Prepared in cooperation with the

State of Hawaii Commission on Water Resource Management

Median and Low-Flow Characteristics for Streams under 

Natural and Diverted Conditions, Northeast Maui, Hawaii

U.S. Department of the Interior

U.S. Geological Survey

Scientific Investigations Report 2004-5262

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Median and Low-Flow Characteristics 

for Streams under Natural and Diverted 

Conditions, Northeast Maui, Hawaii

By Stephen B. Gingerich

Prepared in cooperation with the 

State of Hawaii Commission on Water Resource Management

Scientific Investigations Report 2004-5262

U.S. Department of the Interior

U.S. Geological Survey
U.S. Department of the Interior

Gale A. Norton, Secretary

U.S. Geological Survey

Charles G. Groat, Director

U.S. Geological Survey, Reston, Virginia: 2005

For sale by U.S. Geological Survey, Information Services

Box 25286, Denver Federal Center

Denver, CO 80225

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Telephone: 1-888-ASK-USGS

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Any use of trade, product, or firm names in this publication is for descriptive purposes only and does not imply 

endorsement by the U.S. Government.

Although this report is in the public domain, permission must be secured from the individual copyright owners to 

reproduce any copyrighted materials contained within this report.

Suggested citation:

Gingerich, S.B., 2005, Median and Low-Flow Characteristics for Streams under Natural and Diverted Conditions, 

Northeast Maui, Hawaii: Honolulu, HI, U.S. Geological Survey, Scientific Investigations Report 2004-5262, 72 p.
iii

Contents

Abstract ............................................................................................. 1

Introduction ................................................................................................ 1

Purpose and Scope ................................................................................. 2

Description of Study Area ........................................................................ 2

Previous Studies .................................................................................... 2

Numbering System for Surface-Water Gaging Stations ....................................... 4

Acknowledgments ................................................................................. 4

Streamflow Characteristics at Continuous-Record Stream-Gaging Stations ..................... 4

Index station selection ........................................................................... 11

Adjustments to streamflow characteristics for a common period using the index-station 

method ....................................................................................... 11

Estimation of Flow Characteristics of Ungaged Streams ............................................. 14

Drainage-Basin Characteristics .................................................................. 14

Morphometric characteristics ............................................................... 14

Hydrologic and geologic characteristics ................................................... 16

Development of regression equations ............................................................ 16

Accuracy and limitations of the regression equations ....................................... 33

Application of the regression equations to ungaged sites .................................... 43

Most-reliable Estimates of Natural Flow-Duration Statistics ....................................... 58

Discussion of results for selected streams ...................................................... 58

Estimates of Flow-Duration Statistics under Diverted Conditions ................................. 63

Needs for Additional Data .............................................................................. 68

Summary and Conclusions .............................................................................. 68

References Cited .......................................................................................... 70

Appendix A: Selected Drainage-Basin Characteristics Quantified Using Basinsoft ......... 72

Figures

 Figure 1. Northeast Maui study area, island of Maui, Hawaii ....................................... 3

 Figure 2. Flow-duration curves of total streamflow and base flow at gaging station 5180 on West 

Wailuaiki Stream, northeast Maui, Hawaii, for period 1914-2002 ........................ 6

 Figure 3. Relation between water level and stream discharge at diversions on selected streams 

within the 1,700- to 1,200-ft altitude interval, northeast Maui, Hawaii .................. 7

 Figure 4. Annual median streamflow and base flow for 1914-2002 at gaging stations 5180 on 

West Wailuaiki Stream and 5080 on Hanawi Stream, northeast Maui, Hawaii ...... 12

 Figure 5. Correlation between flows at gaging stations 5170 (East Wailuaiki Stream) and 5180 

(West Wailuaiki Stream), based on discharge of equal percentage duration for period 

of concurrent record 1914-17 and 1922-58, northeast Maui, Hawaii .................. 15

 Figure 6. Unadjusted and adjusted flow-duration curves of total streamflow and base flow at 

gaging station 5170 on East Wailuaiki Stream, northeast Maui, Hawaii ............... 16

 Figure 7. Correlation of flows at selected gaging stations in northeast Maui, Hawaii with flow at 

index station 5180 (West Wailuaiki Stream) based on discharge of equal percentage 

duration and unadjusted and adjusted duration curves of total streamflow and base 

flow ............................................................................................. 17
iv

 Figure 8. Mean annual rainfall, east Maui, Hawaii ................................................... 31

 Figure 9. Generalized surficial geology, northeast Maui, Hawaii ................................. 32

 Figure 10. Relation between measured and estimated flow statistics (in log10 cubic feet per 

second) for selected gaged basins used in determining the regression equations, 

northeast Maui, Hawaii ..................................................................... 35

 Figure 11. Relation between measured and estimated flow statistics (in log10 cubic feet per 

second) for gaged basins not used (outliers) in determining regression equations, 

northeast Maui, Hawaii ..................................................................... 42

 Figure 12. Distribution of relative error between measured and equation-estimated median 

total flow (TFQ50) at gaging-stations, northeast Maui, Hawaii ........................... 44

 Figure 13. Distribution of relative error between measured and equation-estimated median 

base flow (BFQ50) at gaging-stations, northeast Maui, Hawaii ........................... 45

 Figure 14. Distribution of relative error between measured and equation-estimated Q95 total 

flow (TFQ95) at gaging-station, northeast Maui, Hawaii ................................. 46

 Figure 15. Distribution of relative error between measured and equation-estimated Q95 base 

flow (BFQ95) at gaging-station, northeast Maui, Hawaii ................................. 47

 Figure 16. Distribution of relative error between measured and equation-estimated Q95 total 

flow (TFQ95) at ungaged sites in the study area and at selected gages west of the study 

area, northeast Maui, Hawaii ............................................................... 59

 Figure 17. Estimated low-flow duration curves of natural and diverted streamflow at lower 

West Wailuaiki and Waikamoi Streams, northeast Maui, Hawaii ..................... 67

 Figure 18. Reduction in Q95 total flow (TFQ95) due to diversions at selected ungaged and 

gaged sites in the study area, northeast Maui, Hawaii ................................. 69

Plate 1: Surface-Water Gaging Stations and Drainage

 Basins of Streams, Northeast Maui, Hawaii

Tables

 Table 1. Continuous-record surface-water gaging stations operated by the U.S. Geological 

Survey, northeast Maui, Hawaii ............................................................ 5

 Table 2. Selected estimated median and low-flow characteristics for continuous-record sites, 

northeast Maui, Hawaii ..................................................................... 9

 Table 3. Comparison of flow statistics computed for stream sites where natural flows are estimated, using data from multiple continuous-record gaging stations, northeast Maui, 

Hawaii .......................................................................................... 10

 Table 4. Trend analysis of annual median flow at active gaging station records for West 

Wailuaiki (5180) and Hanawi (5080) Streams, northeast Maui, Hawaii .................. 13

 Table 5. Comparisons of base-flow to total-flow duration statistics and streamflow characteristics at selected stations to those at index gaging station 5180 on West Wailuaiki 

Stream, northeast Maui, Hawaii ............................................................ 26

 Table 6. Watershed characteristics for selected gaged stream drainage basins, northeast 

Maui, Hawaii ................................................................................. 27

 Table 7. Watershed characteristics for selected ungaged stream drainage basins, northeast 

Maui, Hawaii ................................................................................. 29
v

Multiply By To obtain

Length

inch (in.) 2.54 centimeter (cm)

inch (in.) 25.4 millimeter (mm)

foot (ft) 0.3048 meter (m)

mile (mi) 1.609 kilometer (km)

Area

acre 0.004047 square kilometer (km2)

square foot (ft2) 0.09290 square meter (m2)

square mile (mi2) 2.590 square kilometer (km2) 

Volume

million gallons (Mgal) 3,785 cubic meter (m3)

Flow rate

foot per second (ft/s) 0.3048 meter per second (m/s)

cubic foot per second (ft3/s) 0.02832 cubic meter per second (m3/s)

million gallons per day (Mgal/d) 0.04381 cubic meter per second (m3/s)

Vertical coordinate information is referenced relative to local mean sea level.

Horizontal coordinate information is referenced to North American Datum of 1983 (NAD 83).

Altitude, as used in this report, refers to distance above the vertical datum.

 Table 8. Summary of regression equations developed for estimating selected flow-duration statistics of northeast Maui streams, Hawaii ................................................ 34

 Table 9. Streamflow statistics estimated using regression equations, lower and upper confidence intervals, standard errors, measured flows, and relative errors for continuousrecord sites, northeast Maui, Hawaii ...................................................... 36

 Table 10. Streamflow statistics estimated using regression equations, lower and upper confidence intervals, standard errors, measured flow, and relative errors for ungaged 

basins, northeast Maui, Hawaii ............................................................ 48

 Table 11. Estimates of natural (undiverted) streamflow statistics for gaged and ungaged basins, 

northeast Maui, Hawaii ..................................................................... 60

 Table 12. Estimates of diverted streamflow statistics and percent flow reduction for gaged and 

ungaged basins, northeast Maui, Hawaii ................................................... 64

Abstract

Flow-duration statistics under natural (undiverted) 

and diverted flow conditions were estimated for gaged and 

ungaged sites on 21 streams in northeast Maui, Hawaii. The 

estimates were made using the optimal combination of continuous-record gaging-station data, low-flow measurements, 

and values determined from regression equations developed as 

part of this study. Estimated 50- and 95-percent flow duration 

statistics for streams are presented and the analyses done to 

develop and evaluate the methods used in estimating the statistics are described. Estimated streamflow statistics are presented for sites where various amounts of streamflow data are 

available as well as for locations where no data are available.

Daily mean flows were used to determine flow-duration 

statistics for continuous-record stream-gaging stations in the 

study area following U.S. Geological Survey established standard methods. Duration discharges of 50- and 95-percent were 

determined from total flow and base flow for each continuousrecord station. The index-station method was used to adjust 

all of the streamflow records to a common, long-term period. 

The gaging station on West Wailuaiki Stream (16518000) 

was chosen as the index station because of its record length 

(1914–2003) and favorable geographic location. Adjustments 

based on the index-station method resulted in decreases to the 

50-percent duration total flow, 50-percent duration base flow, 

95-percent duration total flow, and 95-percent duration base 

flow computed on the basis of short-term records that averaged 7, 3, 4, and 1 percent, respectively.

For the drainage basin of each continuous-record gaged 

site and selected ungaged sites, morphometric, geologic, soil, 

and rainfall characteristics were quantified using Geographic 

Information System techniques. Regression equations relating 

the non-diverted streamflow statistics to basin characteristics 

of the gaged basins were developed using ordinary-leastsquares regression analyses. Rainfall rate, maximum basin 

elevation, and the elongation ratio of the basin were the basin 

characteristics used in the final regression equations for 50-

percent duration total flow and base flow. Rainfall rate and 

maximum basin elevation were used in the final regression 

equations for the 95-percent duration total flow and base flow. 

The relative errors between observed and estimated flows 

ranged from 10 to 20 percent for the 50-percent duration total 

flow and base flow, and from 29 to 56 percent for the 95-percent duration total flow and base flow.

The regression equations developed for this study were 

used to determine the 50-percent duration total flow, 50-percent duration base flow, 95-percent duration total flow, and 

95-percent duration base flow at selected ungaged diverted and 

undiverted sites. Estimated streamflow, prediction intervals, 

and standard errors were determined for 48 ungaged sites in 

the study area and for three gaged sites west of the study area. 

Relative errors were determined for sites where measured 

values of 95-percent duration discharge of total flow were 

available. East of Keanae Valley, the 95-percent duration discharge equation generally underestimated flow, and within and 

west of Keanae Valley, the equation generally overestimated 

flow. Reduction in 50- and 95-percent flow-duration values 

in stream reaches affected by diversions throughout the study 

area average 58 to 60 percent.

Introduction

For more than a century, surface-water diversion systems 

have transported water from the wet, northeastern part of 

Maui, Hawaii, to the drier, central part of the island, mainly 

for large-scale sugarcane cultivation. Since the 1930’s, the Territory and then the State issued water permits to Alexander and 

Baldwin, Inc., Hawaiian Commercial and Sugar Co., and East 

Maui Irrigation Co., Ltd. (EMI), for the diversion of water 

from streams in northeast Maui. The collection system consists of 388 separate intakes, 24 miles of ditches, and 50 miles 

of tunnels, as well as numerous small dams, intakes, pipes, and 

flumes (Wilcox, 1996). With few exceptions, the diversions 

capture all of the base flow, which represents the ground-water 

contribution to total streamflow, and an unknown percentage 

of total streamflow at each stream crossing. During 1925–97, 

total flow for the diversion systems measured at Honopou 

Stream, to the west of the study area where records of total 

diversion-system flow are most complete, averaged about 163 

Mgal/d (million gallons per day) (Gingerich, 1999). The highest average flow for an individual ditch system was measured 

in the Koolau/Wailoa Ditch system, where total flow crossing Honopou Stream averaged 110 Mgal/d for 1924–87. The 

source of diverted water is a watershed with an area of about 

56,000 acres, about two-thirds of which is owned by the State 

(Wilcox, 1996) and managed by the State Department of Land 

and Natural Resources.

The Hawaii State Water Code mandates that the Commission on Water Resource Management (CWRM) establish 

Median and Low-Flow Characteristics for Streams under 

Natural and Diverted Conditions, Northeast Maui, Hawaii

By Stephen B. Gingerich
a statewide instream-use protection program (Chapter 174C71, Hawaii Revised Statutes). The principal mechanism that 

CWRM has for the protection of instream uses is establishing 

instream flow standards. “Each instream flow standard shall 

describe the flows necessary to protect the public interest in 

the particular stream. Flows shall be expressed in terms of 

variable flows of water necessary to protect adequately fishery, 

wildlife, recreational, aesthetic, scenic, or other beneficial 

instream uses in the stream in light of existing and potential 

water developments including the economic impact of restriction of such use” (Chapter 174C-71, Hawaii Revised Statutes). 

CWRM has recognized certain instream uses as beneficial, 

including: (1) maintenance of fish and wildlife habitat, (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) 

maintenance of water quality, (6) conveyance of irrigation 

and domestic water supplies to downstream points of diversion, and (7) protection of traditional and customary Hawaiian 

rights.

The U.S. Geological Survey, in cooperation with CWRM 

and in collaboration with the Maui Department of Water Supply, the Hawaii State Board of Land and Natural Resources, 

and East Maui Irrigation Co., Ltd., undertook an investigation 

to assist in determining equitable, reasonable, and beneficial 

instream and off-stream uses of the surface-water resources of 

northeast Maui. The overall objectives of the 3-year study are 

to (1) assess the effects of existing surface-water diversions on 

flow characteristics for perennial streams in northeast Maui, 

(2) characterize the effects of diversions on instream temperature variations, and (3) estimate the effects that streamflow 

restoration (full or partial) will have on habitat availability 

for native stream fauna (fish, shrimp, and snails) in northeast 

Maui. Scientific information generated by the overall study 

will allow CWRM to complete its work on documenting water 

rights and uses associated with northeast Maui streams and 

analyzing the economic effects of curtailing existing uses 

on the streams, and to then establish technically defensible 

instream flow standards for those streams.

Purpose and Scope

This report addresses objective 1 described above. This 

report presents selected estimated flow-duration statistics for 

streams in northeast Maui, Hawaii, and describes the analyses 

done to develop and evaluate the methods used in estimating 

the statistics. Estimated streamflow statistics are presented for 

sites where various amounts of streamflow data are available 

and for locations where no data are available. Morphometric, 

hydrologic, and geologic basin characteristics are provided for 

each stream basin in the study area. Equations used to estimate 

the 50- and 95-percent duration flows of total streamflow and 

stream base flow at ungaged locations are presented. An evaluation of the accuracy of the equations and limitations for their 

use is also provided. Most-reliable estimates of streamflow 

statistics for natural (undiverted) and unnatural (diverted) sites 

on 21 streams and the basis for these estimates are provided. 

The statistics for undiverted and diverted flow were compared 

to assess the effects of existing surface-water diversions on 

flow characteristics for perennial streams in northeast Maui.

Description of Study Area

The study area lies on the northern flank of the East 

Maui Volcano (Haleakala), which forms the eastern part of 

the island of Maui, the second-largest island in the Hawaiian archipelago. The study area, covering about 67 mi2, is 

bounded to the north by about 11 mi of coastline and lies 

between (and includes) the drainage basins of Kolea Stream 

to the west and Makapipi Stream to the east (fig. 1). Land-surface altitudes range from sea level to 10,000 ft at the summit 

of Haleakala. The topography is gently sloping except for the 

steep sides of gulches and valleys that were eroded by the 

numerous streams. The largest valley is Keanae Valley, which 

extends from the coast to Haleakala Crater where the valley 

walls are nearly 1,000 ft high. Most of the study area is made 

up of forest reserves; at intermediate altitudes, rain forests 

densely cover the slopes up to about 7,000 ft. Grasses and 

shrubs cover the upper slopes to the north wall of Haleakala 

Crater. Two small villages (Keanae and Wailua) are at low altitudes along the coast at the mouth of Keanae Valley. Land use 

around the villages is mainly small-scale agriculture, including 

wetland taro cultivation.

Streams flow generally south to north from the high 

altitude flank of Haleakala to the coast. Twenty-two named 

streams reach the coast in the study area. Access to streams is 

made difficult by the steep rugged terrain of the incised stream 

valleys and dense native and non-native vegetation. Rainfall 

is highly orographic and rates average between about 45 in/yr 

at the summit of Haleakala to greater than 350 in/yr at about 

2,500-ft altitude. Rainfall at the coast ranges from 120 to 160 

in/yr (Giambelluca and others, 1986).

Previous Studies

Low-flow duration statistics have not previously been 

estimated specifically for ungaged streams in the study area of 

northeast Maui. Fontaine and others (1992) developed regression equations (one for Oahu, Molokai, and Hawaii, and one 

for Maui and Kauai) to estimate median flows at ungaged, 

unregulated, perennial streams in the State. Data from gaging 

stations on ten streams in the northeast Maui study area were 

used in developing the median-flow equations. Hirashima 

(1965) and Matsuoka (1983) computed flow statistics for gaging stations throughout the State of Hawaii, including some 

stations in the study area. Yamanaga (1972) developed regression equations for low-flow frequency to describe annual 

minimum 7-day and 30-day mean flows at 2- and 20-year 

recurrence intervals using data from selected windward and 

leeward gaged basins across the State, including 14 stations in 

the current study area. The equations and flow-duration statistics presented in this report supersede any previously reported 

equations or flow-duration statistics. Gingerich (1999) 

2 Median and Low-Flow Characteristics for Streams under Natural and Diverted Conditions, Northeast Maui, Hawaii
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Figure 1. Northeast Maui study area, island of Maui, Hawaii.

Introduction 3
described the ground-water occurrence and contribution to 

streamflow for northeast Maui covering an area encompassing the current study area. That report detailed the amount of 

streamflow, base flow, and surface-water diversions in streams 

and gave detailed descriptions of low-flow measurements 

made in many of the streams in the current study area.

Numbering System for Surface-Water Gaging 

Stations

The surface-water gaging stations mentioned in this 

report are numbered according to the USGS “downstream 

order” numbering system. Station numbers increase in a 

downstream direction along the main stream. All stations on 

a tributary entering upstream from a mainstream station have 

lower station numbers. A station on a tributary that enters 

between two mainstream stations is given a number between 

those two station numbers. In this report, the complete 8-digit 

downstream-order number for each gaging station has been 

abbreviated to the middle four digits, for example, 16518000 

becomes 5180.

Acknowledgments

The author would like to thank Chiu Yeung and ChienHwa Chen for delineating drainage basins and determining the 

basin characteristics, and Richard Fontaine and Michael Wong 

for assistance with the statistical analysis used in this report. 

Layout work on this report was done by Luis Menoyo. East 

Maui Irrigation Co., Ltd. provided cooperation and assistance 

in accessing the study area.

Streamflow Characteristics at 

Continuous-Record Stream-Gaging 

Stations

Values of daily mean flow are used to determine total 

streamflow and base flow flow-duration statistics for continuous-record stream-gaging stations. The USGS has operated 16 

continuous-record stream-gaging stations for various periods 

at unregulated sites in or near the northeast Maui study area 

since 1910 (Fontaine, 1996), although only two of these stations (station 5080 on Hanawi Stream near Nahiku and station 

5180 on West Wailuaiki Stream near Keanae) are currently 

active (Plate 1, table 1). In addition, records from 17 continuous-record stream-gaging stations on regulated sites are available for analysis.

The USGS established standard methods for estimating 

flow-duration statistics for stream-gaging stations (Searcy, 

1959). A flow-duration curve is a graphical representation of 

the percentage of time streamflows for a given time interval 

(usually daily) are equaled or exceeded over a specified period 

at a stream site (fig. 2). Flow-duration curves are constructed 

by first ranking all of the daily mean discharge values for 

the period of record at a gaging station, next computing the 

probability of each value being equaled or exceeded, and 

then plotting the discharges against their associated exceedance probabilities. Flow-duration statistics are points along 

the flow-duration curve. For example, the 50-percent duration 

streamflow (or median streamflow; Q50) has been exceeded 50 

percent of the time during the specified period. Flow-duration 

statistics reflect streamflow conditions only for the period of 

record for which they were calculated. If the period of record 

analyzed is sufficiently long, the flow-duration statistics can be 

considered an indicator of probable future conditions (Searcy, 

1959). In an analysis of the data from five long-term stream 

gages on Oahu, the median discharge determined from a 10-yr 

streamflow record had a standard error of 15 percent, whereas 

the standard error for the median discharge determined from a 

50-yr record improved to 6 percent (Fontaine, 1996).

At three regulated gaging stations (5090, 5110, and 

5210), total unregulated streamflow was calculated by adding 

the daily flows for the gaging station of interest to the corresponding daily flows for an upstream gaging station on the 

same stream but above the 1,300-ft (Koolau Ditch) diversion (the flows at stations 5080, 5100, and 5190 plus 5200, 

respectively). Flow-duration statistics were then calculated 

using the combined record. This technique is appropriate for 

estimating the low flows of interest in this study because the 

diversion captures all low flows much greater than the value of 

the median total flow, TFQ50, so that the downstream gaging 

station on each stream measures only that flow gained below 

the diversion. Combined flows at the downstream gaging station estimated from this technique are incorrect only when the 

diversion is overtopped, which is generally 20 to 30 percent of 

the time.

The assumption that the diversion systems within the 

1,700- to 1,200-ft altitude interval intercept all low streamflows up to at least the TFQ50 is based on measurements made 

at four stream diversions in the study area. The overtopping 

discharges in the four monitored streams were significantly 

greater than the TFQ50 discharge for each stream. These sites 

are separated into two categories: (1) sites on West Wailuaiki 

and Hanawi Streams where water levels at the diversion structures and streamflow were measured concurrently at active 

continuous-record gaging stations, and (2) sites on Waikamoi 

and Honomanu Streams, where water levels at the diversion 

structures were measured concurrently with water levels at 

staff plates from former continuous-record gaging stations

(fig. 3). At all four sites, submersible transducers were used 

to monitor the water level in the stream every 15 minutes relative to the crests of the diversion dams preventing water from 

flowing further downstream. When a transducer indicated that 

the water level was higher than the crest of the diversion dam, 

it was assumed that water was flowing downstream past the 

diversion dam. When the transducer indicated that the water 

level was lower than the crest of the diversion dam, it was 

assumed that all flow in the stream was captured by the diver4 Median and Low-Flow Characteristics for Streams under Natural and Diverted Conditions, Northeast Maui, Hawaii
Table 1. Continuous-record surface-water gaging stations operated by the U.S. Geological Survey, northeast Maui, Hawaii.

[Abbreviated station numbers are highlighted in bold; active station locations are shown in bold italics]

Gagingstation 

number

Station location Period of record Station altitude 

(feet)

Low flow 

regulated during 

period of record

16507000 Makapipi Stream 1932-45 920 Yes

16508000 Hanawi Stream 1914-15, 1921-Present 1,318 No

16509000 Hanawi Stream 1932-47, 1992-95 500 Yes

16510000 Kapaula Gulch 1921-63 1,346 No

16511000 Kapaula Gulch 1932-47 540 Yes

16513000 Waiaaka Stream 1932-47 650 Yes

16514000 Paakea Gulch 1932-47 650 Yes

16515000 Waiohue Gulch 1921-63 1,316 No

16516000 Kopiliula Stream 1914-17, 1921-1958 1,292 No

16517000 East Wailuaiki Stream 1914-17, 1922-58 1,329 No

16518000 West Wailuaiki Stream 1914-17, 1921-Present 1,343 No

16519000 West Wailuanui Stream 1914-17, 1921-58 1,268 No

16520000 East Wailuanui Stream 1914-17, 1921-58 1,287 No

16521000 Wailuanui Stream 1932-36, 1938-47 620 Yes

16522000 Palauhulu diversion ditch to Keanaea 1934-68 51 Yes

16524000 Honomanu Stream 1921-27, 1932-34, 1962-68 2,900 No

16527000 Honomanu Stream 1914-17, 1921-64 1,733 No

16531000 Kula diversion from Haipuaena Stream 1946-68 4,320 Yes

16531100 Haipuaena Stream 1946-68 4,320 Yes

16535000 Haipuaena diversion ditch to Kolea Stream 1938-60 1,866 Yes

16536000 Haipuaena Stream 1946-60 1,512 Yes

16542000 East Branch Puohokamoa Stream 1921-27, 1931-33 2,800 No

16543000 Middle Branch Puohokamoa Stream 1921-27, 1932-34, 1962-69 2,900 Yes

16544000 West Branch Puohokamoa Stream 1921-28, 1932-34 2,800 Yes

16545000 Puohokamoa Stream 1914-17, 1921-71 1,322 Yes

16552800 Waikamoi Stream 1953-68 4,487 Yes

16554000 Waikamoi Stream 1921-28, 1932-34 3,000 Yes

16554500 East Branch Waikamoi Stream 1921-28, 1932-33 3,020 Yes

16555000 Waikamoi Stream 1922-57 1,294 Yes

16556000 Waikamoi Stream 1914-17, 1921-22 1,150 Yes

16557000 Alo Stream 1914-17, 1921-57 1,248 No

16565000b Kaaiea Gulch 1921-62 1,310 No

16566000b Oopuola Stream 1930-57 1,205 No

16570000b Nailiihaele Stream 1910-11, 1913-75 1,205 No

16577000b Kailua Stream 1910-11, 1913-58 1,253 No a USGS station previously published as “Taro patch feeder ditch at Keanae, Maui”

b

 located west of current study area

Streamflow Characteristics at Continuous-Record Stream-Gaging Stations 5
sion and the stream was dry immediately downstream of the 

diversion.

At West Wailuaiki and Hanawi Streams, the water 

levels were compared with discharge determined from stage 

measurements made every 15 minutes at the active continuous-record gaging stations upstream (stations 5180 and 5080, 

respectively). Relation plots of water level and stream discharge show the range of discharges at which the diversion 

dam is overtopped and flow continues downstream. For West 

Wailuaiki Stream, the overtopping is initiated at discharge 

ranging from 20 to 30 ft3/s (TFQ30 to TFQ20 on the basis of 

the flow-duration plot in fig. 2). In other words, streamflow 

does not pass the diversion dam at 1,300 ft on West Wailuaiki 

Stream roughly 70 to 80 percent of the time. On Hanawi 

Stream, the overtopping discharge ranges from 15 to 30 ft3/s 

(TFQ25 to TFQ15 on the basis of the flow-duration plot for 

station 5080 discussed later in fig. 7). Streamflow does not 

pass the dam at 1,300 ft on Hanawi Stream roughly 75 to 85 

percent of the time.

At Honomanu and Waikamoi Streams, the water levels 

relative to the crests of the diversion dams were compared to 

water levels collected every 15 minutes at staff plates bolted 

into the bedrock in former gaging station pools upstream from 

the dams. Ratings for these staff plates are available from the 

U.S. Geological Survey archives for the time when the stations 

were discontinued in 1957. Although some erosion on the 

bedrock and concrete controls at these former gaging stations 

was observed, the assumption was made that the ratings for 

staff plates would still provide a reasonable range of flow 

estimates in the stream to estimate the overtopping discharge. 

At Honomanu Stream, the overtopping discharge ranges from 

15 to 18 ft3/s (TFQ25 to TFQ22 on the basis of the flow-duration plot for station 5270 discussed later in fig. 7). Therefore, 

streamflow does not pass the diversion dam at 1,720 ft on 

Honomanu Stream roughly 75 to 78 percent of the time. On 

Waikamoi Stream, where the water level-discharge relation 

recorded is more variable, the overtopping discharge is at least 

25 ft3/s (TFQ20 on the basis of the flow-duration plot for station 5550 discussed later in fig. 7). Streamflow does not pass 

the diversion dam at 1,200 ft on Waikamoi Stream roughly 80 

percent of the time.

The technique used to determine the combined median 

and low-flow statistics for a gaging station downstream of the 

major diversion can be illustrated by using data from Hanawi 

Stream. From gaging station 5080, upstream of the Koolau 

diversion, TFQ50 is 7.1 ft3/s (table 2) and from gaging station 

5090, downstream of the Koolau diversion and several spring 

inflows, TFQ50 is 22 ft3/s. Because the Koolau Ditch captures 

at least 15-30 ft3/s at Hanawi Stream near 1,300 ft altitude, 

the median flows measured at gaging station 5090 are only 

those flows gained downstream of the Koolau diversion. The 

combined TFQ50 at gaging station 5090 is estimated to be 29 

ft3/s (7.1 + 22 ft3/s). Median and low-flow statistics for 5090 

were generated in two ways, from combined daily flows at 

the two stations and by adding the statistics calculated from 

each station’s daily flows individually (Table 3). The results 

of each calculation compare favorably, indicating that, for the 

study area, flow statistics for sites on gaining streams above 

and below the major diversion can be estimated by adding the 

statistics for each site. For the three stations in the study area 

(5090, 5110, and 5210), the value determined from adding 

the flow statistics was always less than the value determined 

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Figure 2. Flow-duration curves of total streamflow and base flow at gaging station 

5180 on West Wailuaiki Stream, northeast Maui, Hawaii, for period 1914-2002.

6 Median and Low-Flow Characteristics for Streams under Natural and Diverted Conditions, Northeast Maui, Hawaii
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Figure 3. Relation between water level and stream discharge at diversions on selected streams within the 1,700- to 1,200-ft altitude interval, northeast Maui, Hawaii. 

Streamflow Characteristics at Continuous-Record Stream-Gaging Stations 7
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Figure 3. Relation between water level and stream discharge at diversions on selected streams within the 1,700- to 1,200-ft altitude interval, northeast Maui, Hawaii–Continued.

8 Median and Low-Flow Characteristics for Streams under Natural and Diverted Conditions, Northeast Maui, Hawaii
Table 2. Selected estimated median and low-flow characteristics for continuous-record sites, northeast Maui, Hawaii.

[Qxx is the xx-percent flow duration of streamflow; ft3/s, cubic feet per second; base period is 1914-17, 1921-2001; active stations are shown in bold italics; +, combined with record from indicated station; index station is station 5180; --, no adjustment; NA, not applicable]

Gaging-station 

number

Length of 

concurrent 

record 

(years)

Q50 total flow 

Q50 base flow 

Q95 total flow 

Q95 base flow 

during

concurrent 

period

(ft3/s)

adjusted to 

index station

(ft3/s)

during

concurrent 

period

(ft3/s)

adjusted to 

index station

(ft3/s)

during

concurrent 

period

(ft3/s)

adjusted to 

index station

(ft3/s)

during

concurrent 

period

(ft3/s)

adjusted to 

index station

(ft3/s)

5070 13 2.9 2.2 1.6 1.3 0.00 0.00 0.00 0.005080 82 7.1 -- 4.6 -- 2.4 -- 2.2 --5090+5080 18 29 28 25 24 19 19 19 195100 42 5.2 4.9 2.9 2.8 1.3 1.1 1.0 0.905110+5100 15 8.1 7.5 5.3 5.1 3.4 3.3 3.1 3.05130 15 0.90 0.86 0.79 0.77 0.54 0.54 0.54 0.535140 15 4.2 4.0 3.9 3.8 3.1 3.0 3.1 3.05150 42 6.5 6.2 5.0 5.0 3.1 3.0 2.9 2.85160 40 9.1 8.0 5.4 5.0 2.6 2.3 2.1 2.05170 39 10 9.1 6.1 5.7 3.1 2.8 2.6 2.55180 83 10 -- 6.0 -- 2.5 -- 2.1 --5190 40 5.1 4.4 2.7 2.4 1.1 1.0 0.93 0.855200 40 3.7 3.2 2.2 2.0 1.0 0.90 0.82 0.805210+5190+5200 13 9.8 10 5.6 6.1 2.4 2.5 2.1 2.05220a 34 3.4 -- NA NA 2.4 -- NA NA5240 14 2.0 2.2 0.88 0.93 0.31 0.37 0.28 0.305270 46 6.2 5.7 3.0 2.8 1.2 1.0 0.82 0.745311+5310a 22 0.46 0.50 0.15 0.17 0.05 0.03 0.03 0.035360+5310a+5350 14 6.8 6.8 3.5 3.5 2.1 1.7 1.6 1.35420 8 0.93 0.88 0.58 0.53 0.31 0.29 0.19 0.275430 15 1.3 1.4 0.62 0.67 0.18 0.21 0.12 0.155440 9 1.9 1.9 1.1 1.0 0.46 0.55 0.37 0.445450 53 13 12 6.8 6.4 2.8 2.5 2.2 2.15528 15 0.12 0.14 0.05 0.06 0.02 0.02 0.02 0.015540 7 2.5 2.5 1.3 1.2 0.62 0.69 0.32 0.465545 8 1.5 1.3 0.80 0.72 0.46 0.47 0.37 0.435550 35 7.9 7.0 3.8 3.5 1.3 1.1 0.89 0.805560 4 15 7.1 5.1 3.6 2.0 1.5 1.6 1.05570 39 3.1 2.7 1.6 1.4 0.77 0.70 0.62 0.58

a gaging station on diversion ditch

Streamflow Characteristics at Continuous-Record Stream-Gaging Stations 9
Table 3. Comparison of flow statistics computed for stream sites where natural flows are estimated, using data from 

multiple continuous-record gaging stations, northeast Maui, Hawaii.[All flows are in cubic feet per second; relative error is (column 4 – column 5)/column 4 x 100]

Flow 

statistic

Downstream 

gaging station

Upstream gaging 

station

Sum of upstream 

and downstream 

flow statistic

Flow statistic based 

on combined upstream and downstream daily flows Relative error, in percent

5090 5080

TFQ50 19 7.1 26 28 -7BFQ50 19 4.6 24 24 0TFQ95 16 2.4 18 19 -5BFQ95 16 2.2 18 19 -5

5110 5100

TFQ50 4.7 2.4 7.1 7.5 -5BFQ50 2.8 2.2 5.0 5.1 -2TFQ95 1.1 1.9 3.0 3.3 -9BFQ95 0.90 1.9 2.8 3.0 -7

5210 5190 5200

TFQ50 1.6 4.4 3.2 9.2 10 -8BFQ50 1.0 2.4 2.0 5.4 6.1 -11TFQ95 0.39 1.0 0.90 2.3 2.5 -8BFQ95 0.32 0.85 0.80 2.0 2.0 0

10 Median and Low-Flow Characteristics for Streams under Natural and Diverted Conditions, Northeast Maui, Hawaii
by first combining the concurrent daily flows, but the relative 

error in the value determined from adding the flow statistics 

was less than or equal to 10 percent in each case.

On Haipuaena Stream (plate 1), gaging station 5310 

recorded diverted flow into the Upper Kula Pipeline near 

4,300 ft altitude, and gaging station 5311 recorded streamflow 

past the diversion (Fontaine, 1996). These two records were 

added together to obtain the total streamflow at this altitude. 

Further downstream, flow diverted in Kolea Stream was 

measured at gaging station 5350. This flow was added to that 

at gaging station 5360 (1,512 ft altitude) upstream of Spreckels Ditch and gaging station 5310 to obtain a value for total 

streamflow at 1,512 ft altitude.

Gingerich (1999) used a computerized base-flow separation method described by Wahl and Wahl (1995) to estimate 

the base-flow component of streamflow for northeast Maui 

streams. Two variables, N (number of days) and f (turningpoint test factor) must be assigned values in the method. The 

method divides the daily streamflow record into non-overlapping N-day periods and determines the minimum flow within 

each N-day window. If the minimum flow within a given Nday window is less than f times the minimums in the adjacent 

N-day windows, then the central window minimum is made 

a turning point on the base-flow hydrograph. Wahl and Wahl 

(1995) recommend a value of 0.9 for the turning-point test factor for most applications. The value of N determined for each 

stream is shown in table 2 of Gingerich (1999). A base-flowduration curve can than be constructed using the daily baseflow data (fig. 2).

Streamflow records generally are adjusted to a common 

base period for comparison so that differences in flow among 

stations reflect spatial differences in climate and drainagebasin characteristics and not simply temporal differences 

in rainfall. Flow-duration curves based on short records are 

unreliable for predicting the future flow pattern, but they can 

be made more reliable by adjusting them to represent longer 

periods. The index-station method described in Searcy (1959) 

was used to adjust all of the streamflow records used in this 

analysis to a common period (called the base period).

Index station selection

The two currently active continuous-record gaging stations (5180 on West Wailuaiki Stream and 5080 on Hanawi 

Stream) are the obvious candidates for index stations in this 

study. Both have been operated nearly continuously from 1914 

to the present (2004), with a break during 1918–1920. The 

median total (TFQ50) and median base flow (BFQ50) for gaging station 5180 are 10 ft3

/s and 6.0 ft3/s, respectively, and the 

TFQ50 and BFQ50 for gaging station 5080 are 7.1 ft3/s and 4.6 

ft3/s, respectively (fig. 4 and table 2).

The records for gaging-stations 5180 and 5080 appear 

to have long-term downward trends in annual median total 

flow and base flow during the period 1914–present (fig. 4) 

and a Kendall’s Tau trend test (Helsel and Hirsch, 1992) on 

those flow statistics confirms such a trend (table 4). Rather 

than decreasing monotonically, the flow might actually have 

decreased in a stepwise manner, and examination of figure 

4 indicates that such a stepwise decrease may have occurred 

about 1941–42. The median total flow at gaging station 5180 

during 1914–42 was 14 ft3/s, and after 1942 was 9.6 ft3/s. 

Analysis of a subset of the data, for the period 1942–2001, 

shows no statistical trend in median streamflow after the indicated earlier stepped decrease in flow (table 4). No obviously 

apparent reason exists for such a stepped decrease in median 

total flow and base flow about 1941–42. Such stepped changes 

in flow trends are typically caused by changes in a watershed 

such as reforestation or by the addition of a streamflow diversion but there is little evidence that these factors caused the 

changes in flow at stations 5180 (on West Wailuaiki Stream) 

and 5080 (on Hanawi Stream). Helsel and Hirsch (1992) 

strongly caution against performing step-trend analysis without prior knowledge of an event that would contribute to such 

a change in streamflow. Additionally, rainfall records for this 

area do not cover the entire period of streamflow record so it 

is not possible to determine if rainfall patterns have changed 

similarly to the flow. Therefore, flow statistics for these stations were calculated on the basis of the entire period of record 

with no adjustments made for monotonic or step-wise trends 

in the data.

Gaging station 5180 on West Wailuaiki Stream is favorably located geographically as an index station, because it is 

near the center of the study area, whereas gaging station 5080, 

on Hanawi Stream, is at the eastern end of the study area. 

Therefore, all adjustments of streamflow characteristics to a 

common base period for the continuous-record stations were 

made using only gaging station 5180 as the index station. The 

record for gaging station 5080 was not adjusted because the 

record was the same length as the index-station base period.

Adjustments to streamflow characteristics for a 

common period using the index-station method

Relations between the index station and each shorter-term 

record at the other gaging stations were developed using the 

following steps (Searcy, 1959):

1. Flow-duration curves were developed for the station 

with a short-term record and the index-station record 

for concurrent periods of record.

2. Discharges for 13 flow-duration points, ranging from 

1 to 99 percent, at the short-term station were plotted 

on logarithmic scales against the same flow-duration 

points at the index station.

3. A line or smooth curve was drawn through the points. 

The upper part of the line is typically a 45-degree line 

parallel (assuming 1 log cycle on x-axis is same length 

as 1 log cycle on y-axis) to lines of equal yield (drainage-area ratio) and equal flow (rainfall ratio) if the 

Streamflow Characteristics at Continuous-Record Stream-Gaging Stations 11
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Figure 4. Annual median streamflow and base flow for 1914-2002 at gaging stations 5180 on West Wailuaiki Stream and 5080 on Hanawi Stream, northeast Maui, Hawaii. 

12 Median and Low-Flow Characteristics for Streams under Natural and Diverted Conditions, Northeast Maui, Hawaii
Table 4. Trend analysis of annual median flow at active gaging station records for West Wailuaiki (5180) and Hanawi (5080) Streams, northeast Maui, 

Hawaii.[Statistically significant trends shown in bold]

Gaging station 

number Annual median streamflow Period of record Kendall’s Tau P-level Slope of trend

5180 Total flow 1914-17, 1921-2001 -0.171 0.022 -0.0395180 Base flow 1914-17, 1921-2001 -0.210 0.005 -0.0255080 Total flow 1914-15, 1921-2001 -0.194 0.010 -0.0305080 Base flow 1914-15, 1921-2001 -0.296 0.000 -0.0255180 Total flow 1942-2001 0.012 0.893 0.0005180 Base flow 1942-2001 0.005 0.964 0.0015080 Total flow 1942-2001 -0.010 0.919 0.0005080 Base flow 1942-2001 -0.069 0.440 -0.005

Streamflow Characteristics at Continuous-Record Stream-Gaging Stations 13
streams have similar high flow characteristics. Deviation from the line at the lower points is commonly an 

indication of different geologic characteristics that 

effect low flows between the stream basins.

4. The adjusted discharges at the various flow-duration 

points for the short-term station are graphically determined from the plot using the corresponding flowduration points from the index station for the entire 

period of record (base period) of the index station.

For example, selected flow-duration points for total 

flow and base flow at gaging station 5170 on East Wailuaiki 

Stream, which was operated during 1914–17 and 1922–58, are 

plotted against the flow-duration points for the index station 

(5180) during the same period on logarithmic axes (fig. 5) and 

smooth fitting lines are drawn through the points. Matching 

base period flow-duration points are determined from the relation plot (e.g. base period TFQ50 at station 5180 = 10 ft3

/s and 

adjusted TFQ50 at station 5170 = 9.0 ft3/s; base period TFQ95

at station 5180 = 2.5 ft3/s and adjusted TFQ95 at station 5170 = 

2.8 ft3/s) and then plotted to determine the adjusted flow-duration curve for station 5170 (fig. 6). Similar relation plots and 

adjusted flow-duration curves were computed for 26 continuous-record gaging stations for streams in the study area (fig. 

7).

The adjusted Q50 and Q95 statistics for total flow and base 

flow for the 26 stations are listed in table 2. Adjustments to 

TFQ50 ranged from a 17-percent increase (station 5528) to a 

53-percent decrease (station 5560), and averaged a 6-percent 

decrease. Adjustments to TFQ95 ranged from a 20-percent 

increase (station 5440) to a 40-percent decrease (stations 5310 

+ 5311) and averaged a 5-percent decrease. Adjustments to 

BFQ50 ranged from a 20-percent increase (station 5528) to a 

29-percent decrease (station 5560) and averaged a 4-percent 

decrease. Adjustments to BFQ95 ranged from a 44-percent 

increase (station 5540) to a 50-percent decrease (station 5528) 

and averaged a 1-percent decrease. In general, the largest 

adjustments were needed for stations with the shortest record 

lengths.

The point on the total flow-duration curve at which 

streamflow is equivalent to median base flow provides added 

information about the ground-water contribution to streamflow. BFQ50 ranges from 56 percent to 78 percent on the total 

flow-duration curve for the gaged basins and averages 70 percent (table 5). BFQ95 ranges from 95 percent to 98 percent on 

the total flow duration curve for the gaged basins and averages 

96 percent. Gaging stations east of the index station on West 

Wailuaiki Stream all have the same or higher rainfall-normalized low flow relative to the index station, indicating a higher 

ground-water contribution to these streams. The mapped 

springs that contribute to the low flows in these streams are 

listed in the “Comments” column in table 5. Gaging stations 

west of the index station generally have the same or lower 

rainfall-normalized low flows relative to the index station, 

indicating that the ground-water contribution to streamflow 

is relatively less to the west. The effects of minor upstream 

diversions in this area also are apparent from the relatively 

lower low-flows measured at the gaging stations.

Estimation of Flow Characteristics of 

Ungaged Streams

Multiple linear-regression analysis is a standard technique used to develop equations for estimating streamflow 

statistics for ungaged sites (Koltun and Schwartz, 1986; 

Vogel and Kroll, 1990; Ludwig and Tasker, 1993; Ries and 

Friesz, 2000). In this study, a selected streamflow statistic 

(the duration discharges TFQ50, TFQ95, BFQ50, or BFQ95) at 

unregulated, gaged sites was the dependent variable and the 

quantified basin characteristics, rainfall rates, and surficial 

geologic units were the independent variables used as input 

in the regression analysis. The regression analysis statistically 

relates the dependent variable to the independent variables and 

results in an equation that can be used to estimate the selected 

streamflow statistic for a site where no streamflow data are 

available. The goal of the regression algorithm is to minimize 

the differences between the values of the dependent variable 

used in the analysis (observed values) and the corresponding 

values provided by the regression equations (estimated or fitted values).

Drainage-Basin Characteristics

For the drainage basin of each continuous-record gaged 

site and selected ungaged sites, the morphometric, geologic, 

and rainfall characteristics were quantified using Geographic 

Information System (GIS) techniques.

Morphometric characteristics

Drainage basins were delineated on the basis of 10-meter 

digital elevation model (DEM) data and the GIS program 

GISWeasel (U.S. Geological Survey, 2004). The drainage 

basins thus delineated (plate 1) were checked against existing 

manually determined drainage-basin boundaries for gaged 

sites to ensure the reliability of the computerized delineation 

routine. Minor adjustments were made to the boundaries of 

those drainage basin for which the computer-delineated drainage area differed from the manually determined drainage area 

by more than 5 percent (Chiu Yeung, U.S. Geological Survey, 

written commun., 2003). The GIS program Basinsoft (Harvey 

and Eash, 1996) was used to quantify basin characteristics 

considered in the regional regression analysis. Basinsoft uses 

GIS data layers of drainage divides, hydrography, and a digital 

elevation model to automatically and efficiently quantify 22 

morphometric characteristics for each drainage basin selected. 

These characteristics are described in Appendix A. Computed 

basin characteristics for the gaged basins are listed in Table 

6 and those for selected ungaged basins are listed in table 7. 

14 Median and Low-Flow Characteristics for Streams under Natural and Diverted Conditions, Northeast Maui, Hawaii
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Figure 5. Correlation between flows at gaging stations 5170 (East Wailuaiki Stream) and 5180 (West Wailuaiki Stream), based on discharge of equal percentage duration for period of concurrent record 1914-17 and 1922-58, northeast Maui, Hawaii.

Estimation of Flow Characteristics of Ungaged Streams 15
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Figure 6. Unadjusted and adjusted flow-duration curves of total streamflow and 

base flow at gaging station 5170 on East Wailuaiki Stream, northeast Maui, Hawaii.

The ungaged basins are denoted by an abbreviation for the 

stream name followed by a U, M, or L for upper, middle, or 

lower locations on the stream (plate 1). These three locations 

on each stream roughly correspond to the following settings: 

(U) upstream of the main diversion ditch at around 1,700- to 

1,200-ft altitude; (M) roughly 600- to 500-ft altitude; and (L) 

near the stream mouth. These locations were chosen to help 

meet the goals of objective 3 of this study regarding the habitat 

available in the stream for native species.

Hydrologic and geologic characteristics

Average yearly total rainfall rates for each drainage basin 

were determined using GIS techniques by overlaying the 

drainage-basin boundaries on a map of mean annual rainfall 

isohyets from Giambelluca and others (1986) (fig. 8). The 

overlying GIS layers created polygons that were assigned 

rainfall rates, in inches per year, equal to the average of the 

two bounding isohyets of each polygon. Each polygon area, in 

square feet, was multiplied by the assigned rainfall rate, after 

converting the rainfall rate to feet per second, to determine a 

volume rainfall rate, in cubic feet per second, for each polygon. Final rainfall rates were then determined by summing 

the rainfall volumes in a basin. In areas of equal rainfall rates, 

larger drainage basins would have larger total rainfall volumes 

and smaller drainage basins would have smaller total rainfall 

volumes. Average annual rainfall rates in the gaged basins 

ranged from 1.3 to 76 ft3/s (table 6). Average annual rainfall 

rates in the ungaged basins ranged from 1.9 to 192 ft3/s (table 

7).

Distributions of surficial geologic units in each gaged 

drainage basin were determined from a digital geology map by 

Sherrod and others (2003) (fig. 9). Three geologic units were 

considered, the Honomanu Basalt, the Kula Volcanics, and the 

Hana Volcanics (table 6). The percentage of each unit in the 

basin was determined by dividing the area of each unit in the 

basin by the total basin area and multiplying the result by 100. 

Only two gaged basins contained surficial exposures of Honomanu Basalt, both having less than 1 percent of the total area 

of each basin, so only Kula and Hana Volcanics were included 

in the following analysis.

Development of regression equations

Linear equations generated by use of regression analysis 

have the general form

Y b i = +0 1 b X1 2 + + b X2 + + b Xn n i ε (1)

where Yi is the estimate of the dependent variable for 

site i, X1 to Xn are the n independent variables, b0 to bn are the 

n+1 regression model coefficients, and ei is the residual error 

(difference between the observed and estimated value of the 

dependent variable for site i). Regression analysis results must 

be evaluated to make sure that the following assumptions are 

met: (1) equation 1 adequately describes the relation between 

the dependent and independent variables, (2) the mean of ei

is zero, (3) the variance of ei is constant and independent of 

the value of Xn, (4) values of ei are normally distributed, (5) 

values of ei are independent of each other, (6) all independent 

variables selected are statistically significant at the 5-percent 

level, (7) independent variables are not correlated, and (8) the 

16 Median and Low-Flow Characteristics for Streams under Natural and Diverted Conditions, Northeast Maui, Hawaii
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Estimation of Flow Characteristics of Ungaged Streams 17
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flow–Continued.

18 Median and Low-Flow Characteristics for Streams under Natural and Diverted Conditions, Northeast Maui, Hawaii
Figure 7. Correlation of flows at selected gaging stations in northeast Maui, Hawaii with flow at index station 5180 (West Wailuaiki 

Stream) based on discharge of equal percentage duration and unadjusted and adjusted duration curves of total streamflow and base 

flow–Continued.

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Estimation of Flow Characteristics of Ungaged Streams 19
Figure 7. Correlation of flows at selected gaging stations in northeast Maui, Hawaii with flow at index station 5180 (West Wailuaiki 

Stream) based on discharge of equal percentage duration and unadjusted and adjusted duration curves of total streamflow and base 

flow–Continued.

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20 Median and Low-Flow Characteristics for Streams under Natural and Diverted Conditions, Northeast Maui, Hawaii
Figure 7. Correlation of flows at selected gaging stations in northeast Maui, Hawaii with flow at index station 5180 (West Wailuaiki 

Stream) based on discharge of equal percentage duration and unadjusted and adjusted duration curves of total streamflow and base 

flow–Continued.

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Estimation of Flow Characteristics of Ungaged Streams 21
Figure 7. Correlation of flows at selected gaging stations in northeast Maui, Hawaii with flow at index station 5180 (West Wailuaiki 

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22 Median and Low-Flow Characteristics for Streams under Natural and Diverted Conditions, Northeast Maui, Hawaii
Figure 7. Correlation of flows at selected gaging stations in northeast Maui, Hawaii with flow at index station 5180 (West Wailuaiki 

Stream) based on discharge of equal percentage duration and unadjusted and adjusted duration curves of total streamflow and base 

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Estimation of Flow Characteristics of Ungaged Streams 23
Figure 7. Correlation of flows at selected gaging stations in northeast Maui, Hawaii with flow at index station 5180 (West Wailuaiki 

Stream) based on discharge of equal percentage duration and unadjusted and adjusted duration curves of total streamflow and base 

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24 Median and Low-Flow Characteristics for Streams under Natural and Diverted Conditions, Northeast Maui, Hawaii
Figure 7. Correlation of flows at selected gaging stations in northeast Maui, Hawaii with flow at index station 5180 (West Wailuaiki 

Stream) based on discharge of equal percentage duration and unadjusted and adjusted duration curves of total streamflow and base 

flow–Continued.

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Estimation of Flow Characteristics of Ungaged Streams 25
Table 5. Comparisons of base-flow to total-flow duration statistics and streamflow characteristics at selected stations to those at index gaging station 5180 on West 

Wailuaiki Stream, northeast Maui, Hawaii[Qxx is the xx-percent flow duration of streamflow; +, combined with record from indicated station]

Gaging-station number

Equivalent total flow durationdischarge, in percent Rainfall-normalized flow relative to index station

Comments

Q50 base flow

Q95 base flow Low flow relative to index station High flow relative to index station

5070 62 -- Lower Same Intermittent flow; dry 30 percent of time; Q95 not comparable5080 69 97 Higher Same5090+5080 66 96 Higher Same Includes Big and Hanawi Springs5100 72 98 Same Lower5110+5100 71 97 Higher Same Includes Pali Spring5130 56 95 Higher Same Includes unnamed springs5140 60 95 Higher Same Includes numerous unnamed springs5150 67 97 Higher Same5160 71 98 Higher Same5170 73 97 Higher Same5180 72 97 -- -- Index station5190 73 98 Same Same5200 72 97 Higher Same5210+5200+5190 71 97 Same Same Combination of several gages5240 78 97 Lower Same Lower low flows due to minor diversion at 3,000 ft altitude5270 75 98 Lower Same Lower low flows due to minor diversion at 3,000 ft altitude5311+5310 76 97 Lower Same Combination of two gages5360+5311+5310+5350 75 98 Same Lower Combination of several gages5420 75 98 Same Lower5430 72 98 Lower Same Lower low flows due to diversions at 3,000 ft and 4,300 ft altitude5440 74 97 Same Same Diversion effects not apparent5450 77 96 Same Lower Lower low flows due to diversions at 3,000 ft and 4,300 ft altitude5528 74 97 Lower Same 4,487 ft altitude; intermittent flow; dry 1 percent of time5540 74 95 Same Same5550 78 96 Lower Same Lower low flows due to diversions at 3,000 ft and 4,300 ft altitude5560 74 98 Same Same Gage operated before minor upstream diversions were active5570 76 97 Same LowerAverage 70 96

26 Median and Low-Flow Characteristics for Streams under Natural and Diverted Conditions, Northeast Maui, Hawaii
Table 6. Watershed characteristics for selected gaged stream drainage basins, northeast Maui, Hawaii

[Abbreviation definitions and units are described in appendix A; gaging stations in bold italics were used to develop the final regression equations for estimating flow-duration statistics; precipitation data modified from Giambelluca and others (1986); ft3/s, cubic feet per second; geology data from Sherrod and others (2003); ND, not determined]

Gaging-station 

number BL BP BR BS BW CCM CR DA ER MAXELEV MCL MCS MCSP MCSR MINELEV RB RN

5070 4.92 10.94 4283 1038 0.39 0.17 2.24 1.89 0.32 5219 4.6 887 0.16 0.94 936 10 254005080 6.34 14.90 6775 1557 0.57 0.18 2.21 3.62 0.34 8093 6.0 1036 0.19 0.95 1318 9 387985090 7.01 17.86 7587 1433 0.74 0.17 2.22 5.15 0.37 8093 7.0 971 0.23 1.00 506 7 450085100 5.40 9.19 2968 854 0.13 0.12 3.12 0.69 0.17 4325 4.1 690 0.16 0.76 1357 33 248945110 5.44 11.55 3787 1099 0.17 0.14 3.35 0.95 0.20 4325 4.9 745 0.18 0.90 538 25 275275130 1.66 2.42 881 1008 0.05 0.09 2.27 0.09 0.21 1587 1.1 922 0.04 0.63 706 24 102645140 3.15 4.39 1741 1023 0.11 0.11 2.10 0.35 0.21 2373 2.2 808 0.08 0.69 632 22 153305150 3.54 4.70 1413 885 0.15 0.16 1.83 0.53 0.23 2771 2.4 567 0.10 0.69 1358 19 89735160 7.37 15.83 6993 1652 0.53 0.15 2.27 3.88 0.30 8372 6.4 956 0.21 0.86 1379 11 465895170 7.58 16.02 7186 1527 0.46 0.16 2.41 3.51 0.28 8527 6.2 946 0.20 0.81 1341 13 441135180 8.33 17.08 7518 1761 0.44 0.16 2.51 3.69 0.26 8857 6.5 941 0.21 0.78 1339 15 471745190 7.14 17.19 6706 1797 0.26 0.17 3.54 1.88 0.22 8055 6.1 741 0.22 0.85 1349 21 386885200 2.67 5.92 1424 1162 0.19 0.17 2.34 0.51 0.30 2733 2.5 595 0.10 0.92 1309 11 85315210 9.18 19.51 7467 1736 0.30 0.18 3.32 2.75 0.20 8055 7.3 749 0.27 0.80 588 24 416355240 5.81 14.47 5420 1619 0.44 0.18 2.55 2.57 0.31 8331 5.4 965 0.18 0.94 2911 10 303195270 7.44 18.48 6594 1670 0.41 0.18 2.97 3.07 0.27 8331 6.9 915 0.23 0.93 1737 14 363385311 1.99 4.47 1645 1073 0.13 0.15 2.45 0.27 0.29 5979 1.7 952 0.06 0.87 4334 12 109865360 7.14 15.14 4468 1577 0.17 0.15 3.90 1.20 0.17 5979 6.0 714 0.22 0.84 1511 33 297335420 0.78 2.44 773 1793 0.18 0.16 1.82 0.14 0.55 3645 0.8 802 0.03 1.07 2872 3 48355430 3.50 7.98 2705 1639 0.14 0.13 3.24 0.48 0.22 5613 3.5 754 0.13 0.99 2908 20 216755440 2.41 5.23 1610 1779 0.18 0.17 2.22 0.44 0.31 4470 2.1 844 0.07 0.85 2860 10 97565450 6.74 14.99 4304 1795 0.34 0.17 2.78 2.31 0.26 5620 6.4 625 0.26 0.95 1316 15 259145528 5.42 12.49 4864 1422 0.46 0.18 2.24 2.48 0.33 9329 5.0 849 0.17 0.93 4465 9 278005540 6.77 17.39 6340 1399 0.46 0.17 2.77 3.13 0.30 9329 7.1 794 0.25 1.04 2989 12 370285550 10.11 24.81 8034 1516 0.38 0.17 3.56 3.87 0.22 9329 9.9 722 0.37 0.98 1295 21 484265560 10.34 25.29 8195 1525 0.38 0.17 3.61 3.90 0.22 9329 10.2 717 0.38 0.99 1134 22 496895570 2.34 5.38 1270 1551 0.20 0.16 2.22 0.47 0.33 2505 2.2 491 0.10 0.92 1235 9 78365650 3.44 7.65 1835 1572 0.19 0.15 2.70 0.64 0.26 3140 3.1 542 0.13 0.91 1305 15 122245660 1.62 3.74 784 1451 0.15 0.12 2.16 0.24 0.34 2014 1.5 555 0.06 0.93 1230 9 63135700 9.43 16.92 5469 1185 0.38 0.16 2.51 3.61 0.23 6686 7.8 658 0.30 0.82 1217 19 347245770 6.12 11.95 3712 1165 0.39 0.20 2.18 2.39 0.29 4975 5.9 571 0.25 0.97 1263 12 18981

Estimation of Flow Characteristics of Ungaged Streams 27
Table 6. Watershed characteristics for selected gaged stream drainage basins, northeast Maui, Hawaii—Continued

[Abbreviation definitions and units are described in appendix A; gaging stations in bold italics were used to develop the final regression equations for estimating flowduration statistics; precipitation data modified from Giambelluca and others (1986); ft3/s, cubic feet per second; geology data from Sherrod and others (2003); ND, not determined]

Gagingstation 

number

RR SD SF SR TSL

Annual

basin 

rainfall

(ft3/s)

Ratio of gage to index 

station annual basin 

rainfall

Percent coverage by surficial geologic unit

Honomanu 

Basalt

Kula

Volcanics

Hana

Volcanics

5070 392 5.93 12.8 0.85 11.2 35 0.71 0 0 1005080 455 5.73 11.1 0.67 20.7 51 1.03 0 11 895090 425 5.93 9.5 0.68 30.6 76 1.55 0 7 925100 323 8.39 42.2 0.81 5.8 13 0.26 0 0 1005110 328 7.27 31.2 0.68 6.9 17 0.34 1 0 995130 365 11.65 30.5 0.91 1.1 1.3 0.03 0 0 1005140 397 8.81 28.5 0.79 3.1 5.5 0.11 0 0 1005150 301 6.35 23.8 0.64 3.3 9.7 0.20 0 9 915160 442 6.66 14.0 0.58 25.9 50 1.01 0 58 425170 449 6.14 16.4 0.62 21.6 48 0.97 0 100 05180 440 6.28 18.8 0.53 23.1 49 1.00 0 93 75190 390 5.77 27 0.41 10.8 24 0.81 0 63 375200 241 5.99 14.0 0.51 3.0 9.1 0.19 0 98 25210 383 5.58 30.6 0.43 15.3 38 0.77 0 74 265240 375 5.59 13.1 0.60 14.4 33 0.66 0 100 05270 357 5.51 18.0 0.55 16.9 43 0.86 0 100 05311 368 6.68 14.9 0.89 1.8 3.3 0.07 0 100 05360 295 6.65 42.5 0.45 8.0 20 0.41 0 100 05420 317 6.25 4.2 0.45 0.9 2.8 0.06 0 100 05430 339 8.01 25.4 0.46 3.9 8.0 0.16 0 100 05440 308 6.06 13.1 0.47 2.7 7.6 0.15 0 100 05450 287 6.02 19.6 0.35 13.9 40 0.82 0 100 05528 389 5.72 11.9 0.60 14.1 15 0.30 0 100 05540 365 5.84 14.7 0.57 18.3 26 0.52 0 100 05550 324 6.03 26.4 0.48 23.4 38 0.78 0 100 05560 324 6.06 27.4 0.47 23.7 39 0.79 0 100 05570 236 6.17 11.7 0.32 2.9 6.8 0.14 0 100 05650 240 6.66 18.6 0.35 4.2 9.8 ND ND ND ND5660 210 8.05 11.0 0.38 1.9 3.1 ND ND ND ND5700 323 6.35 24.7 0.56 22.9 50 ND ND ND ND5770 311 5.11 15.7 0.49 12.2 37 ND ND ND ND

28 Median and Low-Flow Characteristics for Streams under Natural and Diverted Conditions, Northeast Maui, Hawaii
Table 7. Watershed characteristics for selected ungaged stream drainage basins, northeast Maui, Hawaii

[Basins and abbreviations listed from east to west; L, lower; M, middle; U, upper; watershed characteristic abbreviation definitions and units are described in appendix A; precipitation data modified from Giambelluca and others (1986); ft3/s, cubic feet per second; values in bold fall outside the range shown in table 8 used to develop the regression equations]

Stream location BL BP BR BS BW CCM CR DA ER MAXELEV MCL MCS MCSP

Hanawi lower (HwL) 9.02 19.24 8040 1488 0.59 0.17 2.34 5.36 0.29 8093 7.6 947 0.25Kapaula lower (KL) 5.79 12.46 4151 1186 0.19 0.14 3.40 1.07 0.20 4325 5.3 732 0.20Waiaaka lower (WaL) 1.85 3.62 1482 1485 0.08 0.10 2.71 0.14 0.23 1546 1.44 1119 0.04Paakea lower (PaL) 3.10 0.03 2296 1303 0.17 0.14 2.43 0.53 0.27 2372 2.74 866 0.09Paakea upper (PaU) 1.90 3.61 1059 801 0.12 0.10 2.14 0.23 0.28 2372 1.63 642 0.06Waiohue lower (WeL) 3.84 7.78 2738 1270 0.24 0.18 2.30 0.91 0.28 2766 3.63 791 0.13Waiohue middle (WeM) 3.49 6.70 2269 1078 0.21 0.17 2.19 0.75 0.28 2766 3.23 671 0.13Puakaa middle (PuM) 3.15 6.80 1889 1338 0.13 0.12 3.06 0.39 0.23 2491 3.00 655 0.12Puakaa upper (PuU) 2.06 4.65 1177 1113 0.13 0.12 2.52 0.27 0.29 2491 2.08 602 0.09Kopiliula lower (KpL) 8.29 19.80 8343 1699 0.57 0.16 2.58 4.70 0.30 8372 8.0 837 0.28Kopiliula middle (KpM) 8.95 18.88 7800 1688 0.47 0.15 2.60 4.19 0.26 8372 7.5 855 0.26East Wailuaiki lower (EWL) 8.92 20.94 8498 1630 0.44 0.17 2.98 3.94 0.25 8527 8.0 812 0.28East Wailuaiki middle (EWM) 8.35 19.77 8096 1582 0.46 0.17 2.86 3.80 0.26 8527 7.5 843 0.26West Wailuaiki lower (WWL) 9.46 21.77 8822 1833 0.43 0.16 3.04 4.07 0.24 8857 8.3 819 0.29West Wailuaiki middle (WWM) 8.97 20.58 8385 1796 0.44 0.16 2.92 3.97 0.25 8857 7.8 839 0.27Wailuanui lower (WL) 9.17 22.69 8017 1772 0.35 0.19 3.56 3.24 0.22 8055 8.2 777 0.29Waiokomilo lower (WoL) 10.44 23.09 6459 1405 0.25 0.18 4.01 2.63 0.18 6483 9.2 686 0.35Waiokomilo middle (WoM) 8.41 18.94 5977 1478 0.25 0.17 3.68 2.11 0.20 6483 7.5 828 0.26Waiokomilo upper (WoU) 7.42 15.75 5108 1314 0.20 0.16 3.66 1.48 0.19 6483 6.2 828 0.22Ohia lower (OL) 2.10 2.92 388 821 0.11 0.15 1.75 0.22 0.25 413 1.2 358 0.06Palauhulu lower (PhL) 8.62 20.48 5745 1510 0.32 0.17 3.49 2.74 0.22 5816 8.2 666 0.32Palauhulu middle (PhM) 7.43 16.57 5299 1587 0.33 0.17 3.01 2.41 0.24 5816 6.7 772 0.24Kano upper (KoU) 4.99 11.09 3792 1251 0.20 0.13 3.17 0.97 0.22 5816 4.3 827 0.15Hauoli Wahine upper (HWU) 1.34 3.94 1052 1280 0.27 0.15 1.85 0.36 0.51 3049 1.4 749 0.05Piinaau lower (PiL) 16.45 36.91 9976 1984 1.07 0.22 2.48 17.58 0.29 10011 14.9 620 0.60Piinaau middle (PiM) 11.92 33.25 9536 1993 1.40 0.21 2.30 16.63 0.39 10011 13.3 652 0.52Piinaau upper (PiU) 10.47 29.95 8689 2019 1.43 0.21 2.19 14.96 0.42 10011 11.7 664 0.45Nuaailua lower (NL) 4.25 9.18 2389 1967 0.28 0.23 2.38 1.19 0.29 2409 3.5 698 0.13Nuaailua middle (NM) 3.07 6.51 1891 1726 0.16 0.17 2.66 0.48 0.25 2409 2.6 710 0.10Nuaailua upper (NU) 1.18 2.80 653 1036 0.10 0.11 2.30 0.12 0.33 2409 1.0 609 0.04Honomanu lower (HnL) 9.86 23.91 8304 2115 0.52 0.19 2.99 5.09 0.26 8331 8.9 946 0.29Honomanu middle (HnM) 8.81 21.63 7654 1867 0.49 0.18 2.93 4.34 0.27 8331 8.0 960 0.26Punalau lower (PlL) 3.89 8.75 2531 1947 0.22 0.16 2.70 0.84 0.27 2566 3.5 648 0.14Punalau middle (PlM) 3.56 7.89 2053 1748 0.22 0.16 2.52 0.78 0.28 2566 3.2 604 0.13Haipuaena lower (HaL) 9.44 21.05 5709 1758 0.17 0.15 4.70 1.60 0.15 5979 8.4 652 0.33Haipuaena middle lower (HaML) 8.80 19.65 5509 1771 0.17 0.15 4.59 1.46 0.16 5979 7.8 647 0.31Haipuaena middle upper (HaMU) 8.04 17.87 5042 1744 0.17 0.15 4.31 1.37 0.16 5979 7.2 675 0.28Puohokamoa lower (PL) 8.78 19.69 5599 1801 0.36 0.17 3.14 3.12 0.23 5613 8.5 594 0.35Puohokamoa middle lower (PML) 8.20 18.44 5100 1752 0.36 0.17 3.02 2.97 0.24 5613 7.9 592 0.33Puohokamoa middle upper (PMU) 7.56 17.01 4700 1799 0.35 0.17 2.95 2.65 0.24 5613 7.3 617 0.30Wahinepee lower (WpL) 1.56 4.46 1247 1642 0.26 0.19 1.98 0.40 0.46 1320 1.7 679 0.07Wahinepee middle (WpM) 1.06 3.14 746 1353 0.26 0.17 1.69 0.28 0.56 1320 1.2 603 0.05Waikamoi lower (WiL) 12.23 29.77 9205 1650 0.39 0.17 3.86 4.74 0.20 9329 12.0 686 0.46Waikamoi middle lower (WiML) 11.60 28.29 8834 1623 0.40 0.17 3.69 4.67 0.21 9329 11.4 701 0.43Waikamoi middle upper (WiMU) 11.22 27.54 8594 1609 0.41 0.17 3.62 4.61 0.22 9329 11.1 703 0.42Kolea lower (KaL) 3.08 7.02 1808 1833 0.20 0.15 2.51 0.62 0.29 1846 2.7 627 0.11Kolea middle (KaM) 2.53 5.83 1321 1688 0.20 0.15 2.30 0.51 0.32 1846 2.2 603 0.09

Estimation of Flow Characteristics of Ungaged Streams 29
Table 7. Watershed characteristics for selected ungaged stream drainage basins, northeast Maui, Hawaii—Continued

[Basins and abbreviations listed from east to west; L, lower; M, middle; U, upper; watershed characteristic abbreviation definitions and units are described in appendix A; precipitation data modified from Giambelluca and others (1986); ft3/s, cubic feet per second; values in bold fall outside the range shown in table 8 used to develop the regression equations]

Stream location MCSR MINELEV RB RN RR SD SF SR TSL

Annual basin 

rainfall

(ft3/s)

Hanawi lower (HwL) 0.84 53 12 47070 418 5.85 15.20 0.64 31.4 79Kapaula lower (KL) 0.91 174 25 28937 333 6.97 31.30 0.62 7.5 18Waiaaka lower (WaL) 0.78 64 19 15036 410 10.15 24.16 0.75 1.44 1.9Paakea lower (PaL) 0.89 76 14 16286 366 7.09 18.12 0.67 3.76 7.9Paakea upper (PaU) 0.86 1313 12 11139 293 10.52 15.84 0.80 2.39 3.8Waiohue lower (WeL) 0.94 28 13 15317 352 5.59 16.21 0.62 5.10 15Waiohue middle (WeM) 0.93 497 13 13356 339 5.89 16.26 0.62 4.40 13Puakaa middle (PuM) 0.95 602 20 15238 278 8.07 25.28 0.49 3.17 6.4Puakaa upper (PuU) 1.01 1314 12 9734 253 8.27 15.71 0.54 2.24 4.7Kopiliula lower (KL) 0.97 29 11 54003 421 6.47 14.61 0.49 30.4 62Kopiliula middle (KM) 0.84 572 15 50530 413 6.48 19.11 0.51 27.1 54East Wailuaiki lower (EWL) 0.89 29 16 50650 406 5.96 20.21 0.50 23.5 54East Wailuaiki middle (EWM) 0.90 431 14 48633 409 6.01 18.35 0.53 22.8 52West Wailuaiki lower (WWL) 0.87 35 17 53722 405 6.09 21.98 0.45 24.8 54West Wailuaiki middle (WWM) 0.87 472 16 51549 407 6.15 20.29 0.47 24.4 53Wailuanui lower (WL) 0.89 38 20 41455 353 5.17 25.96 0.44 16.8 44Waiokomilo lower (WoL) 0.88 24 33 36511 280 5.65 41.42 0.49 14.9 40Waiokomilo middle (WoM) 0.89 506 26 34370 316 5.75 33.53 0.56 12.1 34Waiokomilo upper (WoU) 0.83 1375 29 31821 324 6.23 37.28 0.63 9.2 24Ohia lower (OL) 0.57 25 16 2582 133 6.66 19.85 0.44 1.5 2.2Palauhulu lower (PhL) 0.95 71 21 33102 280 5.76 27.11 0.44 15.8 48Palauhulu middle (PhM) 0.90 517 18 31149 320 5.88 22.89 0.49 14.2 44Kano upper (KoU) 0.87 2024 20 28683 342 7.56 25.61 0.66 7.3 18Hauoli Wahine upper (HWU) 1.05 1997 4 6995 267 6.65 4.93 0.59 2.4 7.5Piinaau lower (PiL) 0.91 35 12 46178 270 4.63 15.38 0.31 81.4 192Piinaau middle (PiM) 1.12 475 7 44633 287 4.68 8.55 0.33 77.9 181Piinaau upper (PiU) 1.12 1322 6 41236 290 4.75 7.32 0.33 71.0 152Nuaailua lower (NL) 0.83 20 12 10462 260 4.38 15.22 0.36 5.2 16Nuaailua middle (NM) 0.84 518 16 10927 290 5.78 19.86 0.41 2.8 7.1Nuaailua upper (NU) 0.88 1756 9 5752 234 8.81 11.81 0.59 1.0 2.0Honomanu lower (HnL) 0.91 27 15 44236 347 5.33 19.09 0.45 27.1 76Honomanu middle (HnM) 0.91 677 14 42645 354 5.57 17.90 0.51 24.2 65Punalau lower (PlL) 0.89 35 14 15897 289 6.28 18.06 0.33 5.3 12Punalau middle (PlM) 0.89 513 13 13070 260 6.37 16.26 0.35 5.0 12Haipuaena lower (HaL) 0.90 270 44 37942 271 6.65 55.84 0.37 10.6 25Haipuaena middle lower (HaML) 0.89 470 42 36866 280 6.69 52.98 0.37 9.8 24Haipuaena middle upper (HaMU) 0.89 937 37 33587 282 6.66 47.31 0.39 9.1 23Puohokamoa lower (PL) 0.96 14 19 33088 284 5.91 24.66 0.33 18.5 50Puohokamoa middle lower (PML) 0.97 513 18 30273 277 5.94 22.64 0.34 17.6 49Puohokamoa middle upper (PMU) 0.97 913 17 28077 276 5.97 21.55 0.34 15.8 45Wahinepee lower (WeL) 1.09 73 5 6702 280 5.37 6.07 0.41 2.2 4.1Wahinepee middle (WeM) 1.09 574 3 4335 237 5.81 4.06 0.45 1.6 3.0Waikamoi lower (WiL) 0.98 124 25 55302 309 6.01 31.55 0.42 28.5 50Waikamoi middle lower (WiML) 0.98 495 23 52895 312 5.99 28.83 0.43 27.9 49Waikamoi middle upper (WiMU) 0.99 735 21 51440 312 5.99 27.26 0.44 27.6 49Kolea lower (KaL) 0.89 38 12 11996 257 6.64 15.26 0.34 4.1 7.0Kolea middle (KaM) 0.87 525 10 8924 227 6.76 12.52 0.36 3.4 6.1

30 Median and Low-Flow Characteristics for Streams under Natural and Diverted Conditions, Northeast Maui, Hawaii
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Estimation of Flow Characteristics of Ungaged Streams 31
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Figure 9. Generalized surficial geology, northeast Maui, Hawaii (modified from Sherrod and others, 2003).

32 Median and Low-Flow Characteristics for Streams under Natural and Diverted Conditions, Northeast Maui, Hawaii
signs and magnitudes of the coefficients determined for the 

significant, independent variables are hydrologically reasonable (Fontaine and others, 1992; Iman and Conover, 1983, p. 

367).

Streamflow and basin characteristics used in hydrologic 

regression usually are log-normally distributed; therefore, the 

variables must be transformed to logarithms to satisfy regression assumption 2. The dependent and independent variables 

were transformed using log-base 10 units. Where values of 

percent coverage of Kula Volcanics were 0 percent, they were 

set to 1 percent before log transformation.

Ordinary-Least-Squares (OLS) regression analysis was 

used to develop the equations presented in this report. Because 

streamflow data are correlated spatially and in time, assumption 5 for use of regression is not strictly satisfied. A theoretically more appropriate method, Generalized-Least Squares 

(GLS) regression, was developed by Tasker and Stedinger 

(1989) to allow weighting to compensate for length-of-record 

and spatial correlations. However, Vogel and Kroll (1990) 

found that the equation parameters (b0 to bn) were nearly 

identical when either OLS or GLS was used to develop the 

equation, even though OLS does not correct for length-ofrecord or spatial differences. Ries and Friesz (2000) used 

Weighted-Least-Squares (WLS) regression analysis to predict 

duration flows because WLS can compensate for length-ofrecord differences. They found that equations developed using 

WLS and GLS methods were nearly identical. Because the 

streamflow statistics used in the development of the equations 

in this report were adjusted to equivalent lengths of record, 

and the spatial correlations between gaged basins in the study 

area are relatively insignificant, OLS regression analysis was 

determined to be the most appropriate for this study.

Regression assumption 7 was addressed by removing 

independent variables having high correlation (> 90 percent) 

with several other independent variables in the analysis. For 

example, Drainage Area (DA) was highly correlated with Total 

Stream Length (98 percent), Basin Relief (94 percent), Rainfall (93 percent), and Basin Width (91 percent), and therefore 

DA was removed from further analysis. Other basin characteristics removed from further consideration because of high 

correlations were Basin Perimeter (BP), Rotundity of Basin 

(RB), and Main Channel Length (MCL).

A variable-selection algorithm was applied to the remaining independent variables to aid in determining which combination of independent variables provides the best estimates 

of the dependent variables. The algorithm used was a leapsand-bounds implementation with Mallow’s Cp as the selection criterion (Insightful Corporation, 2002). Subsets of the 

independent variables were evaluated and ranked according to 

the lowest value of Mallow’s Cp for each subset of 1, 2, 3 ... 

n independent variables. The subsets of 1, 2, 3, and 4 independent variables having the lowest Mallow’s Cp were then 

further analyzed using OLS regression to select a final model 

for each statistic.

During equation development, several gaging stations 

were eliminated from the analysis because (1) the sites were 

known outliers on the basis of observed hydrologic differences or (2) plots of Cook’s distance (Draper and Smith, 1998) 

indicated that the flow statistics for a particular gaging station 

were statistically biasing the results. Gaging stations eliminated for hydrologic reasons prior to the Mallow’s Cp analysis 

were stations 5070, 5311, and 5528 (intermittent streams); 

station 5090 (has anomalous spring input); and stations 5110, 

5130, 5140, and 5210 (regulated streams). Gaging stations 

5240 and 5420 were eliminated because of high Cook’s distance values determined during the analyses. The final number 

of gaging stations from which data were used to develop the 

equations was 17 (n = 17).

The final models were selected on the basis of the following parameters: (1) Mallow’s Cp statistic; (2) R2

, the 

proportion of total variation about the mean explained by the 

regression; (3) SEr, the average standard error of the estimates; 

and (4) Pr (>|t|), the probability of significance for an independent variable in the regression. Pr (>|t|) had to be lower than 5 

percent for each independent variable used in the regression 

model for that independent variable to be included.

The retransformed regression equations are biased 

because they predict the median rather than the mean response 

of the dependent variable. In the case of streamflow data, 

the median tends to be lower than the mean. Duan’s (1983) 

“smearing estimate”, the mean error of the retransformed 

residuals, was used as the bias-correction factor (BCF) to 

adjust the retransformed b0 coefficient. This BCF is advantageous in that it does not require normally distributed regression residuals and is simple to calculate (Ries and Friesz, 

2000).

Accuracy and limitations of the regression 

equations

Regression equations for predicting duration discharges 

TFQ50, TFQ95, BFQ50, and BFQ95 at unregulated sites were 

developed using OLS regression as described above. The 

equations, along with several measures of model adequacy and 

the BCF for each equation, are presented in table 8. The measures of model adequacy include (1) the coefficient of determination (R2

); (2) the average standard error of estimate (SEr), 

in percent; (3) the average standard error of prediction (SEp), 

in percent; and (4) the median absolute deviation (MAD), in 

percent. The R2 is a measure of the proportion of the variation 

in the dependent variable that is explained by the independent variables. The SEr

 is a measure of the average precision 

with which the regression equations estimate the streamflow 

statistics for stations used in the analyses, whereas the SEp

indicates the average precision with which the equation can be 

used to estimate streamflow statistics for ungaged sites with 

basin characteristics similar to those for the stations used in 

the regression analyses. About 68 percent of streamflows estimated using the regression equations would have errors within 

the noted average standard errors. Half of the regression-equation estimates for stations used in the analyses had absolute 

Estimation of Flow Characteristics of Ungaged Streams 33
errors, in percent, that were greater than the MAD, and half 

of them were less than the MAD. Scatter plots comparing 

observed and estimated flow-duration statistics show the fit 

of the regression equations for sites used in determining the 

equations (fig. 10).

The rainfall rates for stations used in developing the 

regression equations ranged from 51 to 6.8 ft3/s and averaged 

28 ft3/s (table 8). For all four equations, rainfall has a positive 

coefficient, thus higher rainfall rates lead to higher estimated 

flows. The value of MAXELEV ranged from 9,329 to 2,505 ft 

and averaged 6,602. For all four equations, MAXELEV has a 

negative coefficient, thus higher elevations lead to lower estimated flows. The value of ER ranged from 0.34 to 0.17 and 

averaged 0.26. Only the median flow equations included ER, 

which has a negative coefficient in both equations. Therefore, 

short and wide drainage basins (higher ER), will have lower 

median flows. Estimates of flow-duration statistics derived by 

using the regression equations for drainage basins with characteristics outside the ranges (table 8) used in equation development could be subject to substantial errors.

Values of estimated streamflow statistics and several 

measures of estimation error for each continuous-record gaging station in the study area and at four gaged stations (5650, 

5660, 5700, and 5770) west of the study area can be compared 

to the observed statistics to evaluate the performance of the 

equations (table 9). Statistics were generated for the gaged 

stations west of the study area to provide an additional indication of the accuracy of the equations for sites where measured 

streamflows are available. Estimated streamflow, in cubic feet 

per second, is the value determined by applying the regression 

equation. Prediction intervals (90 percent lower confidence 

limit [90% LCL], 90 percent upper confidence limit [90% 

UCL]), in cubic feet per second, indicate the uncertainty 

inherent in the use of the regression equations. Assurance is 

90 percent that the true value of the streamflow statistic will 

be within the prediction interval. Standard error, in percent, is 

a measure of the precision with which the equation estimates 

the streamflow statistic. Measured flow, in cubic feet per second, is the observed streamflow statistic determined from the 

continuous record and adjusted to the long-term index station. 

Relative error, in percent, is calculated from [100(estimated 

flow – measured flow)/measured flow], and where available, 

indicates how well the estimated value matches the measured 

value. The value of MAD for each equation (table 8) is the 

average of relative errors for all stations used in the development of the regression equations.

At the stations used in the development of the equations, 

the equations tend to predict more accurately the higher flow 

statistics, TFQ50 and BFQ50, than the lower flow statistics, 

TFQ95 and BFQ95. At the outlier stations eliminated from the 

regression analysis, the accuracy of the equation estimates 

generally is poor, indicating that a factor not considered in 

the regression analysis is probably affecting the streamflow 

statistics at these stations (fig. 11). The most likely factor is 

variable subsurface geology that can control where streams are 

intermittent and where springs discharge high flow to streams. 

At the stations on intermittent streams (stations 5070 and 

5528), the equations overestimate the flow-duration statistics. 

At stations on streams with notable springs (stations 5090, 

5110, 5130, 5140), the equations underestimate the flow-duration statistics, especially at lower flows. At two (stations 5110 

and 5210) of the three regulated stations where streamflow 

statistics were determined on the basis of combined records of 

the upstream and downstream gaging stations, the equations 

provide a reasonably accurate estimate of the flow statistics at 

the downstream stations. At stations 5110 and 5210, the relaTable 8. Summary of regression equations developed for estimating selected flow-duration statistics of northeast Maui 

streams, Hawaii.

[Statistic: TF is total flow; BF is base flow, Qxx is the xx-percent duration flow; Statistic estimator: Rainfall is area-weighted rainfall rate (cubic feet per 

second); MAXELEV is maximum drainage-basin elevation (feet); ER is elongation ratio (dimensionless); R2: Coefficient of determination (percent); SEr

and SEp: Average standard error of estimate and prediction (percent);MAD: Median absolute deviation (percent); BCF: Bias correction factor; n = 17 for 

all equations]

Statistic Statistic estimator R2 SEr SEp MAD BCF

TFQ50 3,184(Rainfall)1.338(MAXELEV)-1.366(ER)-0.946 94.9 15.3 20.9 12 1.009

BFQ50 25,384(Rainfall)1.525(MAXELEV)-1.735(ER)-0.937 91.0 22.5 30.5 17 1.019

TFQ95 56,267(Rainfall)1.478(MAXELEV)-1.750 76.6 38.1 50.3 21 1.059

BFQ95 409,732(Rainfall)1.620(MAXELEV)-2.054 75.3 43.0 56.5 28 1.073

Range used in analysis

Minimum Mean Maximum

Rainfall ............ 6.8 28 51

MAXELEV ...... 2,505 6,602 9,329

ER .................... 0.17 0.26 0.34

34 Median and Low-Flow Characteristics for Streams under Natural and Diverted Conditions, Northeast Maui, Hawaii
Figure 10. Relation between measured and estimated flow statistics (in log10 cubic feet per second) for selected gaged basins used in determining the regression equations, northeast Maui, Hawaii. Equations are listed in table 8.

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Estimation of Flow Characteristics of Ungaged Streams 35
Table 9. Streamflow statistics estimated using regression equations, lower and upper confidence intervals, standard errors, measured flows, and relative errors for 

continuous-record sites, northeast Maui, Hawaii—Continued[Gaging stations in bold were used to develop the final regression equations for estimating low-flow statistics; TFQxx is the xx-percent flow duration of total streamflow; BFQxx is the xx-percent flow duration of base flow; estimated and measured flow and confidence intervals are in cubic feet per second; 90% LCL and 90% UCL is 90-percent lower and upper confidence level; Standard error is in percent; Relative error is the percent difference between the measured statistic and the estimated statistic; measured flows in bold italics are within the 90-percent confidence interval of the computed estimate; NA, not applicable]

Gaging-station number Statistic TFQ50 BFQ50 TFQ95 BFQ95

5070 Estimated flow

90% LCL90% UCLStandard errorMeasured flowRelative error

9.18.0

10

7.82.2

310

6.04.97.3

11.4

1.3

360

3.42.44.6

17.6

0.00

NA

3.02.24.3

19.7

0.00

NA

5080 Estimated flow

90% LCL90% UCLStandard errorMeasured flowRelative error

7.76.88.87.57.18

4.63.85.6

11.1

4.60

2.72.13.5

14.2 

2.4

13

2.21.73.0

15.9

2.20

5090 + 5080 Estimated flow

90% LCL90% UCLStandard errorMeasured flowRelative error

12101510.328

-57

7.96.1

1015.224

-67

4.93.47.1

21.5 19

-74

4.32.86.6

24.119

-77

5100 Estimated flow

90% LCL90% UCLStandard errorMeasured flowRelative error

5.74.86.68.94.9

16

3.32.64.1

13.0

2.8

18

1.10.881.3

11.3

1.10

0.890.711.1

12.7

0.90

-1

5110 + 5100 Estimated flow

90% LCL90% UCLStandard errorMeasured flowRelative error

6.75.97.66.97.5

-11

4.13.44.9

10.2

5.1

-20

1.51.21.9

11.8

3.3

-55

1.31.01.7

13.2

3.0

-57

5130 Estimated flow

90% LCL90% UCLStandard errorMeasured flowRelative error

0.810.621.0

15.2

0.86

-6

0.440.290.65

22.4

0.77

-43

0.200.100.37

37.4

0.54

-63

0.160.080.33

42.1

0.53

-70

Table 9. Streamflow statistics estimated using regression equations, lower and upper confidence intervals, standard errors, measured flows, and relative errors for continuous-record sites, northeast Maui, Hawaii.[Gaging stations in bold were used to develop the final regression equations for estimating low-flow statistics; TFQxx is the xx-percent flow duration of total streamflow; BFQxx is the xx-percent flow duration of base flow; estimated and measured flow and confidence intervals are in cubic feet per second; 90% LCL and 90% UCL is 90-percent lower and upper confidence level; Standard error is in percent; Relative error is the percent difference between the measured statistic and the estimated statistic; measured flows in bold italics are within the 90-percent confidence interval of the computed estimate; NA, not applicable]

36 Median and Low-Flow Characteristics for Streams under Natural and Diverted Conditions, Northeast Maui, Hawaii
Table 9. Streamflow statistics estimated using regression equations, lower and upper confidence intervals, standard errors, measured flows, and relative errors for 

continuous-record sites, northeast Maui, Hawaii—Continued[Gaging stations in bold were used to develop the final regression equations for estimating low-flow statistics; TFQxx is the xx-percent flow duration of total streamflow; BFQxx is the xx-percent flow duration of base flow; estimated and measured flow and confidence intervals are in cubic feet per second; 90% LCL and 90% UCL is 90-percent lower and upper confidence level; Standard error is in percent; Relative error is the percent difference between the measured statistic and the estimated statistic; measured flows in bold italics are within the 90-percent confidence interval of the computed estimate; NA, not applicable]

Gaging-station number Statistic TFQ50 BFQ50 TFQ95 BFQ95

5140 Estimated flow

90% LCL90% UCLStandard errorMeasured flowRelative error

3.32.83.99.44.0

-18

2.01.62.6

13.8

3.8

-45

0.860.601.2

21.0

3.0

-71

0.760.501.1

23.5

3.0

-75

5150 Estimated flow

90% LCL90% UCLStandard errorMeasured flowRelative error

5.24.56.18.26.2

-15

3.42.74.2

12.1

5.0

-32

1.51.12.1

18.9

3.0

-50

1.40.92.0

21.2

2.8

-52

5160 Estimated flow

90% LCL90% UCLStandard errorMeasured flowRelative error

8.17.39.06.18.01

4.84.15.69.05.0

-4

2.51.93.1

13.6

2.34

2.01.52.6

15.2

2.00

5170 Estimated flow

90% LCL90% UCLStandard errorMeasured flowRelative error

8.07.38.85.59.1

-12

4.64.05.38.15.7

-21

2.31.82.8

13.0

2.8

-21

1.81.42.4

14.5

2.5

-28

5180 Estimated flow

90% LCL90% UCLStandard errorMeasured flowRelative error

8.57.79.35.4

10

-15

4.84.25.68.06.0

-20

2.21.72.8

13.1

2.5

-12

1.81.42.3

14.7

2.1

-14

Estimation of Flow Characteristics of Ungaged Streams 37
Table 9. Streamflow statistics estimated using regression equations, lower and upper confidence intervals, standard errors, measured flows, and relative errors for 

continuous-record sites, northeast Maui, Hawaii—Continued[Gaging stations in bold were used to develop the final regression equations for estimating low-flow statistics; TFQxx is the xx-percent flow duration of total streamflow; BFQxx is the xx-percent flow duration of base flow; estimated and measured flow and confidence intervals are in cubic feet per second; 90% LCL and 90% UCL is 90-percent lower and upper confidence level; Standard error is in percent; Relative error is the percent difference between the measured statistic and the estimated statistic; measured flows in bold italics are within the 90-percent confidence interval of the computed estimate; NA, not applicable]

Gaging-station number Statistic TFQ50 BFQ50 TFQ95 BFQ95

5190 Estimated flow

90% LCL90% UCLStandard errorMeasured flowRelative error

4.33.94.85.74.4

-2

2.21.92.68.52.4

-12

0.890.701.1

13.1

1.0

-11

0.660.510.86

14.6

0.85

-22

5200 Estimated flow

90% LCL90% UCLStandard errorMeasured flowRelative error

3.93.34.48.13.2

22

2.52.03.1

11.9

2.0

25

1.41.02.0

18.9

0.90

56

1.30.891.9

21.2

0.80

63

5210 + 5200 + 5190 Estimated flow

90% LCL90% UCLStandard errorMeasured flowRelative error

8.67.79.66.2

10

-14

4.94.15.79.16.1

-20

1.81.52.2

11.1

2.5

-28

1.41.11.8

12.4

2.0

-30

5240 Estimated flow

90% LCL90% UCLStandard errorMeasured flowRelative error

4.54.05.06.12.2

100

2.42.12.99.00.93

160

1.31.11.6

11.1

0.37

250

1.00.831.3

12.4

0.30

230

5270 Estimated flow

90% LCL90% UCLStandard errorMeasured flowRelative error

7.36.98.05.05.7

28

4.23.64.77.32.8

50

2.01.62.4

11.9

1.0

82

1.61.22.0

13.3

0.74

120

38 Median and Low-Flow Characteristics for Streams under Natural and Diverted Conditions, Northeast Maui, Hawaii
Table 9. Streamflow statistics estimated using regression equations, lower and upper confidence intervals, standard errors, measured flows, and relative errors for 

continuous-record sites, northeast Maui, Hawaii—Continued[Gaging stations in bold were used to develop the final regression equations for estimating low-flow statistics; TFQxx is the xx-percent flow duration of total streamflow; BFQxx is the xx-percent flow duration of base flow; estimated and measured flow and confidence intervals are in cubic feet per second; 90% LCL and 90% UCL is 90-percent lower and upper confidence level; Standard error is in percent; Relative error is the percent difference between the measured statistic and the estimated statistic; measured flows in bold italics are within the 90-percent confidence interval of the computed estimate; NA, not applicable]

Gaging-station number Statistic TFQ50 BFQ50 TFQ95 BFQ95

5311 + 5310 Estimated flow

90% LCL90% UCLStandard errorMeasured flowRelative error

0.350.250.49

19.3

0.50

-30

0.140.090.23

28.7

0.17

-18

0.080.040.17

45.6

0.03

170

0.050.020.12

51.6

0.03

67

5360 + 5310 + 5350 Estimated flow

90% LCL90% UCLStandard errorMeasured flowRelative error

6.65.77.68.26.8

-3

3.73.04.6

12.1

3.56

1.21.01.49.21.7

-29

0.940.791.1

10.2

1.3

-28

5420 Estimated flow

90% LCL90% UCLStandard errorMeasured flowRelative error

0.300.200.45

22.5

0.88

-66

0.140.080.25

33.5

0.53

-74

0.150.080.27

34.9

0.29

-48

0.100.050.20

39.4

0.27

-63

5430 Estimated flow

90% LCL90% UCLStandard errorMeasured flowRelative error

1.61.41.99.41.4

14

0.780.611.0

13.8

0.67

16

0.330.220.50

22.9

0.21

57

0.240.150.37

25.7

0.15

60

5440 Estimated flow

90% LCL90% UCLStandard errorMeasured flowRelative error

1.51.31.89.11.9

-21

0.780.620.99

13.4

1.0

-22

0.460.330.63

18.4

0.55

-16

0.350.240.50

20.7

0.44

-20

Estimation of Flow Characteristics of Ungaged Streams 39
Table 9. Streamflow statistics estimated using regression equations, lower and upper confidence intervals, standard errors, measured flows, and relative errors for 

continuous-record sites, northeast Maui, Hawaii—Continued[Gaging stations in bold were used to develop the final regression equations for estimating low-flow statistics; TFQxx is the xx-percent flow duration of total streamflow; BFQxx is the xx-percent flow duration of base flow; estimated and measured flow and confidence intervals are in cubic feet per second; 90% LCL and 90% UCL is 90-percent lower and upper confidence level; Standard error is in percent; Relative error is the percent difference between the measured statistic and the estimated statistic; measured flows in bold italics are within the 90-percent confidence interval of the computed estimate; NA, not applicable]

Gaging-station number Statistic TFQ50 BFQ50 TFQ95 BFQ95

5450 Estimated flow

90% LCL90% UCLStandard errorMeasured flowRelative error

121114

7.5

12

0

7.96.59.6

11.0

6.4

23

3.62.65.0

18.1

2.5

44

3.32.34.6

20.3

2.1

57

5528 Estimated flow

90% LCL90% UCLStandard errorMeasured flowRelative error

1.20.981.5

13.2

0.14

760

0.550.390.78

19.5

0.06

820

0.330.210.53

26.8

0.02

1600

0.220.130.37

30.1

0.01

2100

5540 Estimated flow

90% LCL90% UCLStandard errorMeasured flowRelative error

2.92.53.38.02.5

16

1.41.11.7

11.9

1.2

17

0.760.571.0

16.4

0.69

10

0.550.400.76

18.4

0.46

20

5550 Estimated flow

90% LCL90% UCLStandard errorMeasured flowRelative error

6.66.07.35.67.0

-6

3.53.14.18.33.50

1.41.11.7

12.6

1.1

27

1.10.831.4

14.0

0.80

38

5560 Estimated flow

90% LCL90% UCLStandard errorMeasured flowRelative error

6.76.17.45.6

 7.1 

-6

3.63.14.28.33.60

1.41.11.7

12.5

1.5

-13

1.10.841.4

14.0

1.0

10

40 Median and Low-Flow Characteristics for Streams under Natural and Diverted Conditions, Northeast Maui, Hawaii
Table 9. Streamflow statistics estimated using regression equations, lower and upper confidence intervals, standard errors, measured flows, and relative errors for 

continuous-record sites, northeast Maui, Hawaii—Continued[Gaging stations in bold were used to develop the final regression equations for estimating low-flow statistics; TFQxx is the xx-percent flow duration of total streamflow; BFQxx is the xx-percent flow duration of base flow; estimated and measured flow and confidence intervals are in cubic feet per second; 90% LCL and 90% UCL is 90-percent lower and upper confidence level; Standard error is in percent; Relative error is the percent difference between the measured statistic and the estimated statistic; measured flows in bold italics are within the 90-percent confidence interval of the computed estimate; NA, not applicable]

Gaging-station number Statistic TFQ50 BFQ50 TFQ95 BFQ95

5570 Estimated flow

90% LCL90% UCLStandard errorMeasured flowRelative error

2.72.33.29.32.70

1.71.32.2

13.7

1.4

13

1.10.761.5

19.9

0.70

57

0.960.651.4

22.3

0.58

66

5650a Estimated flow

90% LCL90% UCLStandard errorMeasured flowRelative error

4.03.54.56.62.6

54

2.52.12.99.71.4

79

1.20.941.6

16.0

0.71

69

1.10.801.5

17.9

0.61

80

5660 a Estimated flow

90% LCL90% UCLStandard errorMeasured flowRelative error

1.21.01.5

12.2

1.09

0.730.531.0

18.0

0.42

74

0.500.320.78

26.0

0.25

100

0.420.260.70

29.2

0.21

100

5700 a Estimated flow

90% LCL90% UCLStandard errorMeasured flowRelative error

151317

8.1

16

-6

9.37.5

1111.9

9.5

-2

3.72.75.1

17.8

4.5

-18

3.32.34.6

19.9

4.0

-18

5770 a Estimated flow

90% LCL90% UCLStandard errorMeasured flowRelative error

121014

8.38.9

35

7.96.49.8

12.2

5.0

58

4.02.85.7

20.3

2.1

99

3.72.55.5

22.7

1.7

110

a located west of current study area

Estimation of Flow Characteristics of Ungaged Streams 41
Figure 11. Relation between measured and estimated flow statistics (in log10 cubic feet per second) for gaged basins not used (outliers) in determining regression equations, northeast Maui, Hawaii. Equations are listed in table 8.

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42 Median and Low-Flow Characteristics for Streams under Natural and Diverted Conditions, Northeast Maui, Hawaii
tive errors for TFQ50 and BFQ50, range from -10 to -20 percent 

and for TFQ95 and BFQ95, the relative errors range from -28 

to -57 percent. At the third regulated station (station 5090) 

where streamflow statistics were determined on the basis of 

combined records, the estimates have relative errors ranging 

from -57 to -77 percent, indicating that the anomalous input 

from springs to Hanawi Stream is not accounted for by the 

equations.

The regression equation for TFQ50 estimates that statistic 

within a relative error of ±25 percent at 20 of the continuousrecord gaging stations. Flow at 15 stations is underestimated 

and flow at 12 stations is the same as the measured statistic 

or overestimated. All but one of the TFQ50 flows at stations 

east of Keanae Valley and downstream of the Koolau ditch are 

underestimated, indicating the influence of springs with high 

discharge volume in this area (fig. 12). The only overestimate 

east of Keanae Valley is at gaging station 5070 on an intermittent reach of Makapipi Stream. The regression equation for 

BFQ50 estimates that statistic within a relative error of ±25 

percent at 18 of the continuous-record gaging stations. Flow 

at 13 stations is underestimated and flow at 14 stations is the 

same as measured or overestimated. Most of the flow at stations east of Keanae Valley is underestimated with the stations 

downstream of the Koolau ditch having the greatest errors (fig. 

13). The regression equation for TFQ95 estimates that statistic 

within a relative error of ±50 percent at 15 of the continuousrecord gaging stations. The errors are higher for lower flows 

because, for the same absolute error in flow, the relative error, 

in percent, increases as the actual flow decreases. For example, 

at station 5180, an absolute error of 1.0 ft3/s is 10 percent of 

TFQ50 (10 ft3/s) but 17 percent of BFQ50 (6.0 ft3/s). Flow at 

13 stations is underestimated and flow at 14 stations is the 

same as the measured statistic or overestimated. The cluster of 

underestimated stations east of Keanae Valley and downstream 

from the Koolau ditch is apparent at lower flows (fig. 14). The 

regression equation for BFQ95 estimates that statistic within 

a relative error of ±50 percent at 12 of the continuous-record 

gaging stations. Flow at 12 stations is underestimated and flow 

at 15 stations is the same as the measured statistic or overestimated. The cluster of underestimated stations east of Keanae 

Valley and below the ditch is persistent at this lowest flow 

statistic (fig. 15).

The results of applying the equation for TFQ50 developed 

in this study can be compared with results using an equation 

for TFQ50 developed by Fontaine and others (1992) for streams 

on Maui and Kauai:

TFQ50 = 4.49(DA) 0.808(CE)-0.641(P) 0.985 , (2)

where: TFQ50 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, 

and 

P is mean annual precipitation, in inches.

For this comparison, CE was calculated using the relation 

0.5[MAXELEV+MINELEV], and P was calculated using the 

relation 13.53719[Rainfall/DA] for each drainage basin from 

the data in table 5, because the original values from Fontaine 

and others (1992) were not available. For the 17 stations from 

which data were used to develop the regression equations for 

this study, equation 2 (1992 study) provides a MAD of 20 

percent compared with 12 percent determined using the equation for TFQ50 (table 8) developed in this study. The SEr

 and 

SEp for the newly developed equation are also lower (15.3 and 

20.9 percent, respectively) than for the previous equation (46.2 

and 54.3 percent, respectively). Therefore, the newly developed equation for TFQ50 is an improvement over the equation 

determined by Fontaine and others (1992).

Application of the regression equations to 

ungaged sites

The regression equations developed for this study from 

the flow statistics in table 2 and the basin characteristics listed 

in tables 5 and 6 were used to estimate the TFQ50, TFQ95, 

BFQ50, and BFQ95 duration discharges at selected ungaged 

sites in the study area (plate 1). Estimated streamflow, prediction intervals, standard error, measured flow, and relative error 

for 47 ungaged sites are listed in Table 10. Where possible, 

measured flow values were determined using a combination 

of flow-duration statistics for an upstream gaging-station and 

low-flow measurements at ungaged sites downstream of the 

diversions to provide additional basis for evaluating the equation-based estimates.

Generally, an estimate of flow at an ungaged site made 

on the basis of a flow-duration discharge at an upstream gaging station and a single measurement of flow at the ungaged 

site results in a large uncertainty in the estimate. For most 

ungaged sites in the study area, however, these values are all 

the information that is available. This technique is considered 

applicable in the study area because the streams are dry immediately downstream of the diversions at least 50 percent of the 

time, and measured low flow further downstream represents 

only those gains to the stream downstream of the diversions. 

Inflow downstream of the diversions from minor tributaries is 

insignificant.

Low-flow estimates listed in table 10 were derived from 

low-flow measurements from three sources: (1) measurements 

made as part of this study in 2002 and 2003; (2) measurements 

made as part of a previous USGS study in the area during 

1995 to 1999 (Gingerich, 1999); and (3) measurements made 

by EMI in 1928 (reported in Gingerich, 1999). The average 

of all these low-flow measurements were assumed roughly 

equal to TFQ95 flow duration. This is because the flow at 

the index station (5180) during all the USGS measurements 

(1995–99 and 2002–03) ranged from TFQ94 to TFQ97 and the 

flow was at TFQ90 during the 1928 EMI measurements. The 

difference in flow between TFQ90 (3.3 ft3/s) and TFQ95 (2.5 

ft3/s) at 5180 is 0.8 ft3/s, or a relative difference of 32 percent. 

However, because the low-flow measurements were all made 

downstream of the diversion ditches during base-flow periods, 

there is little variation between low flows even as flow at the 

Estimation of Flow Characteristics of Ungaged Streams 43
Figure 12. Distribution of relative error between measured and equation-estimated median total flow (TFQ50) at gagingstations, northeast Maui, Hawaii.

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44 Median and Low-Flow Characteristics for Streams under Natural and Diverted Conditions, Northeast Maui, Hawaii
Figure 13. Distribution of relative error between measured and equation-estimated median base flow (BFQ50) at gagingstations, northeast Maui, Hawaii.

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Estimation of Flow Characteristics of Ungaged Streams 45
Figure 14. Distribution of relative error between measured and equation-estimated Q95 total flow (TFQ95) at gaging-station, northeast Maui, Hawaii.

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46 Median and Low-Flow Characteristics for Streams under Natural and Diverted Conditions, Northeast Maui, Hawaii
Figure 15. Distribution of relative error between measured and equation-estimated Q95 base flow (BFQ95) at gaging-station, northeast Maui, Hawaii.

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Estimation of Flow Characteristics of Ungaged Streams 47
Table 10. Streamflow statistics estimated using regression equations, lower and upper confidence intervals, standard errors, measured flow, and relative errors for 

ungaged basins, northeast Maui, Hawaii—Continued[TFQxx is the xx-percent flow duration of total streamflow; BFQxx is the xx-percent flow duration of base flow; estimated and measured flow and confidence intervals are in cubic feet per second; 90% LCL and UCL is 90-percent lower and upper confidence level; Standard error is in percent; Relative error is ([estimated flow – measured flow]/measured flow x 100), in percent; L, lower; M, middle; U, upper; Measured flows in bold italic fall within the lower and upper 90-percent confidence interval; East Maui Irrigation Co., Ltd (EMI) 1928 measurements from March 16-20 when index station had a Q90 flow (reported in Gingerich, 1999); >, likely greater than; <, likely less than; --, not available]

Stream location Statistic TFQ50 BFQ50 TFQ95 BFQ95 Source of measured flow estimates

Hanawi lower (HwL) Estimated flow

90% LCL90% UCLStandard errorMeasured flowRelative error

161419

9.1

> 28

< -43

10

8.3

1313.4

> 24

< -58

5.13.57.6

22.125

-79

4.63.07.0

24.8

> 19

< -76

TFQ50, BFQ50, BFQ95: combined flow statistics 

from 5080 and 5090 upstream; TFQ95: Average of flow on entire stream Feb. 22, 1995 [

Q97] (Gingerich, 1999) and combined 

Q95 flows from 5080 

and 5090 upstream plus flow Nov. 7, 2003 [

Q94]

Kapaula lower (KL) Estimated flow

90% LCL90% UCLStandard errorMeasured flowRelative error

7.56.68.77.2

> 7.5

0

4.63.95.6

10.6

> 5.1

< -8

1.81.42.2

12.6

> 3.3

< -45

1.51.22.0

14.1

> 3.0

< -50

Combined flow statistic from 5100 and 5110 upstream

Waiaaka lower (WaL) Estimated flow

90% LCL90% UCLStandard errorMeasured flowRelative error

1.31.11.8

13.0

> 0.86

< 63

0.800.571.1

19.2

> 0.77< 4

0.390.220.67

31.9

> 0.54

< -28

0.340.180.62

35.9

> 0.53

< -36

Flow statistics from 5130 upstream; unknown 

amount of upstream diversion at Koolau Ditch

Paakea lower (PaL) Estimated flow

90% LCL90% UCLStandard errorMeasured flowRelative error

4.33.75.18.9

> 4.0< 8

2.82.33.6

13.1

> 3.8

< -24

1.51.02.1

21.7

> 3.0

< -50

1.40.892.1

24.3

> 3.0

< -53

Flow statistics from 5140 upstream; unknown 

amount of upstream diversion at Koolau Ditch

Paakea upper (PaU) Estimated flow

90% LCL90% UCLStandard errorMeasured flowRelative error

1.51.31.8

10.0

----

0.880.681.1

14.7

----

0.500.330.75

23.5

----

0.420.270.66

26.4

----

No data available

Waiohue lower (WeL) Estimated flow

90% LCL90% UCLStandard errorMeasured flowRelative error

7.86.69.39.8

> 6.8

< 16

5.54.37.1

14.4

> 5.6

< -2

2.91.94.4

24.0

> 3.6

< -19

2.81.84.5

26.9

> 3.5

< -20

Flow statistics from 5150 upstream plus EMI 1928 

measurement

Table 10. Streamflow statistics estimated using regression equations, lower and upper confidence intervals, standard errors, measured flow, and relative errors for ungaged basins, northeast Maui, Hawaii.[TFQxx is the xx-percent flow duration of total streamflow; BFQxx is the xx-percent flow duration of base flow; estimated and measured flow and confidence intervals are in cubic feet per second; 90% LCL and UCL is 90-percent lower and upper confidence level; Standard error is in percent; Relative error is ([estimated flow – measured flow]/measured flow x 100), in percent; L, lower; M, middle; U, upper; Measured flows in bold italic fall within the lower and upper 90-percent confidence interval; East Maui Irrigation Co., Ltd (EMI) 1928 measurements from March 16-20 when index station had a Q90 flow (reported in Gingerich, 1999); >, likely greater than; <, likely less than; --, not available]

48 Median and Low-Flow Characteristics for Streams under Natural and Diverted Conditions, Northeast Maui, Hawaii
Table 10. Streamflow statistics estimated using regression equations, lower and upper confidence intervals, standard errors, measured flow, and relative errors for ungaged basins, northeast Maui, Hawaii—Continued[TFQxx is the xx-percent flow duration of total streamflow; BFQxx is the xx-percent flow duration of base flow; estimated and measured flow and confidence intervals are in cubic feet per second; 90% LCL and UCL is 90-percent lower and upper confidence level; Standard error is in percent; Relative error is ([estimated flow – measured flow]/measured flow x 100), in percent; L, lower; M, middle; U, upper; Measured flows in bold italic fall within the lower and upper 90-percent confidence interval; East Maui Irrigation Co., Ltd (EMI) 1928 measurements from March 16-20 when index station had a Q90 flow (reported in Gingerich, 1999); >, likely greater than; <, likely less than; --, not available]

Stream location Statistic TFQ50 BFQ50 TFQ95 BFQ95 Source of measured flow estimates

Waiohue middle (WeM) Estimated flow

90% LCL90% UCLStandard errorMeasured flowRelative error

6.55.57.69.0

> 6.8

< -4

4.43.55.6

13.2

> 5.6

< -21

2.31.63.4

21.9

3.6

-36

2.21.43.4

24.6

> 3.5

< -37

Flow statistics from 5150 upstream plus EMI 1928 

measurement

Puakaa middle (PuM) Estimated flow

90% LCL90% UCLStandard errorMeasured flowRelative error

3.63.14.28.6

----

2.21.82.8

12.7

----

1.00.701.4

20.0

> 0.62

< 61

0.880.601.3

22.4

----

TFQ95: EMI 1928 measurement; unknown amount 

of upstream diversion at Koolau Ditch

Puakaa upper (PuU) Estimated flow

90% LCL90% UCLStandard errorMeasured flowRelative error

1.91.62.29.1

----

1.10.891.4

13.3

----

0.630.440.92

21.3

----

0.540.350.81

23.9

----

No data available

Kopiliula lower (KpL) Estimated flow

90% LCL90% UCLStandard errorMeasured flowRelative error

11

9.7

13

7.2

> 11

 0

6.75.68.1

10.6

> 8.1

< -17

3.42.54.6

16.9

5.4

-38

2.92.14.0

19.0

5.1

-43

Flow statistics from 5160 upstream plus average of 

6 USGS low-flow measurements in 2002-03

Kopiliula middle (KpM) Estimated flow

90% LCL90% UCLStandard errorMeasured flowRelative error

10

9.4

12

6.1

> 9.0

< 11

6.25.37.39.06.0

< 3

2.82.23.6

14.8

3.3

-18

2.31.73.1

16.5

3.0

-23

Flow statistics from 5160 upstream plus average of 

7 USGS low-flow measurements in 2002-03

Estimation of Flow Characteristics of Ungaged Streams 49
Table 10. Streamflow statistics estimated using regression equations, lower and upper confidence intervals, standard errors, measured flow, and relative errors for 

ungaged basins, northeast Maui, Hawaii—Continued[TFQxx is the xx-percent flow duration of total streamflow; BFQxx is the xx-percent flow duration of base flow; estimated and measured flow and confidence intervals are in cubic feet per second; 90% LCL and UCL is 90-percent lower and upper confidence level; Standard error is in percent; Relative error is ([estimated flow – measured flow]/measured flow x 100), in percent; L, lower; M, middle; U, upper; Measured flows in bold italic fall within the lower and upper 90-percent confidence interval; East Maui Irrigation Co., Ltd (EMI) 1928 measurements from March 16-20 when index station had a Q90 flow (reported in Gingerich, 1999); >, likely greater than; <, likely less than; --, not available]

Stream location Statistic TFQ50 BFQ50 TFQ95 BFQ95 Source of measured flow estimates

East Wailuaiki lower (EWL) Estimated flow

90% LCL90% UCLStandard errorMeasured flowRelative error

10

9.3

12

6.0

> 9.4

< 6

6.15.27.18.8

> 6.1

 0

2.72.13.4

14.4

> 3.2

< -16

2.21.72.9

16.2

> 2.8

< -21

Flow statistics from 5170 upstream plus EMI 1928 measurement

East Wailuaiki middle 

(EWM)

Estimated flow90% LCL90% UCLStandard errorMeasured flowRelative error

9.58.5

10

5.8

> 9.4

< 1

5.64.86.48.8

> 6.1

< -8

2.52.03.3

14.0

3.2

-22

2.11.62.8

15.7

2.8

< -25

Flow statistics from 5170 upstream plus EMI 1928 measurement

West Wailuaiki lower 

(WWL)

Estimated flow90% LCL90% UCLStandard errorMeasured flowRelative error

10

9.3

12

6.0

> 11

< -9

6.05.27.18.9

> 6.7

< -10

2.52.03.3

14.2

> 3.3

< -24

2.11.62.7

15.9

> 2.9

< -28

Flow statistics from 5180 upstream plus EMI 1928 measurement

West Wailuaiki middle 

(WWM)

Estimated flow90% LCL90% UCLStandard errorMeasured flowRelative error

9.78.7

11

5.8

> 11

< -12

5.64.86.58.5

> 6.7

< -16

2.41.93.1

13.9

3.3

-27

2.01.52.6

15.6

2.9

-31

Flow statistics from 5180 upstream plus EMI 1928 measurement

Wailuanui lower (WL) Estimated flow

90% LCL90% UCLStandard errorMeasured flowRelative error

9.58.6

10.5

5.8

> 9.5

< -5

5.54.76.48.5

> 5.8

< -17

2.21.72.7

12.2

2.7

-27

1.81.42.2

13.7

> 2.4

< -28

Combined flow statistics from 5190, 5200, and 5210 upstream plus average of 2 USGS low-flow measurements in 2002-03; unknown amount of taro diversion and return flow

50 Median and Low-Flow Characteristics for Streams under Natural and Diverted Conditions, Northeast Maui, Hawaii
Table 10. Streamflow statistics estimated using regression equations, lower and upper confidence intervals, standard errors, measured flow, and relative errors for 

ungaged basins, northeast Maui, Hawaii—Continued[TFQxx is the xx-percent flow duration of total streamflow; BFQxx is the xx-percent flow duration of base flow; estimated and measured flow and confidence intervals are in cubic feet per second; 90% LCL and UCL is 90-percent lower and upper confidence level; Standard error is in percent; Relative error is ([estimated flow – measured flow]/measured flow x 100), in percent; L, lower; M, middle; U, upper; Measured flows in bold italic fall within the lower and upper 90-percent confidence interval; East Maui Irrigation Co., Ltd (EMI) 1928 measurements from March 16-20 when index station had a Q90 flow (reported in Gingerich, 1999); >, likely greater than; <, likely less than; --, not available]

Stream location Statistic TFQ50 BFQ50 TFQ95 BFQ95 Source of measured flow estimates

Waiokomilo lower (WoL) Estimated flow

90% LCL90% UCLStandard errorMeasured flowRelative error

141217

9.8

----

8.76.8

1114.4

----

2.82.23.6

14.2

5.7

-51

2.41.83.2

15.9

----

TFQ95: 1999 USGS low-flow measurement (Gingerich, 1999)

Waiokomilo middle (WoM) Estimated flow

90% LCL90% UCLStandard errorMeasured flowRelative error

10

9.0

12

7.3

----

6.15.07.4

10.7

----

2.21.82.6

11.4

4.9

-55

1.81.42.3

12.8

----

TFQ95: Average of EMI 1928 measurement and 1999 USGS low-flow measurement (Gingerich, 1999)

Waiokomilo upper (WoU) Estimated flow

90% LCL90% UCLStandard errorMeasured flowRelative error

7.06.17.86.9

----

3.93.34.7

10.2

----

1.31.11.69.1

----

1.10.901.3

10.1

----

No data available

Ohia lower (OL) Estimated flow

90% LCL90% UCLStandard errorMeasured flowRelative error

8.75.5

1426.6

----

8.64.3

1740.0

----

4.61.5

1469.1

----

6.11.8

2179.3

----

Ohia Spring average flow is 4.7 cubic feet per second (Stearns and Macdonald, 1942) but little flow reaches the ocean due to infiltration and agricultural evapotranspiration losses

Palauhulu lower (PhL) Estimated flow

90% LCL90% UCLStandard errorMeasured flowRelative error

171420

9.6

----

11

8.9

1514.2

----

4.43.16.3

20.5

> 2.4

< 83

4.02.76.0

23.0

----

TFQ95: TFQ95 flow at 5220, measuring taro diversion from stream; losing stream therefore effects of natural flow addition are unknown

Estimation of Flow Characteristics of Ungaged Streams 51
Table 10. Streamflow statistics estimated using regression equations, lower and upper confidence intervals, standard errors, measured flow, and relative errors for 

ungaged basins, northeast Maui, Hawaii—Continued[TFQxx is the xx-percent flow duration of total streamflow; BFQxx is the xx-percent flow duration of base flow; estimated and measured flow and confidence intervals are in cubic feet per second; 90% LCL and UCL is 90-percent lower and upper confidence level; Standard error is in percent; Relative error is ([estimated flow – measured flow]/measured flow x 100), in percent; L, lower; M, middle; U, upper; Measured flows in bold italic fall within the lower and upper 90-percent confidence interval; East Maui Irrigation Co., Ltd (EMI) 1928 measurements from March 16-20 when index station had a Q90 flow (reported in Gingerich, 1999); >, likely greater than; <, likely less than; --, not available]

Stream location Statistic TFQ50 BFQ50 TFQ95 BFQ95 Source of measured flow estimates

Palauhulu middle (PhM) Estimated flow

90% LCL90% UCLStandard errorMeasured flowRelative error

141216

8.3

----

9.37.5

1212.2

----

3.92.85.4

18.9

----

3.52.45.1

21.1

----

Plunkett Spring average flow is 2.7 cubic feet per second (Stearns and Macdonald, 1942) but stream goes dry due to infiltration losses so effects of natural flow addition are unknown

Kano upper (KoU) Estimated flow

90% LCL90% UCLStandard errorMeasured flowRelative error

4.54.24.94.5

----

2.52.22.86.6

----

1.00.871.29.7

----

0.820.680.99

10.9

----

No data available

Hauoli Wahine upper 

(HWU)

Estimated flow90% LCL90% UCLStandard errorMeasured flowRelative error

1.51.22.0

14.7

----

0.930.641.4

21.8

----

0.880.661.2

16.7

----

0.750.541.0

18.7

----

No data available

Piinaau lower (PiL) Estimated flow

90% LCL90% UCLStandard errorMeasured flowRelative error

40315214.6

----

28194121.6

----

13

7.1

2536.3

> 0.47

< 2700

13

6.3

2540.9

----

TFQ95: EMI 1928 measurement, unknown amount of upstream diversion at Koolau Ditch

Piinaau middle (PiM) Estimated flow

90% LCL90% UCLStandard errorMeasured flowRelative error

28223615.0

----

20132922.2

----

12

6.7

2234.9

> 0.47

< 2500

11

5.8

2239.3

----

TFQ95: EMI 1928 measurement, unknown amount of upstream diversion at Koolau Ditch

52 Median and Low-Flow Characteristics for Streams under Natural and Diverted Conditions, Northeast Maui, Hawaii
Table 10. Streamflow statistics estimated using regression equations, lower and upper confidence intervals, standard errors, measured flow, and relative errors for 

ungaged basins, northeast Maui, Hawaii—Continued[TFQxx is the xx-percent flow duration of total streamflow; BFQxx is the xx-percent flow duration of base flow; estimated and measured flow and confidence intervals are in cubic feet per second; 90% LCL and UCL is 90-percent lower and upper confidence level; Standard error is in percent; Relative error is ([estimated flow – measured flow]/measured flow x 100), in percent; L, lower; M, middle; U, upper; Measured flows in bold italic fall within the lower and upper 90-percent confidence interval; East Maui Irrigation Co., Ltd (EMI) 1928 measurements from March 16-20 when index station had a Q90 flow (reported in Gingerich, 1999); >, likely greater than; <, likely less than; --, not available]

Stream location Statistic TFQ50 BFQ50 TFQ95 BFQ95 Source of measured flow estimates

Piinaau upper (PiU) Estimated flow

90% LCL90% UCLStandard errorMeasured flowRelative error

21162714.4

----

14

9.7

2021.3

----

9.45.5

1631.1

----

8.54.7

1634.9

----

No data available

Nuaailua lower (NL) Estimated flow

90% LCL90% UCLStandard errorMeasured flowRelative error

9.98.0

1212.1

----

7.45.4

1017.8

----

4.02.46.7

29.8

> 0.31

< 1200

4.12.37.2

33.5

----

TFQ95: EMI 1928 measurement; unknown amount of upstream diversion at Spreckels Ditch; effects of natural flow addition are unknown because stream may be gaining or losing

Nuaailua middle (NM) Estimated flow

90% LCL90% UCLStandard errorMeasured flowRelative error

3.93.34.58.6

----

2.52.03.1

12.6

----

1.20.861.8

20.8

> 0.31

< 290

1.10.751.7

23.3

----

TFQ95: EMI 1928 measurement; unknown amount of upstream diversion at Spreckels Ditch; effects of natural flow addition are unknown because stream may be gaining or losing

Nuaailua upper (NU) Estimated flow

90% LCL90% UCLStandard errorMeasured flowRelative error

0.560.430.73

15.1

----

0.280.190.42

22.4

----

0.190.110.34

33.3

----

0.150.080.27

37.5

----

No data available

Honomanu lower (HnL) Estimated flow

90% LCL90% UCLStandard errorMeasured flowRelative error

161419

8.5

< 5.7

> 180

10

8.3

1312.6

< 2.8

> 260

4.63.26.6

20.7

< 1.0

> 320

4.02.76.0

23.2

< 0.74

> 440

Values are maximum estimates using flow statistics from 5270 upstream because stream infiltration losses are unknown; stream goes dry at low flow

Estimation of Flow Characteristics of Ungaged Streams 53
Table 10. Streamflow statistics estimated using regression equations, lower and upper confidence intervals, standard errors, measured flow, and relative errors for 

ungaged basins, northeast Maui, Hawaii—Continued[TFQxx is the xx-percent flow duration of total streamflow; BFQxx is the xx-percent flow duration of base flow; estimated and measured flow and confidence intervals are in cubic feet per second; 90% LCL and UCL is 90-percent lower and upper confidence level; Standard error is in percent; Relative error is ([estimated flow – measured flow]/measured flow x 100), in percent; L, lower; M, middle; U, upper; Measured flows in bold italic fall within the lower and upper 90-percent confidence interval; East Maui Irrigation Co., Ltd (EMI) 1928 measurements from March 16-20 when index station had a Q90 flow (reported in Gingerich, 1999); >, likely greater than; <, likely less than; --, not available]

Stream location Statistic TFQ50 BFQ50 TFQ95 BFQ95 Source of measured flow estimates

Honomanu middle (HnM) Estimated flow

90% LCL90% UCLStandard errorMeasured flowRelative error

131115

7.3

< 5.7

> 130

8.06.69.7

10.8

< 2.8

> 190

3.72.75.0

17.8

< 1.0

> 240

3.12.24.4

19.9

< 0.74

> 320

Values are maximum estimates using flow statistics from 5270 upstream because stream infiltration losses are unknown; stream goes dry at low flow

Punalau lower (PlL) Estimated flow

90% LCL90% UCLStandard errorMeasured flowRelative error

6.55.57.69.4

----

4.53.55.7

13.8

----

2.21.53.4

22.9

----

2.11.43.4

25.7

----

No data available

Punalau middle (PlM) Estimated flow

90% LCL90% UCLStandard errorMeasured flowRelative error

5.84.96.89.1

----

3.93.15.0

13.5

----

2.11.43.1

22.3

0.00

NA

2.01.33.1

25.0

0.00

NA

TFQ95: EMI 1928 measurement; unknown amount of upstream diversion at Spreckels Ditch; effects of natural flow addition are unknown because stream may be gaining or losing; stream goes dry at low flow

Haipuaena lower (HaL) Estimated flow

90% LCL90% UCLStandard errorMeasured flowRelative error

9.78.0

1210.7

6.8

43

5.64.27.4

15.7

3.5

60

1.61.31.99.31.76

1.31.11.6

10.4

1.30

Flow statistics from 5360 upstream plus EMI 1928 measurement; effects of natural flow addition are unknown because stream is losing; stream goes dry at low flow

Haipuaena middle lower 

(HaML)

Estimated flow90% LCL90% UCLStandard errorMeasured flowRelative error

8.87.3

1010.1

6.8

29

5.03.96.5

14.8

3.5

43

1.51.21.79.11.7

-12

1.21.01.4

10.2

1.3

-8

Flow statistics from 5360 upstream plus EMI 1928 measurement; effects of natural flow addition are unknown because stream is losing; stream goes dry at low flow

54 Median and Low-Flow Characteristics for Streams under Natural and Diverted Conditions, Northeast Maui, Hawaii
Table 10. Streamflow statistics estimated using regression equations, lower and upper confidence intervals, standard errors, measured flow, and relative errors for 

ungaged basins, northeast Maui, Hawaii—Continued[TFQxx is the xx-percent flow duration of total streamflow; BFQxx is the xx-percent flow duration of base flow; estimated and measured flow and confidence intervals are in cubic feet per second; 90% LCL and UCL is 90-percent lower and upper confidence level; Standard error is in percent; Relative error is ([estimated flow – measured flow]/measured flow x 100), in percent; L, lower; M, middle; U, upper; Measured flows in bold italic fall within the lower and upper 90-percent confidence interval; East Maui Irrigation Co., Ltd (EMI) 1928 measurements from March 16-20 when index station had a Q90 flow (reported in Gingerich, 1999); >, likely greater than; <, likely less than; --, not available]

Stream location Statistic TFQ50 BFQ50 TFQ95 BFQ95 Source of measured flow estimates

Haipuaena middle upper 

(HaMU)

Estimated flow90% LCL90% UCLStandard errorMeasured flowRelative error

7.86.79.29.06.8

15

4.53.55.6

13.2

3.5

29

1.41.21.69.01.7

-18

1.10.931.3

10.0

1.3

-15

Flow statistics from 5360 upstream; effects of natural flow addition are unknown because stream may be gaining or losing

Puohokamoa lower (PL) Estimated flow

90% LCL90% UCLStandard errorMeasured flowRelative error

18152210.1

> 12< 50

12

9.6

1614.9

> 6.6

< 82

5.03.47.5

22.7

> 2.7

< 85

4.73.07.3

25.4

> 2.3

< 100

Flow statistics from 5450 upstream plus EMI 1928 measurement; effects of natural flow addition are unknown because stream may be gaining or losing

Puohokamoa middle lower 

(PML)

Estimated flow90% LCL90% UCLStandard errorMeasured flowRelative error

171420

9.6

> 12< 42

11

9.0

1514.1

> 6.6

< 67

4.83.37.0

22.0

2.7

78

4.42.96.8

24.7

> 2.3

< 91

Flow statistics from 5450 upstream plus EMI 1928 measurement; effects of natural flow addition are unknown because stream may be gaining or losing

Puohokamoa middle upper 

(PMU)

Estimated flow90% LCL90% UCLStandard errorMeasured flowRelative error

151317

8.7

> 11< 25

9.97.9

12.412.8

> 6.4

< 55

4.33.06.1

20.3

> 2.5

< 72

3.92.65.8

22.8

> 2.1

< 86

Flow statistics from 5450 upstream; effects of natural flow addition are unknown because stream may be gaining or losing

Wahinepee lower (WeL) Estimated flow

90% LCL90% UCLStandard errorMeasured flowRelative error

2.41.83.2

16.6

----

1.81.12.7

24.6

----

1.60.882.8

33.9

> 0.46

< 250

1.60.833.0

38.1

----

TFQ95: EMI 1928 measurement; unknown amount of upstream diversion at Wailoa Ditch; effects of natural flow addition are unknown because stream may be gaining or losing

Estimation of Flow Characteristics of Ungaged Streams 55
Table 10. Streamflow statistics estimated using regression equations, lower and upper confidence intervals, standard errors, measured flow, and relative errors for 

ungaged basins, northeast Maui, Hawaii—Continued[TFQxx is the xx-percent flow duration of total streamflow; BFQxx is the xx-percent flow duration of base flow; estimated and measured flow and confidence intervals are in cubic feet per second; 90% LCL and UCL is 90-percent lower and upper confidence level; Standard error is in percent; Relative error is ([estimated flow – measured flow]/measured flow x 100), in percent; L, lower; M, middle; U, upper; Measured flows in bold italic fall within the lower and upper 90-percent confidence interval; East Maui Irrigation Co., Ltd (EMI) 1928 measurements from March 16-20 when index station had a Q90 flow (reported in Gingerich, 1999); >, likely greater than; <, likely less than; --, not available]

Stream location Statistic TFQ50 BFQ50 TFQ95 BFQ95 Source of measured flow estimates

Wahinepee middle (WeM) Estimated flow

90% LCL90% UCLStandard errorMeasured flowRelative error

1.30.921.8

19.2

----

0.890.541.4

28.5

----

0.970.561.7

32.4

0.46

110

0.940.501.7

36.5

----

TFQ95: EMI 1928 measurement; unknown amount of upstream diversion at Wailoa Ditch; effects of natural flow addition are unknown because stream may be gaining or losing

Waikamoi lower (WiL) Estimated flow

90% LCL90% UCLStandard errorMeasured flowRelative error

10

9.0

12

7.1

< 11

> -9

5.74.86.9

10.4

< 5.9

> -3

2.01.62.6

13.2

< 2.8

> -29

1.61.22.1

14.8

< 2.4

> -33

Flow statistics from 5550 and 5570 upstream plus Waikamoi middle upper and middle lower sites; effects of natural flow addition are unknown because stream is losing; stream goes dry at low flow

Waikamoi middle lower 

(WiML)

Estimated flow90% LCL90% UCLStandard errorMeasured flowRelative error

9.68.6

11

6.6

> 11

-13

5.44.56.49.6

> 5.9

-8

2.01.62.5

13.1

2.8

-29

1.61.22.0

14.7

2.4

-33

Flow statistics from 5550 and 5570 upstream plus Waikamoi middle upper plus average of 9 USGS low-flow measurements in 2002-03

Waikamoi middle upper 

(WiMU)

Estimated flow90% LCL90% UCLStandard errorMeasured flowRelative error

9.28.3

10

6.2

> 10.5

< -16

5.24.46.19.2

> 5.7

< -9

2.01.62.5

13.1

2.6

-23

1.61.22.0

14.6

> 2.2

< -27

Flow statistics from 5550 and 5570 upstream plus average of 10 USGS low-flow measurements in 2002-03

Kolea lower (KaL) Estimated flow

90% LCL90% UCLStandard errorMeasured flowRelative error

4.83.95.9

11.4

----

3.42.54.6

16.9

----

1.91.23.1

28.1

> 0.2

< 1100

1.91.13.2

31.5

----

TFQ95: EMI 1928 measurement; unknown amount of upstream diversion at Wailoa Ditch; effects of natural flow addition are unknown because stream may be gaining or losing

56 Median and Low-Flow Characteristics for Streams under Natural and Diverted Conditions, Northeast Maui, Hawaii
Table 10. Streamflow statistics estimated using regression equations, lower and upper confidence intervals, standard errors, measured flow, and relative errors for 

ungaged basins, northeast Maui, Hawaii—Continued[TFQxx is the xx-percent flow duration of total streamflow; BFQxx is the xx-percent flow duration of base flow; estimated and measured flow and confidence intervals are in cubic feet per second; 90% LCL and UCL is 90-percent lower and upper confidence level; Standard error is in percent; Relative error is ([estimated flow – measured flow]/measured flow x 100), in percent; L, lower; M, middle; U, upper; Measured flows in bold italic fall within the lower and upper 90-percent confidence interval; East Maui Irrigation Co., Ltd (EMI) 1928 measurements from March 16-20 when index station had a Q90 flow (reported in Gingerich, 1999); >, likely greater than; <, likely less than; --, not available]

Stream location Statistic TFQ50 BFQ50 TFQ95 BFQ95 Source of measured flow estimates

Kolea middle (KaM) Estimated flow

90% LCL90% UCLStandard errorMeasured flowRelative error

3.63.04.4

11.3

----

2.51.93.4

16.7

----

1.60.982.5

26.9

> 0.16

< 900

1.50.892.5

30.2

----

TFQ95: EMI 1928 measurement; unknown amount of upstream diversion at Wailoa Ditch; effects of natural flow addition are unknown because stream may be gaining or losing

Estimation of Flow Characteristics of Ungaged Streams 57
index station varied between TFQ90 and TFQ95. Flow-duration 

values for five gaging stations (5090, 5110, 5130, 5140, and 

5210) operated downstream of the Koolau Diversion indicate 

an average relative difference between TFQ90 and TFQ95 of 

11 percent, and absolute differences ranging from 0.05 ft3/s 

at station 5130 to 1.0 ft3/s at station 5090. In general, base 

flows sustained by springs downstream from the diversion 

ditch exhibit less variability. Where measured TFQ50 and 

BFQ50 flow durations are listed in table 10, they are based on 

a combination of upstream flow statistics and the measured 

TFQ95 low flows, but are preceded by a greater than symbol 

(>) indicating that the TFQ95 flow is a minimum value and the 

actual flow is higher by an unknown amount.

Application of the regression equations to estimate flow 

at some of the sites shown in table 10 violates the assumptions 

of the regression analysis because they are intermittent-flow 

sites or have basin characteristics that are outside the range 

used to develop the equations. Some of the poor results shown 

in table 10 can be explained by these violations. A plot of 

the spatial distribution of relative-error values for TFQ95, the 

only duration discharge for which some measured flow values 

are available, shows two distinct groupings of results. East of 

Keanae Valley, the TFQ95 equation generally underestimates 

flow, and within and west of Keanae Valley, the equation generally overestimates flow (fig. 16). This grouping reflects the 

pattern for ground-water occurrence east and west of Keanae 

Valley described by Gingerich (1999). West of Keanae Valley, 

ground water occurs at high elevations in the low-permeability 

Kula Volcanics and at low elevations in the higher permeability Honomanu Basalt. Streams at high elevations gain 

base flow from the upper perched zone and lose water to the 

underlying unsaturated zone nearer the coast. Where streams 

lose water at lower elevations, the regression equations generally overestimate the amount of water in the stream. East of 

Keanae Valley, the discharge of ground water from a vertically 

extensive freshwater lens causes streams to gain flow all the 

way to the coast. The regression equations generally underestimate the additional streamflow gained from springs. Within 

Keanae Valley, streamflow gain from the freshwater lens is 

lost to the veneering lava flows of the Hana Volcanics; hence, 

the equations overestimate streamflow here as well.

Ordinarily, regression equations would be developed for 

each distinct hydrologic regime (east or west of Keanae Valley) to better account for the basin characteristics controlling 

streamflow. However, dividing the gaging stations used to generate the regression equations (n =17) into two groups would 

result in the number of stations in each group (n = 8 and n = 9) 

being too small for significant statistical analyses.

 At sites where flow is underestimated by the regression 

equation, the relative errors range from 7 to 79 percent and 

average 30 percent. At sites where flow is overestimated, the 

relative errors are not always meaningful because many of the 

streams are dry. Therefore, any flow estimate greater than zero 

means that relative error for that site cannot be calculated.

Most-reliable Estimates of Natural 

Flow-Duration Statistics

Most-reliable estimates of flow-duration statistics for 

natural (undiverted) streamflow at ungaged sites on 21 streams 

in the study area were made using a combination of continuous record gaging-station data, low-flow measurements, and 

values determined from the regression equations developed 

as part of this study (Table 11). No estimates were made for 

Piinaau Stream because no flow data were available and the 

regression equations were not applicable to this intermittent 

stream. Furthermore, all three of the basin characteristics 

for Piinaau Stream that are used in the regression equations 

fall outside the range of values used to develop the equations (table 8). The reliability of the estimates depends on the 

combination of data used to develop the estimates. Estimates 

of flow statistics developed on the basis of data from continuous-record gaging stations are deemed the most reliable; those 

estimates developed from the regression equations alone are 

considered the least reliable. Estimates that are developed for 

sites downstream from gaging stations and adjusted on the 

basis of low-flow measurements or the regression equations 

are considered to be of intermediate reliability.

The various data combinations used to develop the 

most-reliable estimates can be described using Hanawi Stream 

as an example. At the Hanawi upper site, the TFQ50, TFQ95, 

BFQ50, and BFQ95 duration discharges were estimated on 

the basis of data available from gaging station 5080. At the 

Hanawi middle site, which is downstream from the Koolau 

ditch, duration discharges were estimated from a combination of daily flows at gaging stations 5090 at the middle site 

and 5080 at the upper site. At the Hanawi lower site, TFQ95

was developed using the estimated TFQ95 at the middle site 

(19 ft3/s), plus the average of gains in streamflow downstream 

from the middle site, which was determined from two pairs of 

low-flow measurements [2.8 ft3/s (TFQ97 at index site); and 3.4 

ft3/s (TFQ94 at index site)]. TFQ50 at the Hanawi lower site was 

estimated using the estimated TFQ50 from the middle site (28 

ft3/s), plus the estimated gain between the lower and middle 

sites, using the TFQ50 regression equation (16 ft3/s – 12 ft3/s = 

4.0 ft3/s). BFQ50 and BFQ95 were estimated in a similar manner 

to TFQ50.

Discussion of results for selected streams

For some streams, the decisions made in developing the 

most-reliable estimates of flow-duration statistics require 

further discussion. Estimates for middle and lower sites on 

Makapipi Stream were not attempted due to lack of flow data 

at these sites and the inapplicability of the regression equations to this intermittent/losing stream.

The TFQ95 estimate at the middle site on Waiokomilo 

Stream was based on flow measurements upstream that 

demonstrated net gains of about 4.1 ft3/s (Gingerich, 1999) 

58 Median and Low-Flow Characteristics for Streams under Natural and Diverted Conditions, Northeast Maui, Hawaii
Figure 16. Distribution of relative error between measured and equation-estimated Q95 total flow (TFQ95) at ungaged sites 

in the study area and at selected gages west of the study area, northeast Maui, Hawaii.

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Most-reliable Estimates of Natural Flow-Duration Statistics 59
Table 11. Estimates of natural (undiverted) streamflow statistics for gaged and ungaged basins, northeast Maui, Hawaii—Continued

[TFQxx is the xx-percent flow duration of total streamflow; BFQxx is the xx-percent flow duration of base flow; all flows are in cubic feet per second; numbers in bold italic are considered maximums at sites downstream of unquantified but known losing reaches; g.s., gaging station; adj., adjustment]

Stream location TFQ50 BFQ50 TFQ95 BFQ95 Source of estimate

Makapipi upper (5070) 2.2 1.3 0.0 0.0 Continuous record gaging stationHanawi lower (HwL) middle (5090) upper (5080)

3228

7.1

2624

4.6

2219

2.4

1919

2.2

Middle site estimate plus equation adj.; TFQ95: Middle site estimate plus low-flow measurementsContinuous record gaging station plus upper site estimateContinuous record gaging station

Kapaula lower (KL) middle (5110) upper (5100)

8.37.54.9

5.75.12.8

3.53.31.2

3.23.01.1

Middle site estimate plus regression equation adj.Continuous record gaging station plus upper site estimateContinuous record gaging station

Waiaaka lower (WaL) middle (5130)

1.4

0.86

1.1

0.77

0.730.54

0.700.52

Middle site estimate plus regression equation adj.Continuous record gaging station

Paakea lower (PaL) middle (5140) upper (PaU)

6.55.51.5

5.54.7

0.90

4.13.5

0.50

4.03.4

0.40

Middle site estimate plus regression equation adj.Continuous record gaging station plus upper site estimateRegression equation

Waiohue lower (WeL) middle (WeM) upper (5150)

8.87.46.2

7.56.05.0

4.53.93.0

3.63.02.9

Middle site estimate plus measurement plus regression equation adj.Upper site estimate plus equation adj.; TFQ95: Upper site estimate plus low-flow measurementContinuous record gaging station

Kopiliula lower (KpL) Middle (KpM) middle (PuM) upper (5160) upper (PuU)

1510

3.68.01.9

9.56.52.25.01.1

5.53.41.12.4

0.60

3.82.3

0.90

2.0

0.50

Middle sites estimates plus equation adj.; TFQ95: Middle sites estimates plus low-flow measurementsUpper site estimate plus equation adj.; TFQ95: Upper site estimate plus low-flow measurementsRegression equation; TFQ95: Upper site estimate plus low-flow measurementContinuous record gaging station Regression equation

East Wailuaiki lower (EWL) middle (EWM) upper (5170)

1111

9.1

7.26.85.8

3.43.22.9

2.92.82.5

Middle site estimate plus equation adj.; TFQ95: Middle site estimate plus low-flow measurementUpper site estimate plus equation adj.; TFQ95: Upper site estimate plus low-flow measurementContinuous record gaging station

West Wailuaiki lower (WWL) middle (WWM) upper (5180)

121110

7.26.86.0

3.53.32.5

2.42.32.1

Middle site estimate plus equation adj.; TFQ95: Middle site estimate plus low-flow measurementUpper site estimate plus equation adj.; TFQ95: Upper site estimate plus low-flow measurementContinuous record gaging station

Wailuanui lower (WL) middle (5210) upper (5200) upper (5190)

1110

4.43.2

6.76.12.52.0

2.72.51.0

0.90

2.32.0

0.900.80

Middle site estimate plus equation adj.; TFQ95: Middle site estimate plus low-flow measurementsContinuous record gaging station plus upper sites estimatesContinuous record gaging stationContinuous record gaging station

Table 11. Estimates of natural (undiverted) streamflow statistics for gaged and ungaged basins, northeast Maui, Hawaii.[TFQxx is the xx-percent flow duration of total streamflow; BFQxx is the xx-percent flow duration of base flow; all flows are in cubic feet per second; numbers in bold italic are considered maximums at sites downstream of unquantified but known losing reaches; g.s., gaging station; adj., adjustment]

60 Median and Low-Flow Characteristics for Streams under Natural and Diverted Conditions, Northeast Maui, Hawaii
Table 11. Estimates of natural (undiverted) streamflow statistics for gaged and ungaged basins, northeast Maui, Hawaii—Continued

[TFQxx is the xx-percent flow duration of total streamflow; BFQxx is the xx-percent flow duration of base flow; all flows are in cubic feet per second; numbers in bold italic are considered maximums at sites downstream of unquantified but known losing reaches; g.s., gaging station; adj., adjustment]

Stream location TFQ50 BFQ50 TFQ95 BFQ95 Source of estimate

Waiokomilo lower (WoL) middle (WoM) upper (WoU)

1410

7.0

8.76.13.9

6.85.41.3

6.85.41.1

Regression equation; TFQ95:measurement plus upper site estimateRegression equation; TFQ95:measurement plus upper site estimateRegression equation Ohia

 lower (OL) 4.7 4.7 4.7 4.7 Spring measurementsPalauhulu lower (5220) middle (PhM) upper (KoU) upper (HWU)

1714

4.51.6

11

9.32.5

0.93

4.31.91.0

0.88

4.01.6

0.820.75

Regression equation; TFQ95, BFQ95: measurements at gaging station plus upper sites estimatesRegression equation; TFQ95, BFQ95: measurements plus upper sites estimatesRegression equationRegression equation Piinaau

 lower (PiL) middle (PiM) upper (PiU)

No estimates available due to lack of data

Nuaailua lower (NL) middle (NM) upper (NU)

9.93.9

0.56

7.42.5

0.28

3.3

0.500.19

3.3

0.400.15

Regression equation; TFQ95, BFQ95: middle site estimate plus equation adj.Regression equation; TFQ95, BFQ95: upper site estimate plus low-flow measurementRegression equation

Honomanu lower (HnL) Middle (HnM) upper (5270)

1511

5.7

9.06.72.8

1.11.11.1

0.700.700.70

Middle site estimate plus equation adj.; TFQ95, BFQ95: Middle site estimate plus low-flow measurementUpper site estimate plus equation adj.; TFQ95, BFQ95: Upper site estimate plus low-flow measurementContinuous record gaging station

Punalau lower (PlL) middle (PlM)

6.55.8

4.53.9

2.32.1

2.22.0

Regression equation Regression equation; TFQ95,BFQ95: low-flow measurement

Haipuaena lower (HaL) middle lower (HaML) middle upper (HaMU) upper (5360)

9.98.98.06.8

5.54.94.33.6

2.02.01.91.7

1.61.61.51.3

Middle-lower site estimate plus equation adj.; TFQ95, BFQ95: Middle-lower site estimate plus lowflow measurementMiddle-upper site estimate plus equation adj.; TFQ95, BFQ95: Middle-upper site estimate plus lowflow measurementUpper site estimate plus equation adj.Continuous record gaging station plus upstream gaging station

Puohokamoa lower (PL) middle lower (PML) middle upper (PMU) upper (5450)

17161412

1110

8.46.4

3.63.63.12.5

3.13.12.72.1

Middle-lower site estimate plus equation adj.; TFQ95, BFQ95: Middle-lower site estimate plus lowflow measurementMiddle-upper site estimate plus equation adj.; TFQ95, BFQ95: Middle-upper site estimate plus lowflow measurementUpper site estimate plus equation adj.Continuous record gaging station

Wahinepee lower (WpL) middle (WpM)

2.41.3

1.8

0.90

1.1

0.50

1.1

0.50

Middle site estimate plus equation adj.Regression equation; TFQ95, BFQ95: low-flow measurement

Most-reliable Estimates of Natural Flow-Duration Statistics 61
Table 11. Estimates of natural (undiverted) streamflow statistics for gaged and ungaged basins, northeast Maui, Hawaii—Continued

[TFQxx is the xx-percent flow duration of total streamflow; BFQxx is the xx-percent flow duration of base flow; all flows are in cubic feet per second; numbers in bold italic are considered maximums at sites downstream of unquantified but known losing reaches; g.s., gaging station; adj., adjustment]

Stream location TFQ50 BFQ50 TFQ95 BFQ95 Source of estimate

Waikamoi lower (WiL) middle lower (WiML) middle upper (WiMU) upper (5570) upper (5550)

131312

2.77.0

7.06.76.61.53.5

2.82.82.6

0.70

1.1

2.01.91.9

0.600.80

Middle-lower site estimate plus equation adj.; TFQ95, BFQ95: Middle-lower site estimate plus lowflow measurementsMiddle-upper site estimate plus equation adj.; TFQ95: Middle-upper site estimate plus low-flow 

measurements

Upper sites estimates plus low-flow measurementsContinuous record gaging station Continuous record gaging station

Kolea lower (KaL) middle (KaM)

4.83.6

3.42.5

0.600.20

0.600.20

Regression equation; TFQ95, BFQ95: Middle site estimate plus equation adj.Regression equation; TFQ95,BFQ95: low-flow measurement

62 Median and Low-Flow Characteristics for Streams under Natural and Diverted Conditions, Northeast Maui, Hawaii
combined with the estimate developed from the regression 

equation at the upper site (1.3 + 5.9 – 1.8 = 5.4 ft3/s). At the 

lower site, additional gains (0.12 ft3/s) and a tributary inflow 

(1.3 ft3/s) increase the undiverted flow estimate to 6.8 ft3/s 

[5.2 ft3/s were diverted from the stream for taro at the time of 

the measurements (Gingerich, 1999)]. The estimate for TFQ95

at the upper site appears high on the basis of reconnaissance 

observations on March 5, 2003, when the stream at the upper 

site was observed to be nearly dry, yet the average daily flow 

at the index station was 5.8 ft3/s (about BFQ50). However, 

because no other measurements are available to support this 

observation, the estimate from the regression equation was not 

adjusted.

Ohia Stream is fed almost entirely by Ohia Spring, which 

discharges about 4.7 ft3/s (Stearns and Macdonald, 1942), 

yet during reconnaissance on March 12, 2003 (about TFQ85

at index station), the stream was nearly dry at the mouth. 

Streamflow is lost to evapotranspiration through watercress 

agriculture and through infiltration to the subsurface where 

stream channel modifications have filled the natural channel 

with soil and vegetation. The regression-equation-derived 

estimates for this stream basin are not reliable because rainfall 

(2.2 ft3/s) and MAXELEV (413 ft) values for this basin are 

outside the ranges used to develop the equations (table 8). 

Therefore, the most-reliable estimates are based on the average 

spring discharge, and are considered maximum values because 

of the unquantified streamflow losses between the spring and 

the coast.

Palauhulu Stream also has sections of losing channel and 

was dry between 800 and 300 ft altitude during reconnaissance on March 12–13, 2003 (about TFQ85 at index station). 

Therefore, estimates of TFQ95 and BFQ95 at the middle site 

(about 500 ft altitude) are maximum values, assuming all flow 

at the upper sites reaches the middle site. Estimates of TFQ95

and BFQ95 at the lower site are based on a continuous record 

gaging station (5220), which measured diversions from the 

stream, plus flow from the middle and upper sites assuming 

that all flow from those sites would reach the lower site.

Estimates of flow-duration statistics for Piinaau Stream 

determined from the regression equations are the highest of 

any sites in the study area (table 10), yet the flow observations, although scarce, indicate that flows are much lower 

than estimated. The stream channel was dry between 1,200 ft 

and 600 ft altitude during reconnaissance on March 14, 2003 

(about TFQ91 at index station), and only a trickle of flow was 

observed upstream of the 1,300-ft diversion. A recent (2001) 

large landslide, which covered the stream at about 1,000 ft 

altitude and filled most of the stream channel downstream to 

600 ft altitude with gravel, cobbles, and boulders, complicates 

flow in the stream. This basin has the highest rainfall and 

MAXELEV in the study area and both are above the range of 

characteristics used to develop the flow-duration regression 

equations. Because the regression equations are not valid for 

this stream and reliable flow measurements are lacking, no 

estimates of stream statistics were made for Piinaau Stream 

sites.

Information about gaining or losing reaches on Nuaailua 

or Punalau Streams is not available and therefore estimates 

were made using the regression equations and single low-flow 

measurements.

Honomanu Stream is known to lose flow and be mainly 

dry downstream of the diversion at 1,700 ft altitude (Gingerich, 1999). However, the amount of streamflow lost has not 

been quantified. Therefore, the estimates of TFQ95 and BFQ95

at the middle and lower sites (table 11) are maximum values, assuming all natural flow at the upper site (station 5270) 

reaches the middle and lower sites. The estimates of TFQ50

and BFQ50 are determined solely from the regression equations and are expected to be overestimates but by an unknown 

amount.

Losses of flow were observed in the lower reaches of 

Waikamoi Stream and are expected but have not been quantified in the lower reaches of Haipuaena, Puohokamoa, Wahinepee, and Kolea Streams. Therefore, estimates at ungaged sites 

in the lower reaches of these streams are expected to be high.

Estimates of Flow-Duration Statistics 

under Diverted Conditions

Estimates of flow-duration statistics for diverted streams 

were made for gaged and ungaged sites on 21 streams in the 

study area downstream from the main diversion systems on 

the basis of a combination of continuous-record gaging-station 

data, low-flow measurements, and values determined from the 

regression equations developed as part of this study (Table 12). 

It is assumed that the diversion systems remove all flow lower 

than TFQ50 above 1,200 ft altitude in all diverted streams. The 

flow-duration statistics for the streams can be easily calculated 

by subtracting the flows above the diversion system from the 

estimated undiverted flows below the diversion system. For 

example, TFQ50 at the lower site on West Wailuaiki Stream 

is calculated by subtracting the TFQ50 flow (from table 2) at 

the upper site (station 5180) from the estimated undiverted 

TFQ50 flow (from table 11) at the lower site (12 ft3/s – 10 ft3/s 

= 2 ft3/s). In this example, it is assumed that all of the 10 ft3/s 

median flow at the upper site is removed from the stream by 

the diversion just downstream from the upper site. Values of 

BFQ50, TFQ95, and BFQ95 are similarly calculated to be 1.2, 

1.0, and 0.3 ft3/s, respectively. West of Keanae Valley, where 

another diversion ditch at lower altitude (Spreckels) captures 

additional low flows, the flow statistics for diverted streams 

are even lower. For example, TFQ50 at the lower site on Waikamoi Stream is calculated by subtracting the TFQ50 regressionequation estimate at the middle upper site from the estimated 

TFQ50 flow at the lower site (10 ft3/s – 9.2 ft3/s = 0.80 ft3/s) to 

account for the diversion of 9.2 ft3/s by Spreckels Ditch. Values of BFQ50, TFQ95, and BFQ95 are similarly calculated to be 

0.50, 0.20, and 0.00 ft3/s, respectively. Flow-duration curves 

of natural and diverted flow for median and lower flows at the 

lower West Wailuaiki and lower Waikamoi sites illustrate the 

Estimates of Flow-Duration Statistics under Diverted Conditions 63
Table 12. Estimates of diverted streamflow statistics and percent flow reduction for gaged and ungaged basins, northeast Maui, Hawaii—Continued

[TFQxx is the xx-percent flow duration of total streamflow; BFQxx is the xx-percent flow duration of base flow; percent reduction is relative to undiverted flow at the same location; all flows are in cubic feet per second; numbers in bold italic are considered maximums at sites downstream of unquantified but known losing reaches]Stream location

TFQ50 BFQ50 TFQ95 BFQ95

Comments

Estimate Percent reduction Estimate Percent reduction Estimate Percent reduction Estimate Percent reduction 

Hanawi lower (HwL) middle (5090) upper (5080)

2519

7.1

2233

0

2119

4.6

2421

0

2016

2.4

9

16

0

1716

2.2

1116

0

Diverted at Koolau DitchDiverted at Koolau DitchNot diverted

Kapaula lower (KL) middle (5110) upper (5100)

3.22.44.9

6168

0

2.62.12.8

5459

0

2.21.91.2

3742

0

2.11.91.1

3437

0

Diverted at Koolau DitchDiverted at Koolau DitchNot diverted

Waiaaka lower (WaL) middle (5130)

1.40.86

00

1.10.77

00

0.730.54

00

0.700.52

00

Diverted at Koolau DitchDiverted at Koolau Ditch

Paakea lower (PaL) middle (5140) upper (PaU)

5.04.01.5

2327

0

4.63.80.90

1619

0

3.63.00.50

1214

0

3.63.00.40

1012

0

Diverted at Koolau DitchDiverted at Koolau DitchNot diverted

Waiohue lower (WeL) middle (WeM) upper (5150)

2.61.36.2

7082

0

2.11.05.0

7283

0

1.40.803.0

6979

0

1.30.702.9

6477

0

Diverted at Koolau DitchDiverted at Koolau DitchNot diverted

Kopiliula lower (KpL) middle (KpM) middle (PuM) upper (5160) upper (PuU)

4.72.01.78.01.9

698053

00

2.81.21.15.01.1

718250

00

1.70.500.602.40.60

698545

00

1.30.500.342.00.50

667862

00

Diverted at Koolau DitchDiverted at Koolau DitchDiverted at Koolau DitchNot divertedNot diverted

East Wailuaiki lower (EWL) middle (EWM) upper (5170)

2.41.59.1

7886

0

1.51.05.8

7985

0

0.400.202.9

8894

0

0.300.202.5

9093

0

Diverted at Koolau DitchDiverted at Koolau DitchNot diverted

Table 12. Estimates of diverted streamflow statistics and percent flow reduction for gaged and ungaged basins, northeast Maui, Hawaii.[TFQxx is the xx-percent flow duration of total streamflow; BFQxx is the xx-percent flow duration of base flow; percent reduction is relative to undiverted flow at the same location; all flows are in cubic feet per second; numbers in bold italic are considered maximums at sites downstream of unquantified but known losing reaches]

64 Median and Low-Flow Characteristics for Streams under Natural and Diverted Conditions, Northeast Maui, Hawaii
Table 12. Estimates of diverted streamflow statistics and percent flow reduction for gaged and ungaged basins, northeast Maui, Hawaii—Continued

[TFQxx is the xx-percent flow duration of total streamflow; BFQxx is the xx-percent flow duration of base flow; percent reduction is relative to undiverted flow at the same location; all flows are in cubic feet per second; numbers in bold italic are considered maximums at sites downstream of unquantified but known losing reaches]Stream location

TFQ50 BFQ50 TFQ95 BFQ95

Comments

Estimate Percent reduction Estimate Percent reduction Estimate Percent reduction Estimate Percent reduction 

West Wailuaiki lower (WWL) middle (WWM) upper (5180)

1.91.2

10

8489

0

1.20.806.0

8388

0

0.300.202.5

9194

0

0.300.202.1

8791

0

Diverted at Koolau DitchDiverted at Koolau DitchNot diverted

Wailuanui lower (WL) middle (5210) upper (5200) upper (5190)

1.71.64.43.2

8584

00

1.11.02.52.0

8584

00

0.810.391.00.90

7084

00

0.560.320.900.80

7684

00

Diverted at Koolau DitchDiverted at Koolau DitchNot divertedNot diverted

Ohia lower (OL) No estimates available due to lack of dataPalauhulu lower (5220) middle (PhM) upper (KoU) upper (HWU)

7.6

7.94.51.6

5544

00

4.85.92.50.93

5636

00

1.90.01.00.88

56

100

00

1.60.00.820.75

60

100

00

Taro diversionLosing streamNot divertedNot diverted

Piinaau lower (PiL) middle (PiM) upper (PiU)

No estimates available due to lack of data

Nuaailua lower (NL) middle (NM) upper (NU)

9.33.30.56

6

15

0

7.12.20.28

4

12

0

3.10.300.19

6

40

0

3.10.250.15

6

37

0

Diverted at Spreckels DitchDiverted at Spreckels DitchNot diverted

Honomanu lower (HnL) middle (HnM) upper (5270)

8.75.75.7

4248

0

5.83.82.8

3643

0

0.000.001.1

100100

0

0.000.000.70

100100

0

Diverted at Spreckels DitchDiverted at Spreckels DitchMinor upstream diversion

Estimates of Flow-Duration Statistics under Diverted Conditions 65
Table 12. Estimates of diverted streamflow statistics and percent flow reduction for gaged and ungaged basins, northeast Maui, Hawaii—Continued

[TFQxx is the xx-percent flow duration of total streamflow; BFQxx is the xx-percent flow duration of base flow; percent reduction is relative to undiverted flow at the same location; all flows are in cubic feet per second; numbers in bold italic are considered maximums at sites downstream of unquantified but known losing reaches]Stream location

TFQ50 BFQ50 TFQ95 BFQ95

Comments

Estimate Percent reduction Estimate Percent reduction Estimate Percent reduction Estimate Percent reduction 

Punalau lower (PlL) middle (PlM)

0.805.8

88

0

0.603.9

87

0

0.202.1

94

0

0.202.0

91

0

Diverted at Manuel Luis Ditch

Haipuaena lower (HaL) middle lower (HaML) middle upper (HaMU) upper (5360)

1.91.01.26.8

818985

0

1.10.500.803.6

809081

0

0.100.100.201.7

959589

0

0.100.100.201.3

949487

0

Diverted at Manuel Luis DitchDiverted at Spreckels DitchDiverted at Wailoa DitchMinor upstream diversion

Puohokamoa lower (PL) middle lower (PML) middle upper (PMU) upper (5450)

3.02.03.0

12

828779

0

2.11.12.06.4

818976

0

0.400.400.702.5

898877

0

0.400.400.602.1

878778

0

Diverted at Manuel Luis DitchDiverted at Spreckels DitchDiverted at Wailoa DitchMinor upstream diversion

Wahinepee lower (WpL) middle (WpM)

1.11.3

54

0

0.900.90

50

0

0.600.50

83

0

0.600.50

83

0

Diverted at Manuel Luis Ditch

Waikamoi lower (WiL) middle lower (WiML) middle upper (WiMU) upper (5570) upper (5550)

0.80.42.32.77.0

949781

00

0.50.21.61.53.5

939777

00

0.20.20.800.701.1

939369

00

0.000.000.500.600.80

100100

74

00

Diverted at Manuel Luis DitchDiverted at Manuel Luis DitchDiverted at Wailoa DitchNot divertedMinor upstream diversion

Kolea lower (KaL) middle (KaM)

1.23.6

75

0

0.92.5

71

0

0.400.20

33

0

0.400.20

33

0

Diverted at Manuel Luis Ditch

Average of diverted sites 58 55 60 58

66 Median and Low-Flow Characteristics for Streams under Natural and Diverted Conditions, Northeast Maui, Hawaii
Figure 17. Estimated low-flow duration curves of natural and diverted streamflow 

at lower West Wailuaiki and Waikamoi Streams, northeast Maui, Hawaii.

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Estimates of Flow-Duration Statistics under Diverted Conditions 67
significant effects of the diversion on streamflow statistics (fig. 

17).

Estimated flow-duration curves are made by connecting the four estimated flow statistics (TFQ50, BFQ50, TFQ95, 

and BFQ95) with a line assuming a linear relation. The values 

of BFQ50 and BFQ95 are plotted at the average equivalent 

total-flow durations from table 5 (72 and 97 percent, respectively). Inspection of the flow-duration curves in fig. 7 shows 

that nearly all the curves can be represented by a straight line 

through TFQ50, BFQ50, TFQ95, and BFQ95 so that it is reasonable to synthesize the estimated curves using a straight line to 

estimate the missing flow-duration points.

In addition to diversions above 1,200 ft altitude, three 

streams in the study area (Wailuanui, Waiokomilo, and 

Palauhulu Streams) also are diverted at lower altitudes for taro 

cultivation. On August 8, 2002, the taro diversion at about 

200 ft altitude on Wailuanui Stream was observed to divert all 

water from the stream and then subsequently allow a significant amount of the diverted water to return to the stream 

channel downstream. An additional unmeasured amount of 

flow was observed to enter the Wailuanui stream channel 

downstream of the taro cultivation. Therefore, the divertedflow statistics for the lower site at Wailuanui were estimated 

by assuming 50 percent of the diverted flow at about 200 ft 

altitude is lost to the stream although measurements to confirm 

this assumption are not available.

Three taro diversions take water from Waiokomilo 

Stream downstream of 540 ft altitude including one at 440 ft 

altitude that takes all low flows (Gingerich, 1999). Flow at the 

middle Waiokomilo Stream site is affected by one diversion 

of relatively constant volume of about 0.40 ft3/s. Additionally, 

flow at the lower site is reduced by at least 3.7 ft3/s at the 440-

ft altitude diversion, 1.1 ft3/s at the 220-ft altitude diversion, 

and an unknown amount of flow is “lost” to individual private 

water diversions at about 250 ft altitude. These estimates 

of diverted volumes are determined from a set of low-flow 

measurements reported in Gingerich (1999). Diverted flow 

statistics at the lower site were calculated on the assumption 

that all low flows are removed at 1,300 ft and again at 440 ft 

altitude (table 12). Because the equations for TFQ50 and BFQ50

estimate less flow than has been measured for TFQ95, the values for TFQ50 and BFQ50 were increased to the value of TFQ95

and should be considered a minimum estimate.

One taro diversion takes water from Palauhulu Stream 

at about 50 ft altitude several hundred feet upstream from the 

stream mouth. A continuous-record gaging station (5220) was 

operated on the diversion during 1934-68 and during that time, 

the statistics for flow in the diversion were 3.4, 3.0, 2.4, and 

2.3 ft3/s for TFQ50, BFQ50, TFQ95, and BFQ95, respectively. 

These values were subtracted from the estimated natural flow 

statistics at the lower Palauhulu Stream site to obtain estimates 

of diverted flow statistics.

 Estimated total reductions in streamflow due to diversions in the study area average 58 percent for TFQ50, 55 

percent for BFQ50, 60 percent for TFQ95, and 60 percent for 

BFQ95. The streams with the lowest relative reduction in 

streamflow are mostly those in the eastern side of the study 

area, where springs discharge below the main diversion (fig. 

18 and table 12).

Needs for Additional Data

Additional data are needed to improve and confirm the 

estimates of median and low-flow statistics in the study area. 

Estimates of flow lost in losing streams would allow better 

definition of flow statistics in these streams. In reaches where 

streams go dry, additional water is needed in the reaches to 

permit accurate measurements of flow losses. Such additional 

water sources include allowing natural streamflow to bypass 

the diversions or releasing water from a diversion system into 

the stream. Streams for which the reliability of flow statistics 

would be most improved by the data provided by additional 

measurements include Ohia, Palauhulu, and Piinaau Streams 

in Keanae Valley; Honomanu Stream; and the lower reaches of 

streams west of Honomanu.

Summary and Conclusions

Median and low-flow statistics were estimated for 

streams in northeast Maui, Hawaii, and analyses were made 

to develop and evaluate the methods used to estimate the statistics. Estimated flow statistics are presented for continuousrecord gaging sites and for other sites where various amounts 

of streamflow data are available, as well as for locations where 

no data are available.

Records of daily mean flows were used to determine 

flow-duration, low-flow frequency, and base flow statistics 

for continuous-record stream-gaging stations in the study area 

following US Geological Survey established standard methods. Duration discharges of 50- and 95-percent were determined from total-flow and base-flow data for each continuous 

record. In order to compare streamflow records to each other, 

records were adjusted to concurrent periods, so that differences between the records were due to differences in climatic 

or drainage-basin characteristics and not to the fact that the 

records cover different times. The index-station method was 

used to adjust all of the streamflow records to a common 

period with the gaging station on West Wailuaiki Stream 

(5180), which was chosen as the index station because of its 

record length (1914–2003) and favorable geographic location near the middle of the study area. Adjusting the record 

length resulted in average decreases to the 50-percent duration 

total flow, 50-percent duration base flow, 95-percent duration 

total flow, and 95-percent duration base flow of 7, 3, 4, and 1 

percent, respectively. In general, the largest adjustments were 

needed for the records with the shortest lengths.

For the drainage basin of each continuous-record gaged 

site and selected ungaged sites, morphometric, geologic, soil, 

and rainfall characteristics were quantified using GIS tech68 Median and Low-Flow Characteristics for Streams under Natural and Diverted Conditions, Northeast Maui, Hawaii
Figure 18. Reduction in Q95 total flow (TFQ95) due to diversions at selected ungaged and gaged sites in the study area, 

northeast Maui, Hawaii.

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Summary and Conclusions 69
niques. Regression equations relating the streamflow statistics 

to basin characteristics of the gaged basins were developed 

using ordinary-least-squares regression analyses. Rainfall rate, 

maximum basin elevation, and the elongation ratio of the basin 

were the basin characteristics used in the final regression equations for 50-percent duration total flow and base flow. Rainfall rate and maximum basin elevation were used in the final 

regression equations for the 95-percent duration total flow and 

base flow. The proportion of the variation in the dependent 

variable that is explained by the independent variables (R2) 

ranged from 94.9 to 75.3 percent, with the highest flows having the highest R2

. Standard errors of prediction ranged from 

20.9 to 56.5 percent, with the highest flows having the lowest 

errors. The relative errors between observed and estimated 

flows ranged from 11 to 20 percent for the 50-percent duration 

total flow and from 29 to 56 percent for the 95-percent duration total flow and base flow.

The regression equations developed for this study were 

used to determine the 50-percent duration total flow, 50-percent duration base flow, 95-percent duration total flow, and 

95-percent duration base flow at selected ungaged sites within 

the study area and at three gaging stations west of the study 

area using the appropriate basin characteristics. Estimated 

streamflow, prediction intervals, and standard errors were 

determined for 47 ungaged sites in the study area and four 

gaging stations west of the study area. Relative errors were 

determined for sites for which observed values of 95-percent 

duration discharge of total flow were available. East of Keanae 

Valley, the 95-percent duration discharge equation generally 

underestimated flow, and within and west of Keanae Valley, 

the equation generally overestimated flow.

Finally, most-reliable estimates of natural (undiverted) 

and diverted streamflow flow-duration statistics at gaged 

and ungaged sites on 21 streams in the study area were made 

using a combination of continuous-record gaging-station data, 

low-flow measurements, and values determined from the 

regression equations developed as part of this study. Average 

reduction in the low flow of streams due to diversions ranges 

from 55 to 60 percent.

References Cited

Draper, N.R., and Smith, Harry, 1998, Applied regression 

analysis: New York, John Wiley and Sons, 706 p.

Duan, Naihua, 1983, Smearing estimate: a non-parametric 

retransformation method: Journal of the American Statistical Association, v. 78, no. 383, p. 605-610.

Fontaine, R.A., 1996, Evaluation of the surface-water quantity, 

surface-water quality, and rainfall data-collection programs 

in Hawaii, 1994: U.S. Geological Survey Water-Resources 

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References Cited 71
Appendix A: Selected Drainage-Basin Characteristics Quantified Using 

Basinsoft 

[Descriptions modified from Harvey and Eash (1996) for purposes of regression analyses of streamflow data from northeast 

Maui, Hawaii]

BL-Basin length, in miles, measured along a line areally centered through the drainage divide from basin outlet to where 

the main channel extended meets the basin divide.

BP-Basin perimeter, in miles, measured along entire drainage-basin divide.

BR-Basin relief, in feet, measured as the difference between the elevation of the highest grid cell and the elevation of the 

grid cell at the basin outlet, BR = MAXELEV-MINELEV

BS-Average basin slope, in feet per mile, measured by the "contour-band" method, within the drainage area (DA). BS = 

(total length of all selected elevation contours) (contour interval) / DA.

BW-Effective basin width, in miles, BW = DA/ BL.

CCM-constant of channel maintenance, in square miles per mile, CCM=DA/TSL=1/SD.

CR-Compactness ratio, dimensionless, the ratio of the perimeter of the basin to the circumference of a circle of equal area, 

CR = BP/2 (π DA)0.5.

DA-Drainage area, in square miles.

DF- Drainage frequency, in number of first-order streams per square mile

ER-Elongation ratio, dimensionless, ratio of (1) the diameter of a circle of area equal to that of the basin to (2) the length of 

the basin, ER = [4 DA/π (BL)2]

0.5 = 1.13 (1/SF)0.5

MAXELEV- maximum basin elevation, in feet

MCL-Main channel length, in miles, measured along the main channel from the basin outlet to where the main channel, if 

extended, meets the basin divide.

MCS-Main-channel slope, in feet per mile, an index of the slope of the main channel computed from the difference in 

streambed elevation at points 10 percent (E10) and 85 percent (E85) of the distances along the main channel from the basin 

outlet to the basin divide. MCS = (E85 –E10) / (0.75 MCL).

MCSP-Main channel slope proportion, dimensionless, MCSP=MCL/(MCS)0.5.

MCSR-Main-channel sinuosity ratio, dimensionless, MCSR = MCL / BL.

MINELEV- minimum basin elevation, in feet

RB-Rotundity of basin, dimensionless, RB = [π (BL)2]/ [4 DA] = 0.785 SF.

RN- Ruggedness number, in feet per mile, RN = (TSL)(BR)/DA

RR-Relative relief, in feet per mile, RR = BR/BP.

RSD- Relative stream density, dimensionless, RF = DF/(SF)2

SD-Stream density, in miles per square mile, SD = TSL / DA.

SF-Shape factor, dimensionless, ratio of basin length to effective basin width, SF = BL/BW.

SR- Slope ratio of main-channel slope to basin slope, dimensionless, SR = MCS/BS

TSL-Total stream length, in miles, computed by summing the length of all stream segments within the DA.

Reference

Harvey, C.A., and Eash, D.A., 1996, Description, instructions, and verification for Basinsoft, a computer program to quantify 

drainage-basin characteristics: U.S. Geological Survey Water-Resources Investigations Report 95-4287, 25 p.

72 Median and Low-Flow Characteristics for Streams under Natural and Diverted Conditions, Northeast Maui, Hawaii