph with the largest total volume.
Peak centerings will typically produce a PMF with a higher peak but a lower volume. Both PMF
hydrographs need to be routed through the dam.
Another good feature of the PMF calculations is that a series of dams all on the same river can be
studied. By allowing the PMP to be centered over subbasins above each individual dam, the
most severe cause of flooding at that dam can be obtained. Concurrent floods above the other
dams on the same river basin can then be calculated for the same PMP event. Once the PMF
hydrographs from the upstream dams are formed and routed through those structures, the
complete PMF series of hydrographs for the downstream dam can be obtained. This is not
always the case with methods based solely on statistical methods.
Local storm hydrographs are also computed for most Reclamation Dams if the HMR series
provides specific data for deriving a separate local storm. Such storms are generally considered
the thunderstorm type events and are limited in durational and areal coverage. Local storms will
generally produce more intense precipitation and are usually most critical for smaller drainage
basins. Local storms are considered spring or summer events and may become critical for dams
and reservoirs where higher water surfaces are allowed in the spring and summer.
Lag time computations and unit hydrographs for Reclamation PMF studies have come from
many past investigations of large floods. Basic unit hydrographs for sites where sufficient data
were recorded were derived by standard means after subtracting out any base flows or snowmelt
flows. With some knowledge of the basin average rainfall total and duration, the resulting
hydrograph could be reduced to a unit hydrograph. The unit hydrographs were then put into a
dimensionless form unique to Reclamation, with the flow ordinate being expressed as a
dimensionless volume of flooding divided by the amount of flooding that could be expected from
1 inch of excess runoff in 24 hours (expressed as ft3/s-day/ft3 or often abbreviated as q). The
time ordinate was expressed as a percent of the basin lag time plus 1/2 of the unit duration for
that basin. Figure 4-16 is a sample of such a dimensionless graph. Over 60 dimensionless
graphs are available to Reclamation engineers, but this number has been reduced to only 6 for
publication in the Flood Hydrology Manual and in the latest edition of Design of Small Dams.
Figure 4-16.Reclamation dimensionless graph.
The physical definition of the lag time used by Reclamation in PMF studies is the time from the
mid-point of a unit of excess rainfall to the mid-point of the total volume of the resulting runoff
hydrograph from that single unit of excess rainfall. With this definition in mind, much of the
historic flood data collected by Reclamation engineers in the 1940 to 1970 time period was used
to define relationships between the physical measurement of the length of the main channel, L
(mi); the length to a point on the main channel opposite of the basin centroid, Lca (mi); and the
basin slope S (ft/mi). Such data were plotted on log-log graphs, and straight lines on these plots
were drawn based on different basin vegetation and soil conditions. Figure 4-17 is a sample of
such a plot from the Reclamation Flood Hydrology Manual.
The locations of the straight lines on these plots reflect the basin vegetation, soils, overall slope
and, to some degree, the basin area and type of PMF being calculated. Such graphs also
represent floods from much smaller events than the PMF, and some judgment must be applied to
the lag numbers. PMF conditions will usually require somewhat shorter lag times than computed
for more common flood events. Lag times for Reclamation PMF studies are based on this type
of historical knowledge, reviews of other PMF studies prepared in the area, and reviews of
pertinent basin topography, soils, and land use maps. For final design-level PMF studies, field
trips to the basin in question by a qualified hydrologist are required to ensure that the information
from the maps and other calculated basin parameters is valid. Generalized equations based on
the lag curves such as displayed above are available to provide a computational procedure for
calculating a lag time for each subbasin and storm type in the basin being studied.
With a computed lag time, drainage area, and dimensionless graph selected, the final unit
hydrograph for each subbasin can be calculated. Procedures for this calculation are given in
Reclamations Flood Hydrology Manual and in Design of Small Dams.
0
1
10
100
0 100 200 300 400 500 600
Percent of Lag + D/2
Dimensionless discharge ordinate q
0.1
1.0
10.0
100.0
0 1 10 100 1,000 10,000
Basin Factor (L*Lca / S0.5)
Lag Time (hours)
Lag = 1.8 *(L*Lca / S0.5)0.33
Lag = 0.77*(L*Lca / S0.5)0.33
Figure 4-17.Lag time versus basin factor data for Great Plains Region
(from Reclamation Flood Hydrology Manual, 1989).
Loss rates for Reclamation studies always assume saturated basin conditions caused by
antecedent flooding. Most often, the loss rates are derived by studying basin soils maps
available from previous Soil Conservation Service (SCS) soils mapping reports or, more
recently, by using the NRCS STATSGO computerized soils database. The SCS divided the soils
into four basic hydrologic groups for rainfall-runoff studies. These groups range from very
porous sandy or gravely soils with high infiltration rates to very tight clay soils with very low
porosity and low loss rates for rainfall-runoff studies. The four soil categories have been
assigned ranges of minimum loss rates. By determining the percentage or amount of the
different soils in each subbasin, an average minimum loss rate can then be selected or computed
from the published minimum loss rate ranges. Initial loss rates are seldom used in Reclamation
PMF studies. The definition of the PMF requires the assumption of saturated soil conditions
before the onset of the PMP. Under such an assumption, the initial loss rates will be completely
satisfied, leaving only a minimum constant loss rate to be considered. It is recognized that more
sophisticated loss rate algorithms exist, but for the PMF computation and assumptions, the use of
a constant loss rate based on minimum losses for the upper soil layers in the basin is considered
adequate.
Antecedent flooding is also considered for general storm PMF hydrograph computations in
Reclamation studies. The general storm most often occurs at a time of the year when flooding is
most likely to occur in the basin. It is likely that previous storms or a melting snow pack will
provide some antecedent streamflow before the onset of the PMP. For basins without significant
snowmelt contributions, the antecedent flood comes from a study of applicable streamflow
records or, if needed, rainfall-runoff analysis. The desire is to derive a 100-year event by
statistical means or by rainfall-runoff modeling if limited stream gage data are available. This
derived flood hydrograph is then placed a number of days in front of the onset of the PMP. In
most parts of the central United States, there is a 3-day separation between the peak of the
antecedent flood and the start of the PMP. This length of time between the antecedent rain flood
hydrograph peak and the start of the PMP will vary near coastal areas. Figure 4-18 displays this
type of application.
0
10000
20000
30000
40000
50000
60000
70000
80000
0 24 48 72 96 120 144 168 192
Time (hours)
Reservoir Inflow (ft3/s)
PMP starts at hour
84.25
Antecedent Flood Peak at
hour 12.25
3-day separation of events
PMF hydrogrpah
100-year antecedent hydrograph
Figure 4-18.PMF with antecedent 100-year floods.
In areas where snowmelt adds to the volume of the flooding, the antecedent flood in Reclamation
PMF studies is often derived from an analysis of stream gage data. The data are limited to the
season when snowmelt adds to the flooding. A large historic snowmelt flood may be selected or
a statistical analysis of the volume of flooding for several different durations may be undertaken.
The result is a 100-year flood volume for a duration longer than the base length of the calculated
PMF rain flood hydrograph. If a historic flood event is selected, the daily flows for the
hydrograph will be adjusted by a ratio such that the resulting volume for the selected duration is
a 100-year volume that can be determined by a statistical analysis of appropriate gage records.
The historic flood hydrograph may also be rearranged in time to provide a more normal
hydrograph shape. If no historic flood hydrograph is appropriate, then the antecedent snowmelt
hydrograph may be derived as a balanced hydrograph. If a snowmelt hydrograph is used as an
antecedent flood, Reclamation places that hydrograph under the rain-generated portion of the
PMF such that the peaks will exactly coincide. Figure 4-19 displays such a derived historic
flood hydrograph for a 15-day antecedent event. Figure 4-20 displays the placement of the
derived balanced hydrograph to coincide with the peak of the rain-generated PMF hydrograph
for a basin.
0
50
100
150
200
250
300
350
400
450
0 24 48 72 96 120 144 168 192 216 240 264 288 312 336 360
Hours
Reseervoir Inflow (ft3/s)
Based on snowmelt flood of 1942 flood on a nearby creek.
Values are rearranged and scaled for a 100-year 15-day volume for PMF Study
15-day volume = 5900 acre-feet
Maximum Daily Peak = 406 ft3/s
Mean daily flow represented by the histogram shape.
Instanteneous Peak not included for base
flood under PMF hydrograph
Figure 4-19.100-year 15-day derived snowmelt flood from an historic snowmelt flood event.
0
1000
2000
3000
4000
5000
6000
0 50 100 150 200 250 300 350 400
Time (hours)
Reservoir Inflow (ft3/s)
Peak = 5,642 ft3/s
15 Day Volume = 12,100 acre-feet
General Storm PMP Starts Hr 130
100-Year Snowmelt
Figure 4-20.General storm PMF with 100-year snowmelt antecedent flood.
When a snowmelt flood is required, the loss rate for the measured or estimated snow-covered
areas in the basin is reduced to a constant 0.05 inch per hour. This is assumed to account for the
fact that the 100-year snowmelt is already in progress at the start of the PMP and most of the
available constant loss rate will have already been taken up by the melting snow.
In areas where deep snow packs are known to occur, such as the high Sierra Mountains in
California, Reclamation will use a snowmelt computation program. This program will account
for the effect of rain falling on a snow pack that may not be fully ripened and ready to melt at the
start of the PMP. The snowmelt program requires additional meteorology data such as wind and
temperature sequences compatible with the PMP derivation. The HMR series will provide good
information in this regard. Additional study of the historic snow gage records in or near the
basin being studied is also required. The depth and initial density of the snow pack at various
elevations in the basin are used in the computations. Such snowmelt computations provide
additional depths of water to be added to the arranged PMP sequence. The combined snowmelt
and PMP depths are then used with the unit hydrograph procedures to derive the desired PMF
hydrographs.
Routing of floods between subbasins is also required. If sufficient data for several large flood
events are available, routing coefficients for the Muskingum Method can be derived. Usually,
little information is available for large floods at more than one gage in the basin being studied.
In lieu of Muskingum routing, the most common procedure is an analytical procedure referred to
as the Tatum Method. This method requires only an assumed travel time between the various
subbasins and will attenuate the routed hydrographs by a simple arithmetical computation. This
procedure does not affect the volume of the flooding, but it does have some impact on the PMF
peak.
Envelope curve comparisons of the PMF peak and sometimes a volume comparison are also
made. The comparison is only to ensure the hydrologist that the PMF peak or volume is not
below experienced flood levels in the region of concern. If the PMF peak falls below an
envelope curve of peak flows for a nearby region, some additional thought must be given to the
derivation of the PMF or the derivation of the envelope curve values. There are no rules about
how far above the envelope curve a PMF peak should be. This would depend on the derivation
of the envelope curve. Envelope curves covering large regions might have additional high-peak
flows and the PMF comparison would be closer. Smaller regions would most likely have PMF
peaks much higher than the envelope curve.
5. Characterization of Hydrologic Hazards
Since no single approach is capable of providing the needed characterization of extreme floods
over the full range of AEPs required for risk assessment, results from several methods and
sources of data should be combined to yield a hydrologic hazard curve. The application of
several independent methods applicable to the same range of AEPs will increase the credibility
and resulting confidence of the results. The previous section of this report describes the
available approaches for estimating the hydrologic hazard.
To compute a hydrologic hazard curve for risk assessment, Reclamation makes use of all
available studies for the site of interest. Often, the PMF and initial flood frequency studies are
the only hydrologic studies available before the start of a probabilistic investigation. If a dam
passes the PMF or a flood with an AEP low enough to meet dam safety risk criteria, no further
studies may be needed. The intent of the hydrologic hazard analysis is to provide information
that will allow decision makers to make appropriate dam safety decisions while minimizing
study costs.
The remainder of this section of the report describes Reclamations approach toward
characterizing the hydrologic hazard for a particular site of interest. The process begins with
Flood frequency analysis and hydrograph scaling for the CFR and may progress through more
detailed studies if the need arises. If detailed studies are already available for a particular site,
these studies would be summarized and would form the basis of the hydrologic hazard
characterization.
5.1 Integration of the PMF into Hydrologic Hazard Evaluations
The PMF is recognized as the upper limit of flood potential at a site, for storm durations defined
by the Probable Maximum Precipitation (Bureau of Reclamation, 2002b). This means that
Reclamation uses the PMF as the upper limit to extreme floods for risk assessment, corrective
action decisions, and dam safety modifications. If a dam does not have a hydrologic safety
deficiency using the PMF as the hydrologic loading condition, no further hydrologic studies are
warranted for evaluation of spillway capacity. If a flood frequency analysis produces peak flows
or volumes that exceed the PMF, then the PMF should be used in evaluating the hydrologic risk
and as a theoretical and practical upper limit to statistical extrapolations. Before applying the
PMF as the upper limit, the hydrologist should ensure that it has been developed using current
procedures with up-to-date data and for a PMP duration suitable for the site of interest.
5.2 Characterization of Hydrologic Risk for the CFR
Hydrologic hazard curves and flood hydrographs are developed for use in evaluating and
prioritizing the need for dam safety modifications at Reclamation and other U.S. Department of
the Interior facilities. These guidelines provide an approach for developing hydrologic hazard
information that will allow decision makers to determine appropriate courses of action to assure
the safety of the dam while minimizing study costs. If detailed hydrologic studies are available
for the site of interest, they should be reviewed for adequacy, then summarized and used for the
CFR. If no study is available, a hydrologic hazard curve and flood hydrographs should be
constructed using flood frequency analysis and hydrograph scaling procedures. The remainder
of this section explains the procedure for developing hydrologic hazard information for the CFR
using these procedures.
The characterization of hydrologic risk is first provided in terms of estimated peak discharges,
which are then used to estimate flood volumes. Peak discharges are estimated using a mixedpopulation
model, and the results are subsequently input to a linear scaling algorithm of volume
critical hydrographs. The hydrologic hazard characterization for the CFR is usually
accomplished with minimal effort, about 15 staff days or less.
The mixed-population model used to estimate peak discharges is described by an LP-III
distribution for return periods from 1 to 100 years and an LN-2 distribution for return periods
greater than 100 years. Historical data are used to calibrate the LP-III model, and an informed
hydrologic estimate of a single flood potential point (SFPP) with a return period of greater than
100 years must be made. The fitting of the LP-III model to the historical data is carried out using
the Method of Moments (MOM) with which a regional skew may be used to fix or weight the
distribution. The fitting of the LN-2 distribution is carried out analytically between the 100-year
flood estimate and the SFPP. The value of the SFPP may take the form of a paleoflood nonexceedance
bound, a paleoflood estimate, a historical data point with an estimated return period
greater than 100 years, or any other estimate of a flood with a return period greater than
100 years believed to characterize the extreme values of the flood potential. Once the initial data
requirements are met, a list of peak-discharge estimates is calculated and the results are provided
in tabular as well as graphical format (table 5-1, figure 5-1). The analysis is extended beyond the
SFPP to floods with AEPs as small as 10-8, but peaks are not allowed to exceed the PMF for the
site of interest.
Table 5-1.Example peak-discharge estimates in
tabular form
Annual
exceedance
probability
Return period
Peak discharge
estimate
(ft3/s)
0.01
100
26,500
0.005
200
31,100
0.002
500
37,700
0.001
1,000
43,200
0.0005
2,000
49,200
0.0002
5,000
57,700
0.0001
10,000
64,800
0.00005
20,000
72,300
0.00002
50,000
83,200
0.00001
100,000
92,000
0.000001
1,000,000
126,000
1E-07
10,000,000
167,800
1E-08
100,000,000
218,800
1.00E+03
1.00E+04
1.00E+05
1.00E+06
Annual Exceedance Probability (%) Peak Discharge (ft3/s)
99.0
95.0
84.0
70.0
50.0
30.0
16.0
5.0
10.0
1.0
0.3
0.1
0.01
0.001
0.0001
1 (10-6)
1 (10-5)
2.5
Peak Discharge
Figure 5-1.Example of peak-discharge estimates in graphical form.
To make a volume estimate, a time series flood hydrograph estimate is required. The time series
flood estimate may be a historical flood hydrograph or a PMF hydrograph; either must be
believed to describe the rainfall-runoff response of the basin of interest at a wide range of return
periods. Flood hydrographs are linearly scaled so that the peaks match the estimates from the
peak-discharge analysis described above. When the hydrograph duration permits, 1-, 3-, 5-, 7-,
and 15-day volumes are calculated as the maximum volume of water transported during the
desired continuous time period.
When a rain-on-snow PMF hydrograph or rain-on-snow historical hydrograph is used as an
input, the analysis technique requires two hydrograph ordinates for each time period one for
the snowmelt portion and one for the rainfall portion. Only the rainfall portion of the hydrograph
is scaled to achieve the desired peak. The snowmelt portion of the hydrograph remains intact.
For all other input hydrographs, the entire hydrograph is scaled linearly to match peak estimates.
When volume estimates are calculated, the results are provided in tabular as well as graphical
format (table 5-2, figure 5-2). Graphical results (peak and volume flows) can be provided within
a combined chart (figure 5-2) or as two separate charts, as desired by the client (figure 5-1 and
figure 5-3).
The major assumption involved with scaling PMF hydrographs to various return periods is that
the dimensionless hydrograph used to develop the PMF is appropriate to describe the rainfallrunoff
response of the basin at all return periods. Because the generation of a hydrograph from a
dimensionless hydrograph involves only the convolution with time distributed rainfall rates,
assumptions are further made that the rainfall spatiotemporal distribution does not change with
flood magnitude, and soil characteristic response is linear in nature. The latter assumption may
be appropriate when floods of interest begin with saturated ground conditions. When these
assumptions are violated, predictions may be inaccurate by orders of magnitude. Similar
assumptions can be made when scaling a historical hydrograph. These assumptions are mainly
that the storm that caused the flood is similar in temporal and spatial characteristics to the storm
that would cause a flood of a different return period and that the initial soil conditions are also
similar. Soil infiltration responses are known to be highly non-linear in the unsaturated
condition; therefore, as with the PMF scaling, it is the initial condition for which the soils are
saturated that this type of scaling is most appropriate.
Reclamation uses the PMF as the upper limit of flood potential at a site for storm durations
defined by the PMP. If peak flows or volumes calculated using probability or statistical-based
hydrology methods exceed those of the PMF, the PMF is used in evaluating the hydrologic risk
and as a theoretical and practical upper limit to statistical extrapolations. If the PMF has been
properly developed, it represents the upper limit to runoff that can physically occur at a particular
site.
Hydrograph ordinates for the peak-scaled hydrographs, produced during the volume analysis, are
also provided for the CFR hydrologic hazard evaluation. Ordinates for the scaled hydrographs
have the same duration and number of ordinates as hydrograph data provided for input to scaling
analysis, thus requiring no interpolation. The scaled hydrographs have an AEP associated with
them, so they are suitable for use in reservoir routing studies and for dam safety risk assessment.
Table 5-2.Example of combined peak-discharge and volume estimates in tabular form
Figure 5-2.Example of combined peak-discharge and volume estimates in graphical form.
1.00E+03
1.00E+04
1.00E+05
1.00E+06
Annual Exceedance Probability (%)
Peak Discharge (ft3/s)
1.00E+04
1.00E+05
1.00E+06
Volume (acre ft)
99.0
95 0
84.0
70.0
50 0
30.0
16.0
5.0
10.0
1.0
0.3
0.1
0.01
0.001
0.0001
1 (10-6)
1 (10-5)
2.5
Peak Discharge
1-Day Volume
3-Day Volume
5-Day Volume
7-Day Volume
15-Day Volume
Figure 5-3.Example of volume only chart.
5.3 Detailed Hydrologic Studies
After developing the hydrologic hazard information for the CFR, more detailed hydrologic
studies may be necessary to better define the hydrologic problem, reduce uncertainty, develop
solutions, or make decisions. The amount of effort expended on analyzing a hydrologic hazard
is dependent on the nature of the problem and potential cost of the solution. Reclamation uses a
staged approach toward solving this problem. Initially, very little effort is expended to determine
the magnitude of the hydrologic hazard. If additional hydrologic studies are needed, a project
plan is developed that tailors the study to the particular needs of the project. The scope of work
attempts to address the specific dam safety issue at the least possible cost while providing
sufficient information to the dam safety decision makers to make informed safety decisions.
Flood characterization for risk assessments uses the length of the data record and other
characteristics of the data to determine the range of credible extrapolation used in the flood
frequency analysis. Because Reclamation risk assessments may require estimation of floods
with AEPs as small as 1 in 100,000,000, extrapolation of flood frequency relationships is
required well beyond the limits warranted by the data. These guidelines provide a reasonable
and reliable approach for characterizing the hydrologic hazard beyond the range of extrapolation
suggested by the data for use in dam safety risk assessments. Reliable flood frequency estimates
are needed for very small AEPs for dam safety decisionmaking, and these estimates should
convey an estimate of the uncertainty in the analysis for the consideration of the decision maker.
1.00E+03
1.00E+04
1.00E+05
1.00E+06
Annual Exceedance Probability (%)
Volume (acre ft)
1.0
0.3
0.1
0.01
0.001
0.0001
1 (10-6)
1 (10-5)
1-Day Volume
3-Day Volume
5-Day Volume
7-Day Volume
15-Day Volume
The uncertainties associated with flood estimates are likely to be substantial and an important
attribute to convey into the risk assessment. Flood characterization should include a best
estimate of the AEP of floods of different magnitudes and a description of the uncertainty in
such results. Such uncertainties need to be honestly represented and considered throughout the
risk assessment process.
Further analyses might be necessary if the hydrologic hazard information provided during the
CFR is insufficient to define and quantify hydrologic dam safety issues and make decisions.
Additional studies may become necessary to address reservoir routing effects of upstream dams,
reduce uncertainty in the flood estimates, verify statistical results before committing large capital
expenditures to dam safety modifications, etc. When planning the next study, the goal is to
achieve a balance between the amount of hydrologic analysis needed to address the issues and
make decisions, and the level of effort required to conduct the study. Generally, studies progress
from those requiring a low level of effort to those requiring a higher level of effort. As the
studies get more detailed, the results should become more precise and contain less uncertainty.
Since each study site is different, no single approach can be identified to address all hydrologic
issues. The method chosen should consider climatic and hydrologic parameters, drainage area
size, amount of upstream regulation, data availability, and level of confidence needed in the
results. The previous chapter of this report described the methods available in Reclamation to
develop hydrologic hazard curves.
Table 5.3 lists various methodologies that were considered for characterizing extreme floods to
support dam safety risk assessment. A flood frequency analysis must be combined with each of
these methodologies to assign annual exceedance probabilities to the floods.
Table 5-3.Alternative methods to develop hydrologic hazard information
Method of Analysis and Modeling
Risk
Analysis/Design
Level1
Level of
Effort2
Flood frequency analysis with historical/paleoflood data
- Graphical method;
- EMA;
- FLDFRQ3
CFR, IE, CAS, FD
Low
Hydrograph Scaling and Volumes
CFR, IE, CAS, FD
Low
GRADEX Method
IE, CAS, FD
Moderate
Australian Rainfall-Runoff Method
IE, CAS, FD
Moderate
Stochastic Event-Based Precipitation Runoff Modeling with SEFM
CAS, FD
High
Stochastic Rainfall-Runoff Modeling with CASC2D
CAS, FD
High
Probable Maximum Flood
CFR, IE, CAS, FD
Moderate
Notes:
1. Risk analysis/design level: CFR - Comprehensive Facility Review, IE - Issue
Evaluation, CAS - Corrective Action Study, and FD - Final Design.
2. Level of effort: Low requires 10-20 staff-days to complete the analysis; moderate
requires 21-75 staff-days; and high requires more than 75 staff-days.
Hydrologic studies usually will proceed from flood frequency and hydrograph scaling to an
analysis using either the GRADEX or Australian Rainfall-Runoff Method. The advantages of
these approaches are that they use regional rainfall data in developing flood estimates and yield
flood hydrographs. Both approaches work best on small drainages (less than 2,000 mi2), and the
Australian Rainfall-Runoff Method works better if snowmelt floods are important.
The SEFM and CASC2D are more sophisticated hydrologic modeling techniques used to address
hydrologic issues driven by large potential dam failure consequences. These approaches are
more suitable for CAS and final designs. They also allow for better quantification of hydrologic
uncertainty. These approaches require a lot of data and are generally more costly than the others.
When multiple methods have been used to determine the hydrologic hazard, sound physical and
scientific reasoning for weighting or combining results is needed. Clearly, a measure of
judgment is required to ensure that appropriate information is included in the dam safety
decisionmaking process. Reclamation develops various weighting schemes to evaluate the
results of multiple analyses and uses a team of hydrologists to select the weighting scheme that
best characterizes the hydrologic conditions for the site of interest. The selection is based on the
experiences of the team members and the assumptions used in each of the analyses. The
A.R. Bowman case study that follows illustrates this approach.
6. Case Studies
Three case studies are presented to illustrate the use of several methods. The study sites are Los
Banos, Fresno, and A.R. Bowman Dams. Each study begins with a flood frequency analysis and
hydrograph scaling. Different solution techniques were used to answer follow-up questions for
each of the following case studies.
6.1 Los Banos Dam
Los Banos Dam is an earthfill structure with an uncontrolled spillway. It was completed
between 1964 and 1965. This dam is located 7 miles southwest of the town of Los Banos,
California, on Los Banos Creek. The drainage basin upstream from the dam has a total area of
approximately 156 mi2. The spillway crest elevation is 353.5 feet and the dam crest elevation is
384.0 feet. The spillway discharge capacity at the dam crest elevation is 11,800 ft3/s. The total
capacity of the dam at water surface elevation 353.5 feet is 34,600 acre-feet. The active capacity
between elevations 296 and 353.5 feet is 26,300 acre-feet. The current PMFs for Los Banos
Dam were computed in 1996 (Bureau of Reclamation, 1996a). The results of these PMF studies
are summarized in table 6-1.
The PMFs were computed using a standard storm arrangement. Routing results indicate that Los
Banos Dam would be overtopped by a flood with a magnitude about 37.6 percent of the general
storm PMF (Bureau of Reclamation, 1996b). The general storm PMF would overtop the dam by
6.2 feet for 30 hours. The thunderstorm PMF does not overtop the dam.
Table 6-1.Probable maximum flood summary for Los Banos Dam, California
Flood Type
HMR
Peak Inflow
(ft3/s)
Volume (acre-feet)
With 100-year
antecedent
storm event
Without 100-year
antecedent
storm event
General storm
58
75,800
146,700 (7 day)
138,000 (4.3 days)
Thunderstorm
58
75,200
27,400 (24 hr)
Because Los Banos Dam is overtopped by the general storm PMF, flood probabilities are needed
to understand and quantify the risk of overtopping and hydrologic hazard for dam safety. A
flood frequency and volume frequency analysis was completed using the procedures
recommended for a CFR.
6.1.1 Los Banos Hydrologic Hazard Curves Using Flood Frequency Analysis and
Hydrograph Scaling
A recent flood study, including paleoflood data, peak-flow frequency, and hydrographs, was
completed for a risk analysis (Weghorst and Klinger, 2002). The streamflow and paleoflood data
from that study are summarized below and then used to compute a hydrologic hazard curve.
Because streamflow gage records for Los Banos Creek at Los Banos Dam were limited, the
records from the gaging station on Orestimba Creek, near Newman, California (U.S. Geological
Survey [USGS] station No. 11274500), were used in this example. This gage is located just
north of Los Banos Dam, has a drainage area of about 134 mi2, and provides 71 years (1932 to
2002) of unregulated peak discharge records. The peak discharge data were adjusted by the
square root of the drainage area ratio (Cudworth, 1989); this factor was (156/134)0.5 = 1.078.
There are several sources of regional and reconnaissance-level paleoflood data that may be
applied to estimates of flood frequency at Los Banos Dam including reconnaissance-level data
on Los Banos Creek and supporting data from site-specific soil stratigraphic information on the
Cantua Stream Group, located about 55 miles south of Los Banos Creek (Weghorst and Klinger,
2002). The hydrometeorologic setting for the Cantua Stream Group and Los Banos Creek, in
general, appears to be very similar to each other; however, no field verification was performed to
confirm this. Each of the basins is located on the eastern flank of the central Coast Ranges, and
the drainage basin areas are close enough in size that differences in their runoff characteristics
would be negligible given similarities in rock types, basin aspect and slope, average elevation,
and vegetation and land use. Therefore, the paleoflood peak discharge bounds and age estimates
from the Cantua Stream Group are believed to be applicable to Los Banos Creek (Weghorst and
Klinger, 2002). Paleoflood bounds were established by scaling (Cudworth, 1989) the peak
discharges for paleoflood data on the Cantua Stream Group to the Los Banos basin. It appears
that peak discharges in the range of 42,000 to 60,000 ft3/s on Los Banos Creek have not been
exceeded in the last 1,800 2,800 years.
A hydrologic hazard curve for Los Banos Dam was constructed using the flood frequency
analysis and hydrograph scaling procedures recommended for a CFR. Peak flow and paleoflood
data and a PMF general storm hydrograph were used to estimate the hazard curve (figure 6-1).
Estimated peak flows and volumes can exceed the PMF peak and volume at this site (table 6-1
and table 6-2). Therefore, the PMF was considered as an upper limit for design and risk analysis
(Bureau of Reclamation, 2002).
Hydrographs for these floods were then routed through Los Banos Reservoir and spillway. The
results from this characterization of the hydrologic hazard and flood hydrograph routing indicate
that Los Banos Dam may potentially be overtopped by a flood with a return period of about
2,800 years (based on peak flow). Using these results, Los Banos Dam does not meet
Reclamation hydrologic hazard criteria for overtopping because it does not pass a 10,000-year
flood (at a minimum). Because this dam does not meet Reclamation criteria, additional studies
for Los Banos are required to further assess the flood risk, estimate the need for any structural
modifications, and determine suitable probability-based design hydrographs for any potential
modification or design alternatives.
6.2 A.R. Bowman Dam
The case study for A.R. Bowman Dam is an example of a project where several hydrologic
studies have been completed. The dam is an earthfill structure with an uncontrolled spillway. It
was completed in 1961. This dam is located about 20 miles upstream from Prineville, Oregon,
on the Crooked River. The drainage basin upstream of the dam has a total area of approximately
2,635 mi2. The spillway crest elevation is 3234.8 feet, and the dam crest elevation is
3264.0 feet. The spillway capacity at the dam crest elevation is 11,500 ft3/s. The total capacity
of the dam at water surface elevation 3257.9 feet is 233,100 acre-feet. The current PMFs for
A.R. Bowman Dam were computed in 1994. The results of these studies are summarized in
table 6-3.
1.00E+01
1.00E+02
1.00E+03
1.00E+04
1.00E+05
Annual Exceedance Probability (%)
Peak Discharge (ft3/s)
1.00E+04
1.00E+05
1.00E+06
Volume (acre ft)
99.0
95 0
84.0
70.0
50 0
30.0
16.0
5.0
10.0
1.0
0.3
0.1
0.01
0.001
0.0001
1 (10-6)
1 (10-5)
2.5
Peak Discharge
3-Day Volume
Figure 6-1.Example of hydrologic hazard curve for Los Banos Dam, California.
Table 6-2.Peak and volume (3-day) estimates at Los Banos Dam, California,
for specified probabilities
Annual
exceedance
probability
Return period
Peak discharge
estimate
(ft3/s)
3-day volume estimate
(acre-feet)
0.01
100
25,400
50,100
0.005
200
30,100
58,500
0.002
500
37,000
70,800
0.001
1,000
42,800
80,800
0.0005
2,000
49,100
91,700
0.0002
5,000
58,300
107,200
0.0001
10,000
65,900
120,000
0.00005
20,000
74,100
133,700
0.00002
50,000
75,800
136,500
Table 6-3.Probable maximum flood summary A.R. Bowman Dam, Oregon
Flood type
HMR
Peak inflow
(ft3/s)
Volume (acre-feet)
With 100-year
antecedent
conditions
Without 100-year
antecedent conditions
February
General storm
57
255,000
770,000
(15 day)
138,000
(4.3 days)
June
General storm
57
83,300
185,600
(15 day)
185,600
(15 day)
August
General storm
57
75,000
112,600
(15 day)
Routings of the PMF hydrographs indicated that the February general storm event, with a
starting water surface elevation of 3211.17 feet, would overtop the dam by 18.6 feet.
A.R. Bowman Dam would only pass approximately 10 to 25 percent of the February general
storm PMF without overtopping. The June and August PMFs did not overtop the dam.
Because A.R. Bowman Dam is overtopped by the February general storm PMF, flood
probabilities are needed to understand and quantify the risk of overtopping and hydrologic
hazard for dam safety. Several investigations have been undertaken since about 1991 to
determine PMF design modification alternatives, including overtopping protection and parapet
walls. In addition, detailed probabilistic flood studies using alternative approaches (stochastic
event flood modeling and paleoflood studies) were completed at A.R. Bowman Dam to better
estimate the flood risk.
Three methods for estimating the hydrologic hazard are discussed in this section: flood
frequency analysis and hydrograph scaling, SEFM, and peak-flow frequency analysis with
detailed paleoflood data. Flood risk results from the three methods and implications for potential
modifications at A.R. Bowman Dam are then discussed.
6.2.1 A.R. Bowman Hydrologic Hazard Curves Using Flood Frequency Analysis and
Hydrograph Scaling
Peak flow data at A.R. Bowman Dam were obtained from three USGS gaging stations:
Crooked River at Post, Oregon (USGS station No. 14079500)
Crooked River above Prineville Reservoir near Post, Oregon (USGS station No. 14079800)
Crooked River near Prineville, Oregon (USGS station No. 14078050)
These gages are the closest to A.R. Bowman Dam; the first two are located upstream from the
reservoir, and the gage near Prineville is located downstream from the dam. The combined
gages provide 38 years (1909 to 1972, with many missing years) of unregulated peak discharge
records. The peak discharge data for the upstream gages were adjusted by the square root of the
drainage area ratio (Cudworth, 1989). The December 1964 flood was treated as a historic peak
with a return period of approximately 140 years (largest since about 1860).
The reconnaissance-level paleoflood data that may be applied to estimate flood frequency at
A.R. Bowman Dam are based on the detailed paleoflood data presented below. Information
from the paleohydrologic bound with the largest discharge was used and was dated based on the
Mount Mazama volcanic eruption 7,600 years ago. Based on this information, it appears that a
peak discharge between 27,000 and 36,000 ft3/s on the Crooked River has not been exceeded in
the last 7,600 to 10,000 years.
A hydrologic hazard curve for A.R. Bowman Dam was constructed using the techniques outlined
in section 5. This example calculation was completed after the results of the SEFM and
paleoflood study were completed. This example represents the first step that might be performed
in future flood studies for Reclamation dam safety. Peak flow and paleoflood data and a general
storm PMF hydrograph were used to estimate the hazard curve (figure 6-2 and table 6-4).
1.00E+03
1.00E+04
1.00E+05
Annual Exceedance Probability (%)
Peak Discharge (ft3/s)
1.00E+04
1.00E+05
1.00E+06
Volume (acre ft)
99.0
95 0
84.0
70.0
50 0
30.0
16.0
5.0
10.0
1.0
0.3
0.1
0.01
0.001
0.0001
1 (10-6)
1 (10-5)
2.5
Peak Discharge
3-Day Volume
Figure 6-2.Example of a hydrologic hazard curve for A.R. Bowman Dam, Oregon.
6.2.2 A.R. Bowman Hydrologic Hazard Estimates Based on a Stochastic Event
Flood Model
MGS Engineering Consultants, Inc., was contracted in November 1997 (Schaefer and Barker,
1997) to perform a hydrologic stochastic analysis to develop magnitude frequency curves for
flood peak discharge, runoff volume, and maximum reservoir elevation. The SEFM was
developed using a deterministic rainfall-runoff model (HEC-1) and treated input parameters that
were selected by Monte Carlo sampling procedures as a probabilistic distribution of values rather
than fixed values. The SEFM is described in section 4.5. After the initial modeling runs and
results at A.R. Bowman Dam were made, the precipitation depth-area relationships were refined
(Schaefer and Barker, 1998) and new flood frequency relationships were developed.
The results from the SEFM include peak flow, volume, and reservoir elevation frequency curves.
These graphs are shown below and include polynomial equations fitted to model output that are
applicable in the range of AEP from 10-2 to 10-5 (Schaefer and Barker, 1998). From these
results, the dam may be potentially overtopped with a maximum reservoir elevation probability
equal to 0.0005 (2,000-year return period) (figure 6-4).
Peak discharge estimate:
Q = 2322Log 2 (AEP) - 2241Log (AEP) + 950 p
Flood Runoff Volume Estimate:
Q = 8385Log 2 (AEP) - 59700Log(AEP) - 39490 v
Maximum reservoir elevation estimate:
0.3993 4 ( ) 6.193 3 ( ) 33.67 2 ( ) 89.81 ( ) 3159.2
max ELEV = - Log AEP - Log AEP - Log AEP - Log AEP +
Table 6-4.Peak and volume (3-day) estimates at
A.R. Bowman Dam, Oregon, for specified probabilities
Annual
exceedance
probability
Return period
Peak discharge
estimate
(ft3/s)
3-day volume estimate
(acre-feet)
0.01
100
16,000
65,100
0.005
200
18,100
71,300
0.002
500
21,000
79,700
0.001
1,000
23,300
86,300
0.0005
2,000
25,700
93,000
0.0002
5,000
29,100
102,100
0.0001
10,000
31,700
109,200
0.00005
20,000
34,500
116,600
0.00002
50,000
38,400
126,600
0.00001
100,000
41,500
134,500
0.000001
1,000,000
52,700
162,400
1E-07
10,000,000
65,500
193,200
1E-08
100,000,000
80,300
227,300
50 40 30 20 10 5 2 1 0.5 0.1 0.01 1E-3 1E-4 1E-5 1E-6
10,000
100,000
1,000,000
10,000
100,000
1,000,000
Qp (Peak Discharge)
Total Volume (acre-ft) for Specified Duration
Peak Discharge (ft3/s)
Annual Exceedance Probability (%)
VT (total volume 15 or 21-day)
Figure 6-3.Peak discharge and total volume frequency curves from the SEFM
for A.R. Bowman Dam, Oregon.
3,240
3,245
3,250
3,255
3,260
3,265
3,270
3,275
3,280
3,285
3,290
3,295
0.01 0.001 0.0001 0.00001
Annual Exceedance Probability
Maximum Reservoir Elevation (feet)
Dam Crest Elevation 3,264 feet
Overtopping Probability 0.0005, Return Period 2,000 years
Figure 6-4.Maximum reservoir elevation frequency curve from the SEFM for
A.R. Bowman Dam, Oregon.
6.2.3 A.R. Bowman Hydrologic Hazard Estimates Using Bayesian Statistical Estimation
To gain information on the magnitude of low probability floods for risk analysis, the Dam Safety
Office, in 1995, requested a paleoflood study on the Crooked River at A.R. Bowman Dam. The
paleoflood study was an alternative approach to the SEFM. The paleoflood report has not been
published because of changing priorities in the Dam Safety Office.
For the Crooked River paleoflood study, two reaches downstream from A.R. Bowman Dam were
selected for detailed hydraulic modeling. These reaches are about 2 and 35 miles downstream
from the dam. At these study reaches, there is geomorphic, stratigraphic, and botanic evidence
to limit the paleostage of floods throughout the Holocene epoch (the past 10,000 years). In one
of the downstream reaches, it is possible to reconstruct the magnitude of the December 1861
flood based on the presence of driftwood piles. In addition to these downstream study reaches, a
third study reach was identified just upstream from Prineville Reservoir, where the stage of
paleofloods during the late Holocene epoch can be related to the peak discharge estimates from
the December 1964 flood.
Stratigraphy and soils were described at eight sites along the Crooked River, including the three
study reaches. At these sites, the soils were described in detail and material was collected for
radiocarbon dating. In total, there are 54 radiocarbon ages for the Crooked River paleoflood
study. In addition to these radiocarbon ages, the Mazama ash forms an important stratigraphic
datum along the river downstream from A.R. Bowman Dam. The calibrated ages of radiocarbon
samples associated with the Mazama ash throughout the western U.S. yield an age of about
7,650 years. The hydraulic geometry of the Crooked River channel is remarkably consistent at
all the study sites. This implies long-term stability of the Crooked River channel and of the
mechanisms that produce large floods on the Crooked River.
The paleoflood data that have been collected and analyzed to date are summarized in table 6-5.
Table 6-5.Detailed paleoflood estimates at A.R. Bowman Dam, Oregon
Type
Preferred age
(years before
present)
Age range
(years)
Preferred
discharge
(ft3/s)
Discharge range
Low
(ft3/s)
High
(ft3/s)
1862 historical bound
140
15,000
13,000
18,000
Paleohydrologic bound
1,100
980 1,210
20,700
18,000
25,000
Paleohydrologic bound
3,150
2,650 3,650
25,000
22,000
30,000
Paleohydrologic bound
3,500
3,350 5,050
27,000
25,000
32,500
Paleohydrologic bound
9,000
7,600 10,000
30,000
27,000
36,000
Historical flood
140
20,700
18,000
25,000
Paleoflood
1,100
980 1,210
20,700
18,000
25,000
The paleoflood data were combined with peak flows from three gaging stations. A frequency
analysis was performed using FLDFRQ3 (OConnell, 1999; OConnell et al., 2002). The peakflow
frequency results for a particular distribution (log-Pearson) are shown in figure 6-5 and
summarized in table 6-6. Based on this peak-discharge frequency curve and scaling model
hydrographs, the dam might be overtopped at exceedance probabilities greater than 0.0001 (more
frequently than the 10,000-year return period).
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
1,000
2,000
3,000
4,000
5,000
6,000
7,000
8,000
9,000
10,000
20,000
30,000
40,000
50,000
60,000
70,000
80,000
90,000
100,000
200,000
Peak Discharge (ft3/s)
Annual Exceedance Probability (%)
Qdata
Q50
Q025
Q975
Figure 6-5.Peak-discharge frequency curve based on paleoflood data for A.R. Bowman Dam, Oregon.
Table 6-6.Peak discharge estimates based on paleoflood data at
A.R. Bowman Dam, Oregon, for specified probabilities
Annual
Exceedance
Probability Return Period
Median (50%) LP3
Model Peak
Discharge Estimate
(ft3/s)
2.5% LP3 Model
Peak Discharge
Estimate (ft3/s)
97.5% LP3 Model
Peak Discharge
Estimate (ft3/s)
0.01 100 13,100 11,100 15,000
0.002 500 17,100 14,600 19,500
0.001 1,000 18,900 16,100 21,800
0.0005 2,000 20,700 17,500 24,400
0.0002 5,000 23,300 19,300 28,200
0.0001 10,000 25,200 20,700 31,500
0.00001 100,000 32,200 24,500 44,900
0.000001 1,000,000 39,800 27,900 63,200
0.0000001 10,000,000 48,200 30,800 87,500
0.00000001 100,000,000 57,100 33,400 119,700
6.2.4 Combined Hydrologic Hazard Estimates for Risk Analysis and
Dam Safety Implications
Both the SEFM and paleoflood study indicate that A.R. Bowman Dam potentially might not
meet Reclamation hydrologic hazard criteria for overtopping because it does not pass the
10,000-year flood (at a minimum). The results from the three approaches (flood frequency
analysis and hydrograph scaling, SEFM, and paleoflood study) were combined to provide a
single estimate of the hydrologic hazard curve for risk analysis. The weighting schemes are
simple numerical weights given to each model result. Three weighting schemes were analyzed
for A.R. Bowman: (1) enveloping all results (figure 6-6), (2) weighting the SEFM and
paleoflood peak flow curves equally (50 percent each) (figure 6-7), and (3) choosing a best
estimate between the SEFM and paleoflood peak flow curves equal to the upper 97.5 percent
confidence limit from the Bayesian analysis (figure 6-8). The third option was selected to
represent the peak discharge flood frequency based on results and decisions made in 1999 for a
risk analysis. A combined hydrologic hazard curve is shown in figure 6-9, which also includes
a volume frequency analysis based on results of the SEFM.
Because A.R. Bowman Dam might not meet Reclamation criteria, additional engineering
studies are ongoing to estimate the need for any potential structural modifications at this site.
Probability-based design hydrographs for any potential modification or design alternatives were
selected based on a combination of the weighting results shown above. Corrective action studies
are ongoing.
1.00E+03
1.00E+04
1.00E+05
1.00E+06
Annual Exceedance Probability (%)
Peak Discharge (ft3/s)
1.0
0.3
0.1
0.01
0.001
0.0001
1 (10-6)
1 (10-5)
Initial Characterization
Bayesian 97.5 CI
SEFM
Envelope Curve
Figure 6-6.Weighted peak-discharge frequency curve based on enveloping results for
A.R. Bowman Dam, Oregon.
1.00E+03
1.00E+04
1.00E+05
1.00E+06
Annual Exceedance Probability (%)
Peak Discharge (ft3/s)
1.0
0.3
0.1
0.01
0.001
0.0001
1 (10-6)
1 (10-5)
Initial Characterization
Bayesian 97.5 CI
SEFM
Equal Weighting
Bayesian Mean
Figure 6-7.Equal (50 percent) weighted peak-discharge frequency curve for
A.R. Bowman Dam, Oregon.
1.00E+03
1.00E+04
1.00E+05
1.00E+06
Annual Exceedance Probability (%)
Peak Discharge (ft3/s)
1.0
0.3
0.1
0.01
0.001
0.0001
1 (10-6)
1 (10-5)
Initial Characterization
Bayesian Method
SEFM
Best Estimate
Bayesian 97.5 CI
Figure 6-8.Best estimate (Bayesian 97.5 percent) weighted peak-discharge frequency curve
for A.R. Bowman Dam, Oregon.
1.00E+03
1.00E+04
1.00E+05
1.00E+06
Annual Exceedance Probability (%)
Peak Discharge (ft3/s)
1.00E+04
1.00E+05
1.00E+06
Volumes (acre-feet)
1.0
0.3
0.1
0.01
0.001
0.0001
1 (10-6)
1 (10-5)
15 Day Volumes
Peak Discharge
Figure 6-9.Final combined hydrologic hazard curve for A.R. Bowman Dam, Oregon.
6.3 Fresno Dam
Fresno Dam is located on the Milk River in north-central Montana, approximately 14 miles
west of the town of Havre (figure 6-10). The compacted earthfill dam was constructed from
1937 to 1939. It is approximately 110 feet high. Previous studies have indicated that the dam
could safely pass Reclamations 1985 PMF hydrograph. Normally, Reclamation would not have
conducted additional hydrologic studies for this dam; however, project beneficiaries wanted to
examine the possibility of enlarging the dam.
6.3.1 Fresno Dam Hydrologic Hazard Curves Using Flood Frequency Analysis and
Hydrograph Scaling
A hydrologic hazard curve for Fresno Dam was constructed using flood frequency analysis
techniques. Peak flow and paleoflood data and a general storm PMF hydrograph were used to
estimate the hazard curve (figure 6-11 and table 6-7).
Figure 6-10.Site and watershed depiction of Fresno Dam, Montana.
Figure 6-11.Example of hydrologic hazard curve for Fresno Dam, Montana.
1.00E+02
1.00E+03
1.00E+04
1.00E+05
1.00E+06
Annual Exceedance Probability (%)
Peak Discharge (ft3/s)
1.00E+04
1.00E+05
1.00E+06
Volume (acre ft)
99.0
95 0
84.0
70.0
50 0
30.0
16.0
5.0
10.0
1.0
0.3
0.1
0.01
0.001
0.0001
1 (10-6)
1 (10-5)
2.5
Peak Discharge
5-Day Volume
Table 6-7.Peak and volume (5-day) estimates at Fresno Dam, Montana, for specified probabilities
Peak flow data at Fresno Dam were obtained from the USGS gaging station, Milk River at
Eastern U.S. Border Crossing (USGS station No. 06135000). The gage provides peak flow
records from 1910 through 2002. No adjustments were performed on these data, as the
associated drainage area and streamflow records were believed to accurately represent the
conditions at Fresno Dam.
The reconnaissance-level paleoflood data that may be applied to estimate flood frequency at
Fresno Dam are based on detailed chronology developed at archaeological sites on the Milk
River. Based on this information, it appears that a peak discharge between 40,000 and
70,000 ft3/s on the Milk River has not been exceeded in the last 2,000 to 4,000 years.
Fresno Dam has a spillway discharge capacity of 51,360 ft3/s at the maximum water surface
elevation of 2591 feet. Comparing this value with the peak-discharge flood frequency curve
indicates that the spillway is capable of passing a flood with a return period of only slightly
longer than 2,000 years. At the time of this study, the methods for determining the volume
frequency relationship had not been developed, so hydrographs were not available for reservoir
routing. Therefore, we decided to develop hydrographs using the GRADEX Method.
6.3.2 Fresno Dam Hydrologic Hazard Analysis Using the GRADEX Method
Daily flow records that approximate the daily inflows to Fresno Dam come from the stream gage
on the Milk River at the Eastern U.S. Border Crossing (USGS station No. 06135000). This gage
record has daily flow data from August 1909 through September 2001. A total of 86 years of
daily flow data is available, with a few missing years. The contributing drainage area at the gage
site is considered to be 2,525 mi2, and the gage is located about 54 river miles upstream from
Fresno Dam. The total possible contributing drainage area at Fresno Dam is considered to be
2,911 mi2 for the rainfall-runoff modeling calculations in this study. These daily flow records
were checked with available reservoir inflow records for concurrent years.
Annual Exceedance
Probability Return Period Discharge Estimate
5-Day Volume Estimate
(acre ft)
0.01 100 18,900 92,000
0.005 200 24,100 103,900
0.002 500 32,300 121,400
0.001 1000 39,700 136,100
0.0005 2000 48,200 152,300
0.0002 5000 61,500 176,000
0.0001 10000 73,100 195,900
0.00005 20000 86,400 217,600
0.00002 50000 106,600 249,500
0.00001 100000 124,200 276,000
0.000001 1000000 199,600 382,100
0.0000001 10000000 307,800 520,800
0.00000001 100000000 459,400 700,300
The information needed from the stream gage record is a set of independent flood volumes,
representing the volume of flooding caused by rainfall for independent storms in the basin. The
process starts by setting a threshold flow value and then counting the number of events that have
continuous days of flow above that value. A threshold flow value was set and adjusted until
about 86 independent flood events above this value were determined. The average duration of
all of the independent flood events was then calculated. This average duration of independent
flood events for the Milk River above Fresno Dam was found to be between 4 and 5 days, with a
threshold value of 1,307 ft3/s. The value of 5 days was selected for further use in the study as the
critical duration for both rainfall and flood events.
The GRADEX Method required that the number of multi-day rain events at each gage be equal
to the number of common years of record for the selected gages. The number of multi-day rain
events was made equal by selecting a threshold 5-day total rainfall for each gage such that
exactly fifty 5-day rain totals were above the threshold value for each gage. Figure 6-10 displays
the locations of the six precipitation gage stations selected for the GRADEX analysis at Fresno
Dam. Table 6-8 lists the six stations used for the remainder of this analysis along with some
pertinent information including the MAP.
Table 6-8.Rainfall data description
Using the 5-day precipitation totals, 5-day flow volumes, drainage area, and other data described
above, the GRADEX Method computations were made as outlined in Naghettini (1994) and
Naghettini et al. (1996). For this study, a special situation arises with respect to selection of the
contributing drainage area above Fresno Dam.
Based on all previous Reclamation IDF and PMF studies for Fresno Dam, the authors of this
study believe that a single-storm precipitation pattern will not cover the entire basin. For this
GRADEX study, a total contributing drainage area of 1,100 mi2 was selected, based primarily on
the use of the hypothetical elliptical patterns used with the PMP studies.
Station State/Prov. Latitude Longitude Elevation M.A.P.
(feet) (inches)
Babb MT 48.93 113.36 4300 18.27
Gold Butte MT 48.98 111.4 3498 13.38
Kremlin MT 48.52 110.1 2860 11.56
Simpson MT 49 110.22 2815 10.24
Sweetgrass MT 49 111.97 3466 13.98
Foremost ALB 49.48 111.45 2899 14.68
Fresno basin mean basin elevation = 3527 feet
Fresno basin mean annual precip. = 13.1 inches
Selected Rainfall Stations with a Period of Record Including 1950-2000
Used with Fresno Dam GRADEX Study for high return period volumes
Table 6-9 and figure 6-12 display the summary results from the calculations for Fresno Dam.
The volume of the PMF volume centered hydrograph from the 1985 Reclamation PMF study is
plotted as a straight line on the frequency curve for comparison. It should be noted that the PMF
is based on a 3-day rainfall, and the Fresno Dam frequency curve is based on 5-day total rainfall
amounts. The GRADEX Method is intended to give flood volume data for very large return
periods, in excess of 200 years. More common methods, such as a LP-III distribution fit to
available streamflow data, should be used for the lower return periods, 100 years and less in this
study.
Table 6-9.Five-day volume frequency curve for Fresno Dam, Montana,
based on GRADEX Method
In most normal years, snowmelt may contribute a large amount to the total volume of inflows to
Fresno Reservoir. Another assumption in the GRADEX Method is that the precipitation that is
measured at the gages is in liquid form and ready for runoff, or if it is snow, the snow will melt
during the critical storm-time period and add to the runoff volume. A simple scheme to separate
purely snowmelt runoff from rain or rain-on-snow runoff was used with the 86 years of daily
flows at the Milk River at Eastern U.S. Border Crossing gage. The 7-day maximum of purely
snowmelt flow was then determined for each year and expressed as a constant flow for 7 days.
The 86-year-long series of 7-day maximum snowmelt flows at the gage site was then analyzed
using a standard LP-III analysis. The lower curve in figure 6-13 displays the frequency curve of
maximum 7-day purely snowmelt flows. The curve is quite flat. This is expected for purely
snowmelt driven volumes. There is a physical limit to how much snow can be melted with
normal ranges of climate variables. The snowmelt volume frequency curves will become quite
flat for larger return periods. The 7-day flows were then converted to volumes in acre-feet and a
similar frequency curve was also plotted in figure 6-13.
Return Five-day Upper Lower
Period Volume Bound Bound
(years) (acre-ft) (acre-ft) (acre-ft)
500 188,700 320,100 112,400
1,000 214,700 358,700 131,100
5,000 275,100 448,200 174,700
10,000 301,100 486,800 193,500
20,000 327,100 525,400 212,300
50,000 361,600 576,400 237,200
100,000 387,600 615,000 256,000
500,000 448,000 704,600 299,600
1,000,000 474,100 743,100 318,500
1000
10000
100000
1000000
1 100 10000 1000000
Return Period (years)
5-day volume into Fresno Reservoir (acre-ft)
5-day rain volumes by GRADEX method
Upper 95% confidence bound on 5-day rain volumes by GRADEX Method
Lower 95% confidence bound on 5-day rain volumes by GRADEX Method
PMF Volume Centered maximum 5-day volume (based on 3 days of rain)
50,000 year location
Historic 5-Day Volumes
Volume Centered PMF
5-day volume 389,400 acre-ft
50,000 years
5-day volume
GRADEX curve
applies only to large return periods
(> 200-years)
Different
distributions
apply to 5-day
volume data for
lower return periods
Figure 6-12.Fresno Dam, Montana, 5-day rain-generated volumes by GRADEX Method.
The 5-day volumes of the GRADEX rain flood volumes from this study were then added to the
plot. This is the blue curve near the top of figure 6-13. A combined probability curve was then
computed and is shown as the red curve on the top of figure 6-13. The combined probability
curve expresses the probability (or return period) of getting a particular total flood volume by
combining a 7-day snowmelt with a 5-day rain flood volume. The combined probability curve
very closely follows the 5-day rain flood volume curve for the large return periods.
Hourly inflow hydrographs were developed for Fresno Dam for the desired return periods by
applying indexed rainfall amounts to the HEC-HMS models calibrated to the 1906 and 1964
rainfall flood events. The rainfall amounts for the 1964 and 1906 storm hyetographs were
uniformly increased in each subbasin until the 5-day volume of the respective return periods,
determined by the GRADEX Method, was achieved. Figure 6-14 displays the results for the
1964 flood computations. Figure 6-15 displays the results of increasing the 1964 precipitation
amount to calculate hydrographs with the GRADEX volumes for specified return periods.
The peak versus volume relationship was developed using a LOWESS technique (Cleveland,
1979). The 86 years of peak and 5-day volume data from the USGS gage at the Milk River at
Eastern Border were plotted. In addition, the 30 peak-flow and 5-day volumes generated from
Fresno Dam Montana
Snowmelt and Rainflood Volume Frequency Curve Comparisons
100
1000
10000
100000
1000000
1 10 100 1000 10000 100000 1000000
Return Period (years)
Maximum 7-Day Snowmelt Flow
(Ft3/S) or Ac-Ft
Maximum 7-Day Average Snowmelt Flows extrapolated LPIII frequency curve
Maximum 7-day snowmelt flows at gage data points
Total snowmelt 7-day volume in ac-ft
Rain flood 5-day volume by GRADEX WITH DA = 1100 sq. mi..
Extended Gradex to Low Return Periods
Combined Probability 5-Day rain + 7 day snowmelt volume (ac-ft)
Log-Pearson III Fit extended to 1,000,000 years of 7-day mean snowmelt
flows at Milk River at East U. S. border (ft3/s-days)
Maximum 7-Days Snowmelt (ac-ft)
5-Day rainfall volume based on GRADEX method with
1100 sq. mi. (ac-ft)
Combined 7-day snowmelt + 5-day rain volume curve (ac-ft)
Figure 6-13.Fresno Dam, Montana, snowmelt and rainflood volume frequency curve comparisons.
the HEC-HMS models originally calibrated to both the 1906 and 1964 flood events were run. In
each run, the lag time was varied or the rainfall was increased in a systematic manner to cover a
range of possible values for greater storm events. A LOWESS fit was done using the entire set
of peak versus volume points and is shown in figure 6-16. This relationship was used to
determine the peak discharge estimates that correspond to the selected 5-day return period
volumes computed using the GRADEX Method.
The results of this calculation can be used to derive a peak-flow flood frequency curve. The
information for the peak flow and volumes for the return periods of interest in this study is
summarized in table 6-10. In this study, the reported paleohydrology information indicated a
non-exceedance peak flood bound with an age between 2,000 and 4,000 years and a magnitude
between 40,000 and 70,000 ft3/s. The paleohydrology information was in agreement with the
GRADEX results.
For Fresno Dam, the results of the GRADEX Method were used for the risk assessment because
flood volumes were needed to evaluate the safety of the dam. Since only peak flow data were
available at the time of the first analysis, the GRADEX study was conducted. Hydrographs
could then be routed through the reservoir to take advantage of the flood attenuation effects of
the large surcharge storage in the reservoir.
0
1000
2000
3000
4000
5000
6000
7000
8000
9000
0 50 100 150 200 250 300
Time (hours)
Reservoir Inflow (cfs)
Fresno Reservoir
Inflow Hydrograph
June 1964
Fresno Reservoir
Calibrated HECHMS
Reservoir
Inflow Hydrograph
June 1964
Figure 6-14.Comparison of gage record and HEC-HMS calibration run.
0
20000
40000
60000
80000
100000
120000
0 50 100 150 200 250 300
Time (hour)
Reservoir Inflow (cfs)
1,000-year 10,000-year 50,000-year
Figure 6-15.Fresno Dam, Montana, 1,000-, 10,000-, and 50,000-year hydrographs.
Hydrographs from 1964 precipitation pattern with volume from GRADEX Method.
0
50000
100000
150000
200000
250000
0 100000 200000 300000 400000 500000 600000 700000 800000
5-Day Volume (acre-ft)
Peak inflow (ft3/s)
50,000 year 5-day volume = 361,600 acre-ft
10,000 year 5-day volume = 301,100 acre-ft
1,000 year 5-day volume = 214,700 acre-ft
83,000 ft3/S
98,000 ft3/S
PMF Peak Centered
PMF Volume Centered
Paleo hydrology non-exceedance
2,000 - 4,000 year bound
40,000 ft3/s to 70,000 ft3/s
61,000ft3/S
Figure 6-16.Fresno Dam, Montana, 5-day volumes versus peaks.
Table 6-10.Fresno Dam, Montana, GRADEX Method results
7. Summary
This report summarizes Reclamations approach toward developing hydrologic hazard curves for
use in evaluating dam safety issues. The procedure relies on extracting information from
existing studies to the fullest extent possible. The characterization of hydrologic risk for a CFR
can usually be accomplished with minimal effort. CFR hydrologic hazard curves display peak
Return
Period
Peak
Inflow
5-Day
Volume
(year) (cfs) (acre-ft)
1,000 61,000 214,700
10,000 83,000 301,100
50,000 98,000 361,600
flow and volume relationships for a full range of Annual Exceedance Probabilities necessary for
decision making. The procedures and analysis techniques defined in this report allow for the
possibility, and even plausibility, that peak discharge and volume estimates may exceed the
PMF. This is a function of the uncertainty and inconsistency among and between analysis
techniques. Therefore, in these cases, the PMF is believed to represent the upper limit to
hydrologic risk.
The procedure for developing hydrologic hazard curves considers the dam safety decision
criteria, potential dam failure mode, and dam characteristics, available hydrologic data, possible
analysis techniques, resources available for analysis, and tolerable level of uncertainty. Dam
safety decision criteria determine the probabilistic range of floods needed to address hydrologic
issues (Bureau of Reclamation, 2003a). The potential dam failure mode and dam characteristics
impact the type of hydrologic information needed to assess the problem. The specific elements
selected to be incorporated in an analysis of hydrologic hazards should consider the tolerable
level of uncertainty. Reducing the uncertainty in the estimates may require additional data
collection and use of more sophisticated solution techniques. It is believed that increasing the
level of effort and the sophistication of analysis techniques increases the reliability and level of
confidence associated with the results.
Reclamation currently uses a combination of seven hydrologic methods to develop hydrologic
hazard curves. These general techniques include: flood frequency analysis with historical and
paleoflood data, hydrograph scaling and volumes, the GRADEX Method, the Australian
Rainfall-Runoff Method, stochastic event-based precipitation runoff modeling with the SEFM,
stochastic rainfall-runoff modeling with CASC2D, and the PMF. Each method is described
within these guidelines.
The hydrologic methods described in these guidelines are not all inclusive. New techniques for
developing hydrologic hazard information can be added to these guidelines as they are developed
by the hydrology community.
The amount of effort expended on analyzing a hydrologic hazard depends on the nature of the
problem and the potential cost of the solution. A staged approach toward evaluating a
hydrologic safety issue is recommended. Initially, very little effort is expended to determine the
magnitude of the hydrologic hazard. Reclamation attempts to make use of all available studies
for the site of interest. Often, the PMF and initial flood frequency studies are the only
hydrologic studies available before the start of a probabilistic investigation. When other
hydrologic studies have been performed, available data will be used to decrease uncertainty in
results as well as to provide an overall assessment of hydrologic risk.
Dam safety evaluations usually begin with a characterization of hydrologic risk. If detailed
studies have been conducted for the site of interest, they are summarized and presented to the
risk assessment team. About two-thirds of Reclamations dams can safely accommodate the
PMF; when the PMF is selected as the IDF, no additional work may be required unless other
hydraulic issues need evaluation. Additional hydrologic work begins with a flood frequency
analysis and hydrograph scaling to develop a peak-discharge relationship and frequency flood
hydrographs. It is believed that this type of information is sufficient to address hydrologic issues
and make dam safety decisions at about 80 percent of the remaining dams. For the sites that still
have potential safety problems, project plans can be developed for studies to address the specific
hydrologic issues. These studies require more work and more sophisticated solution techniques
than flood frequency analysis and hydrograph scaling.
When planning more detailed studies, it is recommended that the goal be to achieve a balance
between the amount of hydrologic analysis needed to address the issues and the level of effort
required to conduct the study. As the studies get more detailed, the results should become more
precise and contain less uncertainty. An example is a hydrologic study that proceeds from flood
frequency analysis and hydrograph scaling to an analysis using the GRADEX Method, the
Australian Rainfall-Runoff Method, a stochastic rainfall-runoff model, or any other statistical
estimation technique available.
When multiple methods are used, alternative hazard curves are developed by weighting results
from the individual analyses. A team of hydrologists evaluates the alternatives and selects a
weighting scheme that is most representative of the site for use in the risk assessment. Selection
of the final hydrologic hazard curve depends on the experience of the hydrologists and the
assumptions that went into each analysis.
Three case studies, Los Banos, Fresno, and A.R. Bowman Dams, have been presented to
illustrate the variety of methods available. These sites were chosen to demonstrate the use of the
various techniques for characterization of the flood hazard. The A.R. Bowman example shows
how multiple studies were combined into a single-flood hazard curve for use in risk assessment.
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A FRAMEWORK FOR CHARACTERIZATION OF EXTREME
FLOODS FOR DAM SAFETY RISK ASSESSMENTS
Robert E. Swain5, David Bowles6, and Dean Ostenaa7
Abstract
Risk-based decisions require different types of information than standards-based
decisions. Traditional sources of information used for estimating probabilities of extreme
loods include gaged streamflo
f
precipitation records. Generally these data sources have records that are less tha
years in length. This framework for flood characterization for risk assessments us
length of the data record and other characteristics of the data to determine the credible
extrapolation limits used in the flood frequency analysis. Because risk assessments
equire estimation of floods with annual exceedance probabilities of
r
e
h
ood informatio
e probabilities
d
important attribute to convey into the risk assessment.
No single approach is capable of providing estimates of extreme floods over the
full range of annual exceedance probabilities required for risk assessment. Therefore
results from a number of approaches need to be combined to yield a composite flo
characterization; this means several methods and sources of data are needed. T
application of several independent methods applicable to the same range of annu
exceedance probabilities will increase the credibility and resulting confidence in
esults.
r
Introduction
The U.S. Bureau of Reclamation is now making extensive use of quantitative ri
assessment in support of dam safety decision making (Von Thun and Smart, 199
important input to Dam Safe
e
ro
s
li
s
fe
ecision Level Risk Assessment: At this level, more detailed evaluation of
d to provide decision makers with the information necessary to reac
safety deficiencies, selecting among risk reduc
effectively
ses, and consequence evaluations are developed for all significant issues. This typ
risk assessment focuses on reducing uncertainties in the risk estimates and evaluating
reduction actions.
Data Sources
The proposed framework for developing probabilistic extreme flood estimates for
sment uses the length of record and other characteristics of the data to determine
olation limits for flood frequency analysis. Traditional sources of information used for floo
d analyses include streamflow and precipitation records. Generally, these data sources h
ds that are less than 100 years in length, although in some cases these records can be exten
out 150 years using historical information. Regional
data sets from short periods of observation, and paleoflood data can extend record
s to periods of up to several thousand years.
mflow Data
Many different types of streamflow information are used in developing probabilistic extr
estimate
nd maintained by
vernment organizations. Streamflow records consist of data collected at establi
g stations and indirect measurements of streamflow at other sites. Streamflow data can inc
ates of peak discharge, as well as average or mean discharge for various time periods. M
flow measurements on U.S. streams began after 1900 with only a few records dating back
Most often, streamflow records at a single site range in length from about 20 to 60 ye
pleteness of the data set may vary from station to station.
ns, as well as remote sensing information and radar information for broader region
available from various source
. Some of these types of data (i.e., snowfall, snow water equivalent, solar radiatio
127 Paper 18 Swain, Bowles, O
ited to record lengths of less than about 30 years; basic rainfall and temperature data are
available for some stations for up to 150 years, but in most cases are limited to less than 100 years.
Historical Data
Historical data can provide a means for extending the length of record for many types of
data, in particular for observations of the most extreme events. These data are most commonly used
to extend streamflow records of peak discharge prior to organized stream gaging. Historical
observations can provide information for other types of data such as weather patterns and the
frequency of extreme storm events, or changes in land use or vegetation that may be significant to
runoff mod
bservations must be carefully assessed and compared to the other types of data used in the
analysis.
Paleoflood Data
Paleoflood hydrology is the study of past or ancient flood events which occurred prior to the
time of human observation or direct measurement by modern hydrological procedures (Baker, 1987).
Unlike h
I
of past floods, as well
a
often possible to develop records that are 10 to 100 times longer than conventional or historical
records from other data sources in the western United States. In addition, the paleoflood record is a
long-term measure of the tendency of a river to produce large floods. In many cases, paleoflood
studies can provide a long-term perspective, whic
e
Paleoflood data generally include records of the largest floods, or commonly the limits on the
of the largest floods over long time periods. This information can be converted to peak
ges using a hydraulic flow model. Generally, paleoflood data consist of two independent
ents. One component is a peak discharge estimate; the second is a time period or age over
the peak discharge estimate applies. Paleoflood studies can provide estimates of peak
ge for specific floods in the past, or they can provide exceedance and non-exceedance bounds
ended time periods. Each of these differing types of paleoflood data must be appropriately
in flood frequency analyses.
The primary basis for a limit on credible extrapolation of extreme flood estimates derives
e characteristics of the data and the record length used in the analysis. The data used in the
s provide the only basis for verification of the analysis or modeling results, and as such,
ons beyond the data cannot be verified. Different risk assessments require flood estimates for
nt ranges of annual exceedance probability (AEP), and therefore analysis procedures and
s
cred e estimates of extreme floods can be achieved by combining regional data from multiple
. Thus, analysis approaches that pool data and information from regional precipitation,
l streamflow, and regional paleoflood sources should provide the highest assurance of
e characterization of low AEP floods.
For many Reclamation dam safety risk assessments, flood estimates are needed for AEPs of
,000 and ranging down to 1 in 100,000, or even lower. Developing credible estimates at these
Ps generally require combining data from multiple sources and a regional approach. Table 1
different types of data which can be used as a basis for flood frequency estimates, and the
and optimal limits of credible extrapolation for AEP, based on workshop discussions or
ent communications. The limits presented in the table represent a general group consensus;
o
data which would
m
Many factors can affect the equivalent independent record length for the optimal case. For
example, gaged streamflow records in the western United States only rarely exceed 100 years in
length, and extrapolation beyond twice the length of record, or to about 1 in 200 AEP, is generally
not recommended (IACWD, 1982). Likewise, for regional streamflow data the optimal limit of
credible extrapolation is established at 1 in 1,000 AEP by considering the number of stations in the
region, lengths of record, and degree of independence of these data (Hosking and Wallis, 1997). For
paleoflood data, only in the Holocene epoch, or the past 10,000 years, is climate judged to be
sufficiently like that of the present climate, for the
e
limit for extrapolat
s
e of the difficulty in collecting sufficient station-years of clearly independent precipitation
records in the orographically complex regions of the western United States. Combined data sets of
regional gaged and regional paleoflood data can be extended to smaller AEPs, perhaps to about 1 in
40,000, in regions with abundant paleoflood data. Analysis approaches that combine all types of
data are judged to be capable of providing credible estimates to an AEP limit of about 1 in 100,000
under optimal conditions.
In many situations, credible extrapolation limits may be less than optimal. Typical limits
would need to reflect the practical constraints on the equivalent independent record length that apply
for a particular location. For example, many at-site streamflow record lengths are shorter than 100
years. If in a typical situation the record length is only 50 years, then the limit of credible
extrapolation might be an AEP of about 1 in 100. Similarly, m
to
length of abou
b
The information presented in Table 1 is intended as a guide; each situation is different and
should be assessed individually. The limits of extrapolation should be determined by evaluating the
length of record, number of stations in a hydrologically homogeneous region, degree of correlation
between stations, and other data characteristics which may affect the accuracy of the data.
Ideally, one would like to construct the flood frequency distribution for all floods that could
conceivably occur. However, the limits of data and flood experience for any site or region place
p
be sufficient data
li
eristics of the data and the record length, will fall short of the probable maximum flood
(PMF) for a site. PMF estimates provide a useful reference to past practice and can be compared
with extreme floods characterized for risk assessment. However, the workshop participants
concluded that there is limited scientific basis for assigning an AEP to the PMF. For precipitation
data, similar limitations apply to extrapolations that approach values described by probable
maximum precipitation.
Table 1.
Limit of Credible Extrapolation
for Annual Exceedance
Probability
Type of Data Used for Flood Frequency Analysis
Typical
Optimal
At-site streamflow data
1 in 100
1 in 200
Regional streamflow data
1 in 750
1 in 1,000
At-site streamflow and at-site paleoflood data
1 in 4,000
1 in 10,000
Regional precipitation data
1 in 2,000
Regional streamflow and regional paleoflood data
1 in 15,000
1 in 40,000
Combinations of regional data sets and extrapolation
1 in 40,000
1 in 100,000
Methods of Analysis
At Site Flood Frequency Analysis
alysis is an information problem: if one had a sufficiently
f
od precision, so long as change over time due to anthropogenic or natural processes did not
alter the distribution of floods. In most situations available data are insufficient to precisely define
the annual exceedance probability of large floods. This forces hydrologists to use practical
knowledge of the physical processes involved, and efficient and robust statistical techniques, to
develop their estimates (Stedinger et al., 1993).
Fitting a distribution to data sets allows both a compact and smoothed representation of the
frequency distribution revealed by the available data, and a systematic procedure for extrapolation to
frequencies beyond the range of the data set. Given a family of distributions, one can estimate the
parameters of that distribution so that require
model. Appropriate choices for distribution functions can be based upon examination of the
data using probability plots, the physical origins of the data, previous experience, or prescriptive
guidelines.
Several general approaches are available for estimating the parameters of a distribution. A
simple approach is the method of moments, which uses the available sample to compute estimators of
the distributions parameters. The Federal guidelines published in Bulletin 17B (IACWD, 1982)
recommend fitting a Pearson type 3 distribution to the common base 10 logarithms of the peak
discharges. It uses at-site data to estimate the sample mean and variance of the logarithms of the
flood flows, and a combination of at-site and regional information to estimate skewness.
Ano
cy analysis is the Expected Moments Algorithm (EMA). EMA (Cohn et al., 1997) is a
moments-based estimation procedure and is identical to the existing Bulletin 17B (IAWCD, 1982)
approach when no high or low outliers are present. The EMA method was developed to utilize
historical and paleoflood information in a censored data framework. This approach explicitly
acknowledges the number of known and unknown values above and below a threshold, similar to a
maximum-likelihood approach. Three types of at-site flood information are used: systematic stream
gage records; information about the magnitudes of historical floods; and knowledge of the number of
years in the historical period when no large flood occurred.
Still another method, which has strong statistical motivation, is the method of maximum
likelihood. Maximum likelihood estimators (MLEs) have very good statistical properties in large
samples, and experience has shown that they generally do well with records available in hydrology.
In many cases MLEs cannot be reduced to simple formulas, so estimates must be calculated using
numerical methods (Stedinger et al., 1988; OConnell, 1997).
L-moments are another way to summarize the statistical properties of hydrologic data.
Sample estimators of L-moments are linear combinations (and hence the name L-moments) of the
ranked observations, and thus do not involve squaring or cubing the observed values as do the
product-moment estimator
n and skewness are almost unbiased and have very nearly a normal distribution (Hosking and
Wallis, 1997).
Regional Flood Frequency Analysis
In hydrology, sufficient information is seldom available at a site to adequately determine the
frequency of rare events using frequency analysis. This is certainly the case for the extremely rare
events which are of interest in dam safety risk assessment.
posed several general strategies, including substituting space for time for estimating extreme
floods. One substitutes space for time by using hydrologic information at different locations in a
region to compensate for short records at a single site.
Three approaches (Cudworth, 1989) have been considered for regional flood
h. With the average parameter approach, some parameters are assigned average values
based upon regional analyses, such as the log-space skew or standard deviation. Other parameters
are estimated using at-site data, or regression on physiographic basin characteristics, perhaps the real
or log-space mean. The index flood method is a special case of the average parameter approach.
The specific frequency approach employs regression relationships between drainage basin
characteristics and particular quantiles of a flood frequency distribution.
Index Flood Method. The index flood procedure is a simple regionalization technique with
a long history in hydrology and flood frequency analysis (Dalrymple, 1960). It uses data sets from
several sites in an effort to construct more reliable flood-quantile estimators. A similar
regionalization approach in precipitation frequency analysis is the station-year method, which
combines precipitation da
to
distributions of floods at different sites in a "region" are the same except for a scale or index-flood
th
rm better that index flood methods in many cases (St
en 100 years, 2-parameter estimators with a good
se
in length, procedures that estimat
ape parameter, have been shown t
d Lu, 1995). For record le
a
ractive.
tt
Regional Regression. Regional analy
lues of various hydrologic statistics (inclu
d
o derive eq
ndard devi
on
to predict
quantiles, a
a
ormalized regional flood q
graphic cha
s
stics and ot
quares (GLS) regression methodology to addres
alization of
logic statisti
dvantages of the GLS procedure include more efficie
hort records, an unbiased model-error estimator, and a
m
ter estimates
cription of th
en
some sites ha
ionship betwe
h
D
e floods. A single set of hydrometeorological parameters and watershed characteristics are
used to simulate a design flood event. The major inputs to a design event-based precipitation-runoff
model are: (1) climate data (rainfall, snowfall, and other variables needed to predict snowmelt); (2)
losses (infiltration/interception); (3) physical watershed characteristics for runoff and routing
simulations (drainage areas, watershed and channel slopes, lag times, antecedent moisture, etc.); (4)
precipitation-runoff transformation function; and (5) runoff conveyance/routing mechanisms. Model
output includes runoff hydrographs at user-spec
volumes. Examples of this type of model include HEC-1 (USACE, 1990) and RORB
(Laurenson and Mein, 1995).
Stochastic Event-Based Precipitation-Runoff Modeling
In the stochastic approach, hydrologic model inputs are treated as random variables. Monte
Carlo sampling procedu
d distributions, including the observed dependencies among some climatic and hydrologic
parameters. The use of the stochastic approach with regional precipitation information allows the
estimation of flood magnitude-frequency curves for flood peak discharge, flood runoff volume, and
reservoir level. An example of this type of model is discussed by Barker et al. (1997).
Atmospheric Storm Modeling and Continuous Precipitation-Runoff Modeling
This method combines the work of atmospheric modelers and regional precipitation analysis
to derive a precipitation magnitude-frequency curve (Chin et al., 1997). The atmospheric model is
used to generate storms over the watershed, and the findings from the regional analysis are used to
estimate the annual exceedance probability of point and areal precipitation generated by the model.
Using distributed precipitation-runoff modeling, snowpack and other antecedent conditions can be
combined to estimate a simulated flood frequency curve using a Monte Carlo approach.
Data Generation and Continuous Simulation Modeling
The data generation and continuous simulation modeling approach is based on Monte Carlo
generation of long and detailed sequences of hydrometeorological variables, including precipitation,
air temperature, and wind speed and direction. In order to represent spatial differences across the
watershed adequately, it is necessary to generate hydromete
rently. Hydrological models of watershed behavior and hydraulic models of confluences,
wave effects and reservoir outlets are used to simulate the reservoir water level continuously. An
estimated magnitude-frequency relationship of maximum reservoir stages is input to the risk
assessment (Calver and Lamb, 1996).
No single approach is capable
o
lar, characterization of floods with AEPs less than 1 in 10,000 can be expected to require that
results from a number of approaches, based on multiple data sources, need to be combined to yield a
composite flood frequency description. The application of several independent methods and types of
data applicable to the same range of annual exceedance probabilities will increase the credibility and
resulting confidence in the results.
Table 2 lists various methodologies that were co
dam safety risk assessment. A flood frequency analysis must be combined with each of
these methodologies to assign annual exceedance probabilities to the floods.
The framework developed for Reclamation does not propose a specific methodology for
rigorously combining information from these differing data sources and methodologies in an overall
statistical framework. In some cases the information may be combined statistically, and in other
cases one set of results may be used as a bound on the frequency distribution obtained by analysis of
other data. Clearly, this process will require a measure of judgement. Regardless of the approach
taken for combining results, it should incorporate sound physical an
ing or combining results.
All floods characterized for the risk assessment process should display the uncertainties
resulting from the analysis. As the risk assessment moves from the screening and scoping levels to
the decision level, uncertainty should be reduced and better quantified so that appropriate
information is included in the dam safety decision-making process.
Table 2. Applicability of Hydrologic Methods of Analysis to Various Risk Assessment
Levels
Risk Assessment Level
Method of Analysis
Screening
Scoping
Decision
Flood frequency analysis
Yes
Yes
Yes
Design event-based precipitation-runoff modeling
No
Yes
Yes
Stochastic event-based precipitation-runoff modeling
No
Yes
Yes
Distributed s
Atmospheric modeling and distributed precipitation-runoff modeling
No
No
Yes
Evaluation of Uncertainty
Uncertainty can be evaluated by applying Monte Carlo analysis to the overall risk assessment
calculations. For example, consider the estimation of threat to life consequences and probability of
failure associated with an existing dam and various risk reduction alternativ
w
system response estimates, population at risk, warning
it
e the threat to life and probability of failure. The expected annual life loss and the annual
exceedance probability of failure, which are both used as Reclamation Public Protection Guidelines
(USBR, 1997b), could be computed for each iteration. By generating many replicates, one obtains
samples that describe the possible values of these risk measures (performance metrics).
Averaging over the replicates provides expected values of the quantities reflecting both the
modeled probability distributions of the phenomena (risk assessment inputs) that are considered to
be random variables, and the uncertainty in the parameters describing those distributions. The
sample standard deviations describe the variability of the performance metrics. Replicates can be
used to estimate frequency distributions which can be used for describing and evaluating the
decision implications of uncer
Calibration to Flood Frequ
The ability of a flood event model to reproduce historic events certainly gives some
confidence to the validity of subsequent estimates. However, even in a well gaged watershed the
annual exceedance probabilities of the calibration floods are likely to range between 1 in 5 to 1 in
20, and only occasionally up to 1 in 100. While it would be expected that floods of these
magnitudes will activate some floodplain storage, the non-linear nature of drainage basin flood
response is such that the routing characteristics of larger events may be considera
T
basin, caution is needed when using the calibrated model to estimate floo
m
Calibration to flood frequency quantiles using design rainfall inputs can provide important
information on flood response characteristics for extreme design events (Nathan and Bowles, 1997;
Nathan, 1992). With this approach, design rainfall information is prepared for a specified AEP, and
then used with a given set of model parameters and input assumptions to derive a design hydrograph.
The peak (or volume) of the design hydrograph can then be compared to the corresponding quantile
obtained from a combined at-site/regional flood frequency analysis. The model input
w
selected flood quantile. Model calibration should be un
c
For risk-based studies based on a design storm concept, it is necessary to adopt an AEPneutral
approach, where the objective is to derive a flood with an AEP equivalent to its concomitant
precipitation (Nathan and Bowles, 1997). The factors that influence the transfer between
precipitation and runoff can be characterized by probability distributions, and ideally the design
hydrograph should be determined by considering the joint probabilities of all the input factors.
Monte-Carlo methods are ideally suited to the AEP-neutral objective, as they accommodate the
observed variability of the inputs while still preserving the interdependencies between parameters.
Simpler approaches may be appropria
c
opriate to adopt a single representative (mean
d
representative value for the major inputs will introduce bias into the transformation.
Accordingly, for more important inputs it is necessary to adopt a joint probability approach. The
nature of the method can be tailored to suit the relative importance of the parameter concerned.
Conclusions
A framework has been deve
risk assessment. By incorporating regional information on precipitation, floods, and
paleofloods with good at-site records, it is possible to provide scientifically credible flood estimates
to annual exceedance probabilities as low as 1 in 100,000, although higher A
ases. In general, the scientific limit to which the flood frequency relationship can be
extended based upon available data will fall short of the PMF for a site. PMF estimates provide a
useful reference to past practice and can be compared with floods characterized for risk assessment;
however, there is limited scientific basis for assigning an annual exceedance probability to the PMF.
No single approach is capable of providing the needed characterization of extreme floods
over the full range of AEPs required for risk assessment. Therefore, the results from several
methods and sources of data s
tion of several independent methods applicable to the same range of AEPs will increase the
credibility and resulting confidence of the results.
Uncertainties associated with descriptions of flood flow exceedance probabilities are likely to
be substantial and an important attribute for the characterizati
c
different m itudes and a description of the uncertainty in such results. Such uncertainties need to
am safety risk asse
m the U.S., Canada, Australia and
e w
res
mew
hauhan, John England, David Goldman,
ense
an Levish, Jim Mumfo
o
Thom
h
Baker, V.R., 1987. Paleoflood hydrology and extraordinary flood events: Journal of Hydrology, v. 96, p. 79-99.
Barker, B., M.G. Schaefer, J. Mumford, and R. Swain, 1997. A Monte Carlo Approach to Determine the Variability of
PMF Estimates, Final Report on Bumping Lake Dam for the USBR Dam Safety Office, 30 pp.
Calver, A. and R. Lamb, 1996. Flood frequency estimation using continuous rainfall-runoff modeling, Phys. Chem.
Earth, 20, 5/6, p. 479-483.
Chin, W.Q., G.M. Salmon, and W. Luo, 1997. Distributed Physically-Based Precipitation-Runoff Models for Continuous
Simulation of Daily Runoff in the Columbia River Basin, British Columbia, presented at the Canadian
Electricity Association Electricity 97 Conference and Exposition, April 23, 1997, Vancouver B.C.
Cudworth, A.G., Jr., 1989. Flood Hydrology Manual, A Water Resources Technical Publication, US Department of the
Interior, Bureau of Reclamation, US Government Printing Office, Denver, CO, 243 pp.
Cohn, T.
A., W.L. Lane, and W.G. Baier, 1997. An algorithm for computing moments-based flood quantile estimates
when historical flood information is available, Water Resour. Res., 33(9) , p. 2089-96.
Dalrymple, T., 1960. Flood frequency analysis, U.S. Geological Survey, Water Supply Paper 1543-A.
Fill, H., and J. Stedinger, 1997. Using regional regression within index flood procedures and an empirical Bayesian
estimator, submitted to J. of Hydrology, April, 1997.
Hosking, J.R.M., and J.R. Wallis, 1997. Regional Frequency Analysis: An Approach Based on L-moments, Cambridge
Univ. Press, 224 pp.
ouse, P.K., and P.A. Pearthree, 1995. A geomorphic and hydrologic evalua
H
eek, Arizona, Water Resources Research, v. 31, no. 12, p. 3059
ittee on Water Data, 1982. Guidelines for Determining Flood Fl
Virginia.
Laurenson, E.M. and R.G. Mein, 1995. RORB: Hydrograph Synthesis by Runoff Routing: in Singh, V.P. (ed.) Computer
Models of Watershed Hydrology, Water Resources Publications, Highlands Ranch, CO, p. 151-164.
Lu, L., and J.R. Stedinger, 1992. Variance of 2- and 3-parameter GEV/PWM quantile estimators: formulas, confidence
intervals and a comparison, Jour. of Hydrol., 138(½), p. 247-268.
Nathan, R.J., 1992. The derivation of design temporal patterns for use with generalized estimates of probable maximum
precipitation, Civil Engineering Transactions, I.E. Aust., CE34(2), p. 139-150.
Nathan R.J. and D.S. Bowles, 1997. A probability-neutral approach to the estimation of design snowmelt floods,
Conference proceedings, 24th Hydrology and Water Resources Symposium, Auckland, New Zealand.
National Research Council, 1988. Estimating Probabilities of Extreme Floods, Methods and Recommended Research,
Report by the Committee on Techniques
Press, Washington D.C.
OConnell, D.R.H., 1997. FLFRQ3, Three-Parameter Maximum Likelihood Flood-Frequency Estimation with Optional
Probability Regions using Parameter Grid Integration: Users Guide (Beta Edition).
Pilgrim, D.H., and I. Cordery, 1993. "Flood Runoff", Chapter 9 in Maidment, D.R. (ed.) Handbook of Hydrology,
McGraw-Hill, New York, p. 9.1-9.42.
Stedinger, J.R., and G.D. Tasker, 1985. Regional hydrologic analysis, 1. Ordinary, weighted and generalized least
squares compared, Water Resour. Res., 21(9), p. 1421-32.
Stedinger, J.R., and G.D. Tasker, 1986a. Correction to 'Regional hydrologic analysis, 1. Ordinary, weighted and
generalized least squares compared,' Water Resour. Res., 22(5), p. 844.
Stedinger, J.R., and G.D. Tasker, 1986b. Regional hydrologic analysis, 2. Model error estimates, estimation of sigma,
and log-Pearson Type 3 distributions, Water Resour. Res., 22(10), p. 1
r, J.R., R. Surani, and R. Therivel, 1988. Max Users Guide: A Program for Flood Frequency Analysis using
Systematic-Record, Historical, Botanical, Physical Paleohydrologic and Regional Hydrologic Information
Using Maximum Likelihood Techniques, Department of Environmental Engineering, Cornell University.
Stedinger, J.R., R.M.Vogel, and E. Foufoula-Georgiou, 1993. Frequency Analysis of Extreme Events, Chapter 18,
Handbook of Hydrology, D.Maidment (ed.), McGraw-Hill, Inc., New York.
Stedinger, J.R. , and L. Lu, 1995. Appraisal of Regional and Index Flood Quantile Estimators, Stochastic Hydrology and
Hydraulics, 9(1), p. 49-75.
U.S. Army Corps of Engineers, 1990, HEC-1 Flood Hydrograph Package, Users Manual, Hydrologic Engineering
Center, Davis, CA, 283 pp.
U.S. Bureau of Reclamation, 1997a. Risk Assessment Methods for Dam Safety Decision Making, Draft, U.S. Department
of Interior, Denver, CO.
U.S. Bureau of Reclamation, 1997b. Guidelines for Achieving Public Protection in Dam Safety Decision Making, U.S.
Department of Interior, Denver, CO, 19 pp.
Von Thun, J.L. and J.D. Smart, 1996. Risk assessments support dam safety decisions, USCOLD Newsletter, Issue No.
110, Nov 1996, U.S. Committee on Large Dams.
Bureau of Reclamation Hydrologic Research
ydrologic Research Needs for Dam
By
In
The U.S. Bureau of Reclamation is now making extensive use of quantitative ris
assessment in support of dam safety decision-making (Von Thun and Smart, 1996). An
important input to Dam Safety Risk Assessment is the development of probabilistic
extreme flood estimates. The focus has shifted from routing a single maximum even
(i.e. the probable maximum flood, PMF) to consideration of the entire range of plausible
inflow flood
re
Reclam
d
in safety risk assessment. Where practical, Reclamation would like to develop
improved procedures. The following sections of this
re
Flood Hydrology Database
A variety of hydrologic data are used as in
hydrographs, stochastic rainfall-runoff mo
ma ing flood hazard probability statements for use in risk a
understanding and modeling of extreme f
v
, precipitation (rainfall and snowfall) and temperature data, soil data, paleoflood
information, ex
d
capability, and link
The purpose of this research is to continue development of a hydrology database that will
include a variety of hydrology data such as peak discharge estimates, paleoflood dat
precipitation and temperature data, as well as potential sources of infiltration
characteristics and other geologic properties of drainage basins. These data would be
used as input into flood frequency analyses, probabilistic hydrograph development, and
prediction of basin response in stochastic modeling of extreme flooding. This project
focuses on the development of a flood hydrology database that identifies, summarizes
and links hydrologic data that is needed for developing flood frequency analyses and
probabilistic hydrographs, as input for stochastic rainfall-runoff models, and other
h
A
for the Sierra Nevada region of northern California. Paleoflood data have been g
throughout the western U.S., as well as in a database at the University of Arizona,
tree.ltrr.arizona.edu/~katie/paleofld.html. Currently, Reclamation has a paleoflood
database in Microsoft Access and hydrology database in Arcview exist as separate
databases. These databases need to be integrated into one database in order to efficiently
store and access information for flood-related studies. In addition, computer code and
user interface have been developed for the hydrology database
a
friendly database is scheduled for completion. This data information system will require
updating and continual maintenance.
Since the mid 90's, meteorologists in both Reclamations Flood Hydrology Group and
River Systems & Meteorology Group have been addressing the need to revise and up
precipitation-frequency estimates for the United States. The demand for this work is
obvious in that precipitation-frequency atlases presently used by Reclamation are
woefully outdated, with the far majority of the previous studies dating back 30 to 40
years ago, and lack extensions to important meteorological parameters (duration, area
return period, etc.). This information is used in establishing hydrologic design criteria f
the safety evaluation of water control structures (dams, canals, levees, culverts, et
design of other types of construction (roads, bridges, flood warning systems, etc.), and
establishing project operational criteria. Results of this work will provide consisten
p
used in current/future flood hydrology studies.
The project is a cooperative effort among several federal, state, and local agenc
involved in water resource management. The National Weather Service (NW
Hydrometeorological Design Studies Center (HDSC) is the lead agency for
accomplishing the work with participation from other agencies (financial,
in
particular region under investigation. Because of the large amounts of data to
process and the need to test new meteorological and statistical analysis techniques,
the United States and its Possessions were broken into nine separate zones.
Presently, four of these zones are under development in varying degrees. These
zones include: Semiarid Southwest, the Ohio River Basin and Surrounding S
Hawaii, and Puerto Rico and the Virgin Islands. Work on a fifth study reg
Upper Midwest, has been started by Reclamation to assemble maximum daily
precipitation (prior to 1949) data. For the
Virgin Islands zones are scheduled for completion in 2002. Hawaii is scheduled for
ess reports concerning all work underway is
p://www.nws.noaa.gov/oh/hdsc. The precipitation-frequenc
c
e
Flood runoff hydrographs integrate the drainage basin and channel response to
precipitation and snowmelt, given some initial, variable state of moisture throughout
watershed. Probabilistic flood hydrographs are developed to assess the adequacy of the
spillway and reservoir flood/surcharge space to temporarily store a portion of the flood
volume, and to attenuate or pass the hydrograph peak without overtopping the dam.
Flood hydrograph
greater than the maximum spillway capacity; the reservoir has a large, carry-over storage;
and/or the reservoir has dedicated flood control space. The focus of this research is to
develop a simplified approach for estimating probabilistic hydrographs that can be us
for appraisal or feasibility level studies, and to develop a simplified method of
extrapolating flood frequency curves.
estimate properties for proba
d
identification and separation, and direct runoff volume estimation. Peak discharge and
mean-daily streamflow records are used because this source is the best information on
flood magnitudes that are likely to occur in the future, based on what occurred in th
(Pilgrim and Cordery, 1993).
The key idea is calibration or scaling of hydrographs to match a particular peak discharg
for a given probability. The approach relies completely upon the specification of a peak
flow frequency curve that describes the probabilities of interest. Peak discharge
estimates, n-day maximum mean flows, and observed hydrographs at the site of inte
a
peak and volume hydrographs are utilized as a basis to scale.
There are five major assumptions for developing the hydrographs: (1) the prob
peak discharge is sufficient to represent a probability of the composite hydrograph; (2)
unit hydrograph (e.g., linearity) assumptions apply to the basin; (3) direct runoff volume
can be estimated from daily flow hydrographs; (4) peak discharge - maximum mean nday
flow relationships can be extrapolated; and (5) the recorded streamflow observation
historical information, and paleoflood data provide an adequate sample to base
extrapolations to extreme floods.
The anticipated completion date for this project is early 2002.
Improved Flood Frequency Extrapolations and Runoff Modeling
The purpose of this research project is to develop improved methods to extrapolate
frequency curves and develop extreme flood hydrographs. The major approach to fl
frequency extrapolation will be based on a combination of rainfall extrapolation and
derivation from physically based runoff mechanisms. Rainfall-runoff models will be
used to derive the peak discharge frequency distribution from input basin characteristics
and precipitation, and be used as the basis for frequency curve extrapolation. The
CASC2D rainfall-runoff model will be evaluated and tested for application at
Reclamation sites, and compared with a stochastic event runoff model (SEFM) developed
by Dr. Melvin Schaefer for Reclamati
ra
ain precipitation and stochastic components used in SEFM will be added to CASC2D.
w
at Reclamation dams. Input rainfall will be derived from frequency analysis or from
stochastic storm generation. Flood frequency and hydrograph uncertainty bounds will be
approximated by simulation. Models will be compared on a large (>500 mi2) basin
where paleoflood data are available.
Progress has been made in developing hydrograph-scaling techniques for appraisal and
feasibility studies that require low effort and expense. These techniques have been
applied to several projects such as Pineview/Deer Creek, Red Willow, North Platte, an
Folsom Dams. Internal and external reviewers have pointed out several shortcomings of
that work including, assumptions of linear runoff and extrapolation, use of observed
hydrographs, failure to separate rainfall and snowmelt, and the challenges of using the
techniques at larger basins (greater than about 5
a
This research can be applied to Dam Safety projects where flood peaks and hydrograph
are needed with return periods that exceed 1,000 years. The extrapolation resear
be applied to sites where loss of life is large, as floods with return periods greate
10,000 years are sometimes needed. The research will be span three fiscal years an
conclude in 2004.
Rainfall-Runoff Modeling Using National Weather Service 1,000-year Retur
Period Precipitation Estimates at Causey Dam, Utah
Recently, the Flood Hydrology Group completed a study where the frequency estimates
were extrapolated to a return period of 200,000 years. The method used a two-point
extrapolation to 200,000 years using the mean of the gage data and the mean of the
paleoflood range. This was the first attempt to extrapolate frequency data beyond a
10,000-year return period and several assumptions were made that may not be accu
For example, the stream gage data in the Wasatch Range are domin
events, yet the distribution selected in
in
conclusions reached in the previous analysis.
This investigation will use the draft precipitation values developed by the National
Weather Service (NOAA Atlas 14, Vol 1, DRAFT) to produce a 1,000-year assumed
thunderstorm event at Causey Dam, Utah. These values will be input to a rainfall-run
model (HEC-1 or FHAR) to develop the
D
Causey Dam was selected as the te
e
(137 mi2), and it has a significant amount of streamflow and other comparative
developed. The estimated completion date would be June 2001.
Probabilistic Flood Hazard Workshop
The introduction of risk analysis for dam safety signaled a significant change in the way
the Dam Safety Office and the Technical Service Center conduct flood hazard
assessments. The purpose of this project is to compile, review, and evaluate current
state-of-the-knowledge on probabilistic techniques used in flood hazard assessm
External experts in various aspects of f
a
(1-2 hours). Members of the Flood Hydrology Group will subsequently meet with them
to discuss their research in detail and potential technology transfer to Reclamation.
About 12 experts participated in the workshop last year. These experts have helped the
Flood Hydrology Group map out future methods, improve current methods, and plan a
program for probabilistic flood hazard analysis to meet Dam Safety Office needs.
R
Bras, R.L. (1990) Hydrology, An Introduction to Hydrologic Science. Addison-
Wesley, Reading, MA, 643 p.
Chow, V.T., Maidment, D.R. and Mays, L.W. (1988) Applied Hydrology.
McGraw-Hill, New York, 572 p.
Pilgrim, D.H. and Cordery, I. (1993) Flood Runoff. In
Von Thun, J.L. and J.D. Smart (1996) Risk assessments support dam safety
decisions, USCOLD Newsletter, Issue No. 110, Nov 1996, U.S. Committee on
Large Dams.
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GUIDELINES FOR ACHIEVING PUBLIC PROTECTION
IN
DAM SAFETY DECISIONMAKING
UNITED STATES DEPARTMENT OF THE INTERIOR
Bureau of Reclamation
Denver, Colorado
June 15, 2003
(Replaces Interim Guidelines dated April 4, 1997)
TABLE OF CONTENTS
I. Introduction
.
.1
II. Risk Assessment Framework for Dam Safety Decisionmaking
.
...
. 3
A. Background
.3
B. Terminology
4
C. Risk Framework
..5
D. Decisionmaking
...6
III. Public Protection (Risk Evaluation) Guidelines
.8
A. Evidence of a Developing Failure Mode
8
B. Annual Probability of Failure
.8
C. Estimated Risk
9
IV. Determining Appropriate Actions
..
.
..12
A. Development and Presentation of Risk Estimates
..12
B. Assessment of Risk Results
....14
C. Large Downstream Populations
......16
D. Examples of Alternative Actions
...
.16
E. Formulation of Appropriate Risk Reduction Alternatives
..
18
F. Unrecognized Risks
...
..18
1
I. Introduction
Purpose of Guidelines - The Bureau of Reclamation (Reclamation) is responsible for about 370
storage dams and dikes that form a significant part of the water resources infrastructure for the
western United States. As the owner of these facilities, Reclamation is committed to providing
the public and the environment with adequate protection from the risks which are inherent to
collecting and storing large volumes of water for later distribution and/or release. This document
presents:
· The basis and guidance for a risk-based approach to decisionmaking
· Guidelines for evaluating risks at Reclamation dams
· Guidelines for developing and presenting the risk estimates
· Guidelines for interpreting/assessing the risk results
· Example actions that can be taken to address risk at dams
· Guidelines for maintaining a focus on risk reduction when implementing agency
actions
The guidelines are intended to ensure adequate and consistent levels of public protection when
evaluating and modifying existing dams and appurtenant structures and when designing new
dams and/or structures.
Considering a Full Range of Loading Conditions - Historical design and analysis methods
have focused on selecting a level of protection based on loadings from extreme events and
conditions. These extreme events comprise the upper bound of loadings considered to be
reasonably probable. The civil engineering profession generally agrees that dams and dikes
designed to withstand extreme loadings meet an acceptable standard of public safety. In addition
to ensuring public safety for extreme events, Reclamation also is committed to providing public
safety for smaller events and loading conditions, which occur more frequently. For example, an
enlarged spillway designed for a probable maximum flood loading condition may increase the
risks to the public for lesser events. Risk assessment provides a framework for addressing the
most effective way to provide public protection over the full range of loading conditions.
Need for Probabilistic Methods - As a water resources management agency, Reclamation
strives to provide decisionmakers with pertinent information that is founded upon current or
emerging water resources management and public safety practices. Over the past decade, there
has been an inc reasing trend in water resources analysis toward using probabilistic design
methods to evaluate the effectiveness of expending funds for enhancing public safety. There has
also been greater recognition that even the most restrictive design standards result in some
likelihood of failure even though the likelihood may be very small.
Application - This document addresses the incorporation of risk-based evaluations into
Reclamations dam safety decisionmaking process to help assess public risks and allocate
resources. While there are many issues that may be evaluated in a risk context, this document
focuses on the life loss and the public trust components of decisionmaking. Similar applications
of risk-based analysis techniques may be used to address econo mic consequences within the
2
framework of the Principles and Guidelines for water resources planning. 1 Risk-based analysis
may also be used to evaluate environmental and social issues in accordance with the National
Environmental Policy Act (NEPA) by addressing the likelihood of the possible outcomes that
may result from the various loads that a dam experiences. The implementation of risk-based
analysis should consider both usefulness and cost effectiveness in its use.
1Economic and Environmental Principles and Guidelines for Water and Related Land Resources Implementation
Studies from the Water Resources Council, March 10, 1983.
3
II. Risk Assessment Framework for Dam Safety Decisionmaking
A. Background
The mission of the Reclamation Dam Safety Program is:
"To ensure that Reclamation facilities do not present unreasonable risks to the
public, public safety, property, and/or the environment."
The Dam Safety Program is authorized under the Reclamation Safety of Dams Act of
1978.2 This Act was passed in response to several dam failures in the 1960s and 1970s,
including the failure of Teton Dam, a large Reclamation storage dam. The Act provides
for action to be taken when it is determined that a structure presents an unacceptable risk:
In order to preserve the structural safety of Bureau of Reclamation dams and
related facilities, the Secretary of the Interior is authorized to perform such
modifications as he determines to be reasonably required.
To determine the risks associated with its structures, Reclamation has established
procedures to analyze data and assess the condition of its structures. Prior to the failure
of Teton Dam, consideration of dam safety issues was addressed though periodic
examinations and project specific requests for Congressional funding to make necessary
modifications to dams. The failure of Teton Dam demonstrated a need for a more
comprehensive approach to evaluating and addressing dam safety issues.
In 1979, a committee of Federal agency representatives commissioned by the President
developed the Federal Guidelines for Dam Safety to promote prudent and reasonable dam
safety practices among Federal agencies. While the Federal Guidelines recognized that
risk-based analysis was a recent addition to the tools available for assessing dam safety,
they encouraged Agencies to conduct research to refine and improve the techniques
necessary to apply risk-based analysis to dam safety issues:
The agencies should individually and cooperatively support research and
development of risk-based analysis and methodologies as related to the safety of
dams. This research should be directed especially to the fields of hydrology,
earthquake hazard, and potential for dam failure. Existing agency work in these
fields should be continued and expanded more specifically into developing risk
concepts useful in evaluating safety issues.3
Reclamation has established a risk-based framework to meet the objectives of its
program, the Dam Safety Act, and the Federal Guidelines. Risk-based procedures are
used to assess the safety of Reclamation structures, to aid in making decisions to protect
2 The Reclamation Safety of Dams Act of 1978, Public Law 95-578.
3 Federal Guidelines for Dam Safety, Ad Hoc Interagency on Dam Safety, Federal Coordinating
Council for Science Engineering and Technology, Washington, D.C., June 25, 1979.
4
the public from the consequences of dam failure, to assist in prioritizing the allocation of
resources, and to support justification for risk reduction actions where needed. Risk
assessment for dam safety decisionmaking integrates the analytical methods of risk-based
analysis along with the sound professional judgment of engineers, contractors and review
boards in determining reasonable actions to minimize risk at Reclamation facilities.
B. Terminology
The following terminology is provided for terms that are used throughout these
guidelines for defining the risk-based framework for dam safety decisionmaking:
Risk The product of the likelihood of an adverse event and the consequences of
that event
Failure Mode - A potential failure mode is a physically plausible process for dam
failure resulting from an existing inadequacy or defect related to a natural
foundation condition, the dam or appurtenant structures design, the construction,
the materials incorporated, the operations and maintenance, or aging process,
which can lead to an uncontrolled release of the reservo ir.
Risk Analysis A procedure to identify and quantify risks by establishing
potential failure modes, providing numerical estimates of the likelihood of an
event in a specified time period, and estimating the magnitude of the
consequences. The risk analysis should include all potential events that would
cause unintentional release of stored water from the reservoir.
Risk Evaluation The establishment of Reclamation guidelines for agency
response to estimated risks.
Risk Assessment The use of risk estimation for a given dam in the
decisionmaking that leads to agency response according to risk evaluation
guidelines.
Consequences Estimated losses that result from an adverse event leading to a
dam failure scenario.
Failure Probability, Consequences, and Risk Estimates The mean values
calculated from Monte Carlo or similar analyses that include explicit treatment of
input uncertainty. Also, the calculated numerical values when single point
estimates are used in the calculations and the point values are considered
reasonable and plausible estimates of the mean rather than extreme values in a
range. These estimated mean values are also called the expected values. (Note:
This definition must be applied in order to achieve effective and consistent
application of these guidelines.)
5
C. Risk Framework
Risk analysis is a tool that enables technical specialists and decisionmakers to better
understand possible failure mechanisms and the elements of risk involved in the various
issues related to dam safety. It provides an overall picture of risks, the potential impacts
of proposed actions, and the resulting costs (economic, social and other). The results of
risk analyses can contribute to efficient accomplishment of the dam safety program by
quantifying engineering judgments that allow for the evaluation of:
· Factors contributing the greatest risk at a given site,
· The facilities with the greatest risk,
· Identification of additional analyses and/or data collection that are needed to
better understand critical uncertainties,
· Anticipated risk reduction effectiveness of alternative courses of action,
· Allocations of dam safety program funds that will contribute the greatest
overall risk reductions.
The risk framework consists of several steps leading to agency decisions regarding
appropriate actions to be taken to address dam safety risks at Reclamations high- and
significant-hazard dams. These steps are summarized as follows:
Risk Identification As part of the ongoing dam safety evaluations for each highand
significant-hazard dam, Reclamation identifies the conceivable modes of dam
failure. These failure modes are then monitored (through performance monitoring
and examinations) for any indication of changes in performance that would be
indicative of a dam progressing toward a failure condition or toward a significant
risk to the public. If such indications are found, the issue is referred for further
evaluation of the estimated risk. If failure modes are deemed likely, action to
reduce risk may be taken.
Risk Estimation Once a dam safety issue has been identified, it is necessary to
assess and quantify the risk to the public as information to be used by the
decisionmakers. The quantification of risk involves the estimation of the
likelihood (probability) of an unintentional release of stored water and an
estimation of the consequences resulting from the unintentional release. To
facilitate developing the risk estimates, it is frequently convenient to break the
estimating process down into three components including: estimating the
likelihood of an initiating condition existing or an event occurring, estimating the
likelihood of an unintentional release of the reservoir given the event or initiating
condition, and estimating the consequences (life loss) given the unintentional
release of the reservoir.
Risk Evaluation Once risks have been estimated for a dam, decisionmakers
need a framework for evaluating the risks to determine if action is required to
reduce risks. There is currently no commonly accepted industry standard for
determining what risks are considered acceptable.
6
The guidelines portion of this document provides for evaluation of risk by two
measures. The first measure, the annual probability of failure, addresses the
publics expectation that Reclamation dams should not fail by evaluating the
probability of an unintended release of the reservoir. It also addresses the
expectation that risk to the most exposed individual will be managed. The second
measure addresses the expected value of life loss expressed on an annual basis
which combines the annual failure probability estimates with estimates of the
expected life loss consequences given a dam failure. The first measure addresses
agency and individual risk, while the second measure addresses the life loss
component of societal risk.
Risk Reduction Actions When decisionmakers have determined that a risk
reduction action is required, there are usually a number of prudent alternative
actions that can be taken. Dam safety decisionmaking involves the selection of an
appropriate course of action for a given issue based on the magnitude of the risk,
the degree of confidence in (or uncertainties associated with) the estimated risk,
and the likelihood of additional information providing a significantly enhanced
understanding of the risks associated with the identified issues.
Roles of analysis approaches - Although risk-based and standards-based (design
standards, codes or criteria) approaches are often considered to be competing approaches,
each have a role in Reclamations decisionmaking process. Risk assessment is a
diagnostic tool used throughout the evaluation, design, and construction process that
helps decisionmakers formalize and document dam safety decisions. Standards are used
to ensure that the selected corrective actions are well designed and implemented. In other
words, risk-based approaches help decision makers choose the appropriate courses of
action while standards-based approaches assure sound implementation of those actions.
D. Decisionmaking
Policy - Reclamation policy for dam safety decisionmaking delegates decisionmaking
responsibility to the Regional Directors in collaboration with the Chief, Dam Safety
Office and the appropriate Area Manager.4 The Technical Service Center (TSC) staff
provides significant technical advice that is critical to decisionmaking. The risk
framework serves as a tool for aiding decisionmakers in the determination of needs for
risk reduction actions as well as the evaluation of different risk reduction actions that
could be taken to address the identified issues.
Public Trust Responsibility - Decisionmaking to accomplish the Dam Safety Program is
complex and must consider risk to the public as well as economic, environmental, and
cultural impacts. Thus, it is difficult to be prescriptive when developing guidance for
making decisions. While the technical analysis of risks associated with a dam can not
become the sole decisionmaking factor, it must be recognized that addressing these risks
in a technically consistent and timely fashion is an important part of sustaining the
publics trust in Reclamation to manage these facilities in the best interest of the nation.
4 Decisions Related to Dam Safety Issues, Reclamation Manual / Policy FAC P02, Bureau of Reclamation,
Denver, Colorado, June 23, 1998.
7
This public trust responsibility includes operating Reclamation facilities with reasonable
assurance of the safety of persons in the vicinity of and downstream of the dams.
Process - Dam safety decisionmaking is similar to many other aspects of water resources
management in that decisions regarding reasonable courses of action are not always
initially agreed upon by all stakeholders. The most important part of the decisionmaking
process is recognizing that it will generally involve building consensus regarding the
appropriate actions to be taken. However, in the event of an emergency, the time for
developing consensus may be severely shortened or nonexistent. Such a situation would
require the Regional Director to act quickly to avoid or minimize consequences.
8
III. Public Protection (Risk Evaluation) Guidelines
Measures of Risk - These guidelines focus on two assessment measures of risks related
to Reclamation structures: 1) the probability of a dam failure and 2) the life loss
consequences resulting from the unintentional release. The annual probability of failure
guideline addresses agency exposure to dam failure. As a water resource provider,
Reclamation must maintain and protect its dams and dikes that store water. The second
measure addresses the life loss component of societal risk. Protection of human life is of
primary importance to public agencies constructing, maintaining, or regulating civil
works.
Risk Analysis Methods - Reclamations risk analysis process involves the development
of event trees that identify all of the known and potential eve nts, states of nature (existing
conditions, site characterization, etc), dam responses, exposure conditions, and
consequences. The overall risk from the facility is defined as the accumulation of all
risks associated with each of the possible paths through the event trees. The methods to
analyze the risks associated with annual dam failure probability and life loss are briefly
described in the following two sections. Additional information on the methodology for
performing risk analysis can be found in Dam Safety Risk Analysis Methodology.5
Potential Applications - Although these guidelines focus on life loss as a dam failure
consequence, other consequences, such as environmental and economic consequences,
may be applied on specific projects where the decisionmaking process would be
enhanced by presentation of the entire breadth of consequences and risks. Economic
and/or environmental risk assessment may be performed when the potential for life loss
does not provide sufficient or appropriate input for a decision regarding modification of a
structure.
A. Evidence of a Developing Failure Mode
If there is evidence of a developing failure mode, there is a clear need to take action to
reduce risk. These situations should be brought to the immediate attention of the dam
safety decisionmakers to assure a timely response by the agency. Once the evidence is
determined to be credible, efforts should focus on those risk reduction actions that can be
taken to quickly reduce the potential for life loss or an unintended release of the reservoir
regardless of any risk estimates.
B. Annual Probability of Failure (Previously Tier 2)
Measurement Purpose - To manage an effective Dam Safety Program on behalf of the
Federal government and to assure public confidence in the performance of public works,
dam failures and associated large consequences need to be avoided. A high level of
national safety and stewardship of public assets is expected of Reclamation as an agency
5 Dam Safety Risk Analysis Methodology, Bureau of Reclamation, Denver,
Colorado, Version 3.3, September 1999.
9
specifically entrusted to manage a large inventory of dams. Unintended release of the
reservoir can cause significant downstream damage and disruption to routine activities.
Once an unintended reservoir release occurs, public trust is compromised and public
expectations may impose severe and costly constraints on projects. The greater the
inventory of dams and the time of exposure, the more difficult it becomes to ensure that
the agency will not experience a dam failure.
Measurement Definition - For comparison to this guideline, the annual probability of
failure is defined as the probability of a structural failure or condition that results in an
unintentional release of the reservoir that would be expected to result in loss of life. The
annual probability of failure is totaled for all specific loading conditions (seismic, static,
hydrologic, improper operation, etc.) The probability of events that are not expected to
cause life loss are not included, even though there may be some unintended loss of
reservoir storage. For example, if a structure accommodates large flows through rockfill
without breaching and without causing life loss, then the flow condition would not be
included in the probability of failure calculation. Events or conditions that can result in
an unintentional reservoir release are referred to as failure modes. These include failure
due to loadings from normal and extreme events.
Guideline - To ensure a responsible performance level across the inventory of
Reclamation Dams, it is recommended that decisionmakers consider taking action to
reduce risk if the estimate of annual failure probability exceeds 1 chance in 10,000.
Table 1 provides guidelines to evaluate the need and urgency to implement risk reduction
activities based on the annual failure probability estimates:
Table 1. Guidelines to evaluate Annual Probability of Failure Estimates
Estimates for annual
probability of failure
> 0. 0001
The justification to implement risk reduction actions increases as the
estimates become greater than .0001. Actions considered reasonable
and prudent should be considered for implementation when the
annual probability of failure estimate is in this range. A variety of
possible actions may be appropriate (see Section IV.D).
Estimates for annual
probability of failure
< 0. 0001
The justification to implement risk reduction actions diminishes as
the estimates become smaller than .0001. Risk reduction action costs,
uncertainties in the risk estimates, scope of consequences, operational
and other water resources management issues play an increased role
in decisionmaking. Actions considered reasonable and prudent
should be considered for implementation when the annual probability
of failure is in this range.
C. Estimated Risk (Annualized life loss - Previously Tier 1)
Measure ment Purpose - Reclamations primary dam safety concern is to ensure that its
structures do not cause life loss. The estimated risk is calculated for each specific loading
category (seismic, static, hydrologic, improper operation, etc.) at a dam based on the
estimated life loss from dam failure.
10
Measurement Definition For dam safety decisionmaking, risk of life loss is measured
as the product of the probability of dam failure and the consequences (life loss)
associated with that failure. This product is the expected annualized life loss at a given
dam for a given loading condition and is referred to as the estimated risk of life loss.
Guidelines - Table 2 provides guidelines to evaluate the need and urgency to implement
risk reduction activities based on the estimated risk:
Table 2. Guidance for Estimated Risk
Estimated risk is
portrayed to be >. 01
lives/year
Reclamation considers that there is justification for taking expedited
action to reduce risk. While there is a full range of possible risk
reduction actions that can be taken (see section IV.D), Reclamation
should focus on those that can quickly reduce risk or improve
understanding of the uncertainties associated with the risk. As
confidence increases that the risk is in this range, actions considered
should concentrate more on reducing the risk than reducing the
uncertainties. Any reassessment of the risk should be done prior to
increased storage if at all possible, and every effort should be made to
complete the reassessment within 90 days of determining the need for
expedited risk reduction action.
Estimated risk is
portrayed between
.01 and .001
lives/year
Reclamation considers that there is justification for taking action to
reduce risk. When the range of risk estimates falls in this range, there
are a wide variety of possible actions which may be appropriate.
However, the actions can be scheduled into the dam safety program
and coordinated with other needs at the facility or at other facilities.
Actions to reduce risks should be implemented on a schedule that is
consistent with budgeting and appropriations processes. Typically,
risk reduction should be accomplished within 7 years of a decision
that risks need to be reduced. When there is an indicated need for
risk reduction, the time spent on additional loading definition, data
collection, and risk assessment should be completed in a reasonable
timeframe. While it is desirable for this timeframe to be within a
year, other times may be considered reasonable by decisionmakers
based on the severity of the identified risks. Decisions on adequate
time frames should be documented in appropriate decision
documents.
Estimated risk is
portrayed to be
< .001 lives/year
The justification to implement risk reduction actions or conduct
additional studies diminishes as estimated risks become smaller than
.001. Risk reduction action costs, uncertainties in the risk estimates,
scope of consequences, operational and other water resources
management issues play an increased role in decisionmaking.
Actions considered reasonable and prudent should be considered for
implementation when the risk is in this range.
Risk to Small Populations - When life loss estimates are low (less than 10) for a given
11
loading category, a threshold estimated risk of .001 can potentially expose a small
population to failure events with relatively high probabilities. Risk to an individual from
dam failure for these cases may be similar to other societal risks such as auto accidents
and disease. Accordingly, risks associated with a Reclamation storage facility could
contribute significantly to the life risks of an individual in the exposed population. In
these cases, the guidelines related to annual probability of failure (section IV.A) serve as
an upper limit of exposure to such small populations.
12
IV. Determining Appropriate Actions
A. Development and Presentation of Risk Estimates
Use of Risk Estimates - Risk analysis provides a means to quantify judgment and to
identify the parameters that contribute to risk at a site. The intent of a risk assessment is
to review the failure modes for a dam, to decompose the failure modes into separate
events, to assign probabilities to the events, and to provide a range of risk estimates so
that risks can be compared to these guidelines. Valuable outcomes of the risk assessment
include an improved understanding of the critical issues at a dam and a clearer
identification of the issues that are the most significant contributors to risk. This
knowledge can be used to focus attention on those issues, which, if mitigated, will
provide the greatest reduction of risk to the public.
CFR Risk Estimates - Since the risk estimating process during the Comprehensive
Facility Review (CFR) is not a detailed team effort, it may have a higher level of
uncertainty than an issue evaluation risk analysis. The results of a CFR risk assessment
should be presented as the mean estimate or the expected value of risk. If the senior
engineer feels that significant assumptions need to be made, resulting in more than one
possible scenario to be considered, a range of risk estimates may be presented. If a range
of estimates is provided, the CFR must clearly state the specific assumptions or reasons
that form the basis of the range of estimates. If the risk estimate is presented as a single
point, decision makers should be cognizant of the fact that the estimate actually has a
degree of uncertainty associated with it.
Issue Evaluation Risk Estimates - Detailed team risk analyses should also address the
uncertainty associated with the risk estimate. Typically in issue evaluation team risk
analyses, probability density functions are assigned to the estimates in an event tree.
Techniques such as Monte Carlo simulation can be used to show the variability in a
number of trials that sample the assigned probability density functions. The risk estimate
is defined to be the arithmetic mean of the values computed for all trials. Sensitivity
studies may be performed by assigning other reasonable density functions and noting the
change in both the variability of the trial estimates and the calculated mean risk estimate.
Such sensitivity studies provide the decisionmakers with an estimate of a range of the risk
estimate based on the risk model used by the team. If the scatter plots of the Monte Carlo
calculation trials are presented, it should be carefully explained that the individual points
are not risk estimates as defined in Section II.B. These scatter plots may be useful in
analysis and may help communicate the key factors influencing the risk estimates.
Displaying Risk Estimates - The range of risk estimates (annual probability of dam
failure and expected annual life loss) should be presented for each load category on an f-
N diagram as shown in Figure 1. The f-N diagram illustrates the probability of dam
failure, the potential consequences, and the expected annual life loss risk associated with
a given load category on one diagram. The guidelines for considering risk reduction
action are illustrated as dashed bold lines on the f-N diagram.
13
Figure 1. - The f-N Chart for Displaying Probability of Failure, Life Loss, and Risk
Estimates
Portrayal of Risks
1.E-12
1.E-11
1.E-10
1.E-09
1.E-08
1.E-07
1.E-06
1.E-05
1.E-04
1.E-03
1.E-02
0.1 1.0 10.0 100.0 1000.0 10000.0
Life Loss Estimate, N
Annual Failure Probability, f
0.1
0.01
0.001
0.0001
0.00001
1.0
10.0
Justification to take
action to reduce risk
Justification to
take expedited action to
reduce risk
Diminishing
Justification to
take action to
reduce risk.
Diagonal lines
represent expected
annualized risk of
life loss
14
Communicating the Basis of Risk Estimates - It is important to note that the key
objective of the risk analysis is to communicate the current understanding of risk to the
decisionmakers. Decisions will be facilitated by elaboration on the reasons the risk might
be higher or lower and the additional information that might better define the risk. For
example, the range of risk estimates might not be continuous if there is an important lack
of information or if there are alternate interpretations of the available information about a
structure. There could be one range of risk estimates that is high and another that is low
with the difference being the assumption about the information that is lacking or the
interpretation of the available information. This sort of risk estimate communication can
be very useful to the decisionmakers when proposals for gathering additional data or for
more detailed technical analysis are considered.
B. Assessment (Use and Interpretation) of Risk Results
Action Based Decisionmaking - Dam Safety issues may be identified as Reclamation
operates, maintains, monitors, inspects, or analyzes a structure. When issues arise, further
data collection, investigation, and related analysis may be required to better understand
the public safety or economic implications. Reclamation will address the identified
issues by taking an action, prioritizing and scheduling an action, or by documenting a
decision that no action is necessary. In general, many issues are raised without
implications on continued operation of the facility. The dam safety decisio nmakers
should consider the potential severity of issues being addressed in the context of the dam
safety program objectives and determine if continued normal operation of the facility is
appropriate. If a decision is made to continue normal operations while issues are being
addressed, then that decision should be documented.
Prioritization - Reclamation has limited financial resources available to address issues.
It is critical to not only identify future actions but also to identify the priority or the time
frame associated with these actions. The priority for initiating actions to address risks
depends in part on available resources and on the risks throughout Reclamations dam
inventory. The intent is to make the greatest reduction in risk throughout the inventory of
Reclamation dams within the resource limitations of the program while at the same time
assuring that no dam presents an unreasonable risk.
Uncertainty - The quantification of risk estimates is dependent on data and analysis
regarding the design, construction, and current condition of a dam, as well as the
identified loads that the dam could be subjected to over its operating life. All of this
information has some level of uncertainty associated with it. It is acknowledged that the
quantification of risk estimates is subjective and is a function of group dynamics, the
experience and associated judgment of group members, and the available information for
a dam. Thus, uncertainty in the risk estimates is expected. As a consequence, there can
be a range of actions that may be suggested for a given range of risk estimates.
Assessing Ability to Reduce Uncertainty - When making a decision regarding future
actions, one should consider the risk estimates, the issues most influencing the risks, the
15
sensitivity of the risks to particular inputs, the cost of additional actions, and the potential
for reducing uncertainty. Uncertainty may be reduced by performing additional actions
such as collecting more data, by performing more analysis, or by performing a more
detailed analysis of the risks. However, there are occasions when additional efforts may
not result in significant reduction in uncertainty. It is important to recognize when this is
the case and consider the anticipated value of the additional efforts to reduce uncertainty
as a factor in selecting a course of action.
Risk Estimate Ranges (range of means) Straddling the Guidelines - In gathering the
information necessary for dam safety decisionmaking, the decisionmaker will never have
complete or perfect data on which to base the decision. Accordingly, there is some
degree of uncertainty in the risk estimates for each dam. When significant uncertainties
or assumptions related to a lack of data or interpretations of data result in a range of risk
estimates, the results may straddle the guideline values with portions of the risk estimates
range portrayed both above and below the guidelines. In these cases, it is important for
decisionmakers to assess the portion of the risk estimate range that exceeds the guidelines
to determine if it is significant enough to warrant further action or studies. The entire
range should be used to assess the need for future actions as well as an aid in setting the
priority for initiating the actions. If the range extends into the zone that justifies
expedited risk reduction, studies to better define the risk should be the minimum response
of the agency.
Level of Analysis Considerations - Because CFR analyses are not detailed team efforts,
decisions based on CFR-based risk assessments are typically related to improvements in
monitoring, collection of additional data, or performance of additional analyses to reduce
uncertainty or improve confidence in the risk estimates. Decisions to change operations
or initiate modifications are generally not made as a result of these analyses.
Issue evaluation risk analyses are more extensive analyses of risk and draw on a broader
range of expertise. These analyses may require additional data collection, additional
analyses, and include a more detailed breakdown and analysis of risks. Risk estimates
developed during this activity are often computed using a Monte Carlo simulation and
should include sensitivity studies to determine a potential range for the risk estimate.
Risk Reduction Objective - It is important to reduce risk as low as can reasonably be
achieved if it is decided to pursue a risk reduction action. As a result, it is desirable to
lower the entire range within which the risk estimate would be expected to fall given the
uncertainties. An evaluation of the effect of modification alternatives on the range of the
risk estimate will enter into the selection of the preferred alternative. In other words,
selection of a preferred alternative should focus on moving the range of the risk estimate
sufficiently below the guidelines to assure that the dam safety issue doesnt resurface due
to slight differences in interpretations of the risk.
Consideration of Future Developments - Future growth in the downstream flood plain,
increases in the loading estimates, and changes in the state-of-the-art, may result in
increases in risk estimates. Thus, the more risk reduction achieved, the less likely it
becomes that future studies will conclude that the risks no longer meet Reclamations
guidelines. Risk reduction goals should be considered on a cost versus risk reduction
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basis. Ideally, a menu of options, associated costs, and impacts on risk should be
considered by the decisionmakers so that prudent decisions can be made.
C. Large Downstream Populations
When the probability of a given loading category is relatively high and there is high
potential for downstream life loss, a very low probability of unintended release is
required by these guidelines. In such cases, Reclamation focuses on ensuring that there
are sufficient protective (defensive design) measures incorporated into the structure.
These protective measures either increase confidence in the structures ability to perform
satisfactorily without unintended releases, or increase confidence in Reclamations ability
to detect adverse performance with sufficient lead time to intervene and either prevent an
unintended release or provide adequate warning to the public.
In some cases, risk reduction actions may be taken to increase confidence in the
performance of the structure even though the dam shows no significant signs of adverse
performance. In these cases, decisionmakers should work with the technical experts to
ensure that there are sufficient redundancies in the design and operations of the facility to
instill confidence in the future performance of the structure.
D. Examples of Alternative Actions
With increased justification for action, there is a need to propose alternative actions that
will adequately address the risk and/or probability of failure at the dam. It is important to
recognize that there is a broad range of actions that can be taken. These actions can range
from further investigations to better understand the uncertainties associated with the risks
to decisions to modify structures. In many cases, the chosen course may involve a
combination of several actions.
Dam safety decisionmaking generally involves the selection of an appropriate course of
action for a given issue based on the magnitude of the risk, the degree of confidence in
(or uncertainties associated with) the estimated risk, and the likelihood of additional
information providing a significantly enhanced understanding of the issues. The state of
knowledge regarding the dam safety issues can lead to a variety of possible actions.
While the risks associated with each individual facility pose a unique situation, the
following are some of the types of actions which can be taken to either improve
Reclamations understanding of the uncertainties associated with the estimated risk, or to
improve confidence in the ability of a structure to perform satisfactorily.
Risk Management Activities:
Refine Analyses If a risk estimate warrants action primarily due to
uncertainties in key elements contributing to the risk, decisionmakers may
consider gathering additional information in a timely fashion to assist in quickly
reassessing the risk. In pursuing this activity, the decisionmakers should satisfy
themselves that there are no immediately developing failure modes. Any
expedited reassessment of the risk should be done prior to increased storage if at
all possible, and every effort should be made to complete the reassessment within
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90 days of determining the need for action. If the reassessment indicates
expedited risk reduction action is needed, a decision concerning the risk
reduction measures should be made and documented.
Reservoir restrictions - While a reservoir restriction is technically an operational
change, it can result in a significant and immediate change in the risk at a dam.
The risk reduction results from a reduction in the loading condition and the failure
probability. Another benefit is that the reduced storage and reduced head leads to
less potential for adverse consequences in the event of poor performance of the
structure. However, the loss of storage can have a dramatic impact on water users
and the environment. Therefore, consideration of a reservoir restriction requires
consideration of both the expected reduction in risk and the certainty of the lost
project benefits that accrue from limiting storage in the reservoir.
Increased monitoring - If the risks associated with a failure mode are such that
successful intervention would likely be possible or better warning could be
provided to local authorities, a potential course of action is to improve
Reclamations ability to detect the existence of the conditions which would be
indicative of the failure mode developing (i.e. seepage, deformation, etc.)
Operational changes - In some cases, risks can be reduced at a dam by making
changes in the operational and/or maintenance practices at a dam. Examples
include establishing minimum gate openings to minimize potential for cavitation,
checking gates for drift from their set positions, or alternate procedures for filling
reservoirs to lower risks at critical times of the year.
Revised Emergency Action Plan (EAP) - The potential for adverse
consequences can be minimized by reviewing the potential failure modes and by
developing clear guides to decisionmaking for the types of emergency situations
that can be envisioned. Existing EAPs have been developed to detect emergency
events based on site specific loading conditions. If a new loading condition or
potentially adverse response has been identified for a dam, then the EAP initiating
conditions, emergency response levels, expected actions for each response level,
and hazard specific appendices can be revised to reflect the current conditions or
concerns at the facility. While this course of action will not reduce the probability
of an adverse response of the structure, it can help to ensure that people
understand the risks at the dam and know how to respond appropriately. This
may result in a reduction of the life loss risk.
Loading definition - An important part of understanding risk lies in determining
the frequency with which unlikely events affect a dam. In some cases, it is
beneficial to gather data that will improve the understanding of the frequencymagnitude
relatio nship of the loading conditions that can potentially lead to
failure modes. This information would be used to reanalyze the risks.
Data collection - When there is a lack of knowledge of key properties of a
facility, there can be considerable uncertainty in its performance. A prudent
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action may be to collect information so the performance of the dam can be better
predicted. This additional data would be used to reanalyze the risks.
Structural Modifications - When non-structural actions are not expected to
adequately address the risks at a facility, structural modifications to the dam may
be considered when additional information will not change the risk outcome. The
intent of such modifications is to increase confidence in the satisfactory
performance of the structure under the applied loading conditions. Throughout
the design and construction process, the risks should be evaluated to assure that
design and construction decisions are consistent with the risk reduction
objectives.
E. Formulation of Appropriate Risk Reduction Alternatives
Role of Risk Estimates - A key to formulating risk reduction alternatives is using the
risk analysis information to assure that proposed alternatives will result in effective risk
reduction. When developing the alternatives, the event trees should be reviewed to
evaluate which events or conditions are the most significant contributors to the overall
risk and/or probability of failure. In some cases, very significant risk reductions can be
accomplished by focusing on a specific event or condition. In other cases, with multiple
sources of risk, several issues may have to be addressed simultaneously in order to reduce
risk and the associated probability of failure to appropriate levels.
Accumulation of Risk Over Time - During a risk reduction action, one should
remember that Reclamations goal is to reduce overall risk. This includes the sum of the
risk from before, during, and after a risk reduction action. To minimize this total, it is
important to proceed promptly with a risk reduction action when the risk values are high
because delay in risk reduction increases the time accumulation of risk. Likewise, it is
important to consider risks during construction, because these risks contribute to the
accumulation of risk over time. Addressing an annualized potential for dam failure that
could be relatively small by incurring a much higher probability of dam failure during the
period of time that the dam is being modified may not be appropriate because it raises
accumulated risk during the life of the dam to a level higher than would be incurred by
not pursuing risk reduction action at all. This factor may influence the choice of
modification alternatives and reservoir operations during construction. It should not be
used to support a do nothing alternative.
F. Unrecognized Risks
Reclamation recognizes that there will always be a potential for risk associated with
unknown conditions at a dam that have not been recognized in the analysis. Therefore,
an active examinatio n, monitoring, and evaluation program should be in place to provide
a mechanism for early detection of developing and/or potential problems. This early
detection information should be used to assess changes in the perceived risks at
individual dams, and to prioritize funding for the Dam Safety Program for risk reduction
activities. The CFR process provides a framework for assuring that there is a periodic
opportunity to reassess risk due to changes in the state-of-the-art of dam design or
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changes in dam performance. If no such changes are applicable and no new risks are
recognized, then the CFR risk assessment serves as a confirmation of previous risk
analyses.