ESTIMATION OF MEDIAN STREAMFLOWS AT PERENNIAL STREAM SITES IN HAWAII

By Richard A. Fontaine, Michael F. Wong, and Iwao Matsuoka

U.S. GEOLOGICAL SURVEY

Water-Resources Investigations Report 92-4099

Prepared in cooperation with the

STATE OF HAWAII

DEPARTMENT OF LAND AND NATURAL RESOURCES

Honolulu, Hawaii 

1992
U.S. DEPARTMENT OF THE INTERIOR 

MANUEL LUJAN, JR., Secretary

U.S. Geological Survey 

Dallas L. Peck, Director

For additional information 

write to:

District Chief

U.S. Geological Survey

677 Ala Moana Blvd., Suite 415

Honolulu, HI 96813

Copies of this report 

can be purchased from:

U.S. Geological Survey

Books and Open-File Reports Section

Federal Center, Box 25425

Denver, CO 80225
CONTENTS

Page 

Abstract --------------------------------------------------------------- 1

Introduction ----------------------------------------------------------- 1

Background -------------------------------------------------------- 1

Purpose and scope ------------------------------------------------- 2

Estimation of median streamflows at ungaged, unregulated,

perennial sites ---------------------------------------------- 3

Selection of data for analysis ------------------------------------ 3

Site selection ----------------------------------------------- 3

Median-streamflow data --------------------------------------- 4

Basin-characteristic data ------------------------------------ 18

Development of multiple-regression equations ---------------------- 19

Accuracy and limitations of the equations ------------------------- 23

Estimation of median streamflows at regulated, perennial

windward Oahu sites ------------------------------------------ 26

Site selection ---------------------------------------------------- 27

Data collection and analysis -------------------------------------- 27

Accuracy and limitations of median-streamflow estimates ----------- 34

Summary ---------------------------------------------------------------- 35

References cited ------------------------------------------------------- 36

ILLUSTRATIONS 

Figures Page

1-5. Maps showing locations of unregulated streamflowgaging stations used in the regression analyses:

1. Island of Kauai ---------------------------------- 8

2. Island of Oahu ----------------------------------- 9

3. Island of Molokai -------------------------------- 10

4. Island of Maui ----------------------------------- H

5. Island of Hawaii --------------------------------- 12

6. Graph showing water years with complete record for

streamflow-gaging stations used in the regression

analyses, 1910 through 1986 ------------------------------ 14

7. Graph showing plot of observed median streamflow as 

a function of drainage area and the calibrated 

regression line for the Oahu, Molokai, and Hawaii 

geographic grouping -------------------------------------- 25

8. Map showing locations of windward Oahu study basins and

regulated, perennial index streamflow-gaging stations ---- 28

iii
TABLES 

Table Page

1. Unregulated, perennial streamflow-gaging stations used in

the regression analyses ----------------------------------- 5

2. Comparison of long-term median streamflow for the period 1912 

through 1986 at station 16587000, Honopou Stream 

near Huelo, Maui, to that computed for a variety 

of continuous short-term periods -------------------------- 13

3. Estimated base-period (1912-1986) median streamflows for the 

unregulated, perennial streamflow-gaging stations used 

in the regression analyses -------------------------------- 16

4. Basin characteristics for the unregulated, perennial

streamflow-gaging stations used in the regression

analyses -------------------------------------------------- 20

5. Summary of regression equations used to estimate median

streamflows for the base period at ungaged, unregulated, 

perennial stream sites in Hawaii -------------------------- 24

6. Ranges of basin-characteristic values at stations used to

develop regression equations ------------------------------ 26

7. Regulated, perennial windward Oahu sites where medianstreamflow estimates were made ---------------------------- 29

8. Index stations used to estimate median streamflows

for windward Oahu sites ----------------------------------- 32

9. Regression-equation statistics and estimated median streamflows

for selected regulated, perennial windward Oahu sites ----- 33

CONVERSION FACTORS

Multiply By To obtain

foot (ft) 0.3048 meter

cubic foot (ft3 ) 0.02832 cubic meter

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

inch (in.) 25.4 millimeter

mile, statute (mi) 1.609 kilometer

square mile (mi 2 ) 2.590 square kilometer

iv
ESTIMATION OF MEDIAN STREAMFLOWS AT PERENNIAL STREAM SITES IN HAWAII

By Richard A. Fontaine, Michael F. Wong, and Iwao Matsuoka

ABSTRACT

The most accurate estimates of median streamflows at perennial stream 

sites in Hawaii are those made at streamflow-gaging stations. Two alternative 

methods for estimating median streamflows at ungaged sites are described in 

this report. Multiple-regression equations were developed for estimating 

median streamflows at ungaged, unregulated, perennial stream sites. The 

equations relate combinations of drainage area, mean altitude of the main 

stream channel, and mean annual precipitation to median streamflow. 

Streamflow data from 56 long-term continuous-record gaging stations were used 

in the analysis. Median-streamflow data for all 56 sites were adjusted using 

record-extension techniques to reflect base period (1912 through 1986) 

conditions.

Hawaii was subdivided into two geographic groups and multiple-regression 

equations were developed for each. The standard error of prediction for the 

equation developed for the first group, the islands of Oahu, Molokai, and 

Hawaii, is 41 percent. The standard error of prediction for the equation 

developed for the second group, the islands of Kauai and Maui, is 54 percent.

A method for estimating median-streamflow, based on discharge 

measurements and data from nearby streamflow-gaging stations, was also 

developed for 27 regulated, perennial windward Oahu sites. Standard errors of 

prediction for 23 of the sites range from 5 to 34 percent. Median-streamflow 

estimates for the four remaining sites were considered poor and no measures of 

accuracy are provided. Discharge measurements can be used to make estimates 

of median streamflows at ungaged, regulated sites where the regression 

equations developed in this report are not applicable. Discharge measurements 

can also be used to make estimates of median streamflows at ungaged, 

unregulated sites. Estimates of median streamflows based on discharge 

measurements have greater standard errors than estimates based on continuous 

streamflow records and in general have smaller standard errors than estimates 

based on regression equations.

INTRODUCTION

Background

In Hawaii serious concerns exist over possible water shortages and 

uncertainty over ownership of water. In an attempt to deal with these 

problems, the Hawaii State Constitutional Convention of 1978 opted for a State 

Water Code. In 1982, the State legislature created the Advisory Study 

Commission on Water Resources to develop a State Water Code "to recognize,

1
clarify, and systematize legal concepts relating to water resources" (Lee and 

Valenciano, 1986, p. 201). In 1987 the State Water Code was passed by the 

Hawaii State Legislature. General administration of the Code was assigned to 

the Commission on Water Resources'Management.

Part VI of the State Water Code of 1987 calls for the protection of 

instream uses of water. To protect instream uses, the Commission needed to 

specify minimum streamflows or depths of water required in a stream to protect 

fishery, wildlife, recreational, aesthetic, scenic, and other beneficial uses 

(Yuen, 1990, p. V-37). According to the Code, beneficial instream uses 

include, but are not limited to (1) maintenance of fish and wildlife habitats, 

(2) outdoor recreational activities, (3) maintenance of ecosystems such as 

estuaries, wetlands, and stream vegetation, (4) aesthetic values such as 

waterfalls and scenic waterways, (5) navigation, (6) instream hydropower 

generation, (7) maintenance of water quality, (8) the conveyance of irrigation 

and domestic water supplies to downstream points of diversion, and (9) the 

protection of traditional and customary Hawaiian Rights (Yuen, 1990, p. V-37).

The Commission on Water Resource Management, Department of Land and 

Natural Resources selected median streamflow as the quantitative basis for 

establishing standards. Median streamflow is defined as a rate of flow that 

is equaled or exceeded 50 percent of the time at a particular location. In 

1987, the Department of Land-and Natural Resources entered into a cooperative 

study with the U.S. Geological Survey to estimate median streamflows at 

perennial stream sites in Hawaii.

Purpose and Scope

This report describes techniques for estimating the median streamflow for 

ungaged, perennial stream sites in Hawaii that are either unregulated or 

regulated. The report also provides median-streamflow estimates at selected 

partial-record, regulated stream sites in windward Oahu.

To provide a methodology for estimating median streamflow for ungaged, 

perennial stream sites, daily streamflow data collected in Hawaii since 1909 

at a total of 664 sites were reviewed. A total of 56 stations were selected 

from the data base representing sites where flows were both perennial and 

unregulated. Multiple regression analyses relating median streamflow at the 

56 stations to selected basin characteristics were conducted. The regression 

equations developed can be used to estimate median streamflow for ungaged, 

unregulated, perennial streams on the islands of Kauai, Oahu, Molokai, Maui, 

and Hawaii.

To provide median-streamflow estimates at 27 partial-record, regulated, 

perennial stream sites located in windward Oahu, about 12 discharge 

measurements per site were made over a 3-year period. In addition, historic 

data files were reviewed to locate any existing data for the sites. Discharge 

measurements at each site were correlated with data available at nearby, 

hydrologically similar, continuous-record stations. Median streamflow at the
continuous-record stations and the relations established between the partialrecord and continuous-record stations were used to estimate median streamflow 

for the partial-record stations. The techniques applied at the 27 windward 

Oahu sites can be used to provide median-streamflow estimates at both 

unregulated and regulated perennial stream sites in Hawaii.

ESTIMATION OF MEDIAN STREAMFLOWS AT UNGAGED, UNREGULATED, PERENNIAL SITES

Median streamflow can be reliably determined from long-term continuous 

records, but data cannot be collected at all sites where information might be 

needed. Other methods that are based on existing data can be used to estimate 

median streamflows at ungaged sites. Thomas and Benson (1970) demonstrated 

that a practical estimation method is to relate streamflow characteristics at 

gaged sites to basin characteristics by multiple-regression analysis. Results 

of the regression analyses then can be extended to estimate streamflow 

characteristics at the ungaged sites based on easily determined basin 

characteristics. Characteristics used in the multiple-regression analyses, 

the resulting equations, and the accuracy and limitations of the equations are 

discussed in the following sections.

Selection of Data for Analyses

To apply multiple-regression techniques a data set composed of streamflow 

and basin characteristics for gaged sites was compiled. To develop this data 

set it was necessary to screen all sites where data were available to 

determine which were appropriate for inclusion. Once sites were selected, the 

streamflow characteristics of interest (in this case median streamflow) and 

the significant basin characteristics for each of the selected gaged basins 

were determined.

Site Selection

Estimates of median streamflows at ungaged, unregulated, perennial stream 

sites were based on data from unregulated and perennial continuous-record 

stations. Unregulated streamflow stations are defined as those having no 

identified diversions upstream from the gage. An exception to this rule is 

where the diverted flows upstream from the streamflow station are gaged. Here 

it is possible to add diverted flows to data from the gage and, therefore, 

reconstruct what unregulated flows at the gage would have been. Perennial 

streamflow stations are defined as those that have a minimum of 10 years of 

record and have no zero-flow days.

Available surface-water data for the period 1910-1979 in Hawaii have been 

summarized by Matsuoka (1981 and 1983). In addition the U.S. Geological 

Survey (USGS) (1980-87) has published data collected since 1979 in a series of 

annual data reports. In these reports, data-collection stations are listed 

and information including the period of record, the existence of upstream 

diversions or regulation, and if zero-flow days have occurred are provided. A 

total of 664 stations have been gaged for some period of time between 1910 and

3
1986, and 112 of these can be considered unregulated. Included in the 112 

stations is one, Punaluu Stream near Punaluu, Oahu (station 16303000) where 

the upstream diversions were gaged and therefore unregulated .flows can be 

accurately reconstructed.

The 112 unregulated stations were then screened to determine those that 

also met the perennial-flow criteria. Only 56 of the stations had at least 10 

years of record and no zero-flow days. The 56 stations considered 

unregulated, perennial gages that were be used in this study and their periods 

of record are listed in table 1. Locations of the 56 streamflow-gaging 

stations are shown in figures 1 through 5.

Median-Streamflow Data

A flow-duration curve is a cumulative frequency curve that indicates the 

percentage of time specified discharges were equaled or exceeded during a set 

time period (Searcy, 1959, p.l). In this study the flow-duration statistic of 

interest is the median or the streamflow that is equaled or exceeded 50 

percent of the time.

Median streamflows computed for the 56 gaging stations listed in table 1 

were compared with each other as part of the regression analyses and will also 

be used as estimates of future streamflow conditions. Accurate comparison of 

median streamflows assumes that data are based on concurrent periods of 

record. Dissimilarities between median streamflows at gages will then be due 

to differences in climatic or drainage-basin characteristics and not because 

the records cover different periods of time (Searcy, 1959, p. 12). Median 

streamflow computed for the period of record at a gaging station has no timesampling error because the median statistic was based on the entire population 

of daily mean discharges for the period. When median-streamflow estimates are 

used as predictors of future streamflow conditions, time-sampling errors may 

become significant. To minimize the time-sampling errors, records from longterm stations should be used. Calculated median streamflow for short-term 

stations can be improved by adjusting the flow to represent longer periods 

(Searcy, 1959, p. 12).

The problem becomes one of selecting a long-term or base period during 

which physical conditions have remained essentially the same and is of a 

sufficient length to be used to represent future streamflow conditions without 

significant error. The base period needs to be selected such that an adequate 

number of the 56 selected gages have the equivalent of complete record for the 

entire base period. Gages with complete, long-term records for the base 

period will be considered as index stations and their records will be used to 

adjust records from the remaining stations. Index stations therefore need to 

have common or concurrent periods of record with all short-term stations with 

which they are to be correlated.
Table 1. --Unregulated, perennial streamflow-gaging stations used in the 

regression analyses

[p, station in operation as of end of water year 1986; ft, feet]

Station 

number

16010000

16013000

16017000

16019000

16068000

16071500

16097500

16105000

16106000

16108000

16115000

16116000

16117000

16200000

16201000

16206000

16303003

16400000

16402000

16403000

16403900

Latitude

22°08'09"

22°07'13"

22°06'57"

22°05'20"

22°04'19"

22°04'44"

22°10'54"

22°10'15"

22°09'05"

22°08'20"

22°11'20"

22°11'00"

22°09'50"

21°31'09"

21°31'10"

21°30'05"

21°33'33"

21°09'31"

21°07'35"

21°07'25"

21°07'59"

Longitude Station name

Island of Kauai

159° 37 '22" Kawaikoi Stream near Waimea

159° 36 '14" Mohihi Stream at altitude

3,420 ft, near Waimea

159° 33 '53" Koaie Stream at altitude

3,770 ft, near Waimea

159° 34 '18" Waialae Stream at altitude

3,820 ft, near Waimea

159° 25 '05" East Branch of North Fork

Wailua River near Lihue

159° 23' 55" Left Branch Opaekaa Stream

near Kapaa

159° 25 '17" Halaulani Stream at altitude

400 ft, near Kilauea

159° 29 '53" Waioli Stream near Hanalei

159° 31 '40" Lumahai River near Hanalei

159° 33 '38" Wainiha River near Hanalei

159° 35 '50" Hanakapiai Stream near

Hanalei

159° 37 '35" Hanakoa Stream near Hanalei

159° 38 '15" Kalalau Stream near Hanalei

Island of Oahu

157°56'53" North Fork Kaukonahua Stream

above Right Branch, near

Wahiawa

157° 56 '55" Left Branch of North Fork

Kaukonahua Stream near Wahiawa

157° 56' 50" South Fork Kaukonahua Stream

near Wahiawa

157° 54 '06" Combined records of stations

16302000, Punaluu Ditch, and

16303000, Punaluu Stream

near Punaluu

Island of Molokai

156°45'53" Halawa Stream near Halawa

156° 49 '50" Pulena Stream near Wailau

156° 49 '45" Waiakeakua Stream near

Wailau

156° 52 '38" Kawainui Stream near

Period of 

record

1909-1916;

1919-p

1920-1926;

1936-1971

1919-1932;

1954-1968

1920-1932;

1952-p

1912-p

1960-p

1957-p

1914-1932

1914-1917;

1920-1933

1952-1956;

1957-p

1931-1952

1931-1952

1931-1955

1913-1953;

1960-p

1913-1953

1913-1917;

1944-1957

1953-p

1917-1932;

1937-p

1919-1928;

1937-1957

1919-1929;

1937-1957

1968-1980

Pelekunu
Table 1.--Unregulated, perennial streamflow-gaging stations used in the 

regression analyses--Continued

[p, station in operation as of end of water year 1986; ft, feet]

Station 

number

16404000

16404200

16405000

16416000

16502000 

16508000

16510000 

16515000

16516000

16517000

16518000 

16519000

16520000

16524000

16527000

16557000

16565000

16566000 

16577000

16585000

16586000

16587000 

16618000

16620000

16636000

Latitude

21°08'11 M

21°08'08"

21°08'38"

21°05'50"

20°40'55" 

20°48'37"

20°48'46" 

20°49'05"

20°49'05"

20°49'03 W

20°49'16" 

20°49'40"

20°49'24"

20°49'17"

20°50'07"

20°51'46"

20°52'Q2"

20°52'17" 

20°52'35"

20°53'14"

20°53'17"

20°53'20 n 

20°58'54"

20°57'48"

20°53'45"

Longitude

Island

156°52'43 M

156°53'09"

156°52'26 M

156°48'48"

156°02'50" 

156°07'00"

156°07'05 M 

156°07'45"

156°08'12"

156°08'26"

156°08'37 n 

156°08'53 M

156°08'37 M

156°12'14M

156°11'18"

156°11'49"

156°12'17"

156°12'29" 

156°13'25 M

156°14'52"

156°14'35 W

156°15'20" 

156°33'26 W

156 a 35'22 H

156°38'40W

Station name

of Molokai-- continued

Pelekunu Stream near 

Pelekunu

Pilipililau Stream near 

Pelekunu

Lanipuni Stream near 

Pelekunu

Punaula Gulch near Pukoo

Island of Maui

Hahalawe Gulch near Kipahulu 

Hanawi Stream near Nahiku

Kapaula Gulch near Nahiku 

Waiohue Gulch near Nahiku

Kopiliula Stream near Keanae

East Wailuaiki Stream near 

Keanae

West Wailuaiki Stream near 

Keanae 

West Wailuaiki Stream near 

Keanae

East Wailuaiki Stream near 

Keanae

Homomanu Stream at Haiku-uka 

boundary near Kailiili

Homomanu Stream near Keanae

Alo Stream near Huelo

Kaaiea Gulch near Huelo

Oopuola Stream near Huelo 

Kailua Stream near Huelo

Hoolawanui Stream near Huelo

Hoolawaliilii Stream near

Huelo

Honopou Stream near Huelo 

Kahakuloa Stream near 

Honokohau

Honokohau Stream near 

Honokohau

Kanaha Stream above pipeline 

intake, near Lahaina

Period of 

record

1919-1929; 

1937-1957; 

1971-1982

1968-p

1919-1929; 

1937-1957

1947-1972

1927-1969 

1914-1916; 

1921-p 

1921-1963 

1921-1963

1914-1917; 

1921-1958

1913-1917; 

1922-1958

1914-1917; 

1921-p 

1913-1917; 

1922-1958

1914-1917; 

1921-1958

1919-1927; 

1932-1934; 

1962-1968

1913-1964

1910-1957

1921-1962

1930-1957 

1910-1911; 

1913-1918; 

1919-1958

1910-1971

1912-1957

1910-p 

1939-1943; 

1947-1970; 

1974-p 

1913-1920; 

1922-1988

1916-1925; 

1926-1932
Table 1.- -Unregulated, perennial streamflow-gaging stations used in the 

regression analyses--Continued

[p, station in operation as of end of water year 1986; ft, feet]

Station 

number Latitude Longitude Station name

Period of 

record

Island of Hawaii 

16717000 19°46'00" 155°09'16" Honolii Stream near Papaikou

16717800 19°57'20" 155°11'20" Pohakupuka Stream near

Papaaloa

16720000 20°05'18" 155°40'58" Kawainui Stream near Kamuela 

16720300 20°05'13" 155°40'59" Kawaiki Stream near Kamuela 

16737000 20°07'46" 155°39'51" Waiilikahi Stream near

Waimanu

16739000 20°08'50" 155°39'46" Punalulu Stream near Waimanu 

16740000 20°09'05" 155°39'58" Waiaalala Stream near

Waimanu

16741000 20°09'05" 155°40'09" Paopao Stream near Waimanu 

16742000 20°09'15" 155°40'15" Kukui Stream near Waimanu

16757000 20°03'17" 155°40'01" Waikoloa Stream near Kamuela

1911-1913;

1967-p 

1962-1979

1964-p 

1968-p 

1939-1960

1939-1952 

1939-1952

1939-1952 

1939-1952; 

1959-1966 

1947-1971
22< 

15'

159°45' 158°30'

 I 

KAUAI

01234 

Nohili 

Point

5 KILOMETERS

Kokole 

Point

EXPLANATION

A STREAMFLOW-GAGING 

STATION

Note: The two leftmost digits (16) and 

the two rightmost digits (00) of 

each station number are omitted 

on this map for brevity

.HANAPEPE

V,

Puoto Poin

Makahuena Point

Figure 1. Locations of unregulated, perennial streamflow-gaging stations used in t

analyses, island of Kauai.
158*15' 158"

21'

30'

21' 

15'

01

Kaena 

Point

012

WfUANAE

EXPLANATION

A STREAMFLOW-GAGING 

STATION

Note: The two leftmost digits (16) and 

the two rightmost digits (00) of 

each station number are omitted 

on this map for brevity

Barbers 

Point

Figure 2. Locations of unregulated, perennial streamflow-gaging stations used in t

analyses, island of Oahu.
21'

15'

157*15'

I

157* 

Ilk) Point

Laau 

Point

Kahiu Point

Waila

Pebkunu Stre

Stream

VfTinr!:

MOLOKAI

01234 SMILES 

I I I l I l 

III l l l 

012345 KILOMETERS

ISLANDS k

KAMALO

EXPLANATION

A STREAMFLO

STATION

Note: The two leftm

the two right

each station 

on this map 

I

Figure 3. Locations of unregulated, perennial streamflow-gaging stations used in the 

analyses, island of Molokai.
156e45'

21'

20' 

45'

166°30'

Kahakuloa Stream

156° 15*

I

Honopou Stream 

Hoolawanui Stream

KAANAPALI

EXPLANATION

A STREAMFLOW-GAGING 

STATION

Note: The two leftmost digits (16) and 

the two rightmost digits (00) of 

each station number are omitted 

on this map for brevity

Figure 4. Locations of unregulated, perennial streamflow-gaging stations used in the 

analyses, island of Maui.
156« 155"

\ipio Stream

.Honokaia Gulch 

-Ahu&loa Gulch

00*"

HMMMIAN 

ISLANDS

20* Keanuiomano 

Stream

18° 

30'

Kapehu Stream

12 MILES

12 KILOMETERS

EXPLANATION

A STREAMFLOW-GAGING 

STATION

Note: The two teftmoet tfgtts (16) and 

the two rightmost digits (00) of 

each station number are omitted 

on this map for brevity 

_____ _______I

Figure 5. Locations of unregulated, perennial streamflow-gaging stations 

used in the regression analyses, island of Hawaii.

12
Periods of record for the 56 stations listed in table 1 vary 

considerably, making the process of selecting a base period difficult. To 

facilitate the analysis, water years with complete records during the period 

1910 through 1986, for each of the 56 stations were compared graphically (fig. 

6). Water years are the 12-month periods that run from October 1 through 

September 30. Data shown in figure 6 indicate that, to avoid eliminating any 

of the 56 stations, the base period should span as much of the period from 

1910 through 1986 as possible. For example, if the base period did not 

include at least part of the period 1940 through 1986, none of the 10 stations 

on the island of Hawaii would have concurrent record and would therefore be 

eliminated from the analyses.

Station 16587000 has the longest, complete period of record (75 years) of 

the 56 stations shown in figure 6. Data from station 16587000 were analyzed 

to determine how much of the station's period of record would be used as the 

base period and which of the remaining stations qualified as index stations. 

Median streamflows were computed for the entire period of record at station 

16587000 and for numerous combinations of a variety of short-term periods. 

The range of median streamflows computed and the standard errors of median 

base period or long-term estimates based on the variety of short-term periods 

evaluated are shown in table 2. Data in table 2 clearly demonstrate how

Table 2.--Comparison of long-term median streamflow for the period 1912

through 1986 at station 16587000, Honopou Stream near Huelo, Maui, 

to that computed for a variety of short-term periods

[ft3 /s, cubic feet per second]

Length of 

period 

(years)

Number of 

periods 

evaluated

Range of median Standard

streamflow estimates error

(ft3 /s) (percent)

75

70

65

60

50

40

30

20

10

5

1

1

3

3

4

6

6

6

7

8

15

16

2.5

2.4

2.4

2.4

2.3

2.2

2.2

2.0

1.9

1.7

0.9

- 2.5

- 2.5

- 2.6

- 2.7

- 2.7

- 2.8

- 2.8

- 3.0

- 4.0

- 7.7

0.0

2.8

4.0

4.6

6.4

7.8

10.1

12.0

15.4

24.2

69.7

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mmm r , , a nioMiminKmniinioniofliir iminniiiiiir winiiim^ C3

gggSSgS^Sggg^SSSS^SSS

:;:;:;;;!;:;i:;;:;:::;:;:;:;:;:;!::;;!;;;;:;::;i:;;;:;:;:;;;;|g

^^^^Mmmm

38$$3$$$$$%&3f^^

 ^ ^ ^ ^^^^^^

 «»»» n 13-

mmmrnmmmmmmmmmmmmmmmmmmmm

mmmmmmmmmwmmmmmmmmm^^

mmmmfmtmmm^mmmmmmmmm^mmmmmm

;SSS:;SSS:S:5SSS?::5S5;:S;S:;SSSs

:::;!;Sg;s:;:gg;:;ig;iggg;:iS::s:g;:;SSi;i;:g

!?::::S::S:g;SS:s:Sig:5:S;a:;S:;i;SSSS:;S:g

i 1 1 1 1 1 1 1 1 I I 1 1 M 1 1 1 1 I I 1 1 1 1 I 1 I 1 I I 1 1 1 1 1 1 1 1 I I 1 I 1 1 1 M 1 I I 1 M 1 1 1 1 1 I I 1 1 1 1 1 1 1 1 I I 1 1 1 1 1 1

Numberof

Figure 6.

WATER YEAR

Water years with complete record for the streamflow-gaging stations 

used in the regression analyses, 1910 through 1986. Stations marked 

with an asterisk (*) were used as index stations in the analyses.

14
estimates of long-term medians are improved with increased length of record. 

Errors in estimates of long-term median-streamflow for tested combinations 

with at least 60 years of record were less than 5 percent. On the basis of 

these results, the base period for this study was the entire length of record 

at station 16587000, or the period 1912 through 1986 water years. It was 

assumed that any station with at least 60 years of record provides an 

acceptable estimate of the median streamflow for this entire base period and 

therefore long-term conditions. Nine of the 56 stations with at least 60 

years of record are indicated in figure 6 and were used as index stations. 

None of the index stations are located on the island of Hawaii.

To include more of the 56 stations as index stations would require that 

the base period be shortened. None of the 56 stations have between 50 and 60 

years of record. There are four stations that have between 45 and 50 years of 

record. The reduction in the length of base period required to include these 

four stations as index stations would eliminate several stations from the 

analysis entirely. The stations would be eliminated because their periods of 

record would now fall outside the base period. This was not considered an 

acceptable tradeoff.

To compute long-term estimates of median streamflows for the 47 stations 

with less than 60 years of record, the index-station method was used (Searcy, 

1959, p. 12). To apply the index-station method, each of the short-term 

stations needs to be correlated with at least one of the index stations. 

Flow-duration curves were computed for the period of common or concurrent 

record at the stations. Corresponding flow-duration points for the two 

stations were plotted on logarithmic paper, thus establishing a curve or 

relation between the two stations. A basic assumption underlying the indexstation method is that the short-term relation represents the relation between 

the stations for the long-term, or base, period. Given this assumption, the 

median streamflow for the base period at the index station can be used with 

the curve to obtain the base-period median streamflow for the short-term 

station. Estimated base-period (1912-1986) or long-term median streamflows 

for the 56 stations used in the regression analyses are listed in table 3.

15
Table 3.--Estimated base-period (1912-1986) median streamflows for the 

unregulated, perennial streamflow-gaging stations used in the 

regression analyses

[fts /s, cubic feet per second; --, indicates the station is an index-station]

Station Correlated Concurrent 

number index-station years of

record

Median streamflow Base-period median 

for period of streamflow (ft 3 /s) 

record (ft 3 /s)

16010000

16013000

16017000

16019000

16068000

16071500

16097500

16105000

16106000

16108000

16115000

16116000

16117000

16200000

16201000

16206000

16303003

16400000

16402000

16403000

16403900

16404000

16404200

16405000

16416000

16502000

16508000

16510000

16515000

16516000

_ _

16010000

16010000

16010000

16068000

16068000

16010000

16010000

16010000

16010000

16010000

16010000

_ _

16200000

16200000

16200000

_ _

16400000

16400000

16400000

16400000

16400000

16400000

16400000

16508000

16508000

16508000

16518000

_ _

34

14

34

26

28

12

13

28

20

20

22

_ _

18

8

26

_ _

18

18

11

18

18

18

25

31

40

40

21

Island of Kauai

13.4

3.0

8.2

6.8

31.6

1.8

7.5

20.0

66.6

79.3

8.4

1.8

5.2

Island of Oahu

7.3

4.9

5.8

19.8

Island of Molokai

14.2

20.1

7.6

4.9

9.3

1.0

8.3

0.36

Island of Maui

3.2

7.1

5.3

6.7

9.1

13.4

3.0

7.9

6.8

31.6

1.8

7.6

19.3

60.3

80.4

8.7

1.9

5.4

7.3

4.7

6.0

19.1

14.2

19.1

7.1

5.9

8.8

1.1

7.6

0.36

3.2

7.1

4.6

6.2

8.2

16
Table 3. --Estimated base-period (1912-1986) median streamflows for the 

unregulated, perennial streamflow-gaging stations used in the 

regression analyses--Continued

[ft3 /s, cubic feet per second; --, indicates the station is an index-station]

Station Correlated Concurrent 

number index-station years of

record

Median streamflow Base-period median 

for period of streamflow (ft 3 /s) 

record Cft 3 /s)

Island of Maui- -continued

16517000

16518000

16519000

16520000

16524000

16527000

16557000

16565000

16566000

16577000

16585000

16586000

16587000

16618000

16620000

16636000

16717000

16717800

16720000

16720300

16737000

16739000

16740000

16741000

16742000

16757000

16518000

16518000

16518000

16518000

16518000

16587000

16587000

16587000

16587000

16587000

16620000

16620000

16518000

16518000

16518000

16518000

16518000

16518000

16518000

16518000

16518000

16518000

35

35

35

11

41

46

39

27

38

45

23

5

Island

19

17

22

18

20

12

12

13

12

24

10.3

10.4

5.2

3.8

2.1

6.2

3.1

2.9

1.2

9.8

5.6

4.4

2.5

8.8

24.3

5.0

of Hawaii

38.0

7.7

4.2

1.7

4.3

2.4

0.59

1.1

0.91

4.0

8.5

10.4

4.5

3.3

2.5

6.0

2.9

2.8

1.1

9.1

5.6

4.4

2.5

9.1

24.3

4.9

45.0

9.1

5.6

2.2

4.3

2.5

0.60

1.1

0.94

4.0

17
Basin-Characteristic Data

To do regression analyses, basin characteristics that might be related to 

median streamflow need to be determined in a quantitative form. Basin 

characteristics considered in this study can be placed in one of three basic 

categories: basin morphology, land use, and climate. The seven 

characteristics considered are: drainage area, channel length, mean basin 

altitude, mean altitude of the main stream channel, forest cover, swamp cover, 

and mean annual precipitation. The seven characteristics are described below:

Drainage area (DA)--in mi2 ; determined by planimetering the area enclosed by 

basin divides drawn on 1:24,000-scale USGS topographic maps. Previous studies 

have consistently shown that drainage area is an important factor in 

determining streamflow characteristics for a basin (Thomas and Benson, 1970).

Channel length (CD--in mi; is the longest distance measured along a stream 

from the site of interest to the basin divide. The stream channel was defined 

by the blue line on 1:24,000-scale USGS topographic maps and measured using a 

map wheel.

Mean basin altitude (BE)--in ft; determined by placing a uniform grid over the 

basin outline as identified pn 1:24,000-scale USGS topographic maps. The 

altitude at a minimum of 25 grid intersections in the basin were estimated 

from the topographic maps. Mean basin altitude was calculated as the average 

of the altitudes at the grid intersections. Mean basin altitude acts as a 

surrogate index for factors such as temperature, wind, and solar radiation, 

which are difficult to evaluate and may cause streamflow variations (Thomas 

and Benson, 1970).

Mean altitude of the main stream channel (CE)--in ft; determined by averaging 

channel altitudes determined at points located 10 percent and 85 percent of 

the channel length upstream from the gaging station.

Forest cover (FC)--in percent; is the percentage of the drainage area covered 

by forest and vegetation. Forest cover was determined to be the area shown in 

green on the 1:24,000-scale USGS topographic maps and was measured with a 

planimeter. Percent forest cover serves to represent variations in 

evapotranspiration and rainfall interception caused by various degrees of 

vegetation.

Swamp cover (SO--in percent; is the percentage of the drainage area covered 

by swamps. Swamp cover was determined to be the area shown on the 1:24,000- 

scale USGS topographic maps that was identified as swamp or marsh. Area of 

swamp cover was measured with a planimeter. A constant of 0.1 percent was 

added to all sites where the percent of swamp cover was determined to be zero. 

Use of the constant avoids problems caused when using logarithms with a data

18
set that includes zero values. Swamps and wetlands can affect streamflows as 

a result of their ability to store water, provide ground-water recharge, and 

cause increased evapotranspiration (Carter, 1986).

Mean annual precipitation (P)--in in.; determined by placing a uniform grid 

over maps showing lines of equal mean annual precipitation as prepared by 

Giambelluca and other (1986). Mean annual precipitation was determined at a 

minimum of 20 to 25 grid intersections located within the drainage-basin 

boundary. Mean annual precipitation for the basin was calculated as the 

average of the values determined at each of the grid intersections.

Basin characteristics described above are summarized for each of the 56 

unregulated, perennial, streamflow-gaging stations used in the regression 

analyses in table 4. Each of the 56 gaging stations were also classified as 

being located on either the windward or leeward regions of their respective 

island. The divisions between windward and leeward were based on work by 

Yamanaga (1972).

Development of Multiple-Regression Equations

For the regression analysis, the adjusted base-period median-streamflow 

values were the dependent variables and the independent variables were the 

basin characteristics. The multiple-regression technique requires that 

independent and dependent variables be linearly related. An examination of 

the median-streamflow values and the basin characteristics, along with 

previous studies (Thomas and Benson, 1970), have shown that the logarithmic 

transformation creates the required linear relation. The natural log (base e) 

transformation was used for transformation of all variables in this study. A 

problem with logarithmic transformations is the bias introduced when 

regression results are back-transformed from logarithms to the original units 

of measurement. This problem can be corrected^by using a bias-correction 

factor. The smearing estimate (Duan, 1983) was used to estimate this biascorrection factor.

After transforming all variables, the significant independent variables 

for median streamflow were determined by correlation and stepwise regression. 

Correlation measures the degree of the linear relation between two variables. 

This degree of relation is indicated by the Pearson correlation coefficient, 

which ranges from -1 to 1. Values close to -1 or 1 represent high correlation 

among variables. In regression analysis, high correlation among independent 

variables tends to reduce the significance of each variable involved and can 

lead to unstable regression models. To avoid this problem, only the more 

significant and reliable variable should be retained in the regression model.

19
Table 4.--.Basin characteristics for the unregulated, perennial streamflowgaging stations used in the regression analyses

[mi2 , square miles; mi, miles; ft, feet; %, percent; in., inches; L, leeward; 

W, windward]

Station 

number Region

16010000

16013000

16017000

16019000

16068000

16071500

16097500

16105000

16106000

16108000

16115000

16116000

16117000

16200000

16201000

16206000

16303003

L

L

L

L

W

W

W

W

W

W

W

W

W

L

L

L

W

Drainage 

area 

(mi 2 )

3.

1.

1.

1.

6.

0.

1.

1.

6.

10.

2.

0.

1.

1.

1.

1.

2.

95

68

68

79

27

65

90

81

95

2

73

50

55

38

17

93

78

Channel Basin 

length altitude 

(ml) (ft)

6.41

4.42

4.69

4.35

4.30

1.90

2.41

2.88

3.81

6.95

3.51

1.50

1.40

4.84

3.00

5.84

3.02

Island of

3,840

3,920

4,250

4,360

1,390

790

1,110

2,220

2,280

3,210

2,990

3,440

2,890

Island of

1,750

1,700

1,650

1,160

Channel 

altitude 

(ft)

Forest 

cover 

(%)

Swamp Mean annual 

cover rainfall 

(%) (in.)

Kauai

3,

3,

4,

4,

2,

2,

1,

1,

2,

2,

1,

Oahu

1,

1,

1,

720

750

080

240

860

720

500

500

260

620

060

020

460

520

550

490

745

58

72

18

31

100

100

82

100

100

73

100

100

99

100

100

100

100

42

28

82

69

0.

0.

8.

0.

0.

27

0.

0.

0.

0.

0.

0.

0.

1

1

0

1

1

1

1

1

1

1

1

1

132

135

180

146

147

105

139

180

262

274

123

95

90

255

250

243

200

Island of Molokai

16400000

16402000

16403000

16403900

16404000

16404200

16405000

16416000

16502000

16508000

16510000

16515000

16516000

16517000

16518000

16519000

16520000

16524000

W

W

W

W

W

W

W

L

L

W

W

W

W

W

W

W

W

W

4.

4.

1.

1.

2.

0.

1.

0.

0.

3.

0.

0.

4.

3.

3.

1.

0.

2.

62

38

41

18

59

49

09

24

43

49

69

32

31

11

66

93

51

54

5.26

3.69

1.60

1.80

2.16

1.06

1.56

1.10

2.50

6.20

0.54

2.40

6.60

6.50

6.80

6.80

2.50

5.60

2,210

2,200

1,960

2,370

2,330

2,340

2,270

2,430

Island of

2,470

4,630

2,100

2,490

4,600

4,340

4,800

4,650

2,115

5,425

1,

1,

1,

2,

1,

2,

1,

2,

Maui

2,

4,

3,

2,

4,

4,

4,

3,

1,

5,

980

620

930

190

730

160

540

170

360

070

420

000

150

000

000

910

980

280

100

100

100

100

100

100

100

100

95

85

100

100

100

100

100

100

100

100

0.

0.

0.

0.

0.

0.

0.

0.

2.

0.

0.

0.

0.

0.

0.

0.

0.

0.

1

11

1

1

1

1

1

0

1

1

1

11

1

1

1

1

86

130

128

132

131

123

95

119

153

257

257

250

223

226

207

190

241

164

20
Table 4.--.Basin characteristics for the unregulated, perennial streamf'lowgaging stations used in the regression analyses--Continued

[mi 2 , square miles; mi, miles; ft, feet; %, percent; in., inches; L, leeward; 

W, windward]

Drainage Channel Basin Channel Forest Swamp Mean annual

Station area length altitude altitude cover cover rainfall

number Region (mi 2 ) (mi) (ft) (ft) (%) (%) (in.)

Island of Maui--continued

16527000

16557000

16565000

16566000

16577000

16585000

16586000

16587000

16618000

16620000

16636000

16717000

16717800

16720000

16720300

16737000

16739000

16740000

16741000

16742000

16757000

W 

W 

W 

W 

W 

W 

W 

W 

W 

W 

L

L 

W 

W 

W 

W 

W 

W 

W 

W 

W

3.17

0.47

0.58

0.20

2.41

1.34

0.55

0.64

3.47

4.11

1.51

11.6

2.76

1.58

0.45

0.76

0.66

0.12

0.32

0.22

0.78

7.10

2.30

3.80

1.70

6.10

4.90

2.70

3.00

5.70

6.20

3.70

13.4

9.30

2.50

1.70

3.30

3.70

0.47

2.00

1.60

2.00

4,810

1,900

2,125

1,665

3,170

2,350

1,815

1,790

2,285

3,190

3,350

Island of

3,720

2,330

4,620

4,410

3,760

3,220

2,340

2,780

2,580

3,860

4,670

1,790

2,130

1,590

2,840

2,190

1,750

1,830

1,870

2,690

2,660

Hawaii

3,590

2,330

4,330

4,470

3,610

3,100

2,170

2,680

2,550

3,870

100

100

100

100

100

100

100

100

92

99

100

100

85

100

100

100

100

100

100

100

100

0.1

0.1

0.1

0.1

0.1

0.1

0.1

0.1

8.0

0.1

0.1

180

204

201

180

193

165

150

175

154

236

124

0.1

0.1

0.1

0.1

0.1

0.1

0.1

0.1

0.1

0.1

190

191

108

148

166

159

137

152

144

103

21
The stepwise regression procedure adds or deletes variables one by one 

into the regression model according to their level of significance for entry 

and retention (Draper and Smith, 1981). In this study an entry and retention 

significance level of 0.05 (5 percent) was chosen for the F-test used in 

stepwise regression to measure significance. Previous regression analyses 

between streamflow characteristics and basin characteristics in Hawaii have 

shown that a 5 percent significance value usually limits regression models to 

no more than 3 independent variables (Yamanaga, 1972; Nakahara, 1980; Wong, 

1991). The final regression model when back-transformed has the form,

Q5Q - a(Xb )(Yc )(Zd)(BCF),

where: QCQ is the median streamflow in fts /s, 

X,Y, and Z are basin characteristics, 

a is the regression constant, 

b, c, and d are the regression coefficients, or exponents

of the basin characteristics, and 

BCF is the bias-correction factor.

Residuals from the regression analysis of the entire State (56 stations) 

were plotted geographically and analyzed visually for possible regional 

grouping. The use of groupings into homogeneous regions can improve 

regression estimates (Lettenmaier and others, 1987). Possible groupings of 

islands were determined from the residual plots and from existing knowledge of 

the geology and hydrology of the area. These groupings were then tested for 

significance at the 10-percent level by using the Wilcoxon Signed Ranks Test 

(Tasker, 1982) on the regression residuals. The Wilcoxon Signed Ranks Test 

does not statistically verify regions but provides a quantitative index as a 

guide for defining homogeneous regions (Choquette, 1988; Tasker, 1982). In 

addition to the Wilcoxon test, the percent standard error of estimate from 

regression analyses of the various groupings were also used to judge the 

groupings. The results of the Wilcoxon test showed that none of the groupings 

chosen were significantly different from the State as a whole at the 10- 

percent significance level. The regression analysis of the groupings did 

indicate that lumping data for Oahu, Molokai, and Hawaii together and data for 

Kauai and Maui together did provide improved standard errors.

Ordinary-least-squares regression procedures were used to develop the 

final regression models to estimate median streamflows for the Oahu, Molokai, 

and Hawaii grouping and the Kauai and Maui grouping. Final models were tested 

to ensure that (1) all independent variables selected were statistically 

significant at the 5-percent level, (2) the standard error was minimized, (3) 

the coefficient of determination adjusted for degrees of freedom was 

maximized, (4) multicolinearity or correlation between selected variables was 

not a problem, (5) overly influential observations were not present, and (6) 

residual variances were constant. In addition to the statistical measures of

22
acceptability, the signs and magnitudes of the coefficients determined for the 

significant, independent variables were reviewed to ensure that they were 

hydrologically reasonable.

The independent variable that gave the best estimates for median 

streamflow for the Oahu, Molokai, and Hawaii grouping was drainage area. No 

additional independent variable qualified under the 5-percent significancelevel criteria. The independent variables that gave the best estimates for 

median streamflow for the Kauai and Maui grouping were drainage area, mean 

altitude of the main stream channel, and mean annual precipitation. 

Regression equations, used to estimate median streamflow for the two 

groupings, their respective coefficients of determination, and standard errors 

of regression and prediction are shown in table 5. The regression statistics, 

as well as the accuracy and limitations of the equations, are described in the 

next section of the report. Smearing adjustments or bias correction factors 

of 1.055 and 1.090 were incorporated into the regression constants for the 

Oahu, Molokai, and Hawaii and for the Kauai and Maui equations.

Accuracy and Limitations of the Equations

The coefficient of determination, standard error of the regression, and 

standard error of prediction associated with the regression equations are 

shown in table 5. The coefficient of determination provides a measure of the 

proportion of total variation of median streamflow accounted for by the 

regression equations. Standard error of the regression is a measure of the 

average deviation of observed median streamflows from those predicted by the 

regression equations. Standard error of prediction is a measure of average 

deviation to be expected when applying the regression equations at ungaged 

sites. About 68 percent of median-streamflow estimates, using the regression 

equation, should be within the given standard errors of prediction of their 

true values. Standard errors determined from the regression equations are 

comparable to standard errors associated with estimates of long-term median 

streamflow made for station 16587000 (table 2) in which between 1 and 5 years 

of continuous-data are used. To provide a graphical representation of the 

accuracy of the regression equation computed for the Oahu, Molokai, and Hawaii 

geographic group, observed median streamflow is plotted against drainage area 

in figure 7. Drainage area is the only independent variable included in the 

regression equation for the group. The difference between observed and 

predicted median-streamflow data for each of the stations is represented by 

the vertical distance (measured in cubic feet per second) between the circles 

and the regression equation, which is plotted as the straight line in 

figure 7.

Limitations on the use of the equations in table 5 also need to be 

considered. The equations should not be used for sites that are subjected to 

the effects of regulation. The equations are only applicable for perennial 

stream sites on the islands for which they were developed. Within each island 

grouping the equations should be applied only at sites having basin

23
Table 5.--Summary of regression equations used to estimate median streamflow

period at ungaged, unregulated, perennial stream sites in Hawaii

Geographic 

grouping

Oahu, Molokai 

and Hawaii

Kauai and Maui

Number of 

stations

22

34

Regression equation

Q5Q - 4.25 (DA) 1 ' 04

Q5Q -4.49 (DA)°- 808 (CE)- 0 - 641 (P) 0 ' 985

R2

0.91

0.78

Where: QCQ is median streamflow, in cubic feet per second 

DA is drainage area, in square miles

CE is mean altitude of the main stream channel, in feet 

4> P is mean annual precipitation, in inches

R2 is the coefficient of determination, adjusted for lost degrees o

SE is the standard error of the regression, in percent, from units 

logarithms

SE is the standard error of prediction, in percent, from units of n

"logarithms
100

UJ 

CO 

DC

s

6

 0

Z

10

0.1

0.1

1 I I I I 11 Ij I I I 1 I I

1 t I I I I I I I I I I I I I I I [ I t t I I t

1 10 

DRAINAGE AREA. IN SQUARE MILES

100

Figure 7. Plot of observed median streamflow as a function of drainage

area with the calibrated regression line for the Oahu, Molokai, 

and Hawaii geographic grouping.

25
characteristics within the range of values at the gaged sites used to develop 

the equations. Ranges for the basin characteristics used in each of the 

regression equations are summarized in table 6. Application of the regression 

equations at sites with basin characteristics outside the appropriate ranges, 

as indicated in table 6, will provide median-streamflow estimates with unknown 

levels of accuracy.

Table 6.--Ranges of basin-characteristic values at stations used to 

develop regression equations

DA CE P 

Geographic grouping minimum maximum minimum maximum minimum maximum

Oahu, Molokai 

and Hawaii 0.12 11.6 n.a. n.a. n.a. n.a.

Kauai 

and Maui 0.20 10.2 720 5,280 90 274

Where: n.a. indicates not applicable

DA is drainage area, in square miles

CE is mean altitude of the main stream channel, in feet

P is mean annual precipitation, in inches

ESTIMATION OF MEDIAN STREAMFLOWS AT REGULATED, PERENNIAL

WINDWARD OAHU SITES

A significant number of perennial stream sites in Hawaii are subject to 

regulation and the equations developed in the preceding section of this report 

are not applicable at regulated sites. As previously noted, in the section 

"Site Selection," only 112 of the 664 streamflow-gaging stations that have 

been operated in Hawaii for some period of time between 1910 and 1986 can be 

considered unregulated. Accurate median streamflows can be computed at gaged, 

regulated stations. To be representative of future conditions, the median 

streamflows should be based on long-term data collected over a period of 

uniform regulation similar to what is expected in the future. Because medianstreamflow estimates are required at ungaged, regulated sites, a different 

technique is required. In this section of the report, specific regulated 

sites located on the windward side of Oahu were selected. Additional 

hydrologic data collected at selected sites and concurrent data available at 

nearby continuous-record index stations were analyzed by correlation and 

ordinary-least-squares regression to provide estimates of median streamflows. 

Associated accuracies and limitations of the results are also discussed.

The technique of correlating additional hydrologic data collected at 

ungaged sites to concurrent data available at gaged stations was applied only

26
at selected regulated windward Oahu sites in this report. However, the 

technique can be applied to both regulated and unregulated perennial sites in 

other areas on the islands of Oahu as well as on Kauai, Molokai, Maui, and 

Hawaii. The obvious limitation of the technique is that the additional 

hydrologic data must be collected before the estimates of median streamflows 

can be made.

Site Selection

A total of 27 regulated stream sites located on the windward side of Oahu 

were selected for analysis. Selected sites are located in six drainage 

basins: nine sites in the Maunawili basin, five sites each in the Waiahole and 

Waikane basins, three sites each in the Funaluu and Kaluanui basins, and two 

sites in the Kahana basin. Locations of the windward Oahu study basins are 

shown in figure 8. Where possible, sites were selected to coincide with 

locations where data had previously been collected. The sites selected with 

associated site numbers, latitude, longitude, description of location, and 

drainage areas are summarized in table 7. Site numbers are of three types and 

provide information regarding the data collection history of the location. 

Eight-digit site numbers are USGS station numbers and indicate that some 

systematic data collection has previously been done at the location. Two- and 

three-digit numbers indicate that the location coincides with a site where 

miscellaneous low-flow data were collected by Takasaki and others (1969, pi. 

3). Two- and three-digit site numbers followed by a letter or an underscore 

and an additional digit are sites where data have not been collected before 

this study. The leading two or three digits for the third type of site 

numbers represent the nearest site from the study by Takasaki and others 

(1969, pi. 3).

Data Collection and Analysis

To determine median streamflows for the 27 sites listed in table 7, about 

4 discharge measurements per year were made at each of the 27 sites during 

water years 1988 through 1990. Measurements were made over a range of 

discharges that were expected to bracket median streamflows. In addition to 

these data, previous streamflow measurements available at 19 of the sites were 

used. Previous measurements were screened and only those that fell within the 

range of discharges measured at the site during water years 1988 through 1990 

were used. This screening was done to prevent potential bias that might be 

caused by including high- or low-flow measurements in the analysis. An 

exception was made at site 16260500 where 3 years of record are available and 

were used in the analysis. All measured discharges for the 27 sites have been 

published by Takasaki and others (1969), by the USGS in the series of waterresources data reports for Hawaii (1971-91), or in Water-Supply Papers 1937 

and 2137 (U.S.Geological Survey, 1971 and 1977).

27
158° 157°45'

2V30'

iKAHUKU

HAWUIAN 

ISLANDS

OAHU

-Kaluanm' Stream

-Kaluanui drainage basin

 Punaluu Stream

 Punaluu drainage ° 

basin I

OAHU

1234 SMILES

KAAAVW

Kahana drainage basin

Waikane drainage basin 

Waikane Stream

I I ill I

01 2345 KILOMETERS

21' 

15'

WWAHOLE

Waiahole Stream

Waiahole drainage basin

Maunawili 

drainage 

basin

EXPLANATION

A STREAMFLOW-GAGING 

STATION

Note: The two leftmost digits (16) and the two

rightmost digits (00) of each station number 

are omitted on this map for brevity

Figure 8. Locations of windward Oahu study basins and regulated, 

perennial index streamflow-gaging stations.

28
Table 7. --Regulated, perennial windward Oahu sites where median-streamflow 

estimates were made

[mi 2 , square miles; mi, miles; ft, feet]

Site Drainage 

number Latitude Longitude Location area (mi 2 )

Maunawili basin

26 21°21'20 M 157°45'52" Makawao Stream, 1.8 mi southwest 0.84

of Maunawili School and 2.2 mi 

southeast of Hawaii Loa College

28 21°21'26" 157°45'55" Ainoni Stream, 1.7 mi southwest of 0.60

Maunawili School and 2.1 mi 

southeast of Hawaii Loa College

34_5 21 0 21'28" 157°46'13" Maunawili Stream, 1.9 mi southwest 1.09

of Maunawili School and 1.9 mi 

southeast of Hawaii Loa College

35 21°21'51" 157 0 46'05" Maunawili Stream, 1.4 mi southwest 1.19

of Maunawili School and 1.6 mi 

southeast of Hawaii Loa College

38 21°21'56 M 157°46'46 M Omao Stream, 1.3 mi southwest of 0.94

Maunawili School and 1.5 mi 

southeast of Hawaii Loa College

16260500 21°22'51 M 157°45'48" Maunawili Stream, 0.6 mi west of 5.34

Maunawili School and 1.6 mi 

southwest of Kailua Post Office

45 21°22'22 M 157°46'27" Kahanaiki Stream, 1.4 mi southwest 0.36

of Maunawili School and 0.9 mi 

southwest of Hawaii Loa College

16263000 21°22'20" 157°46'25" Kahanaiki Stream, 1.3 mi southwest 0.61

of Maunawili School and 0.9 mi 

southeast of Hawaii Loa College

16264100 21°22'49" 157°46'46" Kahanaiki Stream, 0.9 mi west of 1.43

Maunawili School and 1.0 mi east 

of Hawaii Loa College

Waiahole basin

176_5 21°28'29 M 157°52'39" Waiahole Stream, 1.7 mi southwest 0.92

of Waiahole School and 2.8 mi 

northwest of Kahaluu

178 21°28'59" 157°51'39" Waiahole Stream, 0.6 mi southwest 1.65

of Waiahole School, 2.2 mi 

northwest of Kahaluu, and 

downstream from a diversion ditch

178T 21°28'59" 157°51'43" Waiahole Stream, about 100 ft 1.65

upstream from site 178 and includes 

flow from diversion ditch

16293100 21°28'59" 157°51'47" Waianu Stream, 0.6 mi southwest of 1.64

Waiahole School and 2.3 mi 

northwest of Kahaluu

186_5 21°29'05" 157°50'57" Waiahole Stream, 0.4 mi southwest 3.76

Waiahole School and 1.8 mi 

northwest of Kahaluu

29
Table 7. --Regulated, perennial windward Oahu sites where median-streamflow 

estimates were made--Continued

[mi 2 , square miles; mi, miles; ft, feet]

Site Drainage 

number Latitude Longitude Location area (mi 2 )

Waikane basin

187_5 21°30'21" 157°52'42 North Fork Waikane Stream, 1.7 mi 0.58

west of Waikane and 2.0 mi 

northwest of Waiahole School

187_8 21°30'17 M 157°52'43" Waikane Stream, 1.7 mi west of 0.67

Waikane and 1.8 mi northwest 

of Waiahole School

190 21°30'07 M 157°52'12" Waikane Stream, 1.1 mi west of 1.57

Waikane and 1.4 mi west of 

Waikane School

191 21°30'02" 157°52'14" Waikeekee Stream, 1.1 mi west of 0.43

Waikane and 1.4 mi west of

Waikane School 

198 21°29'56" 157°51'15" Waikane Stream 0.1 mi west of 2.50

Waikane and 0.7 mi north of

Waiahole School

Kahana basin

16295995 21°32'17" 157°53'29" Kahana Stream, 1.8 mi upstream 3.20

from main bridge on Kamehameha 

Highway and 2.8 mi southwest 

of Kaaawa School

16297000 21°32'35" 157°53'51" Kawa Stream, 0.1 mi upstream 2.10

from mouth and 1.0 mi south 

of Kahana

Punaluu basin

236 21°33'12" 157°54'05 M Punaluu Stream, 1.4 mi west of 1.80

Kahana and 2.1 mi southwest of

Punaluu 

241 21°33'15" 157°54'06 M Waiaohi Stream, 1.4 mi west of 0.52

Kahana and 2.1 mi southwest

of Punaluu 

251_5 21°34'41" 157°53'21" Punaluu Stream, 1.4 mi north of 3.51

Kahana and 0.3 mi south of Punaluu

Kaluanui basin

253 21°34'51" 157°54'59" Kaluanui Stream, 1.9 mi west of 0.85

Punaluu Beach Park and 2.3 mi 

south of cemetery in Hauula

253_5 21°34'14" 157°54'44" Kaluanui Stream, 1.5 mi west of 1.96

of Punaluu Beach Park and 1.6 mi 

south of cemetery in Hauula

16304500 21°35'57 M 157°54'24" Kaluanui Stream, 1.2 mi southeast 2.12

of cemetery in Hauula and 1.4 mi 

northeast of Sacred Falls

30
Relations between discharge measurements for each of the 27 sites and 

concurrent daily mean discharge at a number of different continuous-record 

index stations were established using ordinary-least-squares regression. The 

pairing with highest correlation coefficient was selected as providing the 

best relation. Index stations considered for the analysis included those with 

at least 10 years of record that were located near any of the 27 sites. In 

addition, station 16240500, Waiakeakua Stream at Honolulu, was considered for 

use as an index station. Takasaki and others (1969) found station 16240500 to 

be hydrologically similar to windward Oahu basins. Following Searcy (1959), 

logarithmic transformations were made on all streamflow data before 

correlation and regression analysis. Index stations used for the analyses and 

their respective periods of record, drainage areas, and median streamflows are 

summarized in table 8.

Relations developed between discharge at the 27 sites and respective 

index stations can be used with computed median streamflows at the index 

stations to estimate median streamflows at the 27 sites. Regression 

statistics, selected index stations, and estimated median streamflows for the 

27 windward Oahu sites are summarized in table 9. Bias-correction factors 

based on Duan's (1983) smearing estimate were included in the regression 

estimates.

Stedinger and Thomas (1986) have demonstrated that ordinary-least-squares 

regression tends to give biased estimates of low-flow frequency statistics 

when relating base-flow measurements and concurrent daily flows at index 

stations. Techniques recommended to avoid the bias include graphical 

correlation (Searcy, 1959), maintenance of variance procedures (Hirsch, 1982), 

or methods of moments (Gilroy, 1972; Stedinger and Thomas, 1986).

In this study, an estimate for only one value, median streamflow, is 

required. Regression equations are not provided. Hirsch and Gilroy (1984, p. 

708) have demonstrated that when estimating individual values ordinary-leastsquares regression procedures are appropriate, assuming other ordinary-leastsquares regression assumptions (linear relation and constant variance) are 

met. Ordinary-least-squares regression statistics provided in table 9 are 

also appropriate for use especially because the one value estimated, median 

streamflow, is a measure of central tendency. Measures of central tendency 

are not subject to the bias that is often evident with data at the extreme 

ends of fitted regressions.

31
Table 8.--Index stations used to estimate median streamflows for windward Oa

[mi 2 , square miles; ft s /s, cubic feet per second; p, station in operation as 

water year 1991; ft, feet]

Station

number Latitude Longitude Station name

Length

of Period Drainage 

record of area 

(years) record (mi 2 ) 

10

to

16240500 21°19'53" 157°48'12" Waiakeakua Stream 76 1913-21; 1.06

at Honolulu

16254000 21°21'49" 157°46'02" Makawao Stream

near Kailua

1925-p 

39 1912-16; 2.04 

1958-p

16291000 21°28'35" 157°52'30" Waiahole Stream at 14 1955-68; 0.99

1970; 

1988-90 1

altitude 250 ft,

near Waiahole 

16294900 21 0 30'00" 157°51'54" Waikane Stream at 33 1959-p 2.22

altitude 75 ft,

at Waikane 

16296500 21 0 32'37" 157°53'07 lf Kahana Stream at 34 1958-p

altitude 30 ft,

near Kahana 

16303003 21°33'33" 157°54'06" Combined records 38 1953-p

of Punaluu Ditch

(16302000) with

Punaluu Stream

(16303000) near

Punaluu 

16304200 21°35'22" 157°54'38" Kaluanui Stream

near Punaluu

3.74

2.78

24 1967-p 1.11

1 Low-flow partial-record station

2 Median streamflow extended to represent base period 1912 through 1986 (se
Table 9.- -Regression-equation statistics and estimated median streamflows for 

selected regulated, perennial windward Oahu sites

[fts /s, cubic feet per second; --, see footnote]

Site

number

Number of

concurrent

measurements R2 SE

Index station

SE number 

P

Estimated

median

streamflow

(ftVs)

26

28

34 5

15

38

16260500

45

16263000

16264100

176 5

178

178T

16293100 

186 5

187 5

187 8

190

191

198

16295995

16297000

236

241

251 5

14

15

12

16

14

758

12

12

46

11

12

9

15

11

12

12

14

16

12

39

31

13

13

12

Maunawili basin

0.61

0.74

0.69

0.94

0.77

0.75

0.65

0.72

0.75

0.95

0.72

0.85

0.71

0.97

0.74

0.83

0.94

0.77

0.60

0.84

0.90

19.3

29.4

21.2

19.6

22.2

21.5

27.6

22.2

32.2

23.4

19.7

27.3

25.6

28.8

Waiahole basin

7.4 9.2

10.0 13.3

4.4 5.3

17.6 20.4

9.1 10.6

Waikane basin

23.4 28.1

9.4 11.4

16.6 20.1

30.2 33.5

8.1 9.9

Kahana basin

11.6 12.4

27.8 29.9

Punaluu basin

8.1 9.1 

6.6 7.8

Kaluanui basin

16254000

16254000

16254000

16254000

16254000

16254000

16254000

16254000

16254000

16291000

16291000

16291000

16294900

16291000

16294900

16294900

16294900

16294900

16294900

16296500

16294900

16303003

16303003

16303003

1.2

0.98

1 1.6

n.e

1.2

6.7

0.52

0.82

1.3

3.4 

4.8 

6.0 

3.0 

8.5

1.1

0.66

2.7

0.38

4.0

19.2 

3.0

14.7

4.4

1 16.7

253

253 5

163045UO

14

14

6

0.97

0.99

10.7

7.2

13.9

8.4

16304200

16304200

16304200

1.4

1.4

^.53

*No regression statistics are provided and estimated median streamflow 

should be used with caution.

Where: R2 is the coefficient of determination, adjusted for lost degrees of

freedom 

SE is the standard error of the regression, in percent, from units of

natural logarithms

SE is the standard error of prediction, in percent, from units of 

p natural logarithms

33
Accuracy and Limitations of Median-Streamflow Estimates

Median-streamflow estimates at ungaged, regulated sites can be no better 

than the correlation that exists between the site and an index station. The 

site and index stations, to be highly correlated, need to be reasonably 

proximate and subject to similar stresses and regulatory effects. As a result 

all but two of the 27 sites (sites 16293100 and 16297000) in table 9 had the 

highest correlation with an index station located within the same drainage 

basin. The coefficient of determination, standard error of the regression, 

and standard error of prediction are provided as measures of the strengths of 

the relations and accuracies of the estimates.

No regression statistics are provided for sites 34_5, 35, 251_5, and 

16304500. Coefficients of determination for these sites were less than 0.60, 

or in the case of site 16304500, were based on an inadequate number of 

concurrent measurements. Although median streamflows are estimated for the 

four sites, they must be considered poor and of unknown accuracy. Standard 

errors of prediction for the remaining 23 sites vary between 5 and 34 percent 

and average 18 percent. The standard errors of prediction in table 9 

represent an average error associated with estimated median streamflow at the 

site and corresponds only to the period of record at the index station. For 

example, site 187_5 in the Waikane basin was correlated with station 16294900, 

which has a period of record from 1959 to present (33 years). The estimated 

median streamflow for site 187_5 of 1.1 ft3 /s is the estimated median for the 

same period, or 1959 to present, and having a standard error of prediction of 

28 percent. Standard errors provided for 23 of the sites in table 9 are 

comparable only when they are computed for the same period. In this study 

that means they would have had to be correlated to the same index station. 

The standard errors of prediction summarized above for regulated windward Oahu 

sites are likely to be representative of errors to be expected if the 

correlation techniques were applied to other ungaged, regulated or ungaged, 

unregulated perennial sites on the islands of Oahu, Kauai, Molokai, Maui, and 

Hawaii.

Changes in the regulatory patterns currently affecting the windward Oahu 

basins at the time of this study (1992) can alter flow regimes and therefore 

invalidate the estimated median streamflows as indicators of future medianstreamflow conditions. The overall utility or accuracy of an estimated median 

as an indicator of future flow conditions is based on the standard errors of 

prediction provided in table 9 and the length of record at the index station. 

For example, all other statistics being equal, the site correlated with the 

index station having the longest period of record provides the best estimates 

of future conditions. Time-sampling errors introduced by using index stations 

with short-term records are not included in the standard errors given in table 

9. Average time-sampling errors can be estimated by using the mean record 

length for the index stations used in the analysis (30 years) and data from 

table 2. As noted in table 2, the standard error when 30 years of record is

34
available to compute the 1912 to 1986 median for station 16587000 is 10 

percent.

SUMMARY

The State of Hawaii has selected median streamflow as the quantitative 

basis for establishing standards to protect instrearn uses of water. Median 

streamflow computed for the period of record at a gaging station has no timesampling error because the median statistic was based on the entire population 

of daily mean discharges for the period. Estimates of long-term median 

streamflows at gaged sites with only short-term records have errors that are 

inversely proportional to the length of record. For example, at station 

16587000, estimates of median streamflow for the base period 1912 through 1986 

would have a standard error of 24 percent if only 5 years of record were 

available. The standard error would decrease to 6 percent if 50 years of 

record were available. Errors in estimates of long-term median streamflows at 

short-term stations can be reduced when adjusted by correlation with data from 

long-term stations. To estimate median streamflows at ungaged, unregulated, 

perennial stream sites in Hawaii, a total of 56 stations with at least 10 

years of streamflow record that represent both perennial and unregulated 

conditions were identified. To allow direct comparison of median streamflows 

computed for each of the stations, record-extension techniques were used to 

adjust all data to reflect base-period (1912-1986) conditions. Median 

streamflows and basin characteristics for the 56 sites were used to develop 

multiple-regression equations. The equations can be used to estimate median 

streamflows at ungaged, unregulated, perennial stream sites in Hawaii.

As part of the regression analysis, Hawaii was divided into two groupings 

and separate equations were developed for each. The basin characteristics 

selected as providing the best estimates of median streamflow at ungaged, 

unregulated perennial sites were drainage area for Oahu, Molokai, and Hawaii, 

and drainage area, mean altitude of the main channel, and mean annual 

precipitation for Kauai and Maui. Standard errors of prediction for the two 

groupings were 41 percent (Oahu, Molokai, and Hawaii) and 54 percent (Kauai 

and Maui).

Median-streamflow estimates were made for 27 regulated, perennial 

windward Oahu sites. Estimates were based on correlations between discharge 

measurements made at the 27 sites and data available at proximate, 

hydrologically similar, continuous-record stations. Median-streamflow 

estimates provided for four of the sites were considered poor and no measures 

of accuracy were provided. Standard errors of prediction for the remaining 23 

sites vary between 5 percent and 34 percent. These standard errors correspond 

to a median-streamflow estimate only for the period of record available at the 

correlated continuous-record stations. Techniques that use discharge 

measurements at the ungaged, regulated, perennial sites provide reasonable 

estimates of median streamflows. Discharge measurements can also be used to

35
provide estimates of median streamflows at ungaged, unregulated sites. 

Estimates of median streamflows based on discharge measurements have greater 

errors than estimates based on continuous streamflow records and in general 

have smaller standard errors than estimates based on regression equations.

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37

 ffV.S. GOVERNMENT PRINTING OFFICE: 1992 - 688-190/79214