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HYDROLOGICAL DATA AND PEAK DISCHARGE DETERMINATION
OF SMALL HAWAIIAN WATERSHEDS: ISLAND OF OAHU
I-Pai Wu
Technical Report No. 15
HAES Technical Paper No. 939
December 1967
This is a report of cooperative research published with t heapproval of the Director of Wat er Resources Research Centerand the Director of the Hawaii Agricultural Experiment Station.
Project Completion Report
for
PILOT STUDY OF SMALL WATERSHED FLOOD HYDROLOGY, PHASE I
OWRR Project No. B-003-HI, Grant Agreement No. 14-01-0001-1061
Principal Investigator: I-pai Wu
Project Period: July 1, 1966 to August 31,1967
The programs and activities described he~ein were supported in part by fundsprovided by the United States Department Of the Interior as authori zed underthe Water Resources Act of 1964, Public Law 88- 379. It was also partly supported by funds provided by the City and Count y of Honolulu.
ABSTRACT
Basic hydrological data including rainfall, runoff, historical
flood, watershed characteristics, soil type,and land use of Hawaiian
small watersheds on Oahu have been compiled and analyzed. Frequency
analysis for annual peak discharge was made for 23 small watersheds on
Oahu by using Gumbel's extreme value theory. A regional flood formula
has been derived for Honolulu and between mountain ranges of the island
of Oahu through the use of multiple regression. The regional flood
formula expressing peak discharge as a function of watershed area,
length and height and a precipitation index defined as 100-year, 24
hour rainfall in inches can be used to estimate peak discharges for
ungaged areas. The rational formula which is currently used for drain
age areas less than 100 acres has been evaluated through the study of
overland flow.
iii
CONTENTS
LIST OF FIGURES v
LIST OF TABLES vii
INTRODUCTION 1
OBJECTIVES AND SCOPE 2
PROCEDURES 2Part I. Compiling Available Basic Hydrological Data 2
1. Ra i nfa11 22. - Runoff 143. Historical Flood Survey 214. Watershed Characteristics 255. Soil Type and Land Use Classification 336. Others-- Infi ltra ti on, Evapora ti on 33
Part II. Review of Present Design Criteria ; 351. Pre~ent Approaches of Flood Peak Estimation 362. -Des i gn Cri teri a in Hawa i i 37
Part III. Peak Discharge Determination for Small Hawaiian Watersheds .. 421. Peak Discharge Determination for Watershed Area Larger
Than 100 Acres 422. Peak Discharge Determination for Watershed Area Equal
tn or Less Than 100 Acres 56
RESULTS AND CONCLUSIONS. ; ~ 67
AC KNOWLEDGEMENTS ~ 69
BIBLIOGRAPHY 70
APPENDIX 73
LIST OF FIGURES
Figure
Rain gage stations on Oahu, Hawaii (operating in 1966) 3
2 Median annual precipitation - Oahu 7
3 Median monthly rainfall for stations 704, 798, 944 8
4 100-year rainfall, duration from 30 minutes to 24 hours of Oahu,Hawaii (USWB Tech. Paper No. 43) 9
5 Correction factor for converting l-hour rainfall to rainfallintensities of various durations (after Chow) ll
v
LIST OF FIGURES (contld)
6 24-hour probable maximum precipitation for Island of Oahu 12
7 General estimates of SPS index rainfall isohyets--representingdepth of precipitation over one square mile in 24 hours 12
8 Comparison of the depth-duration relation of 100-year frequencyrainfall, probable maximum rainfall, standard project storm ofOahu, Hawaii, with the worldls greatest rainfalls 13
9 Isohyetal map of Oahu, showing maximum 24-hour rainfall,February 3-4, 1965 (from USGS Report R26, 1965) 15
10 Map of Oahu showing location of gaging stations during fiscalyear 1966 (from USGS Progress Report No. 9) 16
11 Hydrograph showing discharge in Waihee Stream, at station 2838,and in Waiahole Stream, at station 2910, Oahu, during theperiod February 3-5, 1965 (from USGS Report R26, 1965) 23
12 The flood areas and frequencies in Oahu (1917-1965) 24
13 Relationship between the daily flood-producing rainfall and its5-dayantecedent rainfall of Honolulu district, Hawaii 26
14 Relationship between the daily flood-producing rainfall and its5-day antecedent rainfall of the windward side, Oahu, Hawaii 27
15 Average hypsometric curves for Oahu small watersheds 30
16 General variation in stream slopes in relation to watershed areas.31
17 Comparison of 100-year peak discharge predicted by Gumbel IS
extreme value analysis with the discharge predicted by envelopecurve 44
18 Regression line for theoretical 100-year instantaneous peakdischarge against watershed characteristics and precipitationindex (for windward side of Oahu, Zone 1) 46
19 Regression line for theoretical 100-year instantaneous peakdischarge against watershed characteristics and precipitationindex (for Honolulu areas, between mountain ranges, leewardside of Oahu, Zones II, III, IV) 47
20 Comparison of 100-year discharge estimated by regression formula,equation 1, with actual data 48
21 Comparison of lOO-year discharge estimated by regression formula,equation 2, with actual data ...... ... . ......................•..... 49
22 Coaxial correlation chart for peak discharge determination byequation 2 52
vi
LIST OF FIGURES (cont 1d)23 Relationship between the n-year and 100-year peak discharge 54
24 Statistical relationship between the designed return periodand project life with respect to percentage of assurance 55
25 Typical experimental results obtained for uniform steady flowon smooth concrete (taken from Paper 17, U. S. WaterwaysExperiment Station, Vicksburg, Mississippi) 59
26 Time to peak discharge against watershed area for small water-shed on Oahu, Hawaii ············· ··· .66
LIST OF TABLES
Tabl e
Rain gage stations on Oahu, Hawaii (operating in 1966) 4
2 Rain gage density of Oahu, 1966 6
3 List of stream gage stations (1966) 17
4 Maximum recorded flood peaks in Oahu (through June 30, 1966) 18
5 Historical flood survey (1917-1965) - type of storm, storm rain-fall, antecedent rainfall condition, and flood situation 22
6 Watershed characteristics 29
7 Soil type and land use of small watersheds on Oahu, Hawaii 34
8 Comparison of the constant infiltration capacity f of somecHawaiian soils and some soils of mai nl and United States 35
9 A survey (1957-1966) of design criteria for drainage facilitiesused by City and County of Honolulu 39
10 ~esign ~~chnique of peak discharge used by different agencies1 n Hawa 11 ••••• •••• • ••••••••••• ••••••• •••• • • • ••••••••••••• ••••••••• 40
11 Comparison of predicted 100-year peak discharge from threedifferent methods and esti mated peak from Chow ls envelopecurve 43
12 Watershed characteristics, precipitation index, and 100-yearpeak discharge for multiple regression analysis for 20 smallwatersheds on Oahu 45
13 Multiple regression formulas for 100-year peak discharge 0100of Oahu sma 11 watersheds 50
vii
INTRODUCTION
Increased utilization of land located in potential flood areas
has created a flood probl em in Hawaii. Inadequate bases for planning and
design of flood protection stem largely from lack of basic rainfall ~n~
stream runoff data. Watersheds in .Hawa i i differ from watersheds in con~
tinental areas in size, precipitation received, topography, infiltration
capacity, vegetation, interflow, and detention storage. Rainfall-runoff
relationships and drainage design criteria are empirically derived under
temperate and continental conditions, resulting in their unsatisfactory
fit to tropical oceanic-island conditions.
The variations of precipitation in Hawaii in both space and time
are so extreme that in spite of the extraordinary density of rain gages,
almost no records of distribution of precipitation in any watershed of
consequence during a storm are available. Derivation of satisfac-
tory relationships and criteri~ for geographical areas like the Hawaii
an Islands will depend on a greatly increased and improved body of data
and a modified theoretical and appropriate empirical basis for their
analyses.
The intent of this project is to make a pilot study of flood
hydrology in Hawaii and to plan a long-term research program. The
initial phase includes:
1. Review of existing rainfall, streamflow, and other data per
taining to floods in Hawaii.
2. Review of the present instrumentation schemes for obtaining
such data.
3. Review of the hydrologic design criteria for drainage.
4. Review of rainfall-runoff relationships previously determined
and trial analyses of additional r elationships.
5. Appraisal of applicability of standard flood flow formulas.
6. Means for putting rainfall-runoff relationships and design
criteria on a sounder basis and utilizing topographic, geolo
gic, soils, and vegetation data.
The above outline is reco gni zed only as a framework in the explor
atory pilot project. It is expected that as experience dictates,
suitable directions for res earch wou l d be i ndi cated .
2
OBJECTIVES AND SCOPE
The objectives of this study are: (i) to analyze and utilize
existing hydrological data to establish a sounder relationship between
rainfall-runoff and design criteria of floods in the Hawaiian Islands,
and (ii) to search and compile basic information on small Hawaiian water
shed hydrology.
This study is based on 37 small watersheds on Oahu, Hawaii.
Their sizes range from 0.03 to 9.73 square miles. However, 33 of these
have an area less than 5 square miles. Hawaii is the only region in
the United States with a fairly long rainfall-runoff record for water
sheds of this size.
PROCEDURES
This study includes three parts: compiling available basic
hydrological data, review of present criteria, and peak discharge
determination for small Hawaiian watersheds.
Part I. Compiling Available Basic Hydrological Data
1. RAINFALL
A. RAIN GAGES. On the island of Oahu, an area of 602 square miles,
there are 49 recording gages, 55 non-recording but daily read gages,
and 172 stations classified as "others." In the latter stations, read
ings are taken after rainfall in 84 stations; weekly readings are taken
in 28 stations; monthly readings are recorded in 54 stations; and 6 sta
tions are recorded irregularly. There has also been 214 discontinued
gages. Most of the daily and recording stations are maintained by the
U. S. Weather Bureau; those classified as others are maintained by dif
ferent agencies, such as the U. S. Army, U. S. Geological Survey, sugar
plantations, and other private agencies which set up rain gages to serve
their own special purpose.
A map of the recording and non-recording rain gages on Oahu
(operating in 1966) and a list of rain gage stations are shown as
Figure 1 and Table 1, respectively.
B. RAI N GAGE NETWORK DENSITY. Rain gage network density in Hawaii
3
724
-------------
•772
o187 1
•o 773.9 o771 118
o78.
118 o',"21
780 ()
• •776 2 780.90 780 5
0
0 0715
7n 112 00
713
7090 101
Figure 1. Rain gage s tat i ons on Oahu, Hawai i (operating in 1966).
4
Table 1. Rain gage stations on Oahu, Hawaii(operating 1966)
Gage stationYear Years
Station name Maintained by established of RemarksNumber Record
I--Recording &nonrecordingstation ()704 Honolulu USGS 1905 62
Substation707 HSPA Expt . Sta. HSPA 1937 30713 Univ . of Hawaii Dept. of 1958 9
Geosciences716 Manoa Tunnel 112 BWS 1929 38718 Pa1010 Valley BWS 1929 38721 Wilhelmina Rise BWS 1927 40724.6 Kaa1akei Mrs. Millie 1965 2
Zapata724.7 Kamehame Hawaii Nat'l 1965 2
Guard725 .2 Hoku10a H.V. von Holt 1965 2771.2 Ha1awa Shaft BWS 1965 2777 Ka1ihi Res . Site BWS 1927 40780 Tantalus Peak BWS!USWB 1965 2784 Pauoa Flats BWS 192!1 38787.1 Maunawili HSPA 1954 13791. 3 Kailua Fire Sta. Ben Nutter 1965 2800.1 Makaha Valley Capital Inv. Co. 1966 1804 Lua1ua1ei US Navy (Public 1965 2
Works Dept .)807 Camp 8 CPC CPC 1942 25837 Wai aho1e Oahu Sugar Co. 1955 12844 Mount Kaala FAA 1965 2847 Wai alua Waialua Agr. Co. 1965 2863 Wah iawa Dam Waialua Agr. Co. 1955 12870 Opaeu1a Waialua Agr. Co. 1941 26881 He1emano Intake Wa ialua Agr. Co. 1957 10884 Puna1uu Kahuku PItn . Co. 1965 2892 Waimea Waialua Agr. Co. 1943 24906.3 Kawe1a Mauka Hawaii Nat '1 1965 2
Guard912 Kahuku Kahuku PItn. Co. 1965 2
Il--Recordinggages •752 Waipio HSPA (Oahu Sugar) 1940 27
752.5 Wa ipio F1d. L HSPA 1960 7754.1 Pearl City J ames Muneno ·1966 1
Terrace771 North Ha1 awa BWS 1929 38772 Moana1ua USGS 1926 41773.3 Ka l i hi Stream USGS (for USCE) 1962 5 Kalihi-waena
#5 School773.9 Kalih i #2 USGS (for USCE) 1962 5776.2 Ka1 ih i #4 USGS (for USCE) 1962 5780.8 Dowsett J.L. Banning 1965 2
Hi ghl ands781.4 Kamooa1ii USGS 1959 8
Stream802.4 Puea Mauka USGS 1960 7
Ditch805 Leilehua CPC 194 2 25809.2 Fie l d 166 Oahu Sugar Co . 1965 2832.2 Kip apa USGS USGS · 1957 10839 Kaha1uu USGS 1935 32842.1 Makaha (USGS) USGS 1959 8877.6 PRI He1emano PRI 1965 2886.4 Kah ana Stream USGS 1961 6
886.6886.7897.1
Waikane StreamWaiahole StreamKamananuiStream
Table I. (continued)
USGSUSGSUSGS
195919601963
874
5
III--Nonrecording(daily) 0700.1702.2
703
705
709
712
715
717.2724724.2724.4
741761
770773
780.5
788
794
796
798
833
836838840.1
855896.3
903
Field 9US Magnetic
Observatory 2Honolulu WBAirport
BeretaniaPumping Sta .
PunchbowlCrater
Manoa
Waialae -Kahala
Waikiki ShellMakapuu PointLunalilo HomePortlock Road
Ewa PItn .Mea Fld 75
MoanaluaKapalama
Tantalus Drive
St. StephensSeminary
Waimanalo
Makaha Kai
Wai anae
Koolau Dam
WaiawaKaneohe RanchCoconut Island
Kemoo Camp 8Waial ee Livestock ResearchFarm
Laie
Ewa PlantationUS Coast &
Geodetic SurveyUSWB
BWS
Nat'l MemorialCemetery
Dr. A.R. Keller
H.W. Butzine
J . PurintonUSCGLunalilo HomeN. Barker
Ewa Pl antationOahu Sugar
J . A. RoxburghKamehameha Schools
M. Newman
St. St ephensSeminary
HWA
Capit al Investment
Capi ta l Investment
US Army (PostEngi neer s,Schof i e l d Br rk s)
Oahu SugarKane ohe -RanchU of H, Marine Lab
Kemoo Camp 8Waialee Li vestock
Research Farm
Kahuku Pl antat ion
Dec. 19631960
1947
1945
1950
1919
1921
1957190719561954
18911907
19011922
1948
1943
1894,
1921
1891
1914
191619441949
19241963
1910
47
20
22
17
48
46
10601113
7660
6645
19
24
73
46
76
53
512318
434
57
Replaced #7026/60
Charts on fileNWRC
BWS Office;Data Mag1946-48
Reloc. 9/53205' N from210' elev.
No data10/51-1/53
Reloc. 6/59Approx.IOO' SSENo data7/58-5/59
Mea Fld 35;Waimalu (500)
Reloc . 4/26from old HSPAExpt. Sta . ;r e Ioc , 1/60345' E from540' elev .
Reloc. 5/57short dist.
Rel oc . 1/55across street;no data1/51-1 2/54
Makaha Makai;data doubtfulprior to 1928
Waianae mi11;r e l oc . 1/483/8 mile NNE
Army reservoir
No dat a2/ 51-11/54
Kemoo 8
is the highest in the United States and has been ranked third in the
world (1). The density of rain gages (operating in 1966) in the Oahu
area is shown as Table 2.
Table 2 . ~al n gage den sity of Oahu, 19M
AreaLoca t i on sq. mi'. Rai n gage s
Zone I - -Wlndwa rd side I n 15
Zone 1I --lIono l ulu dis tri c t III2 30
Zone 111- - be tvecn mounta in r an ge 2<> 2 21
Zone IV- -Ieeward si de 116 III
Oahu bO~ 7<>
U. S . Mainl and'
·Overa II den s I t y for co at I guous Uni t ed Stn t es .(Dat a I s ac curate a . o f ml d-I960 , USWB)
Dens ityno . o f gage s/l OO sq. ml.
12.3
29.4
8 .0
12. 6
0.4
C. MEDIAN ANNUAL RAINFALL AND SEASONAL DISTRIBUTION. The median
annual rainfall of Oahu, based on records for the period 1933 to 1957
(2)1, is shown in Figure 2. It ranges from 20 inches along the beaches
to 250 inches at the top of the Koolau mountain range. In the seasonal
distribution of rainfall shown in Figure 3, the median monthly rainfall
(1933 to 1957) shows a wet season from October to April and a dry season
from May to September.
D. STORM RAINFALL. Heavy rainfall on Oahu, produced by cold fronts
and Kona storms, occurs during the winter season (October-April). Kona
storms approaching from the leeward direction, as opposed to the normal
east northeast tradewind direction, cover a large area and may continue
for several days . Most flood damage has been caused by Kona storms
as will be shown later in the historical flood survey. During the
summer season, tropical storms occur and sometimes produce local flooding.
E. RAINFALL DEPTH- FREQUENCY-DURATION RELATIONS. The most recent
data on rainfall depth-frequency-duration relations of the Hawaiian
Islands have been published in 1963 by the U. S. Weather Bureau in its
Technical Paper 43 (3). A 100-year rainfall map of Oahu with rainfall
duration from 30 minutes to 24 hours is presented as Figure 4. For
durations less than 30 minutes, a correction factor for converting
lA bibliography of earlier (before 1959) literature on Hawaiian rainfallis listed in (2).
7
NOR.TH
•coIII
"oovoIJl
Figure 2. Median annual precipitation - Oahu.
2. °-aO'
NOTE: Isohyets (in inches) based on values from 130 gages for period 1933-1957.(from "Rainfall of the Hawaiian Islands," Hawaii Water Authori ty)
8
~t-~-+---I----+---t-'---+---+-'--+----+----f---t--~
I,,,il
II:
t,I,
II!
~
II
II
II
II
II,
II
II
II
1//
II
cJ)w::r::uz
..J
~lt--'r---l+-'l'--~--+--~I-----+----+---t----+-T---+---1--.-..MU.z«0::
)...I:I:IZa~
J F M A MMONTH OF
J J
YEARA 5 o D
Figure 3. Median monthly rainfall for stations 704, 798, 944.(from "Rainfall of the Hawaiian Islands," Hawaii WaterAuthority)
1
Figure 4. 100-year rainfall, duration from 30 minutes to 24 hours,of Oahu, Hawaii (USWB Tech. Paper No. 43).
10
I-hour rainfall to rainfall intensities of various duration, as in
Figure 5, has been derived by Chow (4).
F. PROBABLE MAXIMUM PRECIPITATION AND STANDARD PROJECT STORM.
The probable maximum precipitation for the Hawaiian Islands, derived
by the U. S. Weather Bureau and published in its Hydrometeorological
Report No. 39 (5), was obtained by first establishing a non-orographic
probable maximum precipitation and then adjusting it to island topography.
The standard project storm (SPS) is defined as an estimated
or hypothetical storm that might be expected from the most severe flood
producing rainfall, depth-area-duration relationships, and isohyetal
pattern that is considered reasonably characteristic of the geographi
cal region involved . The study of SPS was made in 1962 by the U. S.
Army Engineers (6).
Maps showing the 24-hour probable maximum precipitation and
generalized estimates of SPS index rainfall isohyets (24-hour periods
in areas larger than 1 square mile) for Oahu are shown as Figures 6
and 7.
G. COMPARISON WITH THE WORLD 'S GREATES T RAINFALLS. A comparison
of the depth-duration relation of the 100-year frequency rainfall, the
probable maximum precipitation, and the standard project 's t or ms of
Oahu, and the world's highest rainfalls is made in Figure 8.
The rainfall depth-duration relationships can be expressed
by several straight lines that have similar slopes as the line of the
world's greatest rainfall developed by Jennings (7). The probable
maximum precipitation coincides with the world's greatest rainfalls
and the 100-year maximum point .rainfall is nearly in agreement with
the standard project storm. The 100-year rainfall of Honolulu and
windward Oahu can be expressed by a single straight line. Empirical
relations of rainfall depth-duration of Oahu can be expressed as
follows:
i. World's greates t rdinfall
ii. Probable maximum precipi tation
iii. Standard pr oject s torm
iv. l OO-year maximum point rai nf a l l
v. l OO-year rainfal l of Honolulu
area and windward Oahu
R = 15.3 DO.486
R = 13.0 DO.486
R = 7. 2 DO.486
R = 6.5 DO.486
R= 4 . 5 D o . 486
'\- 5 ,32.1.0o.? 0."" 0." 0.60.70 •.2.0.10.rfl
q I I I , I. I.
9
7
..5
t---~ v_""t---~~~ ~ 1- ~ l-", -
,7i...-: - ~s51" -~~"'b~
~I- Os~
-~~
~t-.I- """'iii,,; -I- .~ -I- ~ .... -I- ~~~ -,
i,,~
rco"J
E'",~
~..I- -
. i ;i z .l- i: -
I: zIb Q In ~ I>
rUII I ~ I I I 1 1 I I d" 1111.T11l1 I-I~ I I i I II : 11111 I I I II I I II I I I I. - A -O..05
+
3
:l.
o.o.
o.
o.
o.
o.
o.
o.
xz.Q- ~
It..J ::>-JD
~2 %- W~ ?:
I.!)
It I):x:
I
- >-t:
~~wf-
a ZUI
...J0.. ...Jo.....J
4.1:.2
It~~'i. ~u.. ~
~
z 0
~ ~uwlJln! W~ ~o <.JU Z
DV R.Aj ION OF R.AINFALL I NTE.NS.ITY IN HOURS
Figure S. Correction factor for converting I-hour rainfall torainfall intensities of various durations (after Chow).
f-'f-'
12
Figure 6. 24-hour probable maximum precipitationfor Island of Oahu. (from USWB Hydrometeorological Report No. 39)
+NOA.TH
2.1°~O'
Figure 7. General estimates of SPS index rainfall isohyets - representingdepth of precipitation over one square mile in 24 hours.
(from U.S. Army Corps of Engineers)
20
JI I I II III I I I I I I , I 1 II III I I I III1 I I I T r
~0 • WoRLO'S ~R.EJI,'1kS T .& A.IN F A L L 1.0-'l- •• • -0 -~ <_"2;> 1,- -
:JI- , ~....:;---" -
0I- ,.t>b
~~,.
-~ .
0
,~~-
0<L~ \ .• ••
0I- ~ .- -l- I.....~ .--- POINT ....:0
~~"~l3--EJ PROI!>J>,\3LE MA..XIMUM,
~ j."oll R/l...INFA..LL IN 0"...... , H ........ .... I\ .
0-
<1-i. V- -' -I-
~(~ ~ X *X S T At-l I>A~l) PROJEC.T 5TOR "" .-
J ~~~ --- [.....::: "/ i') Ho....a l..\Jl..u .....1'40 \IoJ I t40w,..ll-()
~.
~ V ~-
~~ ~~
~ !;>- 51l)E OF O ..... KU .
) ~; ........, ~~
l- I ~ .... »<> ./ o 0 e \00 - '1'Et>.R """..... )(. . R ..... I N FALL.., -B -b -- 1.,.00. ~V~ ....... O .....~U • --=
-- ",- J,~V v--- -
it ./ .Il-
V' ~~~ D,D..l!::. 100 - '([,Il,.R RAI W F"A..LL.) -
t- ~ t::J -I.........: ~
HONOLULU ;"'ND 'lN 1.... ow .... ItD2- ,..... (!) 1-1 f>' SIO'- OF OAHU., I 11 -~
l,...-
I II1I I 11'1I II I I II I I I I I I I I II I I I I I I
10080GO
40
200
~
.J
.J<! lu,z:;{0::
~
'-J
";;j! 10~ 8
E,
4
2."
Figure 8 . Compari s on of t he depth-duration relation of I OO- year f r equency r ainf al l, probab l e maximumrainfa l l, s tanda r d pro j ect s t orm of Oahu, Hawaii with . the world 's greatest rainfal ls . f-'
VI
~~E.1..?i:::::·~~~~.h:';';A5i:,: ;;::;';'~~~::::;'~~~.:I'ir::·~;;Mrl~- =~-:;.. . "--....:~---
14
H. DISTRIBUTION OF STORM RAINFALL. The distribution of rainfall
varies greatly in the Hawaiian Islands as reflected by the steep rainfall
gradients (several locations exceed 25 inches per mile). An example
of a storm rainfall distribution, the February 1965 flood (8), is shown
in Figure 9. A 24-hour rainfall ranges from 4 inches to 24 inches with
a maximum rainfall gradient of about 8 inches per mile. Under such
distribution of storm rainfall, it is difficult to characterize a
flood-producing storm based on the present high density of rain gages
or even higher for the small Hawaiian watersheds of a few square miles.
2. RUNOFF
A. STREAM GAGE STATIONS IN OPERATION (1966). Of the 58 stream
gaging stations maintained by the USGS (9), 52 are in streams on Oahu,
and the remaining 35 are water-stage recorder gages. There are only
23 gaging stations which have records longer than 12 years. All crest
stage gages have been in operation for less than 10 years.
Records of streamflow discharge collected by agencies other
than the U. S. Geological Survey (10) are also available for 26 sites,
which report flow from ditches, tunnels, and springs and serve a spe
cial need. A location map of active stations is shown. as Figure 10.
Gaging stations are listed in Table 3 with information on gagingsta
tion number, stream name, length of records, and type of gage.
B. MAXIMUM RECORDED PEAK FLOW. A compilation of recorded maximum
discharge from all stream gaging stations on Oahu is shown in Table 4
(data are up to mid-1966).
C. FREQUENCY ANALYSI S OF ANNUAL PEAK DISCHARGE. In this study,
frequency analyses of annual instantaneous peak discharge were made
for 23 stations where there were 12 or more years of records. Discharge
data used were those reported by the USGS. Analyses were made by using
Gumbel's extreme value and Gumbel's extreme log value, the latter was
used by the USGS, and are presented as the Appendix to this report.
The extreme value analysis is based on the principle that if
the largest (or smallest) value is chosen from each of a number of
samples of a variable, the series of extreme values so chosen will
have a statistical distribution which will be independent of the sta
tistical distribution of the original samples from which the extreme
I '!>I°hE: 10 ' Of,' ,sa"loo' 1~1° Is,' roo ' 4!o ' ''''014-0'
lle)ft'
,. '10'
1 '-2.-'
"
ISLAND OF OAHU
Figure 9. Isohyeta1 map of Oahu, showing maximum 24-hour rainfall, February 3-4, 1965.(from USGS Report R26, 1965)
~
U1
~,'l~l.:..<;':~tr.k'"..1f;"~-~~~¥.r.~·-- -~"" .,. = .. - --- -.-.~
I-'Q'\
MILE S
, ,OAHU
! Il~
'" .......... Izo"
EXPLANATION
aGag ing Slol ion
•Creal slage Slo lion
II I I'"
j ! I"
1°
k I ~
--- ---1--I!
\'\ " i r »:
" , -,\ 6[ /. /'"""'\' ,\ \<" i
"-
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"
".... "
-~" <.". \" i'~ ,. WAIPAH
\ -.~·~_i''2 s-e). f· "
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il
...:. .. .1
/ '
\\\ \
/ " ' ....
i.
.-' \9 211 6 \
/ ../,I "
2 i \8~ .....) JS'" 'J/ ."
..f.5/ ~l'/ ~~'iz~-".' ;·~ . ~I~':" - .-..-/'( ~" ' - ... \" .-' ~"",..,_ .., " "-.
/ , " " -. -',./
,/
-,
""''\:)
D
,o
(1). (1)
~ I
"·II----:------ ---l\
~61 I
" .
4 c l /
., '0 ' 0 ' rae-co- es' ,cr .,. 1~7 ·4 0·
Figure 10. Map of Oahu showing location of gaging stations during fiscal year 1966.__r+_~~m IIcce DrOarAss Deport :!\To 9 c9"1
17
Table 3. List of stream gage stations (1966)
Stat i on No . Stream Drainage Area Length of Remarks·area records
1. St age Sq. mi. Acres YearsRecorder
2000 Kaukonahua. Nor t h Fork 1. 38 883 41,62040 Kaukonahua. North Fork 4.86 3110 20 A2080'" Kaukonahua , South Fork 4.04 2586 92110 Poamoho 1. 79 1146 92116 Makaha 2. 13 1363 72118** Kaupun i 3 .27 2093 62128 Kipapa 4 . 29 2746 102130 Waike1e 45.70 29248 15 B2160'" Waiawa 26.40 16896 14 A2230'" Wai ma1u 6 .0 7 3885 15 A, B2245** Kal auao 2 .5 9 1658 13 A, B2260 North Ha1awa 3.45 2208 132270 Ha1awa 8.78 92280 Moana lua 2. 73 1747 40 B2290 Kalihi 2. 61 1670 53 A, B2293 Kalih i 5 .18 3315 62320 Nuuanu 3.35 2144 53 A, B2390 Mano a , Eas t Branch 1. 06 678 40 A, B2400** Manoa, West Branch 1.14 730 40 A, B2440** Puke1e 1.18 755 40 A2460 Waiomao 1. 04 666 40 A, B2470** Pa101o 3. 63 2323 152540** Makawao 2.04 1306 92739 Kamooa lii 4 .38 2803 82750" Hai ku 0 .97 621 27 A2830 Kaha1uu 0 .28 179 31 A2838 Waihee 0.31 198 52840 Waihee 0.93 595 31 A2910 Wai aho1e 0.99 · 634 11 A2949 Waik ane 2. 22 1421 72965 Kahana 3. 74 2394 73030 Puna1uu 2 . 78 1779 133300'" Kamananui 9 .79 6266 93450** Opaeu1a 2.98 1907 7
II. Crest-Stage lIa/t6
2113 Mak a1eh a 4 . 20 2688 92115 Makua 4. 07 260!'l 92122 Mail i il ii 1. 51 966 92125 Honou1iuli 11.00 7040 112126. 01 Waike1e 6. 35 4064 92127 Waikaka1aua 7.1 4 4570 92165 Waimano 2. 59 1658 12 B2285 Moana1ua 4.16 2662 92354 Wao1ani 1. 28 819 92375 Pauoa 1.52 973 92472 Waia1aenui Gulch 1. 75 1120 92475 Wai 1upe 2.35 1504 92488 (Un-named stream at Wa i manalo) 1. 21 774 92605 Maunawili 5.34 3418 92644 Kawainui Swamp Drainage Canal N/A 52646 Kae1epu1u St ream Tributary 0 ..16 102 42648 Kawai nui 11.00 7040 102744.99 Keaaha 1a 0.59 378 92825 Ahuimanu 2. 16 1382 43045 Ka1uanui 2. 12 1357 93105.01 Ma1aekahana 4.05 25!l2 83110 Oio Stream 2.13 1363 93400 Anahulu River 13 .50 8640 93500 Opaeu1 a 5 .96 2814 11 B
* A-- Sma11 quan ti ty of wat e r diverted occasiona lly for i rrigation or for domestic use .B-- Gage s ite has been moved .
** Di gi t al re corder .
18
Table 4. Maximum reco r ded flood peaks i n Oahu(Thr ough Jun e 30 , 1966)
Stat i on Stream Length of Area Area Dis charge Date cfs/Record , yr. Sq. Mi. Acres cfs acre
A. WINDWARD SI DE
2488 Unnamed s t r eam 9 1. 21 774 900 11/13/65 1.16
2540 Mak awao 4,9 2. 04 1306 6000 2/ 4/ 65 . 4 .60
2605 Maunawili 9 5.34 3418 9690 2/ 4/65 2. 84
2646 Kae1upu1u 4 0 . 16 102 371 11/14/65 3.64
2739 Kamooali i 8 4. 38 2803 6610 10/ 23/58 2.36
2744.9 9 Keaaha1a 9 0. 59 378 2750 5/ 2/65 7. 28
2750 Ha iku 5 , 27 0 .9 7 621 5740 5/ 2/65 9 .25
2780 . 9 Io1 ekaa 26 0 .2 8 179 797 5/ 2/ 65 4 .45
2825 Ahuimanu 4 2. 16 1382 6610 5/2/65 4 .79
2830 Kaha1uu 31 0 .2 8 179 1730 2/4 /65 9.66
2838 Wai hee 5 0 .3 1 198 1700 2/ 4/65 8 .57
2840 Waihee 31 0 ,93 595 5110 2/ 4/65 8 .59
2910 Wai ahole 11 0 .99 634 2230 4/1 5/63 3.525/ 2/ 65
2949 Waikane 7 2.22 1421 8800 2/ 4/65 6.20
2965 Kahana 3,7 3. 74 2394 5430 4/ 15/63 2.27
3030 Puna1uu 13 2. 78 1779 2970 11/1/61 1.672/4/b5
3045 Ka1uanui 9 2. 12 1357 3990 5/2/65 2.95
3105 .01 Malaekahana 8 4. 05 2592 4640 4/15/63 1. 79
3110 Oio 9 2. 13 1363 1390 5/2/65 1.02
None Kawa 0 .2 4 154 900 5/2/65 5.85
None Kawa 1.19 762 4510 2/4/65 5 .92
None Kahanaiki 0.79 506 1370 2/4 /65 2. 71
None Kahanaiki 0.39 250 660 2/4 / 65 2.65
B. HONOLU LU DISTRICT
2280 Moanalua 40 2.73 1747 4580 11/18/30 2. 62
2285 Moanalua 9 4. 16 2662 3790 11/14/65 1.42
2290 Kalihi 53 2. 61 1670 12400 11/18/30 7.44
2293 Ka1i hi 6 5. 18 3315 7000 11/14/65 2. 11
2320 Nuuanu 53 3. 35 2144 6990 1/1 6/ 21 3 .26
2354 Wao1an i '9 1. 28 819 2500 5/14/63 3.05
19
Table 4 (continued)
2375
2390
2400
2440
2460
2470
2472
2475
Pauoa 9
E. B. Manoa 8,40
W. B, Manoa 8,40
Pukele 40
Waiomao 2,40
Palol0 15
Waialaenui Gulch 9
Wailupe 9
1.52
1.06
1.14
1.18
1.04
3.63
1. 75
2.35
973
678
730
755
666
2323
1120
1504
2200
3090
3250
2600
1550
3330
2020
2170
5/14/63
1/16/21
1/16/21
4/11/30
4/11/30
11/14/65
3/5/58
3/5/58
2.26
4.55
4.46
3.44
2.33
1.43
1.81
1.44
C. BETWEEN MOUNTAIN RANGES
L.B.N.F.Kaukonahua 41,6
2165 Waimano
2130 Waikele
2126.01 Waikele
2.07
2.11
1. 76
1.00
1.05
1. 70
1.50
1.56
2.06
3.02
1.08
6.22
1.44
0.96
0.45
0.53
0.49
0.45
1/1/33
4/15/63
4/15/63
4/15/63
12/23/64
3/5/58
4/15/63
5/14/63
11/14/65
11/28/54
11/28/54
5/2/65
5/14/63
2/28/32
11/14/65
2/4/65
10/23/58
12/15/64
2/25/56
2580
5490
2810
2360
1810
2580
5460
4660
4820
5680
2750
3050
3870
6930
6650
6570
4120
16900
15500
2688
3110
2746
1146
2586
883
4570
1658
2208
1658
4064
3885
2814
1907
8640
626f>
29248
16896
4.04
4.20
2.59
7.14
1. 79
4.29
2.59
4.86
1. 38
3.45
6.35
2.98
6.07
8.78
9.79
5.96
26.40
45.70
13.50
15
14
10
9
9
9
20
9
9
15
15
9
7
9
11
4,13
9,1
.12
Kamananui
Anahulu
Halawa
Opaeula
Opaeula
2000
2230 Waimalu
2110 Poamoho
2113 Makaleha
2080 S.F.Kaukonahua
2040 N.F.Kaukonahua
2128 Kipapa
2160 Waiawa
2127 Waiakakalaua
2260 N. Halawa
2270
2245 KalauBo
3300
3400
3500
3450
D. LEEWARD .SIDE
2124.01 Awanui
2122 Mailiilii
2118 Kaupuni
2125 Honouliuli
2.28
0.58
0.86
0.65
0.27
0.90
12/23/64
3/13/62
12/23/64
11/13/65
4/15/63
3/5/58
1170
1520
2200
1350
1520
' 1900
966
2093
2605
1363
1690
7040
2.64
I. 51
4.07
3.27
.2 . 13
11. 00
7
9
9
6
7
11
Makaha
Makua2115
2116
None Puhawai 15 0 .60 384 1330 10/22/39 3.46
20
values are taken. It can be shown (11) that the above statement is cor
rect if the number of individual items in each of the samples is large
and if the number of samples from which the extremes are taken is also
large. The theoretical distribution of the extreme values series can
be expressed mathematically (11). For practical application, a special
probability paper has been designed so that the probability curve for
the extreme values series appears as a straight line. If peak flows
are considered as extreme values,a straight line can be drawn theoreti
cally on Gumbel's extreme values plotting of flood frequency analysis.
There is no theoretical basis for using log-scale for discharge
on Gumbel's extreme-log plotting. It is simply a matter of curve fit
ting. Since 15, 20, or 25 years of recording cannot be considered large
and the plotted points on the extreme value plotting may not form a
straight line pattern as expected, a curve fitting on the log-scale of
Gumbel's extreme value may be suitable.
The frequency analysis of gaging stations of 23 small Oahu
watersheds has been made by following the procedure designed Dy Gumbel
(12, 13) with frequency curves plotted by both methods (see Appendix).
Most of the stations have shown a good straight line fitting
by using Gumbel's extreme value analysis, but a few stations indicate
that this method of analysis fails to account for a recent extreme flood
although it adequately described other flood data. The extreme point
which is far removed from the straight line pattern has been excluded
because the period recurrence of a flood of that magnitude must be far
greater than the period of available records to determine the return
period of such floods with any degree of validity.
A curve fitting Gumbel's extreme-log probability plotting shows
a smooth curve for all points, including the extreme one. However,
extension of the plotted curves lacks theoretical basis for guidance.
Further, with the peak flows plotted in logarithmic scale, the slight
est change in the extended line will result in a greatly different pre
dicted peak flow. Prediction of peak flows with this method cannot
be considered reliable.
D. FLOOD HYDROGRAPH. The flood hydrograph of small watersheds
on Oahu exhibits a rapid rise and recess. The time to peak is short,
usually less than 1 hour. Since the watershed is small with little
21
channel storage to regulate stream flow, a peak flood discharge is
almost an immediate response to a high intensity rainfall. An example
of flood hydrograph of the February 1965 flood (8) is presented in
Fi gur e 11. The isohyetal map of Oahu, showing maximum 24-hour rainfall,
February 3-4, 1965, is presented in Figure 9. The greatest actual
measured r ainfall was 18.17 inches at Waiahole. The rain began just be
fore midnight on the 2nd, with a burst of ~ inch in about 15 minutes.
By midnight of the 3rd, 2.6 inches had accumulated in a series of showers.
In the next four hours 7 inches fell, with 3 inches between midnight and
2:45 a.m. By 8:00 a.m. the accumulation measured 11.5 inches. An intense
rain resumed at about noon and by 2:00 p.m., 2 inches fell. By midnight
of the 4th, additional 3.5 inches was recorded (8).
3. HISTORICAL FLOOD SURVEY
A historical survey of floods that have occurred for the last 100
years on Oahu was made to determine the characteristics of critical
flood-producing storms. A flood damage survey from 1862 to 1965 sup
plied by Pararas-Carayannis (14) was used as basic information. The
amount of rainfall of the flood-producing storm was studied from the
climatological data ,pub l i shed by the U. S. Weather Bureau. Results from
the study of the historical flood survey are as follows:
A. FLOODS OCCURRING BEFORE 1917. There were only eight floods
reported by Honolulu newspapers between the years 1862 to 1917. All
of them were caused by Kona storms. No daily rainfall data is available.
B. FLOODS OCCURRING BETWEEN 1917 AND 1965. Twenty-seven floods have
occurred during this period of 48 years. A survey of the type of the
flood-producing storm, storm rainfall, antecedent rainfall, flood loca
t ion, and classification is shown as Table 5. The storm rainfall as
listed in Table 5 is the maximum point rainfall recorded upstream from
the flooded area. The antecedent rainfall, flood zones, and the flood
classification data are explained in the footnote . During these 48 years,
flooding of Honolulu and wind ward areas sho ws high frequencies of oc
currence in comparison to the rest of Oahu. A map showing the frequen
cies and areas of floodin g is shown as Figure 12. It must be recognized
that floods that occurred in uninhabited areas may not be reported, and
the high frequency of floods between 1917 and 1965 as compared with that
between 1862 and 1917 is probabl y not so much caused by any significant
22
Tabl e 5. Histor ical fl ood s urvey (1 917- 196 5) *- -type of storm, s t orm rai nfall. an tecedent r a infall cond ition and flood situation"
Type Fl ooded Maximum recorded starn ra i nfall upstream from FloodDate of fl ood ed area (inches) Location Classification
St orm ar e a(Zone) (Oamaae)St ation Po PI P1-5 PI- IO PO-5 PO-I O
3-20-17 K Honolulu Kalihi Vly . 12 .88 0. 25 3 . 95 10 .83 16 .83 23. 71 8 LTant alus 11.00 6 . 00 8. 50 12 .70 19.50 23 . 70
Kaneo he Heeia 3. 12 8 . 08. 9. 35 11. 23 12.4 7 14 .35 A4- 20-18 K Hon olulu Luakaha 4.76 0 .00 5 . 07 13 . 85 9 . 83 18 .61 8 L
( lower )Kahana Kaha na 0 .35 2.05 3.80 21. 68 4 .1 5 22.03 A
11-6-19 K Honolu l u Kinau St. 4.5 7 0 .03 0 . 37 0 .52 4.94 5 .07 8 S12- 24- 20 K Honol ul u Kaliula 4 . 36 0 .69 0 .73 1. 02 4 . 73 5 . 38 8 L
Kawai loa Kawailoa 2 .0 7 6 .12 6.24 6 .42 8 .31 8 . 49 C1-15- 23 Hono l ulu Kaliula 2 . 11 5 . 29 12.42 13 .70 14. 53 15.81 8 L
Tantalus 7 .80 2.2 3 16 .90 17.70 24 . 70 25.50Hoaes e Hoaeae 4 . 26 0.00 5 . 18 5 . 43 9 . 44 9 .69 C
1-17-35 K Honolulu Manoa 1.72 0 . 92 2 . 64 5 .4 5 4.36 7 .17 8 S1-1 6- 36 K Hoaese Hoaese 1. 67 0 . 00 0 . 01 0.04 1.68 1. 71 C S
Scho fiel d Wahi awa 1. 45 0 .00 0.20 0 .35 1. 65 1. 80 C S8arracks
1- 25-48 K Hono lu lu Manoa HSPA 3.90 1. 30 4 .56 5 .74 8. 46 9 . 64 8 L1-16- 49 K Hono lu l u Manoa HSPA 9 .3 4 0 .66 0 .88 4.78 10. 22 14 .12 8 L8-1 4-50 Honolulu Ka lih i Re s. 3. 20 1. 24 1. 84 3.16 5. 04 6 .36 8 L
Koko Head Pa lo lo Vl y . 2 . 9 3 1.4 2 1. 97 4.00 4 .90 6 . 93 8Wah i awa Wahiawa 2 .58 0 .04 0 . 16 0 .62 3 .7 4 3 .20 C
3- 25-51 T Honolu l u Kapa l ama 3 . 85 0. 00 2.56 2 .6 4 6 . 41 6 .49 8 LWaimanalo St. Stephens 9 . 36 0.67 4.44 5 .38 13 .8 0 14 . 74 A
Kai l ua10- 27-51 K Hono lu l u Kalihi Res. 7 . 88 0 .08 0.37 2. 13 8 . 25 10.01 8 . L
Ka ilua St. Stephens 3.89 0. 74 I. 22 2 . 04 5 .11 5 .93 A1-18- 52 K Honolulu Kalihi Res . 5 . 75 0 . 00 0 .4 0 1. 70 6.1 5 7 .45 8 L2-28- 53 K Honolu l u Manoa HSPA 1.64 0 . 95 2 . 07 4 .11 3 .71 5 .75 8 S
Kaneohe Kaneohe 1.01 0 .57 3.33 4 .2 4 4. 34 5. 25 ARanch
11- 28-54 T Honol u lu Manoa HSPA 12.1 3 0 . 23 0 . 79 0.89 12.92 13.02 8 L1-21 -55 Hono l ulu Tanta l us 4.41 0 .00 0 .36 1.66 4.77 6. 07 8 S
Nanaku li Lualuale i 2.63 0 . 00 0 .00 0 .06 2. 63 2.69 02- 22-55 K Honolulu Kalih i Res. 8.75 4 .08 5. 63 7 .23 14 .38 15.98 8 L
Kane ohe Waiaho le 4 . 90 0 .10 2 . 97 4 .80 7 . 87 9 . 70 APe arl City Ai ea Fl d . 4 . 75 0.10 1. 83 4. 22 6 .5 8 8.97 C
12-1 9- 55 K Honolulu Pa l o l o Vl y . 6 . 22 6 . 78 6 . 78 7 . 22 13 .00 13.44 8 LKaneohe Kane ohe Ranch 8 .4 8 0 .00 0.03 I. 38 8 .51 9 .86 A
1-1 2-56 Kailua St . Stephe ns 2. 06 2 . 10 2.59 2 .6 3 4 . 65 4.69 A SKaneohe Kaneohe Ran ch 2 .1 3 2 . 17 2. 52 5.66 4 .65 7.79 A
12- 6-56 K Honolulu Kalih i Res. 2.38 0 .0 0 0.20 3.58 2.58 5.96 8 SKail ua St. St eph en s 2. 97 3 .3 2 4. 53 6 .29 7 . 50 A
11- 30- 57 H Honolu lu Pa lol o Vly. 2 .98 0. 90 2.35 14 .88 5 .33 17 .86 8 L1- 17-59 Kaneoh e St. Stephen s 4 . 59 0 .51 2 . 10 2 . 26 6.69 6 .85 A L
Waimana lo Wa i man alo 3 . 50 0 .09 1. 13 1. 45 4.63 4. 95 A10-31-61 Kailua St. Steph ens 1. 9 1 0 . 06 0.8 1 1.03 2.72 3.21 A S
Hono l u l u Mano a HSPA 1. 64 0.04 2. 34 3. 07 3 .98 4 .71 81- 21- 62 Wai alua Kemoo Camp 8 0 . 74 0 . 00 0 . 63 0. 65 I. 37 I. 39 C S1- 6- 63 T Honolulu Kapalama 5. 55 0.00 5. 05 5.05 10.60 10 .60 8 L
4- 17-6 3 K Honolul u Nuuanu R. 0.64 0 .06 7 .58 8 .7 3 8. 22 9.37 8 SKaneo he Kaneohe Mauka 8 .90 3 .10 10 . 31 II. 74 19 .21 20 . 64 A L
5-3- 65 Kai l ua St . Stephens I I. 54 0 . 13 0. 45 0 .6 8 11 .99 12 . 22 A LHono lu l u Tant al us 4.87 I. 96 4 . 54 6 . 12 9.4 1 10 .99 8 L
• Recent fl oods, Feb r uary and November 1965 are no t lis t ed .NOTE:
Type of Sto rm: K - Kena storm ; T - Thunder stonn ; H - Hurricane .Storm ra infall : Po - dail y rainfall before or dur i ng the occurrence of flood.
PI - dail y r a i nfal l, one day be fo r e PO'
PI-5
- ant eced ent r a infall five day t otal before PO'
PI- IO - ant ecedent r ain fall t en day t ot al before PO'
P O- 5 - tota l amoun t of rainfall. Po • PI - 5·PO- IO - t otal amount of rainfal l , Po • PI - I O'
Flood locat ion (z one) :A Windwar d side8 Hono lu lu dist ric tC = Be tween mount ain rangeD = Leeward s i de
Fl ood cl assificat i on (d amage) :L = la rg e flood
A combi nat i on of 4 or 5 f o l lowi ng damage s : s t re e ts floo ded , h ighw ay br idge.
damage d , r oad s bad ly da maged. rcs e rv o i r ove r flowed , person s drowned . homefl oode d , bridge swept away . fa rm rui ned I ai rport flooded.
S s mall fl oodLoca l fl ood ing o f s tree t s . loca l roads washed . br ie f fl ood i ng , minor damage.
23
r>1350IZ50'.--------.----=-=-=-~-------r-------------.
100
750
~0
-c 500
<I)
Z0...J...J« 250(..!)
Z0
--I...J
0~ ioooz ~~\\OOW...(.!J0:::-c 750 WAIHEE. STRE.AMIUen0
500
250
OL.. ---l:~~---=-_=:::=:::::::::L.::::::==:::L~_..l::::::.L_.:::::::========:::::l
+DAYS
5
Figure 11. Hydrograph showing discharge in Waihee Stream at station2838, and in Waiahole Stream, at station 2910, Oahu,during the period February 3-5, 1965.
(from USGS Report R26, 1965)
N-l>o
~ . FLOOD AREA.
o FR~QUE.NC y
CD
<D
J ..---.....
Fi~ure 12. The flood a~e~s and frequencies in_Oahu i~~17-1965).
25
change of weather pattern as by the change of land use pattern and better
gaging network. . It is also found that most of the flooding caused by
Kona storms occurred during the winter.
The floo~s are classified by the damages they caused. Daily
flood-producing rainfall, P , ·pl ot t ed against a 5-day total of antecedento
rainfall, Pl-5, and using flood size as parameters is shown in Figures
13 and 14. Notwithstanding the somewhat arbitrary definition given to
'large' and 'small' floods in the flood damage classification, two zones
clearly reflect the existence of a relation between the maximum daily
rainfall and the 5-day antecedent rainfall experienced on Oahu in the last
50 years. This relation may be useful for issuing flood warnings as a
rainstorm progresses.
The 5-day antecedent rainfall prior to the maximum daily flood
producing storm rainfall is also somewhat arbitrarily assigned because of
the high infiltration and evapotranspiration rates of Hawaiian soils.
Two envelope curves (dotted lines) are drawn to cover all re
corded floods shown in Figures 13 and 14. It was found that a 24-hour
rainfall of 10 to 14 inches would produce a large flood in the Honolulu
and windward areas of Oahu. This daily rainfall is comparable to a 50
year frequency, 24-hour rainfall for those areas .
4. WATERSHED CHARACTERISTICS
"Watershed characteristics" is used to mean those which are simply
defined b~t -quantitatively determined geomorphological watershed charac
teristics, such as, watershed area, length of watershed, height of
watershed, drainage density, area-:-altitude .relation, length of main
stream, mean slope of main stream, and watershed shape.
A. WATERSHED CHARACTERISTICS. Watershed characteristics as used
in this report may be defined as:
i. Watershed area. Area of the watershed directly measured
from topographic maps with a planimeter.
ii. Watershed length. The longest length measured from the
outlet to a point on the boundary of the watershed.
iii. Watershed height. The difference in elevation measured
between the gaging station and the highest point of the
watershed.
26
~ ZONE. OF LAR.GE. FLOOD
lITI]J] ZONE. OF SMA.LL FLOOD
3115 ao2~o
___EN\lIE.I..OPE. CU~VE.
R-s FIVE, D,A.'1' ANTCEDE.NT RAINFJl..LL - INCHES
= I I I I I I I I I I I II I I~ ~-V-- -
1 T; r-
7v- V c:1/
// / I/~ ~I'I-
~ ./ I r--.r-- '/ / <i / / / / / / "' -r-- h / / / / / / / / / / / ,:, V / ............. -r-- ":"" / / / / / 1/ / / / r e ... -r-- / ;-.;. I / / / / / / e v / / / ,-~ / ....
~~ / / / V / /' II V / / / IE=~ / C!)G) ~~ / II / / V v VI/ /1=~ j- \:I /
....,
V V J //1 /
= / G>r-. / / 1/~
~ "'< ...../r-...
V ';(/// -=-- /=- 1--- /== .......... ........... i'11;(/= ...... ........ ~Ci)
=- r...~ i'. -- ..... r-..........- ~ ...- ""-- ......... -- <; ,. -- - ~ -- "- I-.... Ql -~ r-, r-...-====:==- -t=~
~~ -~~
hlllllill 111111111 III1 1111 11111 I I I I 111111111 illdlill I11I 11111 1111 I I I I II 11/1111 111111111 ,
10'Ia7,5
10
0. ...
I
0.'0.&
0.7
0.,0.\
WJ:t-
~z-u~DoIX0-
J
ao9u.
Q}
Figure 13. Relationship between the daily flood-produci ng rainfall and its 5-dayantecedent rainfall of Honolulu district, Hawaii.
27
l~lzONE OF L~RuE FLOOD
ZON E OF ~M~LL FLOOD
E t-l" ELOP E. C.URVE
.2.0I!I+ 5418'\02.0.8 1.0
l- I I I I I I I I I I I I I~I- -lIS r-I- 1\7lil ..I--~ I/~I- (!I) I-
~-~ .., / / / / / ~ I r- .... -
'II-- \/ 1/ 1/ / 1/ / / / / / / 1/ p -.~ ~ ) ) I / / / V / V -7 \1 / / / / V / / V 1/ -~
"~ \) I 1/ V / / / ./ / V /I:51= \V V 1/ / / I:> / J 1/ V l/t:: 1/ II41- I\L 1/ S/ / / V V V II~ I 1I 1Ih,I- ' /
31:=\
\/ ~/ v V V~ -~ / II -t= r- ~E: , I~ f--
"'"2~
K F>l="
eg- -I- -.....I- r- r--..:.....
In
~ -.'1~ -.a -~
11-- -..."==-0.5 =::0"" =t::•.1
~ -E:-~~
.J.~
~c... -t
.E 11111111 Illdllll 11111111111111 I I II 111111111111111111 11II 111111111 I III III JlIIIIo0.1
o
r..J
:(o 0
o
.!)Zu::>a~e,
Ioa..JIL
w:r:I-
a 0
L£JoItoUwri.
D FIVE DA'( ,A..NTEC.E DENT RAIN FALLr I-!» )
I N 00\ E.S
Figure 14. Relationship between the daily flood-producing rainfall and its5-day antecedent rainfall of the windward side, Oahu, Hawaii.
28
iv. Drainage density. Drainage density is defined as the total
length of streams and tributaries in the watershed divided
by its total area, i.e., the length of streams per unit area
of the watershed.
v. Area-altitude relation. The area-altitude relation is de~
termined by using the hypsometric analysis (15, 16) which
relates horizontal cross-section areas of a drainage basin
to relative elevation above the basin mouth. The curves can
be described in a dimensionless plot and then compared ir
respective of true scale. The area under the curve can be
used to find total land mass of the watershed and the shape
of the curve correlates with the general slope of the land.
vi. Length of the main stream. Length of main stream is measured
along the course of streams from the topographic map.
vii. Mean slope of the main stream. The slope of the main stream
. usually varies with its reaches, i. e. , a steeper slope for
upper reaches and a flatter slope for lower reaches. It
is not sufficient to find the slope of the straight line con
necting the upper and lower extremities of the stream profile.
The following theoretical method introduced by Taylor and
Schwarz (17) for determining the mean slope for a stream is
used in this study:
2
S ==
Where N is number of equal reaches and Sl' S2' S3----SN
are the slopes of each reach.
viii. Wat er shed shape. A watershed shape factor compares the
irregular shape of the watershed to an idealized shape, as
a circle. It is defined as the ratio of the perimeter of
the watershed to the perimeter of a circle which has the
same area as that of the watershed studied. The watershed
shape factor is always larger than one, since the perimeter
of a circle is considered the lesser when compared to the
29
perimeter of any irregular shape with the same area. There
fore, the t ar ger the watershed shape factor, the more irreg
ular the shape of the watershed.
B. GEOMORPHOLOGICAL CHARACTERISTICS OF SMALL OAHU WATERSHEDS.
A geomorphological study has been made for 33 small Oahu water
sheds which have water-stage recorders to record streamflow. All meas
urable watershed characteristics are listed in Table 6.
Table 6. Watershed characteristics
AWatershed Watershed
No. Area
DDrainageDensity
tLength of
MainStream
SMean slopeof mainStream
fShapeFactor
LWatershed
Length
HWatershed
Height
200020402080211021132115211621182128216522302245226022802290229323902400244024602470254027392744.992750282528302838284029102949296533003450
sq. mi.
1.384.864 .041. 794.154.072.133.274 .292.596 .072.593 .452.732. 615 .181. 061.141.181.043.632.044.380 .6 20 .9 72.160 .280 .310.930.992.223. 749. 792.98
ft/sq .mi.
22608 . 723798.422861 .423463.713493.914132.711089.214698 .226800. 116741 .317901. 214996 .111785 .111538 .5
8436.810355 .220393 .115052.615000 .013211.513636 .420411. 215482.412000 . 013435.112760 . 65135 .77258 . 18602. 23787 . 9
18072 . 112820.827706 . 830089.9
ft
16840558 204910035000190001812015720120004764026240509403884027440228401466030880
72839100
1170012240224801436025480
74405594
129381438225048753750
13700217006904068300
ft/ft
0.03630 .01 200.00730 .02300 .08760.07860.12400 .13300.02640 .03340 .01580 .03750 . 03770.03500. 04630. 03500 . 12600:14900. 08650 .0 9400 . 04920 .0 4430.0 1150.02070. 11800 . 03880 .23000 . 19700 . 11400 .06920 .0 5930 .02730.02600 . 018 1
1.181.551.941.881. 321.341.371. 231.481. 761. 782 . 511. 391. 331.181. 431.1 21. 361. 341.441. 541. 311. 531. 421. 131. 191. 191. 261.141. 131. 211. 291. 542.08
ft
10100268003200020600199001640013000124002400022800358003490020100171001190026200
78009900
113001180020800108001800076006000
109003100390056006200
12000154003800028000
ft
15101360160014153790298731213566209614002568279225062480227626701920281421412165243525402782920
2128280022222069237725002610263022601740
C. SOME SPECIAL FEATURES OF SMALL OAHU WATERSHEDS.
i. watershed area. Among the 58 stations listed in Table 3,
80 percent have areas less than 5 square miles and 50 per
cent have areas less than 3 square miles. Hawaii is unique
in maintaining fairly complete hydrological data for small
30
A. Watersheds of Kailua, Kaneohe area.
S. Watersheds of Honolulu district ,between mountain ranges andleeward side of Oahu.
C. Watersheds of Waiahole, Kahana areasof windward side of Oahu.
~ \H \
\\
Figure 15. Average hypsometric curves for Oahu small watersheds.
~......
Iq4-1)
0 ,000:000\00010010
AREA. (5Q.. M'LE.'~)WATE.RSl-I£.D
0
00AHU I I I<, 5M"lL WAiE-RSHE.OS
l'III
"" • INDIA.NA c:..MAII ,,,"'a. ' 1- ~""HE.DSr . -'- I . ' +-+-l
I'. ..,'" STREA.MS (LAN(,SEIN"l - ----SLOPE OF TRIBUTA~'(
" e 01'\ I,i~ ~ --------5LOP£ OF P ~I NF
\ ~AL STREA.M( <, •
'"~(!) C!)
.0 -CP~ ~t-, -to-
~II!
I~~ i"'o __
(,i) ...t"-oo ill -'I ""8 "" ...."l ......, I ... t ........ -~ .... .... "-<, .... ~ I-....
ItJ -, "I'"30 I..
I"" "" .... .... ...:1.0
<, ........
~1-- .... ...
....!'~ 14r..
\q ..../)
7 -(, "-5
~.....4- 4 ~. <,
3 • .",~-,
2-
~• !'•I0.1 .1 .3 .+ .~ ., .7 .8.' I :I. 3 S (, "18 . -- -- -- -- ~- . . "\ ZOO .500 4OO!GO - _.
100
LOO
Wc,o...JIII
~.(wItlV>
,..-...uJ...J
2<,~u,
'-"'"
Figure 16. General variation in stream slopes in relation to watershed area.
~"'~~:~;:~J:.lf.·...,~ ~-:>r~.f~-'; ~~~~~=~~---~"":""'''"'' u "" . ~ = .. ~~
32
watersheds of these sizes.
ii. Area-altitude analysis. Through hypsometric analysis of 41 small
watersheds on Oahu (13 in Zone I, windward district; 11 in
Zone II, Honolulu district; 13 in Zone III, between mountain
ranges; 3 in Zone IV, leeward district), three average curves
can be used to show the area-altitude relations of Oahu water
sheds. As shown in Figure 15, curve A is for stations at
Kailua and Kaneohe areas of windward Oahu where there are
steep upper reaches and flat downstreams; curve B is for
stations having similar stream valley shape in the Honolulu
district, between mountain ranges, and the leeward side; curve C
is for Waiahole and Kahana areas where gaging stations are
located in the upstream portion. The shape of the hypsometric
curve is caused by valley contours, mountain ridges, general
land shape, and location of the gaging station.
iii. Relation between watershed area and stream slope. The re
lation of watershed area and stream slope was studied by
Langbein and others (15) in 1947 and a simple linear
relation was developed for watershed area and stream slope
on a log-log scale as shown in Figure 16. This relation was
explained by considering that small watersheds are usually
located relatively upstream where stream slopes are steep.
Data of small watersheds in Oahu (areas from 0.2 to 10 square
miles) and 16 small watersheds in Indiana (areas from 60
to 250 square miles) are also plotted in Figure 16. A
straight line can be drawn through the data of small water
sheds for Oahu and Indiana. The plots do not coincide with
the lines developed by Langbein , probably owing to the dif
ferent method used to calculate the slope. The mean slope
of the main stream of Hawaii (Oahu) and Indiana watersheds
was determined by using the method developed by Taylor and
Schwarz and the stream slope as defined by Langbein was the
quotient of the total fall divided by the corresponding total
length .
\
33
5. SOIL TYPE AND LAND USE CLASSIFICATION
Besides geomorphological f actors, the soil type and l and us e descrip
tions are also important f actors af f ect i ng streamflow. They are especially
significant in Hawaiian water sheds which are small with little channel
storage. Knowledge of soil type will help to determine infiltration loss
and hence storm runoff. The land use classification combined with all
the geomorphological factors of a watershed will control the detention
storage and the distribution of runoff.
A survey of the soil type and land use of Oahu watersheds was made
by comparing watershed location with air photo maps in which the soil
types and land use have been classified and shown. Results of the survey
shown as Table 7 were expressed in percentages to show each soil type
and land use of the watershed as compared with the total area. Soil t ype
has been classified into three groups: group I - clay and silt clay;
group II - stony silt clay and stony clay loam; and group III - rock
land and rough mountain land. Land use has been classified into six
groups: L - cultivated crops, P - pasture, F - forest, B - brush,
H - housing, and X - idle or wasteland.
The air photos used in this study to classify soil type and land use
were taken in 1953 and are the most r ecent ones available. Table 7 gives
an adequate description of soil and land use for rural watershed. The
percent age of urban ar eas may not be correct and further adjustment may
be necessary.
6. INFILTRATION AND EVAPORATION
A. INFILTRATION. Soil types described in Table 7 are mainly cl ay
and silt clay loam in texture but have an infiltration r ate even higher
than those of sandy soils on the mainland United States . (The above
is just a general statement ; soils with s ame textural classifications
vary greatly in infiltration with respect to the clay mi ner a l s they
contain.) This unique characteristic of Hawaii an soils reflects a
typical rainfall-runoff r elationship (Figur e 11). The flood hydrograph
has a sharp rise of flood peak right af t er a short-duration high-intensity
rainfall and the low peak hydrographs indicat e that they were produced
from less intense rainfall which has l argely infiltrated into the ground.
The infiltration capac~ty for uncultivated soil studied by Wi l l ock ,
et al. ~ (18) and the infiltration capacity of some mainland soils studied
li
34Table 7. Soil type and land use of small watersheds on Oahu, Hawaii
(by percent of tota l wat ershed area ;key to classificat ion on next page)
Station GroupI
Soil typeGroup
IIGroup
III H L
Land use
p 8 F x
2.423 . 7
C l E N T D A T A11.9
16.015 . 491.5
C lE N T D A T A )73 .0
11. 9 11. 35 .4 3.3
200020402080211021132115211621282165224522602280229022932320239024002440247027392744275027802825283028402910294929653450
4 .3
17. 5
8.1
44 .521. 06 .1
12.252 .867. 4
11. 943. 019.130.7
90 . 850 .028 .2
100.064. 551. 344 .556 .0
100. 0100. 095.7
100.05.0 77 . 5 5.0( INS U F FIe 'I E N T D A T A
12.1 79 .8100 .0
1.6 53.9 7 .5 29. 679. 0 5.5 6. 593 .987.847 . 2
0 .5 32. 1( I NS UF F5 .8 82.3
57.080.9
28 .2 41. 1(INSUFF I
9 .2 ;50. 071.8
35.548 .755 . 544 .0
( IN S U F FIe lEN T D A T A )100 .0
7. 4
13 .7
17 .5
63. 817.726.219.012.076. 461. 448. 9
5 .814.0
3.5
19.850. 0
8 .176 . 837. 14. 7
14 .274. 6
100.0100.086.3
100.0
36.282.327. 769.088.023.636 .227.4
82 .370.0,81.1
8.5
20 . 1
18. 746. 644 .525 .4
100 .0
77 .5
1.6
7 .250 .071.8
35.548. 741.3
Symbol'>
Group [3 , 20 .
, bO120, 150,170. 300,310, 340,350, 360,520 , 550,570, 610 ,710, 750
Gro up II---Hf,' . 70,
359 . 76U,7BO
Gr oup I I I-golf,910 •
91 2, 930 ,940, 960,
_~o_~L~
Description
Clay, s i l t clay, s i l t
c lay l oam
St ony s i l ty c l ay lo am,stony clay l oam,stony silt c lay
Stony l and, rock l and ,rock out cr op , gu l liedl and , rough bro ken land,mountainous l and
Symbol
L
P
F
B
X
H
Land use
Land used primari ly for
Cul tivated crops
Gras s and forage crops(pas t ure )
Wood crops (forese)
Wat e r shed purposes (brush)
Misce ll aneou s (id le orwasteland)
Housing or ur ban arp.a
No. 3 - Alae l oa silty cl ay10 - Ewa Extr . St ony silt y cl ay l oam20 - Kipapa si l ty c lay60 - Lahaina si l ty c lay70 - Nanoa stony c lay l oam
120 - Nol oka i si lt y clay l oam150 - Wah i awa silty c lay170 - waikapu silty c lay l oam300 - Tantalus s i l t y cl ay l oam310 - Kaneoh e si lt y clay
'340 - Maunawil i si l ty c lay lo am350 - Lol ekaa si lty c lay359 - Lol ekaa s tony s i l ty c l ay360 - Waik ane silty clay
No. 520 - ~Ianana silty cl ay loam550 - Kemao s i l t y c lay570 - Leil ehua si l ty c l ay610 - Kaena ex t re me ly si l ty c l ay710 - Lua l ua l e i c l ay750 - Hanal e i s i l ty c lay7bO - Kawa i hapa i s tony c l ay l oam7BO - Pul ehu ext rumel y s tony clay l oam900 - St ony land; Ewa- Luna 1e i soil complex910 - Rock l and91 2 - !lock out c r op930 - GuII i ed 1and - Nanuna soi 1940 - Sout h br oken land91,0 - Rough br okcn - mountainous l and
35
by Musgrave and Norton (19) are shown in Table 8. Uncultivated Hawaiian
soils have a higher infiltration capacity than mainland soils by as much
as two order of magnitudes.
Table 8. Comparison of the constant infiltration capacityf of some Hawaiian soils and some soils ofm~inland United States
Group f in/hrc
Hawaii U.S. Mainland
Low 0.5 - 2.5 Less than 0.05
Moderate 6 - 10 0.05 - 0.30
High Greater than 10 0.30 - 0.45
B. EVAPORATION (20). There are 12 evaporation stations on Oahu
which have 5 or more years of records. Four of them were discontinued.
Annual evaporation is around 70 inches for all stations and seasonal
distribution of evaporation is about 4 to 6 inches for winter months
and 6 to 8 inches for summer months. There is no significant variation
among stations.
As evaporation is an index of potential evapotranspiration,
it will be useful in determining total water yield and the water resources
of small watershed. However, the peak flood flows, such as the majority
in Hawaii, may not be significantly affected by evapotranspiration
because the total time during flood is short. Therefore, evaporation
and evapotranspiration can be considered as minor losses.
Part II. Review of Present Design Criteria
The determination of peak discharge from a small watershed is
difficult and uncertain because so many variables are involved and there
36
is a lack of basic data. Small watershed hydrology differs from that of
large ones because of short time of concentration, small channel storage,
and the effect of land use to the distribution of runoff . Small watersheds
can be classified as urban or rural. Watershed characteristics of urban
areas include not only those watershed characteristics as outlined before,
but also degree of urbanization, streets, roads, residential area, busi
ness district, and existing drainage systems. Many of these additional
characteristics are complex and difficult to evaluate quantitatively.
Floods, as everyone reali zes, ar e increasing and producing more damage
owing to increased urban utilization of zones of potential flooding.
1. PRESENT APPROACHES OF FLOOD PEAK ESTIMATION
The following seven gener a l approaches for small watersheds are
briefly evaluated: (i) empirical formulas, (ii) rational forumulas,
(iii) frequency analysis , (iv) statistical analysis on regional basis,
(v) envelope curve, (vi) synthetic flood hydrographs, and (vii) Chow's
method.
Kinnison (21) in 1946 and Chow (22) in 1962 have gi ven a complete
list of empirical formulas which have be en proposed in the past for peak
discharge determination. The most frequently used formulas are Talbot's
(23) published in 1887, Meyer's (24) published in 1879, and the r ational
formula originally derived by Mulvan ey (25) in 1850. These old formulas
are still frequently used not because they are based on sound theoretical
bases, but because of their simplicity and ease of appl ication.
For gaged watersheds with fai rl y long records, the peak discharge of
high r eturn periods can be estimated by using frequency analysis to fit
peak stream flow data with a gi ven type of probability distribution. It
is difficult to compare or evaluate the different frequency analyses to
determine which is most suitable because the true probability distribu
tion of the flood discharge is still not clearly understood. However,
frequen~y analysis is based on the actual runoff data of an area.
For ung aged small watersheds, a regional formula can be developed
by using the multiple r egression technique to correlate peak discharge
of a given frequency with measured watershed and rainfall characteristics.
Benson (26) in 1959 found that the slope of the main stream is next in
importance to the drainage area along factors that af f ect runoff. Wu
and Delleur (27) in 1961 developed an empi r i ca l formula for Indiana by
37
correlating peak discharge with ar ea , drainage density, stream slope, mean
relief, and shape factor of small Indiana watersheds.
Maximum experience of flood discharge can also be used as a guideline
to predict design discharge. This is usually expressed as an envelope
curve of all maximum experience peak discharge plotted against its water
shed area.
Another method to predict both peak discharge and the volume of flood
is the so-called synthetic flood hydrograph which is the study of design
storm, hydrograph shape, watershed characteristics, and time parameters
of hydrograph, such as, time of concentration and time to peak. This
technique was first developed by Synder (28) in 1938 .
In 1962, Chow (22) presented a method for the determination of peak
runoff from small rural watersheds of less than io square miles. The
method is general and based on fundamental hydrological principles. It
takes into account the watershed area and major physiographic and clima
tologic conditions of the watershed.
2 . DESIGN CRITERIA IN HAWAII
A . HISTORI CAL SURVEY OF THE DESIGN CRITERIA OF CITY AND COUNTY OF
HONOLULU
i. 1957 design cri teria f or storm drainage faci Zi t ies . The 1957
design criteria were developed by the City and County of Hono
lulu (29). The study was made to set up a design criteria
using the rational formula. Curves of rainfall intensity
duration and average annual rainfall were developed for Oahu
and a formula to determine time of concentration was modified
from the Kirpich formula (32) . Frequency analyses were made
for 11 streams which had relatively long records (longer than
20 years).
ii . 1959 storm dra inage standards. The 1959 storm drainage stan
dards were prepared by Dodo and Ling (30) and reviewed and
modifi ed by Dr. V. T. Chow. The rational formula was us ed
for estimating peak discharge. The determination of time of
concentration was based on the 1957 standard. The depth-dura
tion-frequency maps of the Hawaiian Islands, made by the Bureau
of Plans of the City and County of Honolulu, were adapted to
determine the design rainfall intensity, I, and adjustments
38
were made to increase the runoff coefficient, C, for urban
areas.
iii. 1965 adjustment of desi gn criteria by Chow. The following
adjustments were made in the use of the rational formula:
limiting its use to areas of less than 100 acres instead of
the 640 acres used formerly and use of new depth-duration
frequency maps published in 1962 by USWB (3).
iv. 1966 adjustment of desi gn criteria by Chow (4). Two envelope
curves were developed as guidelines to determine design dis
charge for watershed areas larger than 100 acres. One is for the
windward district of Oahu and the other for the rest of Oahu.
These curves were based on maximum recorded flood peaks in
Oahu.
A chart proposed by the Portland Cement Association (31) for
estimating the runoff coefficient "C" for agricultural and
open areas has been adapted for use in rational formulas.
v. City and County of Honolulu design criteria for drainage.
A review and comparison of the design criteria for drainage
facilities used by the City and County of Honolulu are shown
in Table 9.
B. PRESENT DESIGN CRI TERI A USED BY DIFFERENT AGENCIES IN HAWAII (34)
i. City and Count y of Honolulu. The 1966 design criteria devel
oped by Dr. Chow are used.
ii. Dept. of Land and Natural Reeourcee , St ate of Hawaii. The
1966 criteria as recommended by the City and County of Honolu
lu are used.
iii. Highway Division~ State of Hawaii. The rational formula is
used for a drainage area equal to or less than 1 square mile,
the Jarvis-Myers formula is used for drainage area larger than
1 square mile, and whenever sufficient streamflow records are
available, a frequency analysis of annual peak flows is used.
iv . U. S . Corps of Engineers . When sufficient streamflow records
are available, a frequency curve of annual peak discharge is
constructed for feasibility determination and possibly for
a design flood value. The standard proj ect flood value which
would be expected from a design standard project storm in the
Table 9. A survey (1957-1966) of design criteria for drainage facilitiesused by City and County of Honolulu
Envelopecurve
Frequencyana l ys i s
Determination of"C"
Rat ional formula
Determinationof HI"
Determination of"tell
for ar eales s than
Year -----------
For agricu ltural and open area usethe runoff coefficient designedby Cook (33)
1957
Acres
640 For forest areat =0.01356Ko77(ae r i ved fromdat a)
For low vege t a lcover
tl:=0.01356Ko77(by Ki rp i ch)(32)
Rainfall intensityduration-frequencycurve (by Mitsuda)
For built up areasResidential areasHotel-Apartment areasBusiness areasIndustrial areas
C=0.55-0.75C=0.65-0.80C=0.70-0.90C=0.70-0 .80
Gaged watershedswith sufficientflow records ,
Unga~ed watersheds(larger than1 sq .mi.) withs i milar physiographic conditionof those water~
sheds where frequency analysiswere made.
---------------------------------------------~-------- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -- - - - -- - --- -- - - - - - - - - - - -- -
1959 same same 1959 USWB depthduration-frequencycurve
Adjustment for built up areasResident ial areas C=0.55-0.70
Others are the same.
same
1965 100 same 1962 USWB depthduration-frequencycurve
same same
1966 100 same same For agricultural and open area usechart proposed by the PortlandCement Association .
For arealarger than100 acres,use envelopecurve ofmaximumexperience.
VI\0
~~~ · 41;: .u;~~-.;A~~:;;tQ.O.~...;g~-;- .,.~~·-.",;,;;.: ;.;. ·
40
studied area is preferred when designing flood protection for
an-urban area. For dam spillway design, the maximum probable
flood produced f r om maximum probable storm is normally used.
v. U. S. SoiZ Conservation Service. When suff~cient streamflow
data are available, a flow-frequency curve is developed to deter
mine the design r~noff value. When no streamflow data are
available, design hydrograph is developed by SCS method of
hydrograph synthesis.
vi. Private engi neer i ng consuZting agencies. The design criteria
set up by the City and County of Honolulu are used or special
hydrological investigation is made to serve the project, e.g. 3
Makaha Valley on Leeward Oahu by R. M. Towill Corporation
(35) by using the hydrograph synthesis method.
vii. Counties of Hawaii3 Maui and Kauai. There are no established
drainage criteria for these counties. They have been guided
by the standards of the City and County of Honolulu.
A summary of the above can be shown in Table 10 .
Table 10. Design technique of peak dis charge used bydifferent agencies i n Hawaii-
Design
Technique
Agencies
City & Highway Corps of SoilCounty of DO ° ° E ° Conservation
Honolulu 1V1S1on ng1neerso Service
Dept. of County of Pri vateLand and Hawaii engineeringNat ur a l Maui consulting
Resources Kauai agencies
Rat ionalformula 1* 1
Frequency1 1analysis
Standardpro jectfl ood 1
Probab l emaximumflood 1
Maximumexperi ence 1*
Jarvis -Myersformul a 1
Hydrographsynthes i s
*1966 cr i teri a developed by Chow .
C. DISCUSSI ON OF THE PRESENT DESIGN CRI TERIA. The present design
criteria in Hawaii can be considered in two parts based on the area of
41
the watershed. For an area larger than 100 acres (about 0.2 square miles)
with stream gaging records available for some watersheds, methods that have
been used are: envelope curve of maximum experience, frequency analysis
for gaged watershed with sufficient stream records, estimated peak dis
charge from non-gaged watersheds by a comparison of frequency curves for the
watersheds with similar watershed characteristics, Jarvis-Myers formula,
and synthetic hydrograph. For an area of less than 100 acres with no
available stream gaging, rational formula and hydrograph synthesis have
been used.
TH~ RATIONAL AND JARVIS-MYERS FORMULAS are- about 100 years old. Their
s in.p l i.c i ty and ease of application make them popular. The Jarvis-Myers
formula is a type of empirical formula expressing the peak discharge as
a function of the drainage area. The rational formula expressed peak
discharge as a product of rainfall intensity and watershed area with a
coefficient applied, Q = CIA. The rainfall intensity, I, defined as av
erage rainfall intensity in inches per hour for a duration equal to the
time of concentration of the watershed cannot be determined properly unless
the time of concentration is well defined and precisely determined. The
coefficient "C" is difficult to determine since it reflects the overall
combined effect of storm and watershed characteristics. Present criteria
of selecting "C" are more or less arbitrary and are not rationally deter
mined.
PEAK DISCHARGE is best estimated from streamflow records because flow re
cords reflect the composite phenomenon resulting from storm rain and basin
characteristics. The frequency analysis of annual peak discharge for the
watersheds with fairly long streamflow records is more accurate than other
methods for predicting design discharge. On Oahu there are only 12 sta
tions out of 58 that have records longer than 20 years and those stations
with a short period of records cannot use the frequency analysis.
AN ENVELOPE CURVE~ which covers the maximum peak discharges of all gaged
stations, will, of course, give more conservative predictions. For some
watersheds, the estimate may be too high since there is no clearly defined
relationship between peak discharge and watershed area, and the recorded
point may be far below the envelope line. Furthermore, there is no way
of determining frequenc y of peak discharge so predicted. Envelope curves
developed by Chow are the best conservative estimates for those areas
(larger than 100 acres) where frequency analysis cannot be made.
42
THE TECHNIQUE OF SYNTHETIC HYDROGRAPH requires that several basic ques
tions such as linearity of small watershed hydrograph, infiltration loss
and effective rainfall, and time parameters of hydrograph and hydrograph
shape be solved first, otherwise this method of peak design discharge is
just nothing more than a fancy estimate in a complicated form. The hydro
graph study of small Hawaiian watersheds will be in Phase II of this pro
ject.
Part III. Peak Discharge Determination for Small Hawaiian Watersheds
The study of the determination of peak discharge for small Hawaiian
watersheds are based on available basic data and present design criter~a
characteristics of Oahu watersheds. Studies to improve design criteria
for watershed areas larger t~an 100 acres are being made by utilizing
streamflow records and watershed characteristics. For watersheds equal
to or less than 100 acres,evaluation of the rational formula is being
made to create a better design through a better understanding of the
variables involved.
1. PEAK DISCHARGE DETERMINATION FOR WATERSHED AREA LARGER THAN 100 ACRES
A. FREQUENCY ANALYSES OF EXISTING GAGING STATI ONS. Frequency analyses
of annual instantaneous peak discharge were made for 23 gaging stations
which have 12 or more years of records. Analyses were made by using two
probability plottings, Gumbel's extreme value and Gumbel's extreme-log
value. Frequency curves of the, 23 stations are shown in the Appendix.
The peak discharge of longer return periods can be read from the extended
curves (or lines).
Table 11 compares the predicted lOa-year peak discharge from 23
watersheds obtained from Gumbel's extreme value distribution (from this
study), Gumbel's ext r eme- l og value distribution (from this study, and also
from a USGS study), and Pearson's type III distribution (from an Army Engi
neers study).The frequency curves plotted by Gumbel's extreme-log value
distribution and Pearson type III distribution are on log-scales and the
predicted lOa-year peak discharge is relatively higher than those predic
ted by us ing the Gumbel ext r eme value plotted on an arithmetic scale.
Since there is more confidence in extending the straight line of Gumbel's
extreme value plot than a curve, which is on log-scale, the use of Gum-
bel extreme value method to predict pe ak discharge is recommended.
Tabl e 11 a l so shows that the estimated design discharge from
43
envelope curves yi el ds approximately a 100-year frequency as compared with
Gumbel's extreme value estimates as shown i n Figure 17. The envelope
curves pl ot t ed were based on maximum recorded peak discharges for all
gage stations on Oahu . and the length of records of the gage stations varies
from 3 yea r s to 52 year s . Since the envelope curve covers the maximum
peaks, the predicted val ues from i t might be considered as 50- or 100-
year frequency.
Tab le 11. Comparison of predicted 100- ye ar peak dischargefrom three di f f er ent methods and es timated peakf r om Chow 's env elope cur ve (Discharge i n cfs ).
StationNo .
2 ,0002 ,0402, 1302 , 1602 ,1652, 2302, 2452, 2602 ,2802 ,2902 ,3202 , 3902,4002,4402 ,4602 , 4702, 7502 ,7802 ,8302 ,8402,9103 , 0303 , 500
Gumbel 'sGumbe l 's ext r eme- l og Pearson* Envelope curve
ext reme value value Type III (by Chow)
6 , 650 5 ,800 3,8005, 070 5, 200 8 ,500
19 , 500 35, 000 45,000 20,00029 ,800 22 ,000 17 , 000
750 1,000 5 , 9008 , 350 7 ,600 22 ,000 9 ,5003,950 4, 800 5 ,9007, 250 10 ,400 14,500 6 ,8 004 ,650 5 , 800 7 ,800 6,2008 ,600 13 , 000 16,500 6 ,0005,200 9, 500 10 , 000 6,8002 , 260 3 ,600 2,750 3,1003 ,500 3 , 300 3,3002,560 3, 800 3,850 3 , 4001 , 730 1 , 660 3, 1004,720 5,400 7,2005 ,4 50 5 , 750 9,700 5, 800
200 470 1 , 700600 1,300 1 ,0 50 1 , 700
1 ,980 4 ,000 5, 5003 ,800 10 , 000 5 , 8005 , 800 3 ,500 11 , 3005,900 7,600 8 , 000
*Freque ncy ana lysis made by U.S. Army Corps of Engine ers, Honolulu district .
B. MULTIPLE REGRESSION ANALYSIS FOR DEVELOPING REGIONAL FORMULA FOR
NON-GAGED WATERSHEDS . Two sets of multiple r egression analyses
were done by digital computer. One set correlates peak discharges wi t h
watershed area, drainage density, length of main stream, mean slope of
the mai n stream, and sh ape fact or of t he watershed. The predicted 100-
year peak discharge from Gumbel's extreme value ana l ysis (Table 11) was
used as a dependent variable and the corresponding wat er shed char acter i stics
(as listed in Tabl e 6) wer e used as independent variables. The other
set correlates peak discharge with three simple watershed characterist ics :
area , length and he i ght, and a precipitation index whi ch is defined as a
. 100- year , 24- hour r ainfall (listed in Table 12) . The multiple regression
formulas r esult ing f rom the t wo sets of r egress ion ana lys i s were shown
in Table 13 and it was found that a closer correlat ion exists wi t h the
44
til~ 30,00uz.....UJ:)...J
~UJ 2.5.:E:UJ0::r-XUJ
Vl-...JUJen 2.0,000:E::)<.!J
~0::LL
UJ<.!J0:: 15.:euVl.....0
~«UJ0..
0::10,00
«UJ 0>-I
00.-l G>0 1:)0 eUJr- 5000u.....0UJ0::0..
PREDICTED PEAK DISCHARGE FROM ENVELOPE CURVE IN cfs.
Figure 17. Comparison of lOO-year peak discharge predicted by Gumbel'sextreme value analysis with the discharge predicted byenvelope curve.
(1)
4S
latter set. The following two best regress ion formulas ar e selected on
the basis of their high values of goodness of regression:
(a) For windwar d Oahu (Zone I )
Ql OO
= 7. 4 x 1023 A1.31 LO.89 H-10 p5. 24 .
(b) For the Honolulu area and between mountain ranges of
Oahu (Zones II, III)
Ql OO
= 2.06 x 10- 6 AO. 75 L-O. 38 H1• 39 p3.1 7
Where A = Watershed area, in acres
L = Wat er shed length, in f eet
H = Watershed height, in feetp = 100-year, 24-hour precipitation, in i nches .
Tab le 12. Water sh ed characteri s tics, precipitation index , and100- year peak di sc harge for multip le regression anal ysis of 20 s ma l l watersheds on Oahu .
Q 100 A L 11 P
Watersh ed 100-year water shed wat ershed Watershed Precipit at i onNo. peak di scharge a rea l engt h height Index
c f's , acres ft. ft . in.
2,000 6 ,650 883 10, 100 1, 510 222 , 040 5,070 3, 110 26 , 800 1 , 360 212, 165 750 1,658 22 , 800 1,400 122 ,230 8,350 3 ,885 35 ,800 2 ,568 162,245 3 , 950 1, 658 34 ,900 2, 792 162 ,260 7, 250 2 , 208 20, 100 2 , 506 162,2&0 4, 650 1 ,7 47 17,100 2 ,480 162,290 8 ,600 1 ,670 11 , 900 2 , 276 182,320 5 ,200 2, 144 13, 700 2 , 432 182,390 2,260 678 7,800 1,920 162 , 400 3,500 730 9 , 900 2,814 162,440 2, 560 755 11 , 300 2, 141 162 ,460 1,730 666 11,800 2 , 165 162,470 4,720 2,323 20,800 2,435 152,750· 5,450 621 6 ,000 2 ,128 152,780· 200 179 3 ,300 2 ,450 162,830· 600 179 3 , 100 2 ,222 162,840· 1 , 980 595 5 ,600 2 ,3 77 172,910· 3,800 634 6,200 2,500 183,030· 5,800 1,779 6,800 2,548 16
• Windward watershed s
(2)
The proximi ty of the actual points to the regression curves is
reflected i n Figures 18 and 19. The va l i di ty of the r egression can be
shown by plotting estimated discharge from equations (1) and (2 ) against
the origina l data as shown in Figures 20 and 21 .
Tabl e 13 also shows that the stream dens i t y, main stream l ength,
and slope do not significantl y corre late wit h the peak dischar ge indica
ting that small Hawaii an wat ersheds r anging in s i ze from 0. 2 to S square
46
\02.04 5 (, 73
0000
000/
000
oeo
I'000
V-0 e V
/0
/V00
V ""
/0 .....
/'10 7~....... 770
60 I", /
V5V
AA /
V
300 /
V2.00
l7/
10 0 8 q 2- 3 4 S c; 7 8 'I- -
\0.0'108
"7
~
5
30
40LU
~U(J).......o~
ifja..(J)ffl:::>lHo ()LUZ 0<{ 0I- ..-lZO-
~(J)
Z.......
~
ifj>-I
oo..-l
A =WATERSHED AREA (ACRES)L =WATERSHED LENGTH (FT.)
H =WATERSHED HEIGHT (FT.)P =PRECIPITATION INDEX (IN.)
Figure 18. Regression line for theoretical lOO-year instantaneous peakdischarge aga i ns t watershed characteristics and precipitationindex (for Windward side of Oahu, Zone I).
47
I.':>" '010
(,
2.
2.
v
V1/17'
V
l/l/
~/
cf 1/e7
(.) /\!) V
" / I.... E)
Y E>
3/
VII (i)
V'/
V/
V
., . ;rV
//
/
8 1. " ~ !> 6., Sq 5 ~ 7 e
5
4
4
10'"10
10'"
1
~
L5>-I
oo....
(J) 1Il:J~o ()wZ 0« 0I- ....~CYI(J)Z.....
A =WATERSHED AREA (ACRES)L =WATERSHED LENGTH (FT.)
H =WATERSHED HEIGHT (FT.)P =PRECIPITATION INDEX (IN.)
Figure 19. Regression line for theoretical lOO-year instantaneous peakdischarge against watershed characteristics and precipitationindex (f or Honolulu areas, between mountain ranges of Oahu,Zones II and III).
48
10,000q
a1,
+ 5 '" 7 6 , 10 ,000"I- 5 " 1 8 q 1000
II'V
/V»
V~ /:V
V/
V/
Vvc~
VV
/V
:I
100100
4
4
5
,5
:t
3
1000
q81
<II~
u0..(
.J,. ::>w ~\..!Jet:cLQ«u."IuUI ;t0 Q
til
j. U1uJ
« ~
LLI L!)o, Ul
0::
rt u,>- 0
8 lflZ«
CJ wu.J :£~s >-co:nuJ
100 'fR. PEAK DISC HARGE. ... Q c+':. ,
~ROM FRE.QlJENCY A.NAL'(SIS
Figure 20. Comparison of 100-year discharge estimated by regressionformula , equation 1, with actual data.
49
+ S " , & "10,0002.'" !ro ~ T e '11000
1./
/
T/
ID. V ..~
/ •,.V' ~
~
V•l/Gl
I.
V0
1/'I 1/• ~7
V• V4- /
/s
1/V
•. IOPOO
IOO'1'EARPE.AK DISCHARGE > Qt~ FROM
FREQUE.NCY ANALYSIS
Figure 21. Comparison of lOO-year discharge estimated by regressionformula, equation 2, with actual data.
50
Table 13. Mult iple regress ion formul asfor 100- year peak discharge
Q100 of Oahu small wate rsheds
Independent Regress ion formula* R2**variables
A, 0 , i , s , f Q1 00 = K AO.80 0- 0. 30 i O. 68s0 . 31 f-l. l 0 .69
A, i , s , f A i O. 33 sO. 26 f- O•99 0.68
A, 0 , i , s Al. 3 00 . 25 i - O.69 s -0.04 0.42
A, z, s Al •17 i-O.44 sO.0 24 0. 42
A, s , f Al . 2 i O.13 f- O. 87 0.67
A, 0, s AO.8 0- 0 . 12 sO.15 0.39
A, s AO. 76 so. 15 0.39
A, i Al. l i-O.45 0 .4 2
A, L, H, P Al. 16 L-O.42 Hl . 03 p2. 74 0 . 75
A, L, H Al. 37 L-O. 68 HO.7O 0.63
A, L, P A1.22 L-O.53 p2.3 0 .70
A, H, P AO.85 Hl.14 3.05 0.73. P
A, L, H, P (1) AO. 75 L-O .38 Hl.39 p3.l7 0 .89
A, L, H (1) A1. 20 L- 1. 01 Hl. 03 0.52
A, L, P (1 ) AO . 80 L-O. 4l p2.64 0 .65
A, H, P (1) AO.49 Hl . 40 p3.46 0 .87
A, L, H, P (2) A1. 31 LO .8 9 H-lO p5. 24 0.97
A, L, H (2) AO. 67 L2. 40 H-6. l 1 0.95
A, L, P (2) A- O. 02 L3.85 p- 2.97O.R~
A, H, P (2) Al.66 H-l 1. 2 p6.56 0 .96 7
*K = a coeff i cient of r egres s i on fo r mu la .
**R2 mea sures the goodness of fit of r egression , 1 - R2 measures dev iat ionsfrom r egr ess i on .
(1) For Honolulu area, bet ween mount ain r anges , leeward s ide of Oahu.(2) Windward side of Oahu.
miles are small enough that channel storage is not significant or that
overland flow hydraulics plays an important role in creating peak flood
discharge.
Equation (2) can be ·expl ai ned by considering that discharge is
directly proportional to area, slope (expressed by H/L) , and precipita
tion. Equation (1) indicates an inverse effect of the slope and is con
trary to the general theory of hydraulics. Since equation (1) i s deter
mined by only six watersheds on the windward side of Oahu, the number of
samples may be a limiting factor.
(5)
51
Therefore, it is suggested that equation (1) should not be used
as a regional formula for windward Oahu without further investigation.
However, it may be used as a reference. At present the envelope curve
determined by Dr. Chow is the best criteria for a conservative design
for that area.
Equation (2) is based on 14"small watersheds well distributed in
the Honolulu area and between mountain ranges (Zones II and III). Since
the equation can be reasonably substantiated, equation (2) is suggested
as a regional formula to estimate peak discharges for Zones II and ·111.
The leeward side, Zone IV, has no gaging records long enough to
enable a frequency analysis to be made.Hence,envelope curve developed
by Dr. Chow is the best criteria for a conservative design for this area.
In lieu of computations, equation (2) may be used with the coax
ial correlation chart shown as Figure 22.
C. PEAK DISCHARGE FOR RETURN PERIOD OTHER THAN 100 YEARS. The rela
tionship between the peak discharge for other frequency and the 100-year
peak discharge can be obtained from the slope of the frequency lines
(straight line) of Gumbel's extreme value theory. A derivation of peak
discharge of other frequencies as a function of 100-year peak discharge
can be shown as follows :
Gumbel's extreme value frequency lines in the Appendix, being
linear, permits expressing the differences between 100-year discharge and
peak discharges of other frequencies in equation (3):
1Ql OO - ~ =a (~y) (3)
1Where = Slope of the frequency linea
~y = Difference of reduced value (y) on horizontal scale
from n-year to 100 years
Q = n-year peak dischargen- ~yOr Qn - Ql OO (1 - aQ ) (4)
100
Equation (4) can be expressed in logarithm form:
log Q = log Ql OO + log (1 - Q~Y)n a 100
Both equations (4) and (5) express linear relationship between
Ql OO and Qn if the last term is constant. The expression ~y/aQlOO is
52
;y:I '
I 1
: ~ :, ~
s.ooo+-- +--+----;-+-- +-- -/- - +----,L-------j
A(ACR E ~
3000SCXXl
Quosio.ooo
Figure 22. Coaxial correlation chart for peak discharge determination byequation 2.
53
small compared to "1" and the value of aQlOO for small watersheds on Oahu
ranges from 5 to 7. The average value used is 5.75. Equation (5) then
becomes,
- b.ylog Qn - log Ql OO + log (1 - 5.75) (6)
Since b.y can be read from Gumbel's extreme value distribution
paper and is constant for a certain assigned frequency "n", and also since
the peak discharge ranges from 100 cfs to 30,000 cfs, equation (6) is
plotted as straight lines on log-log paper (in Figure 23) and may be used
to determine peak discharge of frequencies for 75- 50- and 25-year periods.
D. PROBABILITY CONSIDERATION OF DESIGN RECURRENCE INTERVAL IN RELA
TION TO PROJECT LIFE
The theoretical relation of probability consideration of design
recurrence interval (return period) is shown by Linsley (36) as,
J = 1 - pn (7)
Where J = The probability of the event occurring in
any n-year periodp = The probability of non-occurrence of an event
in any year
n = Number of years,
or 1 - J = pn = The probability of non-occurrence of an event
in any n-year period or percentage of assurance.
Since P is the probability of non-occurrence of an event in any year,
1 - P will be the probability of occurrence of an event in any year. The
average return period is defined as,
T =r
11 - P (8)
If the average return period is considered as design return period and
n as numbers of series of years of non-occurrence as project life or
actual return period, the chart shown as Figure 24 can be developed on
the basis of the above theory. For example, for a project life of 25
years with a percentage of assurance of 75 percent of non-occurrence,
the design return period should be 90 years. Therefore, if most of the
small hydraulic structures are considered for a life span of 25 years
and with a 75 percent assurance that a design peak discharge will not
occur, a design return period of 100 years (close to 90 years) should
54
0
/.
2.~~
g ~~V
'I
7
(,
s Ai,~~1I
'\'i~/.V/
~~ 17~
g ~
~~',,1'~
/.
~~
~~
h ~V/
~r/~V
"
10,000
~o,oo
5
7
8
lJJI.!>a:.{:r 10 0 0
~ 'I
Ci 8
100 YEAR PEAK DISCHARGE
2.00 4- 6 (, 7 8 'I 1000 2.000 4- II , 7 8 'I 10000 a.oooo 10000
Figure 23. Relationship between the n-year and .I OO- year peak discharge.
55
wu,
.-l
~~R.CE.NT~GI of 1"~~uR./""olC.E = •l- I I I , I I I I I I I I I~
"' II-,
I-aI- /7I- / ~
F /V V~
/ l/../ /
30 /
/V V -:F- / V::to
/
/ / l/I- / -
VV / /V\0 /
l- /' /' -'I
l- V / -80
/ / /I- -I- / V / -
" // V /II
V / VV /II
/ V / // /a
/ VF- / / V 1-/ /
%/
~/ / / VI- / I-
I II I I Y111 L ,I/
I I I I I I I I I I L III I I I II t' I II
!> " 1 , 10 IS ~o 30 40 50 ~ 100 lOO 360 500 I
50%
75'70
DE51GNED RETUR l-J PER IOD
Figure 24 . Statistical r e lationship between t he des i gned return period andproject l ife wit h respect to percentage of assurance.
56
be used. The 100-ye ar base frequency has been chosen in developing region
al flood formula partly for this reason.
2. PEAK DISCHARGE DETERMINATION FOR WATERSHED AREA EQUAL TO OR LESS THAN
100 ACRES
As shown in Table 3, there are no gaging stations in watershed areas
of less than 100 acres on Oahu and for these watersheds frequency analysis
and flood hydrograph that require streamflow records are not possible.
The peak discharge can be only estimated by indirect methods as the ra
tional formula or the recent (1955 to 1967) approach of studying the hydro
dynamics of overland flow. The former is over-simplified and the deter
mination of a coefficient in the formula is arbitrary and approximate;
the latter is complicated in mathematical form (hyperbolic partial differ
ential equations) and difficult to solve owing to the necessity of eval
uating such terms as friction and infiltration. Because of the simplicity
and ease of application, with no better method developed thus far, the
100-year old rational formula is still popular and used not only in Hawaii
but also in most areas of continental United States. A critical evalua
tion of the rational formula and a new approach to an improved technique
of using the rational formula follows:
A. GENERAL EXPLANA TION OF THE RATIONAL FORMULA. The rational formu-
la, Q = CIA, is used to predict peak discharge by knowing the area of the
watershed . A, a certain intensity of rainfall with a duration equal to
the time of concentration of the watershed , I, and a runoff coefficient,
C. The time of concentration is arbitrarily defined as the time required
for a drop of water from the most distant point in the drainage ar ea to
reach the outlet. The rat ional formula is reasonably correct if the area
is small and the rainfall uniform both in time and space, is sUbjected to con-
stant loss rates, after being sustained long enough beyond the time of concen
tration. The increasing discharge through the outl et will level off at
a rate appr oa chi ng equil ibrium discharge which is defined as the same
as the r at e of eff ect i ve inflow, I A, where I i s defined as effectiveo 0
rainfall. The ratio of ef f ect i ve r ainfall ,I ,and act ua l r ainfall inteno
sity,I,can be expr es sed as a runoff coef fici ent C. The peak discharge
Q, therefore, can be ca l cu lated by the produc t of C, I, and A.
However, i n r eal ity, the above f ormul a is app l i ca bl e only f or a
small area of several square f eet wher e the ra in is uniform both i n time
57
and space and lasts long enough to permit the entire area to contribute.
For a larger area, the rain may not be uniform in time and in space
and may not last long enough to develop the equilibrium discharge. The
base of the rational formula is questionable and the coefficient is not
reflected by the infiltration loss alone, but other variables including
size of watershed, non-uniform distribution of rain, and flood-routing
through channels to the outlet as well. In engineering practice, there
is no clear definition to show limitations of the size of the area in
which the rational formula may be applied. The Hydrology Handbook pub
lished by ASCE (37) suggests use of the rational formula in areas less
than 1 square mile and up to areas of 100 square miles. The local use of
the rational formula to areas up to 100 acres (less than 0.2 square miles)
is much more restrictive than its use in continental United States.
B. OVERLAND FLOW APPROACH OF EVALUATING THE RATIONAL FORMULA
i. Simple overland flow equation . Without getting into energy
or momentum relations, the following equation has been sug
gested by Horton (38) (39) by considering the conservation
of mass,
AI dt - Qdt = Adyo (9)
Where A = Area of watershed, in acres
I = Inflow, rainfall excess or effective rainfall,oin inches per hour
Q = Discharge, in cfs
y = Average depth of surface detention, in feet.
Equation (9) can take the following explicit form for dt,
Adydt = AI _ Q .
o(10)
The relation between surface detention and discharge can be
expressed as,
mq = ky . (11)
Where q = Discharge, in cfs per unit width
k = A coefficient
m = An exponential value dependent upon whether flow
is laminar or turbulent.
58
Substitution of equation (11) into equation (10) gives
equation 12,
(12)AdymAI - wkyo
d t = ----=---
Where w = Average width' of the watershed, in feet.
Equation (12) can be solved by simple integration of m equals
2 or 3. As in Figure 25, an experimental study in Mississippi
(40) showed the overland flow can be classified into four
regions: 'l ami nar flow m = 3, transition zone, turbulent flow
m = 2, turbulent flow m = 5/3. These relations were also
shown by Izzard (41). If the value of m can be assumed as 2
(Horton (30) also assumed that m=2 as the value of a 75 per
cent turbulent flow, equation (12) can be solved by simple
integration.
t = A
2-VAI wko
loge
AI + y-VAI wko 0
AI - y-VAI wko 0
(13)
ii. Time of equi. l.i bx-ium, t. Time of equilibrium is defined asethe time when flow is 97 percent of the supply rate (41).
For the time of equilibrium, equation (13) can be expressed
as,
t =eA
2-VAI wko
loge
AI + Y "AI wko e e
(14)
Since q = ky 2 ,equat i on (14) can be written as,e e
t eA
= -2V-;;::'A;;;;;;I;;::;w;;;'"ko
AIolog
e AIo
+ -Vq AI we 0
- -V q AI we 0
(15)
59
o
I /0 to'.'1
>C It: r I8/ I? V /
71./ 1 ! J
, / ,( I~ J
.: 1/ ) V s
1/ I;: /
V 33
II. / / I./1/ , /:z.
It'' If II10/ j
r !ill // V / T U fI a.UI IT R. "'N~I-. £'" E0
I 2-
87 I 1/
/ 1/ .I I-r-1/ 5' 1/
" / Ii 101 V5
" 1/ II... ..~
x If I - 1- f--- -X rc- - - -3
)ltl / TR ~WSITIC N F ....N !':IEe
IIX! 0 II:l.
0° ~
} 11' 17 rt 0 SI OPE ' o. poe 5
/xl / Itl'-N( E.0 SI1°f'E. o.JOOlp
/ j X :>1 OPE. l=- o. POl f.-i e -f J I IIIl.q
.J T I8 I T II tT1
I"
/ J
5 I /r
"l-
f0 1 .0 . 0 2- O.O~ 0 .0+ 0.0"" (10& 0.08 0.10 0 .2- O.?> 0 .'1- 0_"" 0 ." 0 .8 I.
0 .0
0 .0
0 .0
0.0
0 .0
0.00
r,oae,o,
0 .00 .00
0.00
o.cio
0 .00
o,
c,
o.
0.\
0 .0'10 .0
0 .01
e.
0.00
0.00o .
z
AVERAGE DEPTH OF SUR FACE. DE.TENTION (':I) IN FEE,T
Figure 25. Typical experimental results obtained for uniform steadyflow on smooth concrete [t aken from paper 17, U. S.Waterways Expt. Sta., Vi cksbur g, Miss. (40) ] .
60
Further substituting Q = q w and Qe = AIe e 0 '
Ay AI + Qt e log 0 e
( 16 )=e 2 -V AI Q e AI - Qo e 0 e
Theoretically,t ~ 00 as Q = AI , for practical design Qe e 0 ei s assigned as 0.97 AI , therefore,o
Ay 1. 97 AIt e log 0
= 2.03 Q 0.03 AIe ee 0
or,
Ay 4 .2 Ay 2 . 07 Aye log 66 e e(17)t = 2.03 Q = =e e 2. 03 Q Qee e
which is close to the expression as given by I zzard (42),
t e
2ve= Qe(18)
For convenience, equation (18) is used for
~ will occur at
equilibrium t e
where v = Ay .e edeter mining t .eTime t o peak~ t. Time to peak, t , is defined as the time
p pinterval from be ginning of r unof f t o time of peak discharge.
If the watershed is r elatively large and the duration of a
storm is l ess t han time of equi l i br i um , the peak discharge
time to peak t whi ch i s less than time top
Equation (13) can be expressed as,
i ii .
t =P
A-t=== l og2 VAl kw e
o
AI + Y "'\fAI kwo P V 0
AI - Y -VAl kwo P o .
( 19)
where yp2
61
yp is the average surface detention in the
watershed when peak discharge occurs, or ,
t =P
AyP
2-VAI~loge
,AI O +-VAlo~
Al o --VAr.o~
since Q = AI (theoretically)e 0
tP
=Ay
P
2-VQe~logeQe+~
Qe - -VQe~
if, Qp = A2 Qe (A2 < 1),
then,
loge1 + A1 A
(20)
iv. Time of aonaentration~ t. The time of concentration, t ,a cis defined as the time required for water from the most distant
point in the drainage area to reach the outlet and can be
determined by dividing length of the watershed by the mean
velocity of overland flow . If the land slope is not uniform,
the time of concentration can be calculated as the sum of time
of concentration for all reaches, as ,
Q..
t L1.=
C -v.1.
(21)
By considering a small watershed with uniform slope, the time
of concentration is simply,
t c =R.v
62
where £ = Watershed length
v = Average velocity = ky (for m = 2),
or,
t =c(22)
This expression can also be derived from equation (18), the
time of equilibrium, rewritten as,
t =e
2 Aye
wqe=
2 Aye
wky 2e
=2 £ky
e
Since y is the maximum depth, if the mean depth is consideredeto be one-half of the Ye' the mean velocity, v can be shown as,
v =kye-2-
and the time of equilibrium can be written as,
t =e
'or ,
t =e
£v
(23)
This proves that time of concentration, t , and time ofcequilibrium are identical or almost the same for overland
flow of small watersheds,
t = t =e c
It can also be assumed that for small watersheds with uniform
rainfall and uniform land slop~ the time to peak approaches
t and thus is equal to time of concentration. Therefore,e
63
t = t = tP e c
v. Determination of peak dischapge 3 Qp As explained in the pre-
ceding paragraphs, peak discharge can be estimated as equili
brium discharge if duration of rainfall is long enough,or it
can be expressed as,
or,
Qp = CIA, (24 )
where C is a coefficient to express the ratio of I and I and. 0 .
is affected mainly by the infiltration rate of soil.
The peak discharge determination for small watersheds, where
the area is large enough and the time of concentration and
time to peak are less than time of equilibrium, the peak
discharge, T , y,rill be ,p
or ,
Q = ).2 CIA.P
If ,
C' ,
then,
Qp = CI IA.
By rearranging equation (19) in following form ,
(25)
64
t =P
A loge1 + A1 A (26)
if t p' A, 10
, w, and k are known, A can be determined.
Both equations (24) and (25) are forms of the rational
formula, Q = CIA.
C.APPLICATION OF RATIONAL FORMULA FOR SMALL WATERSHED IN HAWAII
The use of equations (24) and (25) depends on size of the water~
shed and intensity 'of rain. If the watershed is small with high intensity
rainfall, the t ime to equilibrium is short. If the duration of that high
intensity rain lasts long enough to build up the equilibrium discharge,
the coefficient,C,will be , mainly affected by infiltration (assuming the
interception and evaporation are minor losses and can be neglected). If
the watershed is large and the rainfall duration is shorter than time of
equilibrium, the coefficient,C,will be estimated not only by infiltration,
but also by the area of the watershed, rainfall characteristics, and hy
draulics of overland flow.
Considering that the 100 acres, which is the upper limit of using
the rational formula in Hawaii, is small and a rainfall of high intensity
may last long enough to produce equilibrium discharge, since the time of
concentration of these watersheds is small ; equation (24) is suggested
for estimating peak discharge, where C is an estimate of the infiltration
rate of the watershed. (This criteria may be revised at a later date
when more is known of the basic hydraulics of overland flow of Hawaiian
watersheds.)
Use of equation (24) is recommended in the following procedures:
i. Determination of t ime of concentration
The formula of determining t is given in equation (21) as,c
to1
t = E v.C 1
or,
51,.1
t = E kyoc 1
65
Since values of k and y, which must be evaluated on the basis
of experimental results, are not available fat small watersheds
in Hawaii, approximate average velocities of runoff must be
used to calculate t , as suggested by Chow (4). The resultsc
may be checked against Figure 26, the plot of time to peak
for 27 small watershedS from hydrograph analysis. A possible
range of time to peak (or time of concentration) is shown as
5 to 15 minutes. The range was also given by Roe and Ayres
(43) who showed a t of less than 17 minutes for an area lessc ;than 100 acres.
ii. Design rainfaZZ i ntens ity "I". For agricultural land, it
is suggested that the 50-year return period be used by con
sidering a project life of 15 years and a percentage of as
surance of 75 percent. For urban areas, a 100-year return
period by assuming a project life of 25 years is suggested.
Rainfall intensity can be therefore determined from rainfall
depth-frequency-duration for the Hawaiian Islands (3).
iii. Determinat i on of coeffi ci ent "C". Discharge of equilibrium
can be used to estimate peak discharge in watershed areas of
less than 100 acres. The coefficient,C,which is a ratio of
excess rainfall and total rainfall can be determined by
studying the infiltration loss, if the evaporation and inter
ception losses are negligible. Infiltration is a significant
problem in Hawail because of the excessively high intake
rate of Hawaiian soils; however, where swollen clay exists
the infiltration can be considered nil. Based on these
conditions, the C values, which were developed for the United
States mainland, cannot be used in the Hawaiian Islands.
There is very little information available about infiltration
loss from Hawaiian soil under different land uses. It is
hoped that the hydrograph analysis (phase II of this study)
will yield some infi~tration data for small Hawaiian water
sheds. The present design criteria for determining C can be
based on the recommendation by Chow (4).
'"o.
00
AREA (SQ.UARE MILE.S)
0
i
f --~
""" --L--
~
-""".....~
...~-I -.--I
1.-...,, -~
"" .....--UIUl;
f
,l - - ...-- i-- - -
I
I,
I
;,
sx f- M NI~ ur~ If '" IE TO FE,lo,.K
~
0 f- M:"'>l IJ\U M IT I~ TC PE,..,KI
"
IO.:!> 0.4- 0.6 0.8 2- 3 4 '" " 7 8
'I 0
2
o,
00
o,o,o.oo.
o.
0 .0'1
OD
0 .0
0 00'
0 00
0.00.0\ 0.02. o.<n> 0.05.01 0.\
~ I100 ""JU:S
.;
~<{W0..
10'IB7G
5
..
w~ 0.0
I-
oI- 0.0.
Q..
r-
<:» 0 0
z
'if\'D£?o:J:
Figure 26. Time to peak discharge against watershed area for small watershed on Oahu, Hawaii.
67
RESULTS AND CONCLUSIONS
1. The rain gage network density in Hawaii is the highest in the' United
States and ranks third in the world with the average dens~ty (number
of gages per 100 square miles) being 12.6 compared with only a 0.4
overall density for continental United States. However, it does not
give a synoptic view of storm rainfall owing to the steep rainfall
gradient (several locations exceed 25 inches per mi~e.) The existing
rainfall data cannot be used to study rainfall-runoff relationships
using the technique of unit hydrograph especially for small watersheds
in an area of less than "5 square miles.
2. A study of rainfall depth-duration relationship has shown that the
probable maximum precipit~tion coincides with the world's greatest
rainfalls and the 100-year maximum point rainfall is nearly in agree
ment with the standard project storm. The 100-yearrainfall of Hono
lulu and windward Oahu can be expressed by a single straight line which
is R = 4.50°·486.
3. Frequency analysis for annual peak discharge was made for 23 stations
where 12 or more years of records were available. The l2-year cri
terium is purely arbitrary. A study of runoff of seven watersheds
which have about SO years of records has shown a tendency of dry and
wet years in cycles of 3 to 4 years. The l2-year records may be consid
ered sufficiently inclusive to cover the high and low points and as
random samples representing peak flow frequency distribution.
4. The historical flood survey has shown that a 24-hour rainfall of 10
to 14 inches would produce a large flood in the Honolulu and windward
side of Oahu. This 24-hour rainfall is comparable to a SO-year fre
quency rainfall for these areas. No distinct relationship has been
found with respect to size of flood for daily flood-producing rainfall,
Po' and its S-day total antecedent rainfall, Pl-S' largely because the
size of flood is arbitrarily assigned. Two zbneshave been defined
to show a possible combination of Po and Pl-S to cause large or small
floods.
S. Among the 58 gaged watersheds on Oahu, 44 watersheds have areas less
than 5 square miles. Hawaii is unique in maintaining fairly complete
hydrological data for such small watersheds. A study of general
68
variation in stream slope, in relation to watershed are~s, shows a
linear relation for both Hawaii's and Indiana's small watersheds on a
log-log plot. A hypsometric curve typifies a typical la~dmark of
watersheds on the windward side of Oahu (Figure 15 - Curve A).
6. The preliminary soil-type surveyund land use classification of smallI
watersheds on Oahu (Table 7) have no immediate application in this
study. However, the information may be used in streamflow hydrograph
study (phase II) or in evaluating the coefficient,C,as applied in the
rational formula.
7. The present design criteria developed by Chow for areas larger than
100 acres are the best estimates for a conservative design since his
envelope curve covers all extremes~ By comparing results of
frequency analyses, the estimates made with the envelope curve is
quite comparable to SO to 100-year peak flood frequencies.
8. A regional flood formula for Honolulu and between mountain ranges (Zones
II and III) and for areas larger than 100 acres has been derived through
the use of multiple regresssion. This is to express peak discharge
as a function of watershed area, length and height, and a precipita
tion index defined as 100-year, 24-hour rainfall in inches. A coaxial
chart has been designed for practical application. For Windward and
Leeward Oahu, there is not enough data for a frequency study or mul
tiple regression. Chow's envelope curves are the suitable criteria at
the present time.
9. A critical review of the rational formula for an area equal to or less
than 100 acres has shown that it is valid if the estimates of time of
concentration, t , and discharge coefficient, C, are accurate.. cThe rational formula was evaluated by a study of overland flow.
Simple mathematical equations have been derived to show the variables
involved to determine time of concentration, t , and the coefficient,c
C. Both t c and C need to be specifically determined for Hawaiian
conditions based on typical tropical soil characteristics and land
use. At present, owing to lack of experimental results for evaluating
t and C for Hawaiian watersheds, Chow's recommendations may be used.c .10. This study collected and studied basic hydrological information on
flood hydrology of small Hawaiian watersheds, but frequency analyses
and regional flood formula development was based .on limited available
69
existing data. It is hoped that the results of this study will be
used as an aid to engineering judgment rather than as fixed criteria.
ACKNOWLEDGEMENTS
The project was supported by the City &County of Honolulu and a
grant from the Office of Water Resources Research, U. S. Dept. of Inte
rior.
The author wishes to express his thanks to Mr. Stuart H. Hoffard,
Hydraulic Engineer, Water Resources Division, USGS, Honolulu, Hawaii,
for giving him access to the flow records used in this study, and Dr.
L. S. Lau, Associate Director, Water Resources Research Center, Uni
versity of Hawaii, who provided helpful discussion and reviewed the
manuscript.
70
BIBLIOGRAPHY
1. Chow, V. T. Handbook of Applied Hydroology. McGraw-Hill Book' Com
pany, New York, Section 9, p. 7, 1964.
2. Hawaii Water Authority. Rainfall of the Hawaiian Islands. State of
Hawaii, 1959.
3 . U.S. Weather Bureau. Rainf all-Frequency Atlas of the Hawaiian Is
lands--for Ar~as to 200 Square Miles~ Duration to 24 Hours~ and
Return Periods from 1 t o 100 Years . Technical Paper No. 43, 1962.
4. Chow, V. T. An Investigation of the Drainage Problems of the City
and County of Honolulu. 1966.
5. U.S . Weather Bureau. Probable Maxi mum Precipitation in the Hawaiian
Islands. Hydrometeorological Report No. 39, 1963.
6. U.S. Army Corps of Engineers. St andard Project StOY'ITI DeteY'lTlinations~
Hawaiian Islands. 1962.
7. Jennings, A. M. World's Greates t Observed Point Rainfall. Monthly
Weather Rev., v. 78, pp. 4-5, 1950.
8. Hoffard, S. H. Floods of December 1964 - February 1965 in ,Hawaii.
USGS, Water Resources Division, Honolulu, Hawaii , Report R26, 1965.
9 . Hoffard, S. H. and W. C. Vaudrey. An Investigation of Floods in
Hawaii through June 30~ 1966. USGS, Water Resources Division, Hono
lulu, Hawaii, 1966.
10. Surface Water Branch. Sur f ace Water Records of Hawaii and Other
Pacific Areas . USGS, Honolulu, Hawaii, 1961.
11. Gumbel, E. J. Statistics of Extremes. Columbia University Press,
New York, 1958.
12. National Bureau of Standards. Statistical Theory of Extreme Values
and Some Practical Appl i cat i ons . (A series of lecture by E. J. Gumbel),
U.S. Dept. of Commerce, Applied Mathematics Series 33, 1954.
13. National Bureau of Standards. Probability Tables for the Analysis of
Extreme-Value Data. U.S. Dept. of Commerce , Applied Mathem:atics
Series 22, 1953.
14. Pararas-Carayannis, G. Historical Flood Survey on Oahu. Hawaii In
stitute of Geophysics, University of Hawaii, unpublished data, 1967.
15. Langbein, W. B., eti , al. Topographic Characteristics of Drainage
Basins. USGS, Water-Supply Paper 968-t:, 1947.
71
16. Strahler, A. N. Hypsometric (area-aLtitude) AnaLysis of ErosionaL
Topography. Bull. Geol. Soc. Amer., v. 63, pp. 1117-1142, 1952.
17. Taylor, A. B. and H. E. Schwarz. Unit~HydrographLag and Peak FLow
Related to Basin Characteristics. Trans. AGU, v. 33, pp ~ 235-246,
1952.
18. Willock, J. T., R. H. Esaki, R.K. Yukumoto, and t. S. Lau. A FieLd
Investigation of InfiLtration for Some SoiLs on Oahu~ Hawaii. Manu
script Report, Dept. of Civil Engineering, University of Hawaii,
30 pp., May 1961.
19. Musgrave, G. W. and R. A. Norton. SoiL ana Water Conservation Inves
tigations at the SoiL Conservation Experiment Station~ Missouri
VaLLey Loess Region~ CLarinda~ Iowa. Sta. Prog. Rpt. 1931-1935 and
U.S. Dept. Agr., Tech. BUll. 558, pp. 58-60, 1937.
20. Dept. of Land and Natural Resources. Pan Evaporation Data~ State of
Hawaii. State of Hawaii, 1961.
21. Kinnison, H. B. FLood FLow FormuLas. Jour. Boston Soc. Civil Engineer,
v. 33, pp. 1-19, January 1946.
22. · Chow, V. T. HydroLogic Determination of Waterway Area for the Design
of Drainage Structures in SmaLL Drainage Basins. Engineering Experi
ment Station Bulletin No. 462, University of Illinois, 1962.
23. Talbot, A. N. The Determination of Waterway for Bridges and CuLvert.
Selected Papers of the Civil Engineers' Club, Technograph No.2,
University of Illinois, pp. 14-22, 1887.
24. Cleemann, T. M. Proper Amount of Waterway for CuLverts. Proceedings,
Engineers' Club of Philadelphia, v. 1, pp. 146-149, 1879.
25. Mulvaney, T. J. On the Use of SeLf-Registering Rain and Flood Gauges
in Making Observations of the ReLations of RainfaLL and of FLood
Discharges in a Given Catchment. Transaction of the Institution of
Civil Engineers of Ireland, v. 4, Part II, p. 18, 1850-51.
26. Benson, M. A. ChanneL-SLope Factor in FLood Frequency AnaZysis.
Jour . Hydr . Ddv , , A.S.C.E., April 1959.
27. Wu, I.P. and J. W. Delleur . . Study of Runoff from Smal.l: Watersheds~
for Hi ghway Drainage Design in Indiana. Progress Report No.1, Joint
Highway Research Project, Purdue University, 1961.
28. Snyder, F. F. Synt het i c Unit Graphs. Trans. Am. Geophys. Union,
v. 19, Part I, pp. 447-454, 1938.
72
29. City &County of Honolulu. Design Criteria for StOY'l7l Drainage Fa
cilities. 1957.
30. Dodo, S. and W. Y. H. Ling. A Report on StOY'l7l Drainage Design
Criteria-~Design Criteria for Storm Drainage Facilities. Planning
Section, Bureau of Plans, City Planning Cornmision, Dept. of Public
Works, City and County of Honolulu, 1958.
31. Portland Cement Association. Handbook of Concrete Culvert Pip e
Hydraulics. 1964.
32. Kirpich, Z. P. Time of Concent ra t ion of Small Agricultural Wat er
sheds . Civil Engineering, v. 10, No.6 , p. ,362, 1940.
33. U.S. Soil Conservation Service. Engineering Handbook for FaY'l7l
Planners, Upper Mis si ssippi Valley Region III. Agr. Handbook No. 57,
U.S. Government Printin;g Office, 1953.
34 . . Dept. of Land and Natural Resources. Drainage Criteria Meeting.
State of Hawaii, Circular C40, 1966 •
. 35. R. M. Towill Corporation. StOY'l7l Drai.naqe of Makaha Valley on Leeward
Oahu. Unpublished paper, 1965.
36 . Linsley, R.K., Jr., M. A. Kohler, and J. L. H. Paulhus. Hydrology
for Engineers. McGraw-Hill, New York, p. 258, 1958.
37. A.S.C.E. Hydrology Handbook. 1948.
38. Horton, R. E. Hydrologic Interrelations of Water and Soi l s . Soil
. Science Soc. ·of Am . Proc., v , 1, p. 401,1937.
39. Horton, R. E. The Interpretation of Appl i cat i on of Runoff plot
Experiment s wi t h Reference to Soil Ero sion Problems. Soil Science
Soc. of Am. Proc., v. 3, p. 340, 1938.
40. U.S. Waterways Expt. Sta., Vicksburg, Miss. Studies of Riverbed
Materials and Their Movement, with Special Reference to the Lower
Mi ssi s si ppi Ri ver. Paper 19, 1935.
41. Izzard, C. F. The Surface -Pro fi le of Overland Flow. Trans. Am.
Geophys. Union, Part VI,p. 959, 1944.
42. I zzard, C. F. HydPauU es of Runoff from Developed Sur f aces. Pro
ceedings of the 26t h Annual Meeting of the Highway Research Board,
v. 26, pp. 129-146, 1946.
43 . Roe, H. B. and Q. C. Ayres. Engineering fo r Agricultural Drainage .
McGraw-Hill, New York, p. 103, 1954.
APPENDIX
Frequency Curves of 23 Small Oahu Watersheds Plotted By
Gumbel's Extreme Value and Gumbel's Extreme-Log Methods
75
2000 . Nor t h Fork Kaukonahua Stream abo veRight Branch , near Wahia wa .
1.01 2 100 200 1000
.• .• - - - - t - - "- ==.:' :.......:-: _. _._.-..... ... .... ... .. .. -- I,.... 1- -- - --
-:: , r-+ -- -- - - - - I:;, f-
- p _._..+--- - --- - ... - f-- -- --
_. 1- - .- ~-r-.--_.. _. ..- ._- _..- -------1- .-
_.. -_..- _.. _ -
1--
c-- - ' .._ . - +-H -+-H H - 1 .. - - I9000 ~.: . ::: .. .. ::: - ... :: :.: " ::: L ~.:: .~ r:
::::::: :::: ": :- ..- ::: -. ': - 1 :: :: !. m11 reg~-=::. .:: :::: :.:..::: _ - - .. t __ ._r
~ eooo1--+-++ ·++-++-++1++H -tt1I+H-HH - - ' 1::: '= :: .. ::-.-: -~: :: 1 _1.= = -=- - '=......-::t ... _... r
.. - .- - ... -- f-- _ .. .....- --- I--'.~ -- - -- _: - '- ::::: :: .: ::: .. :: ~~ - .. .- -- -- -- --
•. •• •.L.. ... .._ _ . _ . .. ~:..- .:::::: '== ::.._. _=
.. =;:. .; .~.$~ ? ?~ .:~. ; :~ ..:: ;~: ~: ~~:2: .~~~ :::::===.r.n: ~ :: t:.=~. ::=. :::' t =.~ ::=== ~: :: ~ .=: ~-= :=:.::~~
.. ... .... - I' -.- ..... ... ...... ..- ..... ....- . .. .- ...--.....-
... .... ...- ._..- ._.-'- - _.-.. .- -.. - - 1-----
-·I+++-+-+
~ _.
i :
1=0='
: ! ! I
, i
! :
1 i
.j I :! I
i l i i !
l ! I I! I II ! I·! I,!!
I I i ~ e~ ; 1 : 1 !-! : :i n !i:
w.; i ' T : ' ! '" n i . I f l - ' i-ot ·, I !i !-l ! i ii! ,I I! j . '
: : tt 81 -;:., ..: ~ ... ~ I=ttf :; _l±+- trr~ mj jii! .. !m i · Ci' _.
tlll i i !
i : i
i I I
i ! i ~ I
! t d ~ l:t+1 I;;;I • ; ! ,jIl l j !;
! j
i i ' i
I I i1 1 I I
i t!i! :
!l!
'J.
. ! !-· 1 !
1=f- 1
10 00'~':: - t:
10'0001~: ..~. mllm~illE:-i 7j:·
E ·· -=
.noI
0'
!'"o
i; i !-- - i I i: i
.1 . i
1 L. l : j : : 1 II i j:i
, I I
- - : ..~:.~ -.-.... ;~.: . :
:~~:~ - h=-C:';.:.::i:j~ ." I: !i . ~ j 1 .;=;1 i.i ! : lj J . + I
1=:1.q qill ~ :'f :~ ·· 1 :100t=:t...:t l lll1 fit rtH: r J :1.0 1 LI 1.2 U .U U
j • : ..~ .r " · .'~- =- :-+ _.:: .:..-:- r::-..:: . ~:- . -.....~ . ~~.,· .H : ~ ~ ..1".:': : :..: . -- •. .. ·· i ; :.. 100
76
20 40 . Nort h For k Kauko nahua Stream near Wah iawa .
not" r " Period (y" " r o)
-'---'--"
._.- --_.. ..._.-._- -
_.. --, ...... - -_._ -
... ..
.... .. ..
..' _ .•. • ..• _ _. ..1_ .P_.__.. _
- I-+--t- ,, +-- -4
- t--f- - - -I-- - -l
H--+- t-t-..- - -- _ ._-•.
9
- "
;- --t- o-i .-I--H-t-l-'-t.... I
... ! .. .. .., ....iI
.... ... '10 .r . '. ::.•••• :. : : . ":: o • • • • :' I=- :.:::: .. .. :. ., ::::
. .. 1' - - ._..:.~. ~'. ~,- T: :': :~" .... :~ ::~ - :.~. :. :::. .-" ---.-----
- _I. 1- --t++-+- t--.. • . .... L M ••• • • • •
.. .. , . . .1. ..I
-90
"... .." J , __ .." ..'1' J " " _.. .. :j.'.. :.L . " :_....
J '.," ' ! :.. -'- 1 ~ .... ...
+HHHI+H+H H -I-+ +-I-I+II-t-'I-f-H-+-t-I-+t- t-t-t-t-" 1- f-..
Ifll,ll lfi'"J:-11~l{<', ------ rI f ' ;~>. t·: '1- -.+. -t-t-tf'-l.. -:!.I-._,_ -._.-i. -+---1
I I .~ :.:.'. L ::.' :~: "..~ :
Pr obp.h:U1t.y - /1'1r ce nt
I Lt ' 'I I I, I I ,~.u.U l.u.LLFLL.J..ubLLLLLLu4LLu.LLLU.k Ll "U..Ll.l_u.~Reduced Va rlat..
... ["
1 ' 1II
" t!
.r. I1 .. · - ..
. 104
2rIi
-- _. ._+- - i- - .. - I - ..II
4OOO1--t-I~"'H- '= -, - .. i:'-++ +l-I11111"~..- " l. I
l .. . I'I---+-+-HH-+-IH-~- t- ~
1_ =- ':::. - ::....1= =- ::: .::: r I'= =-~..:::::::: .:::::: _: " I .. :: .... I
~ )000 '-. :-::: ':.:":: ... - .r: :.r ri ':.::: : ::: ::: -::: _. '" r .:. :: :.,r..Il. 1:1I'111"11
1'0 .. :=:: ~~ :: f=:...: ~: .. ~i~~ "
!...~~; ~b~ ~ ~~l~ t; jC~ _ ~~ ~ ;~~=~ : i ' -::~::: I-~'~j+l:1+1H~++'H!H+I+H++l-HI-+--H'++-HI--I+t-+-+-H-H-+-t-t-+-.- 1,-
'.._, - - -- -" -·· .. r :_{
:~=2 ; =- -1-·u.:o, 0 2lJ )0 jl,u '.,0 l1()tJ
!.L1.i,ili.u . I, I I I I , I U ~ , I I I:l-~ -:t 1)
I!t : ,
i i: I
i I' : i
.!I .-t . -+
: i•.1 •• ··t·· I
I II
1-::,' l :ti l III
I~ +H'H+fffltttl!' ;
.. . ' t..
I I
t i 'l:i ..
n:
I ! Ii
ltd!!, :i!: iii!iii , i . 1
i ~ i
I I
111
,11
i : I ! ; ; I I ! i ':! ...I ! ! I , J i
j i i i I !Ii 1; j j: :
: I ! ': l l i l i . ~ ! I! !
i I ! I I! I I l l ! I ! ;! i : j
I I ! i: : ! i ! I HI! ! I j I ji j
~ : : I
; ! I
l l i i I
d!! !
1 ! i
.... ...... ... _ 1"} -t: 1:
i l l i ' j• 1I 11 t
: :.!.
I I" " ilII. j , I, I . ' I
i i
;, ,.. ..
I, ,, I
,., I •11 1
;
rn 11 !
I i I ;
f+tt++++ItH;tI
, I, ,i ! :ill ! :
I I.1 i Jill I i I I I I
--- "L! WI I I
I' ' I ' " II ! j I Ii! il:l
mti:mtt:tmt::t::t:mm
::uI
CY
IIII
o
.. .. L.;.A. ..,..~~: : ? .
11 , 11 I " 15
.. .
... - -_. - : ..
. , . , .AKUI'f.nc"fl(.rv.I. lflyt'l1
........
'" ... .,
-, .: J.. .. ",i
77
2130 . Wa i ke l e St rea m at Wa i pabu .
100020010050Retu r n Portod . (years )
5 ]0 252I
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92
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f.-- _. ,. ... . .. .- ._. . - .. . _. ...... - -- -_._._-. 0 2 I. 50 o· 0 90 -9~ ~b 9' Y Y y~ .> " Y?-.U .o 9~ 1'\ FrahahllU;y - p"rront
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Reduco.d Variate
H 200
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5 10 ~~2
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r ... ... ~iol' r - ... ... ... .... ...- ..I.. .. . ....- .. ... .. .. .. .. .. . . _..- ." - '. .. .- - _.......... .... .. - .... ..... ..
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. ~ . I~ Probability ~ percentj i ! I ,'1, , , !.oi' , , I I , I , 'f I I I I I~' I I l' I , , J I I I I ~ ! I I I ,I I ! I I ! I I I ,
Rorlucod Variate
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97
3500. Opaeula Stream near Hale iwa.Return Period (years)
1.01' ." '" ... -.- .. ... _.
2.-. _.
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10 2 So 100 200 s60 1000.-
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