U.S. Department of the Interior

U.S. Geological Survey

Techniques and Methods 4-B4

User’s Manual for Program PeakFQ, Annual Flood-Frequency 

Analysis Using Bulletin 17B Guidelines

Chapter 4 of Book 4, Section B
Cover: The Sorlie Bridge between Grand Forks, North Dakota, and East Grand Forks, Minnesota, during the 

1997 Red River of the North flood (photograph by Steven W. Norbeck, U.S. Geological Survey).
User’s Manual for Program PeakFQ, Annual 

Flood-Frequency Analysis Using Bulletin 

17B Guidelines

By Kathleen M. Flynn, William H. Kirby, and Paul R. Hummel

Chapter 4 of Book 4, Section B

Techniques and Methods 4-B4

U.S. Department of the Interior

U.S. Geological Survey
U.S. Department of the Interior

DIRK KEMPTHORNE, Secretary

U.S. Geological Survey

Mark D. Myers, Director

U.S. Geological Survey, Reston, Virginia: 2006

For product and ordering information:

World Wide Web: http://www.usgs.gov/pubprod

Telephone: 1-888-ASK-USGS

For more information on the USGS--the Federal source for science about the Earth, its natural and living resources, 

natural hazards, and the environment:

World Wide Web: http://www.usgs.gov

Telephone: 1-888-ASK-USGS

Any use of trade, product, or firm names is for descriptive purposes only and does not imply endorsement by the 

U.S. Government.

Although this report is in the public domain, permission must be secured from the individual copyright owners to 

reproduce any copyrighted materials contained within this report.

Suggested citation:

Flynn, K.M., Kirby, W.H., and Hummel, P.R., 2006, User’s Manual for Program PeakFQ Annual Flood-Frequency Analysis 

Using Bulletin 17B Guidelines: U.S. Geological Survey, Techniques and Methods Book 4, Chapter B4; 42 pgs.
iii

Contents

Abstract...........................................................................................................................................................1

Introduction.....................................................................................................................................................1

Peak Streamflow Records............................................................................................................................1

Principles of Computations ..........................................................................................................................2

Systematic-Record Analysis...............................................................................................................2

Outlier Tests ...........................................................................................................................................4

Historic-Record Adjustment ...............................................................................................................4

Conditional-Probability Adjustment...................................................................................................6

Computation of Weighted Skew Coefficient ....................................................................................6

Expected-Probability Adjustment ......................................................................................................7

Confidence Limits..................................................................................................................................8

Probability-Plotting Positions .............................................................................................................8

Estimation of Generalized Skew.........................................................................................................9

Computer Program.......................................................................................................................................10

Windows Version (PKFQWin) ...........................................................................................................10

File Open......................................................................................................................................10

Station Specifications...............................................................................................................11

Output Options............................................................................................................................13

Results .........................................................................................................................................14

Save Specs .................................................................................................................................14

Batch Version ......................................................................................................................................14

REFERENCES CITED ....................................................................................................................................15

APPENDIX A. PeakFQ Diagnostic Messages ........................................................................................17

APPENDIX B. PeakFQ Data Formats .......................................................................................................22

Appendix B.1. Batch Specifications ...............................................................................................22

Appendix B.2. Station Header Records (WATSTORE standard format).....................................25

Appendix B.3. Station Option Record (WATSTORE standard format)........................................26

Appendix B.4. Peak-Flow Records (WATSTORE standard format)............................................28

Appendix B.5. Basin Characteristics Records (WATSTORE standard format).........................31

APPENDIX C. DATA-SET ATTRIBUTES....................................................................................................33

APPENDIX D. SAMPLE FILES ...................................................................................................................36

Appendix D.1. Sample Specification File .......................................................................................36

Appendix D.2. Sample Input File......................................................................................................37

Appendix D.3. Sample Output File...................................................................................................38
iv

Figures

Figure 1. General flow chart for flood-frequency computations (modified from Interagency 

Advisory Committee on Water Data, 1982)...............................................................................3

Figure 2. Definition sketch showing time periods and discharges used in historic record 

adjustment. ....................................................................................................................................5

Figure 3. Example of opening screen of program PKFQWin showing the station specifications 

tab before an input file has been opened...............................................................................10

Figure 4. Example of the File Open window in program PKFQWin, obtained by selecting Open 

from the File menu. .....................................................................................................................11

Figure 5. Example of the Station Specification Tab of program PKFQWin after a file containing 8 sets of data has been opened. .................................................................................12

Figure 6. Example of the Output Options tab of program PKFQWin after an input file has been 

opened..........................................................................................................................................13

Figure 7. Example of the Results tab of program PKFQWin after the Run PEAKFQ button has 

been selected..............................................................................................................................14

Figure 8. Example of the Save Specifications File window in program PKFQWin, obtained by 

selecting the Save Specs button at the bottom of the PKFQWin window. .......................15

Tables

Table 1. Peak-flow codes used by program PeakFQ ..............................................................................2

Table B.1.1. Specification file output keywords that apply to the entire run....................................23

Table B.1.2. Specification file keywords that apply to a specific station..........................................24

Table B.2. WATSTORE station header record formats. ........................................................................25

Table B.3. WATSTORE station option record formats...........................................................................27

Table B.4. WATSTORE peak-flow record formats. ................................................................................28

Table B.5. WATSTORE basin characteristics record formats. ............................................................32

Table C.1. Attributes associated with annual peak-flow data sets....................................................33

Table C.2. Sources of attributes associated with peak-flow data sets .............................................35
v

SYMBOLS

Symbol, explanation:

a, a constant characteristic of a particular plotting position G, generalized skew coefficient. G~

, historically-adjusted station skew coefficient.

G~

 ́, skew coefficient of frequency curve passing through 

Q

*

~ 0.50. 

Q

*

~ 0.10, and 

Q

*

~ 0.01.

|G|, absolute value of the station-skew coefficient.

G, station skew coefficient. GW, weighted-skew coefficient estimate used in final log-Pearson Type III frequency curve.

g, desired skew coefficient.

H, historical period length.

K, confidence coefficient. KN, 10-percent significance-level critical value for outlier test statistic for sample of size N 

from the normal distribution.

K

H, 10-percent significance-level critical value for the outlier test statistic for sample of 

size H, where H is the length of the historic record period.

k

G ̃’

,p, ordinates for skew 

G~

 ́ and exceedance probability (p) for curve passing through 

Q

*

~ 0.50. 

Q

*

~ 0.10, and 

Q

*

~ 0.01.

kg,p, Pearson Type III standardized ordinates for desired skew (g) and exceedance 

probability (p).

kp, standard normal frequency factor for probability p.

k ́

p

, frequency factor for expected probability frequency curve.

k(1-α), standard normal deviate with exceedance probability 1-α. kγ,p, the Pearson Type III frequency factor. M~ , historically-weighted logarithmic mean. Mˆ , Bulletin 17B mean. M~  ́, mean of frequency curve passing through Q*~ 0.50. Q*~ 0.10, and 

Q

*

~ 0.01.

m~ , historically-weighted rank of the mth largest observed peak.

m, rank of the mth largest observed peak.

MSE, mean-square error (standard error of estimate squared).

MSE

G, mean-square error of generalized skew coefficient.

MSE

G, mean-square error of station skew coefficient.

N~ , effective number of peaks above flood base, Q

O

.

NBB, number of peaks below the flood base, including any zeros and low outliers. NHO, number of high outliers. NHP, number of historic peaks. NS

, number of systematic peaks.

N

X, number of peaks between QO and QH

.

N, record length in years.

n, sample size from normal population of flood logarithms. P~m, historically-weighted probability plotting position of the mth ranked observed peak. P~O, estimated probability of a flood exceeding the flood base.

p, exceedence probability.

p ́, normal exceedance probability corresponding to k ́

p

.

Q~

, conditional frequency curve describing only those peaks above the flood base.

Q

*

~ , intermediate unconditional frequency curve. Q*~ p

, ordinates of the unconditional curve.

Qˆ

p, final Bulletin 17B-estimated frequency curve.

Q

H, historical threshold streamflow.

Q

O, flood base streamflow.
vi

Qˆ

s,p, systematic frequency curve ordinate at exceedance probability p.

RMSE, root mean square error.

S, sample logarithmic standard deviation.

S

ˆ, Bulletin 17B standard deviation.

S

~

, historically-weighted logarithmic standard deviation.

S

~

 ́, standard deviation of frequency curve passing through Q*~ 0.50. Q*~ 0.10, and Q*~ 0.01.

t

n-1, Student’s t random variate with n-1 degrees of freedom.

t

n-1,p, Student’s t quantile with n-1 degrees of freedom and exceedance probability p.

W, weight given to systematic peaks below historical threshold.

X ́, logarithmic magnitudes of historic peaks and high outliers.

X, sample logarithmic mean.

X, logarithmic magnitudes of systematic peaks between QO and QH.

XH, logarithmic high-outlier test threshold.

XL, logarithmic low-outlier test threshold.

α, confidence level.

γ, population skew coefficient.

μ, population mean.

σ, population standard deviation.

>, less than.

<, greater than.

≤, greater than or equal to.

Note: Most symbols and explanations from Interagency Advisory Committee on Water 

Data (1982) and Lepkin and others (1979).
Abstract

Estimates of flood flows having given recurrence intervals or probabilities of exceedance are needed for design of 

hydraulic structures and floodplain management. Program 

PeakFQ provides estimates of instantaneous annual-maximum 

peak flows having recurrence intervals of 2, 5, 10, 25, 50, 100, 

200, and 500 years (annual-exceedance probabilities of 0.50, 

0.20, 0.10, 0.04, 0.02, 0.01, 0.005, and 0.002, respectively). 

As implemented in program PeakFQ, the Pearson Type III 

frequency distribution is fit to the logarithms of instantaneous 

annual peak flows following Bulletin 17B guidelines of the 

Interagency Advisory Committee on Water Data. The parameters of the Pearson Type III frequency curve are estimated by 

the logarithmic sample moments (mean, standard deviation, 

and coefficient of skewness), with adjustments for low outliers, high outliers, historic peaks, and generalized skew. This 

documentation provides an overview of the computational 

procedures in program PeakFQ, provides a description of the 

program menus, and provides an example of the output from 

the program.

Introduction

Program PeakFQ performs statistical flood-frequency 

analyses of annual-maximum peak flows (annual peaks) following procedures recommended in Bulletin 17B of the Interagency Advisory Committee on Water Data (1982), referred to 

hereinafter as Bulletin 17B. The following sections document 

the implementation of the Bulletin 17B guidelines in program 

PeakFQ. This information is intended to assist the user with 

selection of program options and interpretation of the program output. Program users should refer to Bulletin 17B for 

the complete and definitive description of the recommended 

procedures.

The Bulletin 17B procedures treat the occurrence of 

flooding at a site as a sequence of annual random events or 

trials. The magnitudes of the annual events are assumed to be 

independent random variables following a log-Pearson Type 

III probability distribution; that is, the logarithms of the annual 

peak flows are assumed to follow a Pearson Type III distribution. This distribution defines the probability that any single 

annual peak will exceed a specified streamflow. Given this 

annual exceedance probability, other probabilities, such as the 

probability that a future design period will be free of exceedances, can be calculated by standard methods, as described 

in Appendix 10 of Bulletin 17B. Program PeakFQ estimates 

the parameters of the log-Pearson Type III frequency distribution from the logarithmic sample moments (mean, standard 

deviation, and coefficient of skewness) of the record of annual 

flows, with adjustments for low outliers, high outliers, historic 

peaks, and generalized peak skew. The parameter values are 

used to calculate the percentage points (or quantiles) of the 

log-Pearson Type III distribution for selected exceedance 

probabilities.

Peak Streamflow Records

The U.S. Geological Survey maintains a peak-flow file 

in the National Water Information System (NWIS) data base. 

The contents and format of data retrieved from the peak-flow 

file are described in Appendices B.2 (Station Header Records) 

and B.4 (Peak-Flow Records). Program PeakFQ uses the station identification number and name to label the printed output 

and may use the station latitude and longitude to look up the 

generalized skew. The Bulletin 17B statistical computations 

use only the annual-peak discharge and discharge-qualification 

codes from the peak-flow records; the gage-height information 

and all information about partial-duration or secondary peaks 

is ignored.

The annual peak-flow data fall into two classes: systematic and historic. The systematic record includes all annual 

peaks observed in the course of one or more systematic 

gaging programs at the site. In a systematic gaging program, 

the annual peak is observed (or estimated) for each year of 

the program. Several systematic records at one site can be 

combined, provided that the hydrologic conditions during the 

periods of record are comparable. The gaps between distinct, 

systematic-record periods can be ignored, provided that the 

lack of record in the interim was unrelated to the hydrologic 

conditions. Thus, if a flood record was interrupted for lack 

of funds for data collection, the interruption could be ignored 

and the available data could be used as if no interruption had 

occurred. On the other hand, if the record was interrupted 

because of prolonged drought or excessive flooding, the interruption should not be ignored but rather should be used, if possible, as evidence for adding one or more estimated peaks to 

the systematic record. Thus, the systematic record is intended 

User’s Manual for Program PeakFQ, Annual FloodFrequency Analysis Using Bulletin 17B Guidelines

By Kathleen M. Flynn1, William H. Kirby1, and Paul R. Hummel2

1

 U.S. Geological Survey

2

 Aqua Terra Consultants
to constitute an unbiased and representative sample of the 

population of all possible annual peaks at the site.

In addition to the systematic record, some stations have 

a historic record consisting of generally isolated high-magnitude peaks that occurred outside the period of systematic data 

collection. In contrast to the systematic record, the historic 

record consists of annual peaks that would not have been 

observed except for a recognition that an unusually large peak 

had occurred. Flood information acquired from old newspaper 

articles, letters, personal recollections, and other historical 

sources almost invariably refers to floods of noteworthy, and 

hence extraordinary, size. Similarly, paleoflood information, 

determined by analysis of geological or botanical evidence, 

is considered historic information and almost always refers to 

extraordinary floods. Thus, historic records, by the conditions 

of their collection, form a biased and unrepresentative sample 

of flood experience. Despite this bias, however, the historic 

record can be used to supplement the systematic record 

provided that all historic peaks above some historic threshold 

have been recorded.

The systematic record also may contain one or more 

large-magnitude peaks for which historic information is available or which exceed some historic peaks. Such peaks are 

called high outliers if they are greater than the high outlier 

threshold. They are not considered historic peaks because 

they are part of the systematic record. In particular, the peak 

of record is not considered a historic peak if it occurred during 

a period of systematic data collection. Although high outliers 

are part of the systematic record, they also are treated in the 

same way as historic peaks in the historic-record adjustment 

procedure.

Qualification codes are assigned to some peaks to 

identify (1) basin or environmental conditions that may have 

affected the magnitude of the streamflow, (2) measurement 

conditions that may have affected the accuracy of the recorded 

value and (3) historic peaks. These codes are described in 

Appendix B.4 and also in the NWIS-Web Help System at 

URL -- http://nwis.waterdata.usgs.gov/nwis/help?codes_

help#flow_qual_cd. Note that an individual peak flow can 

have more than one qualification code associated with it. 

Program PeakFQ recognizes several of these codes and uses 

them to control the statistical computation. For example, 

discharge code 4 (discharge less than indicated value, reported 

as the mnemonic letter code L in the PeakFQ output file) automatically triggers the zero-flow and conditional-probability 

adjustments. Table 1 identifies the peak-flow file qualification 

codes used by program PeakFQ, explains how these codes 

are interpreted by the program, and briefly describes how the 

PeakFQ program handles the associated peaks.

Principles of Computations

The Bulletin 17B computational analysis is illustrated in 

figure 1. The following sections provide an overview of the 

major computational steps.

Systematic-Record Analysis

The systematic-record analysis involves the computation 

of the mean, standard deviation, and coefficient of skewness 

(X, S, and G, respectively) of the common logarithms of the 

annual peak flows in the systematic record. At some sites, 

annual peaks of magnitude zero can occur; more generally, 

the annual peak may occasionally fall below or be equal to 

Table 1. Peak-flow codes used by program PeakFQ

[NWIS--National Water Information System]

PeakFQ code NWIS code PeakFQ Interpretation PeakFQ Action

D 3 Dam failure, non-recurrent flow anomaly Peak always excluded.

G 8 Discharge greater than stated value Peak always excluded.

X 3 and 8 Both D and G Peak always excluded.

L 4 Discharge less then stated value Conditional-probability adjustment

K 6 or C Known effect of regulation, urbanization, or other 

watershed change

Peak excluded by default. Can be included by 

specifying “yes” in the “Urban/Reg Peaks” 

field of the PeakFQ station specifications.

H 7 Historic peak. (Note: Historic peaks are events that 

occur outside periods of systematic data collection. 

The peak of record is not a historic peak if it was 

observed as part of the systematic record collection. 

See text for additional details.)

Peak excluded by default. Can be included by 

specifying a value for historic period in the 

PeakFQ station specifications, in which case 

the historic adjustment will be applied.

- 1, 2, 5, 9, A, B, 

or E

Codes are not considered by PeakFQ Peak always included.

2 User’s Manual for Program PeakFQ
Figure 1. General flow chart for flood-frequency computations (modified from Interagency Advisory Committee on Water Data, 1982).

Principles of Computations 3

Compute empirical probability plotting positions, including any historic adjustment

Compute frequency curve of logarithmic Pearson Type III ordinates, including

conditional probability adjustment and weighted skew calculation

Compute frequency curve extensions:

“expected probability” curve and confidence limits End

Outliers or

historic?

Yes

Detect low outliers;

raise flood base

Detect high outliers and

historic peaks;

set historic period

No

Yes

Yes

No

No

Detect high outliers and

historic peaks;

set historic period

Detect low outliers;

raise flood base

Low

outliers?

Low

outliers?

Yes

Detect low outliers;

raise flood base

Recompute

statistics of

above-base peaks

Detect high outliers and

historic peaks;

set historic period

High outliers

or historic?

Recompute

statistics of

above-base peaks

for historic period

Yes

No

No

Begin

> 0.4

Begin Analyze systematic peaks

Station skew

G

Recompute

statistics of

above-base peaks

for historic period

Recompute

statistics of

above-base peaks

for historic period

< -0.4

-0.4 < G < 0.4

High outliers

or historic?

Recompute

statistics of

above-base peaks

for historic period
some lower limit of measurement called the gage base (which 

usually is zero but may be greater than zero). To account for 

this possibility, the number of peaks below the gage base is 

computed in addition to the mean, standard deviation, and 

skewness of the logarithms of the above-base systematic 

peaks. The statistics of the above-base systematic peaks and 

the number of peaks below the gage base are used to compute 

the systematic-record frequency curve. If there are no zeroes 

or below-base peaks, the systematic-record frequency curve is 

computed as follows:

Qs,p X Skg,p ˆ log = + , (1)

where Qˆ s,p = systematic frequency-curve ordinate at 

exceedance probability p, and 

kg,p = the Pearson Type III standardized ordinates 

for station skew g and exceedance 

probability p.

If there are zeroes or below-base peaks, the statistics of 

the above-base systematic peaks are used to define a conditional above-base systematic-record frequency curve, which 

is then adjusted by the conditional-probability adjustment, as 

described in a subsequent section and in Bulletin 17B, Appendix 5.

The systematic-record frequency curve is an initial 

estimate of the Bulletin 17B frequency curve. This initial 

estimate is adjusted to account for historic data, high and low 

outliers, and regional (generalized) skew information.

Outlier Tests

Peaks that depart substantially from the trend of the 

remaining peaks are outliers. The first adjustments of the 

initial frequency curve involve detecting and accounting for 

high and low outliers. The sequence of these tests and adjustments depends on the station skew coefficient, G, computed 

in the first step. Because a relatively large skew coefficient of 

either sign (G > +0.4 or G < -0.4) is likely to be caused by an 

outlier on the corresponding end of the sample, this possibility 

is checked first and any necessary adjustment is applied before 

checking for outliers on the other end. If the skew coefficient 

is of moderate size (-0.4 ≤ G ≤ +0.4), the existence of both 

high and low outliers can be checked before applying any 

adjustments.

Program PeakFQ tests for high outliers using the following equation:

XH = X + KNS, (2)

where XH = Logarithmic high-outlier test threshold, 

and 

KN = 10-percent significance-level critical value 

for outlier test statistic for samples of 

size N from the normal distribution. (See 

Bulletin 17 B Appendix 4.) 

Program PeakFQ does not automatically use the highoutlier test threshold in the analysis. Flood peaks considered 

high outliers should be evaluated in the context of the flood 

record at the site and at nearby sites. If the records indicate 

a high outlier(s) is the maximum in an extended period of 

time, the outlier(s) should be treated as historic data. For this 

case, the program requires the user to specify the high-outlier 

threshold and length of historic period in order for the highoutlier and historic-peak adjustment to be applied. The computations for performing the adjustment are described in the 

next section. If the record does not contain sufficient information to adjust for high outliers, they should be retained as part 

of the systematic record. For this case, no values are specified 

for the high-outlier threshold and length of historic period.

Program PeakFQ tests for low outliers using the following equation:

XL = X − KNS, (3)

where XL = logarithmic low-outlier test threshold.

If an adjustment for historic data has previously been 

made, then the following equation is used to detect low outliers:

S

~ M K ~ XL = − H , (4)

where

= historically-weighted logarithmic mean, 

KH = 10-percent significance-level critical value 

for outlier test statistic for sample of size 

H, where H is the length of the historic 

record period, and

S

~ = historically-weighted logarithmic standard 

deviation.

The computation of M

~ and S

~

 is described in the next 

section.

The frequency curve is automatically adjusted for the 

effect of low outliers using the conditional probability adjustment described later.

Historic-Record Adjustment

Recalculation of the statistics of the above-base peaks is 

required after the detection of outliers or historic information, 

as specified in Appendix 6 of Bulletin 17B. The logical basis 

for the calculation is the following:

Historic-adjustment criterion: It is assumed that every 

annual peak that exceeded some historic threshold streamflow 

(QH) during the historic period (H) has been recorded as either 

a historic peak or a systematic peak (high outlier). In other 

words, the record is complete for peaks above QH during the 

time period H.

The historic period H includes the systematic-record 

period plus one or more years that have no systematic record. 

This criterion implies that the unrecorded portion of the 

M

~

4 User’s Manual for Program PeakFQ
historic period contains only peaks below the threshold QH. 

Figure 2 presents a definition sketch showing the time periods 

and streamflows used in the historic-record adjustment. 

The Bulletin 17B historic adjustment, in effect, fills in 

the ungaged portion of the historic period with an appropriate 

number of replications of the below-QH portion of the systematic record. The adjustment is accomplished by weighting the 

below-threshold systematic peaks in proportion to the number 

of the below-threshold years in the historic period, as illustrated in figure 2, as follows:

S HO

HP HO

N N

H - N N W −− = , (5)

where W is the weight to be applied to the below-threshold 

systematic peaks and NS, NHP, and NHO are the numbers of systematic peaks, historic peaks, and high outliers, respectively. 

Then the effective number of peaks, Ñ, above the flood base 

(QO) is

( HO BB ) ( BB ) N NHP NHO W NS N N H W N ~ = + + − − = − , (6) 

where NBB is the number of peaks below the flood base, 

including any zeros and low outliers.

The corresponding estimated probability of a flood 

exceeding the flood base is

P = O H  ̃ Ñ. (7)

Applying the historic weight W to those systematic peaks 

below the historic threshold QH (and above the flood base QO) 

yields the following formulas for the historically-weighted 

mean (M

~ ), standard deviation (S

~), and skewness (G

~):

( )

N

~ W X X M

~ ∑ + ∑ ′ = , (8)

( ) ( )

(N 1) ~

M

~ M X ~ W X

S

~ 2 2

−



  − + ′ − = ∑ ∑ , (9)

( ) ( )

( )( ) 3

3 3

S

~ N 2 ~ N 1 ~

N

~ M~ M X ~ W X

G

~

− −

− + ′ − = ∑ ∑ 

 



, and (10)

in which X ́ denotes logarithmic magnitudes of historic 

peaks and high outliers and X denotes logarithmic magnitudes 

of systematic peaks between the flood base QO and the historic 

threshold QH. These formulas are equivalent to those given in 

Appendix 6 of Bulletin 17B.

These formulas remain correct even if there is no historic 

information (in which case H = NS), no high or low outliers, 

and no below-gage base peaks. Thus, these formulas are used 

in PeakFQ to calculate the Bulletin 17B statistics in all cases, 

including the calculation of the unadjusted systematic record 

statistics.

Figure 2. Definition sketch showing time periods and discharges used in historic record adjustment.

Principles of Computations 5

NHP NBB NHO

QO

QH

X

X'

NX

NS

H
Conditional-Probability Adjustment

After the peak-streamflow frequency curve parameters 

have been determined, the historically weighted frequency 

curve can be tabulated. If no low outliers, zero flows, or 

below-gage base peaks are present, this process is simply a 

matter of looking up the Pearson Type III standardized ordinates, kg, p, for the desired skew coefficient (g) and probability 

(p) and computing the logarithmic frequency curve ordinates 

by the formula:

p g,p Sk

~ M

~ Qˆ log = + . (11) 

When peaks below the flood base are present, however, 

the above calculation determines a conditional frequency curve 

Q

~

 describing only those peaks above the base. To account for 

the fraction of the population below the flood base, the following argument is used: the probability that an annual peak 

will exceed a streamflow x (above the flood base) is the probability that the peak will exceed the base at all, multiplied by 

the conditional probability that the peak will exceed x, given 

that the peak exceeds the base. The first of these factors is 

just the probability, P

~

O, calculated in equation (7); the second 

factor is the probability on the conditional frequency curve 

at streamflow x. Thus the unconditional curve, Q*~ , assigns a 

probability [P

~

O]p to the streamflow having exceedance probability p on the above-base curve. Conversely, an exceedance 

probability p on the unconditional curve Q*~ corresponds to the 

probability p/P

~

O on the original above-base curve Q

~

. Thus, the 

ordinates of the unconditional curve can be computed directly 

by the formula:

P ) ~ G,(p/ ~ p O

Sk

~ M

~ Q*~ log = + , (12)

in which M

~ , S

~

, and G

~

 are the logarithmic mean, standard 

deviation, and skew coefficient, respectively, of the above-base 

distribution.

Because this distribution does not have the Pearson Type 

III shape, it is used only as an intermediate step in constructing 

an equivalent Pearson Type III curve. First, the three points 

Q*~ 0.50, Q*~ 0.10, and Q*~ 0.01 are computed using the above 

formula. Then a logarithmic-Pearson Type III curve is passed 

through these three points; the curve mean, standard deviation, 

and skew coefficient, M

~  ́, S

~

 ́, and G

~

 ́, respectively, are found 

by solving the three simultaneous equations:

G,p p ~ Q*~ S k log ~ M

~ ′ + ′ = (for p = 0.50, 0.10, and 0.01). (13) 

An exact solution requires a laborious interpolation in the 

Pearson Type III tables; the Bulletin 17B guidelines present a 

direct formula based on a linear approximation. Note that 

M

~  ́, S

~

 ́, and G

~  ́ represent the contributions of all the observed 

peaks, those below the base as well as those above, whereas 

M

~ , S

~

, and G

~

 do not. The resulting unconditional frequency 

curve, when floods below the base have been detected, then is:

G ,p ~ p S k ~ M

~ Qˆ log ′ = ′ + ′ . (14) 

This defines only the part of the distribution above the 

flood base; the part below the flood base is not defined, and is 

of no practical importance.

These conditional-probability adjustments are used not 

only to construct the final Bulletin 17B frequency curve, but 

also to construct a systematic-record frequency curve that 

takes into account any zero flows or below-gage base peaks 

(but not low outliers).

Computation of Weighted Skew Coefficient

The station- (or sample-) skew coefficient, which reflects 

the average of the cubed deviations from the sample mean, 

is highly sensitive to the observations in both the upper and 

lower tails of the sample. As a result, the estimated stationskew coefficient and extreme-flood quantiles may be strongly 

affected by idiosyncrasies of the sample, and may be unrepresentative of long-term flood characteristics. To help counter 

this problem, Bulletin 17B uses a generalized skew, which is 

a skew coefficient representative of neighboring stations, as 

explained in a subsequent section.

The station skew and generalized skew are combined in 

a weighted average that is expected to be more accurate than 

either of its constituents. Guidelines for estimating generalized skew are given in Bulletin 17B and are summarized in 

a subsequent section of this manual. Program PeakFQ does 

not perform generalized skew estimation. Instead, program 

PeakFQ either looks up the generalized skew from a digitized 

copy of the map in Bulletin 17B or reads it from user-supplied input (see preceding section). The following paragraphs 

explain the weighted skew computation.

The station skew, the generalized skew, and the weighted 

skew are quantities that are estimated from flood records at 

and near the station under study. As such, they are subject 

to estimation errors. The error in each of the skew statistics 

is characterized by two properties, the expected value (bias) 

and the standard deviation (standard error), representing 

systematic errors and random-sampling variability, respectively. The random and systematic errors are combined in a 

single composite property called mean-square error (MSE), 

which is the expected value of the difference between the 

estimated and true values of the statistic (station, generalized, 

or weighted skew). The MSE is the sum of the squares of the 

bias and standard error. The MSE often is reported in terms of 

its square root, the Root Mean Square Error (RMSE), which 

is directly comparable to the quantity being estimated (rather 

than to its square) and can be expressed as a percentage. If 

the bias is small relative to the standard error, the RMSE is 

approximately equal to the standard error. Because of its wide 

availability and usefulness, the RMSE is used as input to program PeakFQ; the program squares the input RMSE to obtain 

the MSE values used in equation 15.

6 User’s Manual for Program PeakFQ
The station- and generalized-skew coefficients are combined in a weighted average to form a better estimate of the 

skew coefficient for a given watershed. Under the assumption 

that the generalized-skew coefficient is unbiased and independent of the station-skew coefficient, the MSE of the weightedskew estimate is minimized by weighting the station- and 

generalized- skew coefficients in inverse proportion to their 

individual MSE’s. This concept is expressed in equation 15, 

adapted from Tasker (1978), which is used in computing the 

weighted-skew coefficient:

( ) ( )

G G

G G

W MSE MSE

MSE G MSE G

G

+

+ = (15)

where GW = weighted-skew coefficient, 

G = station-skew coefficient, 

G = generalized-skew coefficient, 

MSEG = mean-square error of generalized-skew 

coefficient, and 

MSEG = mean-square error of station-skew 

coefficient. 

The MSE (or RMSE) of the generalized skew is estimated in conjunction with the development of the generalized-skew value. In program PeakFQ, if the user does not 

specify a value for the generalized-skew coefficient, the value 

is obtained from a digitized version of Plate 1 of Bulletin 17B, 

and the corresponding value of MSEG= 0.302 is used in equation 15. (The corresponding RMSE value is 0.55.) Otherwise, 

the user must supply the RMSE of the generalized skew as 

input data along with the user-supplied generalized-skew 

value.

The MSE of the station skew for log-Pearson Type III 

random variables is obtained from the results of Monte Carlo 

experiments by Wallis and others (1974). Their results show 

that the MSE of the logarithmic station skew is a function of 

record length and population skew. This function (MSEG) is 

approximated with sufficient accuracy for use in calculating 

the weighted skew by the equation:

[A B[log (N/10)]] G 10 MSE 10 − = (16)

where A = -0.33 + 0.08 |G| if |G| ≤ 0.90,

 -0.52 + 0.30 |G| if |G| > 0.90,

B = 0.94 - 0.26 |G| if |G| ≤ 1.50, and

 0.55 if |G| > 1.50,

in which |G| is the absolute value of the station-skew coefficient (used as an estimate of population-skew coefficient) 

and N is the record length in years. If the historic adjustment 

(Bulletin 17B, Appendix 6) has been applied, the historicallyadjusted skew coefficient, G

~

, and historic period, H, are used 

for G and N, respectively, in equation 16.

Bulletin 17B indicates that equations 15 and 16 may 

underestimate the weight given to the station skew if the station skew is large and the record is long, or if the magnitude 

differs from the generalized skew by more than 0.5. In these 

cases, Bulletin 17B suggests that the peak-flow data and the 

flood-producing characteristics of the basin be examined to 

determine whether greater weight should be given to the station skew.

Expected-Probability Adjustment

The final steps in the Bulletin 17B analysis, as implemented in program PeakFQ, are to compute the expectedprobability frequency curve and a set of upper and lower 

confidence limits. These computations are optional and are 

intended primarily as an aid to the interpretation of the principal Bulletin 17B-estimated frequency curve given by 

Qˆ p above.

The expected probability concept deals with the following problem. A sample of size n will be drawn from a normal 

population (of flood logarithms), and the flood having a specified exceedance probability p will be estimated by the quantity 

X+ kp

S, in which X and S are the ordinary sample mean and 

standard deviation, respectively, and kp is the standard normal 

frequency factor for probability p. Because it is computed 

from a random sample, the estimate X + kpS is a random variable, that usually will differ from the true p-probability flood. 

Thus, one is led to ask how the probability of another flood 

exceeding the estimate X + kpS compares with the specified 

(nominal) probability p. For a normal population, one has:

{ } 











> − > + p = kp S

X X P X X k S P





















 





+ = − >

0.5

n 1 p n 1

n P , t k

(17)

where tn-1 is Student’s t random variate with n-1 degrees 

of freedom. This probability has come to be known as the 

“expected probability” (Beard, 1960; Bulletin 17B, Appendix 11). For nominal exceedance probabilities less than 0.50 

(floods above the median), the expected probability exceeds 

the nominal probability. The expected probability can be 

made equal to the nominal probability by replacing kp by the 

frequency factor:

[( ) ]0.5

p n 1,p k′ = t − n +1 /n , (18)

in which tn-1,p is the Student‘s t value with n-1 degrees of freedom and exceedance probability p. The visible effect of this 

adjustment is to increase the slope of the estimated frequency 

curve in proportion to the statistical variability of the sample 

statistics.

This normal-population result is applied to the Bulletin 17B-estimated Pearson Type III distribution with mean, 

standard deviation, and skew coefficient, Mˆ , S

ˆ, and GW, by 

first looking up the normal exceedance probability p ́ corresponding to k ́p

 and, second, applying the Pearson Type III 

frequency factor, kG, p ́ having skew coefficient and probability, 

to the sample mean and standard deviation, as follows: 

Principles of Computations 7
Mˆ + S

ˆ (kGW,p ́

). Even this estimate, however, when evaluated 

for any particular sample, normally will misrepresent the true 

p-probability flood. With respect to a large number of flood 

records, however, the fraction of floods actually exceeding the 

estimated p-probability floods will be correct. Nonetheless, 

the Bulletin 17B guidelines specify that the basic flood-frequency curve (without expected probability) is the curve to be 

used for estimating flood risk and forming weighted averages 

of independent flood-frequency estimates.

Confidence Limits

Finally, one-sided confidence limits for the p-probability 

flood are computed. A one-sided confidence limit is a sample 

statistic—hence a random variable—having a specified probability (confidence level) of exceeding (or not exceeding) a 

specified population characteristic. In the Bulletin 17B analysis, these statistics are of the form X + KS, where X and S are 

the sample mean and standard deviation, respectively, after all 

Bulletin 17B tests and adjustments and K is a confidence coefficient chosen to satisfy the following equation:

P{X + KS > μ + kγ,p (σ)}= α, (19)

in which α is the confidence limit, μ, σ, and γ are the population mean, standard deviation, and skew coefficient, respectively, kγ,p

 is the Pearson Type III frequency factor, and the 

right-hand side of the inequality is the population p-probability 

flood. The population parameters are unknown, but constant. 

The idea is to find a K-value such that X + KS, which can be 

computed from the sample, and is a random variable, will have 

a high probability of being an upper (or lower) bound on the 

unknown population p-probability flood. In any particular 

sample the computed value X + KS may fail to bound the 

population characteristic, but, over a number of samples, the 

specified fraction, -α (or 1-α), will yield correct bounds. A 

value of α close to unity yields upper confidence limits and a 

value close to zero yields lower limits. In particular, the upper 

95-percent confidence limit has α = 0.95; the lower 95-percent 

limit has α = 0.05. The value of K is found by rearranging the 

probability statement as follows:

(( ) ( ) ( ))

( ) n (K) σ

S/σ

μ X / σ/ n n k

P γ,p =

















< − +

(20)

in which n is the sample size. If the underlying population 

were normally distributed (γ = 0), and if X and S were the 

ordinary sample mean and standard deviation, respectively, 

then the random variable on the left-hand side of the inequality 

would have the noncentral t distribution with n-1 degrees of 

freedom and noncentrality parameter n (kγ,p). If the underlying population had a small skew, if the sample were large, and 

if the population skew coefficient, γ, could be replaced by the 

Bulletin 17B estimated skew coefficient, GW, then one could 

assume that the variate would have approximately the noncentral t distribution. Building upon this foundation, one obtains:

n (K) t , n(k ),(1 α) = n−1 GW ,p − , (21)

which is the noncentral t value with exceedance probability 

l-α. A standard large-sample approximation for the noncentral 

t distribution then yields the result:

( ) ( ) ( )

( )

( )

2(n 1)

1 k

2 n 1

nk k

1

n

k

k

K 2

1 α

0.5 2

G ,p 1 α

2

1 α G ,p W

W

−

−





















−

− + +

=

−

− −

, (22)

in which k(1-α) is the standard normal deviate with exceedance 

probability 1-α and GW is the Bulletin 17B weighted-skew 

coefficient. As stated above, an α-value near unity yields 

upper confidence limits whereas a value near zero yields lower 

limits. This result is equivalent to that in the Bulletin 17B 

guidelines.

Probability-Plotting Positions

Probability plotting positions are estimates of the exceedance probabilities of observed peak flows. They are computed 

by the formula p = (m-a)/(N-2a+1) (equation 10 in Bulletin 

17B), in which m is the rank of an observed peak (m = 1 for 

highest peak), N is the sample size, and a is a constant characteristic of a particular plotting-position formula. Bulletin 17B 

and Program PeakFQ use the Weibull plotting-position formula (a = 0) by default, although other a-values can be specified. The probability-plotting positions are not used in the 

Bulletin 17B computations, but are used in graphic displays of 

the observed data in relation to the fitted frequency curve.

If there is historical information, the probability-plotting 

positions are adjusted using the same logic that underlies the 

calculation of the historically-weighted mean, standard deviation, and skew coefficient. The actual sample of size N is augmented by (W-1) “virtual” copies of the observed peaks below 

the historic threshold to fill out the entire historic period (H). 

In the ranked record, each below-threshold observed peak is 

preceded by (W-1)/2 of its virtual copies and followed by the 

remaining (W-1)/2 copies. In the augmented ranked series, if 

there are Z peaks above the historic threshold, then the rank 

of the first below-threshold observed peak is Z + (W-1)/2 + 1. 

The rank of the second below-threshold observed peak is 

Z + W + (W-1)/2 + 1. In general, the historically adjusted 

rank m

~ of the mth ranked observed peak is:

m

~ = m if m <= Z (23)

 = Z + W ((m-Z) - 1/2) + 1/2 if m > Z

where Z = NHO +NHP.

8 User’s Manual for Program PeakFQ
The historically-weighted plotting positions P

~

m then are:

P

~

m = (m

~ - a) / (H - 2a + 1). (24)

These equations are equivalent to equations 6-6 through 

6-8 in Appendix 6 of Bulletin 17B. As indicated above, 

program PeakFQ uses the Weibull plotting-position formula 

(a = 0) by default, although other a-values can be specified.

Estimation of Generalized Skew

The skew of a frequency distribution has a great effect on 

the shape and thus the values of the distribution, particularly in 

the extreme tail, which is of most concern in flood-risk estimation. The skew coefficient of the station record (station skew 

coefficient, G) is sensitive to extreme events; thus it is difficult 

to obtain an accurate estimate of the skew coefficient from a 

small sample. The accuracy of the estimated skew coefficient 

can be improved by weighting the station-skew coefficient 

with a generalized-skew coefficient estimated by pooling 

information from nearby sites.

Program PEAKFQ does not perform generalized-skew 

estimation. The program either looks up the generalized skew 

in a digitized version of the map (Plate I) in Bulletin 17B or 

reads the generalized skew and its associated RMSE from 

user-supplied input. The estimation of the generalized skew is 

performed by the flood-frequency analyst.

The discussion in this section concerns Bulletin-17B 

guidelines for development of appropriate generalized-skew 

coefficients for flood-frequency analysis. The following discussion is modified from Bulletin 17B (p. 10-14).

Bulletin 17B includes a map (Plate I) showing generalized-skew values that may be used in the absence of detailed 

generalized-skew studies. This map and its corresponding 

MSE of 0.302 (RMSE = 0.550) were developed when Bulletin 

17 was first introduced in 1976 and have not been updated.

Additional peak-flow records have become available 

since that time. Also, the procedures used to develop the map 

do not conform in all respects to Bulletin 17B. Generalizedskew estimates developed in accordance with Bulletin 17B 

procedures should preferably be used if available. Nonetheless, Plate I is still considered an alternative for use with Bulletin 17B for those who prefer not to develop their own generalized-skew estimates. Program PeakFQ contains a digitized 

version of this map, which is used if the user does not specify 

a generalized skew and RMS error.

The Bulletin-17B recommended procedure for developing generalized-skew coefficients requires the use of at least 

40 stations, or all stations within a 100-mile radius. The stations used should have 25 or more years of record. It is recognized that in some locations, a relaxation of these criteria may 

be necessary. The actual procedure includes analysis by three 

methods: (1) skew isolines drawn on a map; (2) skew prediction equation; and (3) the mean skew coefficient from selected 

stations. Each of the methods is discussed separately.

To develop the isoline map, each station-skew coefficient 

is plotted at the centroid of its drainage basin and the plotted 

data are examined for any geographic or topographic trends. 

If a pattern is evident, then isolines are drawn and the average 

of the squared differences between observed and isoline values, MSE, is computed. The square root of the MSE (RMSE 

or RMS error) should be computed to permit a better appraisal 

of the expected magnitude of the discrepancy between the generalized and station skews relative to the absolute magnitude 

of the skews. The MSE or RMSE will be used in appraising 

the accuracy of the isoline map. If no pattern is evident, then 

an isoline map cannot be drawn and is, not considered further.

A prediction equation should be developed that would 

relate either the station-skew coefficients or the differences 

from the isoline map to predictor variables that affect the skew 

coefficient of the station record. These would include watershed and climatologic variables such as drainage area, channel slope, and precipitation characteristics. The prediction 

equation should be used preferably for estimating the skew 

coefficient at stations with variables that are within the range 

of data used to calibrate the equation. The MSE (or RMSE) 

should be computed as the average (or square root of the average) of the residuals between the observed station skews and 

the fitted relation. If the relation is fitted by linear regression, 

then the standard error of regression can be taken as equivalent 

to the RMSE. The MSE (or RMSE) will be used to evaluate 

the accuracy of the prediction equation.

Determine the arithmetic mean and variance (or standard 

deviation) of the skew coefficients for all stations. In some 

cases, the variability of the runoff regime may be so large as to 

preclude obtaining 40 stations with reasonably homogeneous 

hydrology. In these situations, the arithmetic mean and variance of about 20 stations may be used to estimate the generalized-skew coefficient. The drainage areas and meteorologic, 

topographic, and geologic characteristics should be representative of the region around the station of interest. The variance 

(or standard deviation) is taken as comparable to the MSE (or 

RMSE) and is used to appraise the accuracy of the mean value 

as a prediction of the skew.

Select the method that provides the most accurate estimate of the skew coefficient. Compare the MSE from the isoline map to the MSE for the prediction equation. The smaller 

MSE should then be compared to the variance of the data. If 

the MSE is significantly smaller than the variance, the method 

with the smaller MSE should be used and that MSE used in 

equation 15 to predict the weighted skew coefficient. If the 

smaller MSE is not significantly smaller than the variance, 

neither the isoline map nor the prediction equation provides 

a significantly more accurate estimate of the skew coefficient 

than the mean value. In this case, the mean skew coefficient 

should be used because it provides as accurate an estimate as 

the more complicated alternatives; the variance should be used 

in equation 15 for the MSE of the generalized skew MSEG.

The accuracy of a regional generalized skew relations is 

generally not comparable to the accuracy of Plate I in Bulletin 17B. Whereas the average accuracy of Plate I is given, 

Principles of Computations 9
the accuracies of subregions within the United States are not 

given. A comparison should be made only between relations 

that cover approximately the same geographical area.

Computer Program

The following sections describe the computer program 

PeakFQ for performing the Bulletin 17B flood-frequency 

analysis. There are two methods for running PeakFQ: a Windows version (called PKFQWin) and a batch version (called 

PKFQBat).

Windows Version (PKFQWin)

The program PKFQWin provides a user interface to the 

PeakFQ batch model. The opening screen of the program is 

shown below in figure 3.

When first opened, most of the interface is disabled. The 

interface is designed to follow a logical procession toward 

running PeakFQ: Use the File:Open menu item to open a 

PeakFQ data file. View/edit the Station Specifications that are 

populated by the data. View/edit the Output Options. Click 

the Run PEAKFQ button and View Results. Click the Save 

Specs button to store a desired set of specifications for future 

use.

File Open

The File:Open menu item is used to open any of the file 

types that can be used by PeakFQ. These include:

Standard WATSTORE format Peak Flow data, as 

described in Appendices B.2, B.3, and B.4. Data in 

this format can be found on the NWIS-Web at 

http://nwis.waterdata.usgs.gov/usa/nwis/peak.

Watershed Data Management (WDM) files, as 

described in Appendix C.

PeakFQ Specification (PSF) files, as described in 

Appendix B.1.

Selecting the File:Open menu item opens the Open 

PeakFQ File dialogue. As shown in figure 4, this dialogue 

can open any of the three file types discussed above. After 

opening a file, the Station Specifications tab will be populated 

based on the contents of the file. Initial station specification 

values are derived from different sources for the three file 

formats: WATSTORE - station header, station option, and 

peak-flows records; WDM - data and attributes from each 

station’s data set; PSF - data file (WATSTORE or WDM) plus 

specifications for overriding initial values.

•

•

•

PKFQWin

Station Specifications Output Options Results

Run PEAKFQ Save Specs Save Specs

Use File menu to Open PEAKFQ data or PKFQWin spec file.

Update Station and Output specifications as desired.

Click Run PEAKFQ button to generate results.

File Help

PEAKFQ Data File:

PKFQWin Spec File:

Station ID

Include in

Analysis? Year Year

Beginning Ending Historic

Period Option

Skew Generalized

Skew

Gen Skew Mean

Std Error Sqr Err

Low Hist

Peak

Lo-Outlier

Threshold

High Sys

Peak

Hi-Outlier

Threshold

Gage Base

Discharge

Urban/Reg

Peaks Latitude Longitude

Plot

Name

Exit

Figure 3. Example of opening screen of program PKFQWin showing the station specifications tab before an input file has been 

opened.

10 User’s Manual for Program PeakFQ
Station Specifications

Once the selected data file has been opened and read, the 

Station Specifications tab is populated.

The default values on the Station Specifications tab are 

determined by the contents of the input file, including any 

WATSTORE “I” records or WDM attributes that may be present. The default values may be further updated if a PSF file 

was opened that contains station specifications for overriding 

defaults. The example in figure 5 shows many of the different options for the various fields. In particular, note how the 

same station may be run multiple times with different options 

between the runs (see Station IDs 03606500, 06600500, and 

11274500 in figure 5).

By default, all stations found on the data file will be 

included in the analysis. If a station is not to be analyzed, the 

Include in Analysis? field may be changed to no by either 

typing “No” or double-clicking to activate the pull-down 

menu.

By default, the Beginning Year and Ending Year fields 

contain the water years of the first and last peaks, respectively, 

in the input file for the station. If a WATSTORE “I” record 

or WDM attribute is present, positive values in the Beginning Year and (or) Ending Year fields will be provided as the 

defaults. This will determine the period of record to be used 

in the calculations. These fields may be updated interactively 

by clicking in the desired station row and typing the new 

value.

The Historic Period field displays the value of any 

user-specified historic period that may have been present in a 

WATSTORE “I” record or WDM attribute. If no user-specified value has been given, then a value of zero (0) is displayed 

and no historic adjustment is applied during computation, the 

historic peaks are ignored, and any high outliers are treated 

as normal systematic peaks. If positive, the historic period 

contains the systematic record as a subset and historic adjustment will be applied during the computation. This field may 

be updated interactively by clicking in the desired station row 

and typing the new value.

The Skew Option is, by default, “Weighted” between 

“Station” and “Generalized” skews (WTD, Bulletin 17B 

weighted skew.) If a WATSTORE “I” record or WDM attribute is present with a station option code of S or G, the default 

skew option code will be “Station” or “Generalized.” The 

three options are available for selection in a pull-down menu 

in the Skew Option field.

The Generalized Skew is, by default, based on the station latitude and longitude using the generalized-skew map 

accompanying Bulletin 17B. If a WATSTORE “I” record or 

WDM attribtute is present and the generalized skew field is 

non-blank, that value will be provided as the default. This 

field may be updated interactively by clicking in the desired 

station row and typing the new value.

Figure 4. Example of the File Open window in program PKFQWin, obtained by selecting Open from the File menu.

Open PEAKFQ File

History

Desktop

My Documents

Big Red

My Network P... PEAKFQ Watstore Data (*.pkf, *.inp, *.txt)

Look in: Windows Version (PEAKFQWin)

File name:

Files of type: PEAKFQ Watstore Data (*.pkf, *.inp, *.txt)

PEAKFQ Watstore Data (*.*)

PEAKFQ WDM Data (*.wdm)

PKFQWin Spec (*.psf)

Open

Cancel

Computer Program 11
The Gen Skew Std Error field is, by default, 0.55, corresponding to the standard error of the generalized-skew map 

accompanying Bulletin 17B. If a WATSTORE “I” record or 

WDM attribute is present and the standard error of generalized-skew field is non-blank, that value will be provided as the 

default. This field may be updated interactively by clicking in 

the desired station row and typing the new value.

The Low-Outlier-Threshold field displays the value of 

any user-specified low-outlier threshold that may have been 

present in a WATSTORE “I” record or WDM attribute. If no 

user-specified value has been given, then a value of 0.0 is displayed, and the low-outlier threshold is computed by PeakFQ 

using the Bulletin 17-B low outlier test. Any input peaks less 

than the low-outlier threshold are accounted for by the conditional-probability adjustment. Occasionally, it may be necessary or appropriate to override the Bulletin-17-B low-outlier 

test if, for example, the test criterion is very close to one of 

the input peaks or if there are several very low peaks. The 

Low-Outlier-Threshold field may be updated interactively by 

clicking in the desired station row and typing the new value.

The Hi-Outlier Threshold field displays the value of any 

user-specified historic/high-outlier threshold that may have 

been present in a WATSTORE “I” record or WDM attribute. 

If no user-specified value has been given, then a value of 0.0 is 

displayed. This field is used only if the Bulletin-17-B historic-record adjustment has been specified by the user in the 

Historic-Period field. If a value greater than zero is displayed 

in the Hi-Outlier-Threshold field, that value will be used as the 

historic/high-outlier threshold in the Bulletin-17-B historicrecord adjustment. Otherwise, the lowest historic-coded input 

peak will be used as the historic/high-outlier threshold. If 

there are no historic-coded peaks and a historic adjustment 

for a high outlier is needed, the user must specify the required 

high-outlier threshold. The Hi-Outlier-Threshold field may be 

updated interactively by clicking in the desired station row and 

typing the new value.

The Gage Base Discharge represents the lower limit of 

measureable flood peak at a station; this is zero (0) by default. 

If a WATSTORE “I” record or WDM attribute is present, a 

positive value in the field will be provided as the default. A 

negative or zero value will be ignored by the program. If 

positive, this gage-base discharge will supersede the gage base 

inferred from any “less than” NWIS qualification code (4) in 

the peak record. Note that this gage-base discharge is not the 

same as the partial-duration base discharge that may be in the 

station header “Y” record. This field may be updated interactively by clicking in the desired station row and typing the new 

value.

By default, Urban and (or) Regulated Peaks are not 

(“No”) included in the computations. These peaks are indicated by a “6” or “C” in the NWIS qualification code field. If 

a WATSTORE “I” record or WDM attribute is present, this 

field will default to “Yes” if the Station option field contains a 

“K.”

The Latitude and Longitude fields contain, by default, 

the values from the WATSTORE station header “H” record or 

the WDM attributes. They are used to compute the generalized skew if it is not entered. These fields may be updated 

interactively by clicking in the desired station row and typing 

the new value.

The Mean Square Error, Lowest Historic Peak, and 

Highest Systematic Peak fields are informational and cannot be modified. These values are determined from the peak 

record for the station.

PKFQWin

Results

Save Specs Exit

Use File menu to Open PEAKFQ data or PKFQWin spec file.

Update Station and Output specifications as desired.

Click Run PEAKFQ button to generate results.

File Help

PEAKFQ Data File: TEST2.INP

PKFQWin Spec File:

Station Specifications

Station ID

Include in

Analysis? Year Year

Beginning Ending Historic

Period Option

Skew Generalized

Skew

Gen Skew Mean

Std Error Sqr Err

Low Hist

Peak

Lo-Outlier

Threshold

High Sys

Peak

Hi-Outlier

Threshold

Gage Base

Discharge

Urban/Reg

Peaks Latitude Longitude

Plot

Name

Output Options

Run PEAKFQ

03606500

01373500

06600500

06600500

01614000

11274500

11274500

03606500 Yes

Yes

Yes

Yes

Yes

Yes

Yes

Yes

1897

1897

1882

1935

1935

1929

1932

1932

1973

1973

1968

1973

1973

1973

1973

1973

0

77

0

0

82

0

0

0

Weighted

Generalized

Weighted

Weighted

Weighted

Weighted

Weighted

Generalized

-0.5

-0.5

0.6

-0.2

-0.2

0.2

0.2

0.2

0.55

0.55

0.55

0.55

0.55

0.55

0.55

0.55

18500

18500

4400

0

0

0

0

0

0.3025

0.3025

0.3025

0.3025

0.3025

0.3025

0.3025

0.3025

0

0

0

0

0

0

0

0

17000

17000

8800

71500

71500

22400

10200

10200

0

0

0

0

70000

0

0

0

0

0

0

0

0

0

0

0

No

No

No

No

No

No

No

No

36.0386

36.0385

41.5111

42.5767

42.5767

39.5119

37.3169

37.3169

88.2283

88.2283

73.9486

96.3119

96.3119

78.0375

121.128

121.128

03606500

03606500-1

01373500

06600500

06600500-1

01614000

11274500

11274500-1

Figure 5. Example of the Station Specification Tab of program PKFQWin after a file containing 8 sets of data has been opened.

12 User’s Manual for Program PeakFQ
Output Options

The Output Options tab is used to modify options 

for output that will be used for all of the stations processed. 

These include the output file name, saving additional output to 

other files, including additional information in the output file, 

plot types and styles, and confidence limits.

The Output File panel in figure 6 contains the name of 

the file that will be used for all regular output from the program. This includes a summary of the input data, computed 

results in tabular format, and any warning or error messages 

that may be issued. By default, the output file name will use 

the prefix of the input file name and have the .prt suffix. If 

a .psf file is used and the O FILE record is included, that file 

name will be used. A different name may be specified for 

output by choosing the Select button and entering the name 

for the file. See appendix D.3 for an example output file. See 

appendix A for information on the error and warning messages 

that may be written to this file.

Three additional types of information may be included 

in the regular output file by selecting the appropriate check 

boxes. Selecting Output Intermediate Results will result 

in additional messages and tabulated information that may 

be useful for debugging purposes. Selecting this check box 

is equivalent to specifying O DEBUG YES in the .psf file. 

Selecting Print Plotting Positions will result in the Empirical 

Frequency Curves table being included in the regular output; 

this table contains the points used to generate the annual 

exceedance probability plot. Selecting this check box is equivalent to specifying O PLOT PRINTPOS YES in the .psf file. 

Selecting Line Printer Plots results in a plot rendered using 

keyboard characters; this option is included for consistency 

with older versions of the program and is equivalent to specifying PRINTER or BOTH for O PLOT STYLE in the .psf file.

The Additional Output panel contains check boxes 

for two other files. If the peaks are read from a Watershed 

Data Management (WDM) file, the computed statistics may 

be saved as attributes in the WDM file. These statistics are 

identified in appendix C, table C.2. The computed statistics 

may also be saved to a file in the Watstore standard Basin 

Characteristic format; see appendix B.5 for an example and 

a description of this file. By default, the Watstore output file 

name will use the prefix of the input file name and have the 

.bcd prefix. A different name may be specified for Watstore 

output by choosing the Select button and entering the name for 

the file. The Watstore output option is included for consistency with older versions of the program.

Within PKFQWin, a variety of Graphic Plot Formats

are available for the annual exceedance probability plot. These 

include:

Computer Graphics Metafile (CGM)

PostScript (PS)

Raster Bitmap (BMP)

Windows Metafile (WMF)

By default, NONE are produced. Click on the appropriate radio button for the desired format. There will be one 

file for each station analysis. If the radio button for CGM, 

PS, or WMF is selected, temporary BMP files are generated 

to be used for viewing from within PKFQWin; these files 

•

•

•

•

Figure 6. Example of the Output Options tab of program PKFQWin after an input file has been opened.

PKFQWin

Station Specifications

WDM

Use File menu to Open PEAKFQ data or PKFQWin spec file.

Update Station and Output specifications as desired.

Click Run PEAKFQ button to generate results.

File Help

PEAKFQ Data File: TEST2.INP

PKFQWin Spec File:

Results

Run PEAKFQ Save Specs Exit

0

0.95

Plotting Position:

Confidence Limits:

Output Intermediate Results

Print Plotting Positions

Line Printer Plots

Graphic Plot Format

None

BMP

CGM

WMF

PS

Output Options

Output File

Additional Output

Select TEST2.PRT

Select TEST2.bcd

Watstore

Computer Program 13
are deleted at the end of the session. If the BMP format is 

selected, the files are retained at the end of the session.

By default, the Plotting Position used is 0.0, this is the 

Weibull plotting position. Other named plotting positions 

include Median/Beard (0.3), Bolm (0.375), Cunnane (0.4), 

and Gringorten (0.44). The plotting position is entered as a 

numeric value and is not restricted to the named values. See 

the description of O PLOT POSITION in appendix B.1 for a 

description of how the plotting position is computed.

Upper and lower Confidence Limits for the Bulletin 

17B estimates are drawn on the graph and also tabulated in the 

output file. By default, the 95-percent confidence limits are 

used (0.95).

Results

The Results tab shown in figure 7 allows viewing of the 

various forms of PeakFQ results. These include the main output file, the additional output file (if in use), and graphic plots.

The View buttons in the Output File and Additional Output frames are used to open those files for viewing. The files 

will be viewed with the system’s default viewer of Text files.

The Graphs list displays the available plots from the stations that were analyzed. This list is populated only if the user 

selects something other than None for the Graphic Plot Format on the Output Options tab. The default base file names 

are the station IDs. If a station is analyzed more than once, 

an index is attached to the station ID to make its graph name 

unique. The View button under the list of graphs will cause 

the selected graphs to be displayed, each in a separate window.

The graphs viewed from the PKFQWin interface are 

in Bitmap (BMP) format. If, on the Output Options tab, the 

user selected another graphic format (for example, CGM, PS, 

WMF), the graphs will also be stored in that selected format 

for use outside of PeakFQWin. The Bitmap files will not be 

saved for later use unless that was the selected graphic format.

Save Specs

The Save Specs feature shown in figure 8 (menu option 

or command button) allows the user to save a set of specifications for future use. The specifications from the last PeakFQ 

run will be written to a PSF file. The PSF file will contain 

only specifications that are not the default values for the run.

Batch Version

The PeakFQ batch program is run from a command 

prompt by typing the executable file name followed by an 

input specification file. It may be desirable to pipe the output 

to a file to capture any messages. For example:

PEAKFQ TEST2.PSF>TEST2.RUN

Paths to any of these files may also be included.

The batch program is given instructions for the run 

through the PeakFQ specification file (*.psf). The .psf extension is not required, but is useful for file organization. The 

only required elements of the specification file are the input 

PKFQWin

Use File menu to Open PEAKFQ data or PKFQWin spec file.

Update Station and Output specifications as desired.

Click Run PEAKFQ button to generate results.

File Help

PEAKFQ Data File: TEST2.INP

PKFQWin Spec File:

Station Specifications Output Options Results

Output File

Additional Output

View TEST2.PRT

View TEST2.bcd

View

Run PEAKFQ Save Specs Exit

Graphs

03606500

03606500-1

01373500

06600500

06600500-1

01614000

11274500

11274500-1

Figure 7. Example of the Results tab of program PKFQWin after the Run PEAKFQ button has been selected.

14 User’s Manual for Program PeakFQ
data file and the output file. Thus, the simplest example of a 

specification file might look like this:

I ASCI Test2.inp

O FILE Test2.OUT

Defaults for all output and station specifications are 

defined in the code. These specifications may then be updated 

by the input data file either through Watstore “I” cards or 

WDM attributes. Finally, specification updates may be made 

through the PeakFQ specification file.

Details of all specification file elements are found in 

Appendix B.1.

REFERENCES CITED

Beard, L.R., 1960, Probability estimates based on small normal-distribution samples: Journal of Geophysical Research, 

v. 65, no. 7, p. 2143-2148.

Flynn, K.M., Hummel, P.R., Lumb, A.M., and Kittle, J.L., 

Jr., 1995, Users manual for ANNIE, version 2, a computer 

program for hydrologic data management: U.S. Geological 

Survey Water-Resources Investigations Report 95-4085, 211 

p., http://water.usgs.gov/software/annie.html.

Interagency Advisory Committee on Water Data, 1982, 

Guidelines for determining flood-flow frequency: Bulletin 

17B of the Hydrology Subcommittee, Office of Water Data 

Coordination, U.S. Geological Survey, Reston, Va., 183 p., 

http://water.usgs.gov/osw/bulletin17b/bulletin_17B.html.

Kirby, W.H., 1981, Annual flood frequency analysis using 

U.S. Water Resources Council guidelines (program J407): 

U.S. Geological Survey Open-File Report 79-1336-I, WATSTORE User’s Guide, v. 4, chap. I, sec. C, 56 p.

Lepkin, W.D., DeLapp, M.M., Kirby, W.H., and Wilson, T.A., 

1979, National Water Data Storage and Retrieval System 

WATSTORE User’s Guide: U.S. Geological Survey OpenFile Report 79-1336-I, v. 4, ch. I, secs. A, B, and C.

Tasker, G.D., 1978, Flood Frequency Analysis with a Generalized Skew Coefficient: Water Resources Research, v. 14, 

no. 2, p. 373-376.

Wallis, J.R., Matalas, N.C., and Slack, J.R., 1974, Just a 

Moment: Water Resources Research, v. 10, no. 2, p. 211-

219.

History

Desktop

My Documents

Big Red

My Network P...

PEAKFQWin Specification File

File name:

Save as type:

Save in: peakfq

Save

Cancel

TEST2.psf

PKFQWin Spec File (*.psf)

Figure 8. Example of the Save Specifications File window in program PKFQWin, obtained by selecting the Save Specs button at the 

bottom of the PKFQWin window.

REFERENCES CITED 15
16 User’s Manual for Program PeakFQ
APPENDIX A. PeakFQ Diagnostic Messages

Diagnostic messages are produced when real or potential errors are detected. The diagnostic messages included in the 

PeakFQ output file are substantially the same as those produced by the original J407 procedure in WATSTORE (Kirby, 1981). 

These messages are listed and briefly explained below.

Most of the messages have the following general format:

***iiinnns - text data 

in which:

*** represents a variable number, possibly zero, of asterisks, to call attention to the message 

iii identifies the general part of the program producing the message as follows: 

INP - input processing 

PKF -reading the peak flow file retrieval records (WATSTORE card format) 

WCF - flood frequency calculations following Bulletin 17B guidelines 

nnn is a message number

s is a severity indicator. E means error, W means warning, I and J mean routine information, and L means listing of 

data or results.

text is the text of the message 

data is a list of numbers or words generally in the same order as items mentioned in the text 

The messages are listed below approximately in alphabetic and numerical order by identifier and number.

FRQPLT WILL DROP POINTS BELOW PLOT BASE. 

One or more points on the computed empirical frequency curves fall below the lower boundary of the plot. These 

points will not be plotted.

INPUT2 HISTORIC PEAKS OVERFLOWED. nhp i sta-id 

The number of historic peaks (nhp) retrieved for station (sta-id) exceeds the capacity of program PeakFQ (20 historic peaks). Possible system error: check the input for validity; if there are more than 20 historic peaks (code 7), 

notify h2osoft@usgs.gov.

INPUT2 REQUESTED YEARS NOT IN RECORD. beg-yr end-yr first-yr last-yr sta-id 

Probable user error. The years requested on the I-card (beg-yr, end-yr) do not overlap the years available in the 

record (first-yr, last-yr) at the station (sta-id).

INPUT2 STATION HAS NO PEAK FLOW DATA. STA-ID = xxxxx

Informative message. See preceding messages for explanation. Processing continues with next valid input record.

INPUT2 PEAK COUNT EXCEEDS STORAGE CAPACITY npks sta-id

The number of peaks (npks) retrieved for station (sta-id) exceeds the capacity of program PeakFQ (200 peaks). 

Possible system error: check the input for validity; if there are more than 200 peaks, notify h2osoft@usgs.gov.

PKFRD4 PEAK OVERFLOW. NPKS,MAX = n max 

The number of peaks (n) exceeds the storage capacity (max) of program PeakFQ. Probable system error; notify 

WATSTORE User assistance. 

APPENDIX A. PeakFQ Diagnostic Messages 17
PKFRD4 Insufficient data to process, only nnn peaks for station sta-id

Only nnn peaks were identified to be include in the analysis for station id sta-id. A minimum of 3 peaks is 

required.

PKFRD4 CARD types 4, 2, and * are ignored.

card-image

PKFRD4 Unrecognized CARD type. Must be Y, Z, N, H, I, 2, 3, 4, or *.

(2, 4, and * records are ignored.)

card-image

PKFRD4 Error reading input lat. or long. on H card.

card-image

PKFRD4 Error reading I-card

card-image

WCF001J FLOOD FREQUENCY, BULLETIN 17-B. VER n.n (dddddd). 

Unedited machine computations. User is responsible for interpretation and use. n.n (dddddd) = version number 

and date of last revision. Normal beginning-of-job message, if requested. 

WCF002J CALCS COMPLETED. RETURN CODE = n 

Normal end-of-job message. Return codes: 0 = no error detected. 1 = non-standard data accepted, 2 = warning 

– calculations completed, but results may be incorrect. 

WCF003E CALCS ABORTED. RETURN CODE = 3. 

WCF ... Routines were unable to complete the calculations for reasons explained in previous messages. 

WCF004* INTERNAL PROGRAM LOGIC ERROR. Location-code data 

This message should not occur. If it does, contact h2osoft@usgs.gov 

WCF101L INPUT PARAMS GEN OPT GS.E GAG QLW QHI NHIS HIST

 SKU RR EB OUT OUT T PD

 xxx xxx xxx xxx xxx xxx xxx xxx

Routine listing of input data, if requested. 

WCF102E INVALID PEAK COUNTS. NPK, NHIST = nnn nnn 

Either the number of historic peaks (HNIST) is negative or the total number of input peaks is less than NHIST. 

Probable error in counting input peaks. 

WCF103L INPUT PEAKS, HISTORIC FIRST. TOTAL NO. = nnn 

Routine listing of input data, if requested. 

WCF104L INPUT LOG PKS, HIST FIRST. TOTAL NO. = nnn 

Routine listing of input data, if requested. 

WCF107I ACCEPTED GEN SKEW OUTSIDE MAP LIMITS GS m1 m2 

Input generalized skew GS was outside range of values (m1, m2) set at program installation time. (Limits of Bulletin 17B skew map.)

18 User’s Manual for Program PeakFQ
WCF109W PEAKS WITH MINUS-FLAGGED DISCHARGE WERE BYPASSED. nnn 

nnn negative input peaks were found. These are assumed to be codes for unknown discharges. These peaks are 

ignored in the computations, but large negative values are stored in corresponding locations in output logarithm 

vector. If the input has any unknown discharges coded as negative values, ensure that these peaks legitimately can 

be ignored. Otherwise, incorrect input peak counts may cause this message. Warning only—analysis continues. 

WCF111E HISTORIC PEAK HAD MINUS-FLAGGED DISCHARGE . 

One of the historic peaks was negative. Probable error in input data value or count. 

WCF113W NUMBER OF SYSTEMATIC PEAKS HAS BEEN REDUCED TO NSYS - nnn 

Missing-discharge peaks were noted and have been omitted from the sample (WCF109). The correct sample size 

for analysis is nnn. 

WCF117E NO DATA IN SYST RECORD. NSYS NPK NHIST NMISS

 xxx xx xxx xxx 

There is no systematic record at this station. Possible error in input data or input peak count. NPK = total number 

of input peaks. Other as in list of variables. 

WCF118W SYSTEMATIC RECORD SHORTER THAN 17B SPEC. nnn 

Systematic record length nnn is less than that specified in Bulletin 17B. Analysis proceeds, but sample size may be 

too small for reliable conclusions. 

WCF133I SYSTEMATIC PEAKS BELOW GAGE BASE WERE NOTED.

nnn bbb 

nnn = number of below-gage-base peaks. bbb = gage-base-discharge. 

WCF134I NO SYSTEMATIC PEAKS WERE BELOW GAGE BASE. bbb

bbb = gage-base-discharge.

WCF141E SAMPLE SIZE TOO SMALL TO CALC STATS. lll nnn 

NSYS, NBG, NLWOUT, NHIOUT, NHISTN, HISTPN 

xxx xx xx xx xx xx 

Either the systematic or the Bulletin 17B-adjusted record is too short for calculation of mean, variance, and skew 

(less than 3 items). Probable cause—insufficient record length or excessively high gage base or user low-outlier 

criterion. lll = either SYS (systematic) or 17B. nnn = effective sample size. Others as in list of variables. 

WCF143E NEGATIVE VARIANCE OF LOGS. lll vvv 

lll = either SYS (systematic) or 17B. vvv = the computed variance (should be near zero). Probable cause—roundoff error in computing near-zero variance when all input peaks are (nearly) equal. 

WCF151I 17B WEIGHTED SKEW REPLACED BY USER OPTION. www uuu igsopt 

Bulletin 17B weighted skew calculation (www) has been superseded by user-specified skew uuu. An igsopt value 

of 1 means generalized skew; -1 means station skew. 

WCF156I 17B HIGH-OUTLIER TEST SUPERSEDED BY MIN HIST PK. www 

Routine information report of Bulletin 17B high-outlier test criterion (www). Historic peaks were present below 

this threshold, so the historic-high-outlier threshold was lowered to the level of the smallest historic peak. 

APPENDIX A. PeakFQ Diagnostic Messages 19
WCF157W USER HIGH-OUTLIER CRIT LOWERED TO MIN HIST PK. uuu hhh 

Probable user error—if historic peaks are given. The high-outlier base need not be set unless peaks smaller than 

the smallest historic peak are to be treated as high outliers. uuu = user high outlier criterion. hhh minimum historic peak. 

WCF159E HIGH-OUT/HIST-PK BASE BELOW LOW-OUT/GAGE BASE. hhh lll 

Probable user error—perhaps the high-outlier and low-outlier or gage-base data have been entered in the wrong 

order. hhh = high-outlier or historic base. lll = low-outlier or gage base. 

WCF161I USER HIGH-OUTLIER CRITERION REPLACES 17B. uuu www 

The user-specified historic-peak-high-outlier discharge threshold (uuu) has been noted. Its value supersedes the 

Bulletin 17B-recommended value (www). 

WCF162I SYSTEMATIC PEAKS EXCEEDED BY HIGH-OUTLIER CRITERION. nho hhb

One or more (nho) systematic peaks exceeded the high-outlier discharge criterion (hhb). No historic adjustment 

was applied because the user did not specify the length of the historic period. 

WCF163I NO HIGH OUTLIERS OR HISTORIC PEAKS EXCEEDED HHBASE. hhb 

No high outliers or historic peaks were detected. The historic-peak-high-outlier discharge threshold is hhb. 

WCF164W HISTORIC PERIOD IGNORED. histpd 

A historic period length (histpd) was specified, but no high outliers or historic peaks were found. The historic 

period length is ignored and no Bulletin 17B historic adjustment is attempted. Probable user error—the historic 

period length should not be specified unless one or more historic peaks or high outliers are present. 

WCF165I HIGH OUTLIERS AND HISTORIC PEAKS ABOVE HHBASE. nho nhp hhb 

Historic adjustment was applied. nho = number high outliers noted, nhp = number historic peaks, hhb = high outlier/historic base flow. 

WCF167E HIST PERIOD NO LONGER THAN SYS+HIST PEAKS. hhh nnn 

Stated historic period hhh is no longer than actual count of observed peaks nnn. Probable user error - if both hhh 

and nnn are correct there is no point in doing the historic adjustment. 

WCF169I ACCEPTED HISTORIC PERIOD GTR THAN T hhh ttt 

The historic period hhh may be longer than can be justified under the Bulletin 17B criteria for historic information. 

T = 5 * systematic record, up to max of 300 yrs. 

WCF171W NUMBER HI-OUT/HIST PKS EXCEEDS 10PCT OF SYS.PKS. nho nhp 

Excessive number of historic peaks nhp and high outliers nho suggest that historic base may be set too low to 

ensure that every peak exceeding it has been recorded. 

WCF191I USER LOW-OUTLIER CRITERION SUPERSEDES 17B. uuu www 

uuu = user low-outlier criterion, www = Bulletin 17B low-outlier criterion 

WCF193E LOW OUTLIER CRITERION EXCEEDS HIGH-HIST lll hhh 

Probable user error—perhaps the high-outlier and low-outlier or gage-base data have been entered in the wrong 

order. hhh = high-outlier or historic base. lll - low-outlier or gage base. 

WCF195I NO LOW OUTLIERS WERE DETECTED BELOW CRITERION xxxxx 

No peaks above the gage base were below the low-outlier criterion. xxxxx = low outlier criterion adopted (user or 

17B). 

20 User’s Manual for Program PeakFQ
WCF198I LOW OUTLIERS BELOW FLOOD BASE WERE DROPPED. nnn bbb 

Peaks above the gage base and below the low-outlier criterion were noted. The flood base of the Bulletin 17B frequency curve has been set at the low-outlier criterion. nnn = number of low outliers dropped. bbb = Bulletin 17B 

flood base. 

WCF199W NUMBER OF PEAKS BELOW FLOOD BASE EXCEEDS 17B SPEC. nbb bbb maxnbb 

Bulletin 17B specifies a maximum number of peaks that may fall below the flood base for this length of systematic 

record. The actual number nbb of below-base peaks exceeds this limit (maxnbb). The flood base = bbb. Warning—the calculation proceeds but the results may be unreliable. 

WCF213E COND PROB ADJUST FAILED - EXCESSIVE lll PROB BELOW BASE. ppp 

The conditional probability adjustment described in appendix 4 of Bulletin 17B cannot be performed when ppp 

fraction of the peaks are below the flood base. lll = (SYS for systematic rec freq curve, in which case flood base = 

gage base) or 17B. 

WCF215E SKEW OUT OF TABLE RANGE. lll skew-a skew-u gensku 

One or more of the skews to be used in constructing the Pearson Type III curve for either the systematic or Bulletin 17B record is out of the range of the Bulletin 17B Pearson Type III table (+ or - 9.0). lll = either SYS or 17B. 

Skew-a is the skew of the above base peaks. skew-u and gensku may not be present. skew-u is the unconditional 

skew after any conditional probability adjustment or weighted-skew calculation. gensku is the generalized skew, 

and is printed only if the error is detected after the Bulletin 17B weighted-skew calculations. 

WCF217L FREQUENCY CURVE PARAMS lll xxx xxxxx xxxxx xxxxx 

 xxxxx xxxxx xxxxx 

Routine report of frequency curve parameters for curve lll (SYS or 17B). Parameters are—probability of exceeding base; mean, standard deviation, and skew of frequency curve (unconditional—after a conditional probability 

adjustment, if P (BASE) is less than 1.0); mean, standard deviation, and skew of above-base peaks (before conditional probability adjustment). 

WCF219J FREQ CURVE ORDINATES lll 2-YR(.50) 10-YR (.10) 100-YR (.01) 

 xxxxxxx xxxxxxx xxxxxxx 

Routine report of frequency curve ordinates at 2-yr, 10-yr, and 100-yr levels for lll (SYS or 17B) frequency curve. 

WCF233W EXPECTED PROB OUT OF RANGE AT TAB PROB xxxxx yyyyy 

Expected-probability calculation called for table lookup at expected probability xxxxx beyond the limits of the 

computed Bulletin 17B frequency curve. This message normally occurs several times when sample size is less 

than about 10 years and tabular probability yyyyy is less than about 0.10. 

WCF238J FREQ CURVE 17B-EXPECT PROB xxxxxxx xxxxxxx xxxxxxx 

Routine report of ‘expected-probability’frequency curve ordinates at 2-, 10-, and 100-yr levels. ‘Expected­-probability’ curve is based on Bulletin 17B frequency curve. 

WCF239J FREQ CURVE CONF LIMS 17B xx.x xxxxxxx xxxxxxx xxxxxxx 

 xxxxxxx xxxxxxx xxxxxxx 

Upper and lower confidence limits for Bulletin 17B frequency curve ordinates reported in WCF219. xx.x = onesided confidence level.

APPENDIX A. PeakFQ Diagnostic Messages 21
APPENDIX B. PeakFQ Data Formats

Appendix B contains detailed documentation of text files read by PeakFQ. Appendix B.1 describes the PeakFQ specification file used to run the batch program. Appendices B.2 - B.4 describe the WATSTORE standard formats used by PeakFQ.

Appendix B.2 describes the station header records

Appendix B.3 describes the station option records

Appendix B.4 describes the peak-flows records

Appendix B.1. Batch Specifications

This appendix gives detailed descriptions of the PeakFQ specification (PSF) file. Running the batch version of PeakFQ, 

whether stand-alone or from the PKFQWin interface, requires a specification file as a command line argument. There are only 

two required records in PeakFQ specification files. These are the input data file and the main output file. The input data file 

record must start with “I”, followed by either the “ASCI” (for Watstore text files) or “WDM” (for WDM files) keyword, followed by the name of the input data file. Here are examples of each:

I ASCI Test2.inp

I WDM Test.wdm

The main output file record must start with “O”, followed by the “FILE” keyword, followed by the output file name. For 

example:

O FILE Test2.out

Other output specification records (also starting with “O”), are used to define output options that apply to the entire run. 

These specifications are described in table B.1.1.

•

•

•

22 User’s Manual for Program PeakFQ
The remaining specifications are made for each station being analyzed in the run. If specifications are to be made for a station, the first record must indicate the station to which the specifications apply:

STATION <staid>

where <staid> is either the alphanumeric Station ID from the WATSTORE file or the data-set number from the WDM file.

Table B.1.2 describes the available station specifications. This sequence of a STATION record followed by any desired 

specifications is then repeated for each station to be analyzed in the run.

Two additional keywords may be found in PSF files, particularly those generated and used by PKFQWin. These are 

VERBOSE and UPDATE. The VERBOSE keyword will only be found at the start of a PSF file and indicates that all possible 

specifications are written out in the file, even if they are the default value. The UPDATE keyword will only be found at the end 

of a PSF file and indicates that as PeakFQ performs the run, it should write out the PSF file in VERBOSE mode.

The following sample PSF File is written in VERBOSE mode and contains just the first station from the Test2.inp sample 

data file (included in program distribution.)

Table B.1.1. Specification file output keywords that apply to the entire run.

Note: Each keyword is preceded by the letter O and a space.

Keyword Valid Values Default Description

DEBUG YES

NO

NO Yes provides additional printout of intermediate results in the analysis.

ADDITIONAL WDM

WAT

BOTH

NONE

NONE WDM (or BOTH) puts computed statistics on each data set as attributes for 

further statistical analysis.

WAT (or BOTH) puts computed statistics on file in the format described in 

Appendix B.5.

EMA YES

NO

NO NO will run the traditional Bulletin 17B analysis.

YES will run the new EMA analysis.

CONFIDENCE 0.nn 0.95 Where 0.nn is confidence limit percent as a fraction.

PLOT STYLE GRAPHICS

PRINTER

BOTH

NONE

NONE GRAPHICS (or BOTH) will generate a graphic file for each station analyzed.

PRINTER (or BOTH) uses ASCII character set on a line printer, 132 characters wide.

PLOT FORMAT CGM

PS

BMP

WMF

CGM Format for GRAPHICS plots (Note: some file formats may not be available on 

all computer platforms).

PLOT PRINTPOS YES

NO

YES YES provides additional table in the printout listing the observed peaks and 

assigned recurrence intervals.

PLOT POSITION 0.nn 0.00 Plotting position computed as (m-a)/(N+1-2a) where m is order number, N is 

total number of peaks, and a is a parameter where:

a = 0.00 for Weibull

a = 0.30 for Median/Beard

a = 0.375 for Blom

a = 0.4 for Cunnane

a = 0.44 for Gringorten

APPENDIX B. PeakFQ Data Formats 23
I ASCI TEST2.INP

O File TEST2.OUT

O Plot Style None

O Plot PrintPos Yes

O Plot Position 0.00000

O Additional None

O Debug No

O EMA No

O Confidence 0.950000

Station 03606500

 SkewOpt Weighted

 GenSkew -0.500000

 SkewSE 0.550000

 BegYear 1897

 EndYear 1973

 HistPeriod 0.00000

 Urb/Reg No

 LoThresh 0.00000

 HiThresh 0.00000

 GageBase 0.00000

 Latitude 36.0386

 Longitude 88.2283

Table B.1.2. Specification file keywords that apply to a specific station.

Keyword Valid Values Default Description

GENSKEW n.nnn From Generalized skew map 

using lat/lng

Where n.nnn defines the estimated skew based on experience at nearby stations 

or regional analysis.

SKEWSE n.nnn 0.55 Where n.nnn defines the standard error of the generalized skew. If not specified, the standard error of the generalized skew map, 0.55, will be used.

BEGYEAR nnnn From data file Where nnnn defines the first water year of data to be used in the analysis.

ENDYEAR nnnn From data file Where nnnn defines the last water year of data to be used in the analysis.

HISTPERIOD nn 0.0 Where nn defines the length of historic period in years (entering 0.0 will 

cause the historic peaks to be ignored). Must be greater than the systematic 

period.

SKEWOPT GENERALIZED

WEIGHTED

STATION

WEIGHTED STATION- station skew computed from recorded peaks

GENERALIZED - generalized skew from map or regional analysis

WEIGHTED - weighted between STA and GEN

URB/REG YES

NO

NO Peaks affected by urban development or upstream regulation will be ignored 

unless this is YES.

LOHIST nnnn 0.0 Where nnnn displays the lowest historic peak. This value is only informational 

for display in the PKFQWin interface. 

LOTHRESH nnnn 0.0 Where nnnn defines the low-outlier discharge criteria. If greater than 0.0, will 

override the Bulletin 17-B computed low-outlier criteria.

HISYS nnnn 0.0 Where nnnn displays the highest systematic peak. This value is only informational for display in the PKFQWin interface. 

HITHRESH nnnn 0.0 Where nnnn defines the high outlier threshold.

GAGEBASE nnnn 0.0 Where nnnn defines the lower limit of measurable flood peak discharge. If 

greater than 0.0, will supersede the gage base discharge inferred from any 

“less than” qualification codes.

LATITUDE nn.nn From data file Where nn.nn defines latitude, in degrees, for computing generalized skew.

LONGITUDE nnn.nn From data file Where nnn.nn defines longitude, in degrees, for computing generalized skew.

24 User’s Manual for Program PeakFQ
Appendix B.2. Station Header Records (WATSTORE standard format)

The optional station header records are described in table B.2. These records contain some fields not read by PeakFQ; 

for completeness, these fields are included in the description. If latitude and longitude are not provided on an H record, either 

latitude and longitude or generalized skew must be input elsewhere.

If included in the input file, the H, N, and Y records must contain the station identification number. The Record identifier is required for all records in the input file. Only fields described as required or optional are read by the PeakFQ program. 

Example:

columns 1 2 3 4 5 6 7 8

 ----+----0----+----0----+----0----+----0----+----0----+----0----+----0----+----0

 Z USGS

 H 03606500 3602190881342004747017SW 6040005 205.00 380.58

records N 03606500 BIG SANDY RIVER AT BRUCETON, TENN

 Y 03606500 2000.00

Table B.2. WATSTORE station header record formats—continued.

Record Column Format WDM Attribute Description

Z Agency Indentification Record - optional

1 “Z” -- Record identifier. Required.

33-37 A5 AGENCY Agency code as assigned by WATSTORE.

H Station Header Record - optional

Note: If LATDEG and LNGDEG are not entered, latitude and longitude or generalized skew must be input elsewhere.

1 “H” -- Record identifier. Required.

2-16 A15 STAID or ISTAID Station identification number. Required.

17-31 --- Station locator. Required.

3I2 LATDEG Latitude, DDMMSS. - Optional.

I3,2I2 LNGDEG Longitude, DDDMMSS. - Optional.

I2 Sequence number.

32-33 A2 STFIPS Numeric state code where station is located.

34-35 A2 DSCODE For USGS sites only, the district (numeric state code) of the alpha project code of 

the office responsible for collecting and storing the data.

36-38 A3 COCODE FIPS county code where the station is located.

39-40 A2 SITECO Site code indicating the major class of data collected at the site:

SW - stream GW - well

SP - spring LK - lake or reservoir

ES - estuary ME - meteorological

41-48 I8 HUCODE Hydrologic unit code from the USGS state hydrologic unit maps.

49-55 F7.0 DAREA Total drainage area, in square miles.

56-62 F7.0 CONTDA Contributing drainage area, in square miles.

63-70 F8.0 DATUM Datum, feet above mean sea level.

71-79 F9.0 WELLDP Well depth, in feet.

N Station Name Record - optional

1 “N” -- Record identifier. Required.

2-16 A15 STAID or ISTAID Station identification number. Required.

17-64 A64 STANAM Station name. Required.

65-72 A8 GUCODE Major geologic unit codes as assigned by WATSTORE.

.

APPENDIX B. PeakFQ Data Formats 25
Table B.2. WATSTORE station header record formats—continued.

Record Column Format WDM Attribute Description

73 A1 AQTYPE Aquifer type code assigned by WATSTORE:

U - unconfined single aquifer

N - unconfined multiple aquifers

C - confined single aquifers

M - confined multiple aquifers

X - mixed multiple aquifers

Y Base Discharge Record - ignored.

1 “Y” -- Record identifier.

2-16 A15 STAID or ISTAID Station identification number. Required.

7-23 F7.0 BASEQ Base discharge. Note: this is not the Gage Base Discharge used in PeakFQ.

Appendix B.3. Station Option Record (WATSTORE standard format)

The station option record is described in table B.3; it is optional. If included in the input file, the I record must contain the 

station identification number, all other fields are optional and may be left blank. Program PeakFQ reads all of the fields on this 

record. The description column describes how blank fields are handled. Example:

columns 1 2 3 4 5 6 7 8

 ----+----0----+----0----+----0----+----0----+----0----+----0----+----0----+----0

records I -.2 82. 70000.

26 User’s Manual for Program PeakFQ
Table B.3. WATSTORE station option record formats.

Record Column Format WDM Attribute Description

I Station option record - optional

1 “I” -- Record identifier. Required.

2-16 A15 STAID or ISTAID Station identification number. Required.

17-24 F8.0 Generalized skew. If not specified, the generalized skew will be determined 

based on gage latitude and longitude using the generalized skew map accompanying the Bulletin 17B guidelines.

25-32 F8.0 Length of historic period in years. A positive value must be supplied in order for 

the historic adjustment to be applied. The historic period contains the systematic 

record period as a subset. If this field is left blank, any input historic peaks will 

be ignored and any high outliers will be treated as normal systematic peaks.

33-40 F8.0 User-specified historic-high-outlier discharge threshold. Used only in conjunction with the historic period, this threshold is used to override the Bulletin 

17B-computed high-outlier threshold. If this field is left blank, the Bulletin 17B 

threshold will be lowered automatically to equal the smallest historic peak(s) if 

one is known. If a positive value is specified in this field, all peaks that exceed 

this value will be used in the historic adjustment. Any historic peaks lying below 

this value will be ignored.

41-48 F8.0 User-specified low-outlier discharge criterion. This criterion, if a postive number, 

will override the Bulletin 17B computed low-outlier criterion. A blank, negative 

value, or zero will be ignored.

49-56 F8.0 Gage base discharge, representing a lower limit of measurable flood peak discharge at the site. This discharge, if a positive number, will supersede the gage 

base inferred from any “less than” qualification codes of the input peak flow 

records. A blank, negative value, or zero will be ignored. (The gage base discharge is not the same as the partial-duration base discharge that may be recorded 

in the Station Header record.)

57-64 F8.0 Standard error for the generalized skew. If not specified, a value of 0.55, corresponding to the standard error of the generalized skew map accompanying the 

Bulletin 17B guidelines, will be used.

65-69 5A1 Station-option codes selected from the following list. The codes may be in any 

order or combination and may be in any available column. In case of conflict, 

the rightmost code is used. The available options are:

S - Station-skew option. Causes the station skew, adjusted for outliers and 

historic data, rather than the Bulletin 17B weighted skew, to be used for the final 

frequency curve. 

G - Generalized-skew options. Causes the generalized skew, rather than the Bulletin 17B weighted skew, to be used in the final frequency curve. 

K - Known regulation/urbanization input option. Allows peaks with the known 

regulation or urbanization codes (6 or C) to be included in the statistical analysis. 

H - Historic peak input option. Allows all historic peaks to be used, whether or 

not they exceed the user-specified historic-high-outlier discharge threshold. The 

program will print a warning message if it finds any below-threshold historic 

peaks and will lower the threshold to include them. Use of the option may cause 

the historic adjustment to include some historic and systematic peaks that are not 

representative of the historic period.

71-74 F4.0 Begin year: first water year of retrieved records to be included in the statistical 

analysis; earlier years are ignored. This value must be either blank or a four-digit 

number. If blank or less than the first year of the input record, no years will be 

dropped from the beginning of the record.

75-78 F4.0 End year: last water year of retrieved records to be included in the statistical 

analysis; later years will be ignored. This value must be either blank or a fourdigit number. If blank or greater than the last year of the input record, no years 

will be dropped from the end of the record.

APPENDIX B. PeakFQ Data Formats 27
Table B.4. WATSTORE peak-flow record formats—continued.

Record Column Format Description

3 Peak-Flow Data Record - required.

Fields in columns 44 - 75 are ignored.

1 “3” Record identifier. Required

2-16 A15 Station identification number. Required.

17-20 I4 Year peak occurred - required:

• Calendar year if columns 21-22 contain a valid moth.

• Water year if columns 21-22 are blank or 99

21-22 I2 Month the annual peak discharge occurred. Blank if month is not known.

23-24 I2 Day of the month the annual peak discharge occurred. Blank if day is not known.

25-31 F7.0 Annual peak discharge, right justified. Field may be blank.

32-43 A12 Annual peak discharge qualification codes. More than one code may be associated with a 

peak, except as noted below. Field may be blank.

1 - discharge is a maximum daily average

2 - discharge is an estimate

3 - discharge is affected by dam failure

4 - discharge is less than indicated value, which is minimum recordable discharge at this site *

5 - discharge affected to unknown degree by regulation or diversion **

6 - discharge affected by regulation or diversion **

7 - discharge is an historic peak ***

8 - discharge actually greater than indicated value

9 - discharge due to snowmelt, hurricane, ice-jam or debris dam breakup

A - year of occurrence is unknown or not exact

B - month or day of occurrence is unknown or not exact

C - all or part of the record affected by urbanization, mining, argicultural changes, channelization, or others

D - base discharge changed during this year

E - only annual maximum peak available for this year

* Code 4 cannot occur simultaneously with codes 1, 2, 3, 7, or 8

** Codes 5 and 6 cannot occur simultaneously.

*** Code 7 should indicate that the value for the particular year is a historic peak and the 

particular year occurred before or after the systematic record, or during a break in systematic 

record.

44-51 F8.0 Gage height associated with annual peak discharge, right justified in field. Ignored.

52-55 A4 Gage height qualification codes. More than one code may be associated with a gage height. 

Field may be blank. Ignored.

1 - gage height affected by backwater

2 - gage height not the maximum for the year*

3 - gage height at different site and/or datum

4 - gage height below minimum recordable elevation (con’t)

.

Appendix B.4. Peak-Flow Records (WATSTORE standard format)

The peak-flow data records are described in table B.4. The peak-flow record contains some fields that are not read by 

PeakFQ. The partial duration peak-flow data record is completely ignored by PeakFQ. For completeness, all fields for both 

record types are included in the description; the fields that are not read are shown with a light gray background. The peak-flow 

records may be preceded by station header records. Example:

columns 1 2 3 4 5 6 7 8

 ----+----0----+----0----+----0----+----0----+----0----+----0----+----0----+----0

records 3 03606500 192612 185007 16.50

 3 03606500 19300109 9100 13.98

28 User’s Manual for Program PeakFQ
Table B.4. WATSTORE peak-flow record formats—continued.

Record Column Format Description

(con’t) (con’t) 5 - gage height is an estimate

6 - gage datum changed during this year

* If code 2 is given here, then a date and data entries should be made for the maximum annual gage height (cols 60-75)

56-59 I4 “Highest since” year -- representing the calendar year after which the given peak discharge 

(cols 25-31) is known to be the highest. This year is determined from historic newspaper 

accounts, local information, or other sources.

60-61 I2 Month in which the annual peak gage height occurred. While this month may not be in the 

same calendar year as the annual peak, it is in the same water year.

62-63 I2 Day of the month of the annual peak gage height.

64-71 F8.0 Annual peak gage height.

72-75 A4 Annual peak gage height qualification codes.

1 - gage height affected by backwater 

3 - gage height at different site and/or datum 

5 - gage height is an estimate 

6 - gage datum changed during this year

4 Partial Duration Peak Flow Data Record - Ignored.

1 “4” Record identifier. Required.

2-16 A15 Station identification number. Required.

17-20 I4 Year data on this record occurred.

• Calendar year if columns 21-22 contain a valid month

• Water year if columns 21-22 are blank or 99

This entry may or may not be the same as on the preceding type 3 record if one is present, but 

the month and year must have occurred in the same water year as the peak discharge. 

21-22 I2 Month the partial duration peak occurred. Blank if month is not known.

23-24 I2 Day of the month the partial duration peak occurred. Blank if day is not known. 

25-31 F7.0 Partial duration peak discharge, right justified.

32-43 A12 Partial duration peak discharge qualification codes. More than one code may be associated 

with a peak,

1 - discharge is a maximum daily average 

2 - discharge is an estimate 

3 - discharge affected by dam failure 

4 - discharge less than indicated value, which is minimum recordable discharge at this site * 

5 - discharge affected to unknown degree by regulation or diversion ** 

6 - discharge affected by regulation or diversion **

7 - discharge is an historic peak *** 

8 - discharge actually greater than indicated value 

9 - discharge due to snowmelt, hurricane, ice-jam or debris dam breakup 

A - year of occurrence is unknown or not exact

B - month or day of occurrence is unknown or not exact 

C - all or part of the record affected by urbanization, mining, agricultural changes, channelization, or others 

D - base discharge changed during this year 

E - only annual maximum peak available for this year

* Code 4 cannot occur simultaneously with codes 1, 2, 3, 7, or 8. 

** Codes 5 and 6 cannot occur simultaneously. 

*** Code 7 should indicate that the value for the particular year is a historic peak and the 

particular year occurred before or after the systematic record, or during a break in the systematic record. 

44-51 F8.0 Partial duration peak gage height.

APPENDIX B. PeakFQ Data Formats 29
Table B.4. WATSTORE peak-flow record formats—continued.

Record Column Format Description

52-55 A4 Partial duration peak gage height qualification codes. More than one code may be associated 

with a gage height.

1 - gage height affected by backwater

3 - gage height at different site and/or datum

4 - gage height below minimum recordable elevation

5 - gage height is an estimate

6 - gage datum changed during this year

30 User’s Manual for Program PeakFQ
Appendix B.5. Basin Characteristics Records (WATSTORE standard format)

Table B.5 describes the format and contents of the basin characteristics file. PeakFQ outputs this file when the Watstore 

check box is selected for Additional Output on the Output Options tab. Example:

columns 1 2 3 4 5 6 7 8

 ----+----0----+----0----+----0----+----0----+----0----+----0----+----0----+----0

 103606500 BIG SANDY RIVER AT BRUCETON HIST B-17-B

 203606500 75 2940 76 5000 77 8280 78 10700 79 13800 80 16300

records 203606500 81 18900 82 21500 83 3.691 84 0.267 85 -0.187178 25100

 203606500 179 -0.188180 3.691181 0.267196 44197 44

APPENDIX B. PeakFQ Data Formats 31
Table B.5. WATSTORE basin characteristics record formats.

Record Column Format WDM Attribute Description

1 Station identification record

1 “I” -- Record identifier.

2-16 A15 STAID or ISTAID Station identification number. Required.

17-18 I2 STFIPS Numeric state code where station is locked. May be blank.

19-20 I2 DSCODE For USGS sites only, the district (numeric state code) or the alpha project code of 

the office responsible for collecting and storing the data. May be blank.

21-68 A48 STANAM Stations name and data identifer.

69-75 F8.0 blank

76-80 A5 AGENCY Agency code. May be blank.

2 Basin Characteristics, record 1

1 “2” -- Record identifier.

2-16 A15 STAID or ISTAID Station identification number. Required.

17-76 Pairs of basin characteristics index numbers and the value for the basin characteristic. In the order: index description

I3,F7.0 P1.25 75 Annual flood peak, 2.5-year recurrence interval.

I3,F7.0 P2. 76 Annual flood peak, 2-year recurrence interval.

I3,F7.0 P5. 77 Annual flood peak, 5-year recurrence interval.

I3,F7.0 P10. 78 Annual flood peak, 10-year recurrence interval.

I3,F7.0 P25. 79 Annual flood peak, 25-year recurrence interval.

I3,F7.0 P50. 80 Annual flood peak, 50-year recurrence interval.

2 Basin Characteristics, record 2

1 “2” -- Record identifier.

2-16 A15 STAID or ISTAID Station identification number. Required.

17-76 Pairs of basin characteristics index numbers and the value for the basin characteristic. In the order: index description

I3,F7.0 P100. 81 Annual flood peak, 100-year recurrence interval.

I3,F7.0 P200. 82 Annual flood peak, 200-year recurrence interval.

I3,F7.0 MEANPK 83 Mean of the logarithms, base 10, of systematic annual peak discharge.

I3,F7.0 SDPK 84 Standard deviation of the logarithms, base 10, of systematic annual peak 

discharges.

I3,F7.0 SKWPK 85 Skew of the logarithms, base 10, of systematic annual peak discharges.

I3,F7.0 P500. 178 Annual flood peak, 500-year recurrence interval.

2 Basin Characteristics, record 3

1 “2” -- Record identifier.

2-16 A15 STAID or ISTAID Station identificatio number. Required.

17-76 Pairs of basin characteristics index numbers and the value for the basin characteristics. In the order: index description

I3,F7.0 WRCSKW 179 Skew of logarithms, base 10, of annual peak discharges after outlier and 

historic-peak adjustments.

I3,F7.0 WRCMN 180 Mean of logarithms, base 10, of annual peak discharges after outlier and 

historic-peak adjustments.

I3,F7.0 WRCSD 181 Standard deviation of logarithms, base 10, of annual peak discharges after 

outlier and historic-peak adjustments.

I3,F7.0 YRSPK 196 Number of years of systematic peak flow record.

I3,F7.0 YRSHPK 197 Number of consecutive years used for historic-peak adjustment of flood 

frequency data.

32 User’s Manual for Program PeakFQ
Table C.1. Attributes associated with annual peak-flow data sets—continued.

Name Type Length Update Data-set type Description Time Table

AGENCY Char 8 Yes Opt Opt Agency code.

AQTYPE Char 4 Yes Opt Opt Aquifer type.

U - unconfined single aquifer

N - unconfined multiple aquifers

C - confined single aquifer

M - confined multiple aquifers

X - mixed multiple aquifers

BASEQ Real 1 Yes Opt Opt Base discharge, in cubic feet per second.

COCODE Int 1 Yes Opt Opt County or parish code.

CONTDA Real 1 Yes Opt Opt Drainage area, in square miles, that contributes to surface runoff.

DAREA Real 1 Yes Opt Opt Total drainage area, in square miles, including noncontributing areas.

DATUM Real 1 Yes Opt Opt Reference elevation, to mean sea level.

DSCODE Int 1 Yes Opt Opt State code of the Geological Survey office that operates the station. Usually the same as the state code (STFIPS).

GUCODE Char 12 Yes Opt Opt Geologic unit code.

HUCODE Int 1 Yes Opt Opt Hydrologic unit code (8 digits). These codes are given in the U.S. Geological Survey map series “State Hydrologic Unit Maps,” Open-File 

Report 84-708.

ISTAID Int 1 Yes Opt Opt Station identification number, as an integer.

J407BQ Real 1 Yes Opt Opt Base gage discharge.

J407BY Int 1 Yes Opt Opt Year to begin analysis, used to identify subset of available record.

J407EY Int 1 Yes Opt Opt Year to end analysis, used to identify subset of available record.

J407GS Real 1 Yes Opt Opt Generalized skew.

J407HO Real 1 Yes Opt Opt High outlier discharge criterion.

J407LO Real 1 Yes Opt Opt Low outlier discharge criterion.

J407NH Int 1 Yes Opt Opt Number of historic peaks.

J407SE Real 1 Yes Opt Opt Root mean square error of generalized skew.

J407SO Int 1 Yes Opt Opt Generalized skew option.

-1 - station skew

0 - weighted skew

1 - generalized skew

APPENDIX C. DATA-SET ATTRIBUTES

Data-set attributes in a Watershed Data Management (WDM) file are used to describe the data sets. Attributes may 

describe how the data are stored in the data set, where the data were gathered, physical features of the associated data, and 

statistics computed from the associated data. Over 300 attributes are available for describing data sets. Only a fraction of these 

attributes are used by PeakFQ, but any attribute may be present in the data set.

Table C.1 contains a list and description of the data-set attributes commonly found in annual peak-flow data sets. Table C.2 

contains a list of the attributes that PeakFQ reads and (or) writes or that are commonly associated with annual peak-flow data 

sets and how these attributes are used by the PeakFQ program. The IOWDM program is used to write peak-flow data and most 

of these attributes to the data sets, but the attributes can be manually entered using the ANNIE program. The basin characteristic 

and station header formats are described in Appendices B.2 and B.3. See the IOWDM and ANNIE documentation (Flynn and 

others, 1995) for additional details. Some of these attributes may be modified each time the PeakFQ program is run. Some of 

these attributes are output from PeakFQ. Some of these attributes are ignored by PeakFQ.

.

APPENDIX C. DATA-SET ATTRIBUTES 33
Table C.1. Attributes associated with annual peak-flow data sets—continued.

Name Type Length Update Data-set type Description Time Table

J407UR Int 1 Yes Opt Opt Include urban regulated peaks.

1 - no

2 - yes

LATDEG Real 1 Yes Opt Opt Latitude in decimal degrees.

LATDMS Int 1 Yes Opt Opt Latitude in degrees, minutes, seconds (dddmmss).

LNGDEG Real 1 Yes Opt Opt Longitude in decimal degrees.

LNGDMS Int 1 Yes Opt Opt Longitude in degrees, minutes, seconds (dddmmss).

P1.25 Real 1 Yes Opt Opt Annual flood peak, in cubic feet per second, 1.25-year recurrence interval.

P10. Real 1 Yes Opt Opt Annual flood peak, in cubic feet per second, 10-year recurrence interval.

P100. Real 1 Yes Opt Opt Annual flood peak, in cubic feet per second, 100-year recurrence interval.

P2. Real 1 Yes Opt Opt Annual flood peak, in cubic feet per second, 2-year recurrence interval.

P200. Real 1 Yes Opt Opt Annual flood peak, in cubic feet per second, 200-year recurrence interval.

P25. Real 1 Yes Opt Opt Annual flood peak, in cubic feet per second, 25-year recurrence interval.

P5. Real 1 Yes Opt Opt Annual flood peak, in cubic feet per second, 5-year recurrence interval.

P50. Real 1 Yes Opt Opt Annual flood peak, in cubic feet per second, 50-year recurrence interval.

P500. Real 1 Yes Opt Opt Annual flood peak, in cubic feet per second, 500-year recurrence interval.

SITECO Char 4 Yes Opt Opt Site code.

SW - stream

SP - spring

ES - estuary

GW - well

LK - lake or reservoir

ME - meteorological

STAID Char 16 Yes Opt Opt Station identification, up to 16 alpha-numeric characters.

STANAM Char 48 Yes Opt Opt Station name or description of the data set.

STFIPS Int 1 Yes Opt Opt State FIPS code.

TSTYPE Char 4 Yes Opt Opt User-defined four-character descriptor. Used to describe the contents of 

the data set, for example: 

PRCP, RAIN, SNOW - precepitation

FLOW, DISC, PEAK - discharge

TEMP, TMIN, TMAX - temperature

EVAP, PET - evapotranspiration

Some models and application programs may require a specific TSTYPE 

for data sets they use.

WELLDP Real 1 Yes Opt Opt Depth of well, in feet. The greatest depth at which water can enter the 

well.

WRCMN Real 1 Yes Opt Opt Mean of logarithms, base 10, of annual peak discharges after outlier and 

historic-peak adjustments.

WRCSD Real 1 Yes Opt Opt Standard deviation of logarithms, base 10, of annual peak discharges after 

outlier and historic-peak adjustments.

WRCSKW Real 1 Yes Opt Opt Skew of logarithms, base 10, of annual peak discharge after outlier and 

historic-epak adjustments and generalized skew weighting.

YRSHPK Int 1 Yes Opt Opt Number of consecutive years used for historic-peak adjustment to floodfrequency data.

34 User’s Manual for Program PeakFQ
Table C.2. Sources of attributes associated with peak-flow data sets

WDM file as processed by IOWDM PeakFQ

--------- --------------------------- use * * i - input by user

attribute basin charac statn header ------- r - read from WDM

 name no. name no. name rec i r w p w - written to WDM

---------- ------------ ------------ ------- p - written to “punch”

istaid 51 sta id -- sta id N x

staid 2 sta id -- sta id N x x

stanam 45 sta name -- sta name N x x

latdms 54 x

lngdms 55 x

latdeg 8 lat gage 22 latitude H x x

lngdeg 9 lng gage 23 longitude H x x

yrshpk 81 yrshispk 197 x x

j407by 278 x x

j407ey 279 x x

j407lo 269 x x

j407ho 270 x x

j407so 271 x x

j407gs 272 x x

j407bq 273 x x

j407se 275 x x

j407ur 276 x x

j407nh 274 x x

wrcmn 78 wrc mn 180 x x

wrcsd 79 wrc sd 181 x x

wrcskw 77 wrc skew 179 x x

p1.25 65 p1,25 75 x x

p2. 66 p2 76 x x

p5. 67 p5 77 x x

p10. 68 p10 78 x x

p25. 69 p25 79 x x

p50. 70 p50 80 x x

p100. 71 p100 81 x x

p200. 72 p200 82 x x

p500. 73 p500 178 x x

meanpk 74 meanpk 83 x

sdpk 75 sdpk 84 x

skewpk 76 skewpk 85 x

tmtopk 98 timetopk 21

yrspk 80 yrspk 196 x

darea 11 area 1 area H

contda 43 contda 2 cont area H

agency 40 agency Z

stfips 41 state c -- state code H

dscode 42 dist c -- dist code H

siteco 44 site code H

hucode 4 hyd unit c H

datum 264 datum H

welldp 47 well dpth H

gucode 46 geol unit N

aqtype 48 aquifer tp N

baseq 49 base q Y

APPENDIX C. DATA-SET ATTRIBUTES 35
APPENDIX D. SAMPLE FILES

Appendix D.1. Sample Specification File

I ASCI BigSandy.inp

O File BigSandy.out

O Plot Style Graphics

O Plot Format WMF

Station 03606500

 HistPeriod 77

 SkewOpt Weighted

 GenSkew -0.2

 PlotName 03606500

36 User’s Manual for Program PeakFQ
Appendix D.2. Sample Input File

H 03606500 3602190881342004747017SW 6040005 205.00 380.58

N 03606500 BIG SANDY RIVER AT BRUCETON HIST B-17-B

2 03606500

3 03606500 189703 250007 18.00

3 03606500 191903 210007 17.00

3 03606500 192612 185007 16.50

3 03606500 19300109 9100 13.98

3 03606500 19310327 2060 11.20

3 03606500 19320113 7820 13.60

3 03606500 19330321 3220 11.95

3 03606500 19331218 5580 12.94

3 03606500 19350121 17000 16.16

3 03606500 19360704 6740 13.28

3 03606500 19370121 13800 14.86

3 03606500 19380123 4270 12.67

3 03606500 19390204 5940 13.23

3 03606500 19400319 1680 10.91

3 03606500 19410802 1200 10.00

3 03606500 19420410 10100 14.52

3 03606500 19430320 3780 12.45

3 03606500 19440218 5340 13.07

3 03606500 19450102 5630 13.13

3 03606500 19460109 12000 14.92

3 03606500 19470104 3980 12.53

3 03606500 19480317 6130 13.31

3 03606500 19481120 4740 12.83

3 03606500 19491213 9880 14.37

3 03606500 19510104 5230 13.01

3 03606500 19511216 4260 12.70

3 03606500 19530519 5000 12.95

3 03606500 19540122 3320 12.32

3 03606500 19550322 5480 13.11

3 03606500 19560130 11800 14.85

3 03606500 19570130 5150 13.00

3 03606500 19571116 3350 12.33

3 03606500 19590216 2400 11.83

3 03606500 19591212 1460 10.94

3 03606500 19610609 3770 12.51

3 03606500 19620228 7480 13.71

3 03606500 19630305 2740 12.02

3 03606500 19640310 3100 12.21

3 03606500 19650212 7180 14.07

3 03606500 19660502 1920 11.64

3 03606500 19670515 9060 14.54

3 03606500 19680404 3080 12.64

3 03606500 19681130 2800 12.50

3 03606500 19700403 4330 13.11

3 03606500 19710824 5080 13.36

3 03606500 19720717 12000 15.14

3 03606500 19730421 7640 14.88

APPENDIX D. SAMPLE FILES 37
Appendix D.3. Sample Output File

1

 Program PeakFq U. S. GEOLOGICAL SURVEY Seq.000.000

 Ver. 5.0 Beta 8 Annual peak flow frequency analysis Run Date / Time

 05/06/2005 following Bulletin 17-B Guidelines 04/28/2006 13:03

 --- PROCESSING OPTIONS --- 

 Plot option = Graphics device 

 Basin char output = WATSTORE 

 Print option = Yes

 Debug print = No 

 Input peaks listing = Long 

 Input peaks format = WATSTORE peak file 

 Input files used:

 peaks (ascii) - D:\EX\BIGSANDY.INP

 specifications - PKFQWPSF.TMP

 Output file(s): 

 main - D:\EX\BIGSANDY.PRT

 bcd - BIGSANDY.BCD

1

 Program PeakFq U. S. GEOLOGICAL SURVEY Seq.001.001

 Ver. 5.0 Beta 8 Annual peak flow frequency analysis Run Date / Time

 05/06/2005 following Bulletin 17-B Guidelines 04/28/2006 13:03

 

 Station - 03606500 BIG SANDY RIVER AT BRUCETON HIST B-17-B 

 I N P U T D A T A S U M M A R Y

 Number of peaks in record = 47

 Peaks not used in analysis = 3

 Systematic peaks in analysis = 44

 Historic peaks in analysis = 0

 Years of historic record = 0

 Generalized skew = -0.189

 Standard error = 0.550

 Mean Square error = 0.303

 Skew option = WEIGHTED 

 Gage base discharge = 0.0

 User supplied high outlier threshold = -- 

 User supplied low outlier criterion = -- 

 Plotting position parameter = 0.00

 ********* NOTICE -- Preliminary machine computations. ********* 

 ********* User responsible for assessment and interpretation. ********* 

 **WCF109W-PEAKS WITH MINUS-FLAGGED DISCHARGES WERE BYPASSED. 3

 **WCF113W-NUMBER OF SYSTEMATIC PEAKS HAS BEEN REDUCED TO NSYS = 44

 WCF134I-NO SYSTEMATIC PEAKS WERE BELOW GAGE BASE. 0.0

 WCF195I-NO LOW OUTLIERS WERE DETECTED BELOW CRITERION. 921.3

 WCF163I-NO HIGH OUTLIERS OR HISTORIC PEAKS EXCEEDED HHBASE. 26151.7

 WCF002J-CALCS COMPLETED. RETURN CODE = 2

38 User’s Manual for Program PeakFQ
1

 Program PeakFq U. S. GEOLOGICAL SURVEY Seq.001.002

 Ver. 5.0 Beta 8 Annual peak flow frequency analysis Run Date / Time

 05/06/2005 following Bulletin 17-B Guidelines 04/28/2006 13:03

 

 Station - 03606500 BIG SANDY RIVER AT BRUCETON HIST B-17-B 

 ANNUAL FREQUENCY CURVE PARAMETERS -- LOG-PEARSON TYPE III 

 FLOOD BASE LOGARITHMIC 

 ---------------------- -------------------------------

 EXCEEDANCE STANDARD 

 DISCHARGE PROBABILITY MEAN DEVIATION SKEW 

 -------------------------------------------------------

 SYSTEMATIC RECORD 0.0 1.0000 3.6909 0.2672 -0.187

 BULL.17B ESTIMATE 0.0 1.0000 3.6909 0.2672 -0.188

 ANNUAL FREQUENCY CURVE -- DISCHARGES AT SELECTED EXCEEDANCE PROBABILITIES

 ANNUAL ‘EXPECTED 95-PCT CONFIDENCE LIMITS

 EXCEEDANCE BULL.17B SYSTEMATIC PROBABILITY’ FOR BULL. 17B ESTIMATES

 PROBABILITY ESTIMATE RECORD ESTIMATE LOWER UPPER

 0.9950 902.7 903.1 810.3 604.0 1209.0

 0.9900 1078.0 1078.0 991.8 746.7 1411.0

 0.9500 1728.0 1728.0 1664.0 1306.0 2137.0

 0.9000 2206.0 2206.0 2155.0 1736.0 2660.0

 0.8000 2943.0 2943.0 2910.0 2415.0 3470.0

 0.6667 3827.0 3827.0 3809.0 3229.0 4462.0

 0.5000 5004.0 5004.0 5004.0 4288.0 5847.0

 0.4292 5580.0 5580.0 5589.0 4790.0 6555.0

 0.2000 8278.0 8278.0 8365.0 7017.0 10100.0

 0.1000 10660.0 10660.0 10870.0 8855.0 13480.0

 0.0400 13840.0 13840.0 14320.0 11200.0 18290.0

 0.0200 16310.0 16310.0 17100.0 12960.0 22200.0

 0.0100 18850.0 18860.0 20060.0 14720.0 26360.0

 0.0050 21480.0 21490.0 23210.0 16500.0 30780.0

 0.0020 25080.0 25090.0 27710.0 18890.0 37030.0

APPENDIX D. SAMPLE FILES 39
1

 Program PeakFq U. S. GEOLOGICAL SURVEY Seq.001.003

 Ver. 5.0 Beta 8 Annual peak flow frequency analysis Run Date / Time

 05/06/2005 following Bulletin 17-B Guidelines 04/28/2006 13:03

 

 Station - 03606500 BIG SANDY RIVER AT BRUCETON HIST B-17-B 

 I N P U T D A T A L I S T I N G

 WATER YEAR DISCHARGE CODES WATER YEAR DISCHARGE CODES 

 1897 -25000.0 H 1951 5230.0 

 1919 -21000.0 H 1952 4260.0 

 1927 -18500.0 H 1953 5000.0 

 1930 9100.0 1954 3320.0 

 1931 2060.0 1955 5480.0 

 1932 7820.0 1956 11800.0 

 1933 3220.0 1957 5150.0 

 1934 5580.0 1958 3350.0 

 1935 17000.0 1959 2400.0 

 1936 6740.0 1960 1460.0 

 1937 13800.0 1961 3770.0 

 1938 4270.0 1962 7480.0 

 1939 5940.0 1963 2740.0 

 1940 1680.0 1964 3100.0 

 1941 1200.0 1965 7180.0 

 1942 10100.0 1966 1920.0 

 1943 3780.0 1967 9060.0 

 1944 5340.0 1968 3080.0 

 1945 5630.0 1969 2800.0 

 1946 12000.0 1970 4330.0 

 1947 3980.0 1971 5080.0 

 1948 6130.0 1972 12000.0 

 1949 4740.0 1973 7640.0 

 1950 9880.0 

 Explanation of peak discharge qualification codes

 PEAKFQ NWIS

 CODE CODE DEFINITION

 D 3 Dam failure, non-recurrent flow anomaly

 G 8 Discharge greater than stated value

 X 3+8 Both of the above

 L 4 Discharge less than stated value

 K 6 OR C Known effect of regulation or urbanization

 H 7 Historic peak

 - Minus-flagged discharge -- Not used in computation

 -8888.0 -- No discharge value given

 - Minus-flagged water year -- Historic peak used in computation

40 User’s Manual for Program PeakFQ
1

 Program PeakFq U. S. GEOLOGICAL SURVEY Seq.001.004

 Ver. 5.0 Beta 8 Annual peak flow frequency analysis Run Date / Time

 05/06/2005 following Bulletin 17-B Guidelines 04/28/2006 13:03

 

 Station - 03606500 BIG SANDY RIVER AT BRUCETON HIST B-17-B 

 EMPIRICAL FREQUENCY CURVES -- WEIBULL PLOTTING POSITIONS

 WATER RANKED SYSTEMATIC BULL.17B

 YEAR DISCHARGE RECORD ESTIMATE

 1935 17000.0 0.0222 0.0222 

 1937 13800.0 0.0444 0.0444 

 1946 12000.0 0.0667 0.0667 

 1972 12000.0 0.0889 0.0889 

 1956 11800.0 0.1111 0.1111 

 1942 10100.0 0.1333 0.1333 

 1950 9880.0 0.1556 0.1556 

 1930 9100.0 0.1778 0.1778 

 1967 9060.0 0.2000 0.2000 

 1932 7820.0 0.2222 0.2222 

 1973 7640.0 0.2444 0.2444 

 1962 7480.0 0.2667 0.2667 

 1965 7180.0 0.2889 0.2889 

 1936 6740.0 0.3111 0.3111 

 1948 6130.0 0.3333 0.3333 

 1939 5940.0 0.3556 0.3556 

 1945 5630.0 0.3778 0.3778 

 1934 5580.0 0.4000 0.4000 

 1955 5480.0 0.4222 0.4222 

 1944 5340.0 0.4444 0.4444 

 1951 5230.0 0.4667 0.4667 

 1957 5150.0 0.4889 0.4889 

 1971 5080.0 0.5111 0.5111 

 1953 5000.0 0.5333 0.5333 

 1949 4740.0 0.5556 0.5556 

 1970 4330.0 0.5778 0.5778 

 1938 4270.0 0.6000 0.6000 

 1952 4260.0 0.6222 0.6222 

 1947 3980.0 0.6444 0.6444 

 1943 3780.0 0.6667 0.6667 

 1961 3770.0 0.6889 0.6889 

 1958 3350.0 0.7111 0.7111 

 1954 3320.0 0.7333 0.7333 

 1933 3220.0 0.7556 0.7556 

 1964 3100.0 0.7778 0.7778 

 1968 3080.0 0.8000 0.8000 

 1969 2800.0 0.8222 0.8222 

 1963 2740.0 0.8444 0.8444 

 1959 2400.0 0.8667 0.8667 

 1931 2060.0 0.8889 0.8889 

 1966 1920.0 0.9111 0.9111 

 1940 1680.0 0.9333 0.9333 

 1960 1460.0 0.9556 0.9556 

APPENDIX D. SAMPLE FILES 41
 1941 1200.0 0.9778 0.9778 

 1927 -18500.0 -- -- 

 1919 -21000.0 -- -- 

 1897 -25000.0 -- -- 

1

 End PEAKFQ analysis.

 Stations processed : 1

 Number of errors : 0

 Stations skipped : 0

 Station years : 47

Data records may have been ignored for the stations listed below. 

(Card type must be Y, Z, N, H, I, 2, 3, 4, or *.) 

(2, 4, and * records are ignored.) 

 

 For the station below, the following records were ignored: 

2 03606500 

 FINISHED PROCESSING STATION: 03606500 BIG SANDY RIVER AT BRUCETON H

 For the station below, the following records were ignored: 

 FINISHED PROCESSING STATION:

42 User’s Manual for Program PeakFQ ANNUAL PEAK DISCHARGE CUBIC FEET PER SECOND

105

104

103

102

ANNUAL EXCEEDANCE PROBABILITY, PERCENT

Station - 03606500 BIG SANDY RIVER AT BRUCETON HIST B-17-B

Peakfq 5 run 3/10/2006 15:42

NOTE - Preliminary computation

User is responsible for

assessment and interpretation.

99.5 98 95 90 80 70 50 30 20 10 5 2 1 0.5 0.2

Bull. 17-B frequency

Systematic peaks

Systematic frequency

Historical adjusted

Confidence limits

Note: Graphic from a [wmf] file, curves enhanced for publication.

Flynn, Kathleen M., Kirby, William H., and Hummel, Paul R.—User’s Manual for Program PeakFQ—Techniques and Methods Book 4, Chapter B4

Printed on recycled paper