fs-022-01
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The National Flood-Frequency Program—Methods for Estimating Flood Magnitude
and Frequency for Natural Basins in Texas, 2001
U.S. Geological Survey Fact Sheet 022-01
February, 2001
This report is available in pdf 469KB.
Introduction
Estimates of the magnitude and frequency of flood-peak discharges and flood
hydrographs are used for a variety of purposes, such as for the design of bridges,
culverts, and flood-control structures; and for the management and regulation
of flood plains. To provide simple methods of estimating flood-peak discharges,
the U.S. Geological Survey (USGS) has developed and published regression equations
for every State, the Commonwealth of Puerto Rico, American Samoa, and a number
of metropolitan areas in the United States. In 1993, the USGS, in cooperation
with the Federal Emergency Management Agency and the Federal Highway Administration,
compiled all current USGS statewide and metropolitan area regression equations
into a computer program, titled “The National Flood-Frequency (NFF) Program”
Jennings and others, 1994
).
Since 1993, new or updated regression equations have been developed by the
USGS for various areas of the Nation. These new equations have been incorporated
into an updated version of the NFF Program.
This Fact Sheet describes the application of the updated NFF Program to streams
that drain natural (rural and unregulated) basins in Texas. Information on obtaining
the NFF software and Fact Sheets for other areas of the Nation is provided at
the end of this Fact Sheet.
Overview
Asquith and Slade (
1997
) developed regional regression
equations to estimate peak discharges (Q
) in natural basins in Texas,
with recurrence intervals (T) ranging from 2 to 100 years. These equations are
included in the NFF Program. Asquith and Slade (
1997
defined a natural basin as a basin with less than 10 percent impervious cover,
less than 10 percent of its drainage area controlled by reservoirs, and no other
human-related factors affecting streamflow. Separate sets of equations were
developed for each of 11 hydrologic regions in Texas (
fig. 1
),
which were determined on the basis of physiography and climatic conditions.
For 5 of the 11 regions, the relation between peak discharge frequency and contributing
drainage area was non-linear, requiring that one set of equations be developed
for drainage areas less than 32 square miles and another set be developed for
drainage areas greater than 32 square miles, giving rise to 16 sets of equations
for the state (
table 1
).
Figure 1.
Hydrologic regions of Texas.
Table 1.
Regression equations for estimating peak-streamflow frequency for hydrologic
regions of Texas (
from Asquith and Slade, 1997
[Q
, peak discharge, in cubic feet per
second for recurrence interval, T, in years; A, contributing drainage area,
in square miles; SH, basin shape factor, dimensionless; and SL, stream slope,
in feet per mile]
Regression equation
Weighted
standard
error of
estimate,
in percent
Region
=16.lA
1.04
SH
-0.537
160
=53.2A
0.958
SH
-0.444
111
10
=96.0A
0.921
SH
-0.400
103
25
=178 A
0.885
SH
-0.356
103
50
=263
0.864
SH
-0.330
111
100
=371
0.847
SH
-0.307
120
Region 2
=826A
0.376
SL
-0.689
SH
0.869
120
=6,500A
0.372
SL
-0.933
SH
0.738
92
10
=18,100A
0.369
SL
-1.05
SH
0.673
88
25
=55,300A
0.366
SL
-1.19
SH
0.604
92
50
=108,000A
0.363
SL
-1.27
SH
0.566
99
100
=199,000A
0.361
SL
-.134
SH
0.531
107
Region 3
(Sites with contributing drainage
areas
less than 32 square miles)
=119A
0.592
75
=252A
0.629
78
10
=373A
0.652
88
25
=566A
0.679
103
50
=743A
0.698
120
100
=948A
0.715
134
Region 3
(Sites with contributing drainage
areas
greater than 32 square miles)
=8.05A
0.668
SL
0.659
SH
0.189
60
=42.0A
0.626
SL
0.574
57
10
=91.9A
0.579
SL
0.537
60
25
=233
0.523
SL
0.476
66
50
=448
0.484
SL
0.425
72
100
= 835
0.447
SL
0.372
92
Region 4
(Sites with contributing drainage
areas
less
than 32
square miles)
= 97.1A
0.626
134
=196 A
0.650
SH
0.257
96
10
=293 A
0.697
SH
0.281
92
25
=455 A
0.741
SH
0.311
99
50
=53A
0.927
SL
0.558
SH
0.333
107
100
=51A
0.968
SL
0.627
SH
0.353
120
Region 4
(Sites with contributing drainage
areas
greater than
32 square miles)
=0.0066A
1.29
SL
2.09
72
=0.0212A
1.24
SL
2.18
51
10
=0.0467A
1.20
SL
2.18
49
25
=0.102A
1.16
SL
2.18
54
50
=0.166A
1.13
SL
2.19
60
100
=0.252A
1.11
SL
2.19
69
Region 5
(Sites with contributing drainage
areas
less than 32
square miles)
= 159
0.680
75
= 396
0.773
63
10
= 624
0.820
66
25
= 997
0.866
69
50
= 278
0.973
SL
0.360
72
100
= 295 A
1.01
SL
0.405
78
Region 5
(Sites with contributing
drainage
areas greater than
32 square miles)
= 377
0.498
43
= 1,270
0.534
SH
-0.145
28
10
= 2,310
0.552
SH
-0.221
28
25
= 4,330
0.571
SH
-0.307
31
50
= 6,450
0.583
SH
-0.366
36
100
= 9,180 A
0.594
SH
-0.420
41
Region 6
= 66.2A
0.630
SH
-0.423
96
= 931A
0.424
SL
-0.410
60
10
= 1,720A
0.410
SL
-0.419
49
25
= 3,290A
0.398
SL
-0.428
51
50
= 4,970A
0.391
SL
-0.434
63
100
= 1,780A
0.440
75
Region 7
(Sites with contributing drainage areas greater than 32
square miles)
= 129A
0.578
SL
0.364
66
= 133A
0.605
SL
0.578
54
10
= 178A
0.644
SL
0.699
SH-
0.239
51
25
= 219A
0.651
SL
0.776
SH-
0.267
51
50
= 261A
0.653
SL
0.817
SH-
0.291
54
100
= 313A
0.654
SL
0.849
SH-
0.316
60
Region 8
= 30.7A
0.672
SL
0.652
51
= 87.6A
0.668
SL
0.520
43
10
= 134A
0.675
SL
0.475
43
25
= 191A
0.690
SL
0.444
46
50
= 229A
0.703
SL
0.443
49
100
= 261A
0.718
SL
0.429
51
Region 9
= 278A
0.526
54
= 329A
0.645
SL
0.220
SH-
0.246
49
10
= 350A
0.691
SL
0.343
SH-
0.321
46
25
= 382A
0.743
SL
0.466
SH-
0.413
49
50
= 409A
0.778
SL
0.541
SH-
0.477
49
100
= 438A
0.811
SL
0.607
SH-
0.539
54
Region 10
(Sites with contributing drainage areas less than 32 square
miles)
= 54.9A
0.788
SL
0.279
54
= 80.7A
0.835
SL
0.330
40
10
= 98.2A
0.860
SL
0.359
38
25
= 122A
0.887
SL
0.390
38
50
= 141A
0.904
SL
0.408
41
100
= 159A
0.920
SL
0.426
43
Region 10
(Sites with contributing drainage areas greater than 32 square
miles)
= 16.9A
0.798
SL
0.777
63
= 33.0A
0.790
SL
0.795
51
10
= 51.3A
0.775
SL
0.785
43
25
= 87.9A
0.752
SL
0.760
38
50
= 129A
0.733
SL
0.735
36
100
= 187A
0.713
SL
0.708
36
Region 11
= 159A
0.669
SH-
0.262
43
= 191A
0.696
SL
0.130
SH-
0.186
43
10
= 199A
0.718
SL
0.221
SH-
0.151
49
25
= 201A
0.713
SL
0.313
54
50
= 207A
0.735
SL
0.380
60
100
= 213A
0.755
SL
0.442
66
The regression equations were developed from peak-discharge records through
1993 at 527 streamgaging stations with natural streamflow conditions in Texas.
Asquith and Slade (
1997
) summarized streamgaging-station
information, peak-discharge records, and peak-discharge estimates for 559 gaging
stations in Texas, and 105 streamgaging stations in Arkansas, Louisiana, New
Mexico, and Oklahoma.
Additional regression equations have been developed for some distinct areas
in Texas, including streams in the vicinity of Highland Lakes, central Texas
(Asquith, Slade, and Lanning-Rush,
1996
), and tributaries
to the Brazos River (
Raines, 1998
) and the Colorado River
Asquith, 1998
). These additional regression equations
are not included in the NFF Program. Users interested in documentation for these
equations should contact the Texas District Office of the USGS, Austin, TX.
Asquith and Slade (
1999
) also developed a computer
program that uses a site-specific approach to construct a unique set of regression
equations to estimate Q
for recurrence intervals ranging from 2–100
years for specific ungaged sites in natural basins in Texas. The computer program
uses only streamgaging stations with basin characteristics similar to those
for the ungaged site to develop the site-specific equations. A cluster analysis
selects the stations from a data base that contains a total of 664 streamgaging
stations, 559 in Texas and 105 in Arkansas, Louisiana, New Mexico, and Oklahoma.
The program then uses multivariate generalized least-squares linear regression
to develop the equations. Because a new set of equations is developed each time
the program is run, no equations for this method are included in this fact sheet
and the program is not included in the NFF Program. The report and the software
required to run the program is available on the World Wide Web at URL
Users interested in the site-specific approach may also contact the Texas District
Office of the USGS, Austin, TX.
Procedure
The explanatory variables used in the regional regression equations of Asquith
and Slade (
1997
) are expressed in the inch-pound system
of units; however, the NFF Program will accept and report either the inch-pound
or the metric system of units. The explanatory variables used in the equations
are:
Contributing drainage area (A)
, in square miles,
is the area of the basin contributing to flow in the stream, determined from
USGS topographic maps.
Basin shape factor (SH)
, dimensionless, is the
ratio of the square of the stream length to the contributing drainage area and
represents the ratio of the longest stream length to the mean width of the basin.
Stream length, in miles, is the length of the longest mapped channel, from the
gaging station to the headwaters and is determined from USGS, 1:100,000-scale
topographic maps.
Stream slope (SL)
, in feet per mile, is the
ratio of the change in elevation of the longest mapped channel from the gaging
station to the headwaters to the length of the longest mapped channel determined
from USGS, 1:100,000-scale topographic maps.
The regional regression equations of Asquith and Slade (
1997
and the weighted standard errors of estimate in percent are shown in
table
. The weighted standard error of estimate is a measure of the goodness
of fit between a regression equation and the data used to derive the equation.
Errors in the Q
estimates for about two thirds of the stations used
in the regression analyses were within the given standard errors. Errors in
the Q
estimates for ungaged sites are somewhat larger than the standard
errors of estimate shown in
table 1
, and errors increase
appreciably when any of the basin characteristics used in the equations are
near or beyond the range limits shown in
table 2
. Asquith
and Slade (
1997
) provide procedures to compute the
confidence intervals associated with flood estimates computed from the regression
equations, as well as procedures that can assess the applicability of an equation
to a given set of basin characteristics.
Table 2.
Range of explanatory
variables for which regression equations are applicable (
from Asquith and
Slade, 1997
[mi
, square miles; A, contributing
drainage area (mi
); SH, basin shape factor - ratio of length
of longest mapped channel (stream length) squared to contributing drainage
area (dimensionless); SL, stream slope - ratio of change in elevation of
(1) longest mapped channel from site to headwaters to (2) length of longest
mapped channel (feet per mile)]
Hydrologic
region
SH
SL
Region 1
1.15-2,956
0.11-80.9
2.49-132
Region 2
0.32-4,305
0.51-14.8
9.67-130
Region 3
(Sites with A less
than 32 mi2)
0.10-97.0
0.16-9.32
10.7-105
(Sites with A greater
than 32 mi
11.8-14,635
1.71-75.0
4.81-36.3
Region 4
(Sites with A less
than 32 mi2)
0.19-81.1
0.05-6.52
13.5-226
(Sites with A greater
than 32 mi
12.0-19,819
0.49-19.7
3.52-36.1
Region 5
(Sites with A less
than 32 mi
0.18-22.3
0.50-84.9
20.9-224
(Sites with A greater
than 32 mi2)
45.0-1,861
3.14-20.8
9.86-48.8
Region 6
(Sites with A less
than 32 mi2)
0.36-15,428
0.011-10.9
6.88-98.9
Region 7
(Sites with A less
than 32 mi2)
0.20-78.7
0.037-36.6
7.25-116
(Sites with A greater
than 32 mi2)
13.0-2,615
1.66-36.6
3.85-31.9
Region 8
0.75-7,065
1.94-24.8
3.83-39.5
Region 9
0.24-5,198
0.091-30.1
2.77-70.0
Region 10
(Sites with A less
than 32 mi2)
0.21-100
0.008-1.05
2.00-138
(Sites with A greater
than 32 mi
23.4-6,507
1.77-16.9
1.48-24.5
In regions for which the relation between peak discharge and contributing drainage
area is non-linear and two sets of equations are presented in
table
(Regions 3, 4, 5, 7, and 10), a weighting procedure is suggested to combine
the estimates from the two sets of equations if the contributing drainage area
is between 10 and 100 square miles. The weighted estimate, Q
TW
, is
computed as:
where
TW
is the weighted peak discharge associated
with T-year recurrence interval,
T1
is the peak discharge associated with the
equations for sites with contributing drainage areas less than 32 square
miles,
T2
is the peak discharge associated with the
equations for sites with contributing drainage areas greater than 32 square
miles, and
log(A)
is the common (base 10) logarithm of the
contributing drainage area for the ungaged site.
This weighting procedure is not included in the NFF software. Users of the
software should obtain the estimates from the two sets of equations provided
in NFF and then manually solve the weighted estimate equation.
Prepared by Stephen S. Sumioka and Kernell G. Ries III
References
Asquith, W.H., 1998, Peak-flow frequency
for tributaries of the Colorado River downstream of Austin, Texas: U.S. Geological
Survey Water-Resources Investigations Report 98-4015, 19 p.
Asquith, W.H., and Slade, Raymond, Jr., 1997,
Regional equations for estimation of peak-stream flow frequency for natural
basins in Texas: U.S. Geological Survey Water-Resources Investigations Report
96-4307, 68p.
———1999, Site-specific estimation
of peak-stream flow frequency using generalized least squares regression for
natural basins in Texas:
U.S.
Geological Survey Water-Resources Investigations Report 99-4172, 19 p.
Asquith, W.H., Slade, R.M., Jr., and Lanning-Rush,
Jennifer, 1996, Peak-flow frequency and extreme flood potential for streams
in the vicinity of the Highland Lakes, central Texas: U.S. Geological Survey
Water-Resources Investigations Report 96-4072, 1 sheet.
Jennings, M.E., Thomas, W.O., Jr., and Riggs,
H.C., comp., 1994, Nationwide summary of U.S. Geological Survey regional regression
equations for estimating magnitude and frequency of floods for ungaged sites,
1993, U.S. Geological Survey Water-Resources Investigations Report 94-4002,
196 p.
Raines, T.H., 1998, Peak-discharge frequency
and potential extreme peak discharge for natural streams in the Brazos River
Basin, Texas: U.S. Geological Survey Water-Resources Investigations Report 98-4178,
42 p.
For more information contact:
U.S. Geological Survey
Office of Surface Water
415 National Center
Reston, Virginia 20192
(703) 648-5301
USGS hydrologic analysis software is available for electronic retrieval through
the World Wide Web (WWW) at:
and through anonymous File Transfer Protocol (FTP) from water.usgs.gov (directory:
/pub/software
).
The WWW page and FTP directory from which the National Flood-Frequency software
and user documentation can be retrieved are
and
/pub/software/surface_water/nff
respectively.
Additional earth science information is available from the USGS through the
WWW at
anonymous or
by calling 1-888-ASK-USGS.
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