Appendix A

Glossary

Aggregated stage–damage function with uncertainty –

A composite median stage–damage function for a damage reach. The function is developed by damage categories at the damage reach index location. The stage– damage functions of individual structures are aggregated using a series of water surface profiles to account for the slope in the profiles throughout the reach. Uncertainty, the error in the damage estimates, may also be computed.

Aleatory uncertainty –

See “natural variability.”

Annual exceedance probability –

The probability that flooding will occur in any given year considering the full range of possible annual flood discharges.

Base flood –

The median flood discharge having a 1 percent chance of being equaled or exceeded in any given year.

Bulletin 17B –

A U.S. Geological Survey publication entitled Guidelines for Determining Flood Flow Frequency (USGS, 1982). The publication describes procedures for developing discharge–frequency functions using stream flow records. These procedures are recommended for all federal agency applications.

Conditional nonexceedance probability

The probability that failure will not occur during a flood of a given frequency. For example, a levee



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RISK ANALYSIS AND UNCERTAINTY IN FLOOD DAMAGE REDUCTION STUDIES Appendix A Glossary Aggregated stage–damage function with uncertainty – A composite median stage–damage function for a damage reach. The function is developed by damage categories at the damage reach index location. The stage– damage functions of individual structures are aggregated using a series of water surface profiles to account for the slope in the profiles throughout the reach. Uncertainty, the error in the damage estimates, may also be computed. Aleatory uncertainty – See “natural variability.” Annual exceedance probability – The probability that flooding will occur in any given year considering the full range of possible annual flood discharges. Base flood – The median flood discharge having a 1 percent chance of being equaled or exceeded in any given year. Bulletin 17B – A U.S. Geological Survey publication entitled Guidelines for Determining Flood Flow Frequency (USGS, 1982). The publication describes procedures for developing discharge–frequency functions using stream flow records. These procedures are recommended for all federal agency applications. Conditional nonexceedance probability – The probability that failure will not occur during a flood of a given frequency. For example, a levee

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RISK ANALYSIS AND UNCERTAINTY IN FLOOD DAMAGE REDUCTION STUDIES may have a 90 percent chance of not being overtopped when exposed to a 100-year flood. Confidence limit curves – Error limit curves about a log-Pearson Type III discharge–probability function developed using the noncentral t distribution. Confidence limit curves are used to define the discharge –exceedance probability function's uncertainty. Design flood – The flood that a flood damage reduction project, such as a levee, is based upon. Often the 100-year flood. Discharge–exceedance probability – The relationship of peak discharge to the probability of that discharge being exceeded in any given year. Egress – The ability to evacuate an area threatened by flood. Epistemic uncertainty – See “knowledge uncertainty.” Equivalent record length – Number of years of a systematic record of recorded peak discharges at a stream gage. For probability functions derived at ungaged locations using model or other data, the equivalent record length is estimated based on the overall “worth” or “quality” of the frequency function expressed as the number of years of record. This parameter is important in risk-based analysis because it relates directly to the uncertainty of the flood –discharge probability function. Exceedance probability event – The probability that a specific event will be equalled or exceeded in any given year. For example, the 0.01 exceedance probability event has 1 chance in 100 of occurring in any given year. Expected annual damage – In risk-based analysis, the average or mean of all possible values of damage determined by Monte Carlo sampling of discharge–exceedance probability, stage–discharge, and stage–damage relationships and their associated uncertainties. Calculated as the integral of the damage–probability function. FEMA – U.S. Federal Emergency Management Agency. FEMA administers the National Flood Insurance Program (NFIP) and is jointly responsible (with the U.S. Army Corps of Engineers) for levee certification within the NFIP.

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RISK ANALYSIS AND UNCERTAINTY IN FLOOD DAMAGE REDUCTION STUDIES FIA – Flood Insurance Administration. The federal entity within the Federal Emergency Management Agency responsible for administering the National Flood Insurance Program. Flood damage reduction actions – Measures and actions taken to reduce flood damage. These may include implementation of reservoirs, detention storage, channels, diversions, levees and floodwalls, interior systems, flood-proofing, raising, relocation, and flood warning and preparedness actions. Flood–frequency curve – A graph showing the average interval time (or recurrence interval) within which a flood of a given magnitude will be equaled or exceeded in any given year. Freeboard – An addition to a levee's design height to ensure against overtopping during the design flood. Hydrology and hydraulics – Hydrology involves the estimation of the amount and shape of the runoff–discharge hydrographs throughout the study area. It also includes the frequency of the events. Hydraulics involves analysis of stream water surface profiles, flood inundation boundaries, and other technical studies of stream flow characteristics. Knowledge uncertainty – Uncertainty arising from imprecision in analysis methods and data. Level of protection – A measure in years of the average interval between failures of a flood prevention system such as a levee. Log normal distribution – A two-parameter probability distribution defined by the mean and standard deviation. A nonsymmetrical distribution applicable to many kinds of data sets where the majority (more than half) of values are less than the mean but where values greater than the mean can be extreme, such as with stream flow data. Monte Carlo analysis – A method that produces a statistical estimate of a quantity by taking many random samples from an assumed probability distribution, such as a normal distribution. The method is typically used when experimentation is infeasible or when the actual input values are difficult or impossible to obtain.

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RISK ANALYSIS AND UNCERTAINTY IN FLOOD DAMAGE REDUCTION STUDIES Natural variability – Uncertainty arising from variations inherent in the behavior of natural phenomena (e.g., severity of the maximum flood in any year). NED – National Economic Development. The water resources project planning alternative designed to maximize national economic development, consistent with protecting the nation's environment, and pursuant to national environmental statutes, applicable executive orders, and other federal planning requirements. The NED alternative is required by the Principles and Guidelines (P&G, see below) to be identified in Corps feasibility studies. NFIP – National Flood Insurance Program, enacted by the federal government in 1968 to provide flood insurance for communities and structures at risk of flooding. Nonstructural measures – Measures such as raising, relocating, flood-proofing, and regulatory and emergency actions associated with structures and damageable property that modify the existing and/or future damage susceptibility. Nonstructural measures are not designed to directly affect the flow of flood waters. Normal distribution – A two-parameter probability distribution defined by the mean and standard deviation. A symmetrical “bell shaped” curve applicable to many kinds of data sets where values are equally as likely to be greater than and less than the mean. Also called the Gaussian distribution. One-hundred-year flood – A median flood discharge having a 1 percent chance of being equaled or exceeded in any given year. P&G – Principles and Guidelines. A 1983 U.S. Water Resources Council document that provides water resource project planning guidance to the U. S. Corps of Engineers, the Bureau of Reclamation, the Natural Resources Conservation Service, and the Tennessee Valley Authority. Probability function – A discharge–exceedance or stage–exceedance probability relationship for a reach developed by traditional, site-specific, hydrologic engineering analysis procedures.

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RISK ANALYSIS AND UNCERTAINTY IN FLOOD DAMAGE REDUCTION STUDIES Residual risk – The portion of the flood risk that still exists with the flood damage reduction project implemented. Return period – The average time interval between occurrences of a hydrological event of a given or greater magnitude, usually expressed in years. Risk – The probability of failure during a flood event. For reaches without levees, failure means exceeding a target stage. For reaches with levees, it means a levee failure. Skewness coefficient – A statistic used as a measure of the symmetry of the statistical distribution of data. It is the third moment of a distribution. It is estimated as the number of values times the sum of the cubes of the deviations from the mean divided by the number of values minus 1, times the number of values times 2, times the standard deviation cubed. Stage – The vertical distance in feet (meters) above or below a local or national elevation datum. Stage associated with the median 1-percent chance flood discharge – The stage taken from the stage–discharge curve that corresponds to a discharge taken from the discharge –probability curve of 1 percent. Stage–damage function – Relationship of depth of water to damage at a structure. Damage is normally specified as a percentage of the structure or content value. The functions are generic for similar structures and are not tied to the structure location. Stage–damage functions with uncertainty – Stage–damage functions with uncertainty are computed at each structure and aggregated by damage category to damage reach index locations. Stage is elevation or locally referenced stage associated with the structure and index location. Damage is the median estimate of structure, content, and other inundation reduction damage associated with the stage of floodwaters at the location. Uncertainty in the stage–damage function arises from to errors in estimating the depth–damage function, first-floor stage, structure value, and content-to-structure-value ratio. Stage–discharge function – A graphical relationship that yields the stage for a given discharge at a specific location on a stream or river.

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RISK ANALYSIS AND UNCERTAINTY IN FLOOD DAMAGE REDUCTION STUDIES Referred to as a rating function or curve. These relationships are usually developed by computing water surface profiles for several discharges and plotting the stages vs. discharge relationship at a specific stream location. Stage–discharge functions with uncertainty – Relationship of the water surface stage and discharge. Uncertainty is the distribution of the errors of stage estimates about a specific discharge. Standard deviation – A statistical measure of the spread of a distribution around the mean. Structural measures – Those water resources project measures designed to modify the flow of flood waters. Uncertainty – A measure of the imprecision of knowledge of variables in a project plan.