This glossary is a collection of definitions located throughout HEC-SSP Documentation plus definitions of other pertinent statistical terms. Many of the definitions herein are from the electronic glossaries available from U.S. Geological Survey and the Bureau of Reclamation.

Additional terms commonly used within USACE Flood Risk Management studies can be found here: Key USACE Flood Risk Management Terms.

A

A14: NOAA Atlas 14. A multi-volume document produced by the NWS Hydrometeorological Design Studies Center that contains precipitation-frequency estimates across the United States. Not all areas are covered by a volume of A14, most notably the Northwest.

ACE: annual chance exceedance

AEP: annual exceedance probability

AMS: annual maximum series. A sample containing the largest observation of some variable from each year.

AORC: Analysis of Record for Calibration, a high-resolution meteorological dataset created by assimilation of multiple input datasources including NEXRAD radar, satellite precipitation estimation, and gage data.

ARF: area reduction function/factor. A means for generalizing the behavior of area-averaged precipitation based on the point maximum intensity.

ARI: average return interval

B

Balanced hydrograph: a flood hydrograph pattern in which any nested duration has the same frequency; e.g. the 1-day, 2-day, 3-day, and 4-day volumes all have 1% AEP.

Balanced hyetograph: a storm temporal pattern in which any nested duration has the same frequency; e.g. the 1-hour, 3-hour, 6-hour, 12-hour, and 24-hour totals all have 1% AEP.

B17B: Bulletin 17B (Interagency Advisory Committee on Water Data, 1982).

B17C: Bulletin 17C (England, et al., 2019)

C

Climate division: https://www.ncei.noaa.gov/access/monitoring/reference-maps/conus-climate-divisions

Constrained observation: a time-dependent observation that reflects the systematic method the observations are taken. An example is observations that are taken at 1 calendar day intervals - the maximum of these kinds of observation might be the largest 1 calendar day observation, but not the largest 24 hour observation, which may span two days.

CV: coefficient of variation. A dimensionless measure of dispersion calculated as the standard deviation divided by the mean. May also be called the relative standard deviation. Should only be applied to ratio data (absolute scales), not interval data (relative scales.)

Correlation: The process of establishing a relation between a variable and one or more related variables. Correlation is simple if there is only one independent variable and multiple when there is more than one independent variable. For gaging station records, the usual variables are the short-term gaging-station record and one or more long-term gaging-station records.

D

DAD: Depth-area-duration, an idealized way of representing the spatial-temporal pattern of a precipitation event

DDF: Depth-duration-frequency, a generalization of precipitation-frequency analysis results

E

EAD: expected annual damages

ERL: equivalent record length.  A measure of information content in a regional analysis based on counting the number of independent storms in the regionally-pooled observations.  Also referred to as "equivalent independent record length (EIRL)".

EURL: equivalent uncorrelated record length. A measure of information content in a regional analysis that accounts for the inflation of variance caused by correlation between stations.  It is a generalization of EIRL.

EVT: extreme value theory, the branch of statistics dealing with the behavior of extremes such as the largest or smallest value of repeated samples, all values over a given threshold, etc.

EVT1: the first extreme value theorem, a.k.a. the Fisher-Tippett-Gnedenko theorem. IID block maxima converge in distribution to the GEV distribution.

EVT2: the second extreme value theorem, a.k.a. the Pickands-Balkema-de Haan theorem. Independent samples of a homogeneous population exceeding a sufficiently high threshold converge in distribution to the generalized Pareto distribution.

EMA: Expected Moments Algorithm

F

FFRD: Future of Flood Risk Data; a FEMA initiative featuring exploratory projects meant to define the future direction of the flood insurance mapping program.

Flood: An overflow or inundation that comes from a river or other body of water, and causes or threatens damage. Any relatively high streamflow overtopping the natural or artificial banks in any reach of a stream. A relatively high flow as measured by either gage height or discharge quantity.

Flood Crest: See flood peak.

Flood Event: See flood wave.

Flood Peak: The highest value of the stage or discharge attained by a flood; thus, peak stage or peak discharge. Flood crest has nearly the same meaning, but since it connotes the top of the flood wave, it is properly used only in referring to stage—thus, crest stage, but not crest discharge.

Floodplain: A strip of relatively flat land bordering a stream, built of sediment carried by the stream and dropped in the slack water beyond the influence of the swiftest current. It is called a living flood plain if it is overflowed in times of highwater; but a fossil flood plain if it is beyond the reach of the highest flood. The lowland that borders a river, usually dry but subject to flooding. That land outside of a stream channel described by the perimeter of the maximum probable flood.

Flood Profile: A graph of elevation of the water surface of a river in flood, plotted as ordinate, against distance, measured in the downstream direction, plotted as abscissa. A flood profile may be drawn to show elevation at a given time, crests during a particular flood, or to show stages of concordant flows.

Flood Routing: The process of progressively determining the timing and shape of a flood wave at successive points along a river.

Flood Stage: The gage height of the lowest bank of the reach in which the gage is situated. The term "lowest bank" is, however, not to be taken to mean an unusually low place or break in the natural bank through which the water inundates an unimportant and small area. The stage at which overflow of the natural banks of a stream begins to cause damage in the reach in which the elevation is measured. See also bankfull stage.

Flood Wave: A distinct rise in stage culminating in a crest and followed by recession to lower stages.

Flood-Frequency Curve: A graph showing the number of times per year on the average, plotted as abscissa, that floods of magnitude, indicated by the ordinate, are equaled or exceeded. Also, a similar graph but with recurrence intervals of floods plotted as abscissa.

Floodway: A part of the floodplain otherwise leveed, reserved for emergency diversion of water during floods. A part of the floodplain which, to facilitate the passage of floodwater, is kept clear of encumbrances. The channel of a river or stream and those parts of the floodplains adjoining the channel, which are reasonably required to carry and discharge the floodwater or floodflow of any river or stream.

Flow-Duration Curve: A cumulative frequency curve that shows the percentage of time that specified discharges are equaled or exceeded.

Fluvial Flooding: inundation caused by riverine flooding instead of overland flow or infiltration excess (to contrast pluvial flooding).

G

GEV: the generalized extreme value distribution. It is the probability distribution of IID block maxima, and generalizes the three extreme value distributions (Gumbel, Fréchet, Weibull).

GPA: the generalized Pareto distribution.  It is the probability distribution of IID excesses of a sufficiently high threshold.  GPD is also sometimes used.

GPD: see GPA

H

Heterogeneous/heterogeneity: having different properties (or the degree to which the properties are different).  May also be called "inhomogeneous/inhomogeneity."

Heteroscedasticity: a circumstance in which the variability of a variable of interest is unequal across the range of values of a second variable that predicts it (e.g., flow vs. stage where the variability of flow changes drastically as the stage increases in a typical, incised cross section with a very wide flood plain)

Homogeneous/homogeneity: having the same properties (or the degree to which the properties are similar)

HUC: hydrologic unit code, a unique numeric identifier of watersheds in the United States

I

IID: independent and identically distributed

Isopluvial: Greek for "same rainfall", in the precipitation frequency context, a map showing the precipitation depth for the same AEP and duration everywhere

K

Kriging: an interpolation method that relies on Gaussian processes to describe the relationship between variables across dimensions. Typical application is in 2-dimensional spatial statistics. Kriging is a complicated topic and this definition does not do it justice.

L

L-moments: a descriptor of the shape of a sample or population of data using linear combinations of the values in the dataset.  Also, a fitting method which assumes that the parameters of the sample (child population) are the same as the parent population.  Unequal weights are given to order statistics of observations based upon their ranks.

LPIII: Log-Pearson Type III distribution

LP3: see LPIII

LMRD: L-moment ratio diagram. A plot of L-skewness vs. L-kurtosis that can be used for characterizing sample data and probability distributions.

M

MLE: Maximum Likelihood Estimation.  A fitting method which maximizes a likelihood function such that the observed data is most probable under an assumed statistical model.

MOM: method of moments (see also Product Moments).  A fitting method which assumes that the parameters of the sample (child population) are the same as the parent population.  Equal weights are given to the transformations of the observations.

Mixed populations: refers to flood series comprised of floods caused by different physical processes.

N

NARR: North American Regional Reanalysis; an NCEP reanalysis product for North America

NCEP: National Centers for Environmental Prediction

Non-stationarity: a sample that has properties that are not constant across a dimension; e.g. a time series with a trend

NWS: National Weather Service

O

Objective Function: A mathematical expression that allows comparison between a calculated result and a specified goal. In the program, the objective function correlates calculated discharge with observed discharge. The value of the objective function is the basis for calibrating model parameters.

P

PDS: partial duration series; also called "peaks over threshold." A sample containing all independent observations of some variable greater than a chosen value.

PF: precipitation-frequency

PFDS: Precipitation Frequency Data Server. NOAA/National Weather Service/Hydrometeorological Design Studies Center source for information related to precipitation frequency analysis. https://hdsc.nws.noaa.gov/hdsc/pfds/

Pluvial flooding: inundation caused by precipitation instead of flowing from a river (to contrast fluvial flooding).  Can be caused by overland flow or infiltration excess.

PMF: probable maximum flood

PMP: probable maximum precipitation

Point-to-area reduction: accounting for the difference between the maximum intensity of rainfall at a point, and the average intensity over a larger area. Synonyms: depth-area-reduction, area reduction factor

POR: period of record

POT: peaks over threshold (see PDS)

Product Moments: a numerical description of the shape of a dataset or model.  These moments describe various shape properties of a dataset or model.

PWM: probability-weighted moments

Q

Quasi-Continuous: a hydrologic modeling technique that mimics continuous modeling in an "event mode" by randomly selecting the event date and dependent initial conditions, to capture the full range of variability in hydrologic conditions for design storm modeling.  The initial conditions are drawn from a POR continuous hydrologic simulation.

R

Region/regionalization: a collection of sites grouped together based on similarity that is used to improve estimates for the properties of extremes in that area. In the SWT method, this is typically one of the NWS climate divisions, which is viewed as meteorologically but not necessarily statistically homogeneous

ROI: region of influence. A regionalization method that treats each station as the nucleus of a number of other, homogeneous stations, that form a region. The process is repeated for every station in the study area.

RRFA: regional rainfall-frequency analysis

S

Site: a location where observations of the hydrometeorological variable of interest are taken

Space-for-time substitution: using collections of similar observations of extremes across a geographic extent to increase the effective number of observations of those extremes

Spatial regression: a regression analysis where the predictor(s) and predictand are linked by being co-located in space

SST: stochastic storm transposition

Stationarity: in typical usage, constant with respect to time. More generally, a process does not display trends in any parameter across any dimension. The mean and variance are constant with respect to time (or space, in the case of spatial statistics.)

Station-year: total number of years of record when aggregated over a number of stations. For example, there are 60 station-years in an area where there are two stations, one with 35 years of record, and one with 25.

Storm typing: identifying the causal mechanism behind all rainfall events from a meteorological basis

Sub-region: a subset of sites within a region that offers some refinement of region characteristics, typically used to improve estimates of spatial variability. In the SWT method these are statistically homogeneous collections of sites within a climate division

SWT method: the Schaefer-Wallis-Taylor climate regions method for regionalization of frequency estimates, involving coarse regionalization of sites using common climate divisions, fine regionalization using statistical homogeneity tests, and estimation of L-moments using spatial regression

T

Tobler's First Law of Geography: “Everything is related to everything else, but near things are more related than distant things.”

W

Water Year: The 12-month period, October 1 through September 30. The water year is designated by the calendar year in which it ends and which includes 9 of the 12 months. Thus, the year ended September 30, 1959, is called the 1959 water year.