ER 1105-2-101_Risk Assessment for Flood Risk Management

DEPARTMENT OF THE ARMY ER 1105-2-101

U.S. Army Corps of Engineers

CECW-CP Washington, DC 20314-1000

CECW-CE

Regulation

No. 1105-2-101 15 July 2019

Planning

RISK ASSESSMENT FOR FLOOD RISK MANAGEMENT STUDIES

TABLE OF CONTENTS

Paragraph Page

1. Purpose ......................................................................................................................1

2. Applicability ..............................................................................................................1

3. Distribution Statement...............................................................................................1

4. References .................................................................................................................1

5. Context ......................................................................................................................2

6. Background ...............................................................................................................3

7. Variables in a Risk Assessment.................................................................................5

8. Policy and Required Procedures................................................................................6

9. Example Displays of Risk Assessment Results ......................................................11

Appendixes

Appendix A: Example Displays of Project Engineering and Economic Performance..................13

Table List

Table 1: Project Performance; AEP, Long Term Exceedance Probability and Assurance ...11

Table A1: Expected value and probabilistic values of EAD and EAD reduced ......................12

Table A2: Expected value and probabilistic values of costs ....................................................13

Table A3: Performance described by AEP and LTEP .............................................................15

Table A4: Performance described by AEP and LTEP (alternative display) ............................15

Table A5: Probability comparison............................................................................................17

Table A6: Life Loss..................................................................................................................19

Figure List

Figure 1: Risk conceptualized...................................................................................................4

Figure A1: Expected value and probabilistic values for net benefits ........................................13

Figure A2: Expected value and probabilistic values for Benefit/Cost Ratios ...........................14

Figure A3: AEP uncertainty ......................................................................................................16

Figure A4: Assurance (also CNP) .............................................................................................18

Figure A5: Example scenario ....................................................................................................19

Glossary

ER 1105-2-101 ● 15 July 2019 i

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ER 1105-2-101 ● 15 July 2019 ii

1. Purpose. This regulation provides guidance on risk assessment requirements for flood

management studies including but not limited to feasibility studies, post-authorization changes,

general reevaluation studies, dam and levee safety studies, and major rehabilitation studies. This

regulation is jointly promulgated by Planning and Engineering. The risk framework is a

decision-making process that comprises three tasks: risk assessment, risk communication, and

risk management, which can be advantageously applied to a variety of water resources

management problems. These requirements are part of a broader decision-making process that

includes similar assessments for risks to the natural environment as well as the social and

cultural well-being of people potentially impacted by flood management activities.

2. Applicability. This regulation is applicable to all U.S. Army Corps of Engineers

Headquarters (HQUSACE) elements, major subordinate commands, districts, laboratories, and

field operating agencies having civil works responsibilities. This regulation applies to all

implementation studies for flood risk management projects: riverine and coastal.

3. Distribution Statement. Approved for public release, distribution is unlimited.

4. References.

a. Engineer Regulation (ER) 5-1-11, U.S. Army Corps of Engineers Business Process.

(https://www.publications.usace.army.mil/USACE-Publications/Engineer-Regulations/)

b. ER 1105-2-100, Guidance for Conducting Civil Works Planning Studies.

(https://www.publications.usace.army.mil/USACE-Publications/Engineer-Regulations/)

c. ER 1110-2-401, Operation, Maintenance, Repair, Replacement, and Rehabilitation

Manual for Projects and Separable Elements Managed by Project Sponsors.

(https://www.publications.usace.army.mil/USACE-Publications/Engineer-Regulations/)

d. ER 1110-2-1156, Safety of Dams – Policy and Procedures.

(https://www.publications.usace.army.mil/USACE-Publications/Engineer-Regulations/)

e. Engineer Manual (EM) 1110-2-1619, Risk Assessment for Flood Risk Management

Studies. (https://www.publications.usace.army.mil/USACE-Publications/Engineer-Manuals/)

f. Engineer Pamphlet (EP) 1110-2-8, Explaining Flood Risk.

(https://www.publications.usace.army.mil/USACE-Publications/Engineer-Pamphlets/)

g. Specific Measurable Attainable Risk Informed Timely (SMART) Planning Guide

(https://planning.erdc.dren.mil/toolbox/smart.cfm)

*This regulation supersedes ER 1105-2-101 dated 17 July 2017.

ER 1105-2-101 ● 15 July 2019 1

h. U.S. Army Corps of Engineers (USACE), Hydrologic Engineering Center, 2010. “Flood

Damage Reduction Analysis (HEC-FDA),” Version 1.2.5. Davis, CA.

(http://www.hec.usace.army.mil/software/hec-fda/)

i. National Research Council, 1995. “Flood Risk Management and the American River

Basin: An Evaluation.” Washington, DC: National Academy Press.

(https://www.nap.edu/catalog/4969/flood-risk-management-and-the-american-river-basin-an-

evaluation)

j. “Transforming the Corps into a Risk Managing Organization,” 26 November 2007.

Contributing Authors: Dr. David Moser, USACE, Institute for Water Resources; Todd Bridges,

USACE, Engineer Research and Development Center; Steven Cone, USACE, Institute for Water

Resources; Yacov Haimes, University of Virginia; Brian K. Harper, USACE, Institute for Water

Resources; Leonard Shabman, Resources for the Future; and Dr. Charles Yoe, College of Notre

Dame.

(http://www.corpsriskanalysisgateway.us/data/docs/ref/Explore%20Resources/IWR%20Reports/W

hite_Paper-Transforming_the_Corps_into_a_Risk_Managing_Org.pdf)

k. “USACE Resilience Initiative Roadmap 2016,” 16 May 2016.

(http://cdm16021.contentdm.oclc.org/cdm/ref/collection/p16021coll6/id/1617#img_view_containe

l. U.S. Army Corps of Engineers, Risk Management Center, Best Practices in Dam and

Levee Safety Risk Analysis. (https://www.usbr.gov/ssle/damsafety/risk/BestPractices/Chapters/I-

0-20150612.pdf)

5. Context. Since the enactment of the Flood Control Act of 1917, USACE has played a

significant federal role in managing flood risk nationwide. Flood risk management is the process

of identifying, evaluating, selecting, implementing, monitoring, and modifying actions taken to

reduce and manage risk through shared responsibilities. Scientifically sound, cost-effective,

integrated actions are taken to achieve flood risk management. Social, cultural, ethical,

environmental, fiscal, political, and legal considerations are accounted for in the process. Still,

USACE recognizes that more needs to be done to assess, manage, and communicate flood risks.

In 2006, USACE established the National Flood Risk Management Program to advance the goals

of flood risk identification, communication, response, and management services across all levels

of government to save lives and reduce property damage in the event of floods and coastal

storms. All flood risk managers must balance the insights of USACE’s professional staff with

stakeholder concerns for such matters as residual risks, life safety, reliability, resiliency, and cost

while acknowledging that no single solution will meet all objectives, and tradeoffs must always

be made. Resilience is inherent to flood risk management, and it is the overall ability to

anticipate, prepare for, and adapt to changing conditions and withstand, respond to, and recover

from adverse events, including the ability to avoid, minimize, withstand, and recover from the

adverse effects of a flood. Resilience also refers to the capacity or ability of a project or system

to absorb disturbance and still retain its basic function and structure. For example, project

ER 1105-2-101 ● 15 July 2019 2

resilience measures for a levee embankment can be provided by various forms of surface

hardening, armoring, or resistance to overtopping scour. These measures provide a higher

degree of predictability for levee performance.

6. Background.

a. No project or action that is proposed, evaluated, adopted, and implemented can

completely eliminate or mitigate flood risks. Further, the information used to estimate flood risk,

formulate and evaluate plans, and determine the results of the analyses is uncertain. All measured

or estimated values in project development are to various degrees inaccurate—reflecting both

inherent natural variability in flooding phenomena (e.g., cyclical rainfall patterns) and lack of

knowledge in estimating various parameters (e.g., estimation of Manning’s n-value) relevant to

project works and their performance. Pursuing the management of flood risk within the risk

framework is an explicit means of better understanding both the flooding and associated

consequences, and the uncertainty in their estimation, and thus should support development of

robust strategies for managing flood risk.

b. The risk framework is a decision-making process that comprises three tasks: risk

assessment, risk communication, and risk management. Risk assessment is a systematic approach

for describing the nature of the flood risk, including the likelihood and severity of consequences.

Risk assessments are quantitative whenever possible; however, qualitative assessments may be

appropriate for some activities. Risk assessment includes explicit acknowledgment of the

uncertainties in the parameters used to compute risk. Risk management is a decision-making

process in which risk-reducing and resilience-increasing actions are identified, evaluated,

implemented, and monitored. The purpose of risk management is to take actions to effectively

reduce and manage risks identified in the risk assessment. Risk communication is a collaborative

exchange of information among the risk assessors and those who will use the risk assessment

results and/or those who are affected by the risks and risk management actions. Open

communication improves the understanding of the risks by all parties, and leads to improved risk

assessments and risk management decisions and outcomes. Documenting the results of a risk

assessment framework is an important part of the process, and examples are included in Appendix

A. Clearly presenting the findings of the risk assessment will help inform discussions with

sponsors, stakeholders, and others; however, documentation alone will not fully convey the highly

technical nature of risk assessment results. Open dialogue will likely be required to ensure a

sufficient and common understanding of the risk assessment and mitigation options leading to the

selection of most appropriate actions.

c. A risk framework process can be advantageously applied to a variety of water resources

management problems, including those involving flooding. The approach captures and quantifies

the extent of the risk and uncertainty in the various project development components of an

investment decision. The total effect of uncertainty on the project formulation and consequent

performance related to life safety, economic, social, and environmental concerns can be examined

and conscious decisions made reflecting an explicit tradeoff between risks, performance, and costs.

Risk assessments can be used to compare plans in terms of their physical performance, economic

ER 1105-2-101 ● 15 July 2019 3

success, residual risks, and impacts to life, health, and the environment, including their

uncertainties.

d. Budget constraints for plan selection, increased partner cost-sharing, the public’s interest

in project performance, and concern for life safety as well as social and environmental matters

must be addressed in the analysis of federal water resources investments. Explicit consideration of

risk and uncertainty can help address these issues and improve investment decisions.

e. Risk is broadly defined as a situation or event where something of value is at stake and its

gain or loss is uncertain. Risk is typically expressed as a combination of the likelihood and

consequence of an event. Consequences are measured in terms of harm to people, cost, time,

environmental harm, property damage, and other metrics. Choosing the appropriate risk metrics

and actively using them in decision-making is critical to effective risk management in support of a

vibrant economy, thriving ecosystems, and sustainable communities. Flood risk considers

explicitly the performance consequences of subjecting people and property to the entire range of

likely flood events, given risk management provided by any structural or non-structural measures.

One commonly used metric of economic risk is expected annual damage (EAD) or average annual

equivalent damage when computed on an annual basis over the period of analysis.

f. Flood risk can be conceptualized as a function of the hazard, performance, exposure,

vulnerability, and consequences as depicted in Figure 1.

Figure 1: Risk conceptualized

(1) The “hazard” is what causes the harm: in this case, a flood. The flood hazard is described

in terms of frequency, stage, velocity, extent, and depth.

(2) “Performance” is the system’s reaction to the hazard. In Figure 1, performance refers to

the system features and the capability to contain/manage the flood hazard for the full range of

possible events and as a single event or load. In this regulation, this would be termed “system

performance.” Performance also refers to the metric that describes the capability of the system to

accommodate a single event (Assurance; also Conditional Non-exceedance Probability, CNP) and

the full range of events: Annual Exceedance Probability (AEP) and Long-Term Exceedance

ER 1105-2-101 ● 15 July 2019 4

Probability (LTEP). There are other definitions of performance in addition to system performance.

Performance can also be described by levee breach from loading below the top of levee probability

functions, the interior-exterior functions for leveed areas, unregulated-regulated transforms for

reservoirs and diversions, and elevation-discharge functions (rating curves) for channels. These

also would be considered “system performance.” When the structural integrity of a system or

system component is discussed, such as the fragility function, the reference would be termed

“structural performance.” When the economics of a system are discussed, the reference would be

termed “economic performance” as expressed by EAD and EAD reduced.

(3) “Exposure” describes who and what may be harmed by the flood hazard. Exposure

incorporates a description of where the flooding occurs at a given frequency and what exists in that

area. Tools such as flood inundation maps provide information on the extent and depth of

flooding; structure inventories, population data, crop data, and habitat acreage provide information

on the population and property that may be affected by the flood hazard.

(4) “Vulnerability” is the susceptibility to harm human beings, property, and the

environment when exposed to the hazard. Depth-damage functions, depth-mortality functions, and

other similar relationships can be used to describe vulnerability.

(5) “Consequence” is the harm that results from a single occurrence of the hazard.

Consequences are measured in terms of metrics such as economic damage, acreage of habitat lost,

value of crops damaged, and lives lost.

(6) “Economic risk” is the combination of likelihood and harm to property, infrastructure,

and other assets as well as economic systems (all measured in monetary terms). A common metric

of economic risk is EAD.

(7) “Life loss consequence” is the determination of the population at risk and the estimated

statistical life loss.

7. Variables in a Risk Assessment.

a. The true values of variables and parameters are recognized as important to project

development decisions, are frequently not known with certainty, and can take on a range of values.

The likelihood of a quantity or parameter taking on a particular value can be described by a

probability distribution and the probability distribution may be described by its own parameters,

such as mean and variance for a normal distribution. Quantitative risk assessment combines the

information about the parameters with underlying uncertainty information within a computational

model so that the engineering performance and associated consequences are determined on a

statistical basis represented by a probability distribution. Consequences of interest include

potential for life loss and economic losses and environmental impacts of a proposed project.

b. A variety of variables and their associated uncertainties may be incorporated into the risk

assessment of a flood risk management study. For example, economic variables in an urban

ER 1105-2-101 ● 15 July 2019 5

situation may include, but are not necessarily limited to depth-damage curves, structure values,

content values, structure first-floor elevations, structure types, flood warning times, and flood

evacuation effectiveness. Uncertainties in economic variables include building valuations, inexact

knowledge of structure type or of actual contents, method of determining first-floor elevations, or

timing of initiation of flood warnings. Other key variables and associated uncertainties include the

hydrologic and hydraulic conditions of the system. Uncertainties related to changing climate

should be addressed using the current USACE policy and technical guidance. Uncertainty in the

likelihood of particular discharge and stage exists because record lengths are often short or do not

exist where needed, and the effectiveness of flood flow regulation measures is not precisely

known. Uncertainty in discharge also comes from estimation of parameters used in rainfall runoff

computations, such as precipitation and infiltration. Examples of uncertainty factors that affect

stage might include conveyance roughness, cross-section geometry, debris accumulation, ice

effects, sediment transport, flow regime, and bed form. Uncertainty factors that affect the safety of

human life include the number of routes of egress, time of day, distance to dry land, water

temperature, number of multi-storied structures, demographics, and the existence and adherence to

an emergency action plan. Not all variables are critical to project justification in every instance.

To achieve the ultimate goal, the risk assessment and study effort should concentrate on the

uncertainties of those variables having a significant impact on study conclusions and

recommendations. SMART Planning Principles (Reference 4g) promotes balancing the level of

uncertainty and risk with the level of detail of the study. The level of detail required to make

planning decisions will grow over the course of the study, as the study team moves from an array

of alternatives to a single recommended alternative. For technical details on how to address these

uncertainties, see Reference 4b.

8. Policy and Required Procedures.

a. All flood risk management studies will adopt the risk framework as described herein.

The risk framework approach and results of a risk assessment will be documented in the principal

decision document. The types of documents involved include but are not limited to: feasibility

reports, general and limited reevaluation reports, and project modification impact reports including

water control manuals that reallocate storage requiring reauthorization, and design documentation

reports. Project Management Plans (PMPs) will describe the methods to be used to quantify the

uncertainties of the key variables, parameters, and components and the approach to combining

these uncertainties into higher-level measures for determining overall engineering performance,

life loss, and economic and environmental consequences (Reference 4b). In developing the PMP

for a proposed feasibility study, the level of detail of a risk assessment will be developed to the task

level and included in the PMP. In cases where a general reevaluation report is proposed and where

deterministic assumptions including standard superiority assumptions or other engineering

standards were used that are critical to sizing and/or performance of project features, a

reformulation of the project using a risk assessment, as described in this regulation, will be

undertaken to determine the appropriate project for construction recommendation.

b. The ultimate goal of a risk assessment is a comprehensive approach in which the values

of all key variables, parameters, and components of flood risk management studies are subject to

ER 1105-2-101 ● 15 July 2019 6

probabilistic analysis. Not all variables are critical to project justification in every instance. To

achieve the ultimate goal, the risk assessment and study effort should evaluate the impact of

various variables and their uncertainties, and concentrate on the variables having a significant

impact on study conclusions. When a more detailed assessment is required, at a minimum

uncertainty in the following variables and relationships must be explicitly incorporated in the risk

assessment:

(1) Stage-damage functions from economic studies (with emphasis on structure first-floor

elevation, depth-percent damage relationships, and content and structure values for urban studies).

For studies in agriculture areas, other variables (e.g., time of year, crop type, costs of production)

will be key and should be used in the economic analysis.

(2) Discharge-frequency functions from hydrologic studies (with emphasis on the record

length or hydrologic modeling parameters).

(3) Stage-frequency functions from hydrologic/hydraulic studies (with emphasis on the

record length). A stage-frequency analysis may be used when stage gage data is all that is

available for a study and/or when there is no unique correspondence between flow and stage such

as in locations highly controlled by backwater or tidal conditions or in the case of ice jam floods.

Care should be taken in using this approach because in current analysis practice all uncertainties

are collapsed into a single uncertainty as defined by the period of record.

(4) Regulated-unregulated transform function from reservoir regulation studies (with

emphasis on operational uncertainties, inflow hydrographs, and rating uncertainties of outlet

works).

(5) Stage-discharge functions from hydraulic studies (with emphasis on conveyance

roughness and cross-section geometry).

(6) Stage-probability of failure or unsatisfactory performance functions (fragility curves,

system performance probability curves) for mechanical, electrical, structural, and geotechnical

performance of structures as defined in latest guidance.

(7) Stage-life loss function from life safety studies (with emphasis on rate and depth of

flooding, population at risk, and emergency response plans).

(8) Stage-environmental impact considerations (emphasis on the key ecological and other

factors impacting the environment).

c. Consistent with the Principles and Guidelines the National Economic Development

(NED) Plan must be identified. The NED Plan is the alternative plan that reasonably maximizes

net economic benefits consistent with protecting the nation’s environment. NED will be calculated

explicitly including uncertainties in the key variables specified in the risk register. Consideration

of increments in project scale different from the NED Plan, as well as other plans preferred by the

ER 1105-2-101 ● 15 July 2019 7

cost-sharing sponsor, may be considered. Flood risk management actions may be part of multi-

objective plans as described in Reference 4b.

d. The estimate of net NED benefits and benefit/cost (B/C) ratio will be reported both as an

expected (mean) value and on a probabilistic basis for each alternative. The probability that net

benefits are positive and that the B/C ratio is at or above one (1.0) will be presented for each

alternative.

e. The flood risk management performance of a plan will be presented for the system as a

whole over the plan’s given lifecycle and for each component that makes up that system.

Typically, the system performance will reflect that of the “weakest” component. Reporting the

performance of individual components may assist in the selection of future risk reduction

measures, although consequences should be considered in these decisions as well. The risk

assessment will quantify the performance, resilience, and risk of all scales of all alternatives

considered in formulating the recommendation. The assessment will evaluate and report residual

risk, which includes consequences of project performance or capacity exceedance. This

assessment requires explicit consideration of the joint effects of the uncertainties associated with

key hydrologic, hydraulic, and geotechnical variables and character of floodplain occupancy. This

performance will be reported in the following ways (see glossary for definition of terms):

(1) AEP (metric, value, and designation of with/without performance) with associated

description of uncertainty.

(2) LTEP over 10, 30, and 50 years.

(3) Assurance (also CNP) for the 0.2, 0.1, 0.02, 0.01, 0.004, and 0.002 events. Assurance

can be computed using either a discharge-frequency or stage-frequency function.

(4) The Assurance (also CNP) for specific historic floods.

(5) Economic average annual and single event damage, potential life loss, and environmental

conditions and impacts as required by ER 1105-2-100 (Reference 4b).

(6) Qualitative and quantitative statement of residual, transformed, and/or transferred risk

(paragraph 8g).

f. An assessment of potential life loss, economic, and environmental damage for the

without condition, along with all proposed alternatives is required. For studies where life loss

plays a significant role in formulating and evaluating alternatives, and selecting the recommended

plan, a quantitative assessment of life loss will be performed using accepted USACE methods and

tools. As with the economic damage assessment, explicit consideration of the effects of the

uncertainties associated with key input variables is required. Key input variables in the life loss

estimate include, but are not limited to: warning time, warning effectiveness (both how quickly a

ER 1105-2-101 ● 15 July 2019 8

warning spreads among the population at risk (PAR) as well as the response to a warning by PAR),

flood arrival time, and fatality rate thresholds.

g. The probability distribution of residual flood damage and other relevant aspects of

residual risks (transformed or transferred) will also be displayed. Residual flood risk is the flood

risk that remains after a proposed flood risk management project is implemented. Residual risk

includes the consequence of capacity exceedance as well as consideration of project performance,

robustness, and resiliency. Transformed risk is a risk that emerges or increases as a result of

mitigating another risk. Conceptually, a transferred risk relocates risk or increases risk from

Region A of a system to Region B of the system as a result of action taken in Region A. The

nature of the risk of flooding is different with a levee versus without a levee. A levee reduces the

likelihood that existing improved property will be flooded but can often encourage new

development, which can lead to an overall increase in risk if not managed effectively through

proper land use and building codes. A levee may transform the flood risk from gradual and

observable long before action is necessary to sudden and catastrophic. The residual risk, including

transformed and/or transferred, will be reported as the expected annual probability of each

alternative being exceeded with consideration of unsatisfactory project performance and the

associated consequences. For comparison, the without-project risk in terms of the annual

probability of flood damage occurring and the annual probability of other property hazards (fire,

wind, etc.) will be displayed. To aid this display and to improve the understanding of the residual

risk, inundation maps will be provided showing flood depths should the project be exceeded. A

narrative scenario for events that result in flooding will be provided (see Figure A-5 for an

example). An emergency action plan or community preparedness plan should also be presented as

required by ER 1110-2-401 (Reference 4c). The impacts to residual human health, safety risks,

and the environment should be discussed. Both the inundation map and the narrative scenario will

be provided for each alternative considered for final selection.

h. All project increments comprise different risk management alternatives represented by

the tradeoffs among engineering performance, project cost, economic and environmental

resilience, and life loss consequences. These increments contain differences in flood damage

reduced, residual risk, local and federal project cost, impacts to the environment, and life loss.

USACE must effectively communicate to local sponsors and residents so they understand these

tradeoffs and can participate fully in informing the decision-making process.

i. Many existing USACE projects were authorized and/or designed to the Standard Project

Flood (SPF). The SPF is defined in several legacy ER and EM guidance documents, but the SPF is

no longer a design target. USACE policy (Reference 4b) states that risk analysis (now risk

framework) is to be used, to include the evaluation of a full range of floods (including those that

would exceed the SPF) that will be used in the formulation and evaluation of alternatives.

Comparing performance of the NED Plan and other candidate plans, given the occurrence of the

SPF event, (a rare but historically understood flood event) can play a useful role in the assessment

of residual risks to inform the decision-making process. As a consequence, while current guidance

on project formulation and alternative selection governs, the SPF may have a useful role for

evaluating residual risks, for comparing new project proposals with nearby existing projects that

ER 1105-2-101 ● 15 July 2019 9

were based on the SPF, and as a check and validation of floods computed from statistical

frequency analysis.

j. Special Guidance.

(1) The use of explicit freeboard or similar buffers to account for hydrologic, hydraulic,

geotechnical, and other uncertainties will no longer be used for levee planning and design.

Similarly, the use of freeboard to account for the same uncertainties will no longer be used in

channel planning and design.

(2) Risk assessments for dams and levees must also follow other applicable USACE policy

guidelines, such as Reference 4d.

(3) Evaluation of a levee system for the National Flood Insurance Program must follow

current USACE policy and guidelines.

(4) Project performance will be described by AEP (metric, value, and description of with/

without performance) with uncertainty, Assurance (also CNP), and LTEP. The array of all

performance indices should be displayed on a system-wide basis and on individual components

that make up the system. EP 1110-2-8 (Reference 4f) describes techniques in effectively

communicating flood risk to local officials and the public. A legacy term, Level of Protection

(LOP) was used as a performance index and a levee design concept that was founded on the

principle of providing a high degree of Assurance that the levee system component would neither

breach nor overtop when loaded with a specific recurrence interval flood (e.g., providing a 75-year

LOP if it could contain that event with 90 percent level of Assurance). The recurrence interval of

the flood hazard for this design principle was then used as an expression of the performance of the

levee system. The term is no longer used as it did not include residual risk or structural

performance. LOP should not be used to judge a set of alternatives or to target a specific project

size.

(5) Economic analyses will compute the NED Plan utilizing benefits at the mean of the

probability distribution consistent with ER 1105-2-100. Once the NED (or other Federally

Recommended Plan) has been identified, project performance will be communicated in multiple

ways, including but not limited to: AEP, LTEP, and Assurance (CNP) over a variety of flood

events as shown in the Table 1, to include at least the 2%, 1%, and 0.4% annual exceedance events.

When it is necessary to communicate performance in simpler terms for this plan, then the

exceedance probability at which the project performs with 90% Assurance must be used in

feasibility, design, and in communications with the public. Performance for a project having the

example data in Table 1 may be communicated as: “Given irreducible uncertainties inherent in

flood frequency analysis, the NED Plan will pass the 2% event with 90% assurance.” This is

consistent with standard engineering practice and with the risk expectations of the public.

ER 1105-2-101 ● 15 July 2019 10

Appendix A

Example Displays of Project Engineering and Economic Performance

Results from Risk Assessment

To report probabilistic outputs, a selection of these tables and figures, along with an

accompanying textual explanation, should be chosen to communicate uncertainty information.

This information can be useful in aiding decisions by local sponsors, stakeholders, and Federal

officials by helping to increase their understanding of the uncertainty inherent in each alternative.

A-1. Table A1 contains the EAD for the without-project condition and the with-project

condition for each alternative. The computed values of EAD are uncertain, and their probability

distributions, resulting from the risk and uncertainty assessment described in this ER, are

represented in various ways. The values of EAD reported are each the mean of the probability

(uncertainty) distribution of that alternative. The damage reduced (without-project minus with-

project EAD) is reported with more information about its probability (uncertainty) distribution.

In addition to the mean, the standard deviation and the quartiles of the distribution are included.

The standard deviation describes the width of the probability distribution. The quartiles are the

values of the probability distribution with cumulative probabilities of 25, 50, and 75 percent—

meaning there is the specified likelihood that the value will be greater than the quartile, so these

values describe both the width and the asymmetry of the probability distribution. There is a 50

percent chance that the actual value of damage reduced is between the 0.25 and 0.75 quartiles.

The 0.5 quartile is the median estimate, meaning there is a 50 percent chance the actual value is

greater, and 50 percent chance it is less. The median differs from the mean when the probability

distribution is asymmetrical.

Table A1

Expected value and probabilistic values of EAD and EAD reduced

Alternative

EAD

($1,000)

Damage Reduced

($1,000)

Uncertainty in EAD Reduced;

Probability Distribution

Quartiles ($1,000)

Without

Alternative

With

Alternative

Mean

Standard

Deviation

0.75

0.50*

0.25

20-ft (6-m) levee

575

220

355

316

353

393

25-ft (8-m) levee

575

500

451

503

555

30-ft (9-m) levee

575

570

502

573

626

Channel

575

200

375

328

370

415

Detention basin

575

250

325

263

325

388

Relocation

575

220

355

313

353

396

* The 0.5 quartile is the median estimate; it differs from the mean when the probability distribution is asymmetrical.

A-2. Table A2 provides the same information about annual cost as Table A1 provides for

damage reduced.

ER 1105-2-101 ● 15 July 2019 12

Table A2

Expected value and probabilistic values of costs

Alternative

Annual Cost

($1000)

Uncertainty in Cost;

Probability Distribution Quartiles ($1000)

Mean

Standard

Deviation

0.75

0.50

0.25

20-ft (6-m) levee

300

273

300

327

25-ft (8-m) levee

400

370

400

430

30-ft (9-m) levee

550

510

550

590

Channel

300

280

300

320

Detention basin

275

268

275

282

Relocation

250

237

250

263

A-3. Figure A1 contains a summary of the expected (mean) values of benefits (damage reduced)

and Costs, and more probabilistic information about the Net Benefits (benefits minus costs). The

probability distribution of net benefits is described by the expected (mean) value, the standard

deviation, and the quartile values, as described in Table A1. In addition, the probability that net

benefits are in fact greater than zero is included. The graphs display the entire cumulative

probability distribution of net benefits for two of the alternatives (25-ft (8-m) levee, Relocation),

with markers for the quartiles, a solid vertical line for the mean, and a horizontal arrow

Figure A1. Expected value and probabilistic values for net benefits

ER 1105-2-101 ● 15 July 2019 13

noting the probability that Net Benefit is greater than zero. Notice the inter-quartile range (the

horizontal distance between the 0.75 and 0.25 quartile) is wider for the 25-ft (8-m) levee

alternative than for the Relocation alternative. This difference demonstrates the greater

uncertainty in the net benefits. Table A1 and Table A2 show greater uncertainty in both the

damage reduced and the cost of the 25-ft (8-m) levee alternative, leading to greater uncertainty in

the net benefits.

A-4. Figure A2 contains the same probabilistic information for the B/C ratio as Figure A1

displays for the net benefits. For actual reporting purposes, each graph should be labeled to

include the name of the alternative plan (not shown here and subsequent figures).

Figure A2. Expected value and probabilistic values for B/C ratios

A-5. The Relocation alternative has the highest mean net benefit, closely followed by the 25-

foot (8-m) levee alternative. The range of benefits and costs associated with the Relocation

alternative is also substantially smaller than the range seen with the 25-ft (8-m) levee alternative

as seen in the standard deviation and the inter-quartile range (difference between 75 and 25

percent quartiles). Also, the Relocation alternative has the largest probability of net benefits

being greater than zero (or, B/C ratio being greater than one.) Further note that the mean is not

equal to the 50 percent quartile (the median), which a result of the distribution not being

symmetrical.

A-6. Benefits divided by costs produce B/C ratios. From this, the probability of maintaining a

B/C ratio greater than one is of interest. This example shows that the Relocation alternative has

a probability of 97 percent of the B/C ratio being greater than one, while the probability of the

ER 1105-2-101 ● 15 July 2019 14

25-ft (8-m) levee alternative has a probability of 87 percent of the B/C ratio being greater than

one. At this point only economic justification has been determined.

A-7. Table A3 and Table A4 present the expected or mean AEP and LTEPs computed for each

alternative. The LTEP is the likelihood of exceedance at least once in the specified period and is

computed as 1 - (1 - AEP)

, where N = number of years. Table A3 shows the LTEPs in the

standard manner, and Table A4 displays LTEP in terms of return periods and odds.

Table A3

Performance described by AEP and LTEP

Alternative

Mean

AEP

LTEP

(Probability of Exceedance Over

Indicated Time)

10 Years

30 Years

50 Years

Without

0.250

0.94

1.00

20-ft (6-m) levee

0.020

0.18

0.45

0.64

25-ft (8-m) levee

0.010

0.10

0.26

0.39

30-ft (9-m) levee

0.001

0.01

0.03

0.05

Channel

0.025

0.22

0.53

0.72

Detention basin

0.030

0.26

0.60

0.78

Relocation

0.020

0.18

0.45

0.64

Table A4

Performance described by AEP and LTEP (alternative display)

Alternative

Mean

AEP

LTEP

(Probability of Exceedance Over

Indicated Time)

10 Years

30 Years

50 Years

Without

0.250

1 in 1.1

1 in 1.0

20-ft (6-m) levee

0.020

1 in 5.5

1 in 2.2

1 in 1.6

25-ft (8-m) levee

0.010

1 in 10.5

1 in 3.8

1 in 2.5

30-ft (9-m) levee

0.001

1 in 100.5

1 in 33.8

1 in 20.5

Channel

0.025

1 in 4.5

1 in 1.9

1 in 1.4

Detention basin

0.030

1 in 3.8

1 in 1.7

1 in 1.3

Relocation 0.020 1 in 5.5 1 in 2.2 1 in 1.6

A-8. AEP and LTEP are useful tools to explain the residual probability of flooding for an

alternative. AEP can represent the probability of any event equaling or exceeding a specified

stage in any given year. With levees present, the stage would be the top of levee or effective top

of levee as specified by the geotechnical fragility curves; therefore, AEP represents the

probability of water getting into the interior area of the levee in any given year. In the software

HEC-FDA (Reference 4i), for non-leveed reaches the target stage is determined by the

ER 1105-2-101 ● 15 July 2019 15

exceedance of a percentage of the mean damage associated with a specified event (e.g., the 1

percent AEP event). The without-project and the relocation project have different AEP values

although the hydrology and hydraulics remain the same. LTEP is a way of describing the

probability of flooding over a long period of time, for instance, the project’s lifecycle or the life

of a typical mortgage. As Tables A-3 and A-4 show, percentages or odds can be used to describe

the chance of flooding. As shown in Tables A-3 and A-4, the 30-ft (9-m) levee alternative has

the lowest AEP and LTEP of 1 in 20.5 over 50 years.

A-9. Figure A3 presents the resultant probability (uncertainty) distribution of the AEP, described

by the mean value, the standard deviation, and the quartile values. The standard deviation

describes the width of the probability distribution. The quartiles are the values of the probability

distribution with cumulative probabilities of 25, 50, and 75 percent—meaning there is the

specified likelihood that the value will actually be greater than the quartile, so these values

Figure A3. AEP uncertainty

describe both the width and the asymmetry of the probability distribution. There is a 50 percent

chance that the actual value of damage reduced is between the 0.25 and 0.75 quartiles, while the

0.5 quartile is the median estimate, meaning there is a 50 percent chance the actual value is

greater, and 50 percent chance it is less. The median differs from the mean when the probability

distribution is asymmetrical.

ER 1105-2-101 ● 15 July 2019 16

A-10. As with any risk assessment, not only is the mean of an uncertainty distribution important,

the entire probability distribution for the metric should be considered and compared. A

comparison of the mean AEP for each alternative and the 50 percent quartile, or a look at all

three quartiles, makes it apparent that the distributions of AEP may not be symmetrical. Figure

A3 displays the entire cumulative probability distribution of AEP for two of the alternatives (25-

ft (8-m) levee, Relocation), with markers for the quartiles and a dotted vertical line for the mean.

The plots in Figure A3 provide information that summarizes the uncertainty. For example, the

25-ft (8-m) levee alternative clearly offers higher performance when considering the mean AEP

and the three quartiles, but it also has a longer “tail” so it has a greater chance that the AEP could

be much higher. The Relocation alternative has a shorter tail, and so has less chance that AEP

could be much higher. Another way to understand the uncertainty is if considering the likelihood

the AEP is actually greater than 2 percent, for the 25-ft (8-m) levee alternative, the chance is 22

percent, and for the Relocation alternative, the chance is 55 percent that AEP is greater than 2

percent.

A-11. Table A5 presents the mean AEPs for each alternative along with AEPs of other possible

natural disasters in the area of interest. Evaluating risk associated with an area can be hard

unless compared to events that people can more readily understand.

Table A5

Probability comparison

Alternative

AEP

Without

0.250

20-ft (6-m) levee

0.020

25-ft (8-m) levee

0.010

30-ft (9-m) levee

0.001

Channel

0.025

Detention basin

0.030

Relocation

0.020

Comparable Probability

Fire Damage

0.003

Wind Damage

0.005

Earthquake

0.001

Average 2002–2010 based on home structure fires National Fire Protection Association and U.S. Census housing unit data.

Annual probabilities for other hazards are region specific. Values provided here are for illustrative purposes only.

A-12. Figure A4 contains the Assurance (also CNP) levels, for each alternative for various

exceedance probabilities. These values describe the estimated likelihood that the project can

prevent damage at the specified exceedance probability. The Assurance is based on the

uncertainty in the actual flow and stage associated with a given exceedance probability event, as

well as the geotechnical performance of the project.

ER 1105-2-101 ● 15 July 2019 17

Figure A4. Assurance (also CNP)

A-13. To capture Assurance (also CNP), the upper graphic in Figure A4 shows the uncertainty in

the stage versus frequency (exceedance probability) relationship. That probability (uncertainty)

distribution is then compared to the target stages associated with each alternative to provide

Assurance (also CNP). The lower graphic in Figure A4 shows the probability (uncertainty)

distribution of stage for the 1 percent chance event and compares it to the top of levee stage for

the 30-ft (9-m) levee alternative. The area under the Probability Density Function) curve is

summed to determine the probability of not exceeding the target stage (i.e., the non-exceedance

probability, conditioned on the occurrence of the 1 percent event).

A-14. Table A6 presents life loss estimates for each alternative of the study area. A quantitative

assessment of life loss will be required for risk assessment associated with alternatives. To

completely discuss the transference and transformations of risk, the changes in life loss

associated with all frequency events for each alternative must be discussed. Although there may

be significant decreases in economic losses and life risks for the lower frequency events, there

may be significant increases for the same alternatives at the higher frequency events. The

probability of flood occurrence times the consequence yields the overall risk reduction,

ER 1105-2-101 ● 15 July 2019 18

transformation, and transfer that are going on within the system. A narrative scenario for events

that result in flooding will also be provided, and an example is provided in Figure A5.

Table A6

Life loss

Alternative

Expected

Life Loss

Probable Life Loss for a Given Event

100

Years

250

Years

500

Years

Without

3.700

5.300

8.900

22.000

20-ft (6-m) levee

1.400

6.000

10.500

28.000

25-ft (8-m) levee

1.000

8.500

12.300

33.000

30-ft (9-m) levee

0.850

0.300

14.000

56.000

Channel

2.500

4.300

7.100

18.000

Detention basin

1.500

3.100

4.100

13.000

Relocation

0.010

0.250

0.850

1.200

Should the levees surrounding My City south of the Your River be loaded by floodwaters, residents

could attempt to move to nearby higher ground. The depth of flooding in the neighborhoods in this

area would generally not exceed that at the river's edge although a few areas would experience

flooding of more than 10 feet. New Town, on the other hand, is ringed by levees so that residents

trying to leave the area would have to find their way across the main highway system to areas of higher

ground. Limited routes of egress would make this difficult and thus negatively impacting life safety.

Moreover, because New Town is in a depression, a third of the area would flood to depths over 10 feet.

Some areas would flood to as much as 35 feet. Because of the lengthy duration of flooding and the

lack of natural drainage from this area, flood water would likely remain in New Town for 2 weeks or

more. With the proposed levee, New Town is subject to a 1 in 100 chance of being flooded in any year

but a 1 in 2.5 chance in 50 years. Therefore, the probability of a catastrophic event within the lifetime

of most residents is nearly the same as flipping a coin and getting heads. An emergency action plan

(EAP) has been developed for the communities including response training exercises. Additionally,

the low areas contain many acres of environmentally valuable wetlands that would be severely

damaged from high velocities generated from a levee failure. Resiliency measures could be

considered for each of these communities. These measures address the ability to avoid, minimize,

withstand, and recover from the adverse effects of a flood. For example, both communities have

developed and implemented EAPs including response training exercises. An EAP speaks to the

ability to avoid or minimize damage to structural inventories or reduce the population at risk.

Resiliency measures for a levee can be provided by adding superiority increments to the levee in

higher hazard areas and surface hardening in planned levee overtopping reaches adjacent to low

hazard areas. Resiliency provides a higher degree of predictability for levee performance that can be

useful for floodplain managers and project operators.

SOURCE: Adapted from: National Research Council. 1995. Flood Risk Management and the American River Basin: An

Evaluation. Washington, DC: National Academy Press.

Figure A5. Example scenario

ER 1105-2-101 ● 15 July 2019 19

Glossary

Abbreviations and Terms

To describe effectively the concepts of a risk framework for flood risk management studies, this

Engineer Regulation uses the following terminology:

AEP Annual Exceedance Probability

B/C Benefit/Cost

CNP Conditional Non-Exceedance Probability

EAD Expected Annual Damage

EAP Emergency Action Plan

EC Engineer Circular

EM Engineer Manual

EP Engineer Pamphlet

ER Engineer Regulation

FEMA Federal Emergency Management Agency

HEC-FDA (used in reference h. on page 1)

HQUSACEU.S. Army Corps of Engineers Headquarters

LOP Level of Protection

LTEP Long-Term Exceedance Probability

NED National Economic Development

PAR Population at Risk

PMP Project Management Plan

SPF Standard Project Flood

USACE U.S. Army Corps of Engineers

ER 1105-2-101 ● 15 July 2019 20

Definitions

Annual Exceedance Probability (AEP)

The probability that a certain threshold may be exceeded at a location in any given year,

considering the full range of possible values, and if appropriate, incorporation of project

performance. A threshold consists of a metric and a value, and must be specified for each use of

AEP. If system performance is considered, then performance should be explicitly accounted for

in the description of AEP; similarly, if system performance is not considered then it can be

omitted in the description of AEP. Examples of threshold metrics include the stage, flow, surge,

and floodplain or flooding extent, and corresponding values may be stated in feet, cfs, depth, etc.

Examples of locations include a consequence area index point, a specific grid cell, or a fragility

curve location (also referred to as system response probabilities). An example statement of AEP

without performance is: “The boundary of the Federal Emergency Management Agency

(FEMA) 100-year floodplain has a 1 percent AEP, and the entire FEMA 100-year floodplain

corresponds to the aerial flooding extent where flood depths are greater than 0 feet.” An

example of AEP with performance is: “The resultant AEP with a depth greater than 0 feet at

location XX is 1% while taking into account levee performance.”

Assurance

The probability that a target stage will not be exceeded during the occurrence of a flood of

specified exceedance probability considering the full range of uncertainties. Term selected to

replace “conditional non-exceedance probability” (CNP).

Conditional Non-Exceedance Probability (CNP)

See Assurance.

Consequence

The harm that results from a single occurrence of the hazard. Consequences are measured in

terms of metrics such as economic damage, acreage of habitat lost, value of crops damaged, and

lives lost.

Economic Risk

The combination of likelihood and harm to property, infrastructure, and other assets as well as

economic systems all measured in monetary terms. A common metric of economic risk is

expected annual damage (EAD). EAD is the result of integrating the damage-probability

functions.

Expected Annual Damage (EAD)

EAD is the expected value of storm damages in any given year. Expected annual damage is

calculated by computing the area under the damage-frequency curve using a lifecycle approach.

Expected annual damage is calculated for the with- and without-project conditions. The

difference between the with- and without-project expected annual damage represents the benefit

associated with the with-project alternative.

ER 1105-2-101 ● 15 July 2019 21

Exposure

Describes who and what may be harmed by the flood hazard. Exposure incorporates a

description of where the flooding occurs at a given frequency, and what exists in that area. Tools

such as flood inundation maps provide information on the extent and depth of flooding; structure

inventories, population data, crop data, and habitat acreage provide information on the

population and property that may be affected by the flood hazard.

Hazard (flood)

The “hazard” is what causes the harm, in this case, a flood. The flood hazard is described in

terms of frequency, stage, velocity, extent, and depth.

Level of Protection (LOP)

LOP is used as a performance metric and a levee design concept that was founded on the

principle of providing a high degree of Assurance that the levee system component would neither

breach nor overtop when loaded with a specific recurrence interval flood (e.g., providing a 75-

year LOP if it could contain that event with 90 percent level of Assurance). The recurrence

interval of the flood hazard for this design principle was then used as an expression of the

performance of the levee system. The term is no longer used as it did not include residual risk or

structural performance. LOP should not be used to judge a set of alternatives or to target a

specific project size.

Long-Term Exceedance Probability (LTEP)

The probability of capacity exceedance during a specified period. For example, 30-year

exceedance probability refers to the probability of one or more exceedances of the capacity of a

measure during a 30-year period; formerly long-term risk. This accounts for the repeated annual

exposure to flood risk over time.

Project Performance

The system’s reaction to a hazard. Performance refers to the system features and the capability

to accommodate the flood hazard as a single event or load. In this manual, this would be termed

“system performance” (also termed “engineering performance”). Performance also refers to the

metric that describes the capability of the system to accommodate a single event (Assurance, also

CNP) and the full range of events (AEP and LTEP). In that light, in addition to the levee failure

probability functions, performance can also be described by the interior-exterior functions for

leveed areas, unregulated-regulated transforms for reservoirs and diversions, and elevation-

discharge functions (rating curves) for channels. These too would be considered “system

performance.” When the structural integrity of a system or system component is discussed, such

as the fragility function, the reference would be termed “structural performance.” When the

economics of a system is discussed, the reference would be termed “economic performance.”

The performance of an item is described by various elements, such as flood risk management,

reliability, capability, efficiency, and maintainability. Design and operation affect system

performance.

Probability Distribution

A relationship that describes the likelihood of each possible value of a random variable.

ER 1105-2-101 ● 15 July 2019 22

Residual Risk

The flood risk that remains in the floodplain after a proposed flood risk management project is

implemented. Residual risk includes the consequence of capacity exceedance as well as

consideration of project performance.

Resilience

As per Executive Order 13653, “Preparing the U.S. for the Impacts of Climate Change,”

resilience is the ability to anticipate, prepare for, and adapt to changing conditions and withstand,

respond to, and recover rapidly from disruptions.

Risk

The likelihood and severity of adverse outcomes; for this ER the focus is on the risk from

flooding. Risk is often measured as potential or mean life loss, property damage, and/or

ecosystem losses and may also include uncertainty over the benefits to be gained from a

proposed or actual action taken. Usually, both the likelihood and the consequence are to some

degree uncertain.

Risk Assessment

A systematic approach for describing the nature of the risk, including the likelihood and severity

of consequences. Risk assessments can be qualitative, semi-quantitative, or quantitative. Risk

assessment includes explicit acknowledgment of the uncertainties in the flood risk.

Risk Communication

A two-way exchange of information between risk assessors and those who will use the risk

assessment results or those who are affected by the risks and risk management actions. Open

communication improves the understanding of the risks by all parties and leads to improved risk

assessments and risk management decisions and outcomes.

Risk Framework

A decision-making process that comprises three tasks: risk assessment, risk management, and

risk communication.

Risk Management

A decision-making process in which risk reduction actions are identified, evaluated,

implemented, and monitored. The purpose of risk management is to take actions to effectively

reduce and manage risks identified in the risk assessment.

Robustness

The ability of a system to continue to operate correctly across a wide range of operational

conditions with minimal damage, alteration, or loss of functionality, and to fail gracefully outside

of that range; the wider the range of conditions allowing for good performance, the more robust

the system.

Safety

Thought of as the condition of being free from danger, risk, or injury. However, safety is not

something that can be absolutely achieved or guaranteed. Instead, safety is the condition to

ER 1105-2-101 ● 15 July 2019 23

which risks are managed to tolerable levels. Therefore, safety is a subjective concept based upon

individual perceptions of risks and their tolerability.

Superiority

Superiority simply means providing higher levees at all points except where initial overtopping

is desired. Superiority is an increment of the levee height that increases the likelihood that when

the system approaches capacity, controlled flooding will occur at a specified overtopping section.

Transferred Risk

A result of an action taken in one region of a system to reduce risk, where that action shifts the

risk burden to another region in the system. For example, if a levee is raised in one reach of a

system, thus containing more flow and thereby reducing risk in that reach, that action then results

in increased flow downstream to another reach of the system. Risk has been “transferred” from

one location to another.

Transformed Risk

New risk of flooding that emerges or increases as a result of mitigating another risk. The

magnitude and nature of the risk of flooding is different with a levee compared with conditions

without a levee. A levee reduces the likelihood that originally protected property will be flooded

but may set the stage for development that puts new property at risk. A levee transforms the

flood risk from one that may be gradual and observable before emergency action would be

necessary for the originally protected properties to flood risk that may be sudden and

catastrophic.

Uncertainty

Uncertainty is the result of imperfect knowledge concerning the present or future state of a

system, event, situation, or (sub) population under consideration. Uncertainty leads to lack of

confidence in predictions, inferences, or conclusions. It is important to distinguish uncertainty

that results from a lack of knowledge from the uncertainty that results from natural variability.

Knowledge Uncertainty

Lack of knowledge regarding the true value of a quantity. Uncertainty is a consequence of

reliance on limited data and on conceptual and mathematical models. This category of

uncertainty is formally labeled epistemic uncertainty. Uncertainty is a measure of imprecision of

knowledge of parameters and functions used to describe the hydraulic, hydrologic, geotechnical,

and economic aspects of a project plan.

Natural Variability

The distribution or spread of values within a natural “population” or data set. This array of

possible values in a population is caused by the inherent randomness of natural or social systems

and is formally labeled aleatory uncertainty. The values in the statistical population have some

probability distribution, and only limited knowledge of the entire statistical population and the

probability distribution may exist. Sometimes variability is classed as a type of uncertainty

although generally it should not be confused or interchanged with uncertainty as defined above.

ER 1105-2-101 ● 15 July 2019 24

Variability is the notion that there is a range of possible values that will occur and not the lack of

knowledge about that range or the distribution of those values.

Vulnerability

The susceptibility of harm to human beings, property, and the environment when exposed to a

hazard. Depth-damage functions, depth-mortality functions, and other similar relationships can

be used to describe vulnerability.

ER 1105-2-101 ● 15 July 2019 25