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1 . Report No. 2. Government Accession No. 3. Recipient's Catalog No.
FWRA-WV-79-02 4 . Title and Subtitle 5. Report Dot ,
WEST VIRGINIA DEPARTMENT OF HIGHWAYS October 1980 RESEARCH PROJECT 16 "Runoff Studies on Small Drainage
6. Performing Organization CodeAreas" (Technique for Estimating Magnitude and Frequency of Floods in West Virginia.
8. Performing Organization Report No.
7. Author's)
Gerald S. Runner
9. Performing Organization Name and Address 10. Work Unit No. (TRAIS)
U.S. Geological Survey 3017 Federal Building 11. Contract or Grant No.
Charleston, West Virginia 25301 HPR 13. Type of Report and Period Covered
12. Sponsoring Agency Name and Address
West Virginia Department of Highways Final Report1900 Washington Street, East
Charleston, West Virginia 25305 Sponsoring Agency Code14.
15. Supplementary Notes Prepared in cooperation with the Department of Transportation, Federal Highway Administration and the West Virginia Department of Highways.
16. Abstract
A technique is presented for estimating the magnitude and frequency of floods on unregulated, virtually natural streams in West Virginia. Multiple-regression techniques were used to develop relations between dependent variables, flood peaks, and independent variable, drainage areas. Data collected at 170 stream-gaging sites were used in the analyses.
Analyses of all residuals errors indicated that the best estimate of flood peaks could be made by dividing the state into three regions.
Peak discharges can be estimated for drainage areas from about 0.3 square mile up to 2000 square miles. Graphs are provided to estimate the flood peak having recurrence intervals of 2, 5, 10, 25, 50, 100, and 500 years and drainage areas between 1 and 1000 square miles.. For drainage areas less than 1 and greater than 1,000 square miles peak flows can be estimated using equations listed on each graph.
17. Key Words 18. Distribution StatementFlood peaks, recurrence interval, flood frequency, drainage area
No restriction
19. Security Classif. (of this report) 20. Security Clossif. (of thi s page) 21. No. of Pages 22. Price •
No restrictions • unclassified
'orm DOT F 1700.7 (8-72) Reproduction of completed page authorized
FINAL REPORT
WEST VIRGINIA DEPARTMENT OF HIGHWAYS RESEARCH PROJECT 16
"Runoff Studies on Small Drainage Areas" (Technique for Estimating Magnitude and Frequency of Floods in West Virginia)
BY
G. S. Runner, Hydrologist U.S. Department of the Interior
Geological Survey
A research project conducted in cooperation with the West Virginia Department of Highways
and Department of Transportation, Federal Highway Administration
)n-fito rer (rt Co Stitury
CUSS
The contents of this report reflect the views of the author who is responsible for the facts and the accuracy of the data presented herein. The contents do not necessarily reflect the official views or policies of the State or the Federal Highway Administration. This report does not constitute a standard, specification, or regulation.
October 1980
WEST VIRGINIA DEPARTMENT OF HIGHWAYS
RESEARCH PROJECT 16
"Runoff Studies on Small Drainage Areas"
(Technique for Estimating Magnitude and
Frequency of Floods in West Virginia)
U.S. GEOLOGICAL SURVEY
Open-File Report 80-1218
Prepared in cooperation with the
West Virginia Department of Highways
and the
Federal Highway Administration
UNITED STATES DEPARTMENT OF THE INTERIOR
CECIL D. ANDRUS, Secretary
GEOLOGICAL SURVEY
H. William Menard, Director
For additional information write to:
U.S. Geological Survey 3017 Federal Building 500 Quarrier Street Charleston, West Virginia 25301
CONTENTS
Page
Abstract 1
Research implementation 2
Introduction 3
Analytical techniques 7
Accuracy and limitations 14
List of estimating equations, standard errors, and drainage
area break points 16
Estimating technique 18
Sample computation 19
Summary 21
References 22
ILLUSTRATIONS
Figure 1. Comparison of station Q50 to 50-year flood-frequency
curve for Region 1 12
Figure 2. Comparison of maximum station discharge to Q for Region 1 13100
Figure 3. Map showing Geographic Regions 1 and 2, Ohio River basin,
Region 3, Potomac River basin 23
Figures 4-24 Graphs showing:
4. Relation of 2-year peak discharge to drainage area, Region 1 24
5. Relation of 5-year peak discharge to drainage area, Region 1 25
6. Relation of 10-year peak discharge to drainage area, Region 1 26
7. Relation of 25-year peak discharge to drainage area, Region 1 27
8. Relation of 50-year peak discharge to drainage area, Region 1 28
9. Relation of 100-year peak discharge to drainage area, Region 1 29
10. Relation of 500-year peak discharge to drainage area, Region 1 30
iv
CONTENTS (Cont.)
Illustrations
Page
11. Relation of 2-year peak discharge to drainage area, Region 2 31
12. Relation of 5-year peak discharge to drainage area, Region 2 32
13. Relation of 10-year peak discharge to drainage area, Region 2 33
14. Relation of 25-year peak discharge to drainage area, Region 2 34
15. Relation of 50-year peak discharge to drainage area, Region 2 35
16. Relation of 100-year peak discharge to drainage area, Region 2 36
17. Relation of 500-year peak discharge to drainage area, Region 2 37
18. Relation of 2-year peak discharge to drainage area, Region 3.... 38
19. Relation of 5-year peak discharge to drainage area, Region 3.... 39
20. Relation of 10-year peak discharge to drainage area, Region 3... 40
21. Relation of 25-year peak discharge to drainage area, Region 3... 41
22. Relation of 50-year peak discharge to drainage area, Region 3... 42
23. Relation of 100-year peak discharge to drainage area, Region 3.. 43
24. Relation of 500-year peak discharge to drainage area, Region 3.. 44
ABSTRACT
A technique is presented to provide a method of estimating the
magnitude of peak discharges of T-year frequencies for unregulated,
virtually natural streams in West Virginia. Multiple regression
techniques were used to develop the relation between peak discharges
and drainage area. Data collected at 170 stream gaging sites were
used in the analyses.
Analyses indicated that the best estimating equations could be
derived by dividing the state into three regions, Regions 1 and 2
covering the Ohio River basin in West Virginia and Region 3 covering
the Potomac River basin in West Virginia.
The method is applicable for drainage areas between 0.3 and
2,000 square miles. Graphs are provided to estimate the 2-, 5-,
10-, 25-, 50-, 100-, and 500-year flood peaks for drainage areas be-
tween 1 and 1,000 square miles. Peak discharges for drainage areas
less than 1 or greater than 1,000 square miles can be estimated using
the appropriate equations provided on each graph.
RESEARCH IMPLEMENTATION
Application: Prior to the study, flood frequency estimates were
made using techniques that were, in many instances, based on data from
areas not necessarily similar to those found in West Virginia. Hydro-
logic information was lacking, especially for streams whose drainage
area was less than 50 square miles. The data collection phase of this
research study was designed to provide information on streams having
small drainage areas. The technique discussed in this report was de-
veloped using data obtained from these small drainage area streams,
combined with hydrologic data available from U.S. Geological Survey
long-term sites having drainage areas between 50 and 2,000 square
miles. The technique should therefore be especially applicable to
West Virginia using the data collected over a wide range of hydrologic
conditions.
Implementation: The technique provided in this report could be
implemented through a West Virginia Department of Highways Roadway
Design Division Directive or as an update to the Drainage Manual.
Expected Benefits: The technique should provide an easier, more
reliable, method for estimating peak discharges for drainage areas in
West Virginia. The method was developed from data collected in the
State, therefore, greater confidence could be placed in the flood-
frequency estimates which are necessary for the safe, economical,
design of drainage structures.
2
WEST VIRGINIA DEPARTMENT OF HIGHWAYS
RESEARCH PROJECT 16
"Runoff Studies on Small Drainage Areas"
(Technique for Estimating Magnitude and
Frequency of Floods in West Virginia)
INTRODUCTION
This is the final report in the cooperative project between the
West Virginia Department of Highways, Federal Highway Administration
and the U.S. Geological Survey. This project was designed to provide
a technique for estimating the magnitude of peak discharges of T-year
frequencies on unregulated streams in West Virginia. The project
began in 1963 and continued through 1978. The first phase of the
project required an extensive search for suitable stream-gaging sites.
Therefore, the first three years of the study were used for site recon-
naissance and installation of approximately 60 crest-stage gages.
Later in the project, 20 additional sites were selected as dual
digital sites where both continuous stage and rainfall were collected.
Fifteen of these latter stations were finally selected to use with
the U. S. Geological Survey rainfall-runoff model. The records were
extended to about 70 years by using long-term rainfall records and then
appropriate frequency curves were drawn.
The basic small-streams flood data collected during the project
were supplemented by the regular U.S. Geological Survey stream-gaging
network. This network consists mainly of large drainage-area stations
(greater than 50 square miles) with length of records greater than
3
forty years. The lack of small-stream stations in the regular network
was one of the main reasons for this flood-frequency study. Prior
to this project flood frequency estimates for small drainage areas
in West Virginia were based on empirical relations or data collected
in other parts of the country.
Frye and Runner (1969) presented relations for estimating flood
magnitude and frequency within the State of West Virginia that were
taken from U.S. Geological Survey Water Supply Papers 1672 and 1675.
This flood-frequency study was country-wide and combined available
records from all states to develop regional or major river basin
frequency curves. These relations were only recommended for use
on drainage areas greater than 50 square miles in the Ohio River
basin and 30 square miles in the Potomac River basin.
Another technique for estimating magnitude and frequency on
West Virginia streams is presented in the report "A Proposed Stream-
flow Data Program for West Virginia" (Frye and Runner 1970). This
method used an analytical technique similar to one proposed by Benson
(1962). Data for all natural flow streams in West Virginia with dis-
charge records of 10 years or longer were used in the analysis. Because
of the absence of stations on small streams with the required length of
record, this estimating method was recommended for streams having drainage
areas greater than 50 square miles.
In 1971, "A Preliminary Report on Small Streams Flood Frequency in
West Virginia", provided a method for estimating the 2-, 5-, and 10-
year peak discharges for streams in the Ohio River basin of West Virginia,
having drainage areas between 1 and 50 square miles. This study used
all the peak discharge data made available by the small-streams program
to that date. At that time the length of record for the small-streams
stations averaged about 6 years. These records were correlated with
long-term regular station records to determine time bias and appropriate
corrections made.
Estimates of the magnitude and frequency of floods are needed
for all size drainage areas for safe and economical design of hydrau-
lic structures and flood-plain management. Peak flow records collected
to define small-streams flood frequency were combined with available
long-term U.S. Geological Survey streamflow records to define a complete
range of flood frequency for West Virginia. Multiple-regression tech-
niques were used to correlate flood magnitudes with basin characteristics
to develop regional flood-frequency relations. This report provides
a method for estimating peak discharges for recurrence intervals ranging
between 2 and 500 years for ungaged sites on streams in West Virginia
that have drainage areas between 0.3 and 2,000 square miles. Graphs
are provided to estimate peak discharges for drainage areas between
1 and 1,000 square miles. Peak discharges for other size drainage
areas can be estimated by solving the appropriate equation provided
on each curve.
When developing frequency curves for the larger drainage area
ungaged sites (>100 square miles) the user is instructed to check for
nearby station frequency curves. Within reason, gaged site data may be
transferred to the ungaged site using procedures outlined in U.S. Water
Resources Council, Bulletin 17, 1976. The user is also reminded that
frequency curves may be developed using Soil Conservation Service or
U.S. Army Corps of Engineers routing techniques.
The following factors may be used to convert the inch-pound
units published herein to the International System of Units (SI).
Multiply Inch-Pound Unit By To obtain SI units
square miles (mil) 2.590 2
square kilometers (km )
3cubic feet per second (ft /s) 0.02832
3cubic meters per second (m /s)
This study was conducted during the period 1963-77 by the U.S.
Geological Survey in cooperation with the West Virginia Department of
Highways and the Federal Highway Administration. The basic small-
stream data collected for the study are supplemented by flood data
from the regular stream-gaging network, other cooperative hydrologic
studies, and flood data from studies in Maryland and Virginia. The
opinions, findings, and conclusions in this report reflect the views
of the author who is responsible for the data presented herein. The
contents do not necessarily reflect the policies of the West Virginia
Department of Highways or the Federal Highway Administration.
6
ANALYTICAL TECHNIQUES
Flood frequency curves were computed for 170 stream gaging sites,
using the procedures recommended by the U.S. Water Resources Council
(1976), Bulletin 17. The 2-, 5-, 10-, 25-, 50-, 100-, and 500-year
peak discharges were determined for each station and used as depen-
dent variables in the regression analysis. Regional skew values were
weighted with station skew values and used to adjust each station
record. The regional skew values were taken from the generalized
skew map in WRC Bulletin 17.
Hydrologic data used in the regression analysis, and a listing
of station locations are available in Open-File Report 80-560,
"Hydrologic Data for Runoff Studies on Small Drainage Areas" West
Virginia Department of Highways Research Project 16, 169 p. Other
data used in the study but not contained in the report are available
from U.S. Geological Survey computer files using Wetstore programs.
These files contain unit-rainfall and unit-discharge data for 15
smallstream stations, unit and daily values of rainfall for the
long-term rainfall stations, and pan-evaporation data for two stations.
These data were too voluminous to be included in the hydrologic data
report. Also contained in the data report are maps showing the loca-
tions for all stations used in the regression analyses.
Fifteen small-stream station frequency curves were adjusted
using the U.S. Geological Survey rainfall-runoff model. These were
the only stations in the small-stream network with enough reliable
unit data to justify using the model technique. The model was used
to simulate flood-volume and flood-peak data at stations where con-
current discharge and rainfall data were collected. The model was
developed to generate flood hydrographs for small-drainage basins
using daily evaporation, unit and daily rainfall, and unit and daily
discharges.
The two phases involved in using the model are calibration and
optimization. To calibrate each basin, concurrent runoff and rainfall
data for the site, plus general evaporation data are used to fit the
model to the conditions that exist on the gaged basin. The final
values for basin parameters are determined by an optimization process.
These parameters are then used along with long-term rainfall data as
input to the model to generate a series of flood peaks equivalent to
the length of record at the long-term rainfall station. Evaporation
data from the National Weather Service stations at Sutton Lake, Blue-
stone Lake, and Kearneysville, West Virginia, were used for small
stream sites. Long-term rainfall data from Elkins, and Parkersburg,
West Virginia, and Wytheville, Virginia, were used to synthesize peak
discharges for the fifteen stations. All short-term and long-term data
used to calibrate the model and synthesize the peak discharges are on
U.S. Geological Survey unit value and daily value computer files. A
detailed discussion of the rainfall-runoff model is given in U.S.
Geological Survey Professional Paper 506-B by Dawdy, Lichty, and
Bergmann (1972).
Frequency curves developed using station data and frequency curves
developed using the synthesized flood peaks were combined to give a
composite curve for each of the fifteen stations. These data along
with frequency data for 155 regular and project streamflow stations
were used as input to the regression analysis. The estimating equations
developed by this study are listed on page 16. As an example of the
equations, figure 1 shows station's frequency data for Q50 compared to
the 50-year frequency curve for Region 1. The final curve is a composite
of the long-term station frequency curve and the curve developed by com-
bining the long-term stations with the project stations. The lack of
stations in the range of 10 to 50 square miles in drainage area, or
even 10 to 100 square miles should be noted. The author felt the long-
term stations' frequency could stand alone in a frequency report but
all parties would be better served if all stations were combined in
a single report. This would eliminate the possibility of having dif-
ferent discharge values for the same frequency or discontinuous
frequency curves. Shown on figure 2 are maximum station discharges
in Region 1 for the long-term stations, project stations, and indirect
measurement sites. These values are compared with the Q frequency100
curves for Region 1.
Twelve basin and climatic characteristics were determined for each
station and used as independent variables in the regression analysis.
Those characteristics determined were:
A drainage area, in square miles S . stream slope, in feet per mile measured between 0.1 and
0.85 length L length of stream, in miles from gaging point to divide St storage area of lakes and ponds, in percent of basin area
plus 1.0 percent. E mean basin elevation, in thousands of feet above sea level F forest cover, in percent of drainage area. P mean annual precipitation, in inches.
I24,2 24 hour rainfall intensity at 2-year recurrence interval in inches.
T mean minimum January temperature, in °F. Sn mean annual snowfall, in inches. Si soil index, in inches. R ratio of basin length to width.
Multiple regression techniques were used to relate each of the
specified peak discharges to the basin and climatic characteristics.
This method was described by Benson (1962).
Initially all variables and all stations were used in the
regression analysis. Later analyses separated the stations into
groups having drainage areas less than 50 square miles and those
greater than 50 square miles. Analyses were also conducted using
a breakdown of long-term records versus short-term records, and
with and without regional skew values.
Analysis of the resultant residual errors for each flow char-
acteristic led to the division of the state into three geographic
regions. When using the three regions approach, there was an im-
provement in the standard error of estimate throughout the state.
The analysis for each region required regression analysis:
1) Using all available stations,
2) using stations having less than 50 square miles in
drainage area, and
3) using station with more than 50 square miles of drainage
area.
A study of each regression equation was made by dropping one
significant variable (at 95 percent confidence level) from the
equation at a time and noting the change in standard error. The
final analysis indicates that the most useful estimating equations
for each flow characteristic (Q2, Q5, etc.) would contain only
drainage area as a variable. The results of the final analyses for
the three regions and the final estimating equations are shown on the
graphs in figures 4 through 24 and listed on page 16.
Also present on each figure are the flow characteristic plus one
standard error of estimate and the flow characteristic plus two stan-
dard errors of estimate. These values above the mean curve show
graphically the approximate upper limit of data used in this flood
study. The user of this report should note that at the drainage area
10
breakpoint there are two standard errors (SE). One SE for the equa-
tion using only long-term stations, and one SE for equation that used
all available stations. Rather than have a discontinuous Q + 1 SE and
Q + 2 SE on each graph (figures 4 to 24) an average value was used and
the appropriate curve drawn. This should not introduce any appreciable
error into calculations for frequency plus standard error.
11
I
DISCHARGE, IN CUBICFEETPERSECOND
10
0,0
00
A
I
T I
FT
TI
F
T T
I I
1III
T F
I
IFFI
• •
• •
•
A A
• A
A A A
i* 1 A A
4,,
1•4
40 I
• A
A.789
A *A
Q
50 =
241
/ A
*A
10,000
O
•
Drainage area
• A
break point
1 4
A 99 m12
-450 = 583R.6
A O
A
A
ort-term project stations
Q-Q
50 a erage length of record - 10 yr
gion 1 Long-term regular
A -
Q50
gaging stations.
gion 2 Average length of
*-Q
50
record - 40 yr
100I1
1111
1 1
11
11
11
1
1 LI
1 I
1 I
1 I
1 1
0.3
10
100
1,000
2,000
DRAINAGE AREA, IN SQUARE MILES
Figure 1.--Comparison of station Q50 to 50-year flood-frequency curve for Region 1
�
••
•
100,000
I-1
11
I
11
11
11
1
1 1
1-7-1
I 11
10,0
(0
• ,.
••
• Y
e,
•
MAximum Discharges
• z -
-•
-Regular stations
-Project stations
•
-Miscellaneous sites
•
•
.4)
•
•
•
•
100 _
I __
1 _.
LI II
I
L_
Li
1_1
1_11
11
H
Lid
0 3
1
10
,0o0
2,0
0((
DRAINAGE AREA, IN SQUARE MILES
Fiwire 2.--Comparison of maX1MUM station discharge to Q 00 for Region 1
ACCURACY AND LIMITATIONS
Flood frequency estimates used in this study are based on peak
discharge data through September 1977. These flood frequency values
are probably the most reliable estimates of future peak discharges at
these gaged sites, if basin characteristics remain fairly constant.
All small stream stations installed for this research project were
discontinued at the end of the study.
The standard error of estimate is a measure of how well the
flood peaks, as determined by station frequency analysis of the
observed and simulated annual peak discharge, compared with those
computed using the estimating equations. About two-thirds of
the station flood-frequency values should fall within one standard
error of estimate and 19 out of 20 values should be within two
standard errors of estimate. In this study it was noted that peak-
discharge estimates could be made more reliably for the larger size
drainage areas. When stations having less than 50 square miles of
drainage area were added to the data set, the standard error of
estimate increased.
Separate analyses were made for a range of drainage area sizes.
In general, the division in drainage areas was above and below approx-
imately 50 square miles in the Ohio River basin and above and below
approximately 40 square miles in the Potomac River basin. To develop
the lower section of the frequency curve, a comparison was made,
of the estimating equations and standard errors, when all stations
14
were used in the analysis against the results of using only stations
having less than 50 square miles. The final results indicated that no
loss of accuracy would occur by combining stations with large and small
drainage areas in each region and using these equations to develop the
lower section of the discharge versus drainage area curves for each
frequency (figures 4-24). By combining stations it also assured that
there would not be any discontinuous frequency curves. In all cases
the combined station analysis gave a larger discharge value for a
given frequency up to the drainage area where the curves are equal.
The regression equations, average standard errors, and drainage area
breakpoints for each region (see figure 3) for recurrence intervals
2 to 500 years are listed on following page.
The user of these data should note that there is no relation
between the curves (figures 4-24) and the division of the stations
into those with less than 50 square miles and those greater than
50 square miles in drainage area. The intersections for the curves
were determined mathematically; therefore, each graph has a dif-
ferent drainage area break point and will not necessarily fall at
50 square miles.
15
List of Estimating Equations, Standard Errors, and Drainage Area Break Points
Recurrence Interval yrs.
2
5
10
25
SO
100
500
'
5
10
25
50
100
500
2
5
10
25
50
100
500
Estimating Equation
(All stations)
0.734131 A
0.683235 A
0 655324 A
.
0.625461 A
583 A0.604
724 A°586'
1137 A0'547
0.83085 A
0.792148 A
0.771 201 A
0.748282 A
0.733354 A
0.719437 A
0.689679 A
0.77474 A
0.762141 A
203 A0.754
0.747 303 A
0.743 397 A
.740 511 A0
0.831 556 A
Standard Drainage Area Estimating Error Break Point Equation
(long-term Region 1 stations)
37 160 74 A0.847
37 125 115 A0.831
37 116 149 A0.818
39 106 0.801
203 A
40 99 249 A°'789
42 95 303 A0'777
46 84 A0. 750
462 °.75°
Region 2
43
0.831 39 •586 /15 A
0.818 38 549 149 A
0.801 40 485 203 A
0 789 41 529 249 A
0.77744 530 303 A
0.750 50 552 462 A
Region 3
0.80339 18.4 68 A
98 A0. 845 32 77.8
0.866 33 93.2 122 A
0.887 38 100 159 A
0.899 43 106 191 A
0.910 50 116 228 A
0.930 54 162 335 A
Standard Error
25
25
27
29
32
35
25
27
29
32
35
41
29
27
29
34
38
42
53
16
EXAMPLE
Region 1 - Q50
The regression equation for Q50 using only the larger drainage area
stations (>50 square miles):
0.789Q = 249 A (figure 8)50
The regression equation for Q when all stations for the region are50
included in the analysis is:
0.604Q50 = 583 A
At what point (drainage area) are these equations equal?
0.789 0.604249 A = 583 A
log 249 + .789 log A = log 583 + .604 log A
0.185 log A = .3694
log A = 1.99675
A = 99.3 square miles
In this example the equations will give the same Q for a drainage area50
of 99.3 square miles (9,371 ft3/s). Note that there is one case where the
"break point" did not occur within our range of drainage areas of 0.3 to
2,000 square miles (Q2 - Region 2). In this case, we show the equation
that produces the larger discharge.
The graphs and equations presented in this report should not be
used to estimate peak flows for sites draining urban basins, areas with
significant regulation, karst terrain areas, or where drainage areas
are less than 0.3 square mile or greater than 2,000 square miles.
17
ESTIMATING TECHNIQUE
The magnitude of floods of T-year frequency on unregulated
streams in West Virginia may be estimated using the graphs provided
or the equations on each graph of the form:
b(1) Average QT = aA
(i)
where:
Q = the T-year annual peak discharge, in cubic feet per second(T)
T = recurrence interval of 2, 5, 10, 25, 50, 100, or 500 years.
i = appropriate state region (see figure 3)
A = drainage area in square miles
a = regression constant
b = regression coefficient
Drainage area should be determined from the best available maps.
These are usually either the 71/2-minute or 15-minute series of the U.S.
Geological Survey topographic quadrangle maps.
In addition, discharge values for:
(2) QT + 1 SE (standard error of estimate)
(i)
and
(3) QT + 2 SE (i)
are shown on each graph (figures 4-24). The user of these curves
and equations should realize that there is also a negative standard
error associated with the mean curves. In this study only positive
values are shown.
18
SAMPLE COMPUTATION
Assume it is desired to compute the 50-year discharge for Tug
Fork at Welch, W. Va. The site is located in Region 2 (see figure 3,
page 23).
The drainage area as determined from topographic maps is 87.8
square miles.
Using the equation on figure 15, page 35, or the equation and
standard error on page 16, for Q50 to be used up to a drainage area
size of 529 square miles.
0.733(1) Q = 354 A50
0.733Q = 354 x 87.850
3 3Q = 9410 ft /s (266 m /s)50
3 3(2) Q50 + 1 SE = 9410 (1.41) = 13300 ft /s (377 m /s)
3 3(3) Q + 2 SE = 9410 (1.82 = 17100 ft /s) (484 m /s)50
or reading directly from graph
3 3(1) Q = 9400 ft /s (269 m /s)
50 3 3
(2) Q + 1 SE = 13100 ft /s (371 m /s)50 3 3
(3) Q50 + 2 SE = 16700 ft /s (473 m /s)
If the site in question was on the divide between Regions 1 and
2 and had a drainage area less than 50 square miles, it is suggested
an averaging method be used to estimate peak discharge. The reasons
for averaging at the divide between Regions 1 and 2 are; they are
in the same major river drainage (Ohio River basin) and have similar
19
hydrologic characteristics along the boundary. As an example, if
the site was on the divide and had a drainage area of one square
mile:
To estimate Q50 for 1 square mile:
.Region 1 Q = 583 A° 604 = 583 ft3/s
50 0.733
Region 2 Q = 354 A = 354 ft3/s50
The average estimated Q for Regions 1 and 2 would be about 470 ft3/s.50
Unless the user had specific information about the site in question, the
estimated Q should be used. This averaging method should not be used50
between Regions 1 and 3 because of the different hydrologic characteristics.
Note: If the drainage area in the example had been greater than
529 square miles, we would have used the equation for that
section of theQ curve (Q50 = 249 A°.789) as shown on50
figure 15 and listed on page 16.
On this graph, at 529 square miles either equation could
be used to compute peak discharge. The user is reminded
that each graph presented in this report has a definite
flex point where the equations will provide equal discharge.
SUMMARY
Prior to 1963 small-stream flood data was nonexistent in West
Virginia. The U.S. Geological Survey in cooperation with the West
Virginia Department of Highways and the Federal Highway Administration
began a small-streams research project to develop a method to estimate
flood magnitudes and frequencies. The equations and curves in this
report are the result of that research project.
The State has been divided into three regions, each with a set
of estimating equations. The equations were developed to estimate
flood magnitudes at ungaged sites in West Virginia for recurrence
intervals of 2 to 500 years. The equations relate flood magnitudes
to size of drainage area and apply to streams that are not affected
significantly by urbanization, regulation, or diversion.
In general the report combines two frequency studies. One study
on the regular stream-gaging network with generally long records and a
second analysis on a combination of the small drainage area, short
record project stations and the regular stations.
Standard errors range from 25 to 54 percent for the long-term
stations and 37 to 54 percent for the combination of stations.
The user of the equations in this report should realize that
long-term records close to an ungaged site could provide a more
reliable estimate than the regression equation.
21
REFERENCES
Benson, M. A., 1962, Factors influencing the occurrence of floods in a humid region of diverse terrain: U. S. Geological Survey Water Supply Paper 1580-B, 64 p.
Dawdy, D.R, Lichty, R.W., and Bergmann, J. M., 1972, A rainfall-runoff simulation model for estimation of flood peaks for small drainage basins: U.S. Geological Survey Professional Paper 506-B, 28 p.
Frye, P. M., and Runner, G. S., 1969, Procedure for estimating magnitude and frequency of floods in West Virginia, West Virginia State Road Commission design directive, 10 p.
1970, A proposed streamflow data program for West Virginia, U. S. Geological Survey Open-File Report, 38 p.
1971, A preliminary report on small streams flood frequency in West Virginia, West Virginia Department of Highways design directive, 9 p.
Runner, G.S., 1980, Hydrologic Data for "Runoff Studies on Small Drainage Areas" West Virginia Department of Highways Research Project 16, U.S. Geological Survey Open-File Report 80-56, 169 p.
Speer, Paul R. and Gamble, Charles R., 1965, Magnitude and frequency of floods in the United States, Part 3-A. Ohio River basin except Cumberland and Tennessee River basins, U.S. Geological Survey Water-Supply Paper 1675, 585 p.
Tice, Richard H., 1968, Magnitude and frequency of floods in the United States, Part 1-B. North Atlantic Slope Basins, New York to York River, U.S. Geological Survey, Water-Supply Paper 1672, 630 p.
U.S. Water Resources Council, 1976, Guidelines for determining flood-flow frequency: Bulletin 17, 26 p.
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