1989). Thus, residuals with similar sign and magnitude
are assumed to represent regions with similar flood
characteristics and are grouped together (Choquette,
1988). In practice, regions commonly follow
geographical or political boundaries. Because of the
subjective nature of this method, Tasker (1982)
proposed the use of the Wilcoxon signed-ranks test to
provide some objectivity. This non-parametric test is
used to compare residuals between regions to determine
if the apparent grouping of the residuals represent
consistent differences in the residuals and flood
response (Choquette, 1988). The Wilcoxon signed-
ranks test does not statistically verify the regions but
provides a quantitative index as a guide for defining
“homogeneous” regions (Choquette, 1988; Tasker,
1982). In addition to the Wilcoxon signed-ranks test,
the regression equations for all regions were tested to
insure that they met the regression requirements stated
above.

The residuals in log units from the 50-year
recurrence interval equation, were plotted on a map of
Oahu. On the basis of this residual plot, a number of
geographically continuous regions were determined.
These regions were then checked by the Wilcoxon
signed-ranks test and by regression analysis. For the
Wilcoxon signed-ranks test, all the various groupings
failed at the 0.10 (10 percent) significance level. Failure
of the Wilcoxon signed-ranks test indicates that the
residuals for the individual regions are not statistically
different from those of the island as a whole. In other
words, based only on the Wilcoxon signed-ranks test,
failure indicates that subdivision of the island into
regions is not called for. Groupings based on previous
studies (Yamanaga, 1972; Nakahara, 1980; Wong,
1991) were also tested by the Wilcoxon signed-ranks
test and regression analysis. Using the current data, all
of these previous groupings also failed the Wilcoxon
signed-ranks test. Data from some of the previous and
current groupings, including the island as a whole,
when checked by regression analysis, resulted in poor
equations with high standard errors or violated the
regression assumptions. A grouping was found
however, that while not passing the Wilcoxon signed-
ranks test, did provide regression equations with
smaller uncertainties than the equations for the island as
a whole. The improvement in regression equations
justifies this grouping, dividing Oahu into three regions,
each region with regression equations that met the
regression requirements stated above. These three

16

regions are leeward Oahu, including stations 200000
through 247900 and 343000; windward Oahu,
including stations 248800 through 294900; and north
Oahu, including stations 296500 through 350000. The
divides between the delineated regions were extended to
the coast as shown in figure 1.

REGIONAL REGRESSION EQUATIONS

For the three regions, regression equations, bias-
correction factors, standard errors of estimate and
prediction, and equivalent years of record are given in
tables 6 through 8. The standard errors of estimate for
all the regression equations range from 27 to 58
percent. The average standard error for these equations
was 39 percent.

UMITATIONS AND ACCURACY OF REGRESSION EQUATIONS

The regression equations in tables 6 through 8
apply only to streams where peak discharge is not
significantly affected by diversions, regulations, or
urbanization. As mentioned, diversions were
considered significant at stations where the measured
diversions exceeded 30 percent of the mean daily
discharge on the day of the annual peak discharge,
significant regulation was defined as having a flood-
control reservoir controlling more than 50 percent of the
drainage-basin area, and urbanization was measured as
the percentage of urban cover. Most streams on Oahu
flow through unaltered channels in their upper reaches
and then through residential or urban areas in the lower
reaches before discharging into the Pacific Ocean. Most
gaging stations are located near these residential and
urban areas, so that some effects of these alterations are
present in the gaged record. For ungaged basins where
streamflow is affected by significant urbanization, peak
discharges can be estimated according to the methods
of Sauer and others (1983). Significant urbanization in
this study is defined as any basin having an urban cover
of greater than 36%. As part of this study, flood-peaks
for basins with urban cover were compared with nearby
non-urban basins. No significant trends or differences
in the peak discharges were noted. Thirty-six percent
was the highest value of urban cover (table 5) measured
for any of the basins used in this study.

The standard error of estimate, expressed as a
percentage (%SE), is an approximate measure of the
reliability of the regression equation. The standard error
of estimate is a measure of the model error, whereas the


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37


Table 3. Estimated peak discharges for selected recurrence intervals and maximum known
discharges at stream-gaging stations on Oahu, Hawaii--Continued

Maximum known discharge

Station Q2 Os Q10 O05 O50 100 Water Discharge
number (ft3/s) year (£t3/s)
247500 554 1,070 1,530 2,260 2,920 3,700 1968 3,600
473 1,060 1,620 2,520 3,340 4,290
544 1,070 1,550 2,330 3,050 3,900
247900 375 809 1,260 2,080 2,920 4,010 1988 4,700
252 592 927 1,490 2,010 2,620
353 758 1,160 1,860 2,540 3,380
248800 335 847 1,310 2,010 2,600 3,240 1981 1,600

700 1,500 2,220 3,360 47380 5,590
362 920 1,450 2,300 3,070 3,960

249000 1,300 2,640 3,780 5,520 7,010 8,680 1963 4,560
1,050 2,310 3,460 5,260 6,870 8,770
1,280 2,590 3,720 5,450 6,970 8,710

249100 123 281 423 643 835 1,050 1988 467
168 330 474 703 912 1,160
127 287 432 658 858 1,090

254000 859 1,930 2,970 4,700 6,350 8,320 1965 6,000

1,010 2,220 3,310 5,030 6,570 8,390
870 1,960 3,020 4,770 6,410 8,340

260500 1,790 3,560 5,060 7,300 9,220 11,400 1965 9,690
1,990 4,550 6,890 10,600 13,700 17,700
1,800 3,670 5,340 8,020 10,400 13,300

265000 733 1,620 2,530 4,150 5,780 7,860 1969 5,290
692 1,480 2,190 3,320 4,330 5,520
728 1,600 2,450 3,900 5,270 6,910

270900 183 344 480 686 864 1,060 1971 651
343 703 1,030 1,540 2,000 2,550
201 403 602 943 1,270 1,660

273900 1,700 4,140 6,560 10,600 14,500 19,200 1969 12,000

1,730 3,920 5,930 9,080 11,200 15,200
1,700 4,110 6,430 10,200 13,400 17,700

274499 493 1,070 1,590 2,410 3,130 3,950 1965 2,750
437 909 1,330 2,000 2,610 3,320
489 1,050 1,550 2,320 2,990 3,750

275000 693 1,650 2,470 3,670 4,650 5,680 1965 5,740
599 1,270 1,880 2,830 3,690 4,710
688 1,620 2,410 3,540 4,470 5,470

278000 43 Wil 188 335 492 700 1965 797
256 515 TAT 1,110 1,450 1,840
61 162 285 522 710 1,080

279500 924 2,740 4,760 8,470 12,200 16,800 1965 5,600

926 2,020 3,010 4,570 5,960 7,610
924 2,630 4,400 7,070 10,100 13,300

283000 130 258 384 606 828 1,110 1965 1,730
250 502 727 1,080 1,410 1,790
138 283 433 702 970 1,300

33


Table 2. Peak-discharge statistics at stream-gaging stations on Oahu, Hawaii

[Bulletin 17B weighted statistics based on guidelines in Interagency Committee on Water Data
(1982); Std. dev., one standard deviation]

Peak-discharge statistics from logarithms of annual floods

Station Gaged record Bulletin 17B weighted
number Mean Std. dev. Skew Mean Std. dev. Skew
200000 3,382 0.218 ~0.572 3,382 0.218 0.424
201000 3.010 0.180 0.015 3.010 0.180 0.027
204000 3.401 0.120 0.547 3.401 0.120 0.262
1206000 2.956 0.243 0.655 2.979 0.203 0.021
208000 3.239 0.278 0,091 3.239 0.278 -0.076
1208500 2.703 0.551 -1.100 2.742 0.487 0.436
210500 3.301 0.498 -0.016 3.301 0.498 0.030
211200 3.049 0.541 0.527 3.049 0.541 0.301
211300 2.704 0411 0.043 2.704 0411 0.045
211500 2.354 0.588 0.059 2.354 0.588 0.056
211600 2.478 0.386 0.132 2.478 0.386 0.101
211700 2.708 0.483 0.045 2.708 0.483 0.005
211800 2.440 0.588 0.250 2.440 0.588 0.170
212200 2.424 0.662 0.693 2.424 0.662 0.419
212300 2.760 0.545 0.891 2.760 0.545 0.455
1212450 2.229 0.499 0.822 2.259 0.444 0.297
212500 2.732 0.573 0.713 2.732 0.573 0.420
1212601 2.590 0.490 -1.065 2.645 0.377 0.107
1212700 2.907 0.405 0.532 2.928 0.361 0.004
212800 3.275 0.227 0.508 3.275 0.227 0.285
213000 3.492 0.392 0.163 3.492 0,392 0.125
216000 3.908 0.321 0.625 3.908 0.321 -0.400
2216500 2.422 0.402 1.614 2.422 0.402 0.393
223000 3.244 0.370 0.051 3,244 0.370 0.051
1224500 2.925 0,306 0.807 2.940 0.274 0.253
226000 3.102 0.373 -0.057 3.102 0.373 -0.055
227000 3.296 0.264 0.195 3.296 0.264 0.128
228000 3.005 0.323 0.632 3.005 0.323 0.458
228200 3.056 0.333 0.586 3.056 0.333 0.318
128500 3.271 0.329 -1.252 3.302 0.279 0.425
228600 3.144 0.331 0.215 3.144 0.331 0.085
228900 2.586 0.451 ~0.782 2.586 0.451 ~0.410
229000 3.148 0.403 0.355 3.148 0.403 0.283
1229300 3.365 0.366 0.813 3.384 0.331 0.325
235400 2.732 0.377 0.348 2.732 0.377 0.231
237500 2.556 0.327 0.281 2.556 0.327 0.156
238500 2.827 0.322 0.106 2.827 0.322 0.070
240500 2.719 0.283 0.569 2.719 0.283 0.403
244000 2.620 0.349 0.017 2.620 0.349 0.025
246000 2.565 0.356 ~0.545 2.565 0.356 0.377

10


Results from table 10 show that for the north Oahu
region, the 50-year peak-discharge equation is about
twice as sensitive to possible 2-year, 24-hour rainfall -
intensity error than to drainage-area error. The opposite
is true in the leeward Oahu region where the percentage
of change in the computed 50-year flood is about twice
as large with possible drainage-area error than with
possible errors in median annual rainfall. The windward
Oahu region, with drainage area as the only variable,
had equations as sensitive to variations in drainage area
as did the other two regions. In general, likely errors in
measurement would not be greater than plus or minus
10 percent.

COMPARISON OF WEIGHTED AVERAGE 100-YEAR DISCHARGE
ESTIMATES WITH OTHER METHODS

Because new regression equations were derived to
estimate peak discharges, a graphical comparison was
made to see how these equations compare with other
methods of estimating peak discharge. This comparison
could help to determine which method is best for a
particular application. The graphical comparisons were
made by plotting the weighted average 100-year peak-
discharge estimates, which were determined by
equation 3 below, against the maximum known
discharge (table 3) and the peak-discharge estimates
determined by Bulletin 17B methods (Interagency
Advisory Committee on Water Data, 1982), the 1988
storm drainage standards (City and County of
Honolulu, 1988), and the 100-year peak-discharge
regression equations of Nakahara (1980). The data used
in these comparisons can be found in tables 3 and 11.
The plotted data and lines of equal value are shown in

figure 4,

Figure 4A shows the weighted average 100-year
peak-discharge estimates compared with the maximum
known discharges. Most of the discharges fall above
the line of equal value showing that most of the
weighted 100-year estimates are greater than the
maximum known discharges. Only 9 of the 79 gaging
Stations have maximum observed discharges greater
than the weighted average 100-year estimates. These are
for stations 229000, 240500, 247900, 275000, 283000,
283600, 283700, 284000, and 303000 (table 3). The
lengths of record for these 9 stations range from 19 to
72 years, and have an average of 42 years (table 1).

In figure 4B, the weighted average 100-year peak-
discharge estimates are plotted against the 100-year

20

peak discharges determined by Bulletin 17B methods
(Interagency Advisory Committee on Water Data,
1982). As can be seen, most of the points fall along the
line of equal value. This was expected because the
Bulletin 17B 100-year discharge estimates are the
observed data used to develop the 100-year peak-
discharge regression equations in tables 6 through 8.
The weighted average estimates are higher, however, in
the region around 1,000 ft/s (figure 4B).

Figure 4C shows the weighted average 100-year
peak-discharge estimates plotted against the discharge
estimates determined from plate 6 in the 1988 storm
drainage standards (City and County of Honolulu,
1988). The estimates from plate 6 are listed in table 11.
Most of the 77 discharge estimates fall below the line of
equal value in figure 4C. This shows that most of the
City and County discharge estimates are greater than the
weighted average 100-year peak-discharge estimates.
Of the 23 discharge estimates that fall above the line of
equal value, 12 are from sites located in leeward Oahu
and 11 from windward Oahu.

Figure 4D shows the weighted average 100-year
peak-discharge estimates plotted against the 100-year
peak-discharge estimates from the regression equations
of Nakahara (1980). This figure shows that the
equations of Nakahara (1980) provide estimates that
generally are larger than the weighted average 100-year
peak-discharge estimates from this study. Only 27 of
the 72 estimates fell above the line of equal value. In
comparing the regression equations between these two
studies, in Nakahara's (1980) report, the %SE varied
from 33 to 67 percent, and averaged 48 percent. The
regression equations from this study had an average
%SE of 39 percent. This results in a difference between
the averages of about 9 percent in the %SE. Thus, the
addition of 10 years of data along with improved
computational techniques has improved in %SE of the
regression equations.

ESTIMATION OF PEAK DISCHARGE USING
REGRESSION EQUATIONS

This section provides methods and examples for
computing a peak discharge for a selected recurrence
interval at a specific site. Two methods are provided for
use depending on if the site is gaged or ungaged. Both
methods use the regression equations in tables 6
through 8 for estimating peak discharges on Oahu. The


ESTIMATION OF MAGNITUDE AND FREQUENCY OF FLOODS FOR STREAMS

ON THE ISLAND OF OAHU, HAWAII
By Michael F. Wong
ABSTRACT

This report describes techniques for estimating
the magnitude and frequency of floods for the
island of Oahu. The log-Pearson Type III
distribution and methodology recommended by the
Interagency Committee on Water Data was used to
determine the magnitude and frequency of floods
at 79 gaging stations that had 11 to 72 years of
record. Multiple regression analysis was used to
construct regression equations to transfer the
magnitude and frequency information from gaged
sites to ungaged sites. Oahu was divided into three
hydrologic regions to define relations between peak
discharge and drainage-basin and climatic
characteristics. Regression equations are provided
to estimate the 2-, 5-, 10-, 25-, 50-, and 100-year
peak discharges at ungaged sites. Significant basin
and climatic characteristics included in the
regression equations are drainage area, median
annual rainfall, and the 2-year, 24-hour rainfall
intensity. Drainage areas for sites used in this study
ranged from 0.03 to 45.7 square miles. Standard
error of prediction for the regression equations
ranged from 34 to 62 percent.

Peak-discharge data collected through water
year 1988, geographic information system (GIS)
technology, and generalized least-squares
regression were used in the analyses. The use of
GIS seems to be a more flexible and consistent
means of defining and calculating basin and
climatic characteristics than using manual methods.
Standard errors of estimate for the regression
equations in this report are an average of 8 percent
less than those published in previous studies.

INTRODUCTION

Available peak-discharge data are used in flood-
frequency studies to estimate the magnitude and
frequency of floods that can occur at gaged sites.
Estimates of magnitude and frequency of floods are
used when planning and designing structures such as

dams, bridges, culverts, highways, and buildings.
These estimates are also needed at ungaged sites.
Estimates at ungaged sites may be computed by
regression of flood magnitude and frequency
information at gaged sites with drainage-basin and
climatic characteristics. Because of the need for
assessing existing storm-drainage design standards, and
for preparing new standards, the Department of Public
Works, City and County of Honolulu, entered into a
cooperative study with the U.S. Geological Survey
(USGS) to develop estimates of the magnitude and
frequency of floods for the island of Oahu.

PURPOSE AND SCOPE

The purpose of this report is to present, for
unregulated streams on the island of Oahu, estimates of
the magnitude and frequency of floods at gaged sites
and techniques that can be used to estimate the
magnitude and frequency of floods at ungaged sites. In
addition, this report compares the results of applying
Tegression equations to observed peak discharges, the
log-Pearson Type III estimates, estimates from the
design curves in the 1988 City and County of Honolulu
storm drainage standards, and estimates from
regression equations by Nakahara (1980).

This report uses peak-discharge data collected
through water year 1988 at 79 gaging stations on the
island of Oahu, Bulletin 17B guidelines (Interagency
Advisory Committee on Water Data, 1982) for flood-
frequency analysis, multiple regression techniques,
generalized least-squares regression analysis designed
for use with peak-discharge data, and geographic
information system (GIS) technology for computing
drainage-basin and climatic characteristics.

DESCRIPTION OF STUDY AREA

For this flood-frequency study, information on the
physiographic and climatic characteristics related to
flood hydrology is used to select drainage-basin and
climatic characteristics that can influence the magnitude
of floods. This information is also used to delineate
regional hydrologic boundaries.


Table 3. Estimated peak discharges for selected recurrence intervals and maximum known
discharges at stream-gaging stations on Oahu, Hawail--Continued

Maximum known discharge

Station Q2 Os Q10 O25, O50 Q100 Water Discharge
number (£t3/s) year (£t3/s)
212200 295 978 1,730 3,040 4,280 5,730 1982 2,460

267 646 1,030 1,670 2,280 2,990
292 926 1,580 2,670 3,670 4,800

212300 632 1,680 2,670 4,210 5,530 6,990 1976 3,320
331 905 1,530 2,630 3,710 5,020
582 1,510 2,350 3,650 4,810 6,140

212450 191 434 49 976 1,260 1,560 1980 724
236 606 991 1,660 2,300 3,060
199 471 TAS 1,220 1,670 2,200

212500 592 1,670 2,730 4,440 5,970 7,690 1982 3,500

890 2,230 3,600 5,890 8,050 10,600
630 1,760 2,920 4,850 6,640 8,720

212601 448 920 1,330 1,950 2,500 3,110 1982 1,850
801 1,860 2,900 4,580 6,130 7,920
491 1,070 1,670 2,670 3,640 4,770

212700 849 1,710 2,460 3,630 4,670 5,850 1963 4,830
1,880 3,530 4,960 7,030 8,800 10,700
972 2,000 2,980 4,540 5,940 7,490

212800 1,840 2,900 3,740 4,950 5,970 7,100 1963 5,680
2,600 4,010 5,100 6,560 7,730 8,970
1,930 3,070 4,020 5,370 6,500 7,720

213000 3,160 6,660 9,730 14,500 18,600 23,300 1955 13,600
4,090 8,660 12,900 19,300 24,900 31,100
3,260 6,940 10,300 15,600 20,300 = 25,700

216000 8,500 15,200 20,100 26,500 31,300 36,200 1982 27,900
4,040 7,750 11,000 15,600 19,600 23,900
8,030 14,200 18,400 23,900 28,100 32,400

216500 249 564 895 1,510 2,140 2,970 1955 2,810
468 1,070 1,660 2,620 3,500 4,520
297 705 1,160 1,990 2,790 3,770

223000 1,770 3,600 5,200 7,670 9,840 12,300 1968 8,020

1,820 3,310 4,570 6,370 8,000 9,560
1,780 3,560 5,080 7,340 9,310 11,400

224500 895 1,490 1,920 2,480 2,920 3,360 1963 2,580
928 1,740 2,450 3,490 4,390 5,380
898 1,530 2,020 2,730 3,340 4,000

226000 1,280 2,610 3,780 5,600 7,190 9,000 1932 6,650
1,490 2,580 3,480 4,760 5,830 6,980
1,300 2,610 3,730 5,410 6,840 8,420

227000 2,000 3,300 4,260 5,560 6,590 7,660 1966 6,570
1,900 3,670 5,210 7,500 9,460 11,600
1,980 3,380 4,540 6,260 7,760 9,400

228000 1,070 1,910 2,510 3,290 3,870 4,440 1931 4,580
1,250 2,180 2,950 4,050 4,960 5,970
1,080 1,930 2,560 3,410 4,070 4,750

31


Table 6. Regression equations for estimating peak discharges for streams in leeward Oahu
(region 1), Hawaii

{DA, drainage area; P, median annual rainfall]

Equivalent

Bias-correction Standard error (percent) years
Regression equation factor R2 of estimate _ of prediction of record
Q = 3.26 (DA0-34) (p1.08) (1.115) 0.74 40 43 42
Qs = 25.8 (DA0642) (p0.773) (1.069) 0.73 38 40 58
Qio = 73.5 (DA-46) (p0.621) (1.052) 0.72 36 39 82
Qs = _ 217 (DA0-646) (p0.464) (1.040) 0.71 35 38 114
Qo = 425 (DA-45 y( p0.368) (1.037) 0.70 35 38 13.7
Qioo = 758 (DA°-43) (p0.286) (1.040) 0.69 35 39 15.8

Table 7. Regression equations for estimating peak discharge for streams in windward Oahu
(region 2), Hawaii

[DA, drainage area]

Equivalent
Bias-correction Standard error (percent) years
Regression equation factor R2 of estimate _ of prediction of record
Q = = 525 (DA0-104) (1.165) 0.75 58 62 25
Qs = 1140 (DA2748) (1.138) 0.80 53 58 3.9
Qio = 1700 (DA®.763) (1.129) 0.82 50 54 57
Qs = 2580 (DA2-773) (1.124) 0.83 46 52 8.6
Qs = 3360 (DA2776) (1.125) 0.83 45 51 11.0
Qioo = 4250 (DA2777) (1.133) 0.83 44 50 13.6
Table 8. Regression equations for estimating peak discharge for streams in north Oahu
(region 3), Hawaii
[DA, drainage area; P224, 2-year, 24-hour rainfall intensity]
Equivalent
Bias-correction Standard error (percent) years
Regression equation factor R2 of estimate _of prediction _of record
Q — = 0.00356 (DA2870) (p2745-85) (1.036) 0.90 38 45 3.6
Q5 = 0.151 (DA0-836) (p2244.30) (1.000) 0.90 27 34 8.3
Qio = 1.76 (DA0-805) (p2243.24 (1.000) 0.86 27 34 10.2
Qs = 24.8 (DA0-777) (p2242-10) (1.000) 0.78 31 38 10.7
Q5) =. 125 (DA0-765) (p2241.39) (1.000) 0.70 34 43 10.5
Qtoo = 500 (DA°758) (p2240-792) (1.011) 0.61 39 48 10.1

17


Table 11. Additional data used in comparing the weighted 100-year peak discharge estimates with
other methods for Oahu, Hawaii

[Hydrologic regions shown in fig. 1: 1, leeward Oahu; 2, windward Oahu; 3, north Oahu; Plate 6 curves and discharge
from Storm Drainage Standards (City and County of Honolulu, 1988); ft3/s, cubic feet per second; previous 100-year
peak discharge from Nakahara (1980); --, no data]

Plate 6 Previous 100-year peak

Hydrologic Areain 100 _—_— Plate 6 curve discharge discharge
Station number region acres used (ft3/s) (ft3/s)
200000 1 8.8 B 3,600 5,020
201000 1 77 B 3,450 4,520
204000 1 311 B 9,500 10,500
206000 1 124 B 4,750 -
208000 1 25.8 B 8,100 8,810
208500 1 5.5 B 2,700 2,950
210500 1 248 B 42,000 35,700
211200 1 81.2 B 19,000 15,100
211300 1 26.6 Cc 5,300 5,370
211500 1 271 Cc 5,500 4,940
211600 1 148 Cc 3,500 3,380
211700 1 33.6 Cc 6,200 5,200
211800 1 22.9 Cc 4,850 4,660
212200 1 9.7 Cc 2,600 2,580
212300 1 25.5 Cc 5,100 -
212450 1 10.9 Cc 3,100 2,210
212500 1 70.4 Cc 11,000 9,930
212601 1 40.6 B 12,000 5,310
212700 1 4719 B 13,000 4,550
212800 1 274 B 8,900 9,490
213000 1 292 B 50,000 24,500
216000 1 169 B 33,000 31,600
216500 1 16.8 B 6,100 2,580
223000 1 38.2 B 10,600 11,700
224500 1 16.6 B 6,000 5,890
226000 1 22.1 B 7,500 8,340
227000 1 56.2 B 14,900 14,300
228000 1 17.5 B 6,200 6,870
228200 1 214 B 7,200 -
228500 1 26.6 B 8,700 9,570
228600 1 28.4 B 9,000 -
228900 1 38 B 2,000 1,990
229000 1 16.7 B 6,000 6,560
229300 1 33.2 B 9,600 8,980
235400 1 8.2 B 3,500 2,940
237500 1 9.2 B 3,900 2,830
238500 1 713 B 3,300 3,380
240500 1 6.8 B 3,100 3,260
244000 1 716 B 3,400 3,060
246000 1 6.6 B 3,000 3,040
247000 1 23.2 B 7,600 6,880
247100 1 67.8 B 16,500 11,900
247200 1 11.2 B 4,500 4,330
247500 1 15.0 B 5,500 6,040
247900 1 76 B 3,400 -

23


Table 9. Statistical summary of selected drainage-basin, climatic, and flood-frequency characteristics
by regions for Oahu, Hawaii

{Min-Max, range of minimum to maximum values; Std.dev., one standard deviation; A, draiange area; P, median
annual rainfall; P224, 2-year, 24-hour rainfall intensity; UC, urban cover]

Region
Characteristic 1 (Leeward) 2 (Windward) 3 (North)
Number of stations... 46 20 13
Mean interstation cross-correlation! 0.41 0.50 0.45
Mean gaged record skew.. 0.282 -0.363 0.206
DA (square miles) 0.60-45.7 0.03-5.34 1.11-13.5
3.52 0.98 2.98
6.11 141 432
9.05 1.38 3.54
P (inches)...... 29-239 52-146 66-197
95 98 140
98 99 135
52 28 48
P224 (inches)... 4.72-8.78 5.62-9.10 ° 5.21-9.04
6.34 7.10 7.05
6.50 749 TAL
1.12 0.883 1.10
UC (percent)...... 0-32 0-36 0-0
0 0 0
Mean 5 5 0
Std.dev. 9 10 0
Years of record Min-Max 11-72 13-49 21-35
Median 30 26 30
Mean 31 27 28
Std.dev. 15 9 5

\computed from the cross-correlation matrix in the GLSNET program

Table 10. Results of sensitivity analysis showing percentage of change in computed 50-year peak
discharges within each of the three hydrologic regions on Oahu, Hawali
(DA, drainage area; P, median annual rainfall; P224, 2-year, 24-hour rainfall intensity]
Change in computed 50-year peak discharge (percent)
Error in explanatory variable (percent)
Explanatory variable =30 -20 -10 0 +10 +20 +30
Region 1 (Leeward)
DA

-20.5 -13.4 6.5 0.0 64 12.5 18.5
12.3 78 3.8 0.0 3.6 70 10.2
Region 2 (Windward)
DA... ww 24,2 -16.0 -19 0.0 716 15.1 22.5
Region 3 (North)
DA -23.9 -15.7 -17 0.0 716 15.0 22.3
P224. =39.0 ~26.7 -13.6 0.0 14.2 28.8 44.0

19


Table 3. Estimated peak discharges for selected recurrence intervals and maximum known
discharges at stream-gaging stations on Oahu, Hawaii--Continued

Maximum known discharge

Station Q2 Qs 210 025 O50 Q100 Water Discharge
number (ft/s) year (£t3/s)
228200 1,180 2,190 2,950 3,990 4,810 5,660 1980 4,860

1,340 2,380 3,240 4,490 5,540 6,680
1,210 2,230 3,030 4,170 5,110 6,110

228500 2,100 3,470 4,410 5,590 6,450 7,300 1968 4,150
1,340 2,500 3,450 4,880 6,090 7,420
1,890 3,140 4,000 5,230 6,250 7,370

228600 1,380 2,640 3,720 5,410 6,900 8,600 1980 6,200
1,340 2,510 3,510 4,990 6,260 7,650
1,370 2,610 3,650 5,250 6,620 8,160

228900 414 937 1,380 2,030 2,570 3,140 1980 1,700
458 800 1,080 1,490 1,840 2,220
421 907 1,300 1,840 2,280 2,740

229000 1,470 3,100 4,470 6,490 8,180 10,000 1931 12,400

1,170 2,070 2,810 3,870 4,710 5,740
1,450 3,020 4,300 6,130 7,630 9,230

229300 2,520 4,640 6,240 8,410 10,100 11,900 1974 7,110
1,490 2,790 3,910 5,540 6,940 8,470
2,390 4,320 5,710 7,580 9,060 10,700

235400 558 1,130 1,600 2,300 2,880 3,510 1963 2,500
567 1,080 1,510 2,170 2,740 3,380
559 1,120 1,580 2,260 2,840 3,460

237500 353 674 956 1,400 1,800 2,260 1963 2,200
538 1,060 1,510 2,210 2,820 3,510
375 735 1,070 1,620 2,110 2,680

238500 666 1,250 1,740 2,500 3,160 3,900 1921 3,250

657 1,170 1,590 2,210 2,740 3,320
665 1,240 1,720 2,460 3,080 3,780

240500 501 891 1,230 1,780 2,290 2,880 1921 3,090
609 1,090 1,500 2,090 2,590 3,150
507 906 1,260 1,820 2,340 2,930

244000 418 821 1,160 1,690 2,150 2,660 1930 2,600
570 1,060 1,480 2,110 2,650 3,250
429 843 1,200 1,760 2,250 2,790

246000 387 740 1,010 1,380 1,670 1,960 1930 1,550
492 933 1,310 1,890 2,390 2,940
396 762 1,060 1,480 1,840 2,210

247000 1,360 2,280 2,970 3,920 4,680 5,470 1968 4,270

908 1,830 2,660 3,920 5,030 6,280
1,300 2,200 2,900 3,920 4,800 5,770

247100 2,900 5,320 7,140 9,610 11,500 13,500 1968 10,100
1,890 3,790 5,480 8,020 10,200 12,700
2,730 4,990 6,670 9,050 11,000 13,200

247200 919 1,440 1,790 2,240 2,570 2,900 1958 2,010
431 936 1,410 2,170 2,860 3,640
784 1,270 1,630 2,200 2,730 3,340

32


The convenience and precision in determining the
drainage-basin characteristics were greatly improved by
using the GIS. The use of GIS therefore allowed for a
larger number of characteristics to be considered in the
regression analysis. Among these characteristics were a
number of different basin-shape factors (CLD, PA, and
RF). However, the drainage areas computed from GIS
(DAG) compared with the previously determined
drainage areas (DA) had an mean absolute difference of
0.09 mi2. Ideally, there should be no difference. A
further review of the drainage areas showed that only
two DA's had differences greater than 10 percent, when
compared with the DAG's. These two stations, 211200
and 247100, accounted for 43 percent of the differences
in drainage area. For these two stations, the original
computations were found in error. Drainage areas for
the two stations were revised to the DAG values. After
these corrections, the mean absolute difference between
the DA's and DAG's was 0.05 mi. Because of this
difference, a hypothesis test was done to see if there
were any differences in the mean values between the
DA's and DAG's. For this test, the null hypothesis was
that no differences exist. Using the nonparametric
Wilcoxon signed-ranks tests (Iman and Conover, 1983)
with a significance level of 1 percent (0.01), the null
hypothesis was accepted with a p-value of 0.79. The p-
value being the smallest significance level that would
allow the null hypothesis to be rejected (Iman and
Conover, 1983). Therefore, the use of the GIS-derived
characteristics is acceptable. However, because all the
DA values are previously published, the DA's were
used except for the two stations where corrections were
made in the regression analysis.

REGRESSION ANALYSIS

The ordinary least-squares estimator used in
traditional regression analysis assumes that the errors or
residuals are random, uncorrelated, normally
distributed, and have equal standard deviations (Draper
and Smith, 1981). Therefore, all stations used in the
regression analysis are given equal weight. However,
these conditions are not always met with hydrologic
data, because streamflow records at gaged sites used in
the regression analysis are of different record lengths.
In addition, cross-correlation of concurrent flows
among nearby gaged sites can exist (Stedinger and
Tasker, 1985). To solve these problems, Tasker (1980)
used a weighted least-squares estimator to correct for
unequal record length. Later, Stedinger and Tasker

14

(1985) developed a generalized least-squares estimator
that accounts for cross-correlation among sites as well
as for unequal record length. Both the weighted least-
squares and generalized least-squares estimators assign
each station a different regression weight to improve
model accuracy. Where the ordinary least-squares
assumptions were violated it has been shown that
weighted least-squares and generalized least-squares
estimators are appropriate and provide reduced standard
errors of estimate for the regression equations
(Stedinger and Tasker, 1985).

For the regression analysis, the peak discharges for
specified recurrence intervals were the dependent
variables and the drainage-basin and climatic
characteristics were the independent variables. The
multiple regression technique requires that dependent
and independent variables be linearly related.
Examination of the flood peaks and the basin and
climatic characteristics along with previous studies
(Thomas and Benson, 1970), has shown that the
logarithmically transformed characteristics are linearly
related. Therefore, the variables in this study were
transformed by using the common (base 10) logarithm.

After transforming the variables, the first step of the
regression analysis was to determine the significant
independent variables for each peak-discharge
characteristic. This was done by using correlation and
stepwise regression procedures. Correlation measures
the degree of linear relation between two variables. In
addition to calculating the degree of correlation between
the dependent and independent variables, correlations
between all pairs of independent variables were also
determined. Because high correlation between two
independent variables tends to reduce the statistical
significance of each variable involved in regression
analysis, only the more significant and reliable one
should be retained.

The stepwise regression procedure was used to
determine the most statistically significant predictor
variables. In this procedure, variables are added or
deleted one by one into the regression model according
to their level of significance for entry and retention
(Draper and Smith, 1981). In this study, an entry and
retention significance level of 0.05 (5 percent) was used
in the stepwise regression F-test to limit the number of
variables. Also, the use of the 5-percent significance
level generally limited the final regression equations to


(1973). Cheng and Lau used the Gumbel distribution to
develop flood-frequency curves for gaged streams and
the index-flood method (Dalrymple, 1960) to provide
regionalized flood-frequency estimates. Results from
the index-flood method regionalized Oahu into four
contiguous and one non-contiguous region.

An analysis of the stream-gaging network in
Hawaii by Yamanaga (1972) derived regression
equations for peak flow, mean flow, flow variability,
flood volume, and low flow for the entire State of
Hawaii. The peak-flow equations were for the 2-, 5-,
10-, 25-, and 50-year recurrence intervals and were
geographically regionalized into two regions, the
windward and leeward sides of each island in the State.
These equations related the estimates computed by the
log-Pearson Type III distribution to various
combinations of drainage-basin and climatic
characteristics. Among the characteristics used were
drainage area, main channel length, mean basin altitude,
mean annual precipitation, percentage of gentle slope,
and range in basin altitude. Standard errors of estimates
for the regression equations ranged from 42 to 63
percent.

In 1975 the USGS (Lee, 1978) derived regional
flood-frequency regression equations for Oahu. This
study "regionalized" Oahu by drainage-basin size but
not geographically. However, the study remained
unpublished because of some doubt regarding the
“uniformity” of flood-flow frequencies at that time
(Reuben Lee, written commun., 1978). Nakahara in
1980 applied multiple regression analysis for regional
analysis and divided Oahu into three regions using the
method of residuals (Nakahara, 1980). Flood estimates
for the 2-, 5-, 10-, 25-, 50-, and 100-year recurrence
intervals using guidelines from Bulletin 17A (U.S.
Water Resources Council, 1977) were related to
drainage area, forest cover, and the 2-year, 24-hour
rainfall. Standard errors of estimates for the regression
equations ranged from 33 to 67 percent.

Wong (1991) compared the index-flood method,
cluster analysis, and method of residuals for the
regionalization of drainage basins on Oahu. Results
showed that all three methods gave comparable
regression standard errors of estimates. The method of
residuals was used to regionalize Oahu into four
regions. Standard errors of prediction for the
generalized least-squares regression equations ranged

from 18 to 57 percent.

The present study improves on the work by Wong
(1991) and differs from other previous flood-frequency
studies for Oahu by using additional gaging stations,
longer periods of record, updated guidelines (Bulletin
17B), GIS procedures for computing drainage-basin
and climatic characteristics, and generalized least-
squares regression techniques.

DATA BASE FOR REGRESSION EQUATIONS

Flood-frequency estimates at gaged sites can be
transferred to ungaged sites by regression analysis. For
regression analysis, both the dependent and independent
variables must be available in quantitative form. The
applicability of the derived regression equations
depends on reliable and consistent information derived
from records of peak discharge at gaging stations, a
method to estimate magnitude and frequency of floods,
and procedures to estimate drainage-basin and climatic
characteristics.

ANNUAL PEAK-DISCHARGE DATA

The most fundamental part of a flood-frequency
study is the collection and analysis of annual peak-
discharge data. The annual peak discharge is the largest
instantaneous discharge recorded each year at gaged
sites. As of water year 1988, there were 70 active
gaging stations on Oahu, of which 28 were (continuous
recording) streamflow-gaging stations and 42 were
crest-stage gaging stations (Nakahara and others, 1989).
A continuous-recording gage collects data on the entire
range of streamflows, whereas a crest-stage gage
collects only peak-discharge data. In addition, peak-
discharge data have been collected at gaging stations
that have subsequently been discontinued.

Bulletin 17B guidelines (Interagency Advisory
Committee on Water Data, 1982) recommend a
minimum of 10 years of data for flood-frequency
studies. The use of the 10-year data minimum allows
for a good representative sample of the type of flood
data involved. Because of climatic changes, a small
sample may not be representative of all flow
possibilities. Wu (1967) determined that for Oahu, wet
and dry years alternated in cycles of 3 to 4 years and
recommended a 12-year data minimum. A review of
the current annual peak-discharge data show that this 3
to 4 year cycle was more apparent in the annual peak-


D., eds., Catastrophic flooding: Boston, Allen and
Unwin, p. 267-288.

U.S. Geological Survey, 1987, Digital Elevation Models
(DEM) data user guide 5, USGeoData, National
Mapping Program, Technical Instructions: U.S.
Geological Survey, 38 p.

U.S. Water Resources Council, 1967, A uniform
technique for determining flood flow frequencies:
Washington D. C., Hydrology Committee Bulletin 15,
15 p.

, 1977, Guidelines for determining flood flow
frequency: Hydrology Committee Bulletin 17A,
Washington D. C., 26 p., app. 1-14.

Vaudrey, W.C., 1963, An investigation of floods in
Hawaii with selected data on magnitude and
frequency, Progress Report No. 5: U.S. Geological
Survey Basic Data Release, 192 p.

Wiltshire, S.E., 1985, Grouping basins for regional flood
frequency analysis: Hydrological Sciences Journal,
v. 30, no. 1, p. 151-159.

Wong, M.F., 1991, Regionalization of peak discharges
for streams on the island of Oahu, Hawaii: Honolulu,
University of Hawaii, Master's thesis, 120 p.

Wu, I-Pai, 1967, Hydrological data and peak discharge
determination of small Hawaiian watersheds: Island
of Oahu, Technical Report No. 15: Honolulu, Hawaii,
University of Hawaii Water Resources Research
Center, 97 p.

Yamanaga, George, 1972, Evaluation of the streamflow-
data program in Hawaii, U.S. Geological Survey
Open-File Report, 28 p.

29


O50, = 425(2.730-645 (124 9368 )(1.037),
= 425(1.911)(5.894)(1.037),
= 4,964 f3/s or 4,960 ft3/s, (table 3).

From table 3, the 50-year peak discharge based on the
gaged record (Qso_) is 3,870 ft3/s. The number of years
of record (N) for the gaged record estimate is 61 years
(table 1). The weighted average estimate of the 50-year
peak can now be determined from equation 3.

Qsp,, =[(3,870)(61) + (4,960)(13.7)] / (61 + 13.7),
= (236,070 + 67,952) / 74.7,
= 304,022 / 74.7 = 4,070 ft3/s (table 3).

Therefore, the weighted average estimate of the 50-
year peak discharge at Moanalua Stream (station
228000) is 4,070 ft3/s,

Example 2. Ungaged site near a gaged site on the same
Stream: Estimate the 10-year peak
discharge at an ungaged site upstream of
station 294900, Waikane Stream.

First, check to see if this site is affected by
significant diversions, regulation, or urbanization.
Next, determine in which region the ungaged site is
located. This site is in the windward Oahu region and
there are no significant diversions, regulation, or
urbanization present. The equation to estimate the 10-
year flood is found in table 9:

Qo,= 1,700 (DAP73\(1.129). 0)

For this ungaged site the drainage area is 1.57 mi,
which falls within the range of drainage area values
given in table 13, so that equation 7 can be used. To use
equation 4, the drainage area of the ungaged site must
fall within the 50- to 150-percent limits of drainage area
at the gaged site and be on the same stream. The
drainage area of station 294900 is 2.22 mi? (table 4)
and the 50- to 150-percent lower and upper limits of
drainage area are 1.11 to 3.33 mi2, Because the drainage
area of the ungaged site falls within these limits,
equation 4 can be used. The regression estimate is:

Qo, = 1,700(1.579763)(1.129) = 1,700(1.411)(1.129)
= 2,710 ft3/s.

If the drainage area were less than 1.11 or greater
than 3.33 mi2, then the final estimate for this ungaged
site would be 2,710 ft3/s. The weighted average

26

estimate at the gaged site, station 294900, is 5,830 ft3/s
and the regression estimate is 3,530 ft3/s (table 3).
Applying equation 4 gives:

R = 5,830/3,530 = 1.652, and
Cy = 1.652 - [2(12.22 -1.571y2.22](1.652 — 1.0),
= 1.652 - (0.5856)(0.652),
= 1.652 - (0.3818) =1.270.

Therefore, the final 10-year peak discharge for the
ungaged site, Qo, is

Q10,= Cu (Qo, ) = (1.270)(2,710) = 3,440 ft/s.
SUMMARY

To adequately design bridges, flood control
structures, and buildings located in or adjacent to flood
plains, a reasonable estimate of flood magnitude and
frequency is necessary. Flood-frequency and regression
analyses were used to develop equations for estimating
the 2-, 5-, 10-, 25-, 50-, and 100-year peak discharges
for gaged and ungaged streams on Oahu. Flood-
frequency analysis using the log-Pearson Type III
distribution was done on 79 gaging stations with 11 to
72 years of record. Regression analysis techniques were
used to improve estimates for gaged sites and to
transfer gaged-site estimates to ungaged sites. This
study differs from past studies by using peak-discharge
data collected to water year 1988, additional gaging
Stations, geographic information systems (GIS)
technology, generalized least-squares regression
analysis, and updated flood frequency guidelines.

For regression analysis, peak-discharge estimates
for selected frequencies determined by applying the log-
Pearson Type III distribution to the peaks of record
were related to basin and climatic characteristics. Most
characteristics were computed by GIS. The use of GIS
was found to be a more convenient and consistent
means of defining and calculating basin and climatic
characteristics than the manual methods.

To improve the standard errors of the regression
equations, Oahu was divided into three hydrologically
similar regions. These regions are leeward, windward
and north Oahu. Drainage-basin and climatic
characteristics included in the regression equations are
drainage area and median annual rainfall for the leeward
Oahu region, drainage area for the windward Oahu


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PHYSIOGRAPHY

The island of Oahu is located in the Pacific Ocean at
about latitude 21°30'N and longitude 158°W (fig. 1).
Oahu, with an area of 608 mi, is the third largest island
of the Hawaiian island chain. Like the other Hawaiian
islands, Oahu was created by volcanic activity and
shaped by erosional forces. The current topography is
dominated by two mountain ranges, the Koolau and the
Waianae, both of which are eroded remnants of great
elongated shield volcanoes (Macdonald and others,
1983). The two ranges are approximately parallel and
trend northwest to southeast (fig. 1). The Koolau Range
ranges in altitude from sea level to 3,150 ft, with most
of the crest at altitudes of 2,000 to 2,700 ft. The Koolau
Range is characterized by steep cliffs onthe
northeastern (windward) face and slopes incised by
large, deep valleys on the southwestern (leeward) side
(Amnstrong, 1983). The Waianae Range is similar, but
has its steep cliffs on the southwestem side and slopes
incised by large, deep valleys on the northeastern face
(Amnstrong, 1983). Altitudes range from sea level to
4,025 ft on the Waianae Range, but most of the crest is
between 2,000 and 3,000 ft. Most drainage basins,
regardless of shape, are characterized by amphitheater-
shaped valley heads, steep walls, and gently sloping
floors. Two basin shapes are predominant: the long,
narrow valleys with V-shaped cross-sections and the
short, broader valleys (fig. 2). Most short, broad valleys
are along the windward side of the Koolau Range.
Similar shapes are found along the southwestem side of
the Waianae Range. Long, V-shaped basins are found
on the leeward side and northern part of the Koolau
Range and along the northeastern side of the Waianae
Range.

CUMATE

Oahu has a warm, humid climate and two seasons
per year: a wet winter season from October through
April and a dry summer season from May through
September (Blumenstock and Price, 1967).
Temperature is fairly uniform, both spatially and
temporally, usually ranging between 60 and 80°F.
Rainfall varies seasonally, and most precipitation falls
during the wet season. The median annual rainfall of 20
to 275 in/yr varies spatially (Division of Water and
Land Development, 1982). The wide spatial distribution
of rainfall is caused by the prevailing northeasterly trade
winds and the topography of the island. Orographic

lifting and cooling of the trade winds produces heavier
and more frequent rainfall on the windward side and
near the crest of the Koolau Range. The Waianae
Range, lying in the rain shadow of the Koolau Range,
receives significantly less rainfall.

FLOOD HYDROLOGY

Floods on Oahu, other than those generated by high
ocean waves, are caused by high-intensity rainfall.
Because the predominant northeasterly trade winds do
not usually bring flood-producing rainfall, most major
rainstorms are caused by the non-trade wind or Kona-
wind condition. The Kona-wind condition frequently
occurs from October through April and can bring
intense local showers affecting a small area, sometimes
with thunder and lighting, or it can blanket the entire
island with rain. A review of 2,317 recorded annual
peak discharges with known dates shows that 89
percent of the peaks occurred between October and
May (fig. 3). This distribution of peak discharges
follows the general seasonality of Kona-wind storms.
Hurricanes and tropical storms can also bring heavy
rains as well as high waves. Unrelated to the above
conditions are rare storms caused by low pressure areas
in the upper atmosphere (Blumenstock and Price,
1967). When this condition exists, trade-wind
conditions are capable of producing heavy downpours
(Eker and others, 1971). In fact, some of Oahu's
heaviest rains, such as the New Year's Eve Storm of
1987-88 (Division of Water and Land Development,
1988), have been caused by upper-level low pressure
areas above trade winds.

High-intensity rainfall, small drainage-basin size,
Steep basin and stream slopes, and little channel storage,
produce floods that are flashy. Most drainage basins
have rapid runoff response to rainfall characterized by a
Steep triangular shaped hydrograph and usually with a
time to peak of less than 1 hour (Ekern and others,
1971). Most drainage basins are not homogeneous, and
have different characteristics in upstream and
downstream areas. In general, the upstream ends of
basins are steep mountain slopes, which cause rapid
rates of runoff, and the downstream ends are flat coastal
plains, which result in slower rates of runoff. Extreme
floods also transport large volumes of sediment,
including large boulders, which can scour, damage, and
inhibit flood control works and other hydraulic
structures located downstream. Damaging floods, at


two or three variables. The stepwise procedure was run
for each recurrence interval (2-, 5-, 10-, 25-, 50-, 100-
year) for the whole island and all the individual regions
that were identified.

In choosing variables and regions, a study of the
standard error of estimate in percent (%SE) and the
coefficient of determination, R?, was done on the
stepwise regression results. The %SE is the measure of
model error and lack of fit of the regression equation,
while the R2 is the fraction of the total variability of the
observed dependent variables explained by the
independent variables. In general, use of statistically
significant predictor variables minimized the %SE and
maximized R?. The chosen variables were then used to
develop the regression equations. The resulting
regression equations have the form:

Q, =a(X;"!)(X,°?)...(X,0")(BCF) (1)
where:
Q, = a flood of ¢ (years) recurrence
interval,
X,X2,..., X, = basin and/or climatic characteristics,

a= the regression constant,
bl, 52,..., bn = the regression coefficients or
exponents of the basin and/or
climatic characteristics, and
BCF = the bias-correction factor.

The bias-correction factor is used to correct for
retransformation bias that results when the logarithmic
transformation is used. The use of the bias-correction
factor will give the mean value of predicted discharge,
while not using the bias-correction factor will provide
the median value. Because peak discharge is log-
normally distributed about the regression curve
(Choquette, 1988), the use of the bias-correction factor
will result in a more conservative estimate of peak
discharge. In this study the bias-correction factor was
determined by the "smearing estimate" (Duan, 1983).

The generalized least-squares estimator in the
GLSNET program in ANNIE (Lumb and others,
1990; G.D. Tasker, written commun., 1990) was then
used to compute the final regression equations. The
final models were checked to ensure that all
independent variables were statistically significant, the
coefficients of the independent variables were
hydrologically reasonable, correlation between

15

independent variables was not significant, the standard
error was minimized, the coefficient of determination
was maximized, overly influential observations were
not present, and that residual variances were constant.

REGIONALIZATION OF FLOOD-FREQUENCY ESTIMATES

Regional analysis is a procedure of extending
streamflow records in space (Riggs, 1973). Because
streamflow records are collected at only a few of the
many sites where information is needed, streamflow
characteristics are commonly estimated at ungaged sites
using information obtained from gaged sites. Regional
analysis may also produce improved estimates of the
flow characteristics at the gaged sites (Riggs, 1973).

For regional analysis, basins with similar flood
response or characteristics are grouped into
homogeneous regions. Homogeneity of the region's
flood characteristics can reduce errors in estimates of
peak flood discharge for gaged and ungaged sites,
whereas heterogeneity can increase the estimation error
in these flood estimates (Lettenmaier and others, 1987).
The simplest method of regionalization has been to
group basins geographically. However, continuous
geographical regions are not a guarantee of
homogeneity since adjacent basins can be physically
very different (Wiltshire, 1985).

A regression analysis with all 79 stations was
conducted with the peak flood estimates as the
dependent variables. The significant independent
variables were drainage area, 2-year, 24-hour rainfall
intensity, and mean basin altitude for the 25-, 50-, and
100-years floods. The equations for the 2-, 5-, and 10-
years floods differed by having median annual
precipitation instead of the 2-year, 24-hour rainfall
intensity as an independent variable.

The residuals in log units from the 50-year
recurrence interval equation were chosen to be used for
regionalization. Drainage basins were grouped together
in this study by using the method of residuals. The
method of residuals involves classifying basins into
regions using the sign and magnitude of the residuals
(differences in predicted and observed peak discharges),
basin and climatic conditions, and hydrologic judgment.
The method of residuals assumes that the general trends
in the residuals reflect inherent variations in the flood
response of various regions (Bhaskar and O'Conner,


one time or another, have occurred in most inhabited
areas of Oahu (Wu, 1967; Division of Water and Land
Development, 1983).

PREVIOUS STUDIES

In 1957, the USGS, in cooperation with the
Division of Water and Land Development, Department
of Land and Natural Resources, State of Hawaii; and
the Department of Public Works, City and County of
Honolulu, created a program to collect peak-discharge
data for the investigation of the magnitude and
frequency of floods on Oahu. The ultimate goal of this
program was to define the magnitude and frequency of
floods on a regional as well as an island basis. To
accomplish this, a crest-stage gage network for
measuring peak discharges was created. By the
following year, 1958, the number of streamflow-gaging
stations on Oahu increased from 24 to 28 and 22 crest-
stage gages were installed (Lee, 1978).

From 1958 to 1974, a series of annual reports on
the peak-discharge data-collection program was
published by the USGS under the title "An
Investigation of Floods in Hawaii." This series listed
annual peak discharges at gaged sites. Only reports
number 5 (Vaudrey, 1963) and number 15 (Nakahara,
1973) gave flood-frequency curves for selected
streams. Vaudrey (1963) used the distribution-free
graphical method (Dalrymple, 1960) and Nakahara
(1973) followed the U.S. Water Resources Council
Bulletin 15 guidelines (U.S. Water Resources Council,
1967).

In 1957, T. Mitsuda and J. Tanaka developed the
first storm drainage-design criteria published by the
City and County of Honolulu (1957). This manual
presented flood-frequency curves for 12 streams fitted
by the (Type I extremal) Gumbel distribution. Dodo
and Ling (1958) reproduced the Mitsuda and Tanaka
flood-frequency curves in their storm-drainage report
for the City and County of Honolulu, City Planning
Commission. For ungaged drainage areas, both reports
recommended the use of the rational method and
correlation with gaged basins of similar physiographic
conditions. An earlier effort by Carson (1939)
presented flood-intensity frequency curves for three
streams on Oahu.

A review by Chow (1966) of the above drainage-

design criteria made no mention of frequency curves
but did present two envelope curves based on
maximum recorded peak discharges. These two curves
regionalized Oahu into windward and leeward
(including Honolulu) areas (Chow, 1966). This division
was based on drainage-area size, location of the
streamflow gages, and the probable maximum
precipitation values. The 1969 City and County of
Honolulu storm drainage standards (1969) adopted
Chow's envelope curves. The recurrence intervals for
these envelope curves were determined by Wu (1967)
to be between 50 and 100 years. As a continuing
development, the 1988 storm-drainage standards (City
and County of Honolulu, 1988) modified the envelope
curves into design curves approximating the 100-year
flood and regionalized Oahu geographically into three
regions.

To provide for a uniform technique for determining
flood frequencies, the U.S. Water Resources Council
published Bulletin 15 (U.S. Water Resources Council,
1967). Bulletin 15 guidelines endorsed the log-Pearson
Type III distribution for determining flood-frequency
curves to be adopted by all federal agencies. In 1970,
the State of Hawaii adopted the Bulletin 15 guidelines
(Division of Water and Land Development, 1970). The
log-Pearson Type III methodology has been updated
and currently Bulletin 17B guidelines (Interagency
Advisory Committee on Water Data, 1982) are used.

A study of flood hydrology of drainage basins with
areas of less than 10 mi2 on the island of Oahu by Wu
(1967) gave flood-frequency curves for selected
streams using the Gumbel distribution. Wu was the
first to apply multiple-regression methods on Oahu to
estimate the magnitudes of 100-year floods. Wu (1967)
gave two regional flood formulas for the 100-year flood
using data from 23 drainage basins. These equations
related the 100-year peak to four basin and climatic
characteristics: drainage area, watershed length,
watershed height, and the 100-year, 24-hour rainfall.
The island was divided into four geographic regions;
one equation was applicable for the windward region,
and the other equation for Honolulu and central Oahu
regions. The last region, Waianae, had insufficient data
for analysis. No standard error of estimate for the
regression equations was given.

The last flood-frequency study on Oahu to use the
Gumbel distribution was done by Cheng and Lau


100,000 T T

°

LEEWARD - Region 1 B

WINDWARD - Region 2
10,000 3 eS 4
NORTH - Region 3

>

1,000 F

WEIGHTED 100-YEAR ESTIMATED DISCHARGE,
IN CUBIC FEET PER SECOND
1}
8
°
BS
&

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

MAXIMUM KNOWN DISCHARGE, IN CUBIC FEET PER SECOND

100

100,000 T

°

LEEWARD - Region 1

a

40,000 F WINDWARD - Region 2 . J

4 NORTH - Region 3 09,

Iq B

1,000 F

WEIGHTED 100-YEAR ESTIMATED DISCHARGE,
IN CUBIC FEET PER SECOND
BS
cer)

Ll 1
100 1,000 10,000 100,000

PEAK DISCHARGE, IN CUBIC FEET PER SECOND, ESITMATED
BY LOG-PEARSON TYPE III DISTRIBUTION

100

Figure 4. Relation of weighted average 100-year discharge estimates to; A, maximum known
discharge; B, peak discharge; C, design discharge; and D, 100-year estimated discharge,
Oahu, Hawaii.

21


ESTIMATION OF MAGNITUDE AND FREQUENCY OF FLOODS
FOR STREAMS ON THE ISLAND OF OAHU, HAWAII

By Michael F. Wong

U.S. GEOLOGICAL SURVEY
Water-Resources Investigations Report 94-4052

Prepared in cooperation with the
CITY AND COUNTY OF HONOLULU,
DEPARTMENT OF PUBLIC WORKS

Honolulu, Hawaii
1994


Table 1. Stream-gaging stations on Oahu, Hawaii, used in the study

[Station locations shown in figure 1; p, gage is in operation as of water year 1988; rec, recording gage, either digital or
graphic or both; csg, crest-stage gage]

Type
Station Years of Period of of
number Station name record record gage
200000 = North Fork Kaukonahua Stream above Right Branch near Wahiawa... 64 = 1913-53; Tec
1960-p
201000 —_- Right Branch of North Fork Kaukonahua Stream near Wahiawa. 34 1914-53 rec
204000 North Fork Kaukonahua Stream near Wahiawa... 22 «1947-68 rec
206000 = South Fork Kaukonahua Stream near Wahiaw 13. 1945-57 rec
208000 = South Fork Kaukonahua Stream at East Pump Reservoir near Wahiawa. 31 1958-p rec
208500 Right Branch of South Fork Kaukonahua Stream near Wahiawa... 15 1958-72 rec
210500  Kaukonahua Stream at Waialua. 22 =~ =1963-p csg
211200 = Poamoho Stream near Waialu 22 + ~=1967-p csg
211300 — Makaleha Stream near Waialua. 31 = :1958-p csg
211500 — Makua Stream at Makua...... 30. 1958-p csg
211600 Makaha Stream near Makaha. 29 ~=1960-p rec
211700 = Makaha Stream at Makaha...... 23 «:1966-p csg
211800 Kaupuni Stream at altitude 374 feet near Waianae.. 28 = ©1961-p csg
212200 — Mailiilii Stream near Waianae ....cs 31 = :1958-p csg
212300 — Nanakuli Stream at Nanakuil... 21 :1968-p csg
212450 —Kaloi Gulch tributary near Honoulit 21 = 1968-p csg
212500 —_Honouliuli Stream near Waipahu... 29 1956-p sg
212601 = Waikele Stream at Wheeler Fiel 30 -:1958-p esg
212700 Waikakalaua Stream near Wahiawa. 31 1958-p csg
212800 —_Kipapa Stream near Wahiawa. 32 -1957-p Tec
213000 — Waikele Stream at Waipahu. 36 = 1952-p rec
216000 — Waiawa Stream near Pearl City....... 36 = 1953-p Tec
216500 — Waimano flood channel at Pearl City 15 1955-69 csg
223000  Waimalu Stream near Ai 34 =1952-p csg
224500 — Kalauao Stream at Moanalua Road at Aiea.. 34 = 1954-p csg
226000 North Halawa Stream near Aiea...... 39 = 1930-33; rec
1954p
227000 Halawa Stream at Aiea..... 20 1954-79 csg
228000 = Moanalua Stream near Honolulu.. 61 = 1927-p csg
228200 Moanalua Stream near Aiea... 20 1969-p csg
228500 Moanalua Stream at altitude 100 feet near Honolulu... 11 1958-70 csg
228600 Moanalua Stream near Tripler Hospital. 18 =1971-p csg
228900 Kalihi Stream near Kaneohe. 21 1968-p csg
229000 72 1917-p rec
229300 28 = 1960-p Tec
235400 30. = -1959-p csg
237500 31 :1958-p csg
238500 Waihi Stream at Honoluh 63 1915-83 rec
240500 = Waiakeakua Stream at Honolulu 70 = 1914-p Tec
244000 —- Pukele Stream near Honolulu... 56 = 1927-82 Tec
246000 Waiomao Stream near Honolul 45 1927-71 rec
247000 —_- Palolo Stream near Honolulu..... 27: 1953-79 rec
247100 = Manoa-Palolo drainage canal at Moil 21 = 1968-p csg



discharge data for windward Oahu drainage basins than
for the basins on the leeward side. The annual peak-
discharge data for stations on the leeward side generally
showed a greater variability in year-to-year magnitudes.

There were 82 gaging stations on Oahu with 10 or
more years of record available for flood-frequency
analysis. Three stations were eliminated because their
annual peak discharges were affected by significant
diversion or regulation. Diversions were considered
significant at stations where the measured diversions
exceeded 30 percent of the mean daily discharge on the
day that the annual peak discharge occurred. Significant
regulation was defined as a flood-control reservoir
controlling more than SO percent of the drainage basin.
No stations were eliminated because of urbanization
within the basin boundaries. Annual peak discharge
series for drainage basins with some urbanization
showed no significant trends or differences in the peak
discharges when compared to nearby non-urban basins.
The final 79 stations used in this study are listed in table
1 and shown in figure 1. For this report, the prefix 16
of the eight-digit station number has been dropped. For
example, the abbreviated station number 211500 is
used rather than the complete number 16211500.

Annual peak-discharge records for the 79 gaging
Stations, as of water year 1988, had record lengths
ranging from 11 to 72 years (table 1) and a mean of
29.6 years. Of the 79 stations, 65 had record lengths
longer than 20 years and the total years of record for all
79 stations is 2,335 station-years. Of these 79 stations,
42 are crest-stage gages and 37 are continuous-
recording streamflow-gaging stations (table 1).

FLOOD-FREQUENCY DATA

A flood-frequency analysis uses available annual
peak-discharge data to estimate the frequency and
magnitude of floods that can occur. In a frequency
analysis, a theoretical frequency distribution is assumed
for the population of floods and the statistical
parameters of this distribution are computed from the
peak-discharge sample data (Kite, 1977).

Following the Bulletin 17B (Interagency Advisory
Committee on Water Data, 1982) guidelines, flood-
frequency curves were developed for each gaging
Station by using the log-Pearson Type III distribution.
The log-Pearson Type III distribution is characterized

by three statistics: the mean, standard deviation, and
skew coefficient. These three statistics are computed
from the logarithmic transformation of annual peak
discharges. The skew is the numerical measurement of
the lack of symmetry. If the skew coefficient is zero,
then the log-Pearson becomes identical to the log-
normal distribution (Cudworth, 1989). Bulletin 17B
gives a generalized skew map for determination of
skew. A generalized skew of -0.05 for Hawaii, from
the skew map, was used for all frequency computations
in this report. Lee (1984) computed a generalized skew
of -0.14 for the State of Hawaii. However, this skew
value was reported as not being significantly different
from —0.05 (Lee, 1984) so use of the -0.05 value was
considered satisfactory.

Program J407 in WATSTORE (Kirby, 1979),
which has been updated to Bulletin 17B guidelines, was
used to generate the station frequency curves. As part of
this analysis, the annual peak-discharge series were
tested for outliers. Outliers are data points which depart
significantly from the remaining data and can
significantly affect the statistics used to compute the
flood frequency curve (Interagency Advisory
Committee on Water Data, 1982, p.17). Results for the
five stations that had high outliers detected were not
adjusted because the required historic information was
not available. The 18 stations that had low outliers
deleted (table 2) were adjusted using the conditional
probability adjustment given in Bulletin 17B. The three
Statistics used to characterize the annual peak discharge
series for each station are listed in table 2. Final
frequency curves were determined by making
adjustments as recommended by Bulletin 17B
guidelines,

From the flood-frequency analysis, values of peak
discharge were obtained for the 2-, 5-, 10-, 25-, 50-,
and 100-year recurrence intervals. The estimated peak
discharges for these recurrence intervals and the
maximum known floods of record are given in table 3
(at end of report). The accuracy of these flood estimates
can be computed in terms of standard error in log units
by methods given by Hardison (1969, 1971). The
accuracy of the flood estimate is a function of record
length, standard deviation of the annual peak
discharges, correlation between the mean and standard
deviation of the annual peak discharges, skew
coefficient, and the recurrence interval.


Draper, N.R., and Smith, Harry, 1981, Applied
Regression Analysis (2nd ed.): New York, John Wiley

and Sons, 709 p.
Duan, Naihua, 1983, Smearing estimate: A
Nonparametric retransformation method: Journal of

the American Statistical Association, v. 78, no. 383, p.
605-610.

Ekern, P.C., Lau, L.S., Price, Saul, Peterson, F.L., and
Pulfrey, Ronald., 1971, Hydrologic systems in Hawaii,
in Yevjevich, V., ed., Systems Approach to
Hydrology, Proceedings of the Ist Bilateral U.S.-
Japan Seminar in Hydrology: Fort Collins, Colo.,
Water Resources Publications, p. 187-201.

Giambelluca, T.W., Lau, L.S., Fok, Yu-Si, and
Schroeder, T.A., 1984, Rainfall frequency study for
Oahu, Report R-73: Division of Water and Land
Development, Department of Land and Natural
Resources, State of Hawaii, 34 p. app.

Hardison, C.H., 1969, Accuracy of streamflow
characteristics: U.S. Geological Survey Professional
Paper 650-D, p. D210-D214.

, 1971, Prediction error of regression estimates of
streamflow characteristics at ungaged streams: U.S.
Geological Survey Professional Paper 750-C, p. C228-
C236.

Iman, R.L., and Conover, W.J., 1983, A modern approach
to statistics: New York, John Wiley and Sons, 497 p.

[U.S.] Interagency Advisory Committee on Water Data,
1982, Guidelines for determining flood flow frequency:
Hydrology Subcommittee Bulletin 17B, 28 p., app. 1-
14. [Available from Office of Water Data
Coordination, MS 417, USGS, Reston VA 22092.]

Kirby, W. H., 1979, Annual flood frequency analysis
using U.S. Water Resources Council Guidelines
(Program J407), in WATSTORE National Water Data
Storage and Retrieval System's User's Guide, v. 4,
chapter I, section C: U.S. Geological Survey Open-
File Report 79-1336-I, p. C1-C56.

Kite, G.W., 1977, Frequency and risk analysis in
hydrology: Fort Collins, Colo., Water Resources
Publications, 224 p.

Lee, Reuben, 1978, The U.S. Geological Survey's role in
the collection and analysis of peak-flow data on Oahu,
in Lecture notes for a workshop on storm drainage
management: Honolulu, University of Hawaii, p.B1-
B6.

, 1984, Generalized skew coefficient for flood
frequency computations for the State of Hawaii: U.S.
Geological Survey Water-Resources Investigations
Report 84-4027, 21 p.

Lettenmaier, D.P., Wallis, J.R., and Wood, E.F., 1987,
Effect of regional heterogeneity on flood frequency
estimation: Water Resources Research, v. 23, no. 2,
p. 313-323.

28

Lumb, A.M., Kittle, J.L., and Flynn, K.M., 1990, Users
manual for ANNIE, A computer program for
interactive hydrologic analyses and data management:
U.S. Geological Survey Water-Resources
Investigations Report 89-4080, 236 p.

Lumia, Richard., 1991, Regionalization of flood
discharges for rural, unregulated streams in New York,
excluding Long Island: U.S. Geological Survey
Water-Resources Investigations Report 90-4197,
105 p.

Macdonald, G.A., Abbott, A.T., and Peterson, F.L., 1983,
Volcanoes in the sea: The geology of Hawaii (2nd
ed.): Honolulu, University of Hawaii Press, 517 p.

Nakahara, R.H., 1973, An investigation of floods in
Hawaii through September 30, 1972, Progress Report
No. 15: U.S. Geological Survey Basic Data Release,
207 p.

, 1980, An analysis of the magnitude and
frequency of floods on Oahu, Hawaii: U.S. Geological
Survey Water-Resources Investigations 80-45, 20 p.

Nakahara, R.H., Yee, J.S.S., Yamashiro, Isao, Tateishi,
G.A., and Domingo, J.A., 1989, Water resources data,
Hawaii and other Pacific areas, water year 1988,
Volume 1. Hawaii: U.S. Geological Survey Water-
Data Report HI-88-1, 265 p.

Riggs, H.C., 1973, Regional analysis of streamflow
characteristics: Techniques of Water-Resources
Investigations of the United States Geological Survey,
Book 4, Chapter B3, 15 p.

Sauer, V.B., 1973, Flood characteristics of Oklahoma
streams: U.S. Geological Survey Water-Resources
Investigations 52-73, 307 p.

Sauer, V.B., Thomas, W.O. Jr., Stricker, V.A., and
Wilson, K.V., 1983, Flood characteristics of urban
watersheds in the United States: U.S. Geological
Survey Water-Supply Paper 2207, 63 p.

Stedinger, J.R., and Tasker, G.D., 1985, Regional
hydrologic analysis 1: ordinary, weighted, and
generalized least squares compared: Water
Resources Research, v. 21, no. 9, p. 1421-1432.

Tasker, G.D., 1980, Hydrologic regression with weighted
least squares: Water Resources Research, v. 16, no.
6, p. 1107-1113.

, 1982, Simplified testing of hydrologic regression
regions: Journal of the Hydraulics Division, American
Society of Civil Engineers, v. 108, no. HY10, p. 1218-
1221.

Thomas, D.M., and Benson, M.A., 1970, Generalization
of streamflow characteristics from drainage-basin
characteristics: U.S. Geological Survey Water-Supply
Paper 1975, 55 p.

Thomas, W.O., Jr., 1987, Techniques used by the U.S.
Geological Survey in estimating the magnitude and
frequency of floods, chap. in, Mayer, L., and Nash,



region, and drainage area and the 2-year, 24-hour
rainfall intensity for the north Oahu region. Drainage
areas for sites used in this study ranged from 0.03 to
45.7 mi2. Final regression equations were derived using
generalized least-squares regression techniques. The use
of generalized least-squares regression provided
improvements in the regression estimates by
accounting for cross-correlation and different record
lengths in a set of data for gaging stations in a region.
The standard error of estimate for the regression
equations given ranged from 27 to 58 percent. Standard
error of prediction ranged from 34 to 62 percent. The
use of generalized least-squares regression, and other
improvements incorporated in this study, reduced the
standard error of estimate for the regression equations
by an average of 8 percent compared with previously
published regression equations. A full discussion on the
accuracy and limitations of the regression equations and
asensitivity analysis and sample calculations are given
to help apply the derived regression equations.

The results using the derived regression equations
were compared graphically with other methods used to
estimate peak discharges. The graphical comparisons
were made by plotting the weighted average 100-year
peak-discharge estimates from the regression equations
compared with the maximum observed discharge and
estimates of the 100-year peak discharge determined in
this study and in two previous studies. The comparison
showed that most of the estimates from the regression
equations in this study are lower than the peak-
discharge estimates based on equations from the other
studies.

References Cited

Armstrong, R.W., eds., 1983, Atlas of Hawaii (2nd ed.):
Honolulu, University of Hawaii Press, 238 p.

Benson, M.A., 1962, Factors affecting the occurrence of
floods in a humid region of diverse terrain: U.S.
Geological Survey Water-Supply Paper 1580-B, 64 p.

Bhaskar, N.R., and O'Conner, C.A., 1989, Comparison of
method of residuals and cluster analysis for flood
regionalization: Journal of Water Resources Planning
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Blumenstock, D.I., and Price, Saul, 1967, Climate of
Hawaii, in, Climates of the States, No. 60-51,
Climatography of the United States: U.S. Dept. of
Commerce. p. 614-629.

27

Carson, M.H., 1939, Surface-water resources, in, An
historic inventory of the physical, social and
economic and industrial resources of the Territory of
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Cheng, E.D.H., and Lau, L.S., 1973, A stream gage
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Water Resources Seminar Series No. 5, Water
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11 p.

Choquette, A.F., 1988, Regionalization of peak
discharges for streams in Kentucky: U.S. Geological
Survey Water-Resources Investigations Report 87-
4209, 105 p.

Chow, Ven Te, 1964, Handbook of applied hydrology:
New York, McGraw-Hill, 1453 p.

, 1966, An investigation of the drainage problems
of the City and County of Honolulu: City and County
of Honolulu, 52 p.

City and County of Honolulu, 1957, Design criteria for
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, 1969, Storm drainage standards: Department of

Public Works, 41 p.

, 1988, Storm drainage standards: Department of
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Cudworth, A.G. Jr., 1989, Flood hydrology manual: A
Water Resources Technical Publication, U.S.
Department of the Interior, Bureau of Reclamation,
243 p.

Dalrymple, Tate, 1960, Flood-frequency analysis: U.S.
Geological Survey Water-Supply Paper 1543-A, 80 p.

Davis, L.G., 1974, Floods in Indiana: Technical manual
for estimating their magnitude and frequency: U.S.
Geological Survey Circular 710, 40 p.

Division of Water and Land Development, 1970, Flood
frequencies for selected streams in Hawaii, Report
R36, Department of Land and Natural Resources,
State of Hawaii, 120 p.

-, 1982, Median rainfall, State of Hawaii, Circular

C88, Department of Land and Natural Resources,

State of Hawaii, 44 p.

, 1983, Floods and flood control, v. 1, Circular

C92, Department of Land and Natural Resources,

State of Hawaii, 66 p.

., 1988, Post-flood report, New Year's Eve Storm
December 31, 1987-January 1, 1988 Windward and
Leeward East Oahu, Circular C119, Department of
Land and Natural Resources, State of Hawaii, 55 p.

Dodo, Sadaichi, and Ling, W.Y.H., 1958, A Report on
storm drainage design criteria: Planning Section,
Bureau of Plans, City and County of Honolulu, 24 p.,

app. A-E.



ANNUAL PEAK DISCHARGES, IN PERCENT

1 MILE

oO 1 KILOMETER
APPROXIMATE SCALE

Figure 2. Block diagram showing typical drainage-basin shapes for Oahu, Hawaii
(by SK. Izuka, U.S. Geological Survey).

JAN FEB MAR APR MAY JUNE JULY AUG SEPT OCT NOV DEC
MONTH

Figure 3. Monthly occurrence of 2,317 annual peak discharges for 79 stream-gaging stations,
Oahu, Hawaii, 1913-88.


standard error of prediction (%SP) is a measure of the
model error and the sampling error of the data used in
the regression analysis (G.D. Tasker, oral commun.,
1990). The standard error of prediction was determined
by the GLSNET program in ANNIE (Lumb and
others, 1990; G.D. Tasker, written commun., 1990).
The standard error can also be expressed as the number
of equivalent years of record (EQ) needed at the
ungaged site to achieve the reliability of the regression
equation (Hardison, 1971). The equivalent years of
record, EQ, is calculated by the equation in Hardison
(1971) as applied by the GLSNET program (G.D.
Tasker, written commun., 1990), This equation is:

EQ = K? [SD/SEp]?, (2)

where:

EQ = the equivalent years of record associated with the

regression equation;

K2 = a factor based on the mean skewness of the
logarithms of the annual series of flood peaks at
all stations in a hydrologic region and based on
the recurrence interval, which relates the standard
error associated with a given recurrence interval
to the mean standard deviation of the logarithms
of the annual peaks in a region and the number
of annual peaks;

SD = the mean standard deviation of the logarithms of
the annual peaks at all stations in a hydrologic
region; and

SEp = the standard error of prediction, in log units,

associated with a regression equation.

The standard errors of the regression models apply
only to streamflow estimates for basins that have values
of the independent variable(s) within the range of those
values used to derive that equation. For the equations in
tables 6 through 8, statistical characteristics of the
independent variables are shown in table 9. The use of
the regression equations that have values outside the
range shown in table 9 can result in potentially large
extrapolation errors.

DISCUSSION OF EQUATIONS AND REGIONS

The regression equations for the leeward Oahu
region (table 6) have two significant variables, drainage
area and median annual rainfall. The drainage basins in
the leeward region generally are similar to the long, V-
shaped basin shape, however, drainage basins along the

18

Waianae Coast are similar to the short, broad basins in
shape, but are larger in area. The leeward region has the
highest average drainage areas of all the regions (table
9) because the region includes the two largest drainage
basins on Oahu (gaged by stations 213000 and
210500), which cover most of the central area of Oahu.

In the windward Oahu region (table 7), drainage
area is the only significant variable in all the regression
equations. The windward region contains essentially the
same area as the windward regions determined by Wu
(1967), Yamanaga (1972), Nakahara (1980), and
Wong (1991). All of these windward regions differ
only by the assignment of a few gaging stations. The
drainage basins in the windward region are the smallest
in average drainage area (table 9) of the three regions.
Drainage basins in this region generally are short, broad
basins. The headwaters of these basins all start along
the steep cliffs of the Koolau Range (fig. 1).

The equations for the north Oahu region (table 8)
contain two variables, drainage area and the 2-year, 24-
hour rainfall intensity. The drainage basins in the north
Oahu region generally are long, V-shaped basins and
are similar to those in the leeward Oahu region. The
equations also are similar to those for the leeward Oahu
region, except that 2-year, 24-hour rainfall intensity
replaces median annual rainfall.

SENSITIVITY ANALYSIS

Because the drainage-basin and climatic
characteristics used in the regression equations must be
computed from maps or other data sources,
possibilities exist for error in measurement and
judgment. To determine how much error can be
introduced by computation error, a sensitivity analysis
was done as described by Lumia (1991). The 50-year
peak discharge was computed by the regression
equation using the mean values (table 9) of the relevant
basin and climatic characteristics for that region. This
value represents the "base" 50-year flood. The mean
values of the basin characteristics were then changed by
increasing and decreasing each value by 10, 20, and 30
percent. The resulting percentage of change in the 50 -
year peak-discharge estimates are shown in table 10.
For the two-variable equations, one basin characteristic
was held constant at the mean value while the other
varied.


Table 3. Estimated peak discharges for selected recurrence intervals and maximum known
discharges at stream-gaging stations on Oahu, Hawali--Continued

Maximum known discharge

Station Q2 Qs Q10 025 O50 Q100 Water Discharge
number (f3/s) year (ft3/s)
330000 2,540 4,290 5,580 7,320 8,680 10,100 1980 8,540

2,460 4,510 6,180 8,820 10,800 13,400
2,530 4,340 5,730 7,700 9,220 10,900

331000 69 258 531 1,170 1,970 3,170 1980 2,030
116 357 705 1,480 2,290 3,430
16 286 588 1,270 2,080 3,250

340000 2,750 5,140 7,280 10,700 13,900 17,600 1974 15,900

2,520 4,900 6,960 10,300 13,000 16,500
2,730 5,090 7,200 10,600 13,700 17,300

343000 3,990 9,490 14,500 22,500 = 29,500 37,300 1974 18,200
2,820 5,330 7,490 10,600 13,300 16,200
3,730 8,330 12,000 17,400 21,800 = 26,500

345000 1,920 2,880 3,610 4,630 5,470 6,380 1974 5,540
1,590 2,590 3,310 4,340 5,020 5,900
1,880 2,820 3,530 4,550 5,350 6,260

350000 1,620 3,080 4,340 6,270 7,980 9,940 1974 7,600
1,060 2,200 3,300 5,170 6,710 8,700
1,560 2,900 4,090 6,000 7,670 9,650

35


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36


Table 11. Additional data used in comparing the weighted 100-year peak discharge estimates with

other methods for Oahu, Hawaii--Continued

Plate 6 Previous 100-year peak
Hydrologic Area in 100 Plate 6 curve discharge discharge
Station number region acres used (£t3/s) (£3/s)
248800 2 17 A 4,800 5,520
249000 2 13.8 A 7,400 8,340
249100 2 10 A 750 1,310
254000 2 13.0 A 7,200 8,010
260500 2 34.2 A 18,000 15,900
265000 2 76 A 4,800 -
270900 2 28 A 1,800 2,690
273900 2 27.0 A 14,000 13,800
274499 2 40 A 2,500 3,430
275000 2 6.2 A 4,000 4,720
278000 2 18 A 1,300 2,000
279500 2 1.5 A 7,000 7,320
283000 2 18 A 1,300 1,950
283480 2 148 A 8,200 8,750
283600 2 0.19 A - 398
283700 2 0.20 A - 398
284000 2 6.0 A 3,700 4,580
284200 2 6.2 A 4,000 -
291000 2 63 A 4000 4,790
294900 2 14.2 A 8,000 8,500
296500 3 23.9 A 12,000 12,300
303000 3 17.8 A 9,500 9,980
304200 3 71 A 4,200 5,190
304500 3 13.6 A 7,300 8,230
310501 3 25.9 A 13,900 8,830
311000 3 13.6 B 5,000 4,000
318000 3 16.6 B 6,100 3,990
325000 3 20.0 B 7,000 6,590
330000 3 62.7 B 15,500 15,200
331000 3 143 B 5,400 3,780
340000 3 86.4 B 20,000 21,700
343000 1 90.9 B 20,400 19,700
345000 3 19.1 B 6,800 8,090
350000 3 38.1 B 10,600 11,400

use of the regression equations apply only under the
conditions described in the accuracy and limitations
section.

GAGED SITES

The regression equation for each region was applied
to the gaged sites in that region and the resulting peak-
discharge estimates are listed in table 3. At gaged sites,
two peak-discharge estimates are available, one from
the frequency curves based on gaged record and the
other from the regression equations. Another estimate
would be to combine them. Combining the estimates

provides a regional adjustment to the gaged record. To
combined estimates, a weighted average of the peak
discharges was used. The equation outlined in
Choquette (1988) and described below weighs the two
peak estimates by record length in years. By combining
the regression and gaged record peak-discharge
estimates, time-sampling errors at sites with short
record lengths are reduced, providing an improved
estimate of peak discharge. Weighted average peak -
discharge values have been computed by equation 3
below for all 79 gaged sites used in this study and are
shown in table 3. The weighting equation for peak
discharges at gaged stations is:


TABLES

1. Stream-gaging stations on Oahu, Hawaii, used in the study 8

2. Peak-discharge statistics at stream-gaging stations on Oahu, Hawaii 10

3. Peak discharges for selected recurrence intervals and maximum known discharges at
stream-gaging stations on Oahu, Hawaii 30

4, Drainage-basin and climatic characteristics for gaged basins on Oahu, Hawaii 36

5. Statistical summary of drainage-basin and climatic characteristics for gaged basins on
Oahu, Hawaii 13

6. Regression equations for estimating peak discharges for streams in leeward Oahu
(region 1), Hawaii 17

7. Regression equations for estimating peak discharges for streams in windward Oahu
(region 2), Hawaii 17

8. Regression equations for estimating peak discharges for streams in north Oahu
(region 3), Hawaii 17

’ 9. Statistical summary of selected drainage-basin, climatic, and flood-frequency

characteristics by regions for Oahu, Hawaii 19

10. Results of sensitivity analysis showing percentage of change in computed 50-year
peak discharges within each of the three hydrologic regions on Oahu, Hawaii 19

11. Additional data used in comparing the weighted average 100-year discharge estimates
with other methods for Oahu, Hawaii 23

Conversion Factors

Multiply By To obtain
acre 4,047 square meter
foot (ft) 0.3048 meter
cubic foot (ft3) 0.02832 cubic meter
cubic foot per second (ft3/s) 0.02832 cubic meter per second
inch (in.) 25.4 millimeter
inch per year (in/yr) 2.54 centimeter per year
mile (mi) 1.609 kilometer
square mile (mi2) 2.590 square kilometer

Temperature is given in degrees Fahrenheit (°F) , which can be converted to degrees Celsius (“C) by using the
equation:
°C = (F- 32)/1.8

iv


Table 2. Peak-discharge statistics at stream-gaging stations on Oahu, Hawaii--Continued

Peak-discharge statistics from logarithms of annual floods

Station Gaged record Bulletin 17B weighted
number Mean Std. dev. Skew Mean Std. dev. Skew
247000 3.128 0.272 ~0.145 3.128 0.272 0.107
247100 3.445 0.329 0,583 3.445 0.329 0.322
1247200 2.908 0.330 1381 2.952 0.242 0.289
1247500 2.737 0.364 0.187 2.754 0.330 0.186
2247900 2.603 0.376 1.352 2.603 0.376 0.461
248800 2.485 0.518 0.784 2.485 0.518 0.463
249000 3.106 0.372 0.176 3.106 0372 0.123
1249100 2.043 0.501 0.809 2.071 0.444 0.251
1254000 2.912 0.472 0.555 2.938 0.415 0.054
260500 3.248 0.360 0.141 3.248 0.360 0.108
1265000 2.832 0.518 0.952 2.886 0.395 0316
1270900 2.213 0.453 -1.551 2.265 0.324 0.038
273900 3.226 0.463 0.071 3.226 0.463 0.062
1274499 2.658 0.466 0.762 2.685 0.408 0.122
275000 2.801 0.486 0.728 2.801 0.486 0.491
2278000 1.647 0.481 0.431 1.647 0.481 0.227
279500 2.952 0.574 0.217 2.952 0.574 0.143
283000 2.142 0.333 1.087 2.142 0.333 0.534
2293480 3.078 0.421 0.153 3.078 0.421 0.110
1283600 1.991 0.320 0.686 2.015 0.267 0.179
1283700 1.898 0.329 0.770 1.923 0.273 0.161
2284000 2.613 0.387 0.046 2.613 0.387 0.020
284200 2.669 0.255 ~0.040 2.669 0.255 0.045
291000 2.786 0.333 0411 2.786 0.333 0.147
294900 3.330 0.384 0.839 3.330 0.384 0.479
296500 3.499 0.172 -1.015 3.499 0.172 0.537
303000 3.254 0.240 0.564 3.254 0.240 0.364
304200 2.923 0.270 0.439 2.923 0.270 0.257
304500 3.122 0.300 0.531 3.122 0.300 0.335
310501 2.806 0.621 0,335 2.806 0.621 0.223
311000 2.330 0.487 0.091 2.330 0.487 0.076
1318000 2.203 0.460 0.868 2.235 0.395 0.209
325000 3.086 0.233 0.164 3.086 0.233 0.117
330000 3.398 0.277 0.261 3.398 0.277 0.181
331000 1.858 0.667 0.405, 1.858 0.667 0.190
340000 3.454 0.312 0.515 3.454 0.312 0.286
343000 3.581 0.465 0.529 3.581 0.465, 0.265
345000 3.292 0.203 0.517 3.292 0.203 0.279
350000 3.214 0.328 0.157 3.214 0.328 0.084

\stations with low outliers deleted, conditional probability adjustment applied (18 stations)
2stations with high outliers detected, no adjustment applied (5 stations)

i


MR: The meander ratio, a dimensionless
measurement computed as the ratio of the main-channel
length (CL) to the length of the valley. (MR =
CL/Alength of valley), where the length of the valley was
determined by measuring a straight line or series of
straight lines not exceeding five line segments, that
linearize the stream's path in the drainage basin,
between the gaging station and the basin divide. High
values signify high meandering whereas values close to
one indicate nearly straight streams.

P: The median annual rainfall, in inches, determined
by overlaying a GIS coverage of lines of equal median
annual rainfall on the drainage-basin coverage and then
computing the area-weighted average of rainfall in each
basin. Lines of median rainfall were from the Division
of Water and Land Development (1982).

P224: The 2-year recurrence interval 24-hour
rainfall intensity, in inches, was computed by
overlaying a GIS coverage of the 2-year, 24-hour
rainfall on a drainage-basin coverage and computing the
area-weighted average of rainfall in each basin. Lines of
equal rainfall intensity were from Giambelluca and
others (1984).

PA: The convexity ratio, which is a measure of
boundary regularity. It is computed by dividing the
perimeter of a basin by its area (PA = PER / DAG).

PER: The perimeter of the drainage basin, in miles.
Determined by GIS from the digitized drainage-basin
coverage. For major basins, the perimeter was
determined by summing all line segments that outlined
that basin.

RF: A shape factor determined by dividing the
drainage area by the square of the main channel length
(RF = DAG/CL2). This factor can also be considered as
the basin width divided by channel length (RF =
BW/CL = DAG/CL2).

UC: Urban cover of a drainage basin, in percent.
This variable is the ratio of the drainage area covered by
the urban development, as shown in pink on the
1:24,000 topographic maps, to its total drainage area.
Determined from a GIS coverage, which differentiated
the pink areas within each drainage basin.

Table 5. Statistical summary of drainage-basin and climatic characteristics for gaged basins on Oahu,

Hawaii

Range of values

Characteristic Standard
symbol Description Minimum _Maximum__Median_ Mean __deviation
BW Average basin width, in miles 0.086 2.16 0.616 0.688 0.390
CL Main channel (stream) length, in miles 0.338 264 415 5.90 5.72
CLD Shape factor, dimensionless 0.991 841 2.21 2.56 1.33
cs Main channel slope, in feet/mile 55.0 4980 265 593 882
DA! Area of a drainage basin, in square miles 0.03 45.7 2.59 4.62 7.32
DAG Area of a drainage basin, in square miles, 0.03 46.2 2.57 4.62 7.33
computed by a geographic information
system (GIS)
E Mean basin altitude, in feet 200 2110 1160 1150 399
FC Forest/vegetative cover, in percent 33 100 91 84 18
MR Meander ratio, dimensionless 1,02 3,32 1.19 1.34 0.380
P Mean annual precipitation in inches 29 239 99 105 48
P224 2-year recurrence interval, 24-hour rainfall 472 9.10 6.75 6.85 1.13
intensity, in inches
PA Shape factor, in 1/miles 0.893 278 3.26 4.19 4.17
PER Perimeter of a drainage basin, in miles 0.802 413 7.86 10.2 7.16
RF Form factor, dimensionless 0.011 0.800 0.160 0.211 0.172
UC Urban cover, in percent 0 36 0 4 9

lthe standard drainage area used in the regression analysis

13


CONTENTS

Abstract 1
Introduction 1
Purpose and scope 1
Description of study area 1
Physiography 2
Climate 2
Flood hydrology 2
Previous studies 5
Data base for regression equations 6
Annual peak-discharge data 6
Flood-frequency data 7
Drainage-basin and climatic characteristics computed by a geographic information system (GIS) 11
Regression analysis 14
Regionalization of flood-frequency estimates 15
Regional regression equations 16
Limitations and accuracy of regression equations 16
Discussion of equations and regions 18
Sensitivity analysis 18
Comparison of weighted average 100-year discharge estimates with other methods 20
Estimation of peak discharge using regression equations 20
Gaged sites 24
Ungaged sites 25
Sample computations 25
Summary 26
References cited 27

FIGURES

1. Map showing hydrologic regions used in the study and locations of streamflow- and
crest-stage gaging stations, Oahu, Hawaii 3

2. Block diagram showing typical drainage-basin shapes for Oahu, Hawaii 4

3. Graph of monthly occurrence of 2,317 annual peak discharges for 79 stream-gaging stations,
Oahu, Hawaii, 1913-88 4

4. Graphs showing relation of weighted average 100-year discharge estimates to; A, maximum
known discharge; B, peak discharge; C, design discharge; and D, 100-year estimated
discharge, Oahu, Hawaii 21

iii


Table 3. Estimated peak discharges for selected recurrence intervals and maximum known
discharges at stream-gaging stations on Oahu, Hawaii--Continued

Maximum known discharge

Station Q2 Os 210 05 O50 Q100 Water Discharge
number (ft3/s) year (£t3/s)
283480 1,220 2,720 4,090 6,280 8,250 10,500 1971 7,300

1,100 2,430 3,640 5,540 7,240 9,240
1,210 2,680 4,010 6,100 7,950 10,100

283600 102 172 230 315 388 469 1982 430
52 94 132 193 249 316
98 162 212 285 347 416

283700 82 141 189 260 321 388 1965 376
52 94 132 193 249 316
80 135 179 243 300 363

284000 409 868 1,290 1,960 2,580 3,300 1965 5,110

581 1,230 1,820 2,740 3,570 4,560
418 897 1,350 2,080 2,770 3,590

284200 469 766 988 1,290 1,540 1,790 1982 1,180
599 1,270 1,880 2,830 3,690 4,710
489 876 1,250 1,880 2,490 3,230

291000 600 1,160 1,650 2,430 3,140 3,960 1963 2,230
608 1,290 1,900 2,880 3,750 4,780
601 1,190 1,730 2,610 3,420 4,380

294900 2,290 4,550 6,280 8,600 10,400 12,200 1965 8,800
1,070 2,360 3,530 5,370 7,020 8,960
2,190 4,290 5,830 7,860 9,470 11,200

296500 3,270 4,420 5,090 5,830 6,310 6,750 1963 5,430
4,560 5,880 6,380 7,040 7,320 7,860
3,410 4,740 5,420 6,150 6,580 7,040

303000 1,860 2,880 3,560 4,400 5,010 5,600 1974 5,700
2,540 3,610 4,190 4,970 5,400 6,010
1,920 3,020 3,700 4,530 5,100 5,690

304200 861 1,420 1,820 2,350 2,750 3,160 1982 2,390
620 1,070 1,430 1,960 2,310 2,760
827 1,320 1,700 2,220 2,600 3,030

304500 1,380 2,390 3,120 4,080 4,820 5,560 1982 4,920

784 1,440 2,000 2,870 3,510 4,310
1,320 2,190 2,840 3,770 4,490 5,250

310501 675 2,160 3,850 6,980 10,100 14,100 1963 4,640
1,100 2,090 2,970 4,380 5,450 6,820
720 2,140 3,630 6,300 8,900 12,300

311000 217 552 891 1,480 2,040 2,720 1965 1,390
274 667 1,120 1,980 2,740 3,750
223 576 950 1,610 2,220 2,980

318000 177 372 539 789 1,000 1,240 1974 982
199 547 1,000 1,930 2,830 4,070
180 422 690 1,170 1,610 2,160

325000 1,230 1,920 2,410 3,060 3,560 4,070 1975 3,390

1,690 2,730 3,470 4,530 5,230 6,130
1,290 2,120 2,720 3,500 4,050 4,660

34


WEIGHTED 100-YEAR ESTIMATED DISCHARGE,

WEIGHTED 100-YEAR ESTIMATED DISCHARGE,

100,000 T T
c
° Co
fal © LEEWARD - Region 1 a<«
2
9 RD - Regi a &
8 0000 b WINDWARD - Region 2 5 ‘a |
o NORTH - Region 3 ° Ke)
E A
oi 8 °9 °
a HR
o
ii ° ae
Lu fo) A
ire
Q
a a 6
=) E 4
2 1,000
Zz
100 , t
100 1,000 10,000 100,000
DESIGN DISCHARGE, IN CUBIC FEET PER SECOND, FROM
PLATE 6, CITY AND COUNTY OF HONOLULU (1988)
100,000 T T
D
° °
fa) © LEEWARD - Region 1 a
rol a
8 10,000 | WINDWARD - Region 2 ° é 4
a) 4 NORTH- Region 3 ° B00 &
ia Of
a ° om
5 8 a8 a
wi oO &
a
iS)
a 6
3 4
Q 1,000
2
100 ; 1
100 1,000 10,000 100,000
100-YEAR ESTIMATED DISCHARGE, IN CUBIC FEET PER SECOND,
FROM NAKAHARA (1980)

Figure 4. Relation of weighted average 100-year discharge estimates to; A, maximum known
discharge: B, peak discharge; C, design discharge; and D, 100-year estimated discharge,
Oahu, Hawaii--Continued.

22


U.S. DEPARTMENT OF THE INTERIOR
BRUCE BABBITT, Secretary

U.S. GEOLOGICAL SURVEY
Gordon P. Eaton, Director

Any use of trade, product, or firm names in this publication is
for descriptive purposes only and does not imply endorsement
by the U.S. Government.

For sale by the U.S. Geological Survey
Earth Science Information Center
Open-File Reports Section

Box 25286, MS 517

Denver Federal Center

Denver, CO 80225

For additional information

write to:

District Chief

U.S. Geological Survey

677 Ala Moana Bivd., Suite 415
Honolulu, HI 96813


Table 3. Estimated peak discharges for selected recurrence Intervals and maximum known
discharges at stream-gaging stations on Oahu, Hawaii

[f3/s, cubic foot per second, Estimated peak discharge is Q;, where t= 2, 5, 10, 25, 50, and 100 years. Upper
row, values are from individual frequency curves. Middle row, values were computed by using the regression
equations. Lower row, values are the weighted average of the station Q; (upper row) and regression Q;
(middie row), see equation 3 on page 25. All regression estimates include the retransformation bias-correction
factor]

Maximum known discharge

Station Q2 O5 Q10 025 O50 Q100 Water Discharge
number (ft3/s) _year (ft?/s)
200000 2,500 3,710 4,470 5,380 6,020 6,630 1982 5,640

1,650 2,340 2,850 3,530 4,070 4,640
2,450 3,600 4,290 5,100 5,680 6,240

201000 1,020 1,450 1,740 2,100 2,380 2,660 1940 2,320
1,500 2,120 2,590 3,210 3,710 4,230
1,070 1,550 1,900 2,380 2,760 3,160

204000 2,490 3,160 3,610 4,180 4,610 5,040 1963 4,660
2,840 4,380 5,560 7,140 8,420 9,750
2,550 3,410 4,140 5,190 6,070 7,010

206000 953 1,410 1,730 2,150 2,470 2,800 1955 2,410
1,970 2,830 3,470 4,320 4,990 5,700
1,200 1,850 2,400 3,160 3,760 4,390

208000 1,750 2,980 3,920 5,220 6,280 7,410 1963 5,460
2,340 3,680 4,720 6,130 7,280 8,480
1,820 3,090 4,090 5,460 6,590 7,770

208500 598 1,440 2,180 3,290 4,220 5,220 1968 3,160
503 915 1,260 1,780 2,220 2,710
577 1,290 1,850 2,640 3,260 3,930

210500 2,010 5,260 8,660 14,700 20,700 =. 28,100 1963 15,600

4,300 8,700 12,700 18,500 23,600 29,200
2,380 5,980 9,760 16,000 21,800 28,600

211200 1,190 3,240 5,280 8,660 11,800 15,400 1974 7,340
1,900 3,930 5,780 8,600 11,100 13,800
1,300 3,380 5,420 8,640 11,500 14,700

211300 509 1,120 1,690 2,610 3,450 4,430 1966 3,640
799 1,710 2,560 3,900 5,100 6,460
544 1,210 1,870 2,960 3,960 5,120

211500 229 708 1,270 2,350 3,500 4,980 1976 3,220
647 1,480 2,290 3,590 4,790 6,180
280 833 1,490 2,690 3,900 5,390

211600 306 638 929 1,380 1,780 2,220 1982 1,450
523 1,130 1,710 2,610 3,440 4,380
333 720 1,100 1,730 2,310 2,980

211700 510 1,300 2,120 3,590 5,030 6,820 1976 4,310
664 1,570 2,460 3,940 5,300 6,880
534 1,350 2,210 3,710 5,130 6,840

211800 286 871 1,520 2,720 3,930 5,440 1982 3,640
581 1,330 2,050 3,220 4,300 5,540
324 950 1,640 2,860 4,050 5,480

30


2, =[0,(N)+0, (EO)|(N+E0), — ®

where: Q,, = the weighted average peak discharge, in
cubic feet per second, for the t-year
recurrence interval;

2,, = the t-year peak discharge, in cubic feet
per second, computed from the gaged
record;

Q,, = the regional regression estimate, in cubic
feet per second, from the equation for
the t-year peak discharge;

N = the number of years of gaged record at
the station (table 1); and

EQ = the equivalent years of record associated
with the regression equation (tables 8-
10).

UNGAGED SITES

The purpose of regional analysis is to transfer
flood-frequency data spatially. This is done by using the
derived regression equations for ungaged basins. Flood
estimates for ungaged sites are determined from the
regression equations in tables 8 through 10 depending
on the region in which the ungaged basin lies. If an
ungaged site is near a gaged site on the same stream,
Thomas (1987) provides four equations that use both
the regression equation estimate and the discharges
from the flood-frequency analysis of the gaged record.
A criterion for using these equations requires that the
drainage area of the ungaged site be within 50 to 150
percent of the drainage area of the gaged site. These
equations were evaluated for applicability to streams on
Oahu by using four pairs of gaged sites that met the
drainage-area size criterion. The equation providing the
best results was that originally presented by Sauer
(1973). This equation is:

2,,=C,(C,, 4

where:

Q,, = the final t-year peak discharge, in cubic feet
per second, for the ungaged site;
C,, = an adjustment factor defined as:
C,= R-(2([DA, - DA) /DA,KR-1.0), (5)

where:
R = the ratio of the weighted discharge

25

estimate of Q,, for the gaged site to
the regression estimate of Q, for the
gaged site;
DA, = the drainage area, in square miles, of the
gaged site;
DA, = the drainage area, in square miles, of the
ungaged site;

DA, - DA,| = the absolute value of the difference
between the gaged and ungaged
drainage areas;

Q,,, = the regression estimate of Q; , in cubic
feet per second, at the ungaged site.

A note in using equation 5: The ratio C,, approaches
1.0 when the drainage area of the ungaged site
approaches either 50 or 150 percent of the drainage area
of the gaged site. When the drainage area of the
ungaged site is more than 50 percent smaller or larger
than that of the gaged site, no adjustment is applied to
the regression estimate to account for the data at the
gaged site.

SAMPLE COMPUTATIONS

The following examples illustrate the use of the
methods described in this report for estimating peak
discharges at gaged and ungaged sites.

Example 1. Gaged site: Estimate the 50-year peak
discharge at Moanalua Stream near
Honolulu (station 228000).

First, check to see if site is affected by significant
diversions, regulations, or urbanization. Next,
determine in which region the station is located.Station
228000 is in the leeward Oahu region (fig. 1) and is not
affected by significant diversions, regulations, or
urbanization. Table 6 gives the equation for the 50-year
peak flood as:

Oso,= 425 (DA0-45 )(P 0.368 )( 1.037), ©
with an equivalent years of record (EQ) of 13.7. The
basin characteristics needed are drainage area (DA) and
median annual precipitation (P), which for station
228000 are 2.73 mi2 and 124 in., respectively (table 4).
These values fall within the ranges of values for each
characteristic (table 9), so equation 6 is applicable for
this site. Substituting the respective values in equation
(6) gives the regression estimate:


Table 1. Stream-gaging stations on Oahu, Hawaii, used in the study--Continued

Type

Station Years of Period of of

number __ Station name record record gage
247200 — Waialaenui Gulch at Honolulu... 11 1958-68 csg
247500 = Wailupe Gulch at Aina Haina.. 31 =: 1958-p csg
247900 Kuliouou valley at Kuliouou. 19 1970-p csg
248800 Inoaole Stream at Waimanalo. 31 1958-p csg
249000 Waimanalo Stream at Waimanalo.. 24 =: 1963; 66-p csg
249100 = Kaelepulu Stream tributary at Kailua 26 1966-p csg
254000 Makawao Stream near Kailua.... 31: 1958-p rec
260500  Maunawili Stream at Highway 61 near Kailua. 31 1958p csg
265000 Kawa Stream at Kanehoe. 20 1965; 68-p csg
270900 — Luluku Stream at altitude 220 feet near Kaneohe... 20 1967-87 Tec
273900 —- Kamooalii Stream at Kaneohe womens . 23 ~=—-:1958-80 rec
274499 = Keaahala Stream at Kamehameha Highway at Kaneoh 30 = 1959-p csg
275000 Haiku Stream near Heeia.... 49 = 1915-19, rec

39-77, 83-p

278000 —_Iolekaa Stream near Heeia.. 27 ~—: 1940-70 rec
279500 22 ~=—-1965-p esg
283000 34 1937-71 Tec
283480 26 = 1963-p esg
283600 South Fork Waihee Stream near Hee’ 26 1963-p rec
283700 North Fork Waihee Stream near Heeia.. 26 1963-p Tec
284000 — Waihee Stream near Heeia. 45 1938-82 Tec
284200 — Waihee Stream near Kahaluu..... 14 :1975-p rec
291000  Waiahole Stream at altitude 250 feet near Waiahole. 13° 1956-68 rec
294900  Waikane Stream at altitude 75 feet at Waikane. 29° 1960-p rec
296500 = Kahana Stream at altitude 30 feet near Kahan: 29 1960-p rec
303000 — Punaluu Stream near Punaluu...... 35 1954-p Tec
304200 Kaluanui Stream near Punaluu. 22 + ~=1967-p rec
304500 — Kaluanui Stream at Hauula. 31 =: 1958-p csg
310501 Malaekahana Stream at altitude 30 feet near Kahuku 30 = -:1959-p csg
311000 — Oio Stream near Kahuku... 31: 1958-p csg
318000 § Paumalu Gulch at Sunset Beach. 21 1968p csg
325000 Kamananui Stream at Pupukea Military Road near Maunawai. 25 1964-p Tec
330000 _ Kamananui Stream at Maunawai... 31 =: 1958-p rec
331000 Waimea Gulch near Kawailoa Camp. 21 1968-p csg
340000 = Anahulu River near Haleiwa. 31: 1958-p csg
343000 —_ Helemano Stream at Haleiwa. 15 1968-82 rec
345000  Opaeula Stream near Wahiawa 29 = 1960-p Tec
350000 _ Opaeula Stream near Haleiwa... 33 :1956-p csg



DRAINAGE-BASIN AND CLIMATIC CHARACTERISTICS
COMPUTED BY A GEOGRAPHIC INFORMATION
SYSTEM (GIS)

To perform a regional regression analysis,
drainage-basin and climatic characteristics that can be
related to peak discharges must be quantified in a
consistent manner. GIS software was used to compute
values for 13 of the 15 characteristics described in this
section. The main-channel slope and drainage-basin
area were computed by the manual methods of
Nakahara (1980). The 13 remaining characteristics were
determined using seven digitized coverages that
contained drainage-basin outlines, stream-channel
lengths, area of forest cover, area of urban cover,
topographic contours, lines of equal median annual
rainfall, and lines of equal 24-hour rainfall intensities
that have a 2-year recurrence interval. All coverages
except topographic contours were digitized from the
relevant data on the 1983, 1:24,000 topographic
quadrangle maps of Oahu. The lines depicting median
annual rainfall and the 2-year, 24-hour rainfall intensity
were first transferred to the topographic maps and then
digitized. The topographic contour map was created by
using the digital elevation model for the island of Oahu
(U.S. Geological Survey, 1987). The digital elevation
model was converted by GIS software to a topographic
contour map coverage with contours at 40-meter
intervals. Basin and climatic characteristics for each of
the gaged drainage basins used in this study are listed in
table 4 (at end of report). A statistical summary for each
of the characteristics is given in table 5. Descriptions of
the drainage-basin and climatic characteristics along
with the methods for their computation are given
below.

BW: The average drainage-basin width, in miles,
determined as a ratio of drainage-basin area (DAG) to
main-channel length (CL): BW = DAG / CL. BW is
computed after both drainage area and channel length
have been determined.

CL: The main-channel length, in miles, is the
distance along a stream from the gaging station to the
drainage-basin divide. Channel length was determined
by GIS from digitized 1:24,000-scale topographic
maps. If a stream flowed through many smaller basins
(a major basin stream), the longest possible route was
determined and the lengths of stream segments flowing
through the sub-basins were added together.

12

CLD: A shape factor of a drainage basin computed
by calculating the ratio of main-channel length (CL) to
the diameter of a circle having the same drainage area as
the basin (CLD = CL/diameter). The inverse of this
factor, diameter divided by channel length, is known as
the elongation ratio (Chow, 1964, p.4-51). This shape
factor often is used to relate time of flow concentration
to basin shape (Davis, 1974). Large CLD values
characterize long, narrow basins whereas small values
denote short, wide basins.

CS: The main-channel slope of a drainage basin, in
feet per mile. This value is computed by dividing the
altitude difference between points located at the 10-
percent and 85-percent distances of the main-channel
length (CL) measured upstream from the gaging
Station, by the distance between these points (Benson,
1962). This characteristic was not computed by GIS.

DA: Area of a drainage basin, in square miles.
Determined by planimeter following standard USGS
guidelines on 1:24,000 topographic maps. These values
have been previously published for each gaging station
in the annual data reports (Nakahara and others, 1989).

DAG: Area of a drainage basin, in square miles.
Determined by GIS from digitized basin outlines on
1:24,000 topographic maps. For basins that consist of
more than one drainage basin (major basins), the areas
of the smaller basins (sub-basins) were added together.

E: The mean drainage-basin altitude, in feet above
mean sea level, measured by overlaying a GIS coverage
of drainage basins on a 40-meter contour coverage
created from a digital elevation model and then
calculating the area-weighted average to obtain a mean
altitude in that basin. An area-weighted average is
computed by multiplying the average altitude between
two contours by the area between the same two
contours and then summing up all these products and
dividing by the total basin area. The value in meters was
converted to feet.

FC: Forest/vegetative cover of a drainage basin, in
percent. This variable is the ratio of the drainage area
covered by forests and/or vegetation, as shown in green
on the 1:24,000 topographic maps, to its total drainage
area. Computed from a GIS coverage, which
differentiated the green areas within each drainage
basin.