Estimating the Magnitude and Frequency of Peak Streamflows for Ungaged Sites on Streams in Alaska and Counterminous Basins in Canada

8/10/2019 Estimating the Magnitude and Frequency of Peak Streamflows for Ungaged Sites on Streams in Alaska and Count

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Estimating the Magnitude and Frequency of PeakStreamflows for Ungaged Sites on Streams inAlaska and Conterminous Basins in Canada

ByJanet H. Curran, David F. Meyer, andGary D. Tasker

Anchorage, Alaska

2003

Water-Resources Investigations Report 03-4188

U.S. GEOLOGICAL SURVEY

Prepared in cooperation with theALASKA DEPARTMENT OF TRANSPORTATION AND

PUBLIC FACILITIES


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U.S. DEPARTMENT OF THE INTERIORGALE A. NORTON, Secretary

U.S. GEOLOGICAL SURVEYCharles G. Groat, Director

Any use of trade, product, or firm names in this publication is for descriptive purposes only and doesnot imply endorsement by the U.S. Government.

For additional information write to:

Chief, Water Resources OfficeU.S. Geological SurveyAlaska Science Center4230 University Drive, Suite 201Anchorage, AK 99508-4664

http://alaska.usgs.gov

Copies of this report can be obtained from:

U.S. Geological SurveyInformation ServicesBuilding 810Box 25286, Federal CenterDenver, CO 80225-0286

Suggested citation:

Curran, J.H., Meyer, D.F., and Tasker, G.D., 2003, Estimating the magnitude and frequency of peakstreamflows for ungaged sites on streams in Alaska and conterminous basins in Canada:U.S. Geological Survey Water-Resources Investigations Report 03-4188, 101 p.
http://alaska.usgs.gov/http://alaska.usgs.gov/


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Contents iii

CONTENTS

Abstract ................................................................................................................................................................ 1Introduction.......................................................................................................................................................... 1

Purpose and Scope ...................................................................................................................................... 2Previous Studies .......................................................................................................................................... 2Acknowledgments....................................................................................................................................... 3

Description of Study Area.................................................................................................................................... 3Determination of Drainage-Basin Characteristics................................................................................................ 5Determination of Streamflow Analysis Regions.................................................................................................. 5Estimating Peak Streamflows at Gaged Sites ...................................................................................................... 7

Data Collection............................................................................................................................................ 8Data Adjustment.......................................................................................................................................... 8

High Outliers and Historic Peak Discharges...................................................................................... 9Low Outliers ...................................................................................................................................... 9Discharges Recorded as Less Than a Known Value.......................................................................... 9

Data Not Correlated to Basin Characteristics .................................................................................... 9Generalized Skew Coefficients ................................................................................................................... 10

Regional Equations for Estimating Peak Streamflows ........................................................................................ 11Regression Analysis .................................................................................................................................... 11Accuracy and Limitations of Estimating Equations.................................................................................... 12

Procedures for Estimating Peak Streamflow Magnitude and Frequency............................................................. 15Example Applications ................................................................................................................................. 17Computer Program...................................................................................................................................... 19

Summary .............................................................................................................................................................. 20References ............................................................................................................................................................ 20Appendixes........................................................................................................................................................... 83Appendix A. Years of Record for Annual Peak Streamflows Used in This Report ............................................ 84Appendix B. Accuracy Of Estimating Equations................................................................................................. 93

Site-Specific Standard Error of Prediction.................................................................................................. 93Average Standard Error of Prediction......................................................................................................... 94Equivalent Years of Record ........................................................................................................................ 94Average Equivalent Years of Record.......................................................................................................... 94Confidence Limits ....................................................................................................................................... 94Converting Errors from Log Units to Percentages...................................................................................... 95


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iv Figures

PLATE

[Plate is in pocket]

Plate 1. Map showing streamflow analysis regions and locations of streamflow-gaging and partial-recordstations for which peak-streamflow statistics were computed, Alaska and conterminous basinsin Canada.

FIGURES

Figure 1. Map showing physical features and streamflow analysis regions of Alaska andconterminous basins in Canada.......................................................................................................... 4

Figure 2. Graph showing relation of discharge to drainage area for selected recurrence intervalsfor the Yukon River, Alaska and Canada .......................................................................................... 17


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Tables v

TABLES

Table 1. Description and methods of estimation of basin characteristics used in regression analysis ............ 6Table 2. Generalized skew and summary statistics for Regions 1-7, Alaska and conterminous

basins in Canada ................................................................................................................................ 11Table 3. Regression equations for estimating 2-, 5-, 10-, 25-, 50-, 100-, 200-, and 500-year

peak streamflows for unregulated streams in Regions 1-7, Alaska and conterminousbasins in Canada ................................................................................................................................ 13

Table 4. Station information and peak-streamflow statistics for streamflow-gaging andpartial-record stations in Alaska and conterminous basins in Canada............................................... 22


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vi Conversion Factors and Datums

CONVERSION FACTORS AND DATUMS

CONVERSION FACTORS

Temperature in degrees Fahrenheit (F) may be converted to degrees Celsius (C) as follows:

C=(F-32)/1.8.

DATUMS

Vertical coordinate informationwas referenced to the National Geodetic Vertical Datumof 1929 (NGVD 29).

Horizontal coordinate informationwas referenced to the North American Datum of 1927(NAD 27).

Multiply By To obtain

foot (ft) 0.3048 meter (m)

inch (in.) 25.4 millimeter (mm)

mile (mi) 1.609 kilometer (km)

square mile (mi2) 2.590 square kilometer (km2)

foot per mile (ft/mi) 0.1894 meter per kilometer (m/km)

cubic foot per second (ft3/s) 0.02832 cubic meter per second (m3/s)


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Introduction 1

Estimating the Magnitude and Frequency of Peak

Streamflows for Ungaged Sites on Streams inAlaska and Conterminous Basins in Canada

ByJanet H. Curran, David F. Meyer, andGary D. Tasker

ABSTRACT

Estimates of the magnitude and frequencyof peak streamflow are needed across Alaska forfloodplain management, cost-effective design of

floodway structures such as bridges and culverts,and other water-resource management issues.Peak-streamflow magnitudes for the 2-, 5-, 10-,25-, 50-, 100-, 200-, and 500-year recurrence-interval flows were computed for 301 streamflow-gaging and partial-record stations in Alaska and 60stations in conterminous basins of Canada. Flowswere analyzed from data through the 1999 wateryear using a log-Pearson Type III analysis. TheState was divided into seven hydrologicallydistinct streamflow analysis regions for this

analysis, in conjunction with a concurrent study oflow and high flows. New generalized skewcoefficients were developed for each region usingstation skew coefficients for stations with at least25 years of systematic peak-streamflow data.

Equations for estimating peak streamflowsat ungaged locations were developed for Alaskaand conterminous basins in Canada using ageneralized least-squares regression model. A setof predictive equations for estimating the 2-, 5-,10-, 25-, 50-, 100-, 200-, and 500-year peak

streamflows was developed for each streamflowanalysis region from peak-streamflow magnitudesand physical and climatic basin characteristics.These equations may be used for unregulatedstreams without flow diversions, dams,periodically releasing glacial impoundments, orother streamflow conditions not correlated to basin

characteristics. Basin characteristics should beobtained using methods similar to those used inthis report to preserve the statistical integrity of theequations.

INTRODUCTION

Floods in Alaska have historically causeddamage to towns and villages, highway infrastructure,and aquatic biota. To minimize this damage and protectthe health and safety of humans and wildlife, estimatesof flood frequency are incorporated in engineeringdesign and land management. Estimates of peakstreamflow (flood) magnitudes for specifiedfrequencies at surface-water data-collection stations arecompiled using standardized statistical procedures.

These statistics can be coupled with physical andclimatic characteristics of the drainage basins upstreamfrom the data-collection stations to develop equationsfor estimating peak streamflows at sites where little orno data have been collected. Estimating equations areused across the State for critical applications includingfloodplain management and the cost-effective design ofstructures such as bridges and culverts that conveyflood flows and accommodate fish passage.

Improving peak streamflow estimates requiresupdating the analysis as more stations becomeavailable and record lengths at existing stationsincrease, as improved estimates of basin characteristicsbecome available, or as improved methods fordeveloping the equations become available.Streamflow data for Alaska are collected by the USGS,under cooperative agreements with Federal, State, andlocal agencies, and by the Water Survey of Canada.


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2 Estimating the Magnitude and Frequency of Peak Streamflows for Ungaged Sites on Streams in Alaska and Conterminous Basins in Canada

This streamflow-gaging network is relatively sparse forthe land area it covers, and all but seven of its stationshave records shorter than 50 years. Many stations haverecords shorter than 10 years. The most recent flood-frequency analysis, completed for data through wateryear 1990 (Jones and Fahl, 1994), relaxed the record

length criterion to 8 years from the more typical 10years in order to include data for small streamsthosewith drainage areas less than 50 mi2(square miles)collected under a cooperative study begun in 1962. Bythe end of water year 1999, enough additional years ofdata were available at existing stations, and enoughadditional stations were available, to increase therecord-length criterion to 10 years and update theanalysis. For this reason, the U.S. Geological Survey(USGS), in cooperation with the Alaska Department ofTransportation and Public Facilities, began a study toupdate the peak-streamflow frequency statistics for

streamflow-gaging and partial-record stations inAlaska and conterminous basins in Canada and toupdate the regression equations for estimation of peak-streamflow frequency at ungaged sites. Althoughimproved methods of estimating basin characteristicsare also available, primarily by means of a GeographicInformation System (GIS), existing digital data forAlaska and Canada are not yet extensive and thesemethods could not yet be implemented across the studyarea. GIS methods for determination of basincharacteristics were implemented only for basins

included in the analysis for the first time, all of whichwere in areas with available digital data. The results ofa companion study of high-duration and low-durationflow statistics based on mean daily discharge aredescribed in a separate report (Wiley and Curran,2003).

Purpose and Scope

This report presents new peak-streamflowstatistics for 361 streamflow-gaging stations andpartial-record stations in Alaska and conterminousbasins in Canada that have at least 10 years ofmaximum instantaneous discharge data through wateryear 1999 or that have 8 or 9 years of data and wereused in the most recent USGS peak-streamflowanalysis (Jones and Fahl, 1994). Generalized-skew

coefficients developed using station skew coefficientsfrom stations with at least 25 years of data andregression equations for estimating peak streamfloware presented for seven streamflow analysis regionsspanning the State and conterminous Canadian basins.The estimating equations were developed using peak-

streamflow magnitudes from 355 stations wherestreamflow regulation, streamflow diversion,urbanization, and natural damming and releasing ofwater do not affect the streamflow data. Data fromCanada were included to improve the analysis of theeastern regions of Alaska. This report supersedesprevious reports describing peak-streamflow frequencystatistics and methods for Alaska.

Previous Studies

Five previous analyses of annual peakstreamflow in Alaska are summarized in reports byBerwick and others (1964), Childers (1970), Lamke(1978), Parks and Madison (1985), and Jones and Fahl(1994). All but the earliest study used log-Pearson TypeIII analysis of annual peaks and multiple regressionanalysis with basin characteristics as independentvariables. Each study subdivided the State into regionsand provided a method to estimate streamflowfrequency and magnitude in each region. A commonregion for most studies was the coastal area along thesouthern edge of the State (or sometimes just the

southeastern portion of the coast); other regions varied.In the most recent study of Alaska peak-

streamflow frequency, Jones and Fahl (1994) followedmethods recommended in Bulletin 17B of theInteragency Advisory Committee for Water Data(Interagency Advisory Committee on Water Data,1982) for individual station and regional flood-frequency analysis. To account for the shorter recordsof most Alaska stations, especially those of smallstreams, Jones and Fahl relaxed criteria for minimumyears of record from 10 to 8 years for regionalregression analysis and from 25 to 22 years forgeneralized skew analysis. The benefit of relaxing therecord-length criteria was to increase the number ofstations eligible for analysis; no assessment of the gainor loss of accuracy in estimating equations wasprovided.


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Determination of Streamflow Analysis Regions 5

DETERMINATION OF DRAINAGE-BASINCHARACTERISTICS

Physical and climatic features of the watershedupstream of a given stream location, termed basincharacteristics, can be used as independent variables toestimate streamflow statistics (Thomas and Benson,1970). Nine basin characteristics used in the previousstatewide flood-frequency analysis (Jones and Fahl,1994) were available for all stations: drainage area,main channel slope, main channel length, mean basinelevation, area of lakes and ponds, area of forests, areaof glaciers, mean annual precipitation, and meanminimum January temperature. Although all ninevariables were included in the present analysis, onlydrainage area, mean basin elevation, area of lakes andponds, area of forests, mean annual precipitation, and

mean minimum January temperature were used in thefinal equations.Previously determined basin characteristics were

available for most of the stations used in the presentanalysis (Jones and Fahl, 1994). Definitions of thebasin characteristics and the manual methods used todetermine them are described by Jones and Fahl (1994)and the U.S. Geological Survey (1978) and aresummarized in table 1. Basin characteristics forstations not in the Jones and Fahl (1994) report wereobtained using modified methods, which are alsosummarized in table 1. Automated procedures for

determining selected basin characteristics for newstations were created using the AML programminglanguage with Arc/Info GIS software (EnvironmentalSystems Research Institute, 1997). Only basincharacteristics used in final equations are presented inthis report; additional basin characteristics are availablefrom the Alaska Science Center at the address shown inthe front of this report.

For a statistical analysis such as the regressionsperformed for the present study, all data ideally shouldbe collected in a similar manner to minimize errorwithin individual variables. Although new methods of

estimation or new sources of data for basincharacteristics may produce values that moreaccurately represent the basin, it is best to avoid mixingsuch data with previously obtained data in the sameanalysis. However, in an effort to apply GIS technologyto data-collection methods, some fundamentalvariations in methods and data sources were necessary.A comparison between the original and modified

methods used in this and a companion study of flow-duration statistics noted statistically significantdifferences in some basin characteristics (Wiley andCurran, 2003). Although the variability introduced intothe regression analysis by using the modified methodsfor a few stations is small, the user should be aware that

using modified methods for an individual site couldintroduce significant error. In general, methods used fordetermining basin characteristics at an ungaged siteshould be as consistent as possible with the methodsdescribed by Jones and Fahl (1994) and the U.S.Geological Survey (1978) and summarized in table 1.

DETERMINATION OF STREAMFLOWANALYSIS REGIONS

Dividing areas as large and geographically andclimatically diverse as Alaska into smaller regions foranalysis usually improves the accuracy of estimationequations. Stations within a region should have similarhydrologic characteristics, but a balance must be struckbetween isolating hydrologically similar regions andmeeting minimum sample-size requirements forstatistical analysis. Streamflow analysis regions weredeveloped simultaneously for this study and for high-duration and low-duration flow analyses (Wiley andCurran, 2003). Initial placement of stations intostreamflow analysis regions was guided by hydrologic

unit boundaries (U.S. Geological Survey, 1987) andregional boundaries used in previous reports, inparticular the peak- flow analysis by Jones and Fahl(1994). Refinement of regional boundaries was basedon the geographic distribution of basin characteristicsand residuals from regression analysis of selectedstreamflow statistics against specific basincharacteristics. Specifically, dependent variables Q100and other variables from high-duration and low-duration flow analysis (Wiley and Curran, 2003) wereregressed against independent variables drainage areaand mean annual precipitation. On the basis of these

analyses, the State was divided into sevenhydrologically distinct streamflow analysis regions(fig. 1, plate 1) for both this analysis and the flow-duration analyses of Wiley and Curran. Stationsphysically located in one region but draining a largearea in a neighboring region may be classified in theneighboring region if they are more hydrologicallysimilar to that region.


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Table 1. Description and methods of estimation of basin characteristics used in regression analysis

Basin characteristicname and unit

DescriptionEstimating technique for stationsincluded in Jones and Fahl (1994)

Estimating technique for stations

added to analysis since Jones andFahl (1994)

Drainage area, in square

miles

Area of the drainage basin upstream

from the site

Basin outlined on topographic maps

of various scales; area determinedby planimeter

Basin outlined on paper

topographic maps of variousscales; outline digitized; areaestimated using Arc/Info AMLapplication

Main channel length,in miles

Length of the main channel betweenthe site and the basin dividemeasured along the channel thatdrains the largest basin

Length measured manually alongtopographic map blue lines andextension to basin divide

Sum of lengths of line segmentsrepresenting stream on digitalhydrography data (http://agdc.usgs.gov/data/usgs/to_geo.html ),plus length of line extendeddigitally from stream end tobasin divide

Main channel slope,in feet per mile

Average slope between points 10percent and 85 percent of thedistance along the main channelfrom the site to the basin divide

Main channel length measured fromtopographic map as describedseparately; elevation at specifiedpoints estimated from topographiccontours

Main channel length measuredfrom digital hydrography data asdescribed separately; elevation atspecified points estimated fromdigital elevation data(http://agdc.usgs.gov/data/usgs/to_geo.html)

Mean basin elevation,in feet

Mean elevation of the drainagebasin upstream from the site

Grid sampling from topographicmaps

Arc/Info AML application appliedto digital elevation data(http://agdc.usgs.gov/data/usgs/to_geo.html)

Area of lakes and ponds,in percent

Percentage of the total drainage areashown as lakes and ponds ontopographic map

Planimeter measurement or gridsampling of blue areas ontopographic map

Sum of areas of lake and pondpolygons from digitalhydrography coverage

(http://agdc.usgs.gov/data/usgs/to_geo.html)

Area of forests,in percent

Percentage of total drainage areashown as forested on topographicmap

Planimeter measurement or gridsampling of green areas ontopographic map

Digitized green areas ontopographic map

Area of glaciers,in percent

Percentage of total drainage areashown as perennial snow or iceon topographic map

Planimeter measurement or gridsampling of areas marked as snowor ice on topographic map

Sum of areas of glacier orpermanent snowfield polygonsfrom digital hydrographycoverage (http://agdc.usgs.gov/data/usgs/water/statewide.html )

Mean annualprecipitation,in inches

Mean annual precipitation averagedover drainage basin

Grid sampling from plate 2, Jonesand Fahl (1994) (http://ak.water.usgs.gov/Publications/pdf.reps/wrir93.4179.plate2.pdf)

Arc/Info AML application appliedto Arc/Info coverage of plate 2,Jones and Fahl (1994)(http://agdc.usgs.gov/data/usgs/water/statewide.html/)

Mean minimum Januarytemperature, indegrees Fahrenheit

Mean minimum Januarytemperature averaged overdrainage basin

Grid sampling from plate 1, Jonesand Fahl (1994) (http://ak.water.usgs.gov/Publications/pdf.reps/wrir93.4179.plate1.pdf)

Visual estimation from plate 1,Jones and Fahl (1994) for smallbasins (http://ak.water.usgs.gov/Publications/pdf.reps/wrir93.4179.plate1.pdf)
http://agdc.usgs.gov/data/usgs/to_geo.htmlhttp://agdc.usgs.gov/data/usgs/to_geo.htmlhttp://agdc.usgs.gov/data/usgs/to_geo.htmlhttp://agdc.usgs.gov/data/usgs/to_geo.htmlhttp://agdc.usgs.gov/data/usgs/to_geo.htmlhttp://agdc.usgs.gov/data/usgs/to_geo.htmlhttp://agdc.usgs.gov/data/usgs/to_geo.htmlhttp://agdc.usgs.gov/data/usgs/to_geo.htmlhttp://agdc.usgs.gov/data/usgs/to_geo.htmlhttp://agdc.usgs.gov/data/usgs/to_geo.htmlhttp://agdc.usgs.gov/data/usgs/to_geo.htmlhttp://agdc.usgs.gov/data/usgs/to_geo.htmlhttp://agdc.usgs.gov/data/usgs/water/statewide.htmlhttp://agdc.usgs.gov/data/usgs/water/statewide.htmlhttp://agdc.usgs.gov/data/usgs/water/statewide.htmlhttp://ak.water.usgs.gov/Publications/pdf.reps/wrir93.4179.plate2.pdfhttp://ak.water.usgs.gov/Publications/pdf.reps/wrir93.4179.plate2.pdfhttp://ak.water.usgs.gov/Publications/pdf.reps/wrir93.4179.plate2.pdfhttp://ak.water.usgs.gov/Publications/pdf.reps/wrir93.4179.plate2.pdfhttp://ak.water.usgs.gov/Publications/pdf.reps/wrir93.4179.plate2.pdfhttp://agdc.usgs.gov/data/usgs/water/statewide.html/http://agdc.usgs.gov/data/usgs/water/statewide.html/http://agdc.usgs.gov/data/usgs/water/statewide.html/http://ak.water.usgs.gov/Publications/pdf.reps/wrir93.4179.plate1.pdfhttp://ak.water.usgs.gov/Publications/pdf.reps/wrir93.4179.plate1.pdfhttp://ak.water.usgs.gov/Publications/pdf.reps/wrir93.4179.plate1.pdfhttp://ak.water.usgs.gov/Publications/pdf.reps/wrir93.4179.plate1.pdfhttp://ak.water.usgs.gov/Publications/pdf.reps/wrir93.4179.plate1.pdfhttp://ak.water.usgs.gov/Publications/pdf.reps/wrir93.4179.plate1.pdfhttp://ak.water.usgs.gov/Publications/pdf.reps/wrir93.4179.plate1.pdfhttp://ak.water.usgs.gov/Publications/pdf.reps/wrir93.4179.plate1.pdfhttp://ak.water.usgs.gov/Publications/pdf.reps/wrir93.4179.plate1.pdfhttp://ak.water.usgs.gov/Publications/pdf.reps/wrir93.4179.plate1.pdfhttp://ak.water.usgs.gov/Publications/pdf.reps/wrir93.4179.plate1.pdfhttp://ak.water.usgs.gov/Publications/pdf.reps/wrir93.4179.plate1.pdfhttp://ak.water.usgs.gov/Publications/pdf.reps/wrir93.4179.plate1.pdfhttp://ak.water.usgs.gov/Publications/pdf.reps/wrir93.4179.plate1.pdfhttp://ak.water.usgs.gov/Publications/pdf.reps/wrir93.4179.plate1.pdfhttp://ak.water.usgs.gov/Publications/pdf.reps/wrir93.4179.plate1.pdfhttp://agdc.usgs.gov/data/usgs/water/statewide.html/http://agdc.usgs.gov/data/usgs/water/statewide.html/http://ak.water.usgs.gov/Publications/pdf.reps/wrir93.4179.plate2.pdfhttp://ak.water.usgs.gov/Publications/pdf.reps/wrir93.4179.plate2.pdfhttp://ak.water.usgs.gov/Publications/pdf.reps/wrir93.4179.plate2.pdfhttp://agdc.usgs.gov/data/usgs/water/statewide.htmlhttp://agdc.usgs.gov/data/usgs/water/statewide.htmlhttp://agdc.usgs.gov/data/usgs/to_geo.htmlhttp://agdc.usgs.gov/data/usgs/to_geo.htmlhttp://agdc.usgs.gov/data/usgs/to_geo.htmlhttp://agdc.usgs.gov/data/usgs/to_geo.htmlhttp://agdc.usgs.gov/data/usgs/to_geo.htmlhttp://agdc.usgs.gov/data/usgs/to_geo.htmlhttp://agdc.usgs.gov/data/usgs/to_geo.htmlhttp://agdc.usgs.gov/data/usgs/to_geo.html


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Estimating Peak Streamflows at Gaged Sites 7

Certain neighboring regions were hydrologicallysimilar to one another for peak-flow analysis and high-duration flow analysis but not for low-duration flowanalysis. To avoid the confusion of multiple sets ofregions, a single set of regions was used for allstreamflow analyses. However, hydrologically similar

regions were grouped together for development ofregional equations. Grouping of regions was based onexamination of regression residuals and on comparisonof the standard error of the resulting equations.Specifically, Region 3 was grouped with Region 1 forpeak flows and high-duration flows and with Region 4for low-duration flows. Regions 2 and 7 each containonly 25 stations but could not logically be combinedwith adjoining regions.

ESTIMATING PEAK STREAMFLOWS ATGAGED SITES

Peak-streamflow frequency estimates arecomputed from an annual series of peak-flow data andreported as T-year discharges, where T is a recurrenceinterval, or the number of years during which thedischarge is expected to be exceeded once, on average.Peak-streamflow frequency is perhaps betterunderstood as an exceedance probability, which is thereciprocal of the recurrence interval. In other words,the probability that the T-year flood will be exceeded is

1/T in every year. For example, every year the 50-yearflood has a 1 in 50, or 2 percent, chance of beingexceeded.

Estimates of peak-streamflow frequency areprepared by fitting the logarithms of the annual peakflows to a known statistical distribution, from whichthree statisticsthe mean, standard deviation, andskeware obtained. These statistics describe the mid-point, slope, and curvature of the peak-flow frequencycurve, respectively. The skew coefficient measures thesymmetry of the frequency distribution and is stronglyinfluenced by the presence of one or more particularly

high or low flows. The skew is positive when the meanexceeds the median, typically as a result of particularlyhigh flows. The skew is negative when the mean is lessthan the median, typically as a result of particularly lowflows. From the three statistics of the fitted frequencydistribution, estimates of peak-streamflow magnitudefor a given recurrence interval are computed using theequation:

, (1)

where

The Interagency Advisory Committee on WaterData (IACWD) reviewed several analysis methods andrecommended a standard procedure, the log-PearsonType III frequency distribution analysis, for federalstudies of peak-streamflow frequency (Interagency

Advisory Committee on Water Data, 1982). IACWDsBulletin 17B summarizes the recommendations anddiscusses adjustments to the distribution that takeadvantage of additional information regarding thestation record and the characteristics of nearby stationshaving long periods of record. The USGS computerprogram PEAKFQ automates many of the analysisprocedures recommended in Bulletin 17B, includingidentifying high and low outliers, adjusting for historicperiods and low outliers, weighting station skews withgeneralized skew, and fitting a log-Pearson Type IIIdistribution to the streamflow data. PEAKFQ and the

software used to load input data and display outputdataIOWDM and ANNIE (Flynn and others,1995)are available at http://water.usgs.gov/software/surface_water.html.

PEAKFQ was used to compute streamflowmagnitudes for the 2-, 5-, 10-, 25-, 50-, 100-, 200-, and500-year recurrence intervals for 301 stations in Alaskaand 60 stations in conterminous basins in Canada.These stations had at least 10 years of record, exceptfor 22 stations that had 8 or 9 years of record but wereincluded in the most recent statewide analysis (Jonesand Fahl, 1994). Station locations are shown in plate 1

and station information and streamflow statistics arepresented in table 4(at back of report). The specificwater years for peaks used in the analyses of this reportare listed in Appendix A. The following sectionsdiscuss data collection; adjustment for historic peaks,low outliers, and conditions not correlated to basincharacteristics; and development and application ofgeneralized skew for the present study.

QT is the magnitude of the T-year recurrenceinterval discharge, in ft3/s;

X is the mean of the logarithms of theannual peak streamflows;

K is a factor based on the skew coefficientand the given recurrence interval; and

S is the standard deviation of the logarithmsof the annual peak streamflows

QTlog X KS+=
http://water.usgs.gov/software/surface_water.htmlhttp://water.usgs.gov/software/surface_water.htmlhttp://water.usgs.gov/software/surface_water.htmlhttp://water.usgs.gov/software/surface_water.htmlhttp://water.usgs.gov/software/surface_water.html


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Data Collection

Streamflow data for Alaska were collected bythe USGS in accordance with methods described byRantz and others (1982). Streamflow data for Canadawere collected by the Water Survey of Canada.

Canadian data-collection methods are described in aseries of internal manuals referred to collectively asthe Hydrometric Data Computation ProceduresManual (Lynne Campo, Water Survey of Canada,written communication, 2002). These methods aresimilar or equivalent to USGS methods. Daily meandischarge and annual peak streamflows for USGSstreamflow-gaging stations in Alaska are available athttp://waterdata.usgs.gov/ak/nwis/or by contacting theAlaska Science Center at the address listed at the frontof this report. Canadian streamflow data are availablefrom Environment Canada (Environment Canada,

2002).Data were collected at two types of station

streamflow-gaging stations and partial-record stations.At streamflow-gaging stations, stage (water-level) dataare collected on a continuous basis or at time intervalsshort enough to determine daily mean discharge. Atpartial-record stations, also termed crest-stage partial-record stations, stage data are collected as discretemeasurements on an infrequent basis. At both types ofstations, a rating curve developed from dischargemeasurements over a range of flows relates the stagedata collected, regardless of frequency, to discharge.Annual peak discharge is determined from themaximum instantaneous stage recorded in a year.

For all Alaskan stations, data typically consistedof annual maximum instantaneous discharge for eachwater year (October 1 through September 30).Canadian data are collected on a calendar-year basisbut were converted to a water-year basis to develop theannual series. For many or all years for 10 largeCanadian rivers, maximum instantaneous discharge isnot available. For these rivers, annual maximum dailymean discharge is within 5 to 10 percent of maximum

instantaneous peak discharge, based on comparisonsfor years when both values were available, and wasused as its surrogate. This bias toward smallerdischarge for selected stations is expected to be minorrelative to other errors in the analysis.

Data Adjustment

Data from stations having at least 10 years ofsystematic record, or 8 or 9 years of record for stationsincluded in the most recent statewide analysis (Jonesand Fahl, 1994), were carefully inspected for data

quality and omitted if unsuitable. Preliminary plots ofthe fit of the log-Pearson Type III frequencydistribution to the data then were visually inspected foroutliers, non-homogeneities, and trends that wouldinvalidate statistical procedures. Data adjustmentsincluded omission of selected peak flows, omission ofentire stations, adjustments for historic peaks and highand low outliers, estimation of peaks noted as less thana known value, separation of parts of records affectedby regulation or glacial phenomena, and weightingstation and generalized skew as described in thefollowing sections. Appendix A lists the water years

for peaks used in the final analyses.Station 15236900, Wolverine Creek near

Lawing, Alaska, was included in a previous study(Jones and Fahl, 1994) but was omitted from thepresent study after a review indicated that streamflowdata had a quality rating of poor because of changingstreambed conditions. Nine Canadian stations fromJones and Fahls (1994) studystations 15305040,15305380, 15305385, 15305405, 15305411,15305545, 15305673, 15305692, and 15305693wereomitted because the streamflow data could not beverified.

Standard flood-frequency analyses assume thatstreamflow data are from a single statistical population.Floods in Alaska are most commonly caused bysnowmelt or rainfall, but they also can be caused byglacier icemelt, rainfall on snow, rapid melting of snowand ice during volcanic eruptions, periodic release anddamming of water behind glacial ice, and the suddenrelease of water from breached dams of glacial ice,river ice, avalanche debris, or rock and debris. Adistinction between (1) snowmelt or icemelt and (2)rainfall or rain-on-snow floods has only been recorded

since 1989, making an analysis of the extent ofseparation between these populations impractical.Visual inspection of frequency distributions forselected representative stations with both types ofpeaks did not show a break in the curve that wouldsuggest the presence of a mixed population.
http://waterdata.usgs.gov/ak/nwis/http://waterdata.usgs.gov/ak/nwis/


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Estimating Peak Streamflows at Gaged Sites 9

Peaks from volcanic eruptions have occurred but havenot been captured in gaged records. Isolated naturaldam breaks were omitted from the record unless theyaffected less than about 5 percent of the flow. Stationswith repeated natural dam breaks, such as those withregular glacial outbursts, were few and were included

in the flood-frequency analysis but were omitted fromregional regressions as discussed in a followingsection.

High Outliers and Historic Peak Discharges

Large peak discharges that occur within thesystematic record, defined as the period over whichstreamflow data are collected regularly without regardto streamflow conditions, are termed high outliers.Large peak discharges also can occur outside thesystematic record but within the historical record,

defined as the systematic record plus any period overwhich streamflow data are collected on a one-timebasis for specific events. These isolated measurementsare termed historic peaks. If it is known that a historicpeak is the largest peak in a period extending beyondthe length of the systematic record, the frequencydistribution can be adjusted, resulting in anappropriately longer recurrence interval for the highestdischarges. For the purposes of this historicaladjustment, high outliers are treated as historic peaks,except that high outliers are also treated as part of thesystematic record. For example, if it is known that the

largest peak (either a historic peak or high outlier) at astation with 20 years of peak-streamflow data exceededall other floods in the preceding 50 years, the historicperiod of 50 years will be used to lengthen therecurrence interval for that discharge, drawing downthe frequency curve. Conversely, the estimate of the100-year flood at that site will be decreased relative tothat expected without the historic period information.

All Alaska stations with high outliers andhistoric peaks were reviewed and historic periods wereassigned or revised wherever possible. Where floodingaffected a widespread area, the historic perioddetermined for one station was extended to others inthe vicinity. Historic periods assigned to historic peaksand high outliers are shown in Appendix A. Canadianstations could not be adjusted for historic peaks andhigh outliers because no data regarding historic periodswere available. Where no historic period could beestablished for a historic peak, or where historic peakswere smaller than peaks within the systematic record,the peak was dropped from analysis. Where no historic

period could be established for a high outlier, the peakwas retained in the systematic record but noadjustments were made.

Low Outliers

Peak discharges below a station-specificthreshold value are termed low outliers. Low outlierscan disproportionately influence the statistics of thefrequency distribution by increasing standard deviation(slope) and decreasing skew coefficients (curvature).Bulletin 17B (Interagency Advisory Committee onWater Data, 1982) recommends censoring low outliersand applying a conditional-probability calculation tothe remaining peaks. Low outliers were treated usingthe default options in PEAKFQ, which automaticallyscreens for low outliers and applies the recommendedadjustments.

Discharges Recorded as Less Than a Known Value

Selected peaks at stations 15283500, 15303010,and 15518100 were flagged as less than the indicatedvalue, a condition that typically occurs when aminimum recordable value is not exceeded. Althoughthese flagged peaks could be omitted, this results in aselective censoring of low discharges. Based onestimates of likely ranges of actual values, these peakswere reduced by 10 percent and kept in the systematicrecord. Sensitivity to this reduction was analyzed for

each station involved. Lower Panguingue Creek nearLignite, Alaska, (station 15518100) was omitted fromthe final analysis because results were strongly affectedby the reduction in peak magnitude.

Data Not Correlated to Basin Characteristics

Peaks regulated by dams or diversions,controlled by certain glacial phenomena, or in basinswith indeterminate drainage areas cannot be correlatedto basin characteristics. Flows at these stations can stillbe analyzed by fitting to a frequency distribution butcannot be related to adjacent stations or used to developpredictive equations based on physical and climaticcharacteristics of the basin. Stations subject to theseconditions are footnoted in the Station No. column oftable 4. Station skew is not weighted with generalizedskew to compute flood-frequency statistics for thesestations. Equation-based or weighted estimates of peakstreamflow statistics are not appropriate for thesestations.


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Specific treatment of regulated stations dependedon the nature, length, and timing of regulation. Ifstreamflow regulation or diversion affected low flowsbut not peak flows, regulated stations were included asif unregulated. For peak records affected by regulation,known dates of regulation were used to segregate the

period of record. Any period, regulated or unregulated,with at least 10 years of record was analyzedseparately. Unregulated periods were included in theregression analysis. Only one station, Kenai River(station 15258000), met the record-length requirementfor both a regulated and unregulated period. Twoentries are given for this station in table 4. Kenai Riveris also subject to glacial-outburst floods, so itsunregulated period was not included in the regressionanalysis. All presently regulated stations are noted withan R in the Station No. column of table 4,regardless of whether regulation was in effect during

the period of record.Glacier-related controls on streamflow include

glacial-outburst floods, caused when ice dams pondingwater suddenly burst, and periods of low flow causedas ice-dammed lakes fill. The effect of thesephenomena depends on factors such as the location ofbedrock constrictions and relative positions of mainand tributary glaciers, which cannot be summarized bythe available basin characteristic, the area of the basincovered by glaciers. As for streamflow regulation,known dates of glacier-controlled streamflow were

used to segregate the period of record when possible.Glacier-controlled peaks were treated as for peaks fromsnowmelt or precipitation because a visual examinationsuggested that they fit a log-Pearson Type IIIdistribution. Periods controlled by glaciers wereanalyzed, but because the peak streamflows lackcorrelation with basin characteristics, these periodswere omitted from regression analysis. Uncontrolledperiods were included in the regression analysis. Onlyone station, Knik River (station 15281000), met therecord-length requirement for both a glacier-controlledand uncontrolled period. Two entries are given for this

station in table 4.

Generalized Skew Coefficients

The skew coefficient for an individual station issensitive to particularly high or low streamflows in therecord, especially for stations with short periods ofrecord. To improve the estimate of the skew coefficient

for an individual station, the IACWDs Bulletin 17Brecommends that a generalized skew computed fromnearby long-term stations be used to weight individualstation skews within that region (Interagency AdvisoryCommittee on Water Data, 1982). Althoughgeneralized skew can be obtained from Bulletin 17Bsnational generalized skew coefficient map, improvedestimates can be obtained by one of three methodsrecommended by the IACWD: (1) a more detailed mapdeveloped from study-specific station skews, (2) aprediction equation developed by regressing stationskews against basin characteristics, and (3) an average

of station skews within a region. As with the mostrecent Alaska peak-streamflow frequency analysis(Jones and Fahl, 1994), no contours could be developedfrom plotted station skews and adequate predictionequations could not be developed from regression. Thethird method, averaging station skews, was adopted foreach region across the study area.

Station skews for stations with at least 25 yearsof systematic peak-streamflow data were averaged toobtain generalized skews within each of the sevenstreamflow analysis regions defined for this study. TheIACWD recommends that at least 20 stations be usedto develop generalized skew within a region. Becausestation skews from fewer than 20 stations were used forRegions 2 and 7, streamflow statistics for thesesparsely represented regions should be interpretedcautiously.

Station skews used to compute regional averagesreflect adjustments for historic peaks and high and lowoutliers, as described previously. Station skews alsowere adjusted for bias resulting from record length inaccordance with procedures described by Tasker andStedinger (1986). A nearly unbiased estimate of the


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Regional Equations for Estimating Peak Streamflows 11

population skew coefficient, Gg, can be obtained fromthe station skew, G, and the record length, n, using thefollowing equation:

(2)

The standard error of the generalized skew wascomputed as the standard deviation of Ggfor stationswith at least 25 years of record within each region.

All stations shown in table 4with 25 or moreyears of record, with the exception of station15485500, which has an indeterminate drainage area,were included in the generalized skew analysis. Of the134 stations meeting the criteria, 99 stations are locatedin Alaska and 35 are in Canada. The number of stationsused in each region, the range of Gg, and thegeneralized skew and standard error of the generalized

skew are summarized in table 2.Weighted skew coefficients are computed by

weighting the generalized skew coefficient and thestation skew coefficient in inverse proportion to theirmean square errors (Interagency Advisory Committeeon Water Data, 1982). This provides a better estimateof the skew coefficient for basins that can be correlatedto basin characteristics (that is, those not regulated orsubject to glacier-affected flow phenomena). Thestation skew is not weighted for regulated or glacier-controlled stations because the generalized skew is notrepresentative of these sites. The generalized skew and

standard error of the generalized skew shown in table 2were used in the PEAKFQ program to weight skewsautomatically.

REGIONAL EQUATIONS FOR ESTIMATINGPEAK STREAMFLOWS

Estimated flow statistics are often needed forstreams where no data have been collected. If sufficientrecords are available from a group of streamflow-gaging stations within a region, a regression model canbe developed from flow statistics and basincharacteristics for the stations. Regression equationscan then be used to estimate flow statistics at ungagedsites where basin characteristics can be measured.

Regression Analysis

Multiple-linear regression analysis is used todetermine which of several basin characteristics (theindependent variables) best explain, statistically, the

variations in the flow statistic (the dependent variable).Regression analysis is also used to develop the finalequations that relate the dependent and selectedindependent variables. Ordinary-least-squaresregression (OLS), a common form of regressionanalysis, was used for preliminary analyses in thisstudy. Generalized-least-squares regression (GLS), amore specialized method of regression that accountsfor time-sampling error (a function of record length)and cross-correlation between stations close together,was used to develop final equations. GLS assigns

different weights to each observation based on itscontribution to total variance (Tasker and Stedinger,1989).

Streamflow data and basin characteristicsgenerally are log-normally distributed, so all data werelog-transformed (base 10) before analysis. Thisrequired the addition of a constant value of 1 percent toall percentage data and 32 degrees (Fahrenheit) totemperature data because values equal to or less than 0cannot be log-transformed. The commercial statisticsand data-management software S-Plus (MathSoft, Inc.,1999) was used to perform a backward and forward

stepwise multiple-linear regression of the 100-yearflood, Q100, against all available basin characteristics(table 1) to determine suitable independent variablesfor each streamflow analysis region. An independentanalysis using an all-subsets regression in S-Plusproduced the same suite of independent variables.

Table 2. Generalized skew and summary statistics for Regions 1-7,Alaska and conterminous basins in Canada

Streamflow

analysis

region

Number of

stations

with at

least 25

systematic

peaks

Minimum

unbiased

station

skew

(Gg)

Maximum

unbiased

station

skew

(Gg)

General

-ized

skew

(G)

Standard

error of

the

general-

ized

skew

(SEG

)

1 and 3 23 -0.646 2.09 0.16 0.62

2 14 -1.20 2.62 .31 .96

4 26 -.905 2.05 .60 .81

5 25 -.696 1.22 .28 .48

6 39 -1.41 2.10 .13 .76

7 7 -1.90 .336 -.52 .70

Gg 1 6

n---+

G=


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Independent variables were further screened forstatistical significance, logical relation to streamflow inthat area, and correlation with other variables.Variables were dropped if the equations standard errorfell by less than 5 percent (arbitrarily chosen as thepoint of diminishing returns), or if the variable could

not be correlated logically to streamflow in thatparticular area. Correlation with other variables was nota concern once the other two criteria were met.

GLS regression was used to evaluate the modelssuggested by the preliminary OLS regressions. Thecomputer program GLSNET, available at http://water.usgs.gov/software/surface_water.html, was used for allGLS regressions. Independent variables were droppedor retained on the basis of the results of GLSregression, with a bias toward dropping variableswhere improvement was marginal. Final equationswere developed with GLS for the 2-, 5-, 10-, 25-, 50-,

100-, 200-, and 500-year recurrence-interval peakstreamflow in each region using one to fourindependent variables (table 3). Ranges of variablesused in the final equations are shown in table 3.

Accuracy and Limitations of Estimating Equations

The adequacy of the estimating equations can beevaluated by two measures, the average standard errorof prediction and the equivalent years of record (table3). The standard error of prediction is a measure of the

accuracy of a streamflow statistic for an ungaged siteestimated from the regression equations. Errors in theestimates for about two-thirds of the ungaged sites willbe within the given standard errors. The standard errorof prediction is derived from the model error andsampling error as the square root of the sum of themean-square error of the model and the mean-squaresampling error. The model error is associated with theentire model and remains constant for each site. Thesampling error results from estimating modelparameters from samples of the population, andtherefore varies from site to site. The standard error ofprediction error for an ungaged site can be computedfrom the matrices and matrix algebra proceduresdescribed in Appendix Bor from a computer programavailable at http://pubs.water.usgs.gov/wri034188. Theaverage standard error of prediction for an equation canbe computed by assuming that the gaged sites within a

region form a representative sample of all sites andthen averaging their sampling error. The averagestandard error of prediction is computed in log unitsand converted to percent error for each equation in eachregion (table 3). Average standard errors of predictionfor individual equations ranged from 27 to 66 percent.

Maximum and minimum standard errors for eachregression equation, in percent, can be computed fromthe following equations:

maximum average standard error of

prediction (3)

minimum average standard error of

prediction , (4)

where

A second measure of predictive ability of eachequation is the equivalent years of record, or thenumber of years of systematic streamflow data thatwould have to be collected for a given site to estimatethe streamflow statistic with accuracy equivalent to theestimate from the regression equation (see AppendixB). Average equivalent years of record for individualequations ranged from 0.35 to 7.4 years (table 3).

The adequacy of a prediction for an ungaged sitecan be evaluated by the site-specific standard error ofprediction, equivalent years of record, and a thirdmeasure, the confidence limits of the prediction, orprediction interval (seeAppendix B). Along with thefirst two site-specific values, the 5-percent and 95-percent confidence limits (the 90-percent predictioninterval) must be generated for a particular prediction.A computer program is provided at http://pubs.water.usgs.gov/wri035188to compute thesevalues.

ASEP is the average standard error of prediction, inlog units.

100 10AS EP

1( )=

100 10 A SE P

1( )=
http://water.usgs.gov/software/surface_water.htmlhttp://water.usgs.gov/software/surface_water.htmlhttp://water.usgs.gov/software/surface_water.htmlhttp://pubs.water.usgs.gov/wri034188http://pubs.water.usgs.gov/wri035188http://pubs.water.usgs.gov/wri035188http://pubs.water.usgs.gov/wri035188http://pubs.water.usgs.gov/wri035188http://pubs.water.usgs.gov/wri034188http://water.usgs.gov/software/surface_water.htmlhttp://water.usgs.gov/software/surface_water.html


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Region 5 (44 gaging stations)

Applicable range of variables:

A: 1.02114,000; ST: 030; E: 1,2004,540; F: 12100

Q2= 13,640A1.032(ST+1)-0.5391E -0.5970(F+1)-0.7154 0.260 66 0.35

Q5= 126,000A0.9885(ST+1)-0.5702E -0.8275(F+1)-0.6327 .234 58 .67

Q10= 395,300A0.9641(ST+1)-0.5856E -0.9496(F+1)-0.5769 .221 54 1.1

Q25= 1,256,000A0.9384(ST+1)-0.6004E -1.075(F+1)-0.5128 .210 51 1.7

Q50= 2,518,000A0.9228(ST+1)-0.6088E -1.150(F+1)-0.4708 .210 51 1.7

Q100= 4,532,000A0.9095(ST+1)-0.6158E -1.215(F+1)-0.4329 .202 49 2.8

Q200= 7,526,000A0.8979(ST+1)-0.6219E -1.270(F+1)-0.3981 .201 49 3.3

Q500 = 13,440,000A0.8846(ST+1)-0.6292E -1.335(F+1)-0.3554 .203 49 4.0



A: 1.29321,000; ST: 015; F: 0100

Q2= 52.87A0.8929(ST+1)-0.2676(F+1)-0.3076 .172 41 1.8

Q5= 88.08A0.8479(ST+1)-0.2596(F+1)-0.2648 .176 42 2.5

Q10= 115.7A0.8253(ST+1)-0.2579(F+1)-0.2443 .185 45 3.2

Q25= 154.8A0.8026(ST+1)-0.2585(F+1)-0.2243 .199 48 3.9

Q50= 186.7A0.7885(ST+1)-0.2599(F+1)-0.2124 .211 52 4.3

Q100= 220.6A0.7764(ST+1)-0.2616(F+1)-0.2023 .223 55 4.6

Q200= 256.6A0.7656(ST+1)-0.2636(F+1)-0.1935 .235 58 4.8

Q500= 307.7A0.7530(ST+1)-0.2662(F+1)-0.1833 .252 63 5.0



A: 1.139,520

Q2= 28.07A0.8916 .212 52 1.3

Q5= 47.51A0.8691 .204 50 1.5

Q10= 61.00A0.8588 .203 49 1.9

Q25= 78.33A0.8486 .205 50 2.5

Q50= 91.29A0.8424 .208 51 3.0

Q100= 104.2A0.8370 .211 52 3.3

Q200= 117.1 A0.8322 .216 53 3.6

Q500= 134.2 A0.8266 .223 55 3.9

Table 3. Regression equations for estimating 2-, 5-, 10-, 25-, 50-, 100-, 200-, and 500-year peak streamflows forunregulated streams in Regions 1-7, Alaska and conterminous basins in CanadaContinued

[QT, T-year peak streamflow, in cubic feet per second;A, drainage area, in square miles; ST, area of lakes and ponds

(storage), in percent; P, mean annual precipitation, in inches;J, mean minimum January temperature, in degreesFahrenheit;E, elevation, in feet; F, area of forest, in percent]

Regression equation for specified recurrence interval QT

Averagestandarderror of

prediction(log units)

Averagestandarderror of

prediction(percent)

Averageequivalent

years ofrecord

1

3

2

6 5

4

7

1

3

2

6 5

4

7

1

3

2

6 5

4

7


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Procedures for Estimating Peak Streamflow Magnitude and Frequency 15

These accuracies are applicable for use of theequations within the limitations of the causes of peakstreamflows and the ranges of basin characteristicsused for equation development. The estimatingequations presented in table 3can be used forestimating flow in streams in Alaska and conterminous

basins in Canada that are not affected by natural oranthropogenic streamflow regulation. Streamflow inbasins with urbanization, flow diversions, dams,periodically releasing glacial impoundments, or otherstreamflow conditions not correlated to basincharacteristics cannot be estimated accurately withthese equations. The accuracy given for each equationis only valid when the equations are used for sites withvalues of independent variables that fall within theranges in table 3.

Additional data collection and carefulinterpretation may be required for use of the equations

in sparsely represented regions. Equations for Region 7(the Arctic north and northwest Alaska) must be usedwith particular caution because the equations weredeveloped using a small number of stations over a verywide area, which limits their statistical validity. Theseequations most closely represent the hydrologicconditions that have occurred at existing gagingstations; however, gaging-station conditions may not berepresentative of ungaged sites in the region. Sites witha short period of record may be weighted with theregional estimating equations to provide an improved

estimate. Equations for neighboring regions may beused to perform a sensitivity analysis for criticalapplications.

Estimates have been provided for longrecurrence-interval peaks (that is, the 200-year and500-year peak streamflow) to help users comply withdesign requirements. However, these values should beused with caution in all regions because record lengthsmay not be long enough to fully support extrapolationto this long a recurrence interval. Additional site-specific studies, such as a survey of paleofloodindicators, may be required to support these estimates

for critical applications.

PROCEDURES FOR ESTIMATING PEAKSTREAMFLOW MAGNITUDE ANDFREQUENCY

Within the limitations previously described, the

flow statistics and equations presented in this reportcan be used to estimate peak-streamflow magnitude forthe 2-, 5-, 10-, 25-, 50-, 100-, 200-, and 500-year flowsfor gaged and ungaged streams throughout the State.Procedures for using this report to estimate peakstreamflow at streamflow-gaging or partial-recordstations and several types of ungaged sites follow.1. Gaged Sites. Estimates of peak-streamflow

magnitude for a given recurrence interval T can beread directly from table 4for the streamflow-gaging or partial-record stations. Three estimatesare provided: the value obtained using observed

station data with a weighted skew coefficient(QTsta), the value obtained using the regionalregression equations (QTreg), and a weighted value(QTwtd), where weights are based on the years ofobserved data at the station (N) and the equivalentyears of record for the regional regression equation(EYR) based on the following formula:

(5)

In general, the weighted value provides the best

estimate of peak streamflow, especially forstations with a short period of record.

For gaged sites with at least 5 years of record,formula 5 may be used to weight the observeddata with the regression equation. The equivalentyears of record for a particular site can becomputed from procedures and information inAppendix Bor from the computer programavailable at http://pubs.water.usgs.gov/wri034188.

For gaged sites with less than 5 years of record,

the site should be treated as an ungaged site(Jones and Fahl, 1994). The appropriateregression equations for the given streamflowanalysis region should be applied using one of themethods below.

QTwtdlogQTstalog N QTreglog EY R+

N EY R+-----------------------------------------------------------------=
http://pubs.water.usgs.gov/wri034188http://pubs.water.usgs.gov/wri034188http://pubs.water.usgs.gov/wri034188http://pubs.water.usgs.gov/wri034188http://pubs.water.usgs.gov/wri034188


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2. Ungaged sites. The regression equationsdeveloped for this study from many hydrologicallysimilar stations over a range of years arerecommended for estimating discharge at ungagedsites. The errors presented for these equations arevalid only if the equations are used according to

the procedures described in this report. Forungaged sites having a drainage area in only oneregion and that are not near a streamflow-gagingstation on the same stream, basin characteristicscan be determined from a topographic map (orfrom digital data, as described in table 1) and fromthe precipitation map on plate 2 of Jones and Fahl(1994), available at: http://ak.water.usgs.gov/Publications/pdf.reps/wrir93.4179.plate2.pdfinPDF form and at http://agdc.usgs.gov/data/usgs/water/statewide.htmlas a GIS polygon coverage.If basin characteristics for the ungaged site are

within the range of the basin characteristics shownin table 3, they can then be substituted into theequations from table 3for the appropriate region.

3. Ungaged sites in two regions. For ungaged siteshaving a drainage area that falls in two regions,basin characteristics for the entire basin can bedetermined as described in (2) and substituted intoequations from table 3for each region. The twoestimates then should be weighted by therespective drainage area in each region using the

equation:

(6)

where

4. Ungaged sites on gaged streams. For ungaged siteson a gaged stream having a drainage area between50 and 150 percent of the drainage area of thestreamflow-gaging station, the estimate from thestreamflow-gaging station obtained as for (1) andthe estimate for the ungaged site obtained as for (2)

or (3) can be weighted for an improved estimate(Guimaraes and Bohman, 1991; Stamey and Hess,1993). The weighted estimate for the ungaged siteis computed as:

(7)

where

This procedure was adopted to remain consistentwith methods used by the National Flood

Frequency program (Ries and Crouse, 2002). Itproduces results similar to those obtained usingthe procedure in Jones and Fahl (1994).

5. Sites along the Yukon River. Although theregression equations are valid for sites along theYukon River, determining the full suite of basincharacteristics for an ungaged site with such alarge drainage area requires considerable effort. Inaddition, the overwhelming influence of drainagearea for basins this large limits the usefulness ofother basin characteristics for predicting flood

frequency. As an alternative, the graphical relationof peak streamflow to drainage area (fig. 2) may beused to estimate peak-streamflow statistics forsites along the Yukon River. These curves weredeveloped from data for Yukon River streamflow-gaging stations with at least 20 years of record.

QT is the area-weighted flow statistic;

QT1 is the value for the flow statistic if theentire basin were located in Region 1;

A1 is the drainage area in Region 1;

QT2 is the value for flow statistic if the entirebasin were located in Region 2; and

A2 is the drainage area in Region 2.

QTQT1A1 QT2A2+

A1 A2+--------------------------------------=

QT(u)wtd is the weighted estimate of peak-flow magnitude QTfor recurrenceinterval Tat the ungaged site;

A is the absolute value of thedifference between the drainagearea for the gaged site (Ag) and thedrainage area for the ungaged site(Au), |Ag-Au|;

QT(u)reg is the estimate of QTfor theungaged site computed from theregression equations in table 3andmethods 2 or 3 above for theappropriate streamflow analysisregion(s); and

QT(g)wtd is the weighted estimate of QTforthe gaged site, obtained from theWtd row in table 4.

QT u( )wt d

2A

Ag----------- Q

T u( )re g 1

2A

Ag-----------

Au

Ag------ Q

T g( )wt d+=
http://ak.water.usgs.gov/Publications/pdf.reps/wrir93.4179.plate2.pdfhttp://ak.water.usgs.gov/Publications/pdf.reps/wrir93.4179.plate2.pdfhttp://ak.water.usgs.gov/Publications/pdf.reps/wrir93.4179.plate2.pdfhttp://agdc.usgs.gov/data/usgs/water/statewide.htmlhttp://agdc.usgs.gov/data/usgs/water/statewide.htmlhttp://agdc.usgs.gov/data/usgs/water/statewide.htmlhttp://agdc.usgs.gov/data/usgs/water/statewide.htmlhttp://agdc.usgs.gov/data/usgs/water/statewide.htmlhttp://ak.water.usgs.gov/Publications/pdf.reps/wrir93.4179.plate2.pdfhttp://ak.water.usgs.gov/Publications/pdf.reps/wrir93.4179.plate2.pdf


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DISCHARG

E,

INC

UBIC

FEET

PER

SECOND

DRAINAGE AREA, IN SQUARE MILES

10,000,000

1,000,000

100,000

10,0001,000 10,000 100,000 1,000,000

500

2001005025

10

5

2

Figure 2. Relation of discharge to drainage area for selected recurrence intervals for the Yukon River,Alaska and Canada.

Example Applications

Examples of computation of peak-streamflowstatistics for a selected recurrence interval are providedfor a gaged site, an ungaged site, an ungaged site in tworegions, and an ungaged site on a gaged stream. Foreach example, it is assumed that the user has

determined that the hydrologic characteristics of thestream are within the limitations of the regionalregression equations described in the "Accuracy andLimitations" section.


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Example 1 - Gaged Site

Determine the peak discharge having a 50-yearrecurrence interval for the Nenana River near Healy,gaging station 15518000.

From table 4, the weighted 50-year peak discharge is:Q50wtd= 41,800 ft3/s

This value was computed from formula 5, whichweights the 50-year peak discharge based on stationobservations (42,100 ft3/s) with the 50-year peakdischarge based on the regional regression equationsfor Region 6 (37,800 ft3/s), in proportion to the 29years of record at the station (from table 4) and the 1.9equivalent years of record for the regression equation(from the computer program). Note that substitutingthe published Q50staand Q50reginto formula 5 will

result in a slightly different value than the publishedQ50wtdbecause of differences in rounding.

Example 2 - Ungaged Site

Determine the 100-year peak discharge for the TokRiver at the Alaska Highway bridge, which has thefollowing basin characteristics:

Latitude 6319'4", longitude 14250'0"

Drainage area = 912 mi2

Area of lakes and ponds = 2 percent

Area of forests = 38 percent

From Plate 1 and the site's latitude and longitude, thissite is in Streamflow Analysis Region 6. From table3, the basin characteristics for the Tok River arewithin the range of values used to develop equationsfor Region 6. The 100-year peak discharge isestimated by substituting the basin characteristics intothe appropriate equation from table 3:

Q100= 220.6 (912)0.7764(2+1)-0.2616(38+1)-0.2023

=15,700 ft

3

/s

Example 3 - Ungaged Site in Two Streamflow

Analysis Regions

Determine the peak discharge having a 25-yearrecurrence interval for Quill Creek near Burwash

Flats, an ungaged site with the following basincharacteristics:

Latitude 6130'10", longitude 13919'27"

Drainage area = 27.1 mi2

Mean annual precipitation = 15 in.


Mean basin elevation = 4,000 ft

Area of forest = 34 percent

From Plate 1, the site's latitude and longitude, and anoutline of the site's drainage basin, this site is inStreamflow Analysis Region 5 but has 77.1 percent ofits drainage area in Streamflow Analysis Region 2.The discharge for the ungaged site is estimated as if itwere entirely in first one basin, then the other, andweighting based on the respective drainage areas.

From table 3, the basin characteristics are within therange of values used to develop equations for Regions2 and 5. If the basin were entirely within Region 2,the 25-year peak discharge estimate would be

Q25(2)= 1.374 (27.1)0.9274(0+1)-0.04074(15)0.9713

= 407 ft3/s

If the basin were entirely within Region 5, the 25-yearpeak discharge estimate would be

Q25(5)= 1,256,000 (27.1)0.9384(0+1)-0.6004(4,000)-1.075(34+1)-0.5128

= 602 ft3/s

Weight the two estimates based on the respectivedrainage area within each basin using formula 6:

Q25

Q25 2( )A2 Q25 5( )A5+

A2 A5+( )-------------------------------------------------=

407 20.9( ) 602 6.2( )+20.9 6.2+( )

----------------------------------------------------=

451 ft3/s=


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Computer Program

For a particular site, estimates of standard errorof prediction, confidence limits (prediction intervals)on the estimate of peak-streamflow magnitude, andequivalent years of record can be computed using thematrices and procedures in Appendix B. A computerprogram is available at http://pubs.water.usgs.gov/wri034188that automates the complex matrixcomputations required for these site-specific estimatesof accuracy. The program first computes peak-streamflow frequencies for an ungaged site in one ortwo streamflow analysis regions using methods (2) or(3) described above, then provides positive and

negative standard error of prediction, 5-percent and 95-percent confidence limits, and equivalent years ofrecord for each T-year streamflow estimate for that site.

Example 4 - Ungaged Site on a Gaged Stream

Determine the 50-year peak discharge for the NenanaRiver at Healy, which is a gaging station (station15518040) but has fewer than 5 years of peak-streamflow record. The Nenana River is also gaged at

another location, the Nenana River near Healy(gaging station 15518000), which has more than 10years of record and is included in table 4. The NenanaRiver at Healy site (considered the ungaged site) hasthe following basin characteristics:

Latitude 6351'55", longitude14857'20"

Drainage area = 2,100 mi2


Area of forests = 8 percent

From table 4, the gaged site has a drainage area of

1,910 mi2. The ungaged site's drainage area is 110percent of the gaged site's drainage area, so formula 7for an ungaged site on a gaged stream may be used. (Ifthe ungaged site's drainage area was larger than 150percent or smaller than 50 percent of the gaged site'sdrainage area, it should be treated simply as anungaged site, as for Example 2.)

Determine Q50(u)reg, the regression-based estimate forthe ungaged site, from the appropriate equation fromtable 3. This step is the same procedure as forExample 2. From Plate 1 and the site's latitude and

longitude, the ungaged site is in Streamflow AnalysisRegion 6. From table 3, the basin characteristics of theungaged site are within the range of the variables usedto develop equations for Region 6. The 50-year peakdischarge is estimated for this ungaged site in region 6as:

Q50(u)reg= 186.7 (2100)0.7885(0+1)-0.2599(8+1)-0.2124

= 48,800 ft3/s

Next determine Q50(g)wtd, the weighted estimate for thegaged site, from table 4or from formula 5. FromExample 1, Q50(g)wtdfor the Nenana River near Healyis 41,800 ft3/s.

The regression-based estimate for the ungaged site isweighted with the estimate for the gaged site using thesites' respective drainage areas in formula 7:

QT u )wt d( )2AAg----------- QT u )re g( ) 1

2AAg-----------

AuAg------QT g( )wt d+=

+ 1 2 1910 2100

1910------------------------------------

21001910------------ 41 800 ),(

2 1910 21001910

------------------------------------ 48 800,( )=

= 46,500 ft3/s
http://pubs.water.usgs.gov/wri034188http://pubs.water.usgs.gov/wri034188http://pubs.water.usgs.gov/wri034188http://pubs.water.usgs.gov/wri034188http://pubs.water.usgs.gov/wri034188


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SUMMARY

Estimates of the magnitude and frequency ofpeak streamflows generally can be improved asadditional peak-streamflow data become available. Toprovide the most accurate information possible for

engineering and water-resource managementapplications in Alaska, the U.S. Geological Survey, incooperation with the Alaska Department ofTransportation and Public Facilities, updated estimatesof peak-streamflow magnitude and frequency for gagedsites in Alaska and conterminous basins in Canada andupdated regression equations for estimating peak-streamflow magnitude and frequency at ungaged sites.

Estimates of peak-streamflow magnitude forselected frequencies were computed for 361streamflow-gaging stations and partial-record stationsin Alaska and conterminous basins in Canada usingdata through the 1999 water year. Stations presentedhave at least 10 years of systematic record, or 8 or 9years of record for stations included in the most recentprevious statewide analysis. Streamflow data wereadjusted using additional information where availableand were analyzed using log-Pearson Type III analysisas recommended in Bulletin 17B of the InteragencyCommittee on Water Data. Station skew coefficientsfor 134 stations with at least 25 years of systematicrecord were averaged within each of seven streamflowanalysis regions to determine generalized skew

coefficients. Streamflow analysis regions arehydrologically distinct regions that were defined inconjunction with an analysis of high and low flows thatwas concurrent with this study. For most stations,generalized skew coefficients were weighted withstation skew coefficients to compute estimates of the2-, 5-, 10-, 25-, 50-, 100-, 200-, and 500-year peakstreamflows. For stations where streamflow is notcorrelated to basin characteristics, station skewcoefficients were used alone instead of in combinationwith generalized skew coefficients to estimate thepeak-flow statistics.

Regional equations for estimating peakstreamflows for the selected frequencies weredeveloped from peak-streamflow estimates andphysical and climatic basin characteristics at 355stations. Basin characteristics were obtained fromprevious studies or by modified methods described inthis report; users should obtain basin characteristicsusing similar methods. Ordinary-least-squares

regression was used to establish a preliminary suite ofbasin characteristics as independent variables.Generalized-least-squares regression was used to refinethis list of variables and develop final equations.Drainage area was used in final equations for allregions and all recurrence intervals; the other basin

characteristics used in the final equations were meanannual precipitation, area of lakes and ponds, meanbasin elevation, area of forests, and mean minimumJanuary temperature. Average standard errors ofprediction, a measure of the accuracy of the estimatingequations, range from 27 to 66 percent. Procedures areprovided for using the data and equations in this reportto estimate peak streamflow at gaged and ungagedsites. Digital versions of data and a computer programfor estimating peak streamflow and site-specific errorsare provided at http://pubs.water.usgs.gov/wri034188.

REFERENCES

Berwick, V.K., Childers, J.M., and Kuentzel, M.A., 1964,Magnitude and frequency of floods in Alaska, south ofthe Yukon River: U.S. Geological Survey Circular 493,15 p.

Bobee, B., 1973, Sample error of T-year events computed byfitting a Pearson Type 3 distribution: Water ResourcesResearch, v. 9, no. 5, p. 1264-1270.

Childers, J.M., 1970, Flood frequency in Alaska: U.S.Geological Survey Open-File Report, 30 p.

Childers, J.M., Meckel, J.P., and Anderson, G.S., 1972,Floods of August 1967 in east-central Alaska: U.S.Geological Survey Water-Supply Paper 1880-A, 77 p.

Environmental Systems Research Institute, Inc., 1997,Understanding GIS, the ARC/INFO method: Redlands,Calif., 10 chaps., various pagination.

Environment Canada, 2002, Hydat for Windows, Hydat CDversion 2.01, Surface water and sediment data: WaterSurvey of Canada. CD-ROM.

Flynn, K.M., Hummel, P.R., Lumb, A.M., and Kittle, J.L.,Jr., 1995, User's manual for ANNIE, version 2, acomputer program for interactive hydrologic datamanagement: U.S. Geological Survey Water-Resources

Investigations Report 95-4085, 211 p.Guimaraes, W.B., and Bohman, L.R., 1991, Techniques for

estimating magnitude and frequency of floods in SouthCarolina, 1988: U.S. Geological Survey Water-Resources Investigations Report 91-4157, 174 p.

Hardison, C.H., 1971, Prediction error of regressionestimates of streamflow characteristics at ungaged sites:U.S. Geological Survey Professional Paper 750-C,p. C228-C236.
http://pubs.water.usgs.gov/wri034188http://pubs.water.usgs.gov/wri034188


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References 21

Interagency Advisory Committee on Water Data, 1982,Guidelines for determining flood flow frequency:Hydrology Subcommittee Bulletin 17B, 28 p., 14appendixes.

Jones, S.H., and Fahl, C.B., 1994, Magnitude and frequencyof floods in Alaska and conterminous basins of Canada:U.S. Geological Survey Water-Resources InvestigationsReport 93-4179, 122 p.

Lamke, R.D., 1972, Floods of the summer of 1971 in south-central Alaska: U.S. Geological Survey Open-FileReport 72-0215, 88 p.

1978, Flood characteristics of Alaskan streams: U.S.Geological Survey Water-Resources InvestigationsReport 78-129, 61 p.

1991, Alaska floods and droughts, in Paulson, R.W.,and others, eds., National water summary, 1988-89Hydrologic events and floods and droughts: U.S.Geological Survey Water-Supply Paper 2375, p. 171-180.

Lamke, R.D., and Bigelow, B.B., [revised 1988], Floods ofOctober 1986 in south central Alaska: U.S. GeologicalSurvey Open-File Report 87-391, 31 p.

MathSoft, Inc., 1999, S-Plus 2000 Users Guide: Seattle,Washington, 558 p.

Parks, B., and Madison, R.J., 1985, Estimation of selectedflow and water-quality characteristics of Alaskanstreams: U.S. Geological Survey Water-ResourcesInvestigations Report 84-4247, 64 p.

Rantz, S.E., and others, 1982, Measurement andcomputation of streamflow: Volume 1, Measurement ofstage and discharge; Volume 2, Computation ofdischarge: U.S. Geological Survey Water-Supply Paper

2175, 631 p.

Ries, K.G., III, and Crouse, M.Y., 2002, The National FloodFrequency Program, Version 3: A computer programfor estimating magnitude and frequency of floods forungaged sites: U.S. Geological Survey Water-Resources Investigations Report 02-4168, 42 p.

Stamey, T.C., and Hess, G.W., 1993, Techniques forestimating magnitude and frequency of floods in ruralbasins of Georgia: U.S. Geological Survey Water-Resources Investigations Report 93-4016, 75 p.

Tasker, G.D., and Stedinger, J.R., 1986, Regional skew withweighted LS regression: Journal of Water ResourcesPlanning and Management, American Society of CivilEngineers, v. 112, no. 2, p. 225-237.

1989, An operational GLS model for hydrologicregression: Journal of Hydrology, v. 111, no. 1/4,p. 361-375.

Thomas, D.M., and Benson, M.A., 1970, Generalization ofstreamflow characteristics from drainage-basincharacteristics: U.S. Geological Survey Water-Supply

Paper 1975, 55 p.U.S. Geological Survey, 1978, National handbook of

recommended methods for water-data acquisition,Chap. 7: Physical basin characteristics for hydrologicanalyses: Office of Water Data Coordination, p. 7-1 to7-38.

1995, Hydrologic unit codes map for the State ofAlaska: U.S. Geological Survey map, 1 sheet, availableonline at http://agdc.usgs.gov/data/usgs/water/statewide.html.

Wiley, J.B., and Curran, J.H., 2003, Estimating annual high-flow statistics and monthly and seasonal low-flowstatistics for ungaged sites on streams in Alaska and

conterminous basins in Canada: U.S. GeologicalSurvey Water-Resources Investigations Report 03-4114, 61 p.
http://agdc.usgs.gov/data/usgs/water/statewide.htmlhttp://agdc.usgs.gov/data/usgs/water/statewide.htmlhttp://agdc.usgs.gov/data/usgs/water/statewide.htmlhttp://agdc.usgs.gov/data/usgs/water/statewide.htmlhttp://agdc.usgs.gov/data/usgs/water/statewide.html

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Estimating the Magnitude and Frequency of Peak Streamflows for Ungaged Sites on Streams in Alaska and Counterminous Basins in Canada