

Office of Surface Water 
By Kathleen M. Flynn, William H. Kirby, and Paul R. Hummel
U.S. Geological Survey Techniques and Methods 4B4
The report is available as a pdf.
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). 
Figure 1. General flow chart for floodfrequency computations (modified from Interagency Advisory Committee on Water Data, 1982).
2. Definition sketch showing time periods and discharges used in historic record adjustment.
3. Example of opening screen of program PKFQWin showing the station specifications tab before an input file has been opened.
4. Example of the File Open window in program PKFQWin, obtained by selecting Open from the File menu.
5. Example of the Station Specification Tab of program PKFQWin after a file containing 8 sets of data has been opened.
6. Example of the Output Options tab of program PKFQWin after an input file has been opened.
7. Example of the Results tab of program PKFQWin after the Run PEAKFQ button has been selected.
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.
Table 1. Peakflow codes used by program PeakFQ.
Table B.1.1. Specification file output keywords that apply to the entire run.
Table B.1.2. Specification file keywords that apply to a specific station.
Table B.2. WATSTORE station header record formats.
Table B.3. WATSTORE station option record formats.
Table B.4. WATSTORE peakflow record formats.
Table B.5. WATSTORE basin characteristics record formats.
Table C.1. Attributes associated with annual peakflow data sets.
Table C.2. Sources of attributes associated with peakflow data sets.
Symbol, explanation:
a,  a constant characteristic of a particular plotting position 
Ḡ,  generalized skew coefficient. 
,  historicallyadjusted station skew coefficient. 
,  skew coefficient of frequency curve passing through *0.50. *0.10, and *0.01. 
G,  absolute value of the stationskew coefficient. 
G,  station skew coefficient. 
G_{W},  weightedskew coefficient estimate used in final logPearson Type III frequency curve. 
g,  desired skew coefficient. 
H,  historical period length. 
K,  confidence coefficient. 
K_{N},  10percent significancelevel critical value for outlier test statistic for sample of size N from the normal distribution. 
K_{H},  10percent significancelevel critical value for the outlier test statistic for sample of size H, where H is the length of the historic record period. 
k_{,p},  ordinates for skew and exceedance probability (p) for curve passing through *0.50. *0.10, and *0.01. 
k_{g,p},  Pearson Type III standardized ordinates for desired skew (g) and exceedance probability (p). 
k_{p},  standard normal frequency factor for probability p. 
k´_{p},  frequency factor for expected probability frequency curve. 
k_{(1α)},  standard normal deviate with exceedance probability 1alpha. 
k_{γ,p},  the Pearson Type III frequency factor. 
,  historicallyweighted logarithmic mean. 
,  Bulletin 17B mean. 
',  mean of frequency curve passing through *0.50. *0.10, and *0.01. 
,  historicallyweighted rank of the m^{th} largest observed peak. 
m,  rank of the m^{th} largest observed peak. 
MSE,  meansquare error (standard error of estimate squared). 
MSE_{Ḡ},  meansquare error of generalized skew coefficient. 
MSE_{G},  meansquare error of station skew coefficient. 
Ñ,  effective number of peaks above flood base, Q_{O}. 
N_{BB},  number of peaks below the flood base, including any zeros and low outliers. 
N_{HO},  number of high outliers. 
N_{HP},  number of historic peaks. 
N_{S},  number of systematic peaks. 
N_{X},  number of peaks between Q_{O} and Q_{H}. 
N,  record length in years. 
n,  sample size from normal population of flood logarithms. 
_{m},  historicallyweighted probability plotting position of the m^{th} ranked observed peak. 
_{O},  estimated probability of a flood exceeding the flood base. 
p,  exceedence probability. 
p',  normal exceedance probability corresponding to k'_{p}. 
,  conditional frequency curve describing only those peaks above the flood base. 
*,  intermediate unconditional frequency curve. 
*_{p},  ordinates of the unconditional curve. 
_{p},  final Bulletin 17Bestimated frequency curve. 
Q_{H},  historical threshold streamflow. 
Q_{O},  flood base streamflow. 
_{s,p},  systematic frequency curve ordinate at exceedance probability p. 
RMSE,  root mean square error. 
S,  sample logarithmic standard deviation. 
,  Bulletin 17B standard deviation. 
,  historicallyweighted logarithmic standard deviation. 
',  standard deviation of frequency curve passing through *0.50. *0.10, and *0.01. 
t_{n1},  Student’s t random variate with n1 degrees of freedom. 
t_{n1,p},  Student’s t quantile with n1 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. 
,  sample logarithmic mean. 
X,  logarithmic magnitudes of systematic peaks between Q_{O} and Q_{H}. 
X_{H},  logarithmic highoutlier test threshold. 
X_{L},  logarithmic lowoutlier 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).
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 annualmaximum peak flows having recurrence intervals of 2, 5, 10, 25, 50, 100, 200, and 500 years (annualexceedance 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.
Program PeakFQ performs statistical floodfrequency analyses of annualmaximum 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 logPearson 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 logPearson 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 logPearson Type III distribution for selected exceedance probabilities.
The U.S. Geological Survey maintains a peakflow file in the National Water Information System (NWIS) data base. The contents and format of data retrieved from the peakflow file are described in Appendices B.2 (Station Header Records) and B.4 (PeakFlow 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 annualpeak discharge and dischargequalification codes from the peakflow records; the gageheight information and all information about partialduration or secondary peaks is ignored.
The annual peakflow 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, systematicrecord 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 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 highmagnitude 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 largemagnitude 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 historicrecord 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 NWISWeb 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 zeroflow and conditionalprobability adjustments. Table 1 identifies the peakflow 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.
Table 1. Peakflow codes used by program PeakFQ.
[NWISNational Water Information System]
PeakFQ code  NWIS Code  PeakFQ Interpretation  PeakFQ Action 

PeakFQ code 
NWIS code 
PeakFQ Interpretation 
PeakFQ Action 

D 
3 
Dam failure, nonrecurrent 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 
Conditionalprobability 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, 
Codes are not considered by PeakFQ 
Peak always included. 
The Bulletin 17B computational analysis is illustrated in figure 1. The following sections provide an overview of the major computational steps.
Figure 1. General flow chart for floodfrequency computations (modified from Interagency Advisory Committee on Water Data, 1982).
The systematicrecord analysis involves the computation of the mean, standard deviation, and coefficient of skewness (, 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 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 abovebase systematic peaks. The statistics of the abovebase systematic peaks and the number of peaks below the gage base are used to compute the systematicrecord frequency curve. If there are no zeroes or belowbase peaks, the systematicrecord frequency curve is computed as follows:
,  (1) 
where _{s,p}  =  systematic frequencycurve ordinate at exceedance probability p, and 
k_{g,p}  =  the Person Type III standardized ordinates for station skew g and exceedance probability p. 
If there are zeroes or belowbase peaks, the statistics of the abovebase systematic peaks are used to define a conditional abovebase systematicrecord frequency curve, which is then adjusted by the conditionalprobability adjustment, as described in a subsequent section and in Bulletin 17B, Appendix 5.
The systematicrecord 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.
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:
,  (2) 
where X_{H}  =  Logarithmic highoutlier test threshold and 
K_{N}  =  10percent significancelevel 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 highoutlier threshold and length of historic period in order for the highoutlier and historicpeak 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 highoutlier threshold and length of historic period.
Program PeakFQ tests for low outliers using the following equation:
,  (3) 
where X_{L}  =  logarithmic lowoutlier test threshold. 
If an adjustment for historic data has previously been made, then the following equation is used to detect low outliers:
,  (4) 
where  =  historicallyweighted logarithmic mean, 
K_{H}  =  10percent significancelevel critical value for outlier test statistic for sample of size H, where H, is the length of the historic record period, and 
=  historicallyweighted logarithmic standard deviation. 
The computation of and 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.
Recalculation of the statistics of the abovebase 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:
Historicadjustment criterion: It is assumed that every annual peak that exceeded some historic threshold streamflow (Q_{H}) 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 Q_{H} during the time period H.
The historic period H includes the systematicrecord period plus one or more years that have no systematic record. This criterion implies that the unrecorded portion of the historic period contains only peaks below the threshold Q_{H}. Figure 2 presents a definition sketch showing the time periods and streamflows used in the historicrecord adjustment.
Figure 2. Definition sketch showing time periods and discharges used in historic recordd 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 belowQH portion of the systematic record. The adjustment is accomplished by weighting the belowthreshold systematic peaks in proportion to the number of the belowthreshold years in the historic period, as illustrated in figure 2, as follows:
,  (5) 
where W is the weight to be applied to the belowthreshold systematic peaks and N_{S}, N_{HP}, and N_{HO} are the numbers of systematic peaks, historic peaks, and high outliers, respectively. Then the effective number of peaks, Ñ, above the flood base (Q_{O}) is
,  (6) 
where N_{BB} 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
,  (7) 
Applying the historic weight W to those systematic peaks below the historic threshold Q_{H} (and above the flood base Q_{O}) yields the following formulas for the historicallyweighted mean (), standard deviation (), and skewness ():
,  (8) 
,  (9) 
, 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 Q_{O} and the historic threshold Q_{H}. 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 = N_{S}), no high or low outliers, and no belowgage 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.
After the peakstreamflow frequency curve parameters have been determined, the historically weighted frequency curve can be tabulated. If no low outliers, zero flows, or belowgage base peaks are present, this process is simply a matter of looking up the Pearson Type III standardized ordinates, k_{g,p}, for the desired skew coefficient (g) and probability (p) and computing the logarithmic frequency curve ordinates by the formula:
.  (11) 
When peaks below the flood base are present, however, the above calculation determines a conditional frequency curve 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, _{O}, calculated in equation (7); the second factor is the probability on the conditional frequency curve at streamflow x. Thus the unconditional curve, *, assigns a probability [_{O}]p to the streamflow having exceedance probability p on the abovebase curve. Conversely, an exceedance probability p on the unconditional curve * corresponds to the probability p/_{O} on the original abovebase curve . Thus, the ordinates of the unconditional curve can be computed directly by the formula:
,  (12) 
in which , , and are the logarithmic mean, standard deviation, and skew coefficient, respectively, of the abovebase 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 *0.50, *0.10, and *0.01 are computed using the above formula. Then a logarithmicPearson Type III curve is passed through these three points; the curve mean, standard deviation, and skew coefficient, ´, ´, and ´, respectively, are found by solving the three simultaneous equations:
,  (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 ´, ´, and ´ represent the contributions of all the observed peaks, those below the base as well as those above, whereas , , and do not. The resulting unconditional frequency curve, when floods below the base have been detected, then is:
.  (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 conditionalprobability adjustments are used not only to construct the final Bulletin 17B frequency curve, but also to construct a systematicrecord frequency curve that takes into account any zero flows or belowgage base peaks (but not low outliers).
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 extremeflood quantiles may be strongly affected by idiosyncrasies of the sample, and may be unrepresentative of longterm 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 usersupplied 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 randomsampling variability, respectively. The random and systematic errors are combined in a single composite property called meansquare 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.
The station and generalizedskew 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 generalizedskew coefficient is unbiased and independent of the stationskew 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 weightedskew coefficient:
,  (15) 
where G_{W}  =  weighted skew coefficient, 
G  =  stationskew coefficient, 
Ḡ  =  generalizedskew coefficient, 
MSE_{Ḡ}  =  meansquare error of generalizedskew coefficient, and 
MSE_{G}  =  meansquare error of stationskew coefficient. 
The MSE (or RMSE) of the generalized skew is estimated in conjunction with the development of the generalizedskew value. In program PeakFQ, if the user does not specify a value for the generalizedskew coefficient, the value is obtained from a digitized version of Plate 1 of Bulletin 17B, and the corresponding value of MSE_{Ḡ}= 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 usersupplied generalizedskew value.
The MSE of the station skew for logPearson 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 (MSE_{G}) is approximated with sufficient accuracy for use in calculating the weighted skew by the equation:
,  (16) 
where A  =  0.33+0.08 G if G≤0.90, 
0.52+0.30 G if G>0.90,  
B  =  0.940.26 G if G≤1.50, and 
0.55 if G>1.50, 
in which G is the absolute value of the stationskew coefficient (used as an estimate of populationskew coefficient) and N is the record length in years. If the historic adjustment (Bulletin 17B, Appendix 6) has been applied, the historicallyadjusted skew coefficient, , 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 peakflow data and the floodproducing characteristics of the basin be examined to determine whether greater weight should be given to the station skew.
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 17Bestimated frequency curve given by 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 + k_{p}S, in which and S are the ordinary sample mean and standard deviation, respectively, and k_{p} is the standard normal frequency factor for probability p. Because it is computed from a random sample, the estimate + k_{p}S is a random variable, that usually will differ from the true pprobability flood. Thus, one is led to ask how the probability of another flood exceeding the estimate + k_{p}S compares with the specified (nominal) probability p. For a normal population, one has:
(17) 
where t_{n1} is Student’s t random variate with n1 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 k_{p} by the frequency factor:
,  (18) 
in which t_{n1,p} is the Student‘s t value with n1 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 normalpopulation result is applied to the Bulletin 17Bestimated Pearson Type III distribution with mean, standard deviation, and skew coefficient, , , and G_{W}, by first looking up the normal exceedance probability p´ corresponding to k´_{p} and, second, applying the Pearson Type III frequency factor, k_{G,p´} having skew coefficient and probability, to the sample mean and standard deviation, as follows: + (k_{GW,p´}). Even this estimate, however, when evaluated for any particular sample, normally will misrepresent the true pprobability flood. With respect to a large number of flood records, however, the fraction of floods actually exceeding the estimated pprobability floods will be correct. Nonetheless, the Bulletin 17B guidelines specify that the basic floodfrequency curve (without expected probability) is the curve to be used for estimating flood risk and forming weighted averages of independent floodfrequency estimates.
Finally, onesided confidence limits for the pprobability flood are computed. A onesided 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 + KS, where 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:
(19) 
in which α is the confidence limit, μ, σ, and γ are the population mean, standard deviation, and skew coefficient, respectively, k_{γ,p} is the Pearson Type III frequency factor, and the righthand side of the inequality is the population pprobability flood. The population parameters are unknown, but constant. The idea is to find a Kvalue such that + 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 pprobability flood. In any particular sample the computed value + KS may fail to bound the population characteristic, but, over a number of samples, the specified fraction, α (or 1α), will yield correct bounds. A value of close to unity yields upper confidence limits and a value close to zero yields lower limits. In particular, the upper 95percent confidence limit has α = 0.95; the lower 95percent limit has α = 0.05. The value of K is found by rearranging the probability statement as follows:
(20) 
in which n is the sample size. If the underlying population were normally distributed (γ = 0), and if and S were the ordinary sample mean and standard deviation, respectively, then the random variable on the lefthand side of the inequality would have the noncentral t distribution with n1 degrees of freedom and noncentrality parameter (k_{γ,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, G_{W}, then one could assume that the variate would have approximately the noncentral t distribution. Building upon this foundation, one obtains:
,  (21) 
which is the noncentral t value with exceedance probability 1α. A standard largesample approximation for the noncentral t distribution then yields the result:
,  (22) 
in which k_{(1α)} is the standard normal deviate with exceedance probability 1α and G_{W} is the Bulletin 17B weightedskew coefficient. As stated above, an αvalue 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 are estimates of the exceedance probabilities of observed peak flows. They are computed by the formula p = (ma)/(N2a+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 plottingposition formula. Bulletin 17B and Program PeakFQ use the Weibull plottingposition formula (a = 0) by default, although other avalues can be specified. The probabilityplotting 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 probabilityplotting positions are adjusted using the same logic that underlies the calculation of the historicallyweighted mean, standard deviation, and skew coefficient. The actual sample of size N is augmented by (W1) “virtual” copies of the observed peaks below the historic threshold to fill out the entire historic period (H). In the ranked record, each belowthreshold observed peak is preceded by (W1)/2 of its virtual copies and followed by the remaining (W1)/2 copies. In the augmented ranked series, if there are Z peaks above the historic threshold, then the rank of the first belowthreshold observed peak is Z + (W1)/2 + 1. The rank of the second belowthreshold observed peak is Z + W + (W1)/2 + 1. In general, the historically adjusted rank of the m^{th} ranked observed peak is:
(23) 
where Z  =  N_{HO} + N_{HP}. 
The historicallyweighted plotting positions _{m} then are:
(24) 
These equations are equivalent to equations 66 through 68 in Appendix 6 of Bulletin 17B. As indicated above, program PeakFQ uses the Weibull plottingposition formula (a = 0) by default, although other avalues can be specified.
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 floodrisk 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 stationskew coefficient with a generalizedskew coefficient estimated by pooling information from nearby sites.
Program PEAKFQ does not perform generalizedskew 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 usersupplied input. The estimation of the generalized skew is performed by the floodfrequency analyst.
The discussion in this section concerns Bulletin17B guidelines for development of appropriate generalizedskew coefficients for floodfrequency analysis. The following discussion is modified from Bulletin 17B (p. 1014).
Bulletin 17B includes a map (Plate I) showing generalizedskew values that may be used in the absence of detailed generalizedskew 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 peakflow 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 generalizedskew 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 Bulletin17B recommended procedure for developing generalizedskew coefficients requires the use of at least 40 stations, or all stations within a 100mile 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 stationskew 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 stationskew 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 generalizedskew 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 MSE_{Ḡ}.
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, 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.
The following sections describe the computer program PeakFQ for performing the Bulletin 17B floodfrequency analysis. There are two methods for running PeakFQ: a Windows version (called PKFQWin) and a batch version (called PKFQBat).
The program PKFQWin provides a user interface to the PeakFQ batch model. The opening screen of the program is shown below in figure 3.
Figure 3. Example of opening screen of program PKFQWin showing the station specifications tab before an input file has been opened.
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.
The File:Open menu item is used to open any of the file types that can be used by PeakFQ. These include:
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 peakflows records; WDM  data and attributes from each station’s data set; PSF  data file (WATSTORE or WDM) plus specifications for overriding initial values.
Figure 4. Example of the File Open window in program PKFQWin, obtained by selecting Open from the File Menu.
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).
Figure 5. Example of the Station Specification Tab of program PKFQWin after a file containing 8 sets of data has been opened.
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 doubleclicking to activate the pulldown 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 userspecified historic period that may have been present in a WATSTORE “I” record or WDM attribute. If no userspecified 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 pulldown menu in the Skew Option field.
The Generalized Skew is, by default, based on the station latitude and longitude using the generalizedskew map accompanying Bulletin 17B. If a WATSTORE “I” record or WDM attribtute is present and the generalized skew field is nonblank, 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 Gen Skew Std Error field is, by default, 0.55, corresponding to the standard error of the generalizedskew map accompanying Bulletin 17B. If a WATSTORE “I” record or WDM attribute is present and the standard error of generalizedskew field is nonblank, 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 LowOutlierThreshold field displays the value of any userspecified lowoutlier threshold that may have been present in a WATSTORE “I” record or WDM attribute. If no userspecified value has been given, then a value of 0.0 is displayed, and the lowoutlier threshold is computed by PeakFQ using the Bulletin 17B low outlier test. Any input peaks less than the lowoutlier threshold are accounted for by the conditionalprobability adjustment. Occasionally, it may be necessary or appropriate to override the Bulletin17B lowoutlier 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 LowOutlierThreshold field may be updated interactively by clicking in the desired station row and typing the new value.
The HiOutlier Threshold field displays the value of any userspecified historic/highoutlier threshold that may have been present in a WATSTORE “I” record or WDM attribute. If no userspecified value has been given, then a value of 0.0 is displayed. This field is used only if the Bulletin17B historicrecord adjustment has been specified by the user in the HistoricPeriod field. If a value greater than zero is displayed in the HiOutlierThreshold field, that value will be used as the historic/highoutlier threshold in the Bulletin17B historicrecord adjustment. Otherwise, the lowest historiccoded input peak will be used as the historic/highoutlier threshold. If there are no historiccoded peaks and a historic adjustment for a high outlier is needed, the user must specify the required highoutlier threshold. The HiOutlierThreshold 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 gagebase discharge will supersede the gage base inferred from any “less than” NWIS qualification code (4) in the peak record. Note that this gagebase discharge is not the same as the partialduration 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.
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.
Figure 6. Example of the Output Options tab of program PKFQWin after an input file has been opened.
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:
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 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 95percent confidence limits are used (0.95).
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.
Figure 7. Example of the Results tab of program PKFQWin after the Run PEAKFQ button has been selected.
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.
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.
Figure 8. Example of the Save Specifications File window in program PKFQWin, obtained by selecting the Save Specs button at the bottom of the PEAKFQ window.
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 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.
Beard, L.R., 1960, Probability estimates based on small normaldistribution samples: Journal of Geophysical Research, v. 65, no. 7, p. 21432148.
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 WaterResources Investigations Report 954085, 211 p., http://water.usgs.gov/software/annie.html.
Interagency Advisory Committee on Water Data, 1982, Guidelines for determining floodflow 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 OpenFile Report 791336I, 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 791336I, 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. 373376.
Wallis, J.R., Matalas, N.C., and Slack, J.R., 1974, Just a Moment: Water Resources Research, v. 10, no. 2, p. 211219.
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 staid The number of historic peaks (nhp) retrieved for station (staid) 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. begyr endyr firstyr lastyr staid Probable user error. The years requested on the Icard (begyr, endyr) do not overlap the years available in the record (firstyr, lastyr) at the station (staid).  
INPUT2  STATION HAS NO PEAK FLOW DATA. STAID = xxxxx Informative message. See preceding messages for explanation. Processing continues with next valid input record.  
INPUT2  PEAK COUNT EXCEEDS STORAGE CAPACITY npks staid The number of peaks (npks) retrieved for station (staid) 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.  
PKFRD4  Insufficient data to process, only nnn peaks for station staid Only nnn peaks were identified to be include in the analysis for station id staid. A minimum of 3 peaks is required.  
PKFRD4  CARD types 4, 2, and * are ignored. cardimage  
PKFRD4  Unrecognized CARD type. Must be Y, Z, N, H, I, 2, 3, 4, or *. (2, 4, and * records are ignored.)cardimage  
PKFRD4  Error reading input lat. or long. on H card. cardimage  
PKFRD4  Error reading Icard cardimage  
WCF001J  FLOOD FREQUENCY, BULLETIN 17B. 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 beginningofjob message, if requested.  
WCF002J  CALCS COMPLETED. RETURN CODE = n Normal endofjob message. Return codes: 0 = no error detected. 1 = nonstandard 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. Locationcode data This message should not occur. If it does, contact h2osoft@usgs.gov  
WCF101L 
 
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.)  
WCF109W  PEAKS WITH MINUSFLAGGED 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 MINUSFLAGGED 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 Missingdischarge peaks were noted and have been omitted from the sample (WCF109). The correct sample size for analysis is nnn.  
WCF117E 
 
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 belowgagebase peaks. bbb = gagebasedischarge.  
WCF134I  NO SYSTEMATIC PEAKS WERE BELOW GAGE BASE. bbb bbb = gagebasedischarge.  
WCF141E 
SAMPLE SIZE TOO SMALL TO CALC STATS. lll nnn
 
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 nearzero 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 userspecified skew uuu. An igsopt value of 1 means generalized skew; 1 means station skew.  
WCF156I  17B HIGHOUTLIER TEST SUPERSEDED BY MIN HIST PK. www Routine information report of Bulletin 17B highoutlier test criterion (www). Historic peaks were present below this threshold, so the historichighoutlier threshold was lowered to the level of the smallest historic peak.  
WCF157W  USER HIGHOUTLIER CRIT LOWERED TO MIN HIST PK. uuu hhh Probable user error—if historic peaks are given. The highoutlier 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  HIGHOUT/HISTPK BASE BELOW LOWOUT/GAGE BASE. hhh lll Probable user error—perhaps the highoutlier and lowoutlier or gagebase data have been entered in the wrong order. hhh = highoutlier or historic base. lll = lowoutlier or gage base.  
WCF161I  USER HIGHOUTLIER CRITERION REPLACES 17B. uuu www The userspecified historicpeakhighoutlier discharge threshold (uuu) has been noted. Its value supersedes the Bulletin 17Brecommended value (www).  
WCF162I  SYSTEMATIC PEAKS EXCEEDED BY HIGHOUTLIER CRITERION. nho hhb One or more (nho) systematic peaks exceeded the highoutlier 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 historicpeakhighoutlier 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 HIOUT/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 LOWOUTLIER CRITERION SUPERSEDES 17B. uuu www uuu = user lowoutlier criterion, www = Bulletin 17B lowoutlier criterion  
WCF193E  LOW OUTLIER CRITERION EXCEEDS HIGHHIST lll hhh Probable user error—perhaps the highoutlier and lowoutlier or gagebase data have been entered in the wrong order. hhh = highoutlier or historic base. lll  lowoutlier or gage base.  
WCF195I  NO LOW OUTLIERS WERE DETECTED BELOW CRITERION xxxxx No peaks above the gage base were below the lowoutlier criterion. xxxxx = low outlier criterion adopted (user or 17B).  
WCF198I  LOW OUTLIERS BELOW FLOOD BASE WERE DROPPED. nnn bbb Peaks above the gage base and below the lowoutlier criterion were noted. The flood base of the Bulletin 17B frequency curve has been set at the lowoutlier 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 belowbase 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 skewa skewu 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. Skewa is the skew of the above base peaks. skewu and gensku may not be present. skewu is the unconditional skew after any conditional probability adjustment or weightedskew calculation. gensku is the generalized skew, and is printed only if the error is detected after the Bulletin 17B weightedskew calculations.  
WCF217L 
 
WCF219J 
 
WCF233W  EXPECTED PROB OUT OF RANGE AT TAB PROB xxxxx yyyyy Expectedprobability 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 17BEXPECT PROB xxxxxxx xxxxxxx xxxxxxx Routine report of ‘expectedprobability’ frequency curve ordinates at 2, 10, and 100yr levels. ‘Expectedprobability’ curve is based on Bulletin 17B frequency curve.  
WCF239J 

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.
This appendix gives detailed descriptions of the PeakFQ specification (PSF) file. Running the batch version of PeakFQ, whether standalone 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.
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 
Yes provides additional printout of intermediate results in the analysis. 
ADDITIONAL 
WDM 
NONE 
WDM (or BOTH) puts computed statistics on each data set as attributes for further statistical analysis. 
EMA 
YES 
NO 
NO will run the traditional Bulletin 17B analysis. 
CONFIDENCE 
0.nn 
0.95 
Where 0.nn is confidence limit percent as a fraction. 
PLOT STYLE 
GRAPHICS 
NONE 
GRAPHICS (or BOTH) will generate a graphic file for each station analyzed. 
PLOT FORMAT 
CGM 
CGM 
Format for GRAPHICS plots (Note: Some file formats may not be available on all computer platforms). 
PLOT PRINTPOS 
YES 
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 (ma)/(N+12A) where m is order number, N is total number of peaks, and a is a parameter where: 
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 dataset 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.)
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 that the systematic period. 
SKEWOPT 
GENERALIZED 
WEIGHTED 
STATION  station skew computed from recorded peaks. 
URB/REG 
YES 
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 lowoutlier discharge criteria. If greater than 0.0, will override the Bulletin 17B computed lowoutlier 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. 
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.
Record 
Column 
Format 
WDM Attribute 
Description 
Z 



Agency Indentification Record  optional 

1 
“Z” 
 
Record identifier. Required. 

3337 
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. 

216 
A15 
STAID or ISTAID 
Station identification number. Required. 

1731 
 

Station locator. Required. 


3I2 
LATDEG 
Latitude, DDMMSS.  Optional. 


I3,2I2 
LNGDEG 
Longitude, DDDMMSS.  Optional. 


I2 

Sequence number. 

3233 
A2 
STFIPS 
Numeric state code where station is located. 

3435 
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. 

3638 
A3 
COCODE 
FIPS county code where the station is located. 

3940 
A2 
SITECO 
Site code
indicating the major class of data collected at the site: 

4148 
I8 
HUCODE 
Hydrologic unit code from the USGS state hydrologic unit maps. 

4955 
F7.0 
DAREA 
Total drainage area, in square miles. 

5662 
F7.0 
CONTDA 
Contributing drainage area, in square miles. 

6370 
F8.0 
DATUM 
Datum, feet above mean sea level. 

7179 
F9.0 
WELLDP 
Well depth, in feet. 
N 



Station Name Record  optional 

1 
“N” 
 
Record identifier. Required. 

216 
A15 
STAID or ISTAID 
Station identification number. Required. 

1764 
A64 
STANAM 
Station name. Required. 

6572 
A8 
GUCODE 
Major geologic unit codes as assigned by WATSTORE. 

73 
A1 
AQTYPE 
Aquifer type code
assigned by WATSTORE: 
Y 



Base Discharge Record  ignored. 

1 
“Y” 
 
Record identifier. 

216 
A15 
STAID or ISTAID 
Station identification number. Required. 

723 
F7.0 
BASEQ 
Base discharge. Note: this is not the Gage Base Discharge used in PeakFQ. 
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.
Table B.3. WATSTORE station option record formats.
Record  Column  Format  WDM Attribute  Description 

I  Station option record  optional  
1  "I"    Record identifier. Required.  
216  A15  STAID or ISTAID  Station identification number. Required.  
1724  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.  
2532  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.  
3340  F8.0  Userspecified historichighoutlier discharge threshold. Used only in conjunction with the historic period, this threshold is used to override the Bulletin 17Bcomputed highoutlier 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.  
4148  F8.0  Userspecified lowoutlier discharge criterion. This criterion, if a positive number, will override the Bulletin 17B computed lowoutlier criterion. A blank, negative value, or zero will be ignored.  
4956  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 partialduration base discharge that may be recorded in the Station Header record.)  
5764  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.  
6569  5A1 
Stationoption 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  Stationskew 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  Generalizedskew 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 userspecified historichighoutlier discharge threshold. The program will print a warning message if it finds any belowthreshold 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.  
7174  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 fourdigit number. If blank or less than the first year of the input record, no years will be dropped from the beginning of the record.  
7578  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.  
The peakflow data records are described in table B.4. The peakflow record contains some fields that are not read by PeakFQ. The partial duration peakflow 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 peakflow 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
Table B.4. WATSTORE peakflow record formats.
Record  Column  Format  Description 

3  PeakFlow Data Record  required. Fields in columns 44  75 are ignored.  
1  "3"  Record identifier. Required  
216  A15  Station identification number. Required.  
1720  I4  Year peak occurred  required:
 
2122  I2  Month the annual peak discharge occurred. Blank if month is not known.  
2324  I2  Day of the month the annual peak discharge occurred. Blank if day is not known.  
2531  F7.0  Annual peak discharge, right justified. Field may be blank.  
3243  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, icejam 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.  
4451  F8.0  Gage height associated with annual peak discharge, right justified in field. Ignored.  
5255  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 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 6075)  
5659  I4  "Highest since" year  representing the calendar year after which the given peak discharge (cols 2531) is known to be the highest. This year is determined from historic newspaper accounts, local information, or other sources.  
6061  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.  
6263  I2  Day of the month of the annual peak gage height.  
6471  F8.0  Annual peak gage height.  
7275  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.  
;  216  A15  Station identification number. Required. 
1720  I4  Year data on this record occurred.
 
2122  I2  Month the partial duration peak occurred. Blank if month is not known.  
2324  I2  Day of the month the partial duration peak occurred. Blank if day is not known.  
2531  F7.0  Partial duration peak discharge, right justified.  
3243  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, icejam 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.  
4451  F8.0  Partial duration peak gage height.  
5255  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  
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 B17B 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
Table B.5. WATSTORE basin characteristics record formats.
Record  Column  Format  WDM Attribute  Description 

1  Station identification record  
1  "I"    Record identifier.  
216  A15  STAID or ISTAID  Station identification number. Required.  
1718  I2  STFIPS  Numeric state code where station is locked. May be blank.  
1920  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.  
2168  A48  STANAM  Stations name and data identifier.  
6975  F8.0  blank  
7680  A5  AGENCY  Agency code. May be blank.  
2  Basin Characteristics, record 1  
1  "2"    Record identifier.  
216  A15  STAID or ISTAID  Station identification number. Required.  
1776  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, 2.5year recurrence interval.  
I3,F7.0  P2.  76 Annual flood peak, 2year recurrence interval.  
I3,F7.0  P5.  77 Annual flood peak, 5year recurrence interval.  
I3,F7.0  P10.  78 Annual flood peak, 10year recurrence interval.  
I3,F7.0  P25.  79 Annual flood peak, 25year recurrence interval.  
I3,F7.0  P50.  80 Annual flood peak, 50year recurrence interval.  
2  Basin Characteristics, record 2  
1  "2"    Record identifier.  
216  A15  STAID or ISTAID  Station identification number. Required.  
1776  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, 100year recurrence interval.  
I3,F7.0  P200.  82 Annual flood peak, 200year 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, 500year recurrence interval.  
2  Basin Characteristics, record 3  
1  "2"    Record identifier.  
216  A15  STAID or ISTAID  Station identification number. Required.  
1776  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 historicpeak adjustments.  
I3,F7.0  WRCMN  180 Mean of logarithms, base 10, of annual peak discharges after outlier and historicpeak adjustments.  
I3,F7.0  WRCSD  181 Standard deviation of logarithms, base 10, of annual peak discharges after outlier and historicpeak 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 historicpeak adjustment of flood frequency data.  
Dataset 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 dataset attributes commonly found in annual peakflow data sets. Table C.2 contains a list of the attributes that PeakFQ reads and (or) writes or that are commonly associated with annual peakflow data sets and how these attributes are used by the PeakFQ program. The IOWDM program is used to write peakflow 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.
Table C.1. Attriutes associated with annual peakflow data sets.
Name  Type  Length  Update  Dataset 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," OpenFile Report 84708. 
STAID  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 
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, 1.25year recurrence interval. 
P10.  Real  1  Yes  Opt  Opt  Annual flood peak, in cubic feet per second, 10year recurrence interval. 
P100.  Real  1  Yes  Opt  Opt  Annual flood peak, in cubic feet per second, 100year recurrence interval. 
P2.  Real  1  Yes  Opt  Opt  Annual flood peak, in cubic feet per second, 2year recurrence interval. 
P200.  Real  1  Yes  Opt  Opt  Annual flood peak, in cubic feet per second, 200year recurrence interval. 
P25.  Real  1  Yes  Opt  Opt  Annual flood peak, in cubic feet per second, 25year recurrence interval. 
P5.  Real  1  Yes  Opt  Opt  Annual flood peak, in cubic feet per second, 5year recurrence interval. 
P50.  Real  1  Yes  Opt  Opt  Annual flood peak, in cubic feet per second, 50year recurrence interval. 
P500.  Real  1  Yes  Opt  Opt  Annual flood peak, in cubic feet per second, 500year 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 alphanumeric 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 
Userdefined fourcharacter 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 historicpeak adjustments. 
WRCSD  Real  1  Yes  Opt  Opt  Standard deviation of logarithms, base 10, of annual peak discharges after outlier and historicpeak adjustments. 
WRCSKW  Real  1  Yes  Opt  Opt  Skew of logarithms, base 10, of annual peak discharge after outlier and historicepak adjustments and generalized skew weighting. 
YRSHPK  Int  1  Yes  Opt  Opt  Number of consecutive years used for historicpeak adjustment to floodfrequency data. 
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
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
H 03606500 3602190881342004747017SW 6040005 205.00 380.58 N 03606500 BIG SANDY RIVER AT BRUCETON HIST B17B 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
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 17B 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 17B Guidelines 04/28/2006 13:03 Station  03606500 BIG SANDY RIVER AT BRUCETON HIST B17B 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. ********* **WCF109WPEAKS WITH MINUSFLAGGED DISCHARGES WERE BYPASSED. 3 **WCF113WNUMBER OF SYSTEMATIC PEAKS HAS BEEN REDUCED TO NSYS = 44 WCF134INO SYSTEMATIC PEAKS WERE BELOW GAGE BASE. 0.0 WCF195INO LOW OUTLIERS WERE DETECTED BELOW CRITERION. 921.3 WCF163INO HIGH OUTLIERS OR HISTORIC PEAKS EXCEEDED HHBASE. 26151.7 WCF002JCALCS COMPLETED. RETURN CODE = 2 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 17B Guidelines 04/28/2006 13:03 Station  03606500 BIG SANDY RIVER AT BRUCETON HIST B17B ANNUAL FREQUENCY CURVE PARAMETERS  LOGPEARSON 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 95PCT 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 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 17B Guidelines 04/28/2006 13:03 Station  03606500 BIG SANDY RIVER AT BRUCETON HIST B17B 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, nonrecurrent 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  Minusflagged discharge  Not used in computation 8888.0  No discharge value given  Minusflagged water year  Historic peak used in computation 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 17B Guidelines 04/28/2006 13:03 Station  03606500 BIG SANDY RIVER AT BRUCETON HIST B17B 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 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:
Note: Graphic from a [wmf] file, curves enhanced for publication.
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