Introduction
The Hydrologic Frequency Analysis Work Group is a work group of the
Hydrology Subcommittee of the Advisory Committee on Water Information
(ACWI). The Terms of Reference of this work group were approved by
the Hydrology Subcommittee on October 12, 1999 and are available on
the ACWI web page. The work group was formed to provide guidance on
issues related to hydrologic frequency analysis and replaced the
Bulletin 17B Work Group that had existed since 1989. The Hydrologic
Frequency Analysis Work Group is open to individuals from public and
private organizations. The current members of the work group are also
given on the ACWI web page. The initial objectives of the work group
are to
 Develop a set of frequently asked questions and answers on the
use of Bulletin 17B guidelines,
 Prepare a position paper that provides guidance on determining the
most appropriate methodology for flood frequency analysis for ungaged
watersheds, and
 Prepare a position paper on methodologies for flood frequency
analysis for gaged streams whose upstream flows are regulated by
detention structures.
In response to the first objective above, the work group has prepared
a list of frequently asked questions and answers that provide
additional information relative to the implementation of the Bulletin
17B "Guidelines For Determining Flood Flow Frequency", dated March
1982 and developed by the Hydrology Subcommittee of the Advisory
Committee on Water Data. These questions and answers supplement the
guidelines given in Bulletin 17B and it is envisioned that these
questions and answers will be modified or extended in the future
as better information becomes available.
Any comments on these frequently asked questions and answers or any
new questions and/or answers should be provided by email to Will Thomas, the Chair of the Hydrologic Frequency Analysis Work Group, at WTHOMAS@mbakercorp.com for review by the Work Group.
BULLETIN 17B GUIDELINES FOR DETERMINING FLOOD FREQUENCY
FREQUENTLY ASKED QUESTIONS  October 10, 2002
CONTENTS
100YEAR FLOOD
RECURRENCE INTERVAL
AVAILABILITY OF BULLETIN 17B
LAKE STAGE FLOOD FREQ
SEASONAL FLOOD FREQ
SKEW COMPUTATIONS
MIXED POPULATION
FREQUENCY OF MINOR FLOODS
DATA QUALITY
LOW OUTLIERS
HISTORICAL FLOODS AND HIGH OUTLIERS
OUTLIERS, GENERAL
LIMITS OF FREQENCY CURVE EXTRAPOLATION
===================================================================
100YEAR FLOOD
Question: What is the 100year flood? Twice in the past 10 years, government
officials have said that our river has had a 100year flood? How can this be?
Answer: The 100year flood is the stream flow rate, in cubic feet per second
(cfs) or cubic meters per second (m3/s), or the water surface elevation, in
feet or meters, that is exceeded by a flood peak in one year out of 100, on
the longrun average, or, equivalently, exceeded with a probability of 1/100
(1 percent) in any one year. The 100year terminology does not imply regular
occurrence or that a given 100year period will contain one and only one event.
The 100year flood also is called the 1percentchance flood, and this terminology
calls attention to the fact that each year there is a chance that the 100year
flood will be exceeded. Flood occurrence is a random process, largely unpredictable
over time spans longer than a few days or weeks. Thus, a rash of exceedances
of the 100year flood can occur in a short time by pure random chance and bad
luck. In addition, the true 100year flood is never known with certainty, but
must be estimated from a small sample using uncertain assumptions about the
floodgenerating processes, with the result that the estimated 100year flood
may be lower (or higher) than the true value. Finally, some caution must be
exercised in calculating and interpreting probabilities of events that have
already occurred. Consideration of pure random chance indicates that two exceedances
of the 100year flood could occur in 10 years for the same reason (and with
about twice the likelihood) that three doublesixes could occur in 10 rolls
of a pair of fair dice. The occurrence of either of these events might lead
one to wonder whether the dice really were fair or whether the 100year flood
had been underestimated. However, floods are continually occurring on thousands
of streams around the country; although the probability is small that the 100year
flood would be exceeded twice in a particular 10 year period in any particular
location, the fact that it happened during some 10year period, somewhere in
the country, is not surprising, and the fact that it happened on your river,
rather than someone else's, should not be taken as an indication of anything
wrong.
RECURRENCE INTERVAL
Question: What is a recurrence interval? My house was damaged by a
flood last year, and I'm using my floodinsurance payment to make some improvements
as well as repairs. A government report said that the recurrence interval was
100 years, and my friend who's doing the work says that it's safe to make the
improvements, because another flood won't occur for 99 more years. Is that right?
Answer: A recurrence interval (also called a return period) is the expected
(or average) length of time between occurrences of events of a specified type,
such as floods that exceed a stated stage or discharge. The words "recurrence"
and "period" do not imply regular predictable occurrence in time;
the actual times between successive events may be either greater than or less
than the average. Floods occur approximately as a sequence of independent random
trials, with some probability of occurrence in each year. The average time between
occurrences is equal to the reciprocal of the annual probability of occurrence:
lowprobability events are  on average  widely spaced in time. Mathematically,
the waiting time to the next flood (from either a flood year or a nonflood
year) has the same statistical distribution as the time between floods; thus,
the recurrence interval is also the expected waiting time to the next occurrence
of the event. For example, if the chance of an overflow of the stream banks
is 50 percent (1/2) in any year, then the recurrence interval is 2 years. If
the chance of overtopping a levee, say, is 1 percent (1/100) in any year, then
the recurrence interval is 100 years. Although the average time between overtoppings
and the expected waiting time to the next overtopping are 100 years, it nonetheless
is possible that the levee is overtopped in two successive years: the probability
is 0.01 x 0.01 = 1/10,000. However, if the levee has just been overtopped this
year, the relevant probability issue is not the chance of two successive overtoppings,
but rather the chance that the levee will be overtopped again next year; that
chance is 1/100. Likewise, if the levee has not been overtopped in the past
99 years, the relevant issue is not the law of averages but rather the chance
that the levee will be overtopped next year; that chance is still 1/100. In
both cases, the probability that there will be no overtoppings in the next N
years is just the probability that the flood will be lower than the levee top
in every one of the next N years: that probability is (10.01)**N or 0.99 raised
to the Nth power; the probability of one or more overtoppings in the next N
years is 1  .99**N.
Years(N) 1 2 3 5 10 20 30 50 100 200
P{none} .99 .98 .97 .95 .90 .82 .74 .61 .37 .13
P{>=1} .01 .02 .03 .05 .10 .18 .26 .39 .63 .87
Thus, your chance of being caught by another flood before your
friend finishes his work is pretty slim, but your
chance of being flooded sometime in the next 20 years is a little
higher than the chance of losing at Russian roulette. The chance of
being flooded at some time during the term of a 30year mortgage is
a little higher than that of getting two heads on a row in coin tossing.
The importance of duration of exposure in assessment of risk is clear.
Question: The river in my town had two big floods in one year about
15 years ago, one at Easter time and the other at Labor Day. I remember because
the second one redamaged my house within a month after I finished fixing it
up after the first flood. So I was shocked when the government engineers doing
a flood study in my town didn't show both of those floods, but showed only one
flood for each year. How can a valid flood risk analysis be done if you ignore
half of the floods?
Answer: The Bulletin17B guidelines recommend a procedure for estimating flood
risk based on the maximum flood peak (the socalled "annual flood")
in each year. This analysis yields estimates of the probability that the annual
flood in any year will be greater than (or less than) any specified flow rate.
The probability that the annual flood is less than some discharge x is called
the annual nonexceedance probability for that discharge and often is denoted
F(x); it is the probability that the year will be free of floods exceeding that
level. The complementary probability 1F(x) is called the annual exceedance
probability; it is the probability that the annual flood will exceed level x
in any year. If the annual maximum flood exceeds level x in some year, it is
possible that one or more other floods, smaller than the annual maximum, might
also exceed x. Thus the annual exceedance probability is the probability of
one or more exceedances in the year. It is not the case that half the floods
are ignored; all of the floods in a year have to be examined in order to determine
the maximum  the annual flood. Although the Bulletin17B annualflood methodology
adequately answers the question it addresses  differentiating between the
likelihood of no flooding versus the likelihood of one or more floods in a year
 this information may not be sufficient to answer all questions that may be
important for flood risk evaluation and economic analysis of flood damage. Information
about the number of floods in a year or about the joint probability distribution
of flood magnitudes and dates within the year may be needed for proper evaluation
of flood damage to minor streamside facilities, especially damage due to interruption
of use of lowvolume road crossings, recreational facilities, and some industrial
and commercial facilities. These questions are outside the scope of Bulletin
17B; they may be addressed by socalled "partialduration" or "peaksaboveabase"
frequency analysis, which considers all peaks that exceed a specified flood
threshold (see Linsley,RK et al., 1982, Hydrology for Engineers, pp 359, 373374).
In more typical flood frequency applications such as flood control levees and
100year floodplain delineations, on the other hand, magnitudes of design floods
are high, corresponding annual exceedance probabilities are low, probabilities
of multiple occurrences in a year even lower, and the damages due to failure
are catastrophic and longlasting. In such cases, even if multiple floods do
occur in one year, the damage due to the first is unlikely to be repaired completely
before the second one occurs, and the total damage due to all floods in the
year may be reasonably approximated by the damage due to the maximum flood acting
alone. In these cases, then, the Bulletin17B annualflood approach provides
the floodfrequency information needed for engineeringeconomic planning and
floodrisk evaluation.
AVAILABILITY OF BULLETIN 17B
Question: Where can I obtain a copy of the publication, Guidelines
for Determining Flood Flow Frequency, Bulletin 17B?
Answer: There are two sources. A copy of the original is available from the
National Technical Information Service (NTIS), Springfield VA 22161, as report
no. PB 86 157 278. As of August 2002, the price for a paper copy from NTIS was
about $60, including shipping, and could be ordered by calling (800) 5536847.
A digital copy of Bulletin 17B is available in PDF format from the FEMA web page http://www.fema.gov/plan/prevent/fhm/ft_hydro.shtm. Click on the link to send an email to pdfarchive@floodmaps.net. The PDF document will be delivered by email. The document size is approximately 28 Mbytes."
The Bulletin 17B PDF document also is available from the USGS web page at http://water.usgs.gov/osw/bulletin17b/bulletin_17B.html
This page also has links to many of the Bulletin 17B references and to these Frequently Asked Questions
Suggested format for citation of Bulletin 17B:
U.S. Interagency Advisory Committee on Water Data, 1982,
Guidelines for determining flood flow frequency, Bulletin 17B
of the Hydrology Subcommittee: Reston, Virginia, U.S. Geological
Survey, Office of Water Data Coordination, [183 p.]. [Available
from National Technical Information Service, Springfield VA 22161
as report no. PB 86 157 278 or from FEMA on the WorldWide Web
at http://www.fema.gov/mit/tsd/dl_flow.htm ]
LAKE STAGE FLOOD FREQ
Question: Often lakes are major flood sources for communities. It is
necessary to determine the 1% annual exceedance level (stage, elevation) for
the lakes. Some lakes have more than 40 years of record for annual maximum elevation.
Can the Bulletin 17B procedure be used to estimate stage frequency curves for
these lakes?
Answer: Bulletin 17B was written for riverine floodflow
frequency analysis, not for lakelevel frequency analysis.
Although the basic Bulletin17B methodology (method of moments,
logtransformed data, Pearson Type III distribution) is not
limited to flood flows, it has not been systematically tested and
evaluated for application to lake levels. The Bulletin17B
generalized skew map does not apply to lake levels, and it may be
difficult or infeasible to develop generalized skews for lakes.
In addition, lake levels do not have the natural zero value and
the extreme variability and skewness of flood flows, so the use of
log transforms of lake levels may not be necessary or beneficial.
Thus, Bulletin 17B should not be applied blindly or dogmatically
to lake levels. Instead, graphical frequency analysis should be
used. Consider the Bulletin17B guidance (page 2) on
documentation of floodfrequency studies and on length
of record (at least 10 years) needed for statistical analysis.
Compute probability plotting positions using the
Bulletin17B formula (Weibull formula, equation 11, page 27),
and plot them versus untransformed lake
levels on an arithmeticnormal probability grid. Use the shape
of the plotted curve to decide what distribution to fit, or use a
visually fitted manuallydrawn curve. No distribution has been
established for lake level frequency analysis, as the logPearson
III distribution for stream flow peaks. Extrapolate the
lakelevel frequency curve only with extreme caution: the form of
the lakelevel frequency curve is not known and lake levels may be
much more sensitive to lakeshore topography than the peak flows
are to flood plain topography. Do not extrapolate the
levelfrequency relationship if lake levels are under impacts of
operation of structures or if other constraints exist. An
additional complication is the effect of storage changes on the
timeseries characteristics of the lake level process. If the
lake has an effective surface outlet, flood waters can drain out
rapidly and the lake level returns quickly to its normal level.
In this case, maximum lake levels in successive years will be
substantially independent, so that traditional methods of
estimation can be applied directly to the lake levels. If the
lagone serial correlation is less than about 0.4, then the
impacts of assuming independence is not great. However, if the
lake has no surfacewater outlet (closed lake such as the Great
Salt Lake) or if its outlet has much smaller capacity than the
surface inflows to the lake, there is likely to be substantial
serial dependence between lake levels in successive years. In
this case a short record of the lake levels themselves is unlikely
to show the true longrun distribution; instead, the lakelevel
CHANGES from year to year should be treated as independent random
variables and used to define a distribution of annual lakelevel changes.
A hydrologic timeseries model should be developed to represent the
lake level in any year as the cumulative sum of all past level changes.
The lakelevel distribution then should be computed from
mathematical analysis and/or simulation of the
hydrologic time series model. Such a model recently was developed
for Devils Lake, North Dakota (USGS OpenFile Report 95123,
by G.J.Wiche and A.V.Vecchia). If the serial correlation exceeds
about 0.4, then the time series modeling approach should be used.
SEASONAL FLOOD FREQ
Question: Can the Bulletin 17B procedures be used to develop xyear
flood peaks and volumes for a month or season or other part of a year? Such
information may be needed for defining flood diversion requirements in a river
during construction which is planned during the low flow season.
Answer: Bulletin 17B was written for analysis of
annualmaximum peak flows; flood volumes and partialyear maxima
were not considered and the Bulletin17B procedures were not
tested or evaluated for application to volumes or partialyear
data. Nonetheless, the Bulletin17B procedure will provide a
mathematical solution to a mathematical problem of fitting a
distribution to data. The data can be limited by date. The
largest flood peak or volume for the set range of dates can be
calculated for each year (at least if a partialduration flood
series or continuous daily flow record is available). The 17B
procedure can be applied to the derived data set. The fitted
frequency curve should be scrutinized critically, since the
adequacy of Bulletin17B procedures for partialyear data has not
been established. Bulletin17B map skews cannot be used, only
the computed station skew, unless special generalized skew studies
are performed for the partialyear or volumetric data. The
procedure can be applied using multiple gauge sites if some form
of regional analysis is desired for analysis of an ungaged site.
The result can be useful in defining the diversion flood
requirement for that particular season.
However the result can be very misleading unless clearly
identified with the season or months considered. The 100year
dryseason flood actually is exceeded  during the dry season 
in one year out of 100, on average, and there is, on average,
100year spacing between years containing dry seasons in which the
100year dryseason flood is exceeded. Obviously, however, the
100year dryseason flood may be much less than the 100year flood
based on the maximum flood in the full year, and years containing
any exceedance (not just dryseason exceedances) of the 100year
dryseason flood may occur much more frequently than once in 100
years. Even if floods occur more or less uniformly throughout the
year, restricting attention to a particular time period, say the
month of March, will yield a March 100year flood that is lower
than the ordinary 100year flood, for the same reason that the
maximum of 12 throws of the dice is usually greater than the
result of, say, the third throw.
One problem which often comes up, especially with peak flows, is
that limiting the data by date may severely limit the amount of
data available for analysis. If peaks above a base are available,
then, even if there are no events in some years, the base
discharge can be used to define a conditionalprobability
adjustment for those years. If only annual peaks are available,
however, then it may be necessary to ignore the years in which the
annual peak does not occur in the specified time period; the
probability interpretation of the resulting frequency curve is
very tricky  the curve will give the probability that an annual
peak occurring in March, say, will exceed discharge x, but leaves
unanswered the real question, which is whether any peak in March
will exceed x. Some other analysis to relate peak flow to daily
flow or the use of some other gauge records may be advised. Most
often the procedure is used with dailymean flows which are much
more abundant and more readily divided into seasons without fear
of extreme data losses.
SKEW COMPUTATIONS
Question: What is the applicability of the skew map (Plate I) in Bulletin
17B? What is the maximum watershed drainage area for which it can be used?
Answer: The skew map in Bulletin 17B is provided as a convenience
for users who do not wish to do the regional analysis needed to
develop their own estimates of generalized skew. The use of the
skew map should be consistent
with the data used to develop it. The map was
developed with data from watersheds smaller than 3,000 square
miles and with essentially unregulated peak discharges
(that differ from natural peak discharges by less than 15 percent).
Periods when the annual peak discharge likely differed from
natural flow by more than
about 15 percent were excluded from the skewmap analysis. Thus,
the maps should not be used with regulated flows. The results
were presented as a map largely because it was not possible to find
convincing relations between skew and basin characteristics or
other peak flow statistics. Although basin storage is generally
thought to be important, there is no widely accepted empirical or
theoretical relation tying basin characteristics to logarithmic
skew coefficients. Although the use of the skew map should be
consistent with the data used to develop it, no strict upper limit
on drainage area has been established for use of the map, and no
procedures have been defined for using the map to determine
generalized skew for basins larger than 3000 sq mi. Ideally,
generalized skews for basins larger than 3000 sq mi should be
determined by analysis of skews for nearby basins of similar size,
especially when the map skew varies substantially across the
basin. This is not always possible, however, and undoubtedly the
Bulletin17 skew map has been used for basins larger than
3000 sq mi. Although modest extrapolation may be acceptable, the
Bulletin17 map should not be extrapolated to drainage areas
greater than about 2 or 3 times the size of the basins for which
the map was developed, because the physiographic factors
controlling the skew coefficients of large basins undoubtedly are
different, at least in magnitude, from those effective in smaller
basins.
Question: How should the generalized skew be determined from Plate
I in Bulletin 17B? That is, should the value from the centroid of the basin
or from the station location be selected from the map in Bulletin 17B?
Answer: Using the Bulletin17 skew map (Plate I), the generalized
skew should be determined at the point of interest or outlet of
the watershed rather than at the centroid of the watershed, to be
consistent with how the map was prepared. The Bulletin17 skew
map was developed by plotting station skew values at the latitude
and longitude of the gaging station and plotting isolines. No
information about basin centroid locations was practically
available. If some other skew map or relation is used, the gage
or basin location should be specified in the same manner used in
developing the map or relation.
Question: Should Bulletin 17B be used for regulated watersheds (peak
discharges differ by more than 15 percent from natural peaks), and if so, what
skew value should be used?
Answer: Bulletin 17B can be used for regulated watersheds if
the logarithms of the regulated peak discharges are reasonably
consistent with a Pearson Type III distribution. A graphical
comparison of the plotting positions to the computed frequency curve
should be used to judge the reasonableness of using Bulletin 17B.
However, if the basin is regulated by a reservoir that is generally
quite effective at reducing damaging flood peaks, then there may
be a problem in assuming logPearson Type III shape. If the
reservoir is quite effective, the upper middle range of flood
magnitudes will be lowered relative to the unregulated condition,
but the extreme upper tail, corresponding to overtopping of the
reservoir, will be back up at the same magnitude as the
unregulated flows. The resulting frequency curve will have the
following general shape:
This is not an LPIII shape. Moreover, the actual observed data are likely
to show only the lower and middle (flat) segments, not the steep upper segment,
so the fitted curve also will reflect only the lower flatter segments. Extrapolation
of the fitted curve and observed data therefore are likely to grossly underestimate
the potential magnitude of extreme rare floods.
To get an adequate representation of the upper steep segment of
the frequency curve, one should try to increase the record length
by routing historical floods through current reservoir storage or
by developing and routing hypothetical floods (for a given
frequency).
If Bulletin 17B is judged to be applicable, then station skew
should be used in defining the final frequency curve. The skew
map in Bulletin 17B should not be used in determining a weighted
skew because the Bulletin 17B skew map is based on data for
essentially unregulated watersheds. As always, the final
determination of the skew coefficient and other frequency curve
parameters should include consideration of the data, the
floodproducing factors, the characteristics of the regulation
rules, the characteristics of nearby similar regulated sites (if
any), and the sensitivity of the results.
It is improper to use Bulletin 17B procedures on a nonhomogeneous
data set , i.e., one in which peak flows for certain years are
regulated, and for other years not. The peak flows for the
regulated period should be analyzed by themselves, or
converted into unregulated flows before a frequency
analysis is performed.
Question: What is the basis for giving greater weight to station skew
when the generalized and station skew differ by more than 0.5 (page 15 Bulletin
17B)?
Answer: Bulletin 17B work group members felt that large
deviations between generalized and station skew may indicate that
the flood frequency characteristics of the watershed of interest
are different from those used to develop the skew map. It is
thought that station skew is determined by rainfall skew and basin
storage and that there is considerable variability of response
among different basins with similar observable characteristics, in
addition to the random sampling variability in estimating skew
from a short record. Therefore, it is considered more reasonable
to give greater weight to station skew, after due consideration of
the data and floodproducing characteristics of the basin. The
difference of 0.5 was chosen based on engineering judgement and
considering that the standard error of the Bulletin 17B skew map
is 0.55.
MIXED POPULATION
Question: Floods in my study area are caused by hurricanes, by iceaffected
flows, and by snowmelt, as well as by rainfall from thunderstorms and frontal
storms. How do I determine whether mixedpopulation analysis is necessary or
desirable?
Answer: Flood magnitudes are determined by many factors, in
unpredictable combinations. It is conceptually useful to think of
the various factors as "populations" and to think of each year's
flood as being the result of random selection of a "population",
followed by random drawing of a particular flood magnitude from the
selected population. The resulting distribution of flood magnitudes
is called a mixture distribution. However, the resulting mixture
distribution in many cases is wellapproximated by a logPearson
Type III distribution (LPIII), and in such cases there is no benefit
in going through the lengthy mixture calculation instead of using
the LPIII tables to compute the distribution. In practice, one
determines whether the distribution is wellapproximated by the
LPIII by comparing the fitted LPIII with the sample frequency curve
defined by plotting observed flood magnitudes versus their empirical
probability plotting positions determined by eqn 10 (pg 26). If
the fit is good, and if the flood record includes an adequate
sampling of all relevant sources of flooding (all "populations"),
then there is nothing to be gained by mixedpopulation analysis.
Only if the sample frequency curve has sharp curvature (kinks),
reverse curves, or other characteristics that prevent its being
approximated by the LPIII, or if the available flood record omits
important sources of flooding, is there any reason to perform a
mixedpopulation analysis.
Question: Hurricanes are an important source of flooding in my study
area, but the flood record at my study site is short and contains no hurricane
events (or too few events to define the hurricane population). How do I perform
a mixedpopulation analysis in this case?
Answer: First examine longer records from nearby sites to see if the hurricane
population is inconsistent with an overall LPIII distribution. If mixed population
analysis is indicated, then determine the distribution of hurricaneflood peaks
for the study site. This might be done by determining historical hurricaneflood
peaks at the study site using rainfallrunoff modeling, determination of peakflow/drainagearea
ratios, or other means. Plotting the hurricaneflood peaks versus Weibull probabilityplotting
positions (n/(N+1)) determines the CONDITIONAL distribution of hurricaneflood
magnitudes. The observed record at the site defines the CONDITIONAL distribution
of nonhurricane flood magnitudes. (Any hurricane events in the observed record
first have to be moved to the hurricane record.) The two conditional distributions
can be combined as follows to define the unconditional distribution of all floods
at the site 
F(x) 
= 
P{annual flood X < x}
= 

= 
P{X<x  X is hurricane flood}*P{X is hurricane
flood} +
P{X<x  X is nonhurricane flood} * P{X is
nonhurricane flood} 



wherein 

P{X is hurricane flood} = NH
/ LHHP 

= 
number of hurricanes / length
of historical
period analyzed for hurricanes 



and 

P{X is nonhurricane flood} = 1  NH/LHHP.




Note that ALL hurricanecaused annual floods during the period LHHP must be
included in the analysis to properly define the conditional distribution of
hurricane floods.
FREQUENCY OF MINOR FLOODS
Question: I have to determine the 1.1year flood for use in stream
restoration analysis. The record contains several low outliers, and the computed
frequency curve is not defined for the high exceedance probabilities that correspond
to the 1.1year flood. How do I proceed?
Answer: Bulletin 17 methodology is not designed for and should not be used
to determine highfrequency lowrecurrenceinterval flood magnitudes or to determine
risks due to occurrence of lowmagnitude floods. This is the case whether or
not there are low outliers, even if the computation does yield a value for the
1.1year flood. Bulletin 17 is based on the annualflood probability model,
in which it is assumed that exactly one flood event occurs per year. This probability
model usually is adequate as an approximation for risks due to largemagnitude
lowfrequency floods (which are unlikely to occur at all during any given year,
and extremely unlikely to occur more than once during the year). The annualflood
model, however, does not adequately represent the occurrence of lowmagnitude
floods. In most streams, several lowmagnitude flood events occur in most years.
In most cases, if floods of this magnitude cause damages or other effects of
concern, such as channelforming activity, then each occurrence of such a flood
will contribute to the cumulative effect for the year. Proper accounting of
the risk requires consideration not only of the distribution of individual flood
magnitudes but also of the distribution of the number of events that occur in
a year. The annualflood analysis does not furnish the necessary information
about the likelihood of multiple flood occurrences per year. Generally speaking,
the annualflood model understates the total risk or total effect for the year
because of undercounting of the number of minor floods in the year. Conversely,
it overstates the recurrence interval of minor floods of a given magnitude,
again because of failure to recognize the occurrence of multiple events per
year. A different method of frequency analysis, called the "partial duration"
method (because the "duration" of time associated with each flood
event is only a "partial" year), or "peaks over threshold (POT)"
method, which explicitly considers multiple events per year, is required. This
methodology is described, for example, in Hydrology for Engineers (1982, by
Linsley, Kohler, and Paulhus, McGrawHill, pages 359, 373347) and consists
of selecting all distinct wellseparated flood peaks exceeding a given threshold
magnitude, ranking them, estimating the recurrence intervals by the formula
T = (N+1)/m (where N is the record length, in years, and m is the rank of the
peak), and plotting magnitude versus recurrence interval. The threshold is commonly
set so that a longrun average of about 3 peaks per year will be recorded; thus
recurrence intervals as low as about 1/3 year can be defined. Relating the recurrenceinterval
curve to probabilities of occurrence requires consideration of the frequency
distribution of the number of abovethreshold peaks per year, as summarized,
for example, in the Handbook of Hydrology (1993, D.R. Maidment, editor, McGrawHill,
page 18.37). (That having been said, if administrative or regulatory requirements
necessitate use of the 1.1year annual flood, and if that value is not computed
because of low outliers or zero flows, a value can be determined by graphical
plotting of the low end of the frequency curve or by manual calculation using
the "synthetic" statistics described in appendix 5 and printed by
the computer as "Bulletin17B estimates". If more than 9 percent
of the annual peaks equal zero, then the 1.1year flood equals zero; if more
than 1/3 of the peaks equal zero, then the 1.5year flood equals zero.)
DATA QUALITY
Question: How important is data quality in the validity of Bulletin17B
frequency results? What issues need to be checked?
Answer: Data quality is obviously important to validity of the Bulletin17B
frequency analysis, since the frequency analysis is basically nothing other
than a standardized summary of the underlying flood data set. In a critical
review of the flood data set, two broad sets of issues need to be considered:
1) relevance of the flood data set (and frequency analysis results) to estimation
of future flood risk, and 2) accuracy of the data set as a representation of
the flood events that actually occurred in the past. In the first set of issues,
factors such as flow regulation by dams, dam failures, stormwater management,
effects of development (or reversion to undeveloped conditions) in the flood
plain, stream channel improvement or restoration, and the effects of mining,
forestry, agriculture, or reclamation from those activities, all have the potential
to make all or part of the record unrepresentative of future flood risk. The
significance of these factors and the nature of any adjustments that might be
applied for estimation of future flood risk cannot be predicted in general and
depends on the specific situation at each site; no simple guidelines can be
given that could safely be followed blindly or dogmatically. The application
of records of past floods (including frequency analysis results) to decisionmaking
about the future is outside the scope of frequency analysis and belongs to the
realm of engineeringeconomic decision making.
Regarding the accuracy of the data, it is helpful to consider the process
for computing the flood record, the potential
sources of error, and the steps taken to detect and correct errors. Most
annualpeak flows are determined by sensing the stage or water level
at the gage and reading the flow (discharge) from a stagedischarge
rating curve. The rating curve is made by correlating direct measurements
of discharge, made by current meters or similar devices, with concurrent
measurements of stage. The accuracy of the annual peak flow value
then depends on the accuracy of the stage reading and the
accuracy of the stagedischarge relation. The accuracy
of the stagedischarge relation, in turn, depends on the accuracy, number,
and flow magnitudes of the direct discharge measurements used to establish
the relation. An important factor in promoting accuracy of records is a
longterm organizational commitment and focus on production of records,
along with a regularized process for checking and reviewing the data collection
and
computations, crosschecking the results against records at nearby streams,
and annual publication of the records for public examination and use.
Issues of data accuracy are most likely to affect
the topmagnitude floods
in the data set. These events occur rarely, so there
are fewer opportunities to define the stagedischarge rating
for events in this range. In addition, these are the most destructive
events, and are more likely to destroy or damage the gage,
or impair the operation of the instrumentation. The
uncertainty associated with historical peak
discharges is usually greater than that associated with
peaks that are part of the systematic record. The
analyst should evaluate if the historical peak discharges are
reliable enough to be used in the analysis. Issues that may
be of concern include whether the historical sources provide
sufficient substantive information to associate a stage or
discharge with the historical event, whether the historical stage
is referenced to the same gage datum as the stages used to
develop the stagedischarge rating used to compute the
discharge, and whether the stagedischarge rating adequately
reflects the hydraulic conditions that existed in the channel and
flood plain at the time of the historical event.
For historical data, attention must be paid to what is not
in the data set as well as to the accuracy of the recorded historical
peaks. As explained in more detail below, the Bulletin17B procedure
for historical data involves defining a historical threshold discharge
that separates the record into two classes of peaks which are
given different weights in the computation. Bulletin 17B
requires that the threshold be set
at a level high enough to ensure that it was not exceeded
by any peaks that are not in the record. Any nonsystematic
peaks that are below the threshold are unusable
statistically. Although the precise
numerical value of the threshold is of little consequence, since
it is not used for computation, setting the threshold to correctly
identify the number and magnitudes of the
peaks to be adjusted is
critical to the accuracy of the
historical adjustment. There is a tendency
to casually assume that any peak that is outside
of a period of systematic record is a true historical peak
in the sense of Bulletin 17B, and a tendency
to improperly set the threshold at the level of the lowest such
peak. Occasionally, records contain nonsystematic
peaks that are lower than many of the systematic peaks and
contain few or no higher nonsystematic peaks. In these cases,
it is likely that higher peaks actually did occur outside the
systematic record period but were not included in the
nonsystematic record, thus violating the assumptions
underlying the historical adjustment. Setting the threshold
too low results in improper discounting of the
highmagnitude peaks relative to the belowthreshold
peaks. The analyst should check that the number of peaks
exceeding the threshold during the systematic record period
is consistent with the number during the historical period,
and should check that the threshold level is not so low that
it could have been exceeded without anyone's taking
note of it. Accuracy of the length of the historical
period also is important because the value is used
to compute the amount by which the
abovethreshold peaks are discounted;
knowledge of local history is critical.
Question: What is the relationship of the Federal Data Quality Act
to flood data and floodfrequency analysis?
Answer:The "Federal Data Quality Act" (officially known as Section
515 of Public Law 106554, the Treasury and General Government Appropriations
Act for Fiscal Year 2001) requires the Office of Management and Budget (OMB)
and, through it, all Federal agencies to issue guidelines to ensure the "quality,
objectivity, utility, and integrity" of information issued by the government.
The agencies are required to develop procedures for reviewing and substantiating
the quality (including objectivity, utility, and integrity) of information before
it is released. The agencies also are required to establish administrative procedures
by which persons affected by governmentdisseminated information can seek and
obtain correction of information that does not conform to the quality guidelines.
The general intent of the guidelines is that agencies should make their datacollection,
dataanalysis, and datainterpretation methods "transparent" by providing
documentation of the methods; should ensure data and information quality by
reviewing the methods used (including, as appropriate, consultation with experts
and users); and should keep users informed about corrections and revisions.
These guidelines and procedures apply to governmentdisseminated information
in general, and thus apply to flood data and to the results of statistical flood
frequency analysis. The guidelines and procedures apply not only to information
produced internally by agencies themselves, but also to information supplied
by outside sources.
LOW OUTLIERS
Question: What is a low outlier? How is it different from a zero flow?
Why do we drop low outliers and zero flows? Aren't we overstating flood risk
if we ignore flood peaks that are zero or near zero?
Answer: Outliers are observations that lie far out from the trend of the rest
of the data when plotted on a magnitude versus frequency graph. A smooth trend
line, such as a statistical frequency function, does not fit data sets with
outliers, and the fitted curve usually fails to fit the bulk of the data as
well as the outlier. Low outliers are outliers at the low end of the data set,
near zero, at least in comparison with the rest of the data. On a logprobability
plot, the low outliers impart a strong downward curvature and a downwarddrooping
lower tail to the frequency curve. In comparison with the lower tail, the upper
tail of the lowoutlieraffected curve may appear relatively flat. In the Bulletin17B
context, low outliers differ from zero values in that computations with the
logarithm of zero are impossible, whereas computations with logarithms of low
outliers may be mathematically possible, but may overwhelm the computations
of logarithmic moments (means, standard deviations, and skews) or distort the
fit of the frequency curve to the data in the upper part of the data set, which
are the data that represent significant flood or nearflood events. Since the
zero and nearzero values in a flood data set are not the ones that convey valid
or meaningful information about the magnitude of flooding, their numerical values
are not used in the computation of the moments. However, in contrast to classical
statistical treatments, where outliers are considered utterly spurious and are
simply dropped from the data set, the Bulletin17B procedure recognizes that
zero values and low outliers do convey valid and meaningful information about
the frequency of flooding, and this information is used in Bulletin 17B. Thus,
the Bulletin 17B procedure first uses the nonzero nonlowoutlier data to
define a conditionalprobability curve which applies only to the nonzero nonlowoutlier
events; then the number of zeroes and low outliers is determined and used in
the conditionalprobability or "noverN" adjustment (equation 52)
to adjust the probabilities from the conditional curve to properly reflect the
frequency of occurrence of zeroes and low outliers.
Question: When should low flows that are not identified as low outliers
using the 17B default procedure be censored as a result of the paragraph in
Bulletin 17B on page 18 that reads, "If multiple values that have not been
identified as outliers ... ".
Answer: Bulletin17B detects low outliers by means of a
statistical criterion (the GrubbsBeck test) rather than by
consideration of the influence of lowlying data points on the fit
of the frequency curve. The test is based on the standardized
distances, (x.i  x.bar)/stdv, between the lowest observations and
the mean of the data set. The test is easily defeated by
occurrence of multiple low outliers, which exert a large
distorting influence on the fitted frequency curve, but also
increase the standard deviation, stdv, thereby making the standardized
distance too small to trigger the GrubbsBeck test. Therefore,
Bulletin 17B (pg. 18) permits manually overriding the statistical
criterion. Obviously, the intention is to allow as many low
outliers to be designated as necessary to achieve a good fit to
the part of the data set that contains the significant flood and
nearflood events. Equally obviously, the intention is that the
GrubbsBeck result be used unless the resulting poor fit
gives compelling justification for not doing so.
There is no universal method that can be
followed blindly to achieve a good fit. The sensitivity analysis
alluded to in Bulletin 17B is based on the
engineeringhydrologiccommonsense proposition that the smallest
observations in the data set do not convey meaningful or valid
information about the magnitude of significant flooding, although
they do convey valid information about the frequency of
significant flooding. Therefore, if the upper tail of the frequency
curve is sensitive to the numerical values of the
smallest observations, then that sensitivity is a spurious artifact
based on the mathematical form of the assumed but in fact unknown
flood distribution, and has no hydrologic validity. The
sensitivity analysis determines whether the upper tail of the
frequency curve is sensitive to the magnitude of the
lowest values by iteratively treating them, one
by one, as low outliers and plotting the estimated value of, say,
the 100year flood (or other percentage point or points characteristic of
the upper part of the frequency curve) as a function of the number
of low outliers. Frequently, the estimated 100year flood will
change noticeably and consistently, either increasing or
decreasing, as the first few low outliers are identified, but then
remain relatively constant, perhaps changing erratically, as
additional data points are treated as low outliers. In such cases
the identity of the spuriously influential data points  the low
outliers  is clear, and the lowoutlier threshold is set just above
the magnitude of the highest spuriously influential data point.
Note that the magnitude of the change resulting
from low outlier treatment is not the deciding factor, but rather
the change in the magnitude of change as additional points
are treated as low outliers. In more complex cases,
there may not be a clear
demarcation of the low outliers, and the entire low end of the
data set may be inconsistent with the fitting of the logPearson
Type III distribution to the upper (hydrologically significant)
part of the data. In such cases it may be necessary to rely on
visual assessment of the fit of the upper part of the frequency
curve, and Bulletin 17B allows for this necessity.
Question: Does dropping multiple low outliers improve the estimate
of the 100year flood at the expense of distorting the estimates of the lowerrecurrenceinterval
(10, 20, 50year) floods?
Answer: No. The intent and the result of the low outlier
adjustment are to improve the fit of the entire frequency curve
above the lowoutlier threshold.
HISTORICAL FLOODS AND HIGH OUTLIERS
Question: What is the difference between a high outlier and a historical
flood?
Answer:
High outliers and most historical floods both are exceptionally
large floods. High outliers are exceptionally large floods
that are contained in the systematic record, whereas historical
floods were observed outside the period of systematic record.
Systematic records are collected during periods of
systematic stream gaging, usually
continuous series of years, in which flood data are observed
and recorded annually, regardless of the magnitudes of the floods.
A nonsystematic record is collected and recorded sporadically,
without definite criteria, usually in response to actual, perceived,
or anticipated major flooding. The systematic record can be used
directly in flood frequency analysis. The nonsystematic record
cannot be used unless additional information can be supplied to
relate it to the population of all flood peaks. Bulletin 17B
requires
that the nonsystematic record be a complete record of all flood peaks
that exceeded some threshold level during a definite historical time period.
A high outlier is an extraordinary flood that occurred during the
period of systematic streamgaging. It is part of the systematic
record and is treated just like the other systematic peaks in the
preliminary steps of the Bulletin17B analysis. On a
magnitudevsprobability plot, the high outlier lies well above
the fitted frequency curve, and the fitted frequency curve is
steeper than the trend of the other plotted data points. Often
historical information is available that indicates that the high
outlier was the largest in a period longer than the period of
systematic streamgaging. This historical information is used to
adjust the frequency curve to take proper account of the extended
time period associated with the high outlier. If no usable historical
information is available, the high outlier is retained in the
systematic record and used without adjustment.
A historical flood is a major flood that occurred outside
of the period of systematic streamgaging. The stage or
elevation of the historical flood is usually determined by highwater marks
left by the flood and recorded by local residents, state departments of
transportation (DOTs), railroad companies, local, state or Federal
agencies. Stages of historical floods often are reported in
local newspapers, diaries or Bibles of local residents, unpublished
documents of state DOTs or railroad companies, and/or published
reports of local, state or Federal agencies. Because the historical
event was not observed in accordance with definite statistical
sampling criteria, and is not part of the systematic record,
its relation to the underlying process of flood
occurrence is uncertain. This is so regardless of the accuracy
with which the stage and discharge might have been
determined. For example, a historical flood that
washed out a bridge might
have been recorded although a larger flood that caused
no damage might have gone unremarked.
The historical flood cannot be used in flood frequency
analysis unless additional information (historical
threshold and historical period) is available to relate it to
flood occurrence over a historical time period.
The computational procedures in Bulletin 17B Appendix 6
are applied to both historical floods and high outliers.
Question: Why do we bother with historical floods and high outliers?
Why don't we just use the systematic gage record?
Answer: We bother with historical floods and high outliers because systematic
streamflow records usually are short and may be inconsistent with the longerterm
flood history experienced and recorded nonsystematically by the local community.
Sometimes a short systematic record contains an extraordinary flood peak that
stands head and shoulders above everything else in the systematic record and
everything else experienced in the history of the local community. Conversely,
the longterm community history may record one or more outstanding floods that
are much larger than anything in the systematic record. In either case, the
systematic record disagrees with longterm community experience. Such discrepancies
must be resolved if the frequency analysis is to be a sound basis for planning.
The Bulletin17B historical adjustment procedure provides a basis for reconciling
these discrepancies.
Question: What is the high outlier threshold?
Answer: There are two different quantities that sometimes are
called high outlier thresholds. One is the statistical
highoutlier test criterion or threshold computed by the
GrubbsBeck test and described on page 17 of Bulletin 17B. The
other threshold, which B17 does not not clearly describe or
distinguish from the statistical threshold, is the threshold that
is used in (or implied by) the Bulletin17B historical adjustment
procedure that actually is applied to the flood record. This
threshold may be called the historicaladjustment threshold; it does
not necessarily equal the statistical high outlier test criterion,
and may be either higher or lower than the statistical test.
The statistical highoutlier test criterion is based
on the standardized distance, (x.i  x.bar)/stdv, based
on logarithms of peak flows, between the extreme top observation and
the mean of the data set. The criterion or threshold value
is the value that is unlikely (10 percent chance) to be
exceeded by the LARGEST observation in a sample. If the largest
observation actually is greater than the highoutlier threshold, that
is an indication that the observations above the threshold
are larger than would be expected for the given period of record,
that they may be associated with a longer time period than the
period of systematic record and that they may be distorting the
fit of the frequency curve. The test itself is only a warning,
not a definitive indication of anything wrong, and additional
historical information must be supplied before any adjustment can
be made. If appropriate historical information is available, the
historical adjustment can be made even if the statistical test does
not detect a high outlier.
The historicaladjustment threshold is specified either
explicitly or implicitly in the course of defining the
nonsystematic historical record period and applying the
Bulletin17B historical data adjustment. Bulletin 17B
does not describe or discuss this threshold clearly, but instead
simply assumes that the Z highest peak discharges
in the combined systematic and historical (nonsystematic)
record are known also to be the Z largest in a historical
period longer than the systematic record period. If the
threshold is stated explicitly, then Z is the number of peaks that
exceed the threshold; if Z is given instead, then the threshold is
implied to be somewhere between the Z and Z+1 ranked peaks.
Although the number Z and the historic period length H are
sufficient for computing the historicaldata adjustment, an
actual discharge threshold (or range of values) is needed to
properly document the historical record, and should be reported
along with the results of the historicaldata adjustment. An
actual threshold value or range is needed for two reasons. First,
the number of events Z will become outdated, and will have to be
updated, whenever a new peak occurs that exceeds the previous
Zth ranked peak. Second, and more important, one cannot
legitimately claim, without any support, that the Z largest peaks
in the record at hand are the largest in a longer period; it is necessary
to demonstrate, or at least provide plausible support, that there
actually were no other peaks that occurred but were not included
in the record. In most cases, this support has to be based on
the idea that if any peaks greater than some magnitude had
occurred, people would have noticed and recorded them; that
magnitude, the magnitude that would get almost everyone's
attention and ensure that a record would be made, is the
magnitude that should be determined and documented as the
historicaladjustment threshold to support
the historicaldata adjustment.
It should be noted that the numerical value of the
historicaladjustment threshold is not used in the computation of
the historical data adjustment. The threshold value is used only
to separate the Z largest values from the remaining data points;
the results of the adjustment are the same for threshold values
anywhere between the Z and Z+1 ranked data points. This is
important because
the threshold cannot always
be determined
with much certainty or precision from the available historical
information.
If there is not sufficient historical information available to
determine a historicaladjustment threshold and length of
historical period, then any historical (nonsystematic) peaks are
not usable for statistical analysis, because their relation to
the underlying process of flood occurrence is unknown. Similarly,
if the historical information is inadequate to adjust for the high
outliers, then they should be retained as part of the systematic
record and all peak discharges given equal weight in computing
the moments (mean, standard deviation and skew).
Question: How is the threshold determined in the historical adjustment
procedure?
Answer: The historicaladjustment threshold discharge is chosen
high enough such that all high outliers and historical floods
included in the adjustment procedure are the only floods known to
exceed the threshold in the historical period of H years. In
other words, the record is known to be complete for all events
exceeding the historicaladjustment threshold. There is no single
procedure that can be followed blindly to determine the threshold
from the historical information usually available. Determination
of the threshold usually will be based on consideration of channelbank
and floodplain elevations, elevations of important structures, and
the history of the neighboring community. Although the
determination may involve elements of subjectivity and judgement,
the choice of the historic threshold should be defensible given
the available historical information. The historicaladjustment
threshold often is less than the computed highoutlier threshold.
Question: Must a peak discharge exceed the high outlier threshold to
be included in the historical adjustment procedure?
Answer: No, the high outlier threshold (the statistical test
criterion given by equation 7) is just used as guidance in
determining whether a peak discharge is so large that it
might require use of the Bulletin17B
historical adjustment procedure. If the peak discharge exceeds
the high outlier threshold, then the analyst should determine
whether historical information is available that indicates the high
outlier is the largest flood in a period longer than the systematic
record. If there is useful historical information available, the
high outlier may be adjusted even though it does not exceed the
computed threshold. Therefore, the historic threshold used in
adjusting for high outliers (and historical floods) can be less
than the computed high outlier threshold.
Question: What is the difference in the historical adjustment procedure
for high outliers and historical floods?
Answer: There is no difference in the computation; the
historical adjustment computation does not distinguish between
historical peaks and high outliers. The same threshold is used for
adjusting for both types of floods. The number of peaks above
the threshold is denoted as Z, and no distinction is made
between high outliers and historic peaks in determining the
value of Z. Historically adjusted moments
are computed using a weight of 1.0 for the Z abovethreshold
peaks and a weight W = (HZ)/(N+L) (H = total length of historical
and systematic record; N+L = number of belowthreshold systematic
peaks, including low outliers and zeroes) for all systematic peaks
below the threshold.
Question: Please clarify the definition of the variable "Z"
in the historical adjustment procedure, appendix 6, and clarify the intended
application of the procedure. Bulletin 17 seems to say that historical data
should be used if possible, but appendix 6 seems to indicate that the historical
peaks need to be the largest in the whole record.
Answer: Yes, Bulletin 17 does say that historical data should be
used if possible. And yes, Appendix 6 does indicate that the
historical adjustment is applied to the largest peaks in the whole
record. The key words are "if possible." A couple of
conditions must be met. First, historic peaks and high outliers,
by their nature, are expected to be a biased (unrepresentative)
sample of the population of all peaks. However, the Bulletin 17B
procedure assumes that the high outliers and historic peaks are an
unbiased sample of the population of flood events that exceed the
historicaladjustment threshold magnitude. If there is some
question of that assumption, then the historical information is
wholly or partly unusable. Any historical peaks that do not
exceed the threshold cannot be used because their relation to the
flood population is undefined. If potential high outliers do not
exceed the threshold, they are used in the same way as any other
ordinary systematic peaks. Second, the Bulletin17B historical
adjustment procedure postulates the existence of exceptionally
large floods (historic peaks and high outliers) in the data set.
When such peaks are present, the systematic streamgaging record,
especially if short, may be inconsistent with the neighboring
community's longterm knowledge of flood occurrence, and some
reconciliation of the gage record with the community experience is
required. The historicaladjustment procedure accomplishes this
reconciliation by using the abovethreshold (historic and
highoutlier) peaks with unit weight and the belowthreshold
systematic peaks with the historical weight factor (HZ)/(N+L), in
effect filling in the rest of the extended historical period with
multiple copies of the belowthreshold systematic record. Thus,
Z represents the total number of peaks, systematic and historic,
that exceed the threshold. It is quite possible and acceptable
for Z to consist of, for example, 3 historical peaks that exceed
the threshold, plus 3 systematic peaks that not only exceed the
threshold but also exceed the 3 historical peaks; if there were
several additional historical peaks that did not exceed the
threshold, they would simply be ignored because their relation to
the flood population would be indeterminate. It is also
perfectly acceptable for Z to consist of one or more systematic
peaks (high outliers) and no historical (nonsystematic) peaks at
all. However, if Z = 0 (no large peaks at all, only the
knowledge that no peaks exceeded some threshold), the Bulletin
17B historical adjustment has no effect  the computation can be
performed, but the frequency curve is unchanged.
Question: If all peaks that exceed the historical threshold are treated
the same, why do we have all of this gobbledygook about "systematic peaks
above the threshold," "high outliers," etc? Why don't we just
call them "historical peaks" and be done with it?
Answer: All peaks that exceed the historical threshold are indeed
treated the same IN THE HISTORICAL ADJUSTMENT
COMPUTATION. However,
in the preliminary analysis of the systematic record, the historical
peaks are ignored whereas the high outliers are treated exactly
like the other systematic peaks. Improper treatment of high
outliers and historic peaks in the systematicrecord analysis can
adversely affect the final Bulletin17B frequency curve,
primarily through incorrect skew coefficients and
misidentification of high and low outliers.
The systematic record is that portion of the record in which the
annual peak is determined and documented for each year, regardless
of the magnitude of the peak; if the peak is too small to measure,
it nonetheless is recorded, but with a qualification code indicating
that fact. Thus, the systematic record can be regarded as an
unbiased random sample of the population of all floods, and the
statistics of the sample can be taken as estimates of the
corresponding characteristics of the population. The historical
record consists of flood peaks that were observed outside of a
systematic period of flood record. That is, the historical record
is nonsystematic. One might assume that such peaks were observed
and recorded because they were unusually large and noticeable (or
were expected to be so), but there is no real guarantee of this
unless additional historical evidence is available. Since one does
not know how the historical sample is related to the flood
population, one cannot use it for flood estimation unless additional
historical information is provided. Bulletin 17's historical flood
threshold and historical period together provide the information
needed to make use of the historical peaks. If the threshold and
historical period cannot be defined, or if the historical peaks are
less than the threshold, then the historical peaks cannot be used.
OUTLIERS, GENERAL
QUESTION: Why is there so much emphasis on low and high
outliers?
RESPONSE:
Bulletin 17B does not explain this very well. It lumps
a number of distinct problems and phenomena under the label
"outlier," but does not give much explanation of how the
Bulletin17B conception of outliers differs from the classical
concepts developed in the literature on statistics and analysis of
measurement data.
Bulletin 17B defines outliers as data points that depart
significantly from the trend of the remaining data when plotted as
a frequency curve on magnitudeprobability coordinates. By
implication, outliers are data points that interfere with the
fitting of simple trend curves to the data and, unless properly
accounted for, are likely to cause simple fitted trend curves to
grossly misrepresent the data. This definition is quite nebulous,
furnishes little concrete guidance, and may be confusing to those
unfamiliar with flood frequency analysis. However, flood data
sets often do not conform to common statistical probability
distributions and often contain observations that distort the fit
of simple fitted frequency curves. Most flood data points are
distributed within some range of moderate extent, but some values
extend above the range by factors of 10 or more; thus statistical
analysis usually is based on the logarithms of the flows. In arid
environments, streams sometimes may be dry all year long, so that
the annual maximum "flood" flow may be zero or, perhaps worse, a
factor of 10 or more below the range of ordinary flows, so that
computations with logarithms are impossible or prone to
difficulties. Bulletin 17B rather loosely gathers all of these
issues, which generally may result from a range of causes, but
often manifest themselves as poor fit of the fitted frequency
curve, under the single and somewhat misleading term "outlier."
Classical statistical concepts of outliers involve ideas of rejection
of spurious observations, such as surveying measurements of the
azimuth of the North Church steeple rather than of the Blue Hill
triangulation beacon. These ideas are not generally very relevant
to frequency analysis of properly qualityassured published flood
flow data, and Bulletin 17B does not recommend or provide
procedures for rejection of outliers.
The related and more modern notion of contamination of one
measurement distribution by another is a special case of the
concept of mixed populations mentioned briefly in another section
of Bulletin 17B. Different floodgenerating hydrologic processes
in one basin give rise to mixed populations of floods. The
mixture may manifest itself as outliers, especially if the
populations are quite different and one of them occurs relatively
infrequently. In this case, the outlying observations could be
called hydrologic outliers and could be treated either by the
Bulletin17B outlier adjustments or by mixedpopulation analyses,
as discussed in another one of these FAQs, with substantially
similar results.
Another source of outliers is simply the purely chance occurrence
of extraordinarily large observations in some samples. This kind of
outlier is more common in flood distributions where one tail or
the other generally is somewhat stretched out relative to the
normal distribution, and is especially common in socalled
"heavytailed" distributions such as the Pareto. These may be
called "statistical" outliers, and are exemplified by
the Bulletin17B concept of high outlier, in which it is
postulated that the record length associated with the outlier
is governed by historical (or paleoflood) evidence
rather than simply by the systematic streamgaging record period.
Bulletin17B procedures do not involve "dropping" of outliers.
High outliers are retained in the analysis as systematic peaks if
usable historical information cannot be found. If historical
information is available, the high outlier is properly discounted
to a more appropriate time window. Low outliers are counted, not
"dropped", and their frequency (which is the valid information
that they contain relative to flood risk) is used to properly
account for the occurrence of low outliers by means of the
conditional probability adjustment of a preliminary conditional
frequency curve based on the nonoutlying observations.
The extensive discussion of outliers in Bulletin 17B is necessary
because of the prevalence of outlierlike effects in frequency
analysis of flood data. Despite whatever faults might be found,
the discussion in Bulletin 17B is a generally worthy effort to
provide the theoretical concepts and operational procedures needed
to enable different analysts to produce reasonable and consistent
fitted frequency curves in the variety of problems encountered in
practice.

LIMITS OF FREQENCY CURVE EXTRAPOLATION
Question: What are the limitations on flood frequency curve extrapolation?
We recently had a terrible flood in our town. I own a trailer park that was
above the maximum flood level. I downloaded flood data and used the Bulletin17B
flood frequency methodology to prove that the flood was a 5,320year flood and
that my trailer park was above the 6,000year flood level. I wanted the Flood
Agency to certify my trailer park, but they would say only that the flood was
more than twice as big as the 100year flood and that my park was outside the
100year flood plain. Why doesn't the agency acknowledge the true rarity of
this flood and the true safety of my property?
Answer: Extrapolation of flood frequency curves is limited primarily by the
user's tolerance for uncertainty in the extrapolated results. The user of floodfrequency
data needs to understand that these data carry substantial uncertainties with
them, even if no extrapolation is involved. The user has to accept responsibility
for using these results in such a way that errors in the results do not lead
to catastrophic consequences to actions based on the results. Because of the
vagaries of flood occurrence in time and space, any observed flood record is
likely to give a more or less inaccurate representation of the true magnitude
and frequency of flooding. This socalled randomsampling uncertainty is smallest
near the middle of the flood distribution (the 2year flood) and increases for
larger less frequent flood magnitudes. This uncertainty is represented by the
confidence limits in Bulletin 17B; the limits are farther apart, representing
greater uncertainty, in the tail of the distribution than in the center (near
the 2year flood). Random sampling uncertainty exists and is greater in the
tail of the distribution even if extrapolation is not an issue and even if the
mathematical form of the distribution is known. In practice, the record length
or sample size usually is small (2060 years) in relation to the annual exceedance
probabilities or recurrence intervals of interest (100500 years), so extrapolation
is necessary for obtaining the needed information. Moreover, the mathematical
formula that should be used for the extrapolation is not known with any confidence,
and there is no agreedupon procedure to assess or quantify the uncertainty
in the extrapolation formula. As a result, the following rules generally are
followed: 1) don't extrapolate if you don't have to; 2) if you do have to extrapolate,
do so, but only as far as necessary; 3) seek additional information to provide
independent corroboration of the extrapolated values (see Bulletin 17B, pages
1922); and 4) don't give too much credibility to or place too much reliance
on the extrapolated values. For many types of engineering design and planning,
there are authoritative design criteria that specify recurrence intervals or
exceedance probabilities that must be used; in such situations, extrapolation
to those levels is required, like it or not. Commonly used design recurrence
intervals include 100 years, 500 years for design of scour protection for major
bridges, and shorter intervals for less important works. Bulletin 17B shows
recurrence intervals up to 500 years (annual exceedance probabilities down to
0.002) in the example problems; it may be assumed that there is a consensus
that extrapolation out to that level, if necessary, is acceptable, even if not
necessarily accurate or reliable. In other cases, however, there may be no essential
need to extrapolate. Estimation of the recurrence interval of an observed flood
by long extrapolation of a frequency curve, for example, generally serves no
useful purpose in terms of flood control or flood plain planning and management.
(Think of it  What difference does it make to the winner of a raffle  or
to the losers  whether he had the one winning ticket in 100 or the one winning
ticket in 1000?) If extrapolation is necessary, and, for that matter, even if
it is not, prudence dictates that corroboration be sought, and that more corroboration
be sought the longer the extrapolation. Thus, it is always prudent to compare
atsite Bulletin17B frequency curves with regional flood frequency relations
and, if the extrapolation is longer, with flood records at comparable nearby
sites and with regional rainfall and runoff relations (Bulletin 17B, pages
1922). If long extrapolation is required, it probably is required because of
a concern that exceedance of the design flow would cause catastrophic damage
that must be avoided by setting an extremely high design flow; in such cases,
if the extrapolated design flow is very uncertain, and if the uncertainty cannot
be reduced by comparison with other regional flood information, it might be
prudent to consider whether an alternative system design, having less catastrophic
failure modes, might be preferable.
