U.S. Department of the Interior

U.S. Geological Survey

Low-Flow Characteristics of Streams 

Under Natural and Diversion Conditions,

Waipiÿo Valley, Island of Hawaiÿi, Hawaiÿi

Scientific Investigations Report 2011–5118

Prepared in cooperation with the State of Hawaiÿi Office of Hawaiian Affairs
COVER 

Alakahi Stream in Waipi‘o Valley, Island of Hawai‘i, Hawai‘i. (Photograph by Kolja Rotzoll, University of Hawai‘i at Mänoa, Water 

Resources Research Center).
Low-Flow Characteristics of Streams

Under Natural and Diversion Conditions, 

Waipiÿo Valley, Island of Hawaiÿi, Hawaiÿi

By Richard A. Fontaine

Prepared in cooperation with the State of Hawaiÿi Office of Hawaiian Affairs

Scientific Investigations Report 2011–5118

U.S. Department of the Interior

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

KEN SALAZAR, Secretary

U.S. Geological Survey

Marcia K. McNutt, Director

U.S. Geological Survey, Reston, Virginia 2012

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Suggested citation:

Fontaine, R.A., 2012, Low-flow characteristics of streams under natural and diversion conditions, 

Waipiÿo Valley, Island of Hawaiÿi, Hawaiÿi: U.S. Geological Survey Scientific Investigations Report 

2011–5118, 80 p.

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 iii

Contents

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

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

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

Description of Study Area........................................................................................3

 Acknowledgments ...................................................................................................5

Data and Methods Used to Estimate Low-Flow Statistics ..............................................5

Streamflow Data......................................................................................................6

Historical Data..................................................................................................6

Data Collected for This Study.........................................................................10

Selection of Base Period .......................................................................................10

Record-Extension Techniques...............................................................................13

Continuous-Record Gaging Stations..............................................................16

Low-Flow Partial-Record Stations..................................................................17

Selection of Index Stations and Application of Data..............................................17

Computation of Low-Flow Statistics at Sites with Historical Data .........................17

Computation of Low-Flow Statistics for Ungaged Sites.........................................18

Low-Flow Statistics Under Current (2000–2005) Diversion Practices ..........................18

Short-Term Gaging Stations..................................................................................19

Low-Flow Partial-Record Stations .........................................................................19

Low-Flow Statistics Representative of Natural Conditions ...........................................20

Index and Short-Term Gaging Stations .................................................................20

Low-Flow Partial-Record Stations .........................................................................21

Natural Low-Flow Statistics ...................................................................................22

Effects of Diversion Practices on Low-Flow Statistics ..................................................23

Current (2000–2005) Diversion Practices .............................................................25

Proposed Future Diversion Practices for Lower Hämäkua Ditch...........................25

Computation of Low-Flow Statistics under Proposed Diversion Practices 

at Lower Hämäkua Ditch .....................................................................25

Changes in Low Flow Relative to 2000–2005 Diversion Practices ................33

Changes in Low Flow Relative to Natural Conditions ....................................33

Summary of Effects of Various Diversion Practices at the Downstream Limit of 

Study Area.........................................................................................................33

Summary and Conclusions ..........................................................................................40

References Cited..........................................................................................................43

Appendix 1. Computation of Low-Flow Statistics for Sites with Historical Data............46

Gaging Stations Operated between August 1901 and January 1902 ...................46

Regulated Low-Flow Statistics .......................................................................46

Natural Low-Flow Statistics............................................................................52

Sites with Miscellaneous Discharge Measurements .............................................52

Appendix 2. Computation of Low-Flow Statistics for Ungaged Sites ............................57

Combining Flow-Duration Curves .........................................................................57

Use of Seepage Run Data ....................................................................................57

Regional Analysis..................................................................................................59
iv

Appendix 3. Accounting for Effects of Diversions at Upper and 

Lower Hämäkua Ditches....................................................................................70

Effects of Diversions at Upper Hämäkua Ditch .....................................................70

Effects of Diversions by Lower Hämäkua Ditch.....................................................77

Figures

 1. Waipiÿo Valley study area, Island of Hawaiÿi, Hawaiÿi. .........................................4

 2. Flow-duration curve for streamflow gaging station 

 16720000 on Kawainui Stream, Island of Hawaiÿi, for water years 

 1965–2004. ......................................................................................................7

 3. Location of stream and ditch surface-water gaging stations 

 operated in and adjacent to the Waipiÿo Valley study area, 

 Island of Hawaiÿi, Hawaiÿi..................................................................................9

 4. Locations where discharge measurements were made in 

 Waipiÿo Valley study area during the period 2000–2005, 

 Island of Hawaiÿi, Hawaiÿi................................................................................12

 5. Percent reduction in natural 95-percentile discharge under 

 2000–2005 diversion practices, Waipiÿo Valley study area, 

 Island of Hawaiÿi, Hawaiÿi................................................................................28

 6. Percent reduction in natural 50-percentile discharge under 

 2000–2005 diversion practices, Waipiÿo Valley study area, 

 Island of Hawaiÿi, Hawaiÿi................................................................................29

 7. Percent reduction in natural 95-percentile discharge under 

 proposed, future diversion practices, Waipiÿo Valley study area, 

 Island of Hawaiÿi, Hawaiÿi................................................................................37

 8. Percent reduction in natural 50-percentile discharge under 

 proposed, future diversion practices, Waipiÿo Valley study area, 

 Island of Hawaiÿi, Hawaiÿi................................................................................38

1–A. Location of stream and ditch surface-water gaging stations 

 operated in and adjacent to the Waipiÿo Valley study area, 

 Island of Hawaiÿi, Hawaiÿi................................................................................47

1–B. Low flow-duration discharges reflective of current (2000–2005) 

 regulated conditions extended over the 1965–2004 

 base period at data collection stations in the Waipiÿo Valley 

 study area, Island of Hawaiÿi, Hawaiÿi.............................................................51

1–C. Low flow-duration discharges reflective of natural conditions 

 extended over the 1965-2004 base period at data collection 

 stations in the Waipiÿo Valley study area, 

 Island of Hawaiÿi, Hawaiÿi................................................................................54

2–A. Measured and computed regulated discharges at the 

 time of the September 20–21, 2000, seepage run along 

 streams in the Waipiÿo Valley study area, 

 Island of Hawaiÿi, Hawaiÿi................................................................................60

2–B. Measured and computed discharges at the time of the 

 September 20–21, 2000, seepage run along Lower 

 Hämäkua Ditch, Island of Hawaiÿi, Hawaiÿi. ....................................................61
 v

2–C. Computed natural discharges at the time of the 

 September 20–21, 2000, seepage run along streams in 

 the Waipiÿo Valley study area, Island of Hawaiÿi, Hawaiÿi. ...............................63

2–D. Discharge in Kawainui, Waipiÿo, and Wailoa Streams 

 during the September 20–21, 2000 seepage run and on 

 selected days in 1901 prior to the onset of flow diversions, 

 Waipiÿo Valley study area, Island of Hawaiÿi, Hawaiÿi. .....................................64

2–E. Natural 50-percentile flow-duration discharges, 

 for the 1965–2004 base period, versus drainage area in 

 the Waipiÿo Valley study area, Island of Hawaiÿi, Hawaiÿi. ...............................68

2–F. Regulated 50-percentile flow-duration discharges, for the 

 1965–2004 base period, versus drainage area in 

 the Waipiÿo Valley study area, Island of Hawaiÿi, Hawaiÿi. ...............................69

3–A. Location of stream and ditch surface-water gaging stations 

 operated in and adjacent to the Waipiÿo Valley study area, 

 Island of Hawaiÿi, Hawaiÿi................................................................................71

3–B. Relation between discharge at Upper Hämäkua Ditch 

 (station 16720500) and combined discharge of 

 Kawainui Stream (station 16720000) and Kawaiki Stream 

 (station 16720300), Island of Hawaiÿi, Hawaiÿi, water year 1999. ...................73

3–C. Locations where discharge measurements were made 

 in Waipiÿo Valley study area during the period 2000–2005, 

 Island of Hawaiÿi, Hawaiÿi................................................................................74

3–D. Relation between discharge at Upper Hämäkua Ditch 

 (station 16726000) and the total discharge upstream 

 from Alakahi Stream Upper Hämäkua Ditch intake, 

 Island of Hawaiÿi, Hawaiÿi, water year 1999. ...................................................76

Tables

 1. Surface-water gaging stations operated in and adjacent

 to the Waipiÿo Valley study area, 

 Island of Hawaiÿi, Hawaiÿi..................................................................................8

 2. Locations where discharge measurements were made in the 

 Waipiÿo Valley study area during the period 2000–2005, 

 Island of Hawaiÿi, Hawaiÿi................................................................................11

 3. Discharge measurements at low-flow partial-record stations 

 in Waipiÿo Valley during the period 2000–2005, 

 Island of Hawaiÿi, Hawaiÿi................................................................................13

 4. Discharge measurements at seepage-run sites in 

 Waipiÿo Valley during the period 2000–2001, 

 Island of Hawaiÿi, Hawaiÿi................................................................................14

 5. Selected flow-duration discharges for the period of record 

 and the base period at gaging station 16758000 on 

 Waikoloa Stream, Island of Hawaiÿi, Hawaiÿi...................................................15
vi

 6. Selected flow-duration discharges for the period of record 

 and the base period at gaging station 16010000 on 

 Kawaiköï Stream, Island of Kauaÿi, Hawaiÿi........................................................15

 7. Selected natural flow-duration discharges for the 

 1965–2004 base period at index gaging stations 

 operated in the Waipiÿo Valley area, Island of Hawaiÿi, Hawaiÿi..........................18

 8. Selected natural flow-duration discharges for the 

 1969–1999 concurrent period of record at gaging stations 

 16720300 on Kawaiki Stream and 16720000 on Kawainui Stream, 

 and estimated 1965–2004 base period natural flow-duration 

 discharges at gaging station 16720300 on Kawaiki Stream..............................20

 9. Selected flow-duration discharges for the 1965-1969 

 concurrent period of record at gaging stations 16732200 on 

 Wailoa Stream and 16758000 on Waikoloa Stream, and 

 estimated 1965–2004 base period regulated flow-duration 

 discharges at the gaging station on Wailoa Stream ..........................................21

10. Computed statistics for concurrent discharge measurements at 

 low-flow partial-record stations and daily mean discharges at index 

 stations in Waipiÿo Valley study area, Island of Hawaiÿi, Hawaiÿi. .......................22

11. Estimated regulated flow-duration discharges for the 

 1965–2004 base period that reflect diversion practices 

 during the study period (2000–2005) at low-flow 

 partial- record stations in Waipiÿo Valley, 

 Island of Hawaiÿi, Hawaiÿi...................................................................................23

12. Computed statistics for concurrent discharge measurements 

 adjusted to represent natural conditions at low-flow 

 partial-record stations and daily mean discharges at index 

 stations in Waipiÿo Valley study area, Island of Hawaiÿi, Hawaiÿi. .......................24

13. Estimated natural flow-duration discharges for the 

 1965–2004 base period at low-flow partial-record stations 

 in Waipiÿo Valley, Island of Hawaiÿi, Hawaiÿi.......................................................24

14. Comparison of 95-percentile flow-duration discharges 

 under natural and 2000–2005 diversion practices at gaging 

 stations and data-collection sites in the Waipiÿo Valley study area, 

 Island of Hawaiÿi, Hawaiÿi...................................................................................26

15. Comparison of 50-percentile flow-duration discharges under 

 natural and 2000–2005 diversion practices at gaging stations 

 and data-collection sites in the Waipiÿo Valley study area, 

 Island of Hawaiÿi, Hawaiÿi...................................................................................27

16. Reductions in natural discharge associated with 2000–2005 

 diversion practices on streams in the Waipiÿo Valley 

 study area, Island of Hawaiÿi, Hawaiÿi. ...............................................................31

17. Estimated diversions by Upper and Lower Hämäkua Ditches 

 from 95- and 50-percentile flow-duration discharges under 

 2000–2005 diversion conditions on streams in the Waipiÿo Valley 

 study area, Island of Hawaiÿi, Hawaiÿi ................................................................32

18. Estimated diversions by Upper and Lower Hämäkua Ditches from 

 95- and 50-percentile flow-duration discharges under 

 proposed, future diversion practices on streams in the 

 Waipiÿo Valley study area, Island of Hawaiÿi, Hawaiÿi .......................................32
 vii

 19. Resultant 95- and 50-percentile flow-duration discharge under 

 proposed, future diversion practices at gaging stations and 

 data-collection sites downstream from Lower Hämäkua Ditch in 

 the Waipiÿo Valley study area, Island of Hawaiÿi, Hawaiÿi..................................34

 20. Comparison of 95- and 50-percentile flow-duration discharges 

 under 2000–2005 and proposed, future diversion 

 practices at gaging stations and data-collection sites 

 downstream from Lower Hämäkua Ditch in the 

 Waipiÿo Valley study area, Island of Hawaiÿi, Hawaiÿi........................................35

 21. Comparison of 95- and 50-percentile flow-duration discharges 

 under natural and proposed, future diversion 

 practices at gaging stations and data-collection sites 

 downstream from Lower Hämäkua Ditch in the Waipiÿo 

 Valley study area, Island of Hawaiÿi, Hawaiÿi....................................................36

 22. Relation between 95- and 50-percentile flow-duration discharges 

 under natural, 2000–2005 diversion and proposed, future 

 diversion conditions at gaging stations and data-collection 

 sites downstream from Lower Hämäkua Ditch in the 

 Waipiÿo Valley study area, Island of Hawaiÿi, Hawaiÿi........................................39

 23. Relation between selected flow-duration discharges under 

 natural conditions and diversion conditions during 1965–1969, 

 2000–2005, and proposed for the future, extended to 

 a common base period of 1965–2004, at the downstream 

 limit of the Waipiÿo Valley study area at Wailoa 

 Stream station 16732200, Island of Hawaiÿi, Hawaiÿi.......................................41

1–A. Surface-water gaging stations operated in the Waipiÿo Valley, 

 Island of Hawaiÿi, Hawaiÿi, August 1901–January 1902...................................46

1–B. Selected natural flow-duration discharges for the 1965–2004 

 base period at index gaging stations operated in the 

 Waipiÿo Valley study area, Island of Hawaiÿi, Hawaiÿi........................................48

1–C. Estimated regulated flow-duration discharges for the 

 1965–2004 base period that reflect diversion practices during 

 the study period (2000–2005) at low-flow partial-record stations 

 in Waipiÿo Valley, Island of Hawaiÿi, Hawaiÿi......................................................48

1–D. Estimated natural flow-duration discharges for the 1965–2004 

 base period at low-flow partial-record stations in 

 Waipiÿo Valley, Island of Hawaiÿi, Hawaiÿi..........................................................49

1–E. Computed statistics for concurrent daily discharges during 

 periods of low flow at gaging stations operated between 

 August 1901 and January 1902 in Waipiÿo Valley, 

 Island of Hawaiÿi, Hawaiÿi.................................................................................50

1–F. Estimated regulated flow-duration discharges for the 

 1965–2004 base period that reflect diversion practices 

 during the study period (2000–2005) at gaging stations 

 operated between August 1901 and January 1902 in 

 Waipiÿo Valley, Island of Hawaiÿi, Hawaiÿi..........................................................50

1–G. Estimated natural flow-duration discharges for the 

 1965–2004 base period at gaging stations operated between 

 August 1901 and January 1902 in Waipiÿo Valley, 

 Island of Hawaiÿi, Hawaiÿi.................................................................................53
viii

1–H. Regulated discharge measurements, concurrent daily 

 mean discharges at long-term index stations, and 

 estimated flow-duration discharges for the 1965–2004 base 

 period at surface-water gaging station 16732150 on Waimä 

 Stream, Waipiÿo Valley study area, Island of Hawaiÿi, Hawaiÿi ..........................55

2–A. Selected natural flow-duration discharges for a concurrent

 period of record 1970–1999 at surface-water gaging stations 

 16720000 on Kawainui Stream and 16720300 on Kawaiki 

 Stream, Waipiÿo Valley study area, Island of Hawaiÿi, Hawaiÿi...........................58

2–B. Selected regulated flow-duration discharges for a 

 concurrent period of record 1970–1999 at gaging 

 stations 16720000 on Kawainui Stream, 16720300 on 

 Kawaiki Stream, and 16720500 on Upper Hämäkua Ditch, 

 Waipiÿo Valley study area, Island of Hawaiÿi, Hawaiÿi.......................................58

2–C. Discharge measurements at seepage-run sites in 

 Waipiÿo Valley in September 2000 and September 2001, 

 Island of Hawaiÿi, Hawaiÿi..................................................................................62

2–D. Drainage area and selected natural flow-duration discharges 

 for the 1965–2004 base period at gaging stations and 

 data-collection sites in the Waipiÿo Valley study area, 

 Island of Hawaiÿi, Hawaiÿi..................................................................................66

2–E. Drainage area and selected regulated flow-duration 

 discharges for the 1965–2004 base period at gaging stations 

 and data-collection sites in the Waipiÿo Valley study area, 

 Island of Hawaiÿi, Hawaiÿi..................................................................................67

3–A. Gaging stations on and upstream from the Upper Hämäkua Ditch, 

 Waipiÿo Valley study area, Island of Hawaiÿi, Hawaiÿi........................................72

3–B. Effect of diversions by the Upper Hämäkua Ditch on discharge 

 measurements made during the period 2000–2005 at 

 Kawainui Stream low-flow partial-record site 1, 

 Island of Hawaiÿi, Hawaiÿi..................................................................................75

3–C. Effect of diversions by the Upper Hämäkua Ditch 

 on discharge measurements made during the period 

 2000–2005 at Alakahi Stream low-flow partial-record 

 site 6, Island of Hawaiÿi, Hawaiÿi.......................................................................78

3–D. Effect of diversions by the Upper Hämäkua Ditch on 

 discharge measurements made during the period 

 2000–2005 at Koÿiawe Stream low-flow partial-record 

 site 15, Island of Hawaiÿi, Hawaiÿi.....................................................................78

3–E. Effect of diversions by the Upper Hämäkua Ditch on 

 discharge measurements made during the period 

 2000–2005 at Waimä Stream low-flow partial-record 

 site 18, Island of Hawaiÿi, Hawaiÿi...................................................................79

3–F. Effect of diversions by the Upper and Lower Hämäkua Ditches 

 on discharge measurements made during the period 

 2000–2005 at Wailoa Stream low-flow partial-record site 24, 

 Island of Hawaiÿi, Hawaiÿi..................................................................................80
 ix

Conversion Factors, Abbreviations, and Datums 

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)

cubic foot per second (ft3/s) 0.64599 million gallons per day (Mgal/d)

Vertical coordinate information is referenced to local mean sea level.

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

Altitude, as used in this report, refers to distance above the vertical datum.
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Low-Flow Characteristics of Streams Under 

Natural and Diversion Conditions, Waipiÿo Valley, 

Island of Hawaiÿi, Hawaiÿi

By Richard A. Fontaine

Abstract

Over the past 100 years, natural streamflow in Waipiÿo 

Valley has been reduced by the transfer of water out of the 

valley by Upper and Lower Hämäkua Ditches. The physical 

condition and diversion practices along the two ditch systems 

have varied widely over the years, and as a result, so have their 

effects on natural streamflow in Waipiÿo Valley. Recent renovation and improvements to Lower Hämäkua Ditch system, 

along with proposals for its future operation and water-diversion strategies, have unknown implications. The purpose of 

this report is to quantify the availability of streamflow and to 

determine the effects of current and proposed diversion strategies on the low-flow hydrology in Waipiÿo Valley.

In this report, the low-flow hydrology of Waipiÿo Valley 

is described in terms of flow-duration statistics. Flow-duration 

statistics were computed for three locations in the Waipiÿo Valley study area where long-term surface-water gaging stations 

have been operated. Using a variety of streamflow recordextension techniques, flow-duration statistics were estimated 

at an additional 13 locations where only few historical data are 

available or where discharge measurements were made as part 

of this study. Flow-duration statistics were computed to reflect 

natural conditions, current (2000–2005) diversion conditions, 

and proposed future diversion conditions at the 16 locations. 

At the downstream limit of the study area, on Wailoa Stream 

at an altitude of 190 feet, a baseline for evaluating the availability of streamflow is provided by computed flow-duration 

statistics that are representative of natural, no-diversion 

conditions. At the Wailoa gaging station, 95- and 50-percentile 

discharges under natural conditions were determined to be 86 

and 112 cubic feet per second, respectively. Under 1965–1969 

diversion conditions, natural 95- and 50-percentile discharges 

were reduced by 52 and 53 percent, to 41 and 53 cubic feet 

per second, respectively. Under current (2000–2005) diversion conditions, natural 95- and 50-percentile discharges 

were reduced by 21 and 24 percent, to 68 and 85 cubic feet 

per second, respectively. Under proposed future diversion 

conditions, natural 95- and 50-percentile discharges would be 

reduced by 33 and 24 percent, to 58 and 85 cubic feet per second, respectively. Compared to discharges that reflect current 

(2000–2005) diversion conditions, proposed future diversion 

conditions would reduce 95-percentile discharges, which are 

representative of moderate drought levels in the stream, by 

15 percent. No change would be expected in 50-percentile 

discharges, which are representative of normal conditions. The 

effects of current (2000–2005) and proposed future diversion 

conditions on the natural flow of streams in the Waipiÿo Valley 

study area differ, depending on the location. Under current 

(2000–2005) diversion conditions, reductions in natural 95- or 

50-percentile discharges of greater than 30 percent were found 

in Kawainui Stream downstream from Upper Hämäkua Ditch 

to an altitude of about 1,435 feet and in the reach of Waimä 

Stream between Upper and Lower Hämäkua Ditches. Under 

proposed future diversion conditions, reductions in natural 

95- or 50-percentile discharges of greater than 30 percent were 

found in Kawainui Stream downstream from Upper Hämäkua 

Ditch to an altitude of about 1,435 feet, in the reach of Waimä 

Stream between Upper and Lower Hämäkua Ditches, and 

along most stream reaches downstream from Lower Hämäkua 

Ditch, except for Waimä Stream. 

Introduction

Waipiÿo Valley is a location of great cultural and historical significance to the Hawaiian people. In ancient times, 

Waipiÿo Valley was a noted royal and religious center with a 

large population (Department of Urban and Regional Planning, 1999). To support this population, several hundred acres 

of taro were cultivated, and the cultivation of taro, which 

requires large quantities of freshwater (Penn, 1997), continues 

today on approximately 100 acres of land. The importance 

of streams in Waipiÿo Valley was highlighted by the Hawaiÿi 

Stream Assessment (Hawaiÿi Commission on Water Resource 

Management, 1990), which identified the streams as candidates for protection because of their aquatic, riparian, cultural, 

and recreational resources.

Wailoa Stream and its major tributaries Kawainui, 

Alakahi, Koÿiawe, Waimä, and Waipiÿo Streams historically 

provided an ample supply of freshwater needed to support taro 

cultivation and stream biota in Waipiÿo Valley. Over the past 
2 Low-Flow Characteristics of Streams Under Natural and Diversion Conditions, Waipiÿo Valley, Island of Hawaiÿi, Hawaiÿi

100 years, the natural flow of Wailoa Stream has been reduced 

considerably by diversion systems that transfer water out of 

Waipiÿo Valley. Construction of the Upper Hämäkua Ditch was 

completed in 1907 (Wilcox, 1996). This ditch system diverts 

streamflow, from headwater tributaries that flow into Waipiÿo 

Valley, at altitudes ranging from 4,042 feet down to 3,044 feet. 

Water diverted by the Upper Hämäkua Ditch is transported 

away from Waipiÿo Valley, primarily for use in the Waimea 

area. Construction of the Lower Hämäkua Ditch was completed in 1910 (Wilcox, 1996). This system diverts streamflow 

and captured groundwater resources from within Waipiÿo 

Valley at altitudes ranging from 1,037 feet down to 985 feet. 

Water diverted by the Lower Hämäkua Ditch is transported out 

of Waipiÿo Valley, primarily for use along the Hämäkua coastal 

area between Kukuihaele and Paÿauilo. 

The physical condition and diversion practices of the 

Upper and Lower Hämäkua Ditch systems have varied widely 

over the years, and as a result, so have their effects on natural streamflow in Waipiÿo Valley. When initially constructed, 

Upper Hämäkua Ditch had the capacity to divert an average 

flow of about 23 ft3/s (cubic feet per second), or 15 Mgal/d 

(million gallons per day) (Wilcox, 1996). Streamflow data 

collected by the U. S. Geological Survey (USGS) at gaging 

station 16726000 on the Upper Hämäkua Ditch at 3,020 feet 

elevation indicates that flow diverted from the headwaters 

of Waipiÿo Valley averaged 9.4 ft3/s (6.1 Mgal/d) over the 

20-year period 1975–2004. When initially constructed, Lower 

Hämäkua Ditch had the capacity to divert an average flow of 

about 62 ft3/s (40 Mgal/d) (Wilcox, 1996). The capacity of 

Lower Hämäkua Ditch has decreased significantly over the 

years. In 2003, USGS streamflow data collected at gaging station 16732800 on the Lower Hämäkua Ditch, upstream from 

the main weir, indicated that the average flow being diverted 

out of Waipiÿo Valley was 10.1 ft3/s (6.5 Mgal/d).

Historically, flow diverted by Lower Hämäkua Ditch 

was used primarily by sugar plantations along the Hämäkua 

Coast. However, since the 1993 declaration of bankruptcy by 

Hämäkua Sugar Company (U.S. Department of Agriculture, 

1999) and the subsequent demise of sugar plantations along 

the Hämäkua Coast, a wide variety of users compete for this 

resource. Future diversion plans for the Lower Hämäkua Ditch 

system, now being operated by the Hawaiÿi Department of 

Agriculture (DOA), were proposed in an environmental impact 

statement completed in 1999 (U.S. Department of Agriculture, 

1999). As outlined in the proposed plan of operation for Lower 

Hämäkua Ditch, average rates of flow diversion out of Waipiÿo 

Valley would decrease from the 48 ft3/s (31 Mgal/d) diverted 

during periods when sugar plantations were in operation to 

11 ft3/s (7 Mgal/d). During any future drought conditions, 

diversions would decrease from 28 ft3/s (18 Mgal/d) that were 

typically diverted during past droughts to 20 ft3/s (13 Mgal/d) 

(U.S. Department of Agriculture, 1999, p. 144).

 The availability of streamflow in Waipiÿo Valley to support the new diversion strategies proposed for Lower Hämäkua 

Ditch, and the implications for instream flows downstream 

from points of diversion, were based primarily on results of 

a study completed in 1984 (Mink, 1984). Although the study 

by Mink utilized the best data available at that time, its results 

were based on limited streamflow data from within Waipiÿo 

Valley. The USGS has historically published data for numerous streamflow stations in Waipiÿo Valley, but most were 

operated for only short periods in 1901 and 1902 and none of 

those stations are currently being operated. The USGS operated gaging station 16732200 on Wailoa Stream between 1964 

and 1969 (Fontaine, 1996). The Wailoa Stream gaging station, 

which was located in Waipiÿo Valley at an altitude of about 

190 feet, provided the longest and most current streamflow 

dataset utilized in the Mink study (Mink, 1984).

In cooperation with the State of Hawaiÿi Office of 

Hawaiian Affairs (OHA), the USGS undertook this investigation to quantify availability of low flows in streams in Waipiÿo 

Valley and to investigate how these flows vary with time and 

location along the streams. Historical information, along with 

data collected as part of this study, were analyzed to develop 

current estimates of low-flow characteristics that would be 

representative of long-term conditions and to evaluate the 

effects of current and proposed flow diversions on natural 

low-flow characteristics.

Purpose and Scope

The purposes of this report are to (1) quantify current 

and natural low-flow characteristics along stream reaches both 

upstream and downstream from the Lower Hämäkua Ditch 

diversion intakes, (2) evaluate implications of proposed diversion strategies on low-flow characteristics at points downstream from diversion intakes, and (3) quantify current and 

natural low-flow characteristics of Wailoa Stream as it enters 

the lower part of Waipiÿo Valley, where diversions to support 

taro production commence.

The study focuses on principal tributary streams that contribute flow to the upper reaches of Waipiÿo Valley, including 

Kawainui, Kawaiki, Alakahi, Koÿiawe, and Waimä Streams. 

The study area heads on the subject tributary streams, at locations just upstream from Upper Hämäkua Ditch intakes, and 

continues downstream into Waipiÿo Valley, terminating at an 

altitude of about 190 feet on Wailoa Stream. This location is 

just upstream from the point where initial diversions of taro 

irrigation water from Wailoa Stream take place.

To achieve the purposes of this report, both historical and 

new streamflow data and field observations were analyzed. 

Historical data include records of streamflow and discharge 

measurements collected by the USGS at former and current 

streamflow-gaging stations, as well as data available from 

other agencies. New streamflow data and field observations 

include (1) discharge measurements made at five low-flow 

partial-record stations; (2) seepage runs—a series of concurrent discharge measurements—made along Lower Hämäkua 

Ditch from Kawainui intake downstream to the main weir; 

and (3) seepage runs conducted along Wailoa Stream between 

points on tributary streams, just upstream from the intakes of 
Introduction 3

Lower Hämäkua Ditch, and downstream to the terminus of the 

study area, on Wailoa Stream at an altitude of about 190 feet. 

Description of Study Area

The Waipiÿo Valley study area is on the northeastern 

flank of Kohala Volcano, which forms most of the extreme 

northern part of the Island of Hawaiÿi (fig. 1). The study area 

encompasses about 14.3 square miles and extends from the 

headwaters of Kawainui, Kawaiki, Alakahi, Koÿiawe, and 

Waimä Streams in the Kohala mountains, downstream through 

Waipiÿo Valley, to the location of former USGS gaging station 

16732200 on Wailoa Stream at an altitude of 190 feet. The 

downstream terminus of the study area is just upstream from 

the point where initial diversions of taro irrigation water from 

Wailoa Stream take place. The maximum altitude in the study 

area is about 5,260 feet, on the summit of Puÿu o ÿUmi in the 

headwaters of Kawainui Stream. 

The present-day Island of Hawaiÿi consists of five volcanic mountains, of which Kohala is the oldest (Macdonald 

and others, 1983, p. 345). The materials that make up Kohala 

volcano have been divided into two groups, the Pololü Basalt 

and Häwï Volcanics (Langenheim and Clague, 1987). The 

Pololü Basalt consists primarily of numerous basaltic flows 

that range in thickness from a few feet to as much as 50 feet. 

Pololü basalts extend from the surface, along the flanks of 

Waipiÿo Valley, to below sea level and are exposed throughout 

the walls and interior of Waipiÿo Valley. Pololü basalts are 

considered to be very permeable and, where confined by dikes, 

are able to store large quantities of high-level water (Stearns 

and Macdonald, 1946, p. 228). The younger Häwï Volcanics, 

which in some locations cap the Pololü Basalt, are separated 

from the Pololü basalts by an eroded surface. The existence of 

this surface indicates that Kohala Volcano was likely dormant 

for an extended period after the Pololü flows took place. During this dormant period, weathering formed the eroded surface 

and, especially on the wetter northeastern side of Kohala 

Volcano, deep valleys such as Waipiÿo. Flows of the Häwï Volcanics cap Pololü basalts in the headwaters of the study area 

and extend primarily northwesterly and southeasterly from 

Kohala Volcano. As a result, the deeply eroded Waipiÿo Valley 

was only partly filled by Häwï flows. In general, the Häwï Volcanics store lesser quantities of water than the Pololü Basalt, 

and vertical movement of this water is commonly restricted by 

intervening layers of dense basaltic flows and weathered soil. 

Alluvium covers most of the stream beds in Waipiÿo Valley 

and is evident at altitudes as high as 1,200 feet, especially in 

Kawainui, Alakahi, Waipiÿo, and Wailoa Streams (Stearns and 

Macdonald, 1946; p. 171). All but the most recent, unconsolidated alluvium in Waipiÿo Valley is classified as poorly permeable (Stearns and Macdonald, 1946, p. 172). Thick deposits of 

this alluvium form the broad flat valley near the downstream 

terminus of Waipiÿo Valley.

Although geology played a primary role in the evolution 

of deeply eroded Waipiÿo Valley, plentiful rainfall in the area 

was also an important factor. The highest annual rainfall totals 

in the study area are found in the headwaters of Kawainui 

Stream. In general, annual rainfall totals decrease as one travels from Kawainui Stream eastward towards Waimä Stream 

and then northeast down the valley towards the ocean (fig. 

1). In most of Kawainui Stream watershed upstream from 

Lower Hämäkua Ditch, mean annual rainfall exceeds 160 

inches (Giambelluca and others, 1986). In Alakahi Stream 

watershed, upstream from its confluence with Kawainui 

Stream, mean annual rainfall is between 120 and 160 inches 

(Giambelluca and others, 1986). Upstream from the mouth of 

Koÿiawe and Waimä Streams, mean annual rainfall is between 

80 and 120 inches. In Wailoa Stream watershed, in the lower 

reaches of the study area, mean annual rainfall is about 100 

inches. This abundant rainfall provides large volumes of 

groundwater recharge that ultimately supports low flows in 

Waipiÿo Valley streams.

Most of the study area is undeveloped and covered by 

thick vegetation. Upstream from Upper Hämäkua Ditch, the 

terrain is fairly gentle and is covered with thick, low-level 

shrubs, brush, and small trees. Downstream from Upper 

Hämäkua Ditch, the land surface drops off sharply into 

Waipiÿo Valley. In the valley, terrain is much steeper and vegetation consists of larger trees, except along sheer valley walls, 

where vegetation is sparser. Kawainui, Alakahi, Koÿiawe, and 

Waimä Streams flow into Waipiÿo Valley over waterfalls that 

in total are about 1,000, 1,900, 1,760, and 1,640 feet high, 

respectively. Deeply eroded Waipiÿo Valley cuts through 

numerous, closely spaced dikes and intercepts significant volumes of dike-impounded groundwater (Stearns and Macdonald, 1946; p. 175).

From the ocean, Waipiÿo Valley extends inland in a 

roughly southwesterly direction. Near the confluence of 

Alakahi and Kawainui Streams, the valley makes an abrupt, 

almost ninety-degree bend toward the northwest and up 

Kawainui Stream. This unusual shape is indicative of a geomorphic process commonly referred to as pirating, or capturing of stream reaches. According to Macdonald and others 

(1983, p. 360) it is probable that upper reaches of Kawainui 

Stream once flowed through a notch known as Waimanu Gap 

and formed the headwaters of Waimanu Stream. Because 

of more rapid rates of erosion in Waipiÿo Valley, however, 

Kawainui Stream was eventually intersected and therefore 

forced to flow into Waipiÿo Valley. Thus Waipiÿo Valley drains 

water that would otherwise have flowed in Waimanu Stream 

had erosional processes not altered the drainage pattern.

An important aspect of the study area is the water diversion systems located and operated there. The availability of 

abundant, high-level water in Waipiÿo Valley has long been 

valued (Herschler and Randolph Consulting Engineers, 1961). 

The existence and operation of two major water-diversion 

systems, Upper and Lower Hämäkua Ditches, is a testament to 

that fact. 

Upper Hämäkua Ditch, which roughly follows the 

southern rim of Waipiÿo Valley, diverts water from Kawainui 

Stream (at altitude 4,042 feet), Kawaiki Stream (at altitude 
4 Low-Flow Characteristics of Streams Under Natural and Diversion Conditions, Waipiÿo Valley, Island of Hawaiÿi, Hawaiÿi

Figure 1. Waipiÿo Valley study area, Island of Hawaiÿi, Hawaiÿi.

Kawainui

Str

Waimanu

Str

Alakahi Str

Lalakea

Str

Waiulili

Str

Waipi‘o Str

Wailoa

Str

Upper

Ditch

Lower

Ditch

Hämäkua

Hämäkua

Waimä

Str

Ko‘iawe Str

Kawaiki

Str

Waikoloa

Str

Hauani Gulch

Main

weir

Waimea

0 1 2 KILOMETERS

0 1 2 MILES

155°40' 155°36'

20°04'

20°08'

Waipi‘o 

 Bay

P A C I F I C 

 O C E A N

Kukuihaele

Hi‘ilawe

 Falls

60

80

160

120

20

30

40

60

80

Pu‘u o Umi A

5,260 ft

Pu‘u o ‘Umi

5,260 ft

A

A

A

A

Figure 1. Waipiÿo Valley study area, Island of Hawaiÿi, Hawaiÿi.

Boundary of study area

Line of equal mean annual rainfall, in inches

(modified from Giambelluca and others, 1986)

Major road

Main weir

80

EXPLANATION

HAWAI‘I

Area of map

PACIFIC

OCEAN

Hämäkua

Coast

Paÿauilo

Ä

Base modified from U.S. Geological Survey National

Hydrography Dataset, Transverse Mercator projection,

zone 5, central meridian −153°, North American Datum

1983. Relief from U.S. Geological Survey digital elevation

models, 1:24,000.
 Data and Methods Used to Estimate Low-Flow Statistics 5

4,026 feet), Alakahi Stream (at altitude 3,874 feet), Koÿiawe 

Stream (at altitude 3,355 feet), and Waimä Stream (at altitude 

3,044 feet) at locations just upstream of where they descend 

into Waipiÿo Valley (Hawaii Division of Water and Land 

Development, 1963). Diversion intakes along Upper Hämäkua 

Ditch were designed to capture all the water in the stream 

until the rate of flow almost exceeded the capacity of the 

intake structures. At this point, the water in the streams will 

start to top intake diversion dams and flow downstream into 

Waipiÿo Valley. Upper Hämäkua Ditch, between the uppermost 

intake at Kawainui Stream and the lowermost intake at Waimä 

Stream, is about 5.8 miles long and comprises a complex 

combination of open ditches, tunnels, flumes, and segments 

where water is channeled into existing stream reaches. Beyond 

Waimä intake, water is channeled to the southeast and away 

from Waipiÿo Valley watershed. Historically, the Parker Ranch 

diverted water from Alakahi Stream, well upstream from 

the Upper Hämäkua Ditch intake, through a 4-inch diameter 

pipeline. This pipeline was no longer in use at the time of 

this study (2000-2005). Hawaiÿi County Department of Water 

Supply also diverted water, through an emergency pipeline, 

from a spring source located on top of the north rim of Alakahi 

Canyon. This emergency pipeline was also no longer in use at 

the time of this study.

Lower Hämäkua Ditch diverts water from Kawainui 

Stream (at altitude 1,037 feet), Alakahi Stream (at altitude 

1,030 feet), and Koÿiawe Stream (at altitude 1,000 feet) (U.S. 

Department of Agriculture, 1999, Mink, 1984). Diversion 

intakes along Lower Hämäkua Ditch also were designed to 

capture most of the water in the stream, until the rate of flow 

almost exceeded the intake capacity. Proposed modification of 

intakes would allow controlled diversion of water and maintenance of some flow past the diversion points at all times (U.S. 

Department of Agriculture, 1999). Starting in 1966, pumps 

raised water from lower reaches of Waimä Stream 380 feet 

up into Lower Hämäkua Ditch (Wilcox, 1996, p. 153). These 

pumps, which were operated only during periods of drought 

and originally had a capacity of about 9.3 ft3/s (6 Mgal/d), 

were not operational during the period of this study. Lower 

Hämäkua Ditch intakes are connected by a series of tunnels, cut into valley walls, that are about 8.9 miles in length 

(Wilcox, 1996). The tunnels exit Waipiÿo Valley at a location 

known as the main weir (fig. 1). Water is then transported 

beyond the main weir, away from Waipiÿo Valley, to users 

along the Hämäkua coast as far away as the town of Paÿauilo. 

In addition to carrying the water diverted at three stream 

intakes, the tunnels of Lower Hämäkua Ditch also intersect 

and capture dike-impounded groundwater within the walls of 

Waipiÿo Valley.

Acknowledgments

The list of individuals and organizations that provided 

support and help needed to conduct this study is extensive. At 

the risk of neglecting to mention several of these important 

contributors, the author would like to specifically acknowledge 

the following people: Former and current maintenance supervisors for the Lower Hämäkua Ditch, Kelly Loo and Ernest 

Alfonso, shared their knowledge of Waipiÿo Valley and how to 

access its remote interior. Kia Fronda and other Waipiÿo Valley 

landowners graciously allowed access across their properties. David Young of Wai Engineering provided up to date 

information on maintenance and construction activities along 

Lower Hämäkua Ditch. Todd Presley and numerous other 

USGS employees participated in many challenging field trips 

to remote reaches of Waipiÿo Valley. Finally, John Engott and 

Chiu Yeung assisted with preparation of several illustrations in 

this report.

Data and Methods Used to 

Estimate Low-Flow Statistics

In this report, the low-flow hydrology of the streams in 

Waipiÿo Valley will be described in terms of flow-duration 

curves and their related statistics (Searcy, 1959). Flowduration curves offer an extremely useful way to summarize 

streamflow data (Vogel and Fennessey, 1995). A flow-duration 

curve is a cumulative frequency curve that shows the percentage of time that specified discharges in a stream were equaled 

or exceeded during a given period of record. Daily mean 

discharge will be the basis for flow-duration curves developed 

for this report, but curves can be developed using alternative 

time steps for discharge, such as weekly, monthly, or annual. 

Flow-duration curves are constructed by ranking streamflow 

data collected at a location for a specified period of time, in 

descending order, with the largest flow value first and the 

smallest value last (Ries, 1993, p, 20). The plotting position, 

or exceedance probability, for each streamflow value can then 

be calculated by using the Weibull formula (Helsel and Hirsch, 

2002; Langbein, 1960): 

 Pk = k/(n+1), (1)

where: Pk is the plotting position or exceedance 

 probability for the streamflow value with rank k,

 k is the rank of the given streamflow value, and

 n is the total number of streamflow values for the 

 specified period.

For example, assume that during a 5-day period we had 

the following sequence of daily mean discharge values: 300, 

39, 3, 2, and 1 ft3/s, and we wanted to compute the exceedance 

probability for 3 ft3/s on the basis of these data. The data are 

already ranked in descending order, and the value 3 ft3/s has 

a rank k of 3 (the third largest value). There are a total of 5 

values, so n equals 5. Applying formula (1):

Pk = 3/(5 +1) = 0.50, and converting to a percentage,or 

 flow-duration percentile, 

 Pk = 0.50 x 100 = 50 percent
6 Low-Flow Characteristics of Streams Under Natural and Diversion Conditions, Waipiÿo Valley, Island of Hawaiÿi, Hawaiÿi

For this simplified data set, we have determined that a 

daily mean discharge value of 3 ft3/s was equaled or exceeded 

50 percent of the time during this 5-day period. In this report, 

significantly longer periods of time will be used to compute 

flow-duration statistics, and flow-duration exceedance probabilities will be discussed primarily in terms of percentages or 

flow-duration percentiles.

An example of a flow-duration curve based on daily mean 

discharges for the period 1965–2004 at streamflow-gaging station 16720000 on Kawainui Stream is shown in figure 2. This 

gaging station is upstream from Upper Hämäkua Ditch. One 

of the most frequently referred to points on a flow-duration 

curve is the 50th percentile, or median discharge (abbreviated 

as Q50). This is the discharge that is equaled or exceeded 50 

percent of the time. In figure 2, the indicated median discharge 

is 4.5 ft3/s. In contrast, average discharge for the period 1965-

2004 at station 16720000 is 14.9 ft3/s. On the flow-duration 

curve, it can be determined that the average discharge of 14.9 

ft3/s is equaled or exceeded only about 28 percent of the time. 

In this instance, and for most Hawaiian streams, median discharge provides a more representative measure of typical flow 

conditions than does average discharge. Flow-duration percentiles of 50 and higher (for example, the 95th percentile) are 

typically used to describe low-flow characteristics of streams. 

A tabular listing of selected discharges used to construct the 

flow-duration curve shown in figure 2 is provided in a subsequent section of the report, in table 7. 

Another interesting value can be determined from flowduration curve percentiles. A flow-duration percentile represents the percent of time that a specified discharge is equaled 

or exceeded. The opposite of this value is the percent of time 

that the discharge is less than the specified value. Following the example from above, the 50th percentile discharge is 

4.5 ft3/s (fig. 2). Again, this is the discharge that is equaled 

or exceeded 50 percent of the time. By subtracting the flow 

duration percentile from 100 percent (in this case 100-50 = 50 

percent), we determine the percent of time that the discharge 

is less than 4.5 ft3/s. Also from figure 2, the discharge that is 

equaled or exceeded 95 percent of the time (the 95th percentile) is only 0.29 ft3

/s; this means that 5 percent of the time 

(100-95 = 5 percent), discharge in the stream is less than 0.29 

ft3/s. If you are a taro farmer with fields adjacent to streamflow-gaging station 16720000 on Kawainui Stream that need 

a minimum of 0.29 ft3/s of irrigation water to sustain your 

crop, it is important to understand that for 5 percent of the 

time this level of discharge will not be available in the stream 

for your use.

The shape of a flow-duration curve is indicative of the 

type of streamflow conditions that can be expected at a particular location. Smooth curves indicate unregulated or natural 

flow. Flow-duration curves that “flatten out” and show only 

minor reductions in lower discharges are indicative of sustained 

inflow to the stream, most likely as the discharge of groundwater to the channel. The flow-duration curve for Kawainui 

Stream (fig. 2) is smooth and does not flatten out at low 

discharges, indicating that flow at this location is representative 

of natural conditions, but also that it is not sustained by large 

volumes of groundwater inflow. The flow-duration curve for 

Kawainui Stream does not decline to zero, however, which 

indicates that streamflow at this location is perennial.

Streamflow Data 

To describe the low-flow hydrology of Waipiÿo Valley, a 

combination of historical and new streamflow data, the latter 

collected as part of this study, was used to develop flow-duration curves. Historical data include records of streamflow and 

discharge measurements collected by the USGS at former and 

current streamflow-gaging stations, as well as those available 

from other agencies. New data include miscellaneous discharge measurements made at 27 locations in Waipiÿo Valley 

and along the Lower Hämäkua Ditch.

Historical Data

The value of water resources in Waipiÿo Valley has been 

long recognized (Herschler and Randolph Consulting Engineers, 1961). As a result, an abundance of data, in the form 

of systematic records of daily discharge and miscellaneous 

discharge measurements, has been collected along streams 

and ditches that feed into and drain Waipiÿo Valley (Fontaine, 

1996). To the extent possible, these data are utilized in this 

report to aid in describing the low-flow hydrology of Waipiÿo 

Valley.

In a report that focused primarily on availability of water 

for diversion through Lower Hämäkua Ditch, Mink (1984) 

provided an excellent summary of the data that have been 

collected in the area. According to Mink (1984, p. 7), the first 

streamflow measurements in the Waipiÿo drainage basin were 

made by J.M. Lydgate, over a 10-month period in 1889 and 

1890. Records of these measurements were thought to exist 

at the Bernice Pauahi Bishop Museum (Honolulu) but were 

not recovered or used by Mink (1984) and will not be used in 

this study. Records for most locations where systematic daily 

discharge data have been collected in the area, however, have 

been published in USGS reports (for example, see Martin and 

Pierce, 1913). The locations of these stream and ditch gaging 

stations are shown in figure 3, and the availability of data for 

the stations is summarized in table 1.

At 12 of the surface-water gaging stations listed in table 

1, the only data collected were those obtained by Arthur Tuttle, 

for Bishop Estate, during the period August 1901 through 

January 1902 (Martin and Pierce, 1913, p. 397). Tuttle also 

collected data at a 13th station, on Wailoa Stream at an altitude 

of 190 feet, a site that later became USGS gaging station 

16732200 (tables 1 and 2).

Data collected at these 13 gaging stations provide useful 

information to quantify variations in flow along stream reaches 

in Waipiÿo Valley under natural, undiverted flow conditions 

that existed before the construction of Upper and Lower 

Hämäkua Ditches. The data collected throughout Waipiÿo 
 Data and Methods Used to Estimate Low-Flow Statistics 7

Figure 2. Flow-duration curve for streamflow gaging station 16720000 on Kawainui Stream, Island of

Hawaiÿi, for water years 1965–2004.

0.001

0.01

0.1

1

10

100

1,000

Daily mean discharge, in cubic feet per second

1 10 30 50 70 90 99 99.9 99.99

Percentage of time indicated discharge was equaled or exceeded

Valley by Tuttle were used to justify construction of Lower 

Hämäkua Ditch (Mink, 1984, p. 8). The Hawaiian Irrigation 

Company (HIC) collected flow records for Upper Hämäkua 

Ditch (Hawaii Division of Water and Land Development, 

1963) and Lower Hämäkua Ditch (Mink, 1984) at numerous 

locations. Some of these data, for gaging stations 16732600 

(1910–1913) and 16732900 (1910–1920), were published by 

the USGS (table 1). These data provide historical documentation of how the ditches were formerly operated but are of 

limited use in describing current operational practices and 

capacities of Upper and Lower Hämäkua Ditch systems.

The USGS has collected data at gaging stations on and 

upstream from Upper Hämäkua Ditch and at three surfacewater gaging stations in adjacent watersheds that are useful 

for describing the low-flow hydrology of the Waipiÿo Valley study area (table 1). Three of these stations, Kawainui 

Stream at 4,060 feet (16720000), Alakahi Stream at 3,900 feet 

(16725000), and Waikoloa Stream at 3,460 feet (16758000), 

are still being operated (2009). These three stations currently 

in operation, as well as that on Hauani Gulch at 3,117 feet 

(16759000), which was discontinued in 2004, are all longterm stations that have been in operation for 41 to 58 years. 

The USGS has operated only one gaging station within the 

main part of the Waipiÿo Valley for any extended period, 

Wailoa Stream at 190 feet (16732200). Data from this station 

will be used to help define low-flow characteristics at the 

downstream limit of the study area.

Individual discharge measurements, or series of near-concurrent measurements (seepage runs), have been made at various locations and times throughout the Waipiÿo Valley study 

area. A number of these measurements were made to define 

specific low-flow characteristics in Waipiÿo Valley, and those 

will be of significance in this report. Stearns and Macdonald 

(1946, p. 230-239) summarized discharge measurements that 

were made to document gains and losses in Lower Hämäkua 

Ditch on January 28, 1912; low flow of the main tributaries of 

Waipiÿo Stream during dry weather in December 1944; spring 

flow along Kawainui Stream upstream from Lower Hämäkua 

Ditch on December 6, 1943; and gains in the main tributaries of Waipiÿo Stream in reaches 100 feet downstream from 
8 Low-Flow Characteristics of Streams Under Natural and Diversion Conditions, Waipiÿo Valley, Island of Hawaiÿi, Hawaiÿi

Gagingstation 

number

Station location Period of record Remarks

Gaging stations on and upstream from Upper Hämäkua Ditch and adjacent to the Waipiÿo Valley study area

16720000 Kawainui Stream at 4,060 feet 1965-P Used as index station

16720300 Kawaiki Stream at 4,090 feet 1969-1999

16720500 Upper Hämäkua Ditch at 4,020 feet 1964-2002 Ditch gaging station

16724800 Upper Hämäkua Ditch at 3,890 feet 1968-2000 Ditch gaging station

16725000 Alakahi Stream at 3,900 feet 1965-P Used as index station

16726000 Upper Hämäkua Ditch at 3,020 feet 1974-2004 Ditch gaging station

16757000 Waikoloa Stream at 3,570 feet 1947-1971

16758000 Waikoloa Stream at 3,460 feet 1948-P Used as index station

16759000 Hauani Gulch at 3,117 feet 1957-2004 Used as index station

Gaging stations downstream from Upper Hämäkua Ditch and upstream from Lower Hämäkua Ditch

16721000 Kawainui Stream at 2,120 feet 1901-1902 51 days of data

16721500 Kawainui Stream Branch 3 at 1,700 feet 1901-1902 94 days of data

16722000 Kawainui Stream at 1,435 feet 1901-1902 77 days of data

16722300 Kawainui Stream Branch 2 at 1,405 feet 1901-1902 106 days of data

16722600 Kawainui Stream Branch 1 at 1,380 feet 1901-1902 106 days of data

16723000 Kawainui Stream at 1,040 feet 1911 1 discharge measurement

16728000 Alakahi Stream at 1,200 feet 1901-1902 71 days of data

16730000 Koÿiawe Stream at 1,120 feet 1901-1902 68 days of data

Gaging stations on and downstream from Lower Hämäkua Ditch

16724000 Kawainui Stream at 775 feet 1901-1902 115 days of data

16729000 Alakahi Stream at 730 feet 1901-1902 126 days of data

16731000 Koÿiawe Stream at 610 feet 1901-1902 132 days of data

16732000 Waipiÿo Stream at 580 feet 1911 1 discharge measurement

16732100 Waimä Stream at 790 feet 1901-1902 132 days of data

16732150 Waimä Stream at 385 feet 1901-1902 127 days of data

16732200 Wailoa Stream at 190 feet 1901-1902, 1911, 1964-1969 Downstream end of study area

16732600 Lower Hämäkua Ditch at 1,000 feet 1910-1913 Ditch gaging station

16732800 Lower Hämäkua Ditch upstream from main weir 2002-2004 Ditch gaging station

16732900 Lower Hämäkua Ditch at main weir 1910-1920 Ditch gaging station

16733000 Lower Hämäkua Ditch wasteway 1964-1973 Releases of water at main weir

16733100 Lower Hämäkua Ditch downstream from main weir 1964-1973 Ditch gaging station

Table 1. Surface-water gaging stations operated in and adjacent to the Waipiÿo Valley study area, Island of Hawaiÿi, Hawaiÿi.

[P, in operation 2006 water year]
 Data and Methods Used to Estimate Low-Flow Statistics 9

Figure 3. Location of stream and ditch surface-water gaging stations operated in and adjacent to the Waipiÿo Valley 

study area, Island of Hawaiÿi, Hawaiÿi.

Kawainui

Str

Waimanu

Str

Alakahi

Str

Läläkea 

Str

Waiulili

Str

Waipi‘o Str

Wailoa

Str

Upper

Ditch

Lower

Ditch

Hämäkua

Waima

Str

Ko‘iawe 

Str

Hämäkua

##

#

#

#

##

#

#

#

#

#

#

##

#

#

#

#

#

#

" ""

"

"

"

"

720000

720500

720300

721000

757000

758000

759000

724800

725000

728000

721500

722000

722600

722300

723000

724000

729000

732000

731000

732150

732100

732600

726000

730000

732200

732900

733000

733100

732800

Waimea

0 1 2 KILOMETERS

0 1 2 MILES

Base modified from U.S. Geological Survey National

Hydrography Dataset, Transverse Mercator projection,

zone 5, central meridian −153°, North American Datum 1983.

155°40' 155°36'

20°04'

20°08'

Waipiÿo 

 Bay

P A C I F I C 

 O C E A N

Figure 3. Location of stream and ditch surface-water gaging stations operated in adjacent to the Waipiÿo Valley study area,

Island of Hawaiÿi, Hawaiÿi.

757000

726000 "

# Stream (Index stations are highlighted in yellow)

Ditch

 

Gaging station and abbreviated number—

Complete number is preceded by 16

Major road

EXPLANATION

HAWAI‘I

Area of map

PACIFIC

OCEAN
10 Low-Flow Characteristics of Streams Under Natural and Diversion Conditions, Waipiÿo Valley, Island of Hawaiÿi, Hawaiÿi

Lower Hämäkua Ditch on January 28, 1912. During a severe 

drought in 1962-63 (Giambelluca and others, 1991, p. 35), the 

USGS made numerous discharge measurements along streams 

and ditches in the Waipiÿo Valley study area. These measurements are summarized by Davis and Yamanaga (1963) and 

in the USGS annual data report for 1963 (U.S. Geological 

Survey, 1963). During the period October to December 1963, 

the USGS made three sets of discharge measurements along 

Upper Hämäkua Ditch and its tributary streams (U.S. Geological Survey, 1964). In 1965 and 1966, the USGS made several series of discharge measurements along Waimä Stream, 

although not all measurements were made on the same day in 

each year (U.S. Geological Survey, 1967). On March 9, 1983, 

the USGS made discharge measurements on Waipiÿo Stream 

upstream from the mouth of Waimä Stream and on Wailoa 

Stream at the site of former gaging station 16732200 (fig. 3) 

(Chinn and others, 1984).

Data Collected for This Study

To meet the objectives of this study, additional data 

beyond the historical data already available were required. 

Additional discharge measurements were made at 27 locations 

in Waipiÿo Valley and along Lower Hämäkua Ditch (table 2 

and fig. 4) in order to (1) describe low flow in Waipiÿo Valley 

upstream from Lower Hämäkua Ditch intakes, (2) describe 

variability of low flows along Lower Hämäkua Ditch, and (3) 

describe variability of low flows along stream reaches downstream from Lower Hämäkua Ditch. 

The locations at which additional discharge measurements were made fall into two distinct categories—low-flow 

partial-record stations and seepage-run sites. Multiple discharge measurements are made at each low-flow partial-record 

station, covering a wide variety of low-flow conditions. The 

measurements are timed such that each is made during an 

independent recession in streamflow following periods of 

direct runoff at the station (Fontaine, 2003). Discharge measurements were made at five low-flow partial-record stations. 

The stations are at sites 1, 6, 15, 18, and 24 (fig. 4), which 

are upstream from the intakes of Lower Hämäkua Ditch on 

Kawainui, Alakahi, Koÿiawe, and Waimä Streams and at the 

site of former USGS gaging station 16732200 on Wailoa 

Stream, respectively. The Lower Hämäkua Ditch does not 

actively divert water at Waimä intake. The discharge measurements made at these five low-flow partial-record stations are 

listed in table 3.

During a seepage run, discharge measurements are 

made within a short period of time at several locations along 

a stream reach or ditch. The measurements usually are made 

during periods of low flow, when conditions within a given 

reach of the stream or ditch are relatively steady (Fontaine, 

2003). Seepage runs were made on streams in Waipiÿo Valley 

on September 20–21, 2000, and on September 26, 2001. During these seepage runs, measurements were made at as many 

as 27 sites (the low-flow partial-record stations are included in 

the seepage-run sites); these data are listed in table 4.

Selection of Base Period

Flow-duration curves show the percent of time that specific discharges were equaled or exceeded, but they are applicable only to the time period for which they were computed. 

When selecting a base period for analysis, a reasonable goal 

is to select a period that is long enough to be representative of 

long-term streamflow conditions in the study area of interest 

or concern. If this goal can be met, then flow-duration curves 

computed for the selected base period can also be considered 

representative of future streamflow conditions. In comparing 

flow-duration values computed for a variety of locations, as 

will be done as part of this report, care must be taken to ensure 

that the values represent the same base period at all locations. 

If this is not done, one might end up comparing flow data collected during a period when streamflow was above normal (for 

example, at station A) to flow data collected during a drought, 

when streamflow was below normal (for example, at station 

B). Such comparisons would be misleading. 

In this study of streamflow conditions in the Waipiÿo Valley, the period extending from water year 1965 through water 

year 2004 was selected as the base period. This 40-year period 

was assumed to be long enough to adequately reflect longterm streamflow conditions in Waipiÿo Valley. In addition, a 

continuous record of flow for this entire period is available 

for at least four USGS surface-water gaging stations either 

within or adjacent to the Waipiÿo Valley study area (table 1). 

Flow-duration curves computed for the entire base period at 

these four stations, which also are referred to as index stations 

(see later section “Selection of Index Stations and Application 

of Data”), can be used to extend (in time) the data collected 

at other locations so that they also are representative of the 

1965–2004 base period and thus of long-term flow conditions. 

Extending the base period before 1965 is counterproductive 

because it would eliminate use of two index stations for which 

1965 was the first year of operation. Similarly, extending the 

base period after 2004 would eliminate use of one index station because 2004 was the last year it was operated.

As noted in the previous paragraph, the 40-year base 

period, water years 1965–2004, was assumed to be representative of long-term streamflow conditions in the study area. To 

test this assumption, selected flow-duration discharges were 

computed for the entire period of record and for the 40-year 

base period at gaging stations 16758000 on Waikoloa Stream, 

which drains a valley just to the south of Waipiÿo Valley (fig. 

1 and table 5) and 16010000 on Kawaiköï Stream on the 

Island of Kauaÿi (table 6). In these flow-duration analyses and 

those based on gaging-station records throughout the report, 

only water years with complete records were considered. 

The gaging station on Waikoloa Stream is currently (2006) in 

operation and has records that extend back to 1948, making 

it the station with the longest streamflow record on the Island 

of Hawaiÿi that is not affected by regulation (Fontaine, 1996). 

The gaging station on Kawaiköï Stream has the longest complete streamflow record in the entire State of Hawaiÿi, extending back to 1912. In both cases, flow-duration discharges 

computed for the base period were virtually the same as those 
 Data and Methods Used to Estimate Low-Flow Statistics 11

Site 

number 

(fig. 4)

Gaging-station number Station location Remarks

1 200505155383801 Kawainui Stream us from LHD LFPR, seepage-run site

2 16723000 Kawainui Stream ds from LHD Seepage-run site

3 200502155383601 LHD ds from Kawainui Stream intake Seepage-run site

4 200415155390001 LHD us from Alakahi Stream intake Seepage-run site

5 200414155385901 Alakahi Stream ds from LHD Seepage-run site

6 200413155390301 Alakahi Stream us from LHD LFPR, seepage-run site

7 200413155385901 LHD ds from Alakahi Stream intake Seepage-run site

8 16724000 Kawainui Stream at mouth Seepage-run site

9 16729000 Alakahi Stream at mouth Seepage-run site

10 200430155381801 Waipiÿo Stream ds from confluence of Kawainui and Alakahi 

Streams

Seepage-run site

11 200429155380001 Waipiÿo Stream us from mouth of Koÿiawe Stream Seepage-run site

12 16732000 Waipiÿo Stream ds from mouth of Koÿiawe Stream Seepage-run site

13 16731000 Koÿiawe Stream at mouth Seepage-run site

14 200354155380801 LHD us from Koÿiawe Stream intake Seepage-run site

15 200351155380901 Koÿiawe Stream us from LHD LFPR, seepage-run site

16 200354155380701 Koÿiawe Stream ds from LHD Seepage-run site

17 200353155380801 LHD ds from Koÿiawe Stream intake Seepage-run site

18 200351155372801 Waimä Stream us from LHD LFPR, seepage-run site

19 200354155372601 Waimä Stream ds from LHD Seepage-run site

20 16732600 LHD at Waimä Stream Seepage-run site

21 200424155370301 LHD ds from pump inflow Seepage-run site

22 200434155372001 Waipiÿo Stream us from mouth of Waimä Stream Seepage-run site

23 16732150 Waimä Stream at mouth Seepage-run site

24 16732200 Wailoa Stream at 190 feet LFPR, seepage-run site

25 200542155354501 LHD at Hiÿilawe Falls Seepage-run site

26 200542155354101 LHD at Hakalaoa Falls Seepage-run site

27 16732800 LHD upstream from main weir Seepage-run site

Table 2. Locations where discharge measurements were made in the Waipiÿo Valley study area during the period 2000–2005,

 Island of Hawaiÿi, Hawaiÿi.

[LHD, Lower Hämäkua Ditch; us, upstream; ds, downstream; LFPR, low-flow partial-record station]
12 Low-Flow Characteristics of Streams Under Natural and Diversion Conditions, Waipiÿo Valley, Island of Hawaiÿi, Hawaiÿi

Figure 4. Locations where discharge measurements were made in Waipiÿo Valley study area during the period 

2000–2005, Island of Hawaiÿi, Hawaiÿi.

Kawainui

Str

Waimanu

Str

Alakahi

Str

Läläkea 

Str

Waiulili

Str

Waipi‘o Str

Wailoa

Str

Upper

Ditch

Lower

Ditch

Hämäkua

Waimä

Str

Koiawe

Str

Hämäkua

1

2

3

4

5 6

7

8

9 10

11

12

13

14

15

16

17 18

19 20

21

22

23

24

25 26

27

#

#

##

#

##

#

## ##

#

##

#

# ##

#

#

# #

#

#

#

#

Waimea

0 1 2 KILOMETERS

0 1 2 MILES

155°40' 155°36'

20°04'

20°08'

Waipi‘o 

 Bay

P A C I F I C 

 O C E A N

Figure 4. Locations where discharge measurements were made in Waipiÿo Valley study area during the period 2000–2005,

 Island of Hawaiÿi, Hawaiÿi.

Seepage-run site and number

Seeppage-run site and low-flow

partial-record station and number

Major road

22

6 #

#

Base modified from U.S. Geological Survey National

Hydrography Dataset, Transverse Mercator projection,

zone 5, central meridian −153°, North American Datum 1983.

EXPLANATION

HAWAI‘I

Area of map

PACIFIC

OCEAN
 Data and Methods Used to Estimate Low-Flow Statistics 13

Date

Discharge (ft3/s)

Kawainui 

Stream Site 

1a

Alakahi

 Stream Site 

6a

Koÿiawe 

Stream Site 

15a

Waimä 

Stream Site 

18a

Wailoa 

Stream Site 

24a

08/08/00 --- --- 7.02 0.62 ---

09/20/00 --- 17.4b --- 0.61 ---

09/21/00 26.5 --- 7.53 --- 78.3

01/10/01 18.6 14.1 --- --- 68.8

01/11/01 --- --- 7.28 0.69 ---

03/08/01 59.1 25.7 --- --- ---

03/09/01 --- --- 8.28 0.60 76.5

05/30/01 21.7 14.2 --- --- 73.3

05/31/01 --- --- 7.18 0.53 ---

09/26/01 41.5 --- 10.5 0.86 103

06/26/03 35.0 17.2 --- --- ---

06/27/03 --- --- 8.30 0.67 82.9

09/25/03 22.6 14.3 --- --- 84.6

09/26/03 --- --- 7.52 0.67 ---

10/06/04 16.2 12.5 --- --- 69.4

10/07/04 --- --- 7.32 0.72 ---

02/25/05 11.4 11.4 --- --- ---

04/27/05 --- --- 7.38 --- ---

08/23/05 --- --- --- 0.93 95.7

08/24/05 28.6 13.6 --- --- ---

 a Site numbers correspond to those listed in table 2 and shown in figure 4.

b

 Computed by mass balance as Site 6 = Site 5 + (Site 7 - Site 4), data from table 4.

Table 3. Discharge measurements at low-flow partial-record stations in Waipiÿo Valley during the

 period 2000–2005, Island of Hawaiÿi, Hawaiÿi.

[ft3/s, cubic feet per second; ---, no data available] 

for the entire period of record, thereby supporting the assumption that the 1965–2004 base period selected for this study is 

representative of long-term streamflow conditions. In an analysis of streamflow throughout the State of Hawaiÿi (Fontaine 

and others, 1992, p. 13), median streamflow was computed 

for several 40-year periods at gaging station 16587000 on 

Honopou Stream on the Island of Maui. The standard error 

for the various 40-year median streamflow estimates, when 

compared to long-term median streamflow for the 75-year 

period 1912–1986, was only 7.8 percent, again supporting use 

of a 40-year base period in this current study as representative 

of long-term streamflow conditions. 

Another important factor to consider in the selection of 

a base period and subsequent flow-duration analyses is the 

presence of any trends in the streamflow data being used. 

Oki (2004) conducted an analysis to test for the presence (or 

absence) of trends in streamflow characteristics at long-term 

gaging stations in Hawaiÿi. Included in the analysis was the 

gaging station on Waikoloa Stream (16758000), which is used 

as an index station in this report (table 1). In his analysis, Oki 

tested for trends in annual mean discharges and in 10-, 25-, 50-, 

75-, and 90-percentile flow-duration discharges. No significant 

trends were detected in any of the flow characteristics tested 

(Oki, 2004, p. 32). These results can reasonably be assumed to 

apply to other index stations being used in this report.

Record-Extension Techniques

Except for the gaging stations referred to above as 

index stations, streamflow data for most of the gaging 
14 Low-Flow Characteristics of Streams Under Natural and Diversion Conditions, Waipiÿo Valley, Island of Hawaiÿi, Hawaiÿi

Site 

numbera Stream or ditch Altitude (feet) Discharge (ft3/s)

Sept. 20-21, 2000 Sept. 26, 2001

1 Kawainui Stream 1,070 26.5 41.5

2 Kawainui Stream 1,037 4.7b 26.1b

8 Kawainui Stream 775 11.8 ---

6 Alakahi Stream 1,030 17.4c ---

5 Alakahi Stream 1,000 19.1 ---

9 Alakahi Stream 730 19.7d ---

10 Waipiÿo Stream 720 31.5 ---

11 Waipiÿo Stream 595 34.8 ---

12 Waipiÿo Stream 580 41.2e ---

22 Waipiÿo Stream 400 43.3 ---

15 Koÿiawe Stream 1,020 7.53 10.5

16 Koÿiawe Stream 980 2.2f 1.8f

13 Koÿiawe Stream 610 6.44 ---

18 Waimä Stream 1,040 0.61 0.86

19 Waimä Stream 970 0.6g 0.9g

23 Waimä Stream 385 35.0 ---

24 Wailoa Stream 190 78.3 103

3 Lower Hämäkua Ditch 1,037 21.8 15.4

4 Lower Hämäkua Ditch 1,030 19.8 13.0

7 Lower Hämäkua Ditch 1,030 18.1 11.0

14 Lower Hämäkua Ditch 1,000 18.1 11.9

17 Lower Hämäkua Ditch 1,000 23.4 20.6

20 Lower Hämäkua Ditch 980 23.4 22.1

21 Lower Hämäkua Ditch 975 25.5 20.0

25 Lower Hämäkua Ditch 970 26.8 22.2

26 Lower Hämäkua Ditch 970 21.8h 20.4

27 Lower Hämäkua Ditch 965 22.4 22.2

a Site numbers correspond to those listed in table 2 and shown in figure 4.

b

 Computed by mass balance as Site 2 = Site 1 - Site 3.

c Computed by mass balance as Site 6 = Site 5 + (Site 7 - Site 4).

d Computed by mass balance as Site 9 = Site 10 - Site 8.

e Computed by mass balance as Site 12 = Site 11 + Site 13.

f

 Computed by mass balance as Site 16 = Site 15 - (Site 17 - Site 14).

g

 Estimated as about the same as Site 18, no diversion of water at the ditch intake.

h

 Average of two discharge measurements made at the site.

Table 4. Discharge measurements at seepage-run sites in Waipiÿo Valley during the period 2000–2001, 

Island of Hawaiÿi, Hawaiÿi.

[ft3/s, cubic feet per second; ---, no data available]
 Data and Methods Used to Estimate Low-Flow Statistics 15

Percentage of time 

indicated discharge 

equaled or exceeded

Period of record 

1948-2005 (ft3/s)

Base period 

1965-2004 (ft3/s)

Difference 

in 

percent

99 1.0 0.99 -1.0

95 1.5 1.5 0.0

90 1.8 1.7 -5.6

80 2.3 2.3 0.0

70 2.8 2.8 0.0

60 3.5 3.4 -2.9

50 4.4 4.3 -2.3

40 5.8 5.8 0.0

Table 5. Selected flow-duration discharges for the period of record 

and the base period at gaging station 16758000 on Waikoloa Stream, 

Island of Hawaiÿi, Hawaiÿi.

[ft3/s, cubic feet per second]

Percentage of time 

indicated discharge 

equaled or exceeded

Period of record 

1912-2005 (ft3/s)

Base period 

1965-2004 (ft3/s)

Difference in 

percent

99 2.3 2.3 0.0

95 3.5 3.6 2.9

90 4.4 4.5 2.3

80 6.0 6.0 0.0

70 7.8 7.7 -1.3

60 10 9.7 -3.0

50 13 13 0.0

40 17 17 0.0

Table 6. Selected flow-duration discharges for the period of record and 

the base period at gaging station 16010000 on Kawaiköï Stream, Island 

of Kauaÿi, Hawaiÿi.

[ft3/s, cubic feet per second]
16 Low-Flow Characteristics of Streams Under Natural and Diversion Conditions, Waipiÿo Valley, Island of Hawaiÿi, Hawaiÿi

stations in Waipiÿo Valley, as well as for locations where 

multiple discharge measurements were made, are available 

only for parts of the selected base period, 1965–2004. For 

these latter stations and the measurement locations, recordextension techniques were used to estimate flow-duration 

data for the base period on the basis of available short-term 

records and discharge data. A basic assumption of recordextension techniques is that relations between concurrent 

streamflow data and statistics based on them, at the station 

with short-term record and the index station with complete 

record, are the same for the short-term and extended periods 

of time (Ries, 1993). Although similar in concept, the procedures for extending records at surface-water gaging stations 

differ slightly depending on whether the available shortterm data are for continuous-record stations or for low-flow, 

partial-record stations, where only discharge measurements 

were made. 

Continuous-Record Gaging Stations

The steps used in this study when extending records at 

continuous-record gaging stations are as follows:

1. Low-flow duration discharges for 99-, 98-, 97-, 95-, 90-, 

85-, 80-, 75-, 70-, 65-, 60-, 55-, 50-, and 40-percentiles are 

computed for the entire period of concurrent record at the 

short-term station and at each of the four index stations 

being used in this study.

2. The correlation coefficient between discharges at selected 

flow-duration percentiles at the short-term station and each 

of the four index stations is determined. Only index stations with correlation coefficients greater than 0.80 will be 

used for record extension.

3. Concurrent flow-duration discharges for the short-term 

station and for each of the index stations selected in step 

2 are then plotted, both in linear and log space (base 10 

logarithms were used throughout this study), to determine which index station provided the best relation. In 

general, plots in log space provided the best results. If 

one index station had a significantly higher correlation 

coefficient and clearly provided the best relation with the 

short-term station, then it was selected for use in record 

extension. If correlation coefficients and relations with 

several index stations are similar, then each was used for 

record extension.

4. Plots that reflect the best relation between the short-term 

station and each index station selected in step 3 were evaluated to determine if the best fit relation was linear or curvilinear. If the relation was linear, then the Maintenance Of 

Variance Extension, Type 1 (MOVE.1) technique (Hirsch, 

1982) was used for record extension. If the relation was 

curvilinear, a graphical-correlation method (Searcy, 1959, 

p. 14) was used for record extension.

In the application of the MOVE.1 technique, the data 

format (linear or log) that provided the strongest correlation 

and relation is used. When applying the MOVE.1 technique 

to extend records at short-term stations, the analysis can be 

based on use of either concurrent flow-duration discharges or 

concurrent daily mean discharges at the stations. In this study, 

concurrent flow-duration discharges were consistently used 

for analyses. The mean and standard deviation of the selected 

flow-duration discharges at both the short-term and index stations are then computed. If a logarithmic relation is used, the 

discharges are transformed to log base 10 values before computation of means and standard deviations (Fontaine, 2003, 

p. 16). Estimates of base period (1965–2004) flow-duration 

discharges at the short-term surface-water gaging station are 

then computed by using the MOVE.1 formula as follows:

 Yi =Ym + sy/sx (Xi-Xm) , (2) 

where:

 Yi is the estimated flow-duration discharge

 for the base period at the short-term station,

 Xi is the flow-duration discharge for the base period 

 at the index station,

 Ym is the mean of the concurrent flow-duration 

 discharges at the short-term station,

 Xm is the mean of the concurrent flow-duration 

 discharges at the index station,

 sy is the standard deviation of the concurrent flow- 

 duration discharges at the short-term station, and

 sx is the standard deviation of the concurrent 

 flow-duration discharges at the index station.

 Estimated flow-duration discharges for the base period 

at the short-term stations, which are based on use of data in 

logarithmic form, are converted back to their original units of 

measurement (cubic feet per second) subsequent to the 

application of equation 2.

In the application of the graphical-correlation method, the 

data format (linear or log) that provided the strongest correlation and relation is used and a smooth curve connecting concurrent flow-duration discharges for the short-term and index 

stations is developed. This curve defines the relation between 

flow-duration discharges at the stations and becomes the basis 

for estimating base period flow-duration discharges at the 

short-term station. Finally, using flow-duration discharges for 

the base period at the index station, corresponding base-period 

flow-duration discharges at the short-term station are read 

from the smoothed relation curve.

As noted in step 3 above, if correlation coefficients and 

the relation with several of the index stations are both significant and similar, then each was used for record extension. In 

such cases, more than one independent estimate of base period 

flow-duration discharges for the short-term station will be 

computed. Tasker (1975) noted that when multiple independent 

estimates are available, an improved estimate can be obtained 

by computing an average of the multiple estimates. Therefore, 
Data and Methods Used to Estimate Low-Flow Statistics 17

in this report, variance-weighted averages are computed in all 

cases in which multiple index stations were used for record 

extension. Variance is a measure of how accurately the line 

of relation developed between data for the short-term and 

index stations match the data used to develop it—the better 

the relation, the smaller the variance. A detailed explanation 

of how to compute variance for each independent estimate and 

the variance-weighted average estimates is given by Ries and 

Friesz (2000, p. 11-13) and will not be replicated here. 

Values of variance associated with independent and 

weighted estimates of base period flow-duration discharges 

can be used to compute standard errors for results computed 

using record-extension techniques. These standard errors are 

primarily a reflection of the strength of correlation between 

short-term and index stations and do not account for errors 

associated with discharge measurements and daily mean discharge data used in the analyses. As a result, computed standard errors summarized in this report will underestimate true 

errors. The reader is again referred to Ries and Friesz (2000, p. 

11-13) for a more detailed explanation of how standard errors 

are computed. 

Low-Flow Partial-Record Stations

At low-flow partial-record stations, the data available 

for analysis are multiple discharge measurements, each 

made during independent streamflow recessions. To estimate 

base-period flow-duration statistics at these stations, the same 

procedures outlined above for short-term surface-water gaging stations are used with one minor difference. Estimates 

for short-term gaging stations are based on relations developed from flow-duration discharges computed from concurrent periods of record at the short-term and index stations. 

At low-flow partial-record stations, estimates are based on 

relations developed between discharge measurements at the 

partial-record stations and concurrent daily mean discharges 

at the index stations. On days with variable flow at the index 

stations, mean discharges computed for base-flow parts of the 

day were used in the analysis. Relations developed with each 

of the four index stations are evaluated in terms of their correlation coefficients to determine which are most appropriate 

for use. Based on the nature of relations identified, either the 

MOVE.1 technique (linear) or graphical-correlation method 

(curvilinear) is used for record extension. If multiple index 

stations are used in the analysis, then each of the independent 

results is averaged using variance-weighting techniques. 

Selection of Index Stations and 

Application of Data

Four surface-water gaging stations with a complete 

record of flow for the entire 1965–2004 base period are identified in table 1. Flow-duration discharges representative of the 

base period can be computed directly from the data available 

at each of these stations; they do not have to be estimated by 

record-extension techniques. The availability of a complete 

record and directly computed flow-duration discharges means 

that these four stations can be used as index stations to help 

extend the records of short-term gaging stations and low-flow 

partial-record stations in the Waipiÿo Valley study area.

Flow-duration discharges for the 1965–2004 base period 

at the four index stations have been computed and are summarized in table 7. The values in table 7 have no standard 

errors associated with them because they were not estimated 

by record-extension techniques. Flow-duration discharges 

summarized in table 7 assume use of current (2000–2005) 

diversion practices during the entire base period. However, 

because none of the four index stations are affected by diversions from either the Upper or Lower Hämäkua Ditches, 

the computed-flow duration discharges also reflect natural, 

undiverted conditions. Although complete flow-duration 

curves have been computed for each of the four index stations, 

only the higher percentile duration discharges are shown, in 

keeping with the focus of this report on low-flow hydrology of 

Waipiÿo Valley. Expanded flow-duration discharges are shown 

for the four index stations because these data will be used for 

record-extension techniques at short-term surface-water gaging stations.

The index stations on Kawainui Stream at 4,060 feet 

(16720000) and on Alakahi Stream at 3,900 feet (16725000) 

are located just upstream from Upper Hämäkua Ditch on tributary streams to Waipiÿo Valley (fig. 3). Thus they can be used 

to directly define low-flow hydrology within the study area in 

addition to being used as index stations to extend records. The 

index stations on Waikoloa Stream at 3,460 feet (16758000) 

and on Hauani Gulch at 3,117 feet (16759000) , which are in 

watersheds outside the study area, are actually closer to the 

downstream reaches of Waipiÿo Valley than the index stations on Kawainui and Alakahi Streams (fig. 3). Because of 

the location of these latter two stations, they cannot be used 

to directly define low-flow hydrology within the study area, 

but they still serve as valuable index stations for extending 

records at data-collection sites on reaches farther downstream 

in Waipiÿo Valley. 

Computation of Low-Flow Statistics at 

Sites with Historical Data

In the Waipiÿo Valley study area, historical data, in addition 

to that at index, short-term, and low-flow partial-record stations 

that were described in previous sections of this report, are available for analysis. Historical data can be divided into two basic 

types: data for stations where daily discharge data were collected between August 1901 and January 1902, and data for stations where only miscellaneous discharge measurements were 

made. The analysis of data from the short-term daily discharge 

stations and its application to the 1965–2004 base period, as 

well as the miscellaneous discharge measurements and their 

value in the verification of discharge statistics computed by 

other methods, are described in detail in appendix 1. 
18 Low-Flow Characteristics of Streams Under Natural and Diversion Conditions, Waipiÿo Valley, Island of Hawaiÿi, Hawaiÿi

Percentage of time 

indicated discharge 

equaled or exceeded

Discharge (ft3/s)

Kawainui 

Stream 

16720000

Alakahi 

Stream 

16725000

Waikoloa 

Stream 

16758000

Hauani Gulch 

16759000

99 0.10 0.15 0.99 0.00

98 0.15 0.23 1.2 0.03

97 0.19 0.29 1.3 0.04

95 0.29 0.38 1.5 0.06

90 0.51 0.59 1.7 0.11

85 0.74 0.80 2.0 0.15

80 1.0 1.0 2.3 0.20

75 1.3 1.2 2.5 0.25

70 1.7 1.5 2.8 0.29

65 2.1 1.8 3.0 0.34

60 2.7 2.2 3.4 0.40

55 3.5 2.6 3.8 0.47

50 4.5 3.1 4.3 0.55

40 7.4 4.5 5.8 0.77

 1 Discharge values shown on this table also represent discharge at the index stations under current (2000-2005) 

diversion practices, even though those diversions do not affect flow at the stations.

Table 7. Selected natural flow-duration discharges for the 1965–2004 base period at 

index gaging-stations operated in the Waipiÿo Valley area, Island of Hawaiÿi, Hawaiÿi.1

[ft3/s, cubic feet per second]

Computation of Low-Flow Statistics for 

Ungaged Sites

Streamflow data and associated low-flow statistics are not 

available at all locations in Waipiÿo Valley where they might 

be required, primarily because the collection of data is both 

time consuming and expensive. As a result, it is important to 

consider alternative methods that could be applied to extrapolate hydrologic information collected at gaged sites to ungaged 

sites, where no data are available. Methods that could be used to 

extrapolate data to ungaged sites range from simple techniques, 

such as linear interpolation between gaged sites, to complex 

techniques, such as rainfall-runoff modeling and multivariate 

regional-regression analyses. Descriptions and applications of 

some of the simpler techniques are included in appendix 2. 

Low-Flow Statistics Under 

Current (2000–2005) Diversion 

Practices

Streamflow statistics used in this report to describe 

low-flow characteristics are based on flow-duration curves 

and their associated discharges. All flow-duration discharges 

summarized in this section of the report were computed or 

extended to reflect long-term conditions, assuming that current 

diversion practices in the Upper and Lower Hämäkua Ditches 

were actually followed during the entire 40-year base period 

1965–2004. Current diversion conditions, for the purposes 

of this report, are defined as those in effect during the period 

2000–2005, when additional data required for this study 

were collected. During the period March to November 2003, 

average diversion from Waipiÿo Valley by Upper Hämäkua 

Ditch, as measured at surface-water gaging station 16726000 

at 3,020 feet, was 6.75 ft3/s, and diversion by Lower Hämäkua 

Ditch, as measured at surface-water gaging station 16732800 

upstream from the main weir, was 16.7 ft3/s. March to November 2003 is the longest period of consecutive months during 

the years 2000–2005 when both gaging stations 16726000 and 

16732800 and both ditches were operational.

Flow-duration discharges were computed for the four index 

stations (see table 7 and the footnote there), two short-term gaging stations, and five low-flow partial-record stations. Flow data 

are available for the entire base period for the index stations, but 

for only parts of the base period at the short-term stations. Data 

for multiple discharge measurements, but no continuous records 

of flow, are available for the low-flow partial record stations.
 Low-Flow Statistics Under Current (2000–2005) Diversion Practices 19

Short-Term Gaging Stations

Two gaging stations in the Waipiÿo Valley study area—

Kawaiki Stream at 4,090 feet (16720300) and Wailoa Stream at 

190 feet (16732200) (fig. 3)—have short-term records during 

some part of the 1965–2004 base period (table 1). The availability of concurrent periods of record with one or more of the four 

index stations means that the records at these gaging stations 

can be extended to be representative of the entire base period.

The Kawaiki Stream short-term station (16720300), 

just upstream from the Upper Hämäkua Ditch, has continuous streamflow records for the period 1969–1999; these data 

reflect natural, undiverted, streamflow conditions. Kawaiki 

Stream joins Kawainui Stream a short distance downstream 

from Upper Hämäkua Ditch. The index station on Kawainui 

Stream (16720000) was used to extend short-term records for 

Kawaiki Stream because of its proximity and the strength of 

the correlation between the stations. Selected flow-duration 

discharges for the concurrent period of record (1969–1999) 

at the two stations are shown in table 8. Plots of concurrent 

flow-duration discharges indicate a strong linear relation (correlation coefficient of 0.99) between the low flow-duration discharges at the Kawaiki and Kawainui stations. Normally, this 

would indicate that the MOVE.1 technique should be used to 

extend records. In this case, however, the graphical-correlation 

method was used because an analysis of the correlation plots 

indicated downward curvature for discharges between the 99- 

and 95-percentile durations. Estimated 1965–2004 base period 

flow-duration discharges for the short-term station on Kawaiki 

Stream (16720300), based on graphical-correlation record 

extension, also are shown in table 8. Standard errors were not 

computed for the estimated 1965–2004 base period, flow-duration discharges shown in table 8 because the estimates were 

made by interpolation along a smooth curve fit to concurrent 

flow-duration discharges. Standard errors would be expected 

to be relatively small because the Kawaiki short-term station 

(16720300) had complete streamflow data for 31 years out of 

the 40-year base period. 

The Wailoa Stream short-term station (16732200) is at 

the downstream terminus of the Waipiÿo Valley study area. 

This station has continuous record for the period 1964–1969, 

and a low-flow partial-record station was operated at this 

site during the period 2000–2005. Streamflow data were not 

available for all of 1964, so only those data for the period 

1965–1969 were used in this analysis. During the period 

1965–1969, however, upstream diversions were significantly 

higher than they were under current (2000–2005) conditions. 

Average diversion from Waipiÿo Valley by Lower Hämäkua 

Ditch, as measured at the main weir (combined flow for stations 16733000 and 16733100), was 48 ft3

/s during the period 

1965–1969 versus 10.0 ft3/s during 2003 (station 16732800). 

Estimates of base period flow-duration discharges using 

the period of continuous streamflow record 1965–1969 will 

therefore reflect these higher diversion rates and not current 

diversion (2000–2005) conditions. Estimates reflective of the 

current diversion conditions will be described in the next 

section, where analyses using low-flow partial-record data collected during the period 2000–2005 are summarized.

The index station that had the strongest correlation with 

Wailoa Stream short-term station (16732200) was Waikoloa Stream at 3,460 feet (16758000). Selected flow-duration 

discharges for the concurrent period of record (1965–1969) 

at the two stations are shown in table 9. Plots of concurrent 

flow-duration discharges indicate a strong linear relation (correlation coefficient of 0.99) between the low flow-duration 

discharges at the Wailoa and Waikoloa gaging stations. As in 

the analyses of data for the Kawaiki and Kawainui Streams 

described above, a graphical correlation method was used to 

extend the record of the station on Wailoa Stream, and the 

estimated 1965–2004 base period flow-duration discharges 

are shown in table 9. Standard errors in the estimates were not 

computed but would be expected to be relatively small because 

of the strong correlation between low-flow discharges at the 

short-term and index stations.

Low-Flow Partial-Record Stations

Discharge measurements were made at five low-flow 

partial-record stations in the Waipiÿo Valley study area during 

the period 2000–2005 (table 3). These stations are located at 

sites 1, 6, 15, 18, and 24 (fig. 4), upstream from intakes of 

Lower Hämäkua Ditch, on Kawainui, Alakahi, Koÿiawe, and 

Waimä Streams, and at the site of former USGS gaging station 16732200 on Wailoa Stream, respectively. Estimates of 

base period (1965–2004) flow-duration discharges made on 

the basis of these discharge measurements will reflect current 

(2000–2005) diversion conditions. 

Log base 10 linear correlations were found to exist 

between each of the five low-flow partial-record stations and at 

least one index station. In all cases, estimates of flow-duration 

discharges for the five low-flow partial-record stations were 

computed using the MOVE.1 technique with log base 10 transformed data. Daily mean and flow-duration discharge data for 

all index stations were increased by 1.0 ft3/s before analysis to 

avoid complications associated with attempting log transformations of discharge values of 0.0 ft3

/s. The index station or 

stations that were used in the MOVE.1 computations for each 

low-flow partial-record station, along with the mean, standard 

deviation, and correlation coefficient statistics for concurrent 

discharge measurements and daily mean discharges, are given 

in table 10. 

In the section of the report that described record-extension techniques, it was stated that only those index stations 

with correlation coefficients greater than 0.80 would be used 

in the analyses made in this study. Kawainui Stream at 4,060 

feet (16720000) was used as an index station for the Koÿiawe 

Stream low-flow partial-record station (Site 15), even though 

the correlation coefficient between concurrent discharge values 

at the two sites was 0.791. This was considered a reasonable 

exception because the correlation coefficient was so close to 

the cutoff value and also because final MOVE.1 computations 
20 Low-Flow Characteristics of Streams Under Natural and Diversion Conditions, Waipiÿo Valley, Island of Hawaiÿi, Hawaiÿi

Percentage of time 

indicated discharge 

equaled or exceeded

Concurrent period of record 1969-1999 Base period 1965-2004

Kawainui Stream 

16720000 (ft3/s)

Kawaiki Stream 

16720300 (ft3/s)

Kawaiki Stream 

16720300 (ft3/s)

99 0.09 0.02 0.02

98 0.14 0.04 0.05

97 0.18 0.06 0.07

95 0.26 0.10 0.11

90 0.50 0.16 0.16

85 0.75 0.23 0.23

80 1.0 0.29 0.29

75 1.4 0.38 0.36

70 1.8 0.48 0.46

65 2.2 0.60 0.57

60 2.8 0.77 0.74

55 3.6 0.98 0.95

50 4.6 1.3 1.3

40 7.7 2.1 2.0

Table 8. Selected natural flow-duration discharges for the 1969–1999 concurrent period 

of record at gaging stations 16720300 on Kawaiki Stream and 16720000 on Kawainui 

Stream and estimated 1965–2004 base period natural flow-duration discharges at gaging 

station 16720300 on Kawaiki Stream.

[ft3/s, cubic feet per second]

were weighted with a second index station, on Hauani Gulch 

(16759000), which has a correlation coefficient (0.874) 

greater than the cutoff value. The station on Hauani Gulch 

was used as an index station for Waimä Stream low-flow 

partial-record station (Site 18), even though the correlation 

coefficient was only 0.539. In this case, MOVE.1 computations were run for Waimä Stream (Site 18) independently, 

using each of the four potential index stations. Estimated 

flow-duration discharges based on the four independent analyses were virtually identical. In this instance the consistency of 

results supports use of an index station having a correlation 

coefficient well below the cutoff value. 

All MOVE.1 computations were made using log base 10 

transformed data. Final estimates of base period, flow-duration discharges for the five low-flow partial-record stations 

were converted back into their original units of measurement 

(cubic feet per second). Estimated discharges for 99-, 95-, 

90-, 80-, 70-, 60-, and 50-percentile durations and average 

standard errors are shown in table 11. In the process of computing standard errors for the estimated discharges throughout 

the report, it was assumed that the flow statistics at the index 

gaging stations have no standard errors associated with them 

because they were not estimated using record-extension techniques. Flow-duration discharges summarized in tables 7–9 

were shown for an expanded number of percentiles because 

the extra data were required for the application of recordextension techniques at short-term stream-gaging stations.

Low-Flow Statistics 

Representative of Natural 

Conditions 

Natural streamflow conditions are those in which flow at 

a given location has not been modified or regulated in some 

way by humans. To be representative of natural conditions, 

computed flow-duration discharges at most locations in the 

Waipiÿo Valley study area had to account for diversion of 

water by Upper and Lower Hämäkua Ditches. Natural flowduration discharges were computed for two index stations, 

one short-term surface-water gaging station, and five low-flow 

partial-record stations in the Waipiÿo Valley study area.

Index and Short-Term Gaging Stations

 Two index stations in the Waipiÿo Valley study area 

have a complete record for the entire 40-year base period, 

1965–2004. These stations, on Kawainui Stream at 4,060 feet 
 Low-Flow Statistics Representative of Natural Conditions 21

Percentage of time 

indicated discharge 

equaled or exceeded

Concurrent period of record 1965-1969 Base period 1965-2004

Waikoloa Stream 

16758000 (ft3/s)

Wailoa Streama

16732200 (ft3/s)

Wailoa Streama 

16732200 (ft3/s)

99 0.79 39 39

98 1.0 39 40

97 1.2 40 40

95 1.3 40 41

90 1.6 42 43

85 1.8 43 43

80 2.0 43 44

75 2.2 45 46

70 2.4 46 47

65 2.6 46 47

60 2.9 47 49

55 3.2 48 51

50 3.6 50 53

40 4.6 54 57

Table 9. Selected flow-duration discharges for the 1965–1969 concurrent period of record at 

gaging stations 16732200 on Wailoa Stream and 16758000 on Waikoloa Stream and estimated 

1965–2004 base period regulated flow-duration discharges at the gaging station on Wailoa Stream.

[ft3/s, cubic feet per second]

 a Flow-duration discharges for Wailoa Stream during both the concurrent period of record and the base period are reflective of 

regulated conditions when the average diversion (1965–1969) by the Upper Hämäkua Ditch at station 16720500 below Kawaiki 

Stream was 9.3 ft3/s and the combined diversion by the Lower Hämäkua Ditch at Stations 16733000 and 16733100 at the main 

weir was 48 ft3/s.

(16720000) and Alakahi Stream at 3,900 feet (16725000), are 

just upstream from Upper Hämäkua Ditch (fig. 3). Thus the 

flows at these stations are not affected by diversions at either 

the Upper or Lower Hämäkua Ditches, and flow-duration 

discharges representative of natural conditions for the base 

period can be computed directly from the data available for the 

stations. Natural flow-duration discharges for the 1965–2004 

base period at the two index stations have been computed and 

are summarized in table 7. 

Two gaging stations in the Waipiÿo Valley study area—

Kawaiki Stream at 4,090 feet and Wailoa Stream at 190 

feet—have short-term records during some part of the base 

period (table 1). The Kawaiki Stream station (16720300) is 

upstream from Upper Hämäkua Ditch on a tributary stream to 

Kawainui Stream and Waipiÿo Valley (fig. 3). Thus the flows 

at the Kawaiki station are not affected by diversion associated 

with Upper or Lower Hämäkua Ditches, and flow-duration 

discharges representative of natural conditions for the base 

period can be computed by extending the data available for 

the station. Estimation of natural flow-duration discharges for 

the 1965–2004 base period for the Kawaiki Stream station 

was discussed in a previous section of this report (Low-Flow 

Statistics Under Current (2000–2005) Diversion Practices) and 

the estimates are summarized in table 8. 

The short-term station on Wailoa Stream (16732200) is 

downstream from both Upper and Lower Hämäkua Ditches. 

Streamflow data collected during the period 1964–1969 at this 

station were directly affected by diversions into both ditch 

systems. To compute flow-duration discharges representative 

of natural conditions, the 1964–1969 data would first have 

to be adjusted to account for the effects of these diversions. 

However, daily data that document the total amount of water 

diverted from Waipiÿo Valley by Upper and Lower Hämäkua 

Ditches upstream from Wailoa Stream are not available for the 

period 1964–1969. As a consequence, natural flow-duration 

discharges for the 1965–2004 base period were not computed 

using the Wailoa Stream short-term gaging station data from 

1964–1969.

Low-Flow Partial-Record Stations

 Discharge measurements were made at five low-flow 

partial-record stations in the Waipiÿo Valley study area during 

the period 2000–2005 (fig. 4 and table 3). The stations at sites 

1, 6, 15, and 18 are upstream from intakes of Lower Hämäkua 

Ditch on Kawainui, Alakahi, Koÿiawe, and Waimä Streams, 

respectively. The station at site 24 is on Wailoa Stream, 
22 Low-Flow Characteristics of Streams Under Natural and Diversion Conditions, Waipiÿo Valley, Island of Hawaiÿi, Hawaiÿi

Low-flow partial-record 

stationa Index stationb Meanc Standard deviationc Correlation coefficient

Site 1 Kawainui Stream 1.4040 0.2074 n.a.

16720000 Kawaini Stream 0.4926 0.4201 0.926

16725000 Alakahi Stream 0.4501 0.3142 0.944

Site 6 Alakahi Stream 1.1811 0.1038 n.a.

16720000 Kawaini Stream 0.4581 0.4122 0.896

16725000 Alakahi Stream 0.4268 0.3149 0.938

Site 15 Koÿiawe Stream 0.8908 0.0518 n.a.

16720000 Kawaini Stream 0.4300 0.3113 0.791

16759000 Hauani Gulch 0.1459 0.0936 0.874

Site 18 Waimä Stream -0.1669 0.0731 n.a.

16759000 Hauani Gulch 0.1544 0.0969 0.539

Site 24 Wailoa Stream 1.9068 0.0600 n.a.

16759000 Hauani Gulch 0.1552 0.1018 0.928

a Site numbers correspond to gaging stations listed in table 2 and shown in figure 4.

b

 Station numbers correspond to gaging stations listed in table 1 and shown in figure 3.

c

 Statistics are based on log base 10 values. Daily mean discharge values for index stations were all increased by 1.0 prior to transformation to 

log base 10 values and the subsequent computation of statistics.

Table 10. Computed statistics for concurrent discharge measurements at low-flow partial-record stations and 

daily mean discharges at index stations in Waipiÿo Valley study area, Island of Hawaiÿi, Hawaiÿi.

[n.a., not applicable]

downstream from both Upper and Lower Hämäkua Ditches, at 

the location of the former short-term gaging station 16732200. 

Discharges measured at sites 1, 6, 15, and 18 were modified by 

flow diversions, return flows, and ditch losses that took place 

upstream along Upper Hämäkua Ditch. Discharges measured 

at site 24 were modified by flow diversions, return flows, and 

ditch losses that took place upstream along both of the ditch 

systems. To compute flow-duration discharges representative 

of natural conditions, the discharge measurements at these five 

low-flow partial-record stations have to be adjusted to account 

for the effects of these diversions. 

A basic assumption made in this analysis was that streamflow at low-flow partial-record stations downstream from 

Upper and Lower Hämäkua Ditches would be changed by 

virtually the same amount that was being removed or released 

by the ditches upstream. Following this logic, measured or 

estimated diversion totals could be combined directly with the 

discharge measured at the stations so that the computed flow 

would reflect natural conditions (conditions that would be in 

place if no upstream manipulation of flow by diversion ditches 

was taking place). The validity of this assumption is supported 

by geologic factors and historical streamflow data in the study 

area. Upper Hämäkua Ditch runs along the rim of Waipiÿo 

Valley. A short distance downgradient of the ditch, the deeply 

eroded Waipiÿo Valley cuts through numerous closely spaced 

dikes that intercept large volumes of dike-impounded ground 

water (Stearns and Macdonald, 1946, p. 175). As a result, 

tributary streams entering Waipiÿo Valley could be expected 

to be gaining flow and to flow year round. The gaining and 

perennial nature of Waipiÿo Valley streams is supported by 

historical streamflow data such as that summarized by Mink 

(1984) and Martin and Pierce (1913). In such settings, there 

would be no natural reductions in streamflow to account for, 

but only the changes caused by the diversions.

Natural Low-Flow Statistics

 To compute natural low-flow statistics for the five lowflow partial-record stations in Waipiÿo Valley, discharge measurements made during 2000–2005 first had to be adjusted to 

remove the effects of upstream diversions. These adjustments, 

which are described in detail in appendix 3 and summarized in 

tables 3–B through 3–F in the appendix, allow the computation of what would have been the natural discharge at each of 

the stations when the measurements were made. Estimates of 

flow-duration discharges made on the basis of these adjusted 

discharge measurements represent what natural conditions 

would have been over the 1965–2004 base period. 
Effects of Diversion Practices on Low-Flow Statistics 23

Percentage of time 

indicated discharge 

equaled or exceeded

Dischargea (ft3/s)

Kawainui 

Stream 

Site 1b

Alakahi 

Stream 

Site 6b

Koÿiawe 

Stream 

Site 15b

Waimä 

Stream 

Site 18b

Wailoa Stream 

Site 24b

99 15 12 6.6 0.52 65

95 16 12 6.8 0.54 68

90 18 13 6.9 0.56 70

80 20 14 7.3 0.60 73

70 24 15 7.6 0.63 76

60 28 16 7.9 0.67 80

50 33 18 8.4 0.72 85

Average standard error (percent) 5.1 3.0 2.2 7.8 2.6

a All estimated flow-duration discharges reflect diversion conditions at Upper and Lower Hämäkua 

Ditches in effect during the study period 2000–2005. During the period March to November 2003 average 

diversion from Waipiÿo Valley by Upper Hämäkua Ditch, as measured at surface-water gaging station 

16726000 at 3,020 feet, was 6.75 ft3/s and by Lower Hämäkua Ditch, as measured at surface-water gaging 

station 16732800 upstream from the main weir, was 16.7 ft3/s. March to November 2003 is the longest 

period of consecutive months during 2000–2005 when both gaging stations 16726000 and 16732800 and 

both ditches were operational.

b

 Site numbers correspond to gaging stations listed in table 2 and shown in figure 4.

Table 11. Estimated regulated flow-duration discharges for the 1965–2004 base 

period that reflect diversion practices during the study period (2000–2005) at lowflow partial-record stations in Waipiÿo Valley, Island of Hawaiÿi, Hawaiÿi.

[ft3/s, cubic feet per second]

Linear correlations were found to exist between each of 

the five low-flow partial-record stations and at least one index 

station. In all cases, estimates of flow-duration discharges for 

the low-flow partial-record stations were computed using the 

MOVE.1 technique (see earlier section “Record-Extension 

Techinques”). MOVE.1 computations were based on log 

base 10 transformed data for Kawainui (site 1) and Wailoa 

(site 24) Streams and on untransformed data at Alakahi (site 

6), Koÿiawe (site 15), and Waimä (site 18) Streams. Daily 

mean and flow-duration discharge data for all index stations 

were increased by 1.0 ft3/s before analysis for sites 1 and 24 

to avoid complications associated with attempting log transformations of discharge values of 0.0 ft3

/s. The index station 

or stations that were used in MOVE.1 computations for each 

low-flow partial-record station, along with the mean, standard 

deviation, and correlation coefficient statistics for concurrent 

discharge measurements and daily mean discharges, are given 

in table 12. 

MOVE.1 estimates of base period, natural flow-duration 

discharges for the five low-flow partial-record stations were 

either computed in or converted back into their original 

units of measurement (cubic feet per second), and estimated 

discharges for 99-, 95-, 90-, 80-, 70-, 60-, and 50-percentile 

durations and average standard errors are shown in table 13. 

Flow-duration discharges, summarized in tables 7–9, were 

shown for an expanded number of percentiles because the 

extra data were required for the record-extension techniques at 

short-term stream-gaging stations. 

Effects of Diversion Practices on 

Low-Flow Statistics

Up to this point in the report, the focus has been on the 

data and methods used to derive low-flow statistics at selected 

locations within the Waipiÿo Valley study area. The focus will 

now shift to an evaluation of the effects that various diversion 

practices have on the low-flow hydrology in Waipiÿo Valley 

study area. First, a comparison will be made between low-flow 

hydrology under natural conditions and under 2000–2005 

diversion practices. Second, a comparison will be made 

between low-flow hydrology under proposed future diversion 

practices and low-flow hydrology under 2000–2005 diversion 

practices and under natural conditions. Finally, the effects of 

historical (1965–1969) diversion practices, current (2000–

2005) practices, and proposed future practices on natural lowflow hydrology at the downstream limit of the study area will 
24 Low-Flow Characteristics of Streams Under Natural and Diversion Conditions, Waipiÿo Valley, Island of Hawaiÿi, Hawaiÿi

Low-flow partialrecord stationa Index stationb Mean Standard 

deviation

Correlation 

coefficient

Site 1 Kawainui Stream 1.3933c 0.1977c n.a.

16758000 Waikoloa Stream 0.5624c 0.2338c 0.964

Site 6 Alakahi Stream 15.7d 3.03d n.a.

16720000 Kawainui Stream 1.86d 2.12d 0.922

16725000 Alakahi Stream 1.40d 1.09d 0.931

Site 15 Koÿiawe Stream 8.36d 0.89d n.a.

16758000 Waikoloa Stream 2.69d 1.18d 0.830

16759000 Hauani Gulch 0.33d 0.18d 0.838

Site 18 Waimä Stream 0.97d 0.26d n.a.

16758000 Waikoloa Stream 2.47d 1.26d 0.938

16759000 Hauani Gulch 0.34d 0.24d 0.933

Site 24 Wailoa Stream 2.0154c 0.0721c n.a.

16758000 Waikoloa Stream 0.5841c 0.1773c 0.939

16759000 Hauani Gulch 0.1552c 0.1018c 0.953

a Site numbers correspond to gaging stations listed in table 2 and shown in figure 4.

b

 Station numbers correspond to gaging stations listed in table 1 and shown in figure 3.

c

 Statistics are based on log base 10 values. Daily mean discharge values for index stations were all increased by 1.0 

prior to transformation to log base 10 values and the subsequent computation of statistics.

d Statistics are based on untransformed values.

Table 12. Computed statistics for concurrent discharge measurements adjusted to 

represent natural conditions at low-flow partial-record stations and daily mean discharges at 

index stations in Waipiÿo Valley study area, Island of Hawaiÿi, Hawaiÿi.

[n.a., not applicable]

Percentage of time 

indicated discharge 

equaled or exceeded

Discharge (ft3/s)

Kawainui 

Stream 

Site 1a

Alakahi 

Stream 

Site 6a

Koÿiawe 

Stream 

Site 15a

Waimä 

Stream 

Site 18a

Wailoa 

Stream 

Site 24a

99 15 13 6.9 0.64 80

95 18 13 7.3 0.73 86

90 19 14 7.5 0.77 88

80 23 14 7.9 0.89 95

70 26 16 8.3 0.98 100

60 29 17 8.8 1.1 105

50 34 20 9.5 1.2 112

Average standard error (percent) 5.4 2.8 2.5 4.5 1.9

a

 Site numbers correspond to gaging stations listed in table 2 and shown in figure 4.

Table 13. Estimated natural flow-duration discharges for the 1965–2004 

base period at low-flow partial-record stations in Waipiÿo Valley, Island of 

Hawaiÿi, Hawaiÿi.

[ft3/s, cubic feet per second]
 Effects of Diversion Practices on Low-Flow Statistics 25

be summarized. The downstream limit of the study area is just 

upstream from the site of the current, most upstream diversions for taro production in Waipiÿo Valley.

Current (2000–2005) Diversion Practices

 To evaluate the effects of diversion practices at Upper 

and Lower Hämäkua Ditch systems during the period 

2000–2005 on low-flow hydrology in Waipiÿo Valley study 

area, the 95- and 50-percentile flow-duration discharges 

representative of natural conditions and conditions during 

that period will be compared. These two discharge statistics 

for the gaging stations and data-collection sites in the study 

area under natural conditions and under 2000–2005 diversion 

practices are summarized in tables 14 and 15. The reduction 

in discharge associated with 2000–2005 diversion practices 

is shown as a percent in both tables. The spatial pattern of 

discharge reduction for the 95- and 50-percentile discharges 

is shown in figures 5 and 6.

The 2000–2005 diversion practices of Upper and Lower 

Hämäkua Ditches have no effect on the 95- and 50-percentile discharges at gaging stations 16720000 on Kawaimui 

Stream, 16720300 on Kawaiki Stream, and 16725000 on 

Alakahi Stream, because these stations are upstream from 

both ditches. The most significant reductions in flow-duration 

discharge associated with the 2000–2005 diversion practices 

are shown to take place immediately downstream from Upper 

Hämäkua Ditch intakes on Kawainui and Kawaiki Streams, 

where 95-percentile discharge is reduced by 100 percent and 

50-percentile discharge is reduced by 92 percent. Similar 

computations for locations directly downstream from Upper 

Hämäkua Ditch intakes on Alakahi, Koÿiawe, and Waimä 

Streams were not possible, but similar reduction in flow could 

be expected there. 

Just downstream from Upper Hämäkua Ditch, tributary 

streams to Waipiÿo Valley drop sharply in altitude. As noted 

from analyses of 1901–1902 data (appendix 1) and during 

seepage runs (appendix 2), tributary streams consistently gain 

flow within Waipiÿo Valley. As a result , the effects of 2000–

2005 diversion practices on natural discharge decrease in a 

downstream direction. At locations just upstream from Lower 

Hämäkua Ditch intakes, natural 50-percentile discharges 

have been reduced by 3, 5, 12, and 40 percent on Kawainui, 

Alakahi, Koÿiawe, and Waimä Streams, respectively. The 

reduction in discharge along Waimä Stream is inconsistent 

with those for the other tributary streams because the largest 

gains in discharge along Waimä Stream take place at much 

lower altitudes. 

The percentages by which natural discharges are reduced 

by diversions in 2000–2005 increase sharply downstream 

from the intakes of Lower Hämäkua Ditch. At the mouths of 

Kawainui, Alakahi, Koÿiawe, and Waimä Streams, the 50-percentile discharges have been reduced by 29, 14, 20, and 7 percent, respectively. Once again Waimä Stream is inconsistent 

in that the percent reduction in natural low flows continues to 

decrease downstream from Lower Hämäkua Ditch. 

Along Waipiÿo and Wailoa Streams, the percentages by 

which natural discharges have been reduced as a result of the 

combined 2000–2005 diversion practices of Upper and Lower 

Hämäkua Ditches is relatively consistent. During 95-percentile 

flow conditions, natural discharge reductions range between 

18 and 22 percent. During 50-percentile flow conditions, natural discharge reductions range between 19 and 24 percent.

The ratio of 95-percentile to 50-percentile discharges can 

be used as an index of low-flow variability. Ratios close to zero 

are indicative of more variable and less sustained low flows. 

Ratios closer to one are indicative of less variable and more 

sustained low flows (Oki and others, 2006, p. 15). In most cases, 

the ratio of 95-percentile to 50-percentile discharges under 

2000–2005 diversion practices is greater than that under natural 

conditions at the same gaging station. The average ratio of the 

two discharges for gaging stations in Waipiÿo Valley is 0.76 

under regulated flow conditions and 0.73 under natural flow 

conditions (see tables 2-D and 2-E in appendix 2). This difference indicates that low flows of streams in Waipiÿo Valley are 

smaller and slightly less variable under 2000–2005 diversion 

practices than under natural conditions.

Proposed Future Diversion Practices for 

Lower Hämäkua Ditch

In an environmental impact statement related to future 

operation of Lower Hämäkua Ditch (U.S. Department of Agriculture, 1999, p. 144), diversion rates out of Waipiÿo Valley 

were projected to be 7 Mgal/d (10.8 ft3/s) during average conditions and 13 Mgal/d (20.1 ft3

/s) during drought conditions. 

The effects of these proposed diversion rates are evaluated in 

this section of the report. Low-flow statistics were computed 

for gaging stations and data-collection sites located downstream from Lower Hämäkua Ditch. A detailed description of 

those computations and their analysis follows. 

Computation of Low-Flow Statistics under 

Proposed Diversion Practices at Lower 

Hämäkua Ditch

 Changes in diversion practices of Lower Hämäkua Ditch 

will not have an effect on the low-flow statistics for gaging 

stations and data-collection sites located upstream from it. 

Low-flow statistics for gaging stations and data-collection sites 

downstream from Lower Hämäkua Ditch, however, are modified by diversion practices of both Upper and Lower Hämäkua 

Ditches and therefore will be directly affected. To compute 

low-flow statistics for such downstream locations that reflect 

proposed future diversion practices, the first step is to determine 

the amount by which current diversion practices (2000–2005) 

affect natural discharges. Total diversion effects for downstream 

locations need to be partitioned between those associated with 

diversions by Upper and Lower Hämäkua Ditches.
26 Low-Flow Characteristics of Streams Under Natural and Diversion Conditions, Waipiÿo Valley, Island of Hawaiÿi, Hawaiÿi

Gaging-station or 

site numbera Stream

95-percentile discharge (ft3/s) Difference 

in 

percent

Natural 

conditions

2000-2005 

diversion practices

Upstream from Upper Hämäkua Ditch

16720000 Kawainui 0.29 0.29 0

16720300 Kawaiki 0.11 0.11 0

16725000 Alakahi 0.38 0.38 0

Downstream from Upper Hämäkua Ditch

16720000 + 16720300 Kawainui 0.40 0.00 -100

16721000 Kawainui 14 9.8 -30

16722000 Kawainui 17 13 -24

1 Kawainui 18 16 -11

16728000 Alakahi 12 10 -17

6 Alakahi 13 12 -8

16730000 Koÿiawe 7.5 6.5 -13

15 Koÿiawe 7.3 6.8 -7

18 Waimä 0.73 0.54 -26

Downstream from Lower Hämäkua Ditch

16724000 Kawainui 28 21 -25

16729000 Alakahi 18 15 -17

10b Waipiÿo 46 36 -22

11c Waipiÿo 49 40 -18

16732000b Waipiÿo 61 50 -18

22d Waipiÿo 63 52 -18

16731000 Koÿiawe 12 10 -17

16732150 Waimä 26 24 -8

16732200 Wailoa 86 68 -21

a

 Site numbers correspond to those listed in table 2 and shown in figure 4.

b

 Site 10 data computed by adding flow-duration discharges for stations 16724000 and 16729000. Station 16732000 data computed by adding flow-duration discharges for site 11 and station 16731000.

c

 Translation of site 10 data downstream using seepage run adjustment factors of 1.06 for natural discharge and 1.10 for regulated discharge.

d

 Translation of station 16732000 data downstream using seepage run adjustment factors of 1.03 for natural discharge and 1.05 

for regulated discharge.

Table 14. Comparison of 95-percentile flow-duration discharges under natural conditions and 2000–

2005 diversion practices at gaging stations and data-collection sites in the Waipiÿo Valley study area, 

Island of Hawaiÿi, Hawaiÿi.

[ft3/s, cubic feet per second]
 Effects of Diversion Practices on Low-Flow Statistics 27

Gaging-station or 

site numbera Stream

50-percentile discharge (ft3/s) Difference in 

percent Natural 

conditions

2000-2005 diversion 

practices

Upstream from Upper Hämäkua Ditch

16720000 Kawainui 4.5 4.5 0

16720300 Kawaiki 1.3 1.3 0

16725000 Alakahi 3.1 3.1 0

Downstream from Upper Hämäkua Ditch

16720000 + 16720300 Kawainui 6.0 0.46 -92

16721000 Kawainui 21 14 -33

16722000 Kawainui 24 17 -29

1 Kawainui 34 33 -3

16728000 Alakahi 15 12 -20

6 Alakahi 20 18 -5

16730000 Koÿiawe 9.0 7.4 -18

15 Koÿiawe 9.5 8.4 -12

18 Waimä 1.2 0.72 -40

Downstream from Lower Hämäkua Ditch

16724000 Kawainui 38 27 -29

16729000 Alakahi 21 18 -14

10b Waipiÿo 59 45 -24

11c Waipiÿo 63 50 -21

16732000b Waipiÿo 78 62 -20

22d Waipiÿo 80 65 -19

16731000 Koÿiawe 15 12 -20

16732150 Waimä 44 41 -7

16732200 Wailoa 112 85 -24

a

 Site numbers correspond to those listed in table 2 and shown in figure 4.

b

 Site 10 data computed by adding flow-duration discharges for stations 16724000 and 16729000. Station 16732000 data computed by adding flow-duration discharges for site 11 and station 16731000.

c

 Translation of site 10 data downstream using seepage run adjustment factors of 1.06 for natural discharge and 1.10 for regulated discharge.

d

 Translation of station 16732000 data downstream using seepage run adjustment factors of 1.03 for natural discharge and 1.05 

for regulated discharge.

Table 15. Comparison of 50-percentile flow-duration discharges under natural conditions and 

2000–2005 diversion practices at gaging stations and data-collection sites in the Waipiÿo Valley 

study area, Island of Hawaiÿi, Hawaiÿi.

[ft3/s, cubic feet per second]
28 Low-Flow Characteristics of Streams Under Natural and Diversion Conditions, Waipiÿo Valley, Island of Hawaiÿi, Hawaiÿi

Kawainui Str

Alakahi Str

Lalakea 

Str

Waipi‘oStr

Wailoa

Str

Upper

Ditch

Hämäkua

Waimä Str

Ko‘iawe

Str

Häm

Ditch

Lower

ä

0 kua

0

-30

-24

-11

-25

-17

-22

-18 -18

-17

-18

-8

-26 -7

-13

-17

0 -8

-21 -100

-30

#

#

#

#

#

#

#

#

#

#

#

#

#

#

720000

720300

721000

725000

728000

722000

724000

729000 732000

731000

732150

730000

732200

1

6

10

11

15 18

22

#

#

# #

# #

#

155°42' 155°40' 155°38'

20°04'

20°06'

Base modified from U.S. Geological Survey National

Hydrography Dataset, Transverse Mercator projection,

zone 5, central meridian −153°, North American Datum 1983. 0

0 1

1

2 KILOMETERS

2 MILES

Waimea

155°40' 155°36'

20°04'

20°08'

Waipi‘o 

 Bay

P A C I F I C 

 

155°40' 155°36'

20°04'

20°08'

O C E A N

Figure 5. Percent reduction in natural 95-percentile discharge under 2000–2005 diversion practices, Waipiÿo Valley study area, Island of 

Hawaiÿi, Hawaiÿi.

22 #

6 #

720000 # Gaging station and abbreviated number—

 complete number is preceded by 16

Seepage-run site and number

Seepage-run site and low-flow partial-record

 station and station number

Reduction in streamflow

 Percent reduction at data site

 Less than or equal to 10 percent

 Greater than 10 and less than or equal to 20 percent

 Greater than 20 and less than or equal to 30 percent

 Greater than 30 and less than or equal to 100 percent

EXPLANATION

Area of map

Figure 5. Percent reduction in natural 95-percentile discharge under 2000–2005 diversion practices, Waipiÿo Valley 

study area, Island of Hawaiÿi, Hawaiÿi.
 Effects of Diversion Practices on Low-Flow Statistics 29

Kawainui Str

Alakahi Str

Lalakea 

Str

Waipi‘oStr

Wailoa

Str

Upper

Ditch

Hämäkua

Waimä Str

Ko‘iawe

Str

Häm

Ditch

Lower

ä

0 kua

0

-33

-29

-3

-29

-14

-24

-21 -20

-21

-19

-7

-40 -12

-18

-20

0 -5

-24 # -92

#

#

#

#

#

#

#

#

#

#

#

720000 #

720300

721000

725000

728000

722000

724000

729000 732000

731000

732150

730000

732200

1

6

10

11

15 18

22

#

#

# #

# #

#

155°42' 155°40' 155°38'

20°04'

20°06'

0

0 1

1

2 KILOMETERS

2 MILES

Waimea

155°40' 155°36'

20°04'

20°08'

Waipi‘o 

 Bay

P A C I F I C 

 O C E A N

155°40' 155°36'

20°04'

20°08'

Figure 6. Percent reduction in natural 50-percentile discharge under 2000–2005 diversion practices, Waipiÿo Valley study area, Island

 of Hawaiÿi, Hawaiÿi. 

22 #

6 #

720000

# Gaging station and abbreviated number—

 complete number is preceded by 16

Seepage-run site and number

Seepage-run site and low-flow partial-record

 station and station number

Less than or equal to 10 percent

Greater than 10 and less than or equal to 20 percent

Greater than 20 and less than or equal to 30 percent

Greater than 30 and less than or equal to 100 percent

EXPLANATION

Area of map

Reduction in Streamflow

Base modified from U.S. Geological Survey National

Hydrography Dataset, Transverse Mercator projection,

zone 5, central meridian −153°, North American Datum 1983.

Figure 6. Percent reduction in natural 50-percentile discharge under 2000–2005 diversion practices, Waipiÿo Valley 

study area, Island of Hawaiÿi, Hawaiÿi.
30 Low-Flow Characteristics of Streams Under Natural and Diversion Conditions, Waipiÿo Valley, Island of Hawaiÿi, Hawaiÿi

Diversion effects associated with current diversion 

practices (2000–2005) can be estimated by calculating the 

difference between natural and regulated low-flow statistics 

at the location of interest. Diversion effects will vary with 

location along streams because of the complex manner that 

Upper and Lower Hämäkua Ditches gain and lose water along 

their reaches, and they also will vary with the magnitude of 

low flow. Differences between natural flow and flow under 

2000–2005 diversion practice were computed for 95- and 

50-percentile discharges and are summarized in table 16. 

Differences were computed at locations just upstream from 

the intakes of Lower Hämäkua Ditch at sites 1, 6, 15, and 18 

(fig. 4) to determine diversion effects associated with Upper 

Hämäkua Ditch before diversions by Lower Hämäkua Ditch. 

Differences were computed at the mouths of Kawainui, 

Alakahi, Koÿiawe, and Waimä Streams, at gaging stations 

16724000, 16729000, 16731000, and 16732150, respectively 

(fig. 3), to determine combined diversion effects associated 

with Upper and Lower Hämäkua Ditches at the downstream 

reaches of the tributary streams. Finally, differences were 

computed at gaging station 16732200 on Wailoa Stream to 

reflect total diversion effects at the downstream limit of the 

study area. For example, Upper Hämäkua Ditch reduced the 

95-percentile discharge by 2 ft3/s on Kawainui Stream at site 

1. The combined diversions at Upper and Lower Hämäkua 

Ditches reduced 95-percentile discharge by 7 ft3/s on 

Kawainui Stream at gaging station 16724000.

To partition discharge reductions in the four tributary 

streams—Kawainui, Alakahi, Koÿiawe, and Waimä—between 

Upper and Lower Hämäkua Ditches, a second computation 

was required. Using data from the example given above, it 

follows that of the 7 ft3/s reduction in 95-percentile discharge 

estimated for Kawainui Stream downstream from Lower 

Hämäkua Ditch, 2 ft3/s was associated with Upper Hämäkua 

Ditch. As a result, reduction in discharge associated with 

Lower Hämäkua Ditch can be computed as the difference, 7 

minus 2, or 5 ft3/s. Similar computations for 95- and 50-percentile discharges were made for Alakahi, Koÿiawe, and 

Waimä Streams, and the results are summarized in table 17. 

Total diversions from the four tributary streams for 95- and 

50-percentile discharges, respectively, are 3.69 ft3/s and 4.58 

ft3/s by Upper Hämäkua Ditch and 10.3 ft3/s and 15.4 ft3/s 

by Lower Hämäkua Ditch. As a result, combined totals for 

diversions by both ditches are 14 ft3/s and 20 ft3/s for 95- and 

50-percentile discharges. These combined diversion totals 

are those reflected in discharges of the four tributary streams 

and will not equal diversion totals as noted at the downstream 

limit of the study area at gaging station 16732200 on Wailoa 

Stream. Diversion totals computed at gaging station 16732200 

equal 18 ft3/s and 27 ft3/s for 95- and 50-percentile discharges 

(table 16). Differences in combined diversion totals between 

the four tributary streams and those at the downstream limit 

of the study area can be attributed, in part, to rounding criteria 

applied to each of the computed values. The primary reason 

for the differences, however, is that Lower Hämäkua Ditch 

gains water in several of its tunneled reaches within Waipiÿo 

Valley and these diversion effects are not fully reflected in 

computed low-flow discharges until the downstream limit of 

the study area at Wailoa Stream gaging station 16732200.

 As noted previously, proposed future diversion rates 

out of Waipiÿo Valley by Lower Hämäkua Ditch were projected to be 7 Mgal/d (10.8 ft3

/s) during normal conditions 

and 13 Mgal/d (20.1 ft3/s) during drought conditions (U.S. 

Department of Agriculture, 1999, p. 144). In the same report, 

diversions at each of the four tributary stream intakes were 

shown as 1, 5, 2, and 0 Mgal/d, respectively, at the Kawainui, 

Alakahi, Koÿiawe, and Waimä intakes during normal conditions. During drought conditions, diversion rates were shown 

as 6.6, 3.9, 1.8, and 0 Mgal/d, respectively, at the same intakes. 

When combined, diversion totals at the individual ditch 

intakes do not exactly equal proposed totals of 7 Mgal/d and 

13 Mgal/d because of rounding and gains in Lower Hämäkua 

Ditch tunnels (U.S. Department of Agriculture, 1999, p. 144). 

In this report, these diversion values were converted to units 

of cubic feet per second and were rounded to the nearest unit 

as follows: 2, 8, 3, and 0 ft3/s during normal conditons and 10, 

6, 3, and 0 ft3/s during drought conditions at the Kawainui, 

Alakahi, Koÿiawe, and Waimä intakes, respectively. These values were then used to replace computed diversions by Lower 

Hämäkua Ditch reflective of 2000–2005 conditions, shown in 

table 17, to compute new diversion totals reflective of proposed future diversion practices. These new diversion totals, 

for proposed future practices, are shown in table 18. It can 

be noted from the data in table 18 that no changes are being 

proposed for diversion practices by Upper Hämäkua Ditch, 

so those values remain the same. In addition, no changes are 

proposed for the operation of Waimä intake on the Lower 

Hämäkua Ditch, so the computed diversion totals from table 

17 remain the same in table 18. 

Resultant 95- and 50-percentile discharges under proposed future diversion practices for nine gaging stations 

and data-collection sites located downstream from Lower 

Hämäkua Ditch are shown in table 19. Natural flow-duration 

discharges for these locations are reduced by total proposed 

diversions for future conditions (table 18), for each of the individual streams, to determine resultant discharges. By applying the same principles discussed in the section “Combining 

Flow-Duration Curves” in appendix 2, total proposed diversions can be determined for locations along Waipiÿo Stream 

downstream from the confluence of individual tributaries. For 

example, total proposed diversions for Kawainui Stream at 

gaging station 16724000 and Alakahi Stream at gaging station 

16729000 are 12 ft3/s and 7 ft3/s. Total proposed diversion for 

Waipiÿo Stream at site 10, located just downstream from the 

confluence of Kawainui and Alakahi Streams, is therefore 12 + 

7, or 19 ft3/s. A slight modification to this process is required 

for the gaging station on Wailoa Stream (16732200) at the 

downstream limit of the study area because not all of Lower 

Hämäkua Ditch diversion effects are reflected in four upstream 

tributary streams (see discussion above). For example (using 

95-percentile discharges), to compute total proposed diversion 

effects at the Wailoa Stream gage (16732200), total diversion 
 Effects of Diversion Practices on Low-Flow Statistics 31

Stream and location

Gaging-station 

or 

site numbera

Hydrologic 

condition

95-percentile 

discharge 

(ft3/s)

50-percentile 

discharge 

(ft3/s)

Kawainui us from LHD 1 Natural 18 34

2000–2005b 16 33

Difference 2 1

Kawainui ds from LHD 16724000 Natural 28 38

2000–2005b 21 27

Difference 7 11

Alakahi us from LHD 6 Natural 13 20

2000–2005b 12 18

Difference 1 2

Alakahi ds from LHD 16729000 Natural 18 21

2000–2005b 15 18

Difference 3 3

Koÿiawe us from LHD 15 Natural 7.3 9.5

2000–2005b 6.8 8.4

Difference 0.5 1.1

Koÿiawe ds from LHD 16731000 Natural 12 15

2000–2005b 10 12

Difference 2 3

Waimä us from LHD 18 Natural 0.73 1.2

2000–2005b 0.54 0.72

Difference 0.19 0.48

Waimä ds from LHD 16732150 Natural 26 44

2000–2005b 24 41

Difference 2 3

Wailoa 16732200 Natural 86 112

2000–2005b 68 85

Difference 18 27

a

 Site numbers correspond to those listed in table 2 and shown in figure 4.

b

 Diversion conditions in effect during the 2000–2005 study period.

Table 16. Reductions in natural discharge associated with 2000–2005 diversion practices on streams 

in the Waipiÿo Valley study area, Island of Hawaiÿi, Hawaiÿi.

[ft3/s, cubic feet per second; us, upstream; ds, downstream; LHD, Lower Hämäkua Ditch]
32 Low-Flow Characteristics of Streams Under Natural and Diversion Conditions, Waipiÿo Valley, Island of Hawaiÿi, Hawaiÿi

Stream 

and 

location

Difference in 

Q95 dischargesa

(ft3/s)

Diversion by 

UHD at Q95b

(ft3/s)

Diversion by 

LHD at Q95c

(ft3/s)

Difference in 

Q50d discharges 

(ft3/s)

Diversion by 

UHD at Q50b

(ft3/s)

Diversion by 

LHD at Q50c

(ft3/s)

Kawainui 2 5 1 10

us of LHD 2 1

ds of LHD 7 11

Alakahi 1 2 2 1

us of LHD 1 2

ds of LHD 3 3

Koÿiawe 0.5 1.5 1.1 1.9

us of LHD 0.5 1.1

ds of LHD 2 3

Waimä 0.19 1.81 0.48 2.52

us of LHD 0.19 0.48

ds of LHD 2 3

Total 3.7 10.3 4.58 15.4

Combined totals 14 20

a

 Difference between Q95 discharges for natural and 2000–2005 diversion conditions.

b

 Difference between discharges upstream of Lower Hämäkua Ditch.

c

 Downstream differences in discharge minus upstream differences in discharge.

d Difference between Q50 discharges for natural and 2000–2005 diversion conditions.

Stream 

and 

location

Diversion by 

UHD at Q95a

(ft3/s) 

Diversion by 

LHD at Q95b

(ft3/s)

Total diversion 

at Q95

(ft3/s)

Diversion by 

UHD at Q50a

(ft3/s)

Diversion by LHD 

at Q50b

(ft3/s)

Total diversion 

at Q50

(ft3/s)

Kawainui ds of LHD 2 10 12 1 2 3

Alakahi ds of LHD 1 6 7 2 8 10

Koÿiawe ds of LHD 0.5 3 3.5 1.1 3 4.1

Waimä ds of LHD 0.19 1.81c 2c 0.48 2.52c 3c

Total 3.7 20.8 24.5 4.58 15.5 20.1

a

 Data from table 17.

b

 Proposed diversion data from U.S. Department of Agriculture (1999, p. 144).

c

 No change from 2000–2005 diversion practices proposed for future diversion conditions.

Table 17. Estimated diversions by Upper and Lower Hämäkua Ditches from 95- and 50-percentile flowduration discharges under 2000–2005 diversion conditions on streams in the Waipiÿo Valley study area, Island 

of Hawaiÿi, Hawaiÿi.

[ft3/s, cubic feet per second; Q95, 95-percentile discharge; Q50, 50-percentile discharge; UHD, Upper Hämäkua Ditch; LHD, Lower Hämäkua 

Ditch; us, upstream; ds, downstream]

Table 18. Estimated diversions by Upper and Lower Hämäkua Ditches from 95- and 50-percentile flow-duration 

discharges under proposed, future diversion practices on streams in the Waipiÿo Valley study area, 

Island of Hawaiÿi, Hawaiÿi.

[ft3/s, cubic feet per second; Q95, 95-percentile discharge; Q50, 50-percentile discharge; UHD, Upper Hämäkua Ditch; LHD, Lower Hämäkua Ditch; us, 

upstream; ds, downstream]
 Summary of Effects of Various Diversion Practices at the Downstream Limit of Study Area 33

effects associated with 2000–2005 conditions at the gage of 

18 ft3/s (table 16) are adjusted to reflect the difference in total 

diversions from the four upstream tributary streams under 

proposed future diversion conditions (24.5 ft3/s in table 18) 

and 2000–2005 diversion conditions (14 ft3/s in table 17). The 

total proposed diversions effects are therefore computed as 18 

+ (24.5-14), or 28.5 ft3/s, as shown in table 19.

Changes in Low Flow Relative to 2000–

2005 Diversion Practices

 To evaluate the effects that proposed future diversion 

practices for Lower Hämäkua Ditch will have on current lowflow hydrology in the Waipiÿo Valley study area, flow-duration 

statistics for the 95 and 50 percentiles under 2000–2005 diversion practices and under proposed future diversion practices 

were compared. The 95- and 50-percentile discharges under 

both 2000–2005 and proposed future diversion practices at 

nine gaging stations and data-collection sites downstream 

from Lower Hämäkua Ditch are summarized in table 20. The 

reduction in discharge associated with a change from current 

to proposed, future diversion practices is shown as a percent in 

the table. 

Current (2000–2005) flow-duration discharges for locations upstream from Lower Hämäkua Ditch will not be altered 

by proposed future changes in diversion practices at the ditch. 

The proposed future diversion practices would, however, 

result in discharges downstream from Lower Hämäkua Ditch 

that are distinctly different from those under current diversion 

practices. At gaging stations and data-collection sites along 

Kawainui, Alakahi, and Waipiÿo Streams, current (2000–2005) 

95-percentile discharges will be reduced between 21 and 27 

percent. At gaging stations and data-collection sites along 

Koÿiawe and Wailoa Streams, the magnitude of the flow reduction will be only slightly smaller, at 15 percent. No changes in 

95-percentile discharges will occur along Waimä Stream. The 

only changes in excess of 10 percent of current (2000–2005) 

50-percentile discharges will be at gaging stations and datacollection sites along Kawainui and Alakahi Streams; discharges on Kawainui Stream will increase by 30 percent and 

discharges on Alakahi Stream will decrease by 39 percent. 

Changes in Low Flow Relative to Natural 

Conditions 

 To evaluate the effects that proposed future diversion 

practices for Lower Hämäkua Ditch will have on natural lowflow hydrology in the Waipiÿo Valley study area, flow-duration 

statistics for the 95 and 50 percentiles under proposed, future 

diversion and natural conditions were compared. The 95- and 

50-percentile discharges under both conditions at nine gaging 

stations and data-collection sites downstream from Lower 

Hämäkua Ditch are summarized in table 21. The reduction in 

discharge associated with a change from natural to proposed 

future diversion practices is shown as a percent in the table. 

The spatial patterns of discharge reduction for 95- and 50-percentile discharges are shown in figures 7 and 8.

Natural flow-duration discharges for locations upstream 

from Upper Hämäkua Ditch will not be altered by proposed 

future changes in diversion practices in Lower Hämäkua Ditch. 

Natural flow-duration discharges in stream reaches between 

Upper and Lower Hämäkua Ditches, however, will continue 

to be reduced in response to current (2000–2005) practices in 

effect. Proposed future changes in diversion practices in Lower 

Hämäkua Ditch will not alter these conditions. Changes in discharges in stream reaches between Upper and Lower Hämäkua 

Ditches are summarized in tables 14 and 15. The spatial pattern 

of discharge reduction for stream reaches upstream from Lower 

Hämäkua Ditch, shown in figures 7 and 8 for proposed future 

changes in diversion practices, reflect the above.

 At gaging stations and data-collections sites downstream 

from Lower Hämäkua Ditch—along Kawainui, Alakahi, 

Waipiÿo, and Wailoa Streams—natural 95-percentile discharges will be reduced between 29 and 43 percent. At the 

stations and sites along Waimä Stream, natural 95-percentile discharges will be reduced by 8 percent. The changes in 

50-percentile discharges will be slightly smaller but more 

variable than those for 95-percentile discharges. At gaging 

stations and data-collection sites along Waipiÿo, Koÿiawe, and 

Wailoa Streams, the natural 50-percentile discharges will be 

reduced between 21 and 27 percent. At gaging stations and 

data-collection sites along Kawainui and Waimä Streams, 

the natural 50-percentile discharges will be reduced by 7 to 8 

percent. Changes will be greatest at gaging stations and datacollections sites along Alakahi Stream, where 50-percentile 

discharges will be reduced by 48 percent.

As noted previously, the ratio of 95-percentile to 

50-percentile discharges can be used as an index of low-flow 

variability. In table 22, ratios of 95-percentile to 50-percentile discharges are summarized for nine gaging stations and 

data-collections sites downstream from Lower Hämäkua 

Ditch. Under proposed future diversion conditions, the average 

ratio is 0.66, which is markedly lower than those for natural 

conditions (0.76) and current (2000–2005) diversion conditions (0.78). These differences indicate that low flows under 

proposed future diversion conditions will be more variable.

Summary of Effects of Various 

Diversion Practices at the 

Downstream Limit of Study Area

One of the important aspects of this study was to determine the effects that diversion practices have on the low-flow 

hydrology of Wailoa Stream as it enters the lower part of 

Waipiÿo Valley. It is in the lower parts of the valley that water 

from Wailoa Stream is used to support taro production and 

therefore where the availability of this water is very important. During this study data were collected at gaging station 
34 Low-Flow Characteristics of Streams Under Natural and Diversion Conditions, Waipiÿo Valley, Island of Hawaiÿi, Hawaiÿi

Gaging-station or 

site numbera Stream

Discharge (ft3/s)

Natural 

conditionsb

Total proposed 

diversions Resultant

95-percentile

16724000 Kawainui 28 12 16

16729000 Alakahi 18 7 11

10 Waipiÿo 46 19c 27

11 Waipiÿo 49 19c 30

16732000 Waipiÿo 61 22.5d 39

22 Waipiÿo 63 22.5d 41

16731000 Koÿiawe 12 3.5 8.5

16732150 Waimä 26 2 24

16732200 Wailoa 86 28.5e 58

50-percentile

16724000 Kawainui 38 3 35

16729000 Alakahi 21 10 11

10 Waipiÿo 59 13c 46

11 Waipiÿo 63 13c 50

16732000 Waipiÿo 78 17.1d 61

22 Waipiÿo 80 17.1d 63

16731000 Koÿiawe 15 4.1 11

16732150 Waimä 44 3 41

16732200 Wailoa 112 27.1e 85

a

 Site numbers correspond to those listed in table 2 and shown in figure 4.

b

 Data from tables 14 and 15.

c

 Combined diversions from Kawainui and Alakahi Streams.

d

 Combined diversions from Kawainui, Alakahi, and Koÿiawe Streams.

e Total diversion from upstream from gaging station.

Table 19. Resultant 95- and 50-percentile flow-duration discharges under proposed, future 

diversion practices at gaging stations and data-collection sites downstream from Lower 

Hämäkua Ditch in the Waipiÿo Valley study area, Island of Hawaiÿi, Hawaiÿi.

[ft3/s, cubic feet per second]
 Summary of Effects of Various Diversion Practices at the Downstream Limit of Study Area 35

Gaging-station 

or site numbera Stream

Discharge (ft3/s) Difference in 

percent 2000–2005 

diversion practices

Proposed future 

diversions

95-percentile

16724000 Kawainui 21 16 -24

16729000 Alakahi 15 11 -27

10 Waipiÿo 36 27 -25

11 Waipiÿo 40 30 -25

16732000 Waipiÿo 50 39 -22

22 Waipiÿo 52 41 -21

16731000 Koÿiawe 10 8.5 -15

16732150 Waimä 24 24 0

16732200 Wailoa 68 58 -15

50-percentile

16724000 Kawainui 27 35 30

16729000 Alakahi 18 11 -39

10 Waipiÿo 45 46 2

11 Waipiÿo 50 50 0

16732000 Waipiÿo 62 61 -2

22 Waipiÿo 65 63 -3

16731000 Koÿiawe 12 11 -8

16732150 Waimä 41 41 0

16732200 Wailoa 85 85 0

a

 Site numbers correspond to those listed in table 2 and shown in figure 4.

Table 20. Comparison of 95- and 50-percentile flow-duration discharges under 2000–2005 and 

proposed, future diversion practices at gaging stations and data-collection sites downstream from 

Lower Hämäkua Ditch in the Waipiÿo Valley study area, Island of Hawaiÿi, Hawaiÿi.

[ft3/s, cubic feet per second]
36 Low-Flow Characteristics of Streams Under Natural and Diversion Conditions, Waipiÿo Valley, Island of Hawaiÿi, Hawaiÿi

Gaging-station 

or site numbera Stream

Discharge (ft3/s) Difference in 

Natural percent conditionsProposed future 

diversions

95-percentile

16724000 Kawainui 28 16 -43

16729000 Alakahi 18 11 -39

10 Waipiÿo 46 27 -41

11 Waipiÿo 49 30 -39

16732000 Waipiÿo 61 39 -36

22 Waipiÿo 63 41 -35

16731000 Koÿiawe 12 8.5 -29

16732150 Waimä 26 24 -8

16732200 Wailoa 86 58 -33

50-percentile

16724000 Kawainui 38 35 -8

16729000 Alakahi 21 11 -48

10 Waipiÿo 59 46 -22

11 Waipiÿo 63 50 -21

16732000 Waipiÿo 78 61 -22

22 Waipiÿo 80 63 -21

16731000 Koÿiawe 15 11 -27

16732150 Waimä 44 41 -7

16732200 Wailoa 112 85 -24

 a Site numbers correspond to those listed in table 2 and shown in figure 4.

Table 21. Comparison of 95- and 50-percentile flow-duration discharges under natural and 

proposed, future diversion practices at gaging stations and data-collection sites downstream from 

Lower Hämäkua Ditch in the Waipiÿo Valley study area, Island of Hawaiÿi, Hawaiÿi.

[ft3/s, cubic feet per second]
 Summary of Effects of Various Diversion Practices at the Downstream Limit of Study Area 37

Kawainui Str

Alakahi Str

Lalakea 

Str

Waipi‘oStr

Wailoa

Str

Upper

Ditch

Hämäkua

Waimä

Str

Ko‘iawe

Str

Häm

Ditch

Lower

ä

0 kua

0

-30

-24

-11

-43

-39

-41

-39 -36

-29

-35

-8

-26 -7

-13

-17

0 -8

-33 # -100

#

#

#

#

#

#

#

#

#

#

#

#

#

720000

720300

721000

725000

728000

722000

724000

729000 732000

731000

732150

730000

732200

1

6

10

11

15 18

22

#

#

# #

# #

#

155°42' 155°40' 155°38'

20°04'

20°06'

0

0 1

1

2 KILOMETERS

2 MILES

#

#

#

Waimea

155°40' 155°36'

20°04'

20°08'

Waipiÿo 

 Bay

P A C I F I C 

 O C E A N

155°40' 155°36'

20°04'

20°08'

Figure 7. Percent reduction in natural 95-percentile discharge under proposed, future diversion practices, Waipiÿo Valley study area, 

Island of Hawaiÿi, Hawaiÿi.

Area of map

22 #

6 #

720000 # Gaging station and abbreviated number—

complete number is preceded by 16

Seepage-run site and number

Seepage-run site and low-flow partial-record

 station and station number

Less than or equal to 10 percent

Greater than 10 and less than or equal to 20 percent

Greater than 20 and less than or equal to 30 percent

Greater than 30 and less than or equal to 100 percent

EXPLANATION

Reduction in streamflow

-30 Percent reduction at data site

Base modified from U.S. Geological Survey National

Hydrography Dataset, Transverse Mercator projection,

zone 5, central meridian −153°, North American Datum 1983.

Figure 7. Percent reduction in natural 95-percentile discharge under proposed, future diversion practices, Waipiÿo Valley 

study area, Island of Hawaiÿi, Hawaiÿi.
38 Low-Flow Characteristics of Streams Under Natural and Diversion Conditions, Waipiÿo Valley, Island of Hawaiÿi, Hawaiÿi

Kawainui Str

Alakahi Str

Lalakea 

Str

Waipi‘oStr

Wailoa

Str

Upper

Ditch

Hämäkua

Waimä

Str

Ko‘iawe

Str

Häm

Ditch

Lower

ä

0 kua

0

-33

-29

-3

-8

-48

-22

-21 -22

-27

-21

-7

-40 -12

-18

-20

0 -5

-24 # -92

#

#

#

#

#

#

#

#

#

#

#

#

#

720000

720300

721000

725000

728000

722000

724000

729000 732000

731000

732150

730000

732200

1

6

10

11

15 18

22

#

#

# #

# #

#

Reduction in Streamflow

-30 Percent reduction at data site

155°42' 155°40' 155°38'

20°04'

20°06'

0

0 1

1

2 KILOMETERS

2 MILES

#

#

#

Waimea

155°40' 155°36'

20°04'

20°08'

Waipi‘o 

 Bay

P A C I F I C 

 O C E A N

155°40' 155°36'

20°04'

20°08'

Area of map

Figure 8. Percent reduction in natural 50-percentile discharge under proposed, future diversion practices, Waipiÿo Valley study area,

 Island of Hawaiÿi, Hawaiÿi.

Base modified from U.S. Geological Survey National

Hydrography Dataset, Transverse Mercator projection,

zone 5, central meridian −153°, North American Datum 1983.

22 #

6 #

720000# Gaging station and abbreviated number—

complete number is preceded by 16

Seepage-run site and number

Seepage-run site and low-flow partial-record

 station and station number

Less than or equal to 10 percent

Greater than 10 and less than or equal to 20 percent

Greater than 20 and less than or equal to 30 percent

Greater than 30 and less than or equal to 100 percent

EXPLANATION

Figure 8. Percent reduction in natural 50-percentile discharge under proposed, future diversion practices, Waipiÿo 

Valley study area, Island of Hawaiÿi, Hawaiÿi.
Summary of Effects of Various Diversion Practices at the Downstream Limit of Study Area 39

Gaging-station

 or 

site numbera

Stream

50-percentile 

discharge 

(ft3/s)

95-percentile 

discharge 

(ft3/s)

 Ratio Q95/Q50

Natural conditions

16724000 Kawainui 38 28 0.74

16729000 Alakahi 21 18 0.86

10 Waipiÿo 59 46 0.78

11 Waipiÿo 63 49 0.78

16732000 Waipiÿo 78 61 0.78

22 Waipiÿo 80 63 0.79

16731000 Koÿiawe 15 12 0.80

16732150 Waimä 44 26 0.59

16732200 Wailoa 112 86 0.77

Average 0.76

2000–2005 diversion conditions

16724000 Kawainui 27 21 0.78

16729000 Alakahi 18 15 0.83

10 Waipiÿo 45 36 0.80

11 Waipiÿo 50 40 0.80

16732000 Waipiÿo 62 50 0.81

22 Waipiÿo 65 52 0.80

16731000 Koÿiawe 12 10 0.83

16732150 Waimä 41 24 0.59

16732200 Wailoa 85 68 0.80

Average 0.78

Proposed future diversion conditions

16724000 Kawainui 35 16 0.46

16729000 Alakahi 11 11 1.0

10 Waipiÿo 46 27 0.59

11 Waipiÿo 50 30 0.60

16732000 Waipiÿo 61 39 0.64

22 Waipiÿo 63 41 0.65

16731000 Koÿiawe 11 8.5 0.77

16732150 Waimä 41 24 0.59

16732200 Wailoa 85 58 0.68

Average 0.66

a

 Site numbers correspond to those listed in table 2 and shown in figure 4.

Table 22. Relation between 95- and 50-percentile flow-duration discharges under natural, 

2000–2005 diversion, and proposed, future diversion conditions at gaging stations and datacollection sites downstream from Lower Hämäkua Ditch in the Waipiÿo Valley study area, Island 

of Hawaiÿi, Hawaiÿi.

[ft3/s, cubic feet per second; Q95, 95-percentile discharge; Q50, 50-percentile discharge]
40 Low-Flow Characteristics of Streams Under Natural and Diversion Conditions, Waipiÿo Valley, Island of Hawaiÿi, Hawaiÿi

16732200 on Wailoa Stream at an altitude of 190 feet (fig. 3), 

which is a short distance upstream from the site of the most 

upstream active (2005) taro diversion. In addition, a wide 

variety of current and historical data is available for the Wailoa 

gaging station (table 1); daily discharge records were collected 

at the site in 1901–1902, a discharge measurement was made 

there in 1911, continuous records of daily discharge were collected in 1964–1969, and discharge measurements were made 

between 2000 and 2005 as part of this study (table 3).

Analyses summarized in earlier sections of this report 

document the computation of flow-duration discharges at the 

location of the Wailoa Stream gaging station that are representative of natural conditions, 1965–1969 diversion conditions, 2000–2005 diversion conditions, and proposed, future 

diversion conditions. These data are summarized and compared in table 23. In all cases, computed values reflect what 

the discharges would have been had the indicated conditions 

been in effect over the entire 40-year (1965–2004) base 

period. Conversion to a common base period is required to 

allow direct comparison of various flow-duration discharges.

Diversion practices at the Upper and Lower Hämäkua 

Ditch systems have significant effects on the low-flow hydrology of Wailoa Stream at the downstream limit of the study 

area. In all cases, diversion practices reduced the magnitudes 

of low-flow discharges in Wailoa Stream. Under 1965–1969 

diversion conditions, natural flow-duration discharges were 

reduced between 41 ft3/s (at the 99-percentile discharge) 

and 59 ft3/s (at the 50-percentile discharge). The percentage 

reduction in natural flow-duration discharges was reasonably constant and varied between 51 and 54 percent. Under 

2000–2005 diversion conditions, natural flow-duration 

discharges were reduced between 15 ft3/s (99-percentile) 

and 27 ft3/s (50-percentile). The percent reduction in natural 

flow-duration discharges was reasonably constant and varied 

between 19 and 24 percent. Under proposed future diversion 

conditions, natural flow-duration discharges were reduced 

by 28 ft3/s (95 percentile) and 27 ft3/s (50 percentile). The 

percent reduction in natural flow-duration discharges were 33 

and 24 percent, respectively. 

The effects of the diversions have become less significant over the years as conditions in Upper and Lower 

Hämäkua Ditches have deteriorated and the magnitudes 

of diversion have been reduced. Proposed future diversion 

practices, relative to current (2000–2005) diversion practices, 

will result in increased diversion during periods of drought 

(represented by 95-percentile discharges) and virtually no 

change in diversion during normal conditions (represented 

by 50-percentile discharges). There is a close correspondence 

between total reduction in natural 50-percentile flow-duration discharges of Wailoa Stream at the downstream limit of 

the study area (at gaging station 16732200), and the combined average discharge of Upper Hämäkua Ditch (as measured at gaging station 16726000 above Waimea Reservoir) 

and Lower Hämäkua Ditch (as measured at gaging station 

16732800 upstream from the main weir). For example, during the 2000–2005 study period, the combined average ditch 

discharge at stations 16726000 and 16732800 was about 24 

ft3/s (see footnote on table 11) and the reduction in natural 

50-percentile discharge was 27 ft3/s (table 23). Similar correspondence was noted for 1965–1969 diversion conditions, 

when the average combined ditch discharge upstream from 

Waimea Reservoir and the main weir was about 57 ft3/s (see 

footnote on table 9) and the reduction in natural 50-percentile discharge was 59 ft3

/s (table 23). When they were first 

built, the average diversion capacities of Upper and Lower 

Hämäkua Ditches were 23 and 62 ft3/s, respectively (Wilcox, 

1966). At these maximum historical diversion rates, the combined average ditch discharge of 85 ft3

/s would have reduced 

the natural 50-percentile discharge of 112 ft3/s at the downstream limit of the study area by about 76 percent.

Summary and Conclusions 

Waipiÿo Valley is an area of great cultural and historical significance to the Hawaiian people. Streams in the valley 

have been identified by the Hawaiÿi Commission on Water 

Resource Management as candidates for protection because of 

their importance to the cultivation of taro, a culturally significant agricultural product in Hawai’i. Approximately 100 

acres of taro, which requires large quantities of water, are still 

cultivated in Waipiÿo Valley. 

The availability of abundant, high-level water in 

Waipiÿo Valley has long been valued by Waipiÿo Valley residents as well as by agricultural interests in adjacent areas. 

As a result, two major water diversion systems, Upper and 

Lower Hämäkua Ditches, were constructed in the valley in 

the early 1900’s. Over the past 100 years, natural streamflow 

in Waipiÿo Valley has been reduced by operation of the two 

diversion systems, which transfer water out of the valley to 

other locations on the Island of Hawaiÿi. The physical condition and diversion practices of Upper and Lower Hämäkua 

Ditches have varied widely over the years, and as a result, 

so have their effects on natural streamflow in Waipiÿo Valley. Recent change in ownership of Lower Hämäkua Ditch, 

subsequent renovation and improvements to the system, and 

proposals for its future operation and water diversion strategies provided the impetus for this study. Proposed diversions 

of water out of Waipiÿo Valley would be 7 Mgal/d (10.8 

ft3/s) under normal flow conditions and would increase to 13 

Mgal/d (20.1 ft3/s) during drought conditions. The availability of streamflow in Waipiÿo Valley to support the proposed 

new diversion strategies, and the effects of such diversions 

on streamflow, were the primary focal points for this report.

The availability of water for a variety of conflicting uses 

(for example, out-of-valley diversions, downstream taro cultivation, and support of instream biota) is of particular concern 

during dry periods, when streamflows are low. As a result, 

the primary focus of this report is the low-flow hydrology of 

Waipiÿo Valley. An important consideration in such an analysis 
 Summary and Conclusions 41

Percentage of time 

indicated discharge 

equaled or exceeded

Discharge (ft3/s)

Difference from natural 

condition discharge 

(ft3/s)

Difference from 

natural condition in 

percent

Natural conditionsa

99 80 --- ---

95 86 --- ---

90 88 --- ---

80 95 --- ---

70 100 --- ---

60 105 --- ---

50 112 --- ---

1965–1969 diversion conditionsb

99 39 -41 -51

95 41 -45 -52

90 43 -45 -51

80 44 -51 -54

70 47 -53 -53

60 49 -56 -53

50 53 -59 -53

2000–2005 diversion conditionsc

99 65 -15 -19

95 68 -18 -21

90 70 -18 -20

80 73 -22 -23

70 76 -24 -24

60 80 -25 -24

50 85 -27 -24

Proposed future diversion conditionsd

99 --- --- ---

95 58 -28 -33

90 --- --- ---

80 --- --- ---

70 --- --- ---

60 --- --- ---

50 85 -27 -24

a

 Discharge data from table 13.

b

 Discharge data from table 9.

c

 Discharge data from table 11.

d

 Discharge data from table 19.

Table 23. Relation between selected flow-duration discharges under natural conditions and 

diversion conditions during 1965–1969, 2000–2005, and proposed for the future, extended to a 

common base period of 1965–2004, at the downstream limit of the Waipiÿo Valley study area at 

Wailoa Stream station 16732200, Island of Hawaiÿi, Hawaiÿi.

[ft3/s, cubic feet per second; ---, not computed]
42 Low-Flow Characteristics of Streams Under Natural and Diversion Conditions, Waipiÿo Valley, Island of Hawaiÿi, Hawaiÿi

is the fact that streamflow and the effects of various diversion 

practices are extremely variable over time and at various locations along streams in Waipiÿo Valley.

Low-flow hydrology was described in this report in 

terms of flow-duration statistics, which provide useful summaries of streamflow data. For example, at a location where 

a long-term surface-water gaging station has been operated, 

average streamflow data are available for each day that the 

station has been in operation. To compute flow-duration 

statistics, these data are ranked in descending order, with the 

largest daily streamflow value first and the smallest value 

last. Once this is done, one can readily determine which 

value of daily streamflow was equaled or exceeded 50 percent of the time; note that streamflow will also be less than 

this value 50 percent of the time. This single flow-duration 

statistic, which is referred to as the 50-percentile discharge, 

or the median discharge, is considered an indicator of normal flow conditions in a stream. This same process can be 

repeated for a variety of low streamflow values. For example, 

the 95-percentile discharge is the value of daily streamflow 

that is equaled or exceeded 95 percent of the time; streamflow will also be less than this value 5 percent of the time. 

The 95-percentile discharge is an indicator of moderate 

drought conditions in a stream.

Flow-duration statistics were computed directly from 

available data for three locations in the Waipiÿo Valley 

study area where long-term surface-water gaging stations 

have been operated. At an additional 13 locations where 

only limited historical data are available or where discharge 

measurements were made as part of this study, a variety of 

record-extension techniques were used to estimate flowduration statistics. Flow-duration statistics were computed to 

reflect natural conditions, current (2000–2005) and historical 

(1965–1969) diversion conditions, and proposed future diversion conditions. 

Results contained in this report can best be summarized 

by examining data collected at the gaging station on Wailoa 

Stream at 190 feet elevation. This station is at the downstream 

limit of the study area and a short distance upstream from the 

most upstream active (as of 2005) diversion for taro irrigation 

in Waipiÿo Valley. In addition, the Wailoa Stream station is 

downstream from all Upper and Lower Hämäkua Ditch diversion intakes and thus will reflect the full effects of diversions 

to the ditches.

Flow-duration statistics that are representative of natural, 

no-diversion conditions provide a base line for evaluating the 

availability of streamflow. At the Wailoa Stream gaging station, 

natural 95- and 50-percentile discharges were determined to 

be 86 and 112 ft3/s, respectively. Under 1965–1969 diversion 

conditions, natural 95- and 50-percentile discharges were 

reduced by 52 and 53 percent, to 41 and 53 ft3/s. Under current 

(2000–2005) diversion conditions, natural 95- and 50-percentile 

discharges were reduced by 21 and 24 percent to 68 and 85 ft3/s. 

Under proposed future diversion conditions, natural 95- and 

50-percentile discharges at the station would be reduced by 33 

and 24 percent, to 58 and 85 ft3/s. Compared to discharges that 

result from current (2000–2005) diversion practices, proposed 

future diversion conditions would reduce 95-percentile discharges, which are representative of moderate drought levels 

in the stream, by 15 percent. No change, however, would be 

expected in 50-percentile discharges, which are representative 

of normal conditions.

The effects of current (2000–2005) diversion practices 

on natural 95- and 50-percentile discharges differ along the 

several streams in Waipiÿo Vallely. Reductions in natural 

95-percentile discharges of greater than 30 percent were 

found in Kawainui Stream in the reach downstream from 

Upper Hämäkua Ditch to an altitude of about 2,120 feet. 

Reductions in natural 95-percentile discharges along other 

streams in their reaches downstream from Upper Hämäkua 

Ditch were mostly between 10 and 30 percent. Reductions 

in natural 50-percentile discharges of greater than 30 percent 

were found in Kawainui Stream in the reach downstream 

from Upper Hämäkua Ditch to an altitude of about 1,435 

feet and in the reach of Waimä Stream between Upper and 

Lower Hämäkua Ditches. Reductions in natural 50-percentile discharges along other streams in their reaches downstream from Upper Hämäkua Ditch were mostly between 10 

and 30 percent.

The potential effects of proposed future diversion practices on natural 95- and 50-percentile discharges of streams in 

Waipiÿo Valley also differ slightly from the effects of current 

practices. Reductions in natural 95-percentile discharges 

of greater than 30 percent were found in Kawainui Stream 

downstream from Upper Hämäkua Ditch to an altitude of 

about 2,120 feet, and along most stream reaches downstream 

from Lower Hämäkua Ditch, except for Waimä Stream. 

Reductions in natural 50-percentile discharges of greater than 

30 percent were found in Kawainui Stream downstream from 

Upper Hämäkua Ditch to an altitude of about 1,.435 feet, 

along Alakahi Stream downstream from Lower Hämäkua 

Ditch, and in the reach of Waimä Stream between Upper and 

Lower Hämäkua Ditches. Reductions in natural 50-percentile 

discharges over the remainder of the stream reaches downstream from Lower Hämäkua Ditch were extremely variable, 

from 0 to 10 percent along Kawainui Stream and the lower 

reaches of Waimä Stream and from 20 to 30 percent along 

Waipiÿo and Wailoa Streams.
 References Cited 43

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44 Low-Flow Characteristics of Streams Under Natural and Diversion Conditions, Waipiÿo Valley, Island of Hawaiÿi, Hawaiÿi

Stearns, H.T., and Macdonald, G.A., 1946, Geology and 

ground-water resources of the Island of Hawaii: Hawaii 

Division of Hydrography Bulletin 9, 363 p., 3 pl.

Tasker, G.D., 1975, Combining estimates of low-flow characteristics of streams in Massachusetts and Rhode Island: 

Journal of Research of the U.S. Geological Survey, v. 3, no. 

1, p. 107–112.

U.S. Department of Agriculture, 1999, Watershed plan and 

final environmental impact statement, Lower Hamakua 

Ditch watershed, Hawaii County, Hawaii: U.S. Department 

of Agriculture, Natural Resources Conservation Service 

(Lead Agency), 218 p., 5 app.

U.S. Geological Survey, 1963, Surface water records of 

Hawaii and other Pacific areas 1963: U.S. Geological Survey Water-Data Report HI–63, 189 p.

U.S. Geological Survey, 1967, Water resources data for Hawaii 

and other Pacific areas 1966: U.S. Geological Survey WaterData Report HI–66, 261 p.

Vogel, R.M., and Fennessey, N.M., 1995, Flow duration curves 

II, A review of applications in water resources planning: 

Water Resources Bulletin, v. 31, p. 1029–1039.

Wilcox, Carol, 1996, Sugar water, Hawaii’s plantation ditches: 

Honolulu, University of Hawaiÿi Press, 191 p.
 45

Appendixes 1–3
46 Low-Flow Characteristics of Streams Under Natural and Diversion Conditions, Waipiÿo Valley, Island of Hawaiÿi, Hawaiÿi

Appendix 1. Computation of Low-Flow Statistics for Sites with 

Historical Data

Gaging Stations Operated between 

August 1901 and January 1902

Daily streamflow data were collected by Arthur Tuttle, 

for Bishop Estate, at 13 stations in Waipiÿo Valley during the 

period August 1901 to January 1902 (table 1-A). These data 

were published in a USGS report (Martin and Pierce, 1913, 

p. 397). The length of the records collected at these stations is 

variable, ranging from a minimum of 51 days to a maximum 

of 146 days. Because of the limited length of the records, the 

data cannot be used to compute directly the low-flow duration 

statistics representative of the base period (1965–2004) used 

in the current study. In spite of these limitations, however, the 

data are particularly significant; they were collected during a 

period of natural flow, before construction of Upper and Lower 

Hämäkua Ditch systems, which also is considered to have 

been unusually dry (Mink, 1984, p. 8).

A modified version of record-extension techniques, which 

were described in the main body of this report, was applied to 

the 1901–1902 data to estimate base period, low-flow statistics. In the “standard” application of record-extension techniques, a relation is established between concurrent flows at 

a station with limited or short-term data and flows at a station 

with complete data over the selected base period; the latter 

is typically designated an index station. In such a situation, 

low-flow statistics for the base period at the index station can 

be computed directly. These computed low-flow statistics can 

then be applied to the established relation, based on concurrent data at the short-term and index stations, to estimate base 

period low-flow statistics at the short-term stations. 

Unfortunately, none of the 13 stations operated in 1901–

1902 have data concurrent with data for any of the index stations that were used in this study (fig. 1-A and table 1-B). One 

of the 13 stations operated by Tuttle, Wailoa Stream at 190 

feet, later became USGS gaging station 16732200, where data 

were subsequently collected for short periods—in 1911 and 

from 1964 to 1969—and discharge measurements were made 

between 2000 and 2005. The later of these subsequent periods 

of data collection were concurrent with data collected at the 

index stations used in the current study. Thus estimates of 

low-flow statistics for the base period used in the current study 

(1965–2004) could be computed for regulated and natural 

flow conditions at the Wailoa Stream station (site 24 on tables 

1-C and 1-D). The results of these computations provided a 

basis for applying modified record-extension techniques to the 

1901–1902 data because Wailoa Stream station 16732200 now 

has what is considered concurrent data with the 12 remaining stations operated by Tuttle, and it has low-flow statistics 

for the base period. A limitation of this analysis is that the 

computations of low-flow statistics for the base period at the 

Station 

number Location Days of record 

16721000 Kawainui Stream at 2,120 feet 51

16721500 Kawainui Stream Branch 3 at 1,700 feet 94

16722000 Kawainui Stream at 1,435 feet 77

16722300 Kawainui Stream Branch 2 at 1,405 feet 106

16722600 Kawainui Stream Branch 1 at 1,380 feet 106

16728000 Alakahi Stream at 1,200 feet 71

16730000 Koÿiawe Stream at 1,120 feet 68

16724000 Kawainui Stream at 775 feet 115

16729000 Alakahi Stream at 730 feet 126

16731000 Koÿiawe Stream at 610 feet 132

16732100 Waimä Stream at 790 feet 132

16732150 Waimä Stream at 385 feet 127

16732200 Wailoa Stream at 190 feet 146a

a Data also collected at this station in 1911 and from 1964 to 1969 and 

discharge measurements were made between 2000 and 2005; designated a 

“substitute” index station in analysis of data for other stations listed above.

Table 1–A. Surface-water gaging stations operated in 

the Waipiÿo Valley, Island of Hawaiÿi, Hawaiÿi, August 

1901-January 1902.

gaging station on Wailoa Stream, which was then considered a 

“substitute” index station, are not based on a complete record 

of flow but are in fact estimates themselves. As a result, errors 

associated with the modified record-extension techniques will 

be unknown, and the resulting low-flow statistics must be 

treated as estimates with unknown levels of accuracy.

Regulated Low-Flow Statistics

During the period August 1901 to January 1902, Tuttle 

collected 146 days of streamflow data at the site on Wailoa 

Stream that became gaging station 16732200. Regulated 

low-flow statistics reflective of 1965–2004 base period 

and of diversion practices in place during the study period 

(2000–2005) have been computed for this station and are 

summarized in table 1-C (site 24). Data also were collected at 

an additional 12 stations during the period late 1901 to early 

1902. Computations were not made for three of these stations 

because they were on small, upstream branches of Kawainui 

Stream, at altitudes ranging from 1,380 to 1,700 feet. The data 

for each of the other nine stations were screened, and only 
 Appendix 1. Computation of Low-Flow Statistics for Sites with Historical Data 47

Kawainui

Str

Waimanu

Str

Alakahi

Str

Läläkea 

Str

Waiulili

Str

Waipi‘o Str

Wailoa

Str

Upper

Ditch

Lower

Ditch

Hämäkua

Waima

Str

Ko‘iawe 

Str

Hämäkua

##

#

#

#

##

#

#

#

#

#

#

##

#

#

#

#

#

#

" ""

"

"

"

"

720000

720500

720300

721000

757000

758000

759000

724800

725000

728000

721500

722000

722600

722300

723000

724000

729000

732000

731000

732150

732100

732600

726000

730000

732200

732900

733000

733100

732800

Waimea

0 1 2 KILOMETERS

0 1 2 MILES

155°40' 155°36'

20°04'

20°08'

Waipiÿo 

 Bay

P A C I F I C 

 O C E A N

Figure 1A. Location of stream and ditch surface-water gaging stations operated in adjacent to the Waipiÿo Valley study area,

Island of Hawaiÿi, Hawaiÿi.

757000

726000 "

# Stream (Index stations are highlighted in yellow)

Ditch

 Major road

Gaging station and abbreviated number—

Complete number is preceded by 16

Base modified from U.S. Geological Survey National

Hydrography Dataset, Transverse Mercator projection,

zone 5, central meridian −153°, North American Datum 1983.

EXPLANATION

HAWAI‘I

Area of map

PACIFIC

OCEAN

Figure 1–A. Location of stream and ditch surface-water gaging stations operated in and adjacent to the Waipiÿo 

Valley study area, Island of Hawaiÿi, Hawaiÿi.
48 Low-Flow Characteristics of Streams Under Natural and Diversion Conditions, Waipiÿo Valley, Island of Hawaiÿi, Hawaiÿi

Percentage of time 

indicated discharge 

equaled or exceeded

Discharge (ft3/s)

Kawainui 

Stream 

16720000a

Alakahi 

Stream 

16725000a

Waikoloa 

Stream 

16758000a

Hauani 

Gulch 

16759000a

99 0.10 0.15 0.99 0.00

98 0.15 0.23 1.2 0.03

97 0.19 0.29 1.3 0.04

95 0.29 0.38 1.5 0.06

90 0.51 0.59 1.7 0.11

85 0.74 0.8 2.0 0.15

80 1.0 1.0 2.3 0.20

75 1.3 1.2 2.5 0.25

70 1.7 1.5 2.8 0.29

65 2.1 1.8 3.0 0.34

60 2.7 2.2 3.4 0.40

55 3.5 2.6 3.8 0.47

50 4.5 3.1 4.3 0.55

40 7.4 4.5 5.8 0.77

 a Station numbers correspond to those shown on figure 1-A.

Percentage of time 

indicated discharge 

equaled or exceeded

Dischargea (ft3/s)

Kawainui 

Stream 

Site 1b

Alakahi 

Stream 

Site 6b

Koÿiawe 

Stream 

Site 15b

Waimä 

Stream 

Site 18b

Wailoa 

Stream 

Site 24b

99 15 12 6.6 0.52 65

95 16 12 6.8 0.54 68

90 18 13 6.9 0.56 70

80 20 14 7.3 0.60 73

70 24 15 7.6 0.63 76

60 28 16 7.9 0.67 80

50 33 18 8.4 0.72 85

Average standard error 

(percent) 5.1 3.0 2.2 7.8 2.6

a

 All estimated flow-duration discharges reflect diversion conditions at Upper and Lower Hämäkua Ditches 

in effect during the study period 2000–2005. During the period March to November 2003 average diversion from Waipiÿo Valley by Upper Hämäkua Ditch, as measured at surface-water gaging station 16726000 

at 3,020 feet, was 6.75 ft3/s and by Lower Hämäkua Ditch, as measured at surface-water gaging station 

16732800 upstream from the main weir, was 16.7 ft3/s. March to November 2003 is the longest period of 

consecutive months during 2000–2005 when both gaging stations 16726000 and 16732800 and both ditches 

were operational.

b

 Site numbers correspond to those shown on figures 1-B and 1-C.

Table 1–B. Selected natural flow-duration discharges for the 1965–2004 

base period at index gaging-stations operated in the Waipiÿo Valley study 

area, Island of Hawaiÿi, Hawaiÿi.

[ft3/s, cubic feet per second]

Table 1–C. Estimated regulated flow-duration discharges for the 1965–2004 base 

period that reflect diversion practices during the study period (2000–2005) at lowflow partial-record stations in Waipiÿo Valley, Island of Hawaiÿi, Hawaiÿi.

[ft3/s, cubic feet per second]
 Appendix 1. Computation of Low-Flow Statistics for Sites with Historical Data 49

Percentage of time 

indicated discharge 

equaled or exceeded

Discharge (ft3/s)

Kawainui 

Stream 

Site 1a

Alakahi 

Stream 

Site 6a

Koÿiawe 

Stream 

Site 15a

Waimä 

Stream 

Site 18a

Wailoa 

Stream 

Site 24a

99 15 13 6.9 0.64 80

95 18 13 7.3 0.73 86

90 19 14 7.5 0.77 88

80 23 14 7.9 0.89 95

70 26 16 8.3 0.98 100

60 29 17 8.8 1.1 105

50 34 20 9.5 1.2 112

Average standard error (percent) 5.4 2.8 2.5 4.5 1.9

a

 Site numbers correspond to those shown on figures 1-B and 1-C.

Table 1–D. Estimated natural flow-duration discharges for the1965–2004 base 

period at low-flow partial-record stations in Waipiÿo Valley, Island of Hawaiÿi, Hawaiÿi.

[ft3/s, cubic feet per second]

the data for days when low-flow conditions existed and days 

for which concurrent data were available at the Wailoa index 

station (16732200) were selected for analysis. The results of 

the analyses of the data for the nine stations that met the above 

criteria are shown in table 1–E.

Linear correlations were found to exist between the 

substitute index station on Wailoa Stream (16732200) and 

seven of the nine remaining 1901–1902 stations. On the basis 

of these correlations, MOVE.1 techniques were applied to the 

untransformed data to compute flow-duration discharges at 

these 7 stations. The MOVE.1 computations were based on 

computed mean, standard deviation, and correlation coefficient data summarized in table 1-E and previously computed, 

regulated flow-duration statistics for the substitute index 

station (table 1-C). Estimates of regulated flow-duration 

discharges for the seven stations, reflective of the 1965–2004 

base period and diversion practices in place during the study 

period (2000–2005), are summarized in table 1-F. As noted 

above, the accuracy of these results is unknown because they 

are based on estimated flow-duration statistics for the substitute index station.

Table 1–F includes estimated flow-duration discharges for 

stations on Alakahi Stream (16729000) and Koÿiawe Stream 

(16730000 and 16731000), for which correlation coefficients 

are less than the recommended minimum of 0.80. At two of 

the stations (16729000 and 16731000), the correlation coefficients, 0.777 and 0.791 respectively, were close enough to 

the recommended minimum that results were deemed acceptable. At one of the stations, Koÿiawe Stream (16730000), the 

correlation coefficient of 0.737 was well below the recommended minimum, but results for this station were included in 

table 1–F because they were consistent with those computed 

for low-flow partial-record site 15 (table 1-C), which is only a 

short distance downstream.

The application of MOVE.1 methods to compute flowduration statistics shown in table 1–F was based on correlations established between flow at the substitute index 

station on Wailoa Stream and at seven of the nine remaining 

1901–1902 stations. In this case, correlations are based on 

discharge data for a period of natural (unregulated) streamflow. It was assumed in this analysis that correlations established on the basis of natural discharge could also be used to 

estimate flow-duration discharges representative of regulated 

conditions. This is considered a reasonable assumption in that 

all seven 1901–1902 stations for which estimates were made, 

as well as the substitute index station, are downstream from 

the same diversion ditches and should be affected in a similar 

manner. To evaluate this assumption, estimates of regulated 

flow-duration statistics for the 1901–1902 stations, extrapolated to the 1965–2004 base period (table 1-F), are shown in 

figure 1–B along with comparable estimates made for selected 

additional stations in the Waipiÿo Valley study area. The data 

shown in figure 1–B indicate a smooth pattern of increasing 

magnitudes of flow-duration values when moving downstream 

along Waipiÿo Valley tributaries and streams. Estimates made 

for 1901–1902 stations fit seamlessly into this pattern, and the 

results are therefore considered to be reasonable.

No correlation coefficients greater than 0.80 were found 

between flow at the 1901–1902 stations on Waimä Stream 

(16732100 and 16732150) and flow at the substitute index 

station on Wailoa Stream (16732200). As a result, MOVE.1 

estimates of flow-duration discharges were not made for these 

two stations. Over the 101 days with low-flow discharges, the 

mean value was 8.70 ft3/s and the standard deviation was 0.75 
50 Low-Flow Characteristics of Streams Under Natural and Diversion Conditions, Waipiÿo Valley, Island of Hawaiÿi, Hawaiÿi

Gaging stationa Index stationa

Number of 

concurrent 

daily 

discharges

Meanb Standard 

deviationb

Correlation 

coefficient

16721000 Kawainui Stream 49 9.20 4.58 n.a.

16732200 Wailoa Stream 65.8 17.7 0.881

16722000 Kawainui Stream 67 14.5 5.97 n.a.

16732200 Wailoa Stream 75.1 23.9 0.916

16724000 Kawainui Stream 98 24.9 10.1 n.a.

16732200 Wailoa Stream 78.3 26.6 0.936

16728000 Alakahi Stream 67 11.2 2.45 n.a.

16732200 Wailoa Stream 75.8 24.8 0.884

16729000 Alakahi Stream 105 16.6 2.90 n.a.

16732200 Wailoa Stream 76.4 22.3 0.777

16730000 Koÿiawe Stream 61 6.76 1.18 n.a.

16732200 Wailoa Stream 73.1 20.2 0.737

16731000 Koÿiawe Stream 116 11.7 2.53 n.a.

16732200 Wailoa Stream 80.4 26.6 0.791

16732100 Waimä Stream 101 8.70 0.75 n.a.

16732200 Wailoa Stream 77.4 24.9 0.137

16732150 Waimä Stream 118 18.8 1.14 n.a.

16732200 Wailoa Stream 79.0 24.4 0.25

a

 Station numbers correspond to surface-water gaging stations listed in table 1-A and shown in figure 1-A.

b Statistics are based on untransformed values in cubic feet per second.

Percentage of time 

indicated discharge 

equaled or exceeded

Discharge (ft3/s)

Kawainui 

Stream 

16721000a

Kawainui 

Stream 

16722000a

Kawainui 

Stream 

16724000a

Alakahi 

Stream 

16728000a

Alakahi 

Stream 

16729000a

Koÿiawe 

Stream 

16730000a

Koÿiawe 

Stream 

16731000a

99 9.0 12 20 10 15 6.3 10

95 9.8 13 21 10 15 6.5 10

90 10 13 22 11 16 6.6 11

80 11 14 23 11 16 6.8 11

70 12 15 24 11 17 6.9 11

60 13 16 26 12 17 7.2 12

50 14 17 27 12 18 7.4 12

a

 Station numbers correspond to surface-water gaging stations listed in table 1-A and shown in figure 1-A.

Table 1–F. Estimated regulated flow-duration discharges for the 1965–2004 base period that reflect diversion 

practices during the study period (2000–2005) at gaging stations operated between August 1901 and January 

1902 in Waipiÿo Valley, Island of Hawaiÿi, Hawaiÿi.

[ft3/s, cubic feet per second]

Table 1–E. Computed statistics for concurrent daily discharges during periods of low-flow at gaging 

stations operated between August 1901 and January 1902 in Waipiÿo Valley, Island of Hawaiÿi, Hawaiÿi.

[n.a., not applicable]
 Appendix 1. Computation of Low-Flow Statistics for Sites with Historical Data 51

Figure 1–B. Low flow-duration discharges reflective of current (2000–2005) regulated conditions extended over 

the 1965–2004 base period at data collection stations in the Waipiÿo Valley study area, Island of Hawaiÿi, Hawaiÿi.

Kawainui

Str

Alakahi

Str

Lalakea 

Str

Waipi‘oStr

Wailoa

Str

Upper

Ditch

Hämäkua

Waimä

Str

Ko‘iawe

Str

Hämäkua

Ditch

Lower

##

#

#

#

#

#

#

#

#

720000

720300

721000

725000

728000

722000

724000

729000 731000

730000

0.29

4.5

6.5

7.4

15

18

10

12

21

27

0.38

3.1

0.11

1.3

9.8

14

10

12

13

17

12

18 6.8

8.4 0.54

0.72

16

33 68

1 85

6

15

18

24

#

#

# #

#

0 1 2 KILOMETERS

0 1 2 MILES

155°40'

20°06'

20°04'

155°38' 155°36'

Figure 1B. Low flow-duration discharges reflective of current (2000-2005) regulated conditions extended over the 1965-2004 

base period at data collection stations in the Waipiÿo Valley study area, Island of Hawaiÿi, Hawaiÿi.

Base modified from U.S. Geological Survey National

Hydrography Dataset, Transverse Mercator projection,

zone 5, central meridian −153°, North American Datum 1983.

6 #

720000#

13

21

Gaging station and abbreviated number—

complete number is preceded by 16

Low-flow partial-record station and site

 number

Discharge, in cubic feet per second, equaled 

 or exceeded 95 percent of the time

Discharge, in cubic feet per second, equaled 

 or exceeded 50 percent of the time

EXPLANATION

#

"

#

Waimea

155°40' 155°36'

20°04'

20°08'

Waipi‘o 

 Bay

P A C I F I C 

O C E A N

155°40' 155°36'

20°04'

20°08'

Area of map
52 Low-Flow Characteristics of Streams Under Natural and Diversion Conditions, Waipiÿo Valley, Island of Hawaiÿi, Hawaiÿi

ft3/s for Waimä Stream at 790 feet (station 16732100). Over 

the 118 days with low-flow discharge data for Waimä Stream 

at 790 feet (station 16732100), the mean flow was 18.8 ft3/s 

and the standard deviation was 1.14 ft3/s. Low flows at both of 

the Waimä Stream stations are high relative to the size of their 

respective drainage areas (0.51 and 0.77 mi2).

Natural Low-Flow Statistics

Natural low-flow statistics reflective of 1965–2004 base 

period also have been computed for the substitute index station 

on Wailoa Stream (table 1–D, site 24). On the basis of the 

linear correlations between flow at the substitute index station 

and at seven of the 1901–1902 stations (described in the preceding section) and the computed natural low-flow statistics 

(table 1-D, site 24), MOVE.1 methods were used to estimate 

natural flow-duration discharges for these seven stations (table 

1–G). And as noted above, the accuracy of these discharge 

values is unknown because they are based on estimated flowduration statistics for the substitute index station. 

To qualitatively evaluate the reasonableness of the 

estimated natural flow-duration statistics for the 1901–1902 

stations (table 1-G), they are shown in figure 1–C along with 

comparable estimates for selected additional gaging stations 

in the Waipiÿo Valley study area. The consistent downstream 

increase in magnitude of the natural flow-duration values 

(figure 1–C), similar to the pattern for regulated flow (figure 

1–B), indicates the reasonableness of the computed natural 

flow values. 

As noted previously, the period when Tuttle collected 

data, between August 1901 and January 1902, was said to 

have been unusually dry (Mink, 1984, p. 8). This statement 

can now be evaluated in terms of the computed low-flow 

statistics. For example, at the gaging station on Wailoa Stream 

(16732200), Tuttle collected a total of 146 days of data 

(Martin and Pierce, 1913, p. 397). The average discharge over 

the entire 146-day period was determined to be 97.8 ft3/s; 

this value corresponds to a natural flow-duration percentile of 

about 75 percent (table 1–D). Perhaps even more dramatic is 

the fact that average discharge over 131 days when low-flow 

conditions existed was determined to be 82.1 ft3/s; this value 

corresponds to a natural flow-duration percentile between 95 

and 99 percent (table 1–D).

Sites with Miscellaneous Discharge 

Measurements

In addition to the streamflow data collected by Tuttle 

in the early 1900s, miscellaneous discharge measurements 

have been made at several times and locations throughout 

the Waipiÿo Valley study area. These were often just single 

measurements made during periods when diversion practices 

of Upper and Lower Hämäkua Ditches and pumping of water 

from the lower reaches of Waimä Stream were substantially 

different from those during the study period (2000–2005). 

In most cases, actual diversions and their effects on streamflow when the measurements were being made are unknown. 

These data were not used to estimate flow-duration statistics at 

additional locations, but they can be used to provide valuable, 

independent verifications of results already computed.

Stearns and Macdonald (1946, p, 230) noted, during 

a period of dry weather in December 1944, that Kawainui, 

Alakahi, and Koÿiawe Streams gained at total of 6.2, 5.4, and 

6.2 ft3/s, respectively, between Lower Hämäkua Ditch intakes 

and their mouths. These values compare well with differences 

in computed natural flow-duration statistics between stations 

located at the ditch intakes (table 1–D) and estimated natural 

flow-duration statistics at stations located near the mouths of 

the respective streams (table 1–G), at flow percentiles ranging 

from 60 to 80 percent. 

Numerous discharge measurements were made throughout Waipiÿo Valley study area during a severe drought in 

1962–1963 (U.S. Geological Survey, 1963). During this 

period, several measurements were made at the sites of future 

index gaging stations on Kawainui Stream (16720000) and 

Alakahi Stream (16725000). The lowest discharge measured 

during 1962 was 0.146 ft3/s at Kawainui Stream and 0.135 

ft3/s at Alakahi Stream, on November 16, 1962. These measured discharge values correspond to 98 to 99 percentile 

flow-duration discharges at the Kawainui and Alakahi index 

stations (table 1–B). The lowest discharge measured during 1963 was 0.48 ft3

/s at Kawainui Stream and 0.43 ft3/s at 

Alakahi Stream, on December 10, 1963. These measured 

discharges correspond to 90 to 95 percentile flow-duration 

discharges at the Kawainui and Alakahi index stations. On 

December 12, 1962, a discharge measurement of 0.226 ft3/s 

at the site of future index gaging station on Alakahi Stream 

indicated a flow-duration percentile of about 98 percent. On 

December 11, 1962, discharge measurements at the mouths of 

Alakahi and Koÿiawe Streams indicated gains in streamflow 

between Lower Hämäkua Ditch intakes (assuming all flow was 

diverted at the intakes) and their mouths of 3.22 ft3/s and 4.58 

ft3/s, respectively. These values compare well with differences 

in computed 99-percentile, natural flow-duration statistics, 

between stations located at the ditch intakes (table 1–D) and 

near their mouths (table 1–G), of 4 ft3/s for Alakahi Stream 

and 5.1 ft3/s for Koÿiawe Stream.

As noted earlier, no estimates of flow-duration statistics 

were made for the gaging station near the mouth of Waimä 

Stream (16732150). Tuttle’s 1901–1902 data indicated that 

the mean flow at this station, over 118 days with low-flow 

discharges, was 18.8 ft3/s. Mink (1984, p. 10), however, noted 

that Tuttle experienced difficulty making measurements at this 

location and indicated that the measurements underestimated 

true discharge. On December 11, 1962, when the flowduration percentile at Alakahi Stream (16725000) was about 

98 percent (see paragraph above), a discharge of 21.9 ft3/s 

was measured near the mouth of Waimä Stream (U.S. Geological Survey, 1963). On March 9, 1983, when daily mean 

discharges at the index gaging stations on Kawainui Stream 

(16720000) and Alakahi Stream (16725000) of 0.08 ft3/s and 
 Appendix 1. Computation of Low-Flow Statistics for Sites with Historical Data 53

Percentage of time 

indicated discharge 

equaled or exceeded

Discharge (ft3/s)

Kawainui 

Stream 

16721000a

Kawainui 

Stream 

16722000a

Kawainui 

Stream 

16724000a

Alakahi 

Stream 

16728000a

Alakahi 

Stream 

16729000a

Koÿiawe 

Stream 

16730000a

Koÿiawe 

Stream 

16731000a

99 13 16 26 12 17 7.2 12

95 14 17 28 12 18 7.5 12

90 15 18 29 12 18 7.6 12

80 17 19 31 13 19 8.0 13

70 18 21 33 14 20 8.3 14

60 19 22 35 14 20 8.6 14

50 21 24 38 15 21 9.0 15

 a Station numbers correspond to surface-water gaging stations listed in table 1-A and shown in figure 1-A.

Table 1–G. Estimated natural flow-duration discharges for the 1965–2004 base period at gaging stations 

operated between August 1901 and January 1902 in Waipiÿo Valley, Island of Hawaiÿi, Hawaiÿi.

[ft3/s, cubic feet per second]

0.13 ft3/s indicated flow-duration percentiles of greater than 

99 percent (table 1–B), a discharge of 14.6 ft3/s at the mouth 

of Waimä Stream was computed (Chinn and others, 1984) 

(difference between discharge measurements made upstream 

and downstream from the mouth of Waimä Stream on Waipiÿo 

and Wailoa Streams, respectively). Factoring in upstream 

pumping of about 5 million gallons per day (7.7 ft3/s) from 

Waimä Stream that was taking place at this time (Wilcox, 

1996, p. 153), total discharge at the mouth of Waimä Stream 

would be about 22.3 ft3/s (14.6 plus 7.7). The above data, from 

extremely dry periods in 1962 and 1983, indicate that even 

when flow-duration percentiles are in the range of 98 to 99 

percent, discharge at the mouth of Waimä Stream is about 22 

ft3/s. This value is significantly greater than the mean value of 

18.8 ft3/s based on Tuttle’s 1901-02 data and is also consistent 

with the statement that the 1901–1902 data underestimated 

true discharge (Mink, 1984).

In addition to the above historical data, discharge at the 

mouth of Waimä Stream was measured twice during the current study period (2000–2005). On September 21, 2000, at 

the time when a seepage run was conducted (see discussion 

of seepage runs in appendix 2), a discharge of 35 ft3/s was 

measured. On August 23, 2005, a discharge of 33 ft3/s was 

computed (difference between discharge measurements made 

upstream and downstream from the mouth of Waimä Stream 

on Waipiÿo and Wailoa Streams, respectively). At the upstream 

index stations on Kawainui Stream (16720000) and Alakahi 

Stream, (16725000), concurrent daily mean discharges indicated flow-duration percentiles of about 60 to 65 percent and 

65 to 70 percent, respectively (table 1–B). 

The four discharge measurements made near the mouth 

of Waimä Stream (gaging station 16732150) are summarized 

in table 1–H. Only the measurement made on March 9, 1983, 

was significantly affected by upstream diversions (pumping 

from Waimä Stream up to Lower Hämäkua Ditch was taking place at this time). Within Waimä watershed, only small 

amounts of water are diverted by Upper Hämäkua Ditch, no 

water is diverted by Lower Hämäkua Ditch, and moderate 

amounts of groundwater are intercepted by the tunnels of 

Lower Hämäkua Ditch within Waimä watershed, upstream 

from its mouth. The discharge measurement of 35.0 ft3/s, 

made on September 21, 2000, was part of a seepage run in 

Waipiÿo Valley on that day (see appendix 2). On the basis of 

the seepage-run data and concurrent gaging-station data, it 

was determined that natural discharge at the mouth of Waimä 

Stream at that time would have been 37.5 ft3/s. In other words, 

natural discharge was 7.1 percent greater than regulated 

discharge. Although diversion activity within Waimä watershed was probably not exactly the same when each of the four 

discharge measurements were made, it is reasonable to assume 

that overall differences were relatively minor. Therefore, use 

of 7.1 percent as an average adjustment factor to convert the 

four measurements from regulated to natural discharges should 

not lead to significant errors. 

In the main body of this report and to this point in appendix 1, record-extension techniques have successfully been 

applied to low-flow partial-record stations, where the only data 

available were discharge measurements. In all cases, linear 

relations (using either untransformed or log transformed data) 

between discharge measurements and concurrent daily mean 

discharges at index stations were found to exist, and MOVE.1 

record-extension methods were used. It is recommended that 

a minimum of 10 discharge measurements be used when 

applying the MOVE.1 methods for record extension, but only 

4 discharge measurements are available near the mouth of 

Waimä Stream at station 16732150. In the “Record-Extension 

Techniques” section in the main text of this report, an alternative, graphical method for record extension was described. 
54 Low-Flow Characteristics of Streams Under Natural and Diversion Conditions, Waipiÿo Valley, Island of Hawaiÿi, Hawaiÿi

Kawainui

Str

Alakahi

Str

Lalakea 

Str

Waipi‘oStr

Wailoa

Str

Upper

Ditch

Hämäkua

Waimä

Str

Ko‘iawe

Str

Hämäkua

Ditch

Lower

##

#

#

#

#

#

#

#

#

720000

720300

721000

725000

728000

722000

724000

729000 731000

730000

0.29

4.5

7.5

9.0

18

21

12

15

28

38

0.38

3.1

0.11

1.3

14

21

12

15

17

24

13

20

7.3

9.5 0.73

1.2

18

34 86

1 112

6

15

18

24

#

#

# #

#

0 1 2 KILOMETERS

0 1 2 MILES

155°40'

20°06'

20°04'

155°38' 155°36'

Figure 1C. Low flow-duration discharges reflective of natural conditions extended over the 1965-2004 base period at data collection 

stations in the Waipiÿo Valley study area, Island of Hawaiÿi, Hawaiÿi.

6 #

720000#

13

21

Gaging station and abbreviated number—

complete number is preceded by 16

Low-flow partial-record station and site

 number

Discharge, in cubic feet per second, equaled 

 or exceeded 95 percent of the time

Discharge, in cubic feet per second, equaled 

 or exceeded 50 percent of the time

EXPLANATION

Base modified from U.S. Geological Survey National

Hydrography Dataset, Transverse Mercator projection,

zone 5, central meridian −153°, North American Datum 1983.

Waimea

155°40' 155°36'

20°04'

20°08'

Waipi‘o 

 Bay

P A C I F I C 

O C E A N

155°40' 155°36'

20°04'

20°08'

Area of map

Figure 1–C. Low flow-duration discharges reflective of natural conditions extended over the 1965–2004 

base period at data collection stations in the Waipiÿo Valley study area, Island of Hawaiÿi, Hawaiÿi.
 Appendix 1. Computation of Low-Flow Statistics for Sites with Historical Data 55

Date

Measured 

discharge 

Waimä Stream 

16732150 (ft3/s)

Concurrent daily mean discharge (ft3/s)

Kawainui 

Stream 

16720000

Alakahi 

Stream 

16725000

Wailoloa 

Stream 

16758000

Hauani Gulcha

16759000

12/11/1962 21.9 0.23c 0.15c 0.74 1.00

3/9/1983 22.3b 0.08 0.13 1.1 1.03

9/21/2000 35.0 2.3 2.0 3.3 1.46

8/23/2005 33.0 1.8 1.5 3.9 1.67

Percentage of time 

indicated discharge 

equaled or exceeded

Average 

regulated 

flow-duration 

discharge 

(ft3/s) 

Regulated flow-duration discharge at station 16732150 

using indicated index stationd (ft3/s)

Kawainui 

Stream 

16720000

Alakahi 

Stream 

16725000

Waikoloa 

Stream 

16758000

Hauani Gulch 

16759000

99 23 23 22 23 22

95 24 24 24 25 24

90 25 25 25 26 25

80 28 28 28 28 26

70 31 33 32 30 28

60 35 39 37 33 30

50 41 50 44 37 33

Percentage of time 

indicated discharge 

equaled or exceeded

Average 

natural 

flow-duration 

discharge 

(ft3/s) 

Natural flow-duration discharge at station 16732150 

using indicated index statione (ft3/s)

Kawainui 

Stream 

16720000

Alakahi 

Stream 

16725000

Waikoloa 

Stream 

16758000

Hauani Gulch 

16759000

99 24 24 24 24 24

95 26 26 26 27 25

90 27 27 27 28 26

80 30 30 30 30 28

70 33 35 34 32 30

60 37 42 40 35 32

50 44 54 47 39 35

a Concurrent daily mean discharges in Hauani Gulch were all increased by 1.0 ft3

/s.

b

 Increased by 5.0 million gallons per day (7.7 ft3/s) to account for pumping effects.

c

 Discharge measurements.

d

 Estimated using graphical analysis.

e

 Estimated as regulated value increased by 7.1 percent to account for diversions.

Table 1–H. Regulated discharge measurements, concurrent daily mean discharges at long-term 

index stations, and estimated flow-duration discharges for the 1965–2004 base period at surface-water 

gaging station 16732150 on Waimä Stream, Waipiÿo Valley, Island of Hawaiÿi, Hawaiÿi.

[ft3/s, cubic feet per second]
56 Low-Flow Characteristics of Streams Under Natural and Diversion Conditions, Waipiÿo Valley, Island of Hawaiÿi, Hawaiÿi

Admittedly, record extension using graphical relations 

based on only four discharge measurements is less than ideal. 

In this instance, however, several factors make this a reasonable 

alternative to consider for the Waimä Stream station. As noted 

above, the four available discharge measurements were made at 

times when concurrent daily mean discharges at index stations 

in the Waipiÿo Valley study area were equal to flow-duration 

percentiles between 55 and 99 percent. These flow-duration 

percentiles effectively span the range of low-flow conditions 

of interest in this study. Experience with low-flow partialrecord stations in Waipiÿo Valley indicate that it is reasonable 

to assume linear relations between discharge measurements 

on Waimä Stream (gaging station 16732150) and available 

index stations. Finally, straight lines closely fit all four discharge measurements when plotted against concurrent daily 

mean discharges at each of the four available index stations 

when untransformed data were used. Concurrent daily mean 

discharges for Hauani Gulch (16759000) were all increased 

by 1.0 ft3/s before the analysis because the dischage for one 

of the days, December 11, 1962, was 0.0 ft3/s and use of the 

adjustment provided a better fit to the Waimä Stream data. On 

the basis of these facts, graphical record-extension techniques 

were used to estimate flow-duration statistics of interest for 

Waimä Stream using data from each of the four index stations. 

As can be seen from the results, summarized in table 1–H, 

there is very close agreement among the four independent 

computations for each of the flow-duration percentiles, with the 

possible exception of those for the 50-percentile flow-duration 

discharges. These consistent results provide an extra measure of 

confidence in the estimates and indicate that use of an average 

of the four independent computations for each flow-duration 

percentile would be reasonable. To account for the effects of 

upstream diversions, regulated flow-duration discharges were 

multiplied by a factor of 1.071 (based on computed difference 

between regulated and natural discharge during the September 

2000 seepage run) to estimate natural flow-duration discharges. 

It should be kept in mind, however, that the flow-duration discharges shown in table 1-H are based on the application of less 

than ideal methods and therefore should be treated as estimates 

with unknown levels of accuracy. 
 Appendix 2. Computation of Low-Flow Statistics for Ungaged Sites 57

Appendix 2. Computation of Low-Flow Statistics for Ungaged Sites 

Combining Flow-Duration Curves

At several locations in the Waipiÿo Valley study area 

where two streams join to form a third, larger stream, discharge data have been collected on only two of the three. 

An example of this situation is on Kawainui Stream, where 

gaging stations 16720000 on Kawainui Stream and 16720300 

on Kawaiki Stream have been operated just upstream from 

their confluence, yet no data have been collected immediately 

downstream from the confluence. Flow-duration statistics 

can be computed directly for the two upstream gages using 

available data, but the question becomes how best to compute flow-duration statistics for the combined streams. In the 

case in which natural flow-duration statistics are desired, it is 

assumed that no diversion by Upper Hämäkua Ditch is taking 

place. The first step was to add the daily mean discharges for 

each day of concurrent record from the two upstream gaging 

stations. The next step was to compute natural flow-duration 

statistics on the basis of the combined daily mean discharges, 

which provides theoretically correct values (table 2–A) (see 

section in report titled “Data and Methods Used to Estimate 

Low-Flow Statistics”). 

Determining flow-duration statistics for a point downstream from the confluence of Kawainui and Kawaiki Streams 

poses a complicating factor in that Upper Hämäkua Ditch originates in this area, and a significant amount of the flow of both 

streams is diverted by the ditch just above their confluence. 

To compute regulated flow-duration statistics for the combined flow of the two streams that reflects diversion by Upper 

Hämäkua Ditch, data from gaging station 16720500 (on the 

ditch) must be incorporated into the analysis. Gaging station 

16720500 measures the total amount of flow diverted from 

Kawainui and Kawaiki Streams. In this situation, the first step 

was to add daily mean discharges for each day of concurrent 

record from the two upstream gaging stations (16720000 and 

16720300) and then subtract the concurrent daily mean flow 

that was diverted, as measured at gaging station 16720500. As 

above, the next step was to compute regulated flow-duration 

statistics using the combined daily mean discharges. Regulated 

flow-duration discharges for a location on Kawainui Stream 

just downstream from the point where Kawainui and Kawaiki 

Streams join and where diversion by Upper Hämäkua Ditch 

takes place, based on combination of concurrent daily mean 

discharges, have been computed and are shown in table 2–B.

A more common situation at locations where streams join 

or where streams are subjected to diversions is that gaging stations both above and below the confluence and (or) the diversion point that have concurrent daily mean discharge data are 

unavailable. In such cases, an alternative technique for computing flow-duration statistics is to simply combine estimated 

flow-duration discharges of the two streams for the common percentiles of interest. An example of results based on 

combining flow-duration discharges directly for two streams is 

shown in table 2–A. In this example it was assumed that gaging station data were not available for either Kawainui Stream 

or Kawaiki Stream but that flow-duration discharges were 

available. This would be the case if, for example, low-flow 

partial-record stations had been operated at both locations. As 

can be seen from data summarized in table 2–A, flow-duration 

discharges based on direct combination of discharges for common percentiles gives results that are virtually the same as the 

theoretically correct results based on combination of concurrent daily mean discharges. Only for extreme low flows, such 

as the 99-percentile flow, are errors greater than 10 percent, 

and in this case the absolute error is only 0.04 ft3/s. Direct 

addition of concurrent flow-duration discharges for streams 

that are hydrologically similar should produce statistics for the 

combined flow that have only minimal errors.

The combination of estimated, common flow-duration 

discharges at locations where streams and diversions interact is 

a more complex problem. Regulation associated with diversions often means that flow-duration conditions in effect on the 

stream might not be the same as those in effect at the same time 

on the diversion ditch; in other words, they are not hydrologically similar. For example, 50-percentile flow conditions might 

exist in the stream during a period when the ditch intakes are 

plugged, so that low-flow (99-percentile) conditions exist in 

the ditch. An example of results based on combining common 

flow-duration discharges directly for two streams and a ditch 

is shown in table 2–B. In this example, it was assumed that 

concurrent daily mean discharge data were not available for 

Kawainui or Kawaiki Streams and for Upper Hämäkua Ditch, 

although flow-duration discharges had been estimated. As can 

be seen from the data summarized in the table, flow-duration 

discharges based on direct combination of common percentiles 

gives results that often differ by large percentages and by large 

absolute amounts from the theoretically correct results—those 

based on combination of concurrent daily mean discharges. 

Direct addition of common flow-duration discharges for 

streams and ditches that are hydrologically different should be 

used with caution; results could have large errors.

Use of Seepage Run Data

In a seepage run, discharge measurements are made at 

several locations along a reach of stream and(or) ditch. Seepage runs are most commonly made during periods of low flow, 

when discharge conditions at any given location are relatively 

constant. The total elapsed time between the first and last 

discharge measurements in a seepage run is minimized to 

further reduce the effects of flow variability (Fontaine, 2003). 

Seepage-run results can be used to determine which stream 

or ditch reaches are gaining or losing water and where these 
58 Low-Flow Characteristics of Streams Under Natural and Diversion Conditions, Waipiÿo Valley, Island of Hawaiÿi, Hawaiÿi

Percentage of time 

indicated discharge 

equaled or exceeded

Discharge (ft3/s) Percent error 

using 

combination of 

current

 percentiles

Kawainui 

Stream 

16720000

Kawaiki 

Stream 

16720300

Based on 

combination 

of concurrent 

percentiles

Based on 

combination 

of concurrent 

daily flows

99 0.09 0.02 0.11 0.15 -26.7

95 0.27 0.10 0.37 0.40 -7.5

90 0.51 0.17 0.68 0.71 -4.2

80 1.1 0.29 1.4 1.4 0.0

70 1.8 0.48 2.3 2.3 0.0

60 2.8 0.77 3.6 3.7 -2.7

50 4.6 1.3 5.9 6.0 -1.7

40 7.6 2.1 9.7 9.7 0.0

30 13 3.3 16 17 -5.9

20 23 5.3 28 28 0.0

10 42 9.5 52 51 2.0

5 63 15 78 78 0.0

1 138 32 170 169 0.6

Percentage of time 

indicated discharge 

equaled or exceeded

Discharge (ft3/s) Percent 

error using 

combination 

of current 

percentiles

Kawainui 

Stream 

16720000

Kawaiki 

Stream 

16720300

Upper 

Hämäkua 

Ditch 

16720500

Based on 

combination 

of concurrent 

percentiles

Based on 

combination 

of concurrent 

daily flows

99 0.09 0.02 0.00 0.11 0.00 N.A.

95 0.27 0.10 0.20 0.17 0.00 N.A.

90 0.51 0.17 0.56 0.12 0.00 N.A.

80 1.1 0.29 1.1 0.29 0.00 N.A.

70 1.8 0.48 1.9 0.38 0.00 N.A.

60 2.8 0.77 3.2 0.37 0.13 185

50 4.6 1.3 5.0 0.90 0.46 96.1

40 7.6 2.1 7.5 2.2 1.6 35.0

30 13 3.3 10 6.3 6.1 2.9

20 23 5.3 13 15 16 -6.2

10 42 9.5 15 36 37 -2.7

5 63 15 17 61 63 -3.2

1 138 32 25 145 155 -6.4

Table 2–A. Selected natural flow-duration discharges for the concurrent period of record 1970–

1999 at surface-water gaging stations 16720000 on Kawainui Stream and 16720300 on Kawaiki 

Stream, Waipiÿo Valley area, Island of Hawaiÿi, Hawaiÿi.

[ft3/s, cubic feet per second]

Table 2–B. Selected regulated flow-duration discharges for the concurrent period of record 

1970–1999 at gaging stations 16720000 on Kawainui Stream, 16720300 on Kawaiki Stream, 

and 16720500 on Upper Hämäkua Ditch, Waipiÿo Valley area, Island of Hawaiÿi, Hawaiÿi.

[ft3/s, cubic feet per second; N.A., not applicable]
 Appendix 2. Computation of Low-Flow Statistics for Ungaged Sites 59

changes take place. Seepage runs also provide valuable insight 

into how low-flow and therefore low-flow duration discharges 

vary along stream reaches. Seepage runs along ditches provide 

insight into how diversion systems operate. On September 

20–21, 2000, a seepage run was conducted along major streams 

in Waipiÿo Valley, starting upstream from Lower Hämäkua Ditch 

intakes and extending downstream to Wailoa Stream at 190 feet 

elevation. At the same time, a seepage run was conducted along 

Lower Hämäkua Ditch over its entire reach in Waipiÿo Valley. A 

second seepage run was begun on September 26, 2001, but rapidly increasing streamflow conditions in Waipiÿo Valley near the 

end of that day forced cancellation of data collection. Measured 

and computed discharges during the seepage runs along streams 

in Waipiÿo Valley and Lower Hämäkua Ditch represent regulated 

conditions; the results of the measurements are presented in table 

2–C and shown in figures 2–A and 2–B.

During the September 20–21, 2000, seepage run along 

Lower Hämäkua Ditch, only Kawainui and Koÿiawe Stream 

intakes were actually withdrawing water. There was a net loss 

of water out of Lower Hämäkua Ditch at Alakahi Stream intake, 

and no diversion took place at the Waimä Stream intake. There 

was a net loss of water out of Lower Hämäkua Ditch in the reach 

between Kawainui and Alakahi Stream intakes and no changes 

in discharge in the reaches between Akakahi and Koÿiawe 

Stream intakes and between Koÿiawe and Waimä Stream intakes. 

Between Waimä Stream intake and the main weir (where the 

ditch exits Waipiÿo Valley), there was a net inflow of 4.0 ft3/s of 

groundwater directly into the tunnels of Lower Hämäkua Ditch 

(most of Lower Hämäkua Ditch in Waipiÿo Valley consists of 

tunnels). During the September 21–21, 2000, seepage run, leakage of 5.0 ft3

/s from Lower Hämäkua Ditch was taking place, at 

Hakalaoa waterfall between sites 25 and 26 (see table 2–C); this 

leakage has since been repaired.

In the section “Low-Flow Statistics Representative of 

Natural Conditions” in the main body of this report, computations were made under the assumption that flow in downstream 

tributaries was changed by the same amount that was removed 

or released at upstream points of diversion. This assumpton 

was based, in part, on the fact that downstream tributaries were 

gaining flow. Review of the seepage run results shown in figure 

2–A indicates that flow did in fact increase along stream reaches 

where ditch diversion intakes were not located. Techniques 

outlined in appendix 3, “Accounting for Effects of Diversions 

at Upper and Lower Hämäkua Ditches,” and results from the 

seepage run along Lower Hämäkua Ditch were used to convert 

measured discharges along streams in Waipiÿo Valley to reflect 

what they would have been under natural conditions during the 

time of the September 20–21, 2000, seepage run. Adjustments 

associated with regulation by the Upper Hämäkua Ditch were 

based on average diversions for the 2-day period over which the 

seepage run was conducted. These estimated natural discharges 

are shown in figure 2–C.

During the September 20–21, 2000, seepage run, there 

were significant gains in natural discharges between locations 

where tributary streams first enter Waipiÿo Valley and Lower 

Hämäkua Ditch intakes. Waimä Stream was a notable exception 

to this pattern. In general, the rates at which tributary streams 

gained water decreased downstream from the intakes of Lower 

Hämäkua Ditch. However, Waimä Stream was again a notable 

exception, as natural discharge increased from 1.0 to 37.5 ft3/s in 

the reach between Lower Hämäkua Ditch intake and the stream 

mouth. Estimated natural discharges at index and low-flow partial-record stations at the time of the seepage run were compared 

to computed flow-duration discharges for those stations (tables 7 

and 13 in the main body of this report). On average, the natural 

discharges were between the 60 and 50 flow-duration percentiles. As described in appendix 1, discharge data were collected 

at 13 stations between August 1901 and January 1902, when 

no regulation or diversion of the streams was occurring (Martin 

and Pierce, 1913, p. 397). Concurrent discharge data at these 13 

stations can be used to approximate additional seepage runs. On 

October 29, November 7, and December 6, 1901, streamflow 

conditions were similar to those during the September 20–21, 

2000, seepage run. Concurrent discharge values for those three 

dates in 1901, along with regulated and natural discharges during 

the September 21–21, 2000, seepage run along the main streams 

in Waipiÿo Valley (Kawainui, Waipiÿo, and Wailoa Streams), 

were plotted against altitude of the location where the data were 

collected (figure 2–D). The data in figure 2–D highlight the significant differences between regulated and natural discharges and 

the close correspondence between natural discharge data in 1901 

and estimated natural discharge data in 2000.

Seepage-run results can be used as an aid in extrapolating 

flow-duration discharges to locations where data are lacking. For 

example, during the September 20–21, 2000, seepage run, natural discharge was estimated to be 55.3 ft3

/s at site 10 and 58.6 

ft3/s at site 11 (fig. 2–C). In other words, discharge in this reach 

of Waipiÿo Stream increased by a factor of 1.06 (58.6/55.3). 

The 50-percentile discharge at site 10 is unknown, but using the 

technique of combining flow-duration curves (discussed above), 

50-percentile discharges at station 16724000 (38 ft3/s) and at 

station 16729000 (21 ft3/s) can be combined to estimate a natural 

50-percentile discharge of 59 ft3/s at site 10. Multiplying the estimated 50-percentile discharge of 59 ft3

/s at site 10 by 1.06 (based 

on natural seepage run data) yields an estimated 50-percentile 

discharge of about 63 ft3/s at site 11 (Waipiÿo Stream upstream 

from the mouth of Koÿiawe Stream). Use of seepage run results 

to extrapolate flow-duration discharges will yield the best results 

when adjustment factors are not significantly different from 1.0 

and when they are applied to flow-duration discharges similar 

to those in existence at the time of the September 20–21, 2000, 

seepage run.

Regional Analysis

A commonly applied form of regional analysis is based 

on the concept that multivariate-regression equations can 

be developed to relate computed low-flow statistics to basin 

characteristics at gaged sites (Gingerich, 2005). At ungaged 

sites, these basin characteristics, such as drainage area, can be 

readily measured and then applied in the regression equations to estimate low-flow statistics. A complete regional 
60 Low-Flow Characteristics of Streams Under Natural and Diversion Conditions, Waipiÿo Valley, Island of Hawaiÿi, Hawaiÿi

Kawainui

Str

Alakahi

Str

Lalakea 

Str

Waipi‘o Str

Wailoa

Str

Upper

Ditch

Hämäkua

Waimä

Str

Ko‘iawe

Str

Hämäkua

Ditch

Lower

#

#

"

"

"

720000

720500

724800

725000

726000

43.3

78.3

35.0

0.6

0.61

6.6

7.53

2.2

6.44

41.2

34.8

31.5

19.7

11.8

4.7

26.5

17.4 19.1

2.5

3.2

3.4 4.4

26.5

1

2

5

6

8

9 10

11 12

13

15

16

18

19

22

23

24

# #

#

#

#

## ##

#

#

#

#

#

#

#

#

0 1 2 KILOMETERS

0 1 2 MILES

155°40'

20°06'

20°04'

155°38' 155°36'

Figure 2A. Measured and computed regulated discharges at the time of the September 20–21, 2000, seepage run along streams

 in the Waipiÿo Valley study area, Island of Hawaiÿi, Hawaiÿi.

726000 "

22 #

6 #

720000 # Stream-gaging station and abbreviated number—

complete number is preceded by 16

Ditch-gaging station and abbreviated number—

complete number is preceded by 16

Seepage-run site and number

Seepage-run site and low-flow partial-record

 station and station number 

EXPLANATION

Discharge, in cubic feet per second

Base modified from U.S. Geological Survey National

Hydrography Dataset, Transverse Mercator projection,

zone 5, central meridian −153°, North American Datum 1983.

#

"

#

Waimea

155°40' 155°36'

20°04'

20°08'

Waipi‘o 

 Bay

P A C I F I C 

 O C E A N

155°40' 155°36'

20°04'

20°08'

Area of map

Figure 2–A. Measured and computed regulated discharges at the time of the September 20–21, 2000, seepage 

run along streams in the Waipiÿo Valley study area, Island of Hawaiÿi, Hawaiÿi.
 Appendix 2. Computation of Low-Flow Statistics for Ungaged Sites 61

Kawainui

Str

Alakahi

Str

Lalakea 

Str

Waipi‘oStr

Wailoa

Str

Upper

Ditch

Hämäkua

Hämäkua

Ditch

Lower

19.8

21.8

18.1

23.4

18.1

23.4

25.5

26.8

21.8

22.4

21.8

3

4

7 14

17 20

21

25

26

27

#

#

#

#

# #

#

#

#

#

0 1 2 KILOMETERS

0 1 2 MILES

155°40' 155°38'

20°06'

20°04'

155°36'

Figure 2B. Measured and computed discharges at the time of the September 20–21, 2000, seepage run along Lower Hämäkua

Ditch, Island of Hawaiÿi, Hawaiÿi.

22 #Seepage-run site and number

EXPLANATION

Discharge, in cubic feet per second

Base modified from U.S. Geological Survey National

Hydrography Dataset, Transverse Mercator projection,

zone 5, central meridian −153°, North American Datum 1983.

##

Waimea

155°40' 155°36'

20°04'

20°08'

Waipi‘o 

 Bay

P A C I F I C 

 O C E A N

155°40' 155°36'

20°04'

20°08'

Area of map

Figure 2–B. Measured and computed discharges at the time of the September 20–21, 2000, seepage run 

along Lower Hämäkua Ditch, Island of Hawaiÿi, Hawaiÿi.
62 Low-Flow Characteristics of Streams Under Natural and Diversion Conditions, Waipiÿo Valley, Island of Hawaiÿi, Hawaiÿi

Site numbera Stream or ditch Altitude (feet) Discharge (ft3/s)

Sept. 20-21, 2000 Sept. 26, 2001

1 Kawainui Stream 1,070 26.5 41.5

2 Kawainui Stream 1,037 4.7b 26.1b

8 Kawainui Stream 775 11.8 ---

6 Alakahi Stream 1,030 17.4c ---

5 Alakahi Stream 1,000 19.1 ---

9 Alakahi Stream 730 19.7d ---

10 Waipiÿo Stream 720 31.5 ---

11 Waipiÿo Stream 595 34.8 ---

12 Waipiÿo Stream 580 41.2e ---

22 Waipiÿo Stream 400 43.3 ---

15 Koÿiawe Stream 1,020 7.53 10.5

16 Koÿiawe Stream 980 2.2f 1.8f

13 Koÿiawe Stream 610 6.44 ---

18 Waimä Stream 1,040 0.61 0.86

19 Waimä Stream 970 0.6g 0.9g

23 Waimä Stream 385 35.0 ---

24 Wailoa Stream 190 78.3 103

3 Lower Hämäkua Ditch 1,037 21.8 15.4

4 Lower Hämäkua Ditch 1,030 19.8 13.0

7 Lower Hämäkua Ditch 1,030 18.1 11.0

14 Lower Hämäkua Ditch 1,000 18.1 11.9

17 Lower Hämäkua Ditch 1,000 23.4 20.6

20 Lower Hämäkua Ditch 980 23.4 22.1

21 Lower Hämäkua Ditch 975 25.5 20.0

25 Lower Hämäkua Ditch 970 26.8 22.2

26 Lower Hämäkua Ditch 970 21.8h 20.4

27 Lower Hämäkua Ditch 965 22.4 22.2

a Site numbers correspond to those listed in table 2 and shown in figure 4 in main body of report.

b Computed by mass balance as Site 2 = Site 1 - Site 3.

c Computed by mass balance as Site 6 = Site 5 + (Site 7 - Site 4).

d Computed by mass balance as Site 9 = Site 10 - Site 8.

e Computed by mass balance as Site 12 = Site 11 + Site 13.

f

 Computed by mass balance as Site 16 = Site 15 - (Site 17 - Site 14).

g

 Estimated as about the same as Site 18, no diversion of water at the ditch intake.

h

 Average of two discharge measurements made at the site.

Table 2–C. Discharge measurements at seepage-run sites in Waipiÿo Valley in September 

2000 and September 2001, Island of Hawaiÿi, Hawaiÿi.

[ft3/s, cubic feet per second; ---, no data available]
 Appendix 2. Computation of Low-Flow Statistics for Ungaged Sites 63

Kawainui

Str

Alakahi

Str

Lalakea 

Str

Waipi‘oStr

Wailoa

Str

Upper

Ditch

Hämäkua

Waimä

Str

Ko‘iawe

Str

Hamakua

Ditch

Lower

Hämäkua

Ditch

Lower

##

#

720000

720300

725000

72.9

110

37.5

1.0

1.0

7.98

7.98

12.2

70.8

58.6

55.3

18.9

36.4

30.3

30.3

19.3 19.3

2.5

1.0

3.4

58.6

1

2

5

6

8

9 10

11 12

13

15

16

18

19

22

23

24

# #

#

#

#

## ##

#

#

#

#

#

#

#

#

0 1 2 KILOMETERS

0 1 2 MILES

155°40' 155°38'

20°06'

20°04'

155°36'

Figure 2C. Computed natural discharges at the time of the September 20–21, 2000, seepage run along streams in the Waipiÿo

 Valley study area, Island of Hawaiÿi, Hawaiÿi.

22 #

6 #

720000 # Gaging station and abbreviated number—

 complete number is preceded by 16

Seepage-run site and number

Seepage-run site and low-flow partial-record

 station and station number

EXPLANATION

Discharge, in cubic feet per second

Base modified from U.S. Geological Survey National

Hydrography Dataset, Transverse Mercator projection,

zone 5, central meridian −153°, North American Datum 1983.

Waimea

155°40' 155°36'

20°04'

20°08'

Waipio 

 Bay

P A C I F I C 

 O C E A N

155°40' 155°36'

20°04'

20°08'

Area of map

Figure 2–C. Computed natural discharges at the time of the September 20–21, 2000, seepage run along 

streams in the Waipiÿo Valley study area, Island of Hawaiÿi, Hawaiÿi.
0 20 40 60 80 100 120 140 2,500 2,000 1,500 1,000 500 

Discharge, in cubic feet per second 

Altitude, in feet 

Figure 2D. Discharge in Kawainui, Waipi‘o, and Wailoa Streams during the September 20–21, 2000 seepage run and on selected day

of Hawai‘i, Hawai‘i. 

Sept. 20-21, 2000 regulated discharge Sept. 20-21, 2000 natural discharge Oct. 29, 1901 Nov. 7, 1901 Dec. 6, 1901 

Alakahi Stream inflow

Ko‘iawe Stream inflow

Kawainui Lower Hämäkua Ditch intake

Waimä Stream inflow 

EXPLANATION

to the onset of flow diversions, Waipi‘o Valley, Island 

Figure 2–D. Discharge in Kawainui, Waipiÿo, and Wailoa Streams during the September 20–21, 2000, seepage run and oprior to the onset of flow diversions, Waipiÿo Valley study area, Island of Hawaiÿi, Hawaiÿi.
 Appendix 2. Computation of Low-Flow Statistics for Ungaged Sites 65

multivariate-regression analysis of low flow is well beyond the 

scope of this report. However, to demonstrate how such analyses can be applied, a simple regression analysis was conducted 

using only drainage area as a predictive basin characteristic.

Drainage area and natural 50- and 95-percentile flowduration discharges for the 1965–2004 base period for all 

sites in Waipiÿo Valley study area where the data are available 

are shown in table 2-D; regulated flow-duration discharges 

are shown in table 2–E. Data in these two tables were used to 

quantify linear relations between natural and regulated 50-percentile flow-duration discharges and drainage area shown in 

figures 2–E and 2–F. It is important to note that data for gaging 

stations along the lower reaches of Waimä Stream, downstream 

from Lower Hämäkua Ditch, were not included in this analysis. Low-flow duration discharges (per unit of drainage area) 

of Waimä Stream, downstream from Lower Hämäkua Ditch, 

are significantly higher than those at other gaging stations in 

Waipiÿo Valley. The degree by which flow-duration discharges 

for Waimä Stream, at gaging station 16732150, differ hydrologically is clearly illustrated by the plotting position of estimated 

50-percentile discharges for this gaging station in figures 2–E 

and 2–F. As a result, the simplified regional analysis based on 

drainage area, which was developed in this section, should not 

be applied to Waimä Stream downstream from Lower Hämäkua 

Ditch. The confluence of Waimä and Waipiÿo Streams is also a 

good example of a location where two streams are not hydrologically similar, and therefore combining flow-duration curves 

to determine low-flow statistics should be avoided. A detailed 

analysis of the accuracy of resultant regression equations based 

on drainage area shown in figures 2–E and 2–F is beyond the 

scope of this report. However, a similar drainage-area-based 

regression equation for 50-percentile flow-duration discharge 

developed for the islands of Oÿahu, Molokaÿi, and Hawaiÿi had 

a standard error of prediction of 41.4 percent (Fontaine and others, 1992).

Similar drainage-area based regression equations could 

be developed for other flow-duration discharges, such as the 

95-percentile discharge data shown in tables 2–D and 2–E. In a 

detailed regional analysis of flow-duration discharges in northeast Maui, however, Gingerich (2005) showed that regression 

equations developed for lower flow-duration discharges, such as 

the 95-percentile, have substantially higher errors of prediction. 

An alternative approach is to compute ratios of flow-duration 

discharge of interest to the 50-percentile discharges. This ratio 

could be then used to adjust the computed 50-percentile discharge determined by using the regression equation to estimate 

the flow-duration discharge of interest. In tables 2–D and 2–E, 

ratios of natural and regulated 95-percentile to 50-percentile 

discharges are summarized. 

Selection of the appropriate ratio to use when computing 

alternative flow-duration discharges, such as the 95-percentile 

value, can be based on the known ratio computed at the nearest 

hydrologically similar gaging station. An alternative method 

would be to use average values for the ratios shown in tables 

2–D and 2–E. Ratios of 95-percentile to 50-percentile flowduration discharges at gaging stations in the Waipiÿo Valley 

study area exhibit distinct patterns. Gaging stations upstream 

from Upper Hämäkua Ditch have average ratios for natural 

discharges (0.09; table 2–D) that are much smaller than those 

for gaging stations in Waipiÿo Valley, downstream from Upper 

Hämäkua Ditch (0.73). 

The ratio of 95-percentile to 50-percentile flow-duration 

discharges also can be used as an index of low-flow variability 

(Oki and others, 2006, p. 15). Ratios closer to zero are indicative 

of more variable and less sustained low flows. Ratios closer to 

one are indicative of less variable and more sustained low flows. 

The relatively lower average ratios for gaging stations upstream 

from Upper Hämäkua Ditch reflect the fact that streams there 

are in contact with Häwï Volcanics, which carry lesser quantities 

of water than the underlying Pololü Basalt. The higher average 

ratios for gaging stations in Waipiÿo Valley reflect the fact that 

streams there are in contact with the Pololü Basalt and have 

also eroded down into dike-impounded compartments that hold 

significant quantities of water.

In most cases, the ratios of 95-percentile to 50-percentile 

flow-duration discharges under 2000–2005 regulated conditions 

are greater than those associated with natural discharge conditions at the same gaging station. The average ratio for gaging 

stations in Waipiÿo Valley, under 2000–2005 regulated discharge 

conditions, is 0.76; under natural discharge conditions the ratio 

is 0.73. This difference indicates that 2000–2005 regulated lowflows, although they are smaller than natural flows, are slightly 

less variable at gaging stations in Waipiÿo Valley.

Application of the simplified regional analysis of low-flow 

characteristics outlined above can be demonstrated in a simple 

example. Assume that 50- and 95-percentile flow-duration 

discharges for natural conditions are desired for an ungaged 

site in Waipiÿo Valley. For the purposes of this example, assume 

that the drainage area at the ungaged site was determined to be 

1.0 square mile. Natural 50-percentile flow-duration discharge 

can be computed using the formula shown in figure 2–E as 

4.1578(drainage area)1.3026 , or 4.1578(1.0) 1.3026, which equals

4.2 ft3/s. The average ratio of natural 95-percentile to 50-percentile flow-duration discharges in Waipiÿo Valley is 0.73 (table 

2–D), and the 95-percentile flow-duration discharge can be 

computed as 0.73(4.2), or 3.1 ft3/s. Note that if this ungaged site 

was upstream from Upper Hämäkua Ditch, the average ratio of 

natural 95-percentile to 50-percentile flow-duration discharges 

would be 0.09 and the 95-percentile flow-duration discharge 

would be computed as 0.09(4.2), or 0.38 ft3/s.

When estimating flow-duration discharges at ungaged sites 

in Waipiÿo Valley study area, the most accurate results will be 

obtained at locations where direct combinations of computed 

flow-duration discharges from gaging stations are possible. 

Where ungaged sites of interest are only short distances from 

gaging stations, estimates based on extrapolations using linear 

interpolations or adjustments based on seepage-run data will 

provide results with slightly lower accuracies. The least accurate 

estimates will be those made using the simplified, one-parameter (drainage area) regional analysis method outlined above. If 

multivariate regression equations had been developed, the predictive accuracy of the regional methods would be improved.
66 Low-Flow Characteristics of Streams Under Natural and Diversion Conditions, Waipiÿo Valley, Island of Hawaiÿi, Hawaiÿi

Gaging-station 

or site numbera

Drainage area 

(mi2)

50-percentile 

discharge 

(ft3/s)

95-percentile 

discharge 

(ft3/s)

Ratio 

(Q95/Q50)

Gaging stations or sites upstream from Upper Hämäkua Ditch

16720000 1.58 4.5 0.29 0.06

16720300 0.45 1.3 0.11 0.08

16725000 0.87 3.1 0.38 0.12

Average 0.09

Gaging stations or sites downstream from Upper Hämäkua Ditch

1 5.55 34 18 0.53

6 2.45 20 13 0.65

15 1.85 9.5 7.3 0.77

18 0.49 1.2 0.73 0.61

16721000 3.48 21 14 0.67

16722000 4.43 24 17 0.71

16724000 6.00 38 28 0.74

16728000 1.49 15 12 0.80

16729000 3.14 21 18 0.86

16730000 1.65 9.0 7.5 0.83

16731000 2.23 15 12 0.80

16732150 0.77 44 26 0.59b

16732200 14.3 112 86 0.77

Average 0.73

a

 Site numbers correspond to those listed in table 2 and shown in figure 4 in main body of report.

b

 Not used when computing average.

Table 2–D. Drainage area and selected natural flow-duration discharges for the 

1965–2004 base period at gaging stations and data-collection sites in the Waipiÿo 

Valley study area, Island of Hawaiÿi, Hawaiÿi.

[mi2, square miles; ft3/s, cubic feet per second; Q95, 95-percentile discharge; Q50, 50-percentile discharge]
 Appendix 2. Computation of Low-Flow Statistics for Ungaged Sites 67

Gaging-station or 

site numbera

Drainage area 

(mi2)

50-percentile 

dischargec 

(ft3/s)

95-percentile 

dischargec

(ft3/s)

Ratio 

(Q95/Q50)

Gaging stations or sites downstream from Upper Hämäkua Ditch

1 5.55 33 16 0.48

6 2.45 18 12 0.67

15 1.85 8.4 6.8 0.81

18 0.49 0.72 0.54 0.75

16721000 3.48 14 9.8 0.70

16722000 4.43 17 13 0.76

16724000 6.00 27 21 0.78

16728000 1.49 12 10 0.83

16729000 3.14 18 15 0.83

16730000 1.65 7.4 6.5 0.88

16731000 2.23 12 10 0.83

16732150 0.77 41 24 0.59b

16732200 14.30 85 68 0.80

Average 0.76

a

 Site numbers correspond to those listed in table 2 and shown in figure 4 in main body of report.

b

 Not used when computing average.

c

 Reflective of 2000–2005 diversion conditions.

Table 2–E. Drainage area and selected regulated flow-duration discharges for 

the1965–2004 base period at gaging stations and data-collection sites in the 

Waipiÿo Valley study area, Island of Hawaiÿi, Hawaiÿi.

[mi2, square miles; ft3/s, cubic feet per second; Q95, 95-percentile discharge; Q50, 50-percentile discharge]
0.1 1 10 100 1,000 0.1 1 10 

50-percentile flow-duration discharge, in cubic feet per second Natural Q50 = 4.1578(drainage area)1.3

R2=0.94

Waimä Stream

station 16732150 

Figure 2E. Natural 50-percentile flow-duration discharges, for the 1965–2004 base period, versus drainage area in the Wai

Island of Hawaiÿi, Hawaiÿi 

Drainage area, in square miles 

Figure 2–E. Natural 50-percentile flow-duration discharges, for the 1965–2004 base period, versus drainage area in the WIsland of Hawaiÿi, Hawaiÿi.
0.1 1 

10 

100 

1,000 

0.1 1 10 

Waimä Stream 

 station 16732150 

Figure 2F. Regulated 50-percentile flow-duration discharges, for the 1965–2004 base period, versus drainage area in the WaIsland of Hawaiÿi, Hawaiÿi. 

Drainage area, in square miles

50-percentile flow-duration discharge in cubic feet per second Regulated Q50 = 3.5118 (drainage are

R2=0.9216

Figure 2–F. Regulated 50-percentile flow-duration discharges, for the 1965–2004 base period, versus drainage area in tarea, Island of Hawaiÿi, Hawaiÿi.
70 Low-Flow Characteristics of Streams Under Natural and Diversion Conditions, Waipiÿo Valley, Island of Hawaiÿi, Hawaiÿi

Appendix 3. Accounting for Effects of Diversions at Upper and 

Lower Hämäkua Ditches

Effects of Diversions at Upper Hämäkua 

Ditch

Upper Hämäkua Ditch, along the rim of Waipiÿo Valley, 

diverts water primarily through intakes on Kawainui Stream 

(altitude 4,042 feet), Kawaiki Stream (a tributary to Kawainui 

Stream, at altitude 4,026 feet), Alakahi Stream (altitude 3,874 

feet), Koÿiawe Stream (altitude 3,355 feet), and Waimä Stream 

(altitude 3,044 feet) at locations just upstream of where they 

descend into Waipiÿo Valley (Hawaii Division of Water and 

Land Development, 1963). Diversion intakes along Upper 

Hämäkua Ditch were designed to capture all of the water in 

the stream until the rate of flow exceeded the capacity of the 

intake structures. At this point, water in streams will overtop 

the intake diversion dams and flow downstream into Waipiÿo 

Valley. Unfortunately, accounting for effects of diversions by 

Upper Hämäkua Ditch is not simply a matter of determining 

how much water is withdrawn at each intake. 

Upper Hämäkua Ditch, like most diversion systems in 

Hawaiÿi, does not just withdraw water from streams at established intakes; it also gains and loses water at both diffuse and 

point locations along its entire reach. In addition to the stream 

intakes, Upper Hämäkua Ditch can intercept water along 

open sections where overland runoff and small seeps can flow 

directly into the ditch, as well as along tunneled sections of 

the ditch, where groundwater-saturated rocks are intersected. 

Upper Hämäkua Ditch discharges water at locations in addition to those of intended water users—back into streams at 

maintenance spillways and release gates where it is intentionally or unintentionally released, at points of overflow where the 

capacity of the ditch is exceeded (often due to blockages), and 

at diffuse locations along its reach where there are leakage or 

seepage losses. Water diverted or “lost” via seepage from Upper 

Hämäkua Ditch at diffuse and point locations does not always 

return to the same stream from which the water was originally 

diverted or lost, which further complicates water accounting.

Three gaging stations have been operated on tributaries 

upstream from intakes of Upper Hämäkua Ditch, and three stations have been operated along the ditch itself. These stations 

and the periods during which they have been in operation are 

summarized in table 3-A; their locations are shown in figure 

3–A. Only two gaging stations, Kawainui Stream at 4,060 feet 

(station 16720000) and Alakahi Stream at 3,900 feet (station 

16725000), were in operation during the entire 2000–2005 

study period. As a result, a combination of actual gaging station data and estimates of discharge based on relations established using historical data will be needed to account for the 

effects of diversions by Upper Hämäkua Ditch. To be consistent and as relevant to study-period (2000–2005) conditions as 

possible, historical data from water year 1999 were used when 

estimated diversion relations were required. Water year 1999 

was the most current 12-month period during which all three 

stream-gaging stations and three ditch-gaging stations, on or 

upstream from Upper Hämäkua Ditch, were in operation.

To account for effects of diversions by Upper Hämäkua 

Ditch, computations were run for each day that a discharge 

measurement was made at any of the five low-flow partialrecord stations downstream from the ditch. At the upstream 

limit of Upper Hämäkua Ditch, intakes divert water from 

Kawainui Stream and its tributary Kawaiki Stream. The 

amount of water diverted by Upper Hämäkua Ditch from 

Kawainui Stream watershed (the combined total of water 

diverted at Kawainui and Kawaiki Stream ditch intakes) was 

measured at gaging station Upper Hämäkua Ditch at 4,020 feet 

(16720500) through 2002. 

To estimate the amount of water diverted by Upper 

Hämäkua Ditch from Kawainui Stream watershed for the balance of the study period (2003–2005), the relation shown in 

figure 3-B was developed. In figure 3–B, discharge in Upper 

Hämäkua Ditch at 4,020 feet (station 16720500) is plotted 

against the combined discharge of Kawainui Stream at 4,060 

feet (station 16720000) and Kawaiki Stream at 4,090 feet 

(station 16720300). The graph shows that discharge in Upper 

Hämäkua Ditch is greater than or equal to the combined 

discharge of Kawainui and Kawaiki Streams on most days 

in 1999 when the combined discharge of the streams is less 

than or equal to 9.5 ft3/s. This indicates that at the intakes, 

Upper Hämäkua Ditch will divert all the water in Kawainui 

and Kawaiki Streams up to 9.5 ft3/s. Conversely, the discharge 

in Upper Hämäkua Ditch is less than the combined discharge 

of Kawainui and Kawaiki Streams on all days in 1999 when 

the combined discharge of the streams is greater than 9.5 

ft3/s. This indicates that water will overflow Upper Hämäkua 

Ditch diversion dams at the intakes and flow downstream into 

Waipiÿo Valley (and Kawainui Stream) when the combined 

discharge of Kawainui and Kawaiki Streams is greater than 9.5 

ft3/s. 

The amount of water diverted by Upper Hämäkua Ditch 

from Kawainui Stream watershed (the total diverted from 

Kawainui and Kawaiki Streams) on days when discharge 

measurements were made at low-flow partial-record stations in 

Waipiÿo Valley during the period 2000–2002 equals that measured at the gaging station Upper Hämäkua Ditch at 4,020 feet 

(16720500). The amount of water diverted by Upper Hämäkua 

Ditch during the period 2003-2005 was estimated to equal all 

the combined discharge of Kawainui and Kawaiki Streams up 

to 9.5 ft3/s. Diversion totals were not estimated on days when 

the combined discharge of the two streams was greater than 

9.5 ft3/s. The amount of water available for diversion was measured during the entire 2003–2005 period at Kawainui Stream 
 Appendix 3. Accounting for Effects of Diversions at Upper and Lower Hämäkua Ditches 71

Kawainui

Str

Waimanu

Str

Waikaloa

Str

Alakahi

Str

Läläkea 

Str

Waiulili

Str

Waipi‘o Str

Wailoa

Str

Upper

Ditch

Lower

Ditch

Hämäkua

Waima

Str

Ko‘iawe 

Str

Hämäkua

##

#

#

#

##

#

#

#

#

#

#

##

#

#

#

#

#

#

" ""

"

"

"

"

720000

720500

720300

721000

757000

758000

759000

724800

725000

728000

721500

722000

722600

722300

723000

724000

729000

732000

731000

732150

732100

732600

726000

730000

732200

732900

733000

733100

732800

Waimea

0 1 2 KILOMETERS

0 1 2 MILES

155°40' 155°36'

20°04'

20°08'

Waipiÿo 

 Bay

P A C I F I C 

 O C E A N

Figure 3A. Location of stream and ditch surface-water gaging stations operated in adjacent to the 

Waipiÿo Valley study area, Island of Hawaiÿi, Hawaiÿi.

757000

726000 "

# Stream (Index stations are highlighted in yellow)

Ditch

 Major road

Gaging station and abbreviated number—

Complete number is preceded by 16

EXPLANATION

HAWAI‘I

Area of map

PACIFIC

OCEAN

Figure 3–A. Location of stream and ditch surface-water gaging stations operated in and adjacent to the Waipiÿo 

Valley study area, Island of Hawaiÿi, Hawaiÿi.
72 Low-Flow Characteristics of Streams Under Natural and Diversion Conditions, Waipiÿo Valley, Island of Hawaiÿi, Hawaiÿi

Station number Location Period of 

record Remarks

16720000 Kawainui Stream at 4,060 feet 1965-P Used as index station

16720300 Kawaiki Stream at 4,090 feet 1966-1999

16720500 Upper Hämäkua Ditch at 4,020 feet 1964-2002 Ditch gaging station

16724800 Upper Hämäkua Ditch at 3,890 feet 1968-2000 Ditch gaging station

16725000 Alakahi Stream at 3,900 feet 1965-P Used as index station

16726000 Upper Hämäkua Ditch at 3,020 1974-2004 Ditch gaging station

Table 3–A. Gaging stations on and upstream from Upper Hämäkua Ditch, Waipiÿo Valley study 

area, Island of Hawaiÿi, Hawaiÿi.

[P, in operation during 2006 water year]

(station 16720000). The Kawaiki Stream (station 16720300) 

was discontinued in 1999; therefore concurrent streamflow 

data at that location needed to be estimated. This was done by 

establishing a simple linear regression model between daily 

mean streamflow data at Kawaiki Stream (station 16720300) 

and Kawainui Stream (station 16720000). Data for all days 

in water year 1999 when daily mean discharge of Kawainui 

Stream was less than or equal to 20 ft3/s were used in the 

analysis. The model indicated that the flow of Kawaiki Stream 

could be estimated as 0.2437 x Kawainui Stream flow (in ft3/s) 

+ 0.0627. This model has a correlation coefficient of 0.976, 

which indicates a strong linear relation.

An analysis of discharge data for Upper Hämäkua Ditch 

at 4,020 feet (station 16720500) and at 3,890 feet (station 

16724800) indicated a consistent pattern of diminishing discharge between Kawainui and Kawaiki Stream ditch intakes 

and a point just upstream from Alakahi Stream ditch intake. 

During 2000, when both gaging stations on Upper Hämäkua 

Ditch were in operation, the loss of discharge from the ditch 

could be computed by subtracting concurrent daily mean discharges at the stations. During the balance of the study period 

(2001–2005), this loss of discharge had to be estimated. This 

was done by establishing a simple linear regression model 

between the magnitude of loss of discharge from the ditch and 

discharge at the upstream gaging station on Upper Hämäkua 

Ditch at 4,020 feet (16720500). This model was developed 

for low-flow days during water year 1999, when the upstream 

discharge was 10 ft3/s or less. The model indicated that loss 

of discharge from Upper Hämäkua Ditch between Kawainui 

and Kawaiki Stream intakes and Alakahi Stream intake could 

be estimated as -0.1868 x Flow in Upper Hämäkua Ditch 

at 4,020 feet (in ft3/s) – 0.5396. This model has a correlation 

coefficient of 0.492, indicating that ditch losses are variable 

and at times poorly predicted by the linear regression model.

Measured and estimated losses of water from Upper 

Hämäkua Ditch between Kawainui and Kawaiki Stream 

intakes and Alakahi Stream intake during periods of low flow 

most likely are associated with diffuse leakage or seepage 

losses. Water lost from Upper Hämäkua Ditch is assumed 

to contribute to flow in downgradient streams. In this case, 

the reach of Upper Hämäkua Ditch between Kawainui and 

Kawaiki Stream intakes and the Alakahi Stream intake lies 

within parts of Kawainui and Alakahi Stream watersheds 

that are upstream from low-flow partial-record stations at 

sites 1 and 6 (fig. 3–C). It is not known exactly where along 

Upper Hämäkua Ditch that losses of water take place. For the 

pruposes of this study, it was estimated that the distribution of 

losses from Upper Hämäkua Ditch into Kawainui and Alakahi 

Stream watersheds was directly proportional to the length of 

Upper Hämäkua Ditch within each watershed. For the 9,636-

foot reach of Upper Hämäkua Ditch between the Kawainui 

and Kawaiki intakes and the Alakahi intake (Hawaii Division 

of Water and Land Development, 1963), 57 percent of the 

ditch lies in Kawainui Stream watershed and 43 percent lies in 

Alakahi Stream watershed.

At the time that discharge measurements were made 

at the low-flow partial-record station at site 1 on Kawainui 

Stream (see table 3 in main body of this report), discharge 

had been reduced by the amount of water being diverted by 

Upper Hämäkua Ditch at the Kawainui and Kawaiki intakes 

and increased by losses from the section of the ditch upgradient in the watershed. The magnitudes of these diversions 

and losses were computed, as outlined above, and used to 

estimate what the discharge at site 1 would have been under 

natural conditions had Upper Hämäkua Ditch not been active 

in any way (table 3–B). To estimate natural flow at site 1, 

measured discharge at the site was increased by the amount 

of water diverted upstream by the Upper Hämäkua Ditch. 

However, the measured discharge at site 1 is enhanced by 

upstream losses from Upper Hämäkua Ditch that return to 

Kawainui Stream upstream of the site. Thus, to avoid double 

counting of water, the amount of upstream losses were 

subtracted from measured discharge at site 1. This same type 

of water accounting process was followed at the remaining 

low-flow partial-record stations in Waipiÿo Valley. On average, discharge at site 1 had been reduced by about 3.0 ft3

/s, 
Figure 3–B. Relation between discharge at Upper Hämäkua Ditch (station 16720500) and combined discharge of Kawainui Strand Kawaiki Stream (station 16720300), Island of Hawaiÿi, Hawaiÿi, water year 1999. 0 2 4 6 8 10 

12 

14 

16 

0 2 4 6 8 10 12 14 16 18 20 22 24 

Combined discharge of Kawainui stream and Kawaiki stream, in cubic feet per second 

Figure 3B. Relation between discharge at Upper Hämäkua Ditch (station 16720500) and combined discharge of K

(station 16720000) and Kawaiki Stream (station 16720300), Hawai‘i, water year 1999. 

Line of equality 

Discharge at which overflow at 

ditch intake begins 

(9.5 cubic feet per second) 

Upper Hämäkua, ditch discharge, in cubic feet per second
74 Low-Flow Characteristics of Streams Under Natural and Diversion Conditions, Waipiÿo Valley, Island of Hawaiÿi, Hawaiÿi

Figure 3–C. Locations where discharge measurements were made in Waipiÿo Valley study area during the period 

2000–2005, Island of Hawaiÿi, Hawaiÿi.

Kawainui

Str

Waimanu

Str

Waikaloa

Str

Alakahi

Str

Läläkea 

Str

Waiulili

Str

Waipi‘o Str

Wailoa

Str

Upper

Ditch

Lower

Ditch

Hämäkua

Waimä

Str

Koiawe

Str

Hämäkua

1

2

3

4

5 6

7

8

9 10

11

12

13

14

15

16

17 18

19 20

21

22

23

24

25 26

27

#

#

##

#

##

#

## ##

#

##

#

# ##

#

#

# #

#

#

#

#

Waimea

0 1 2 KILOMETERS

0 1 2 MILES

155°40' 155°36'

20°04'

20°08'

Waipi‘o 

 Bay

P A C I F I C 

 O C E A N

Figure 3C. Locations where discharge measurements were made in Waipiÿo Valley study area during the 

period 2000-2005, Island of Hawaiÿi, Hawaiÿi.

Seepage-run site and number

Seeppage-run site and low-flow

partial-record station and number

Major road

22

6

#

#

EXPLANATION

HAWAI‘I

Area of map

PACIFIC

OCEAN
 Appendix 3. Accounting for Effects of Diversions at Upper and Lower Hämäkua Ditches 75

or 7.2 percent, from natural conditions on the 10 days when 

discharge measurements were made.

Total discharge in Upper Hämäkua Ditch at 3,890 feet 

was determined from data collected at the gaging station 

(16724800) in operation at that location through 2000. During the balance of the study period (2001–2005), discharge 

in Upper Hämäkua Ditch at 3,890 feet and upstream from 

Alakahi Stream was determined to be either the measured or 

estimated discharge in Upper Hämäkua Ditch at 4,020 feet 

(station 16720500) minus estimated loss of discharge in the 

reach of ditch between the two locations (see paragraphs 

above). Just downstream from the gaging station at 3,890 feet, 

Upper Hämäkua Ditch discharges into Alakahi Stream. This 

discharge point is just downstream from the streamflow-gaging station on Alakahi Stream at 3,900 feet (station 16725000) 

and just upstream from Upper Hämäkua Ditch Alakahi Stream 

intake at 3,874 feet. Total discharge in Alakahi Stream, just 

upstream from the ditch intake, can be computed by combining concurrent data measured or estimated in Upper Hämäkua 

Ditch at 3,890 feet (station 16724800) with measured data in 

Alakahi Stream at 3,900 feet (station 16725000). Discharge 

data for Alakahi Stream at 3,900 feet were available at gaging 

station 16725000 during the entire study period (2000–2005). 

The amount of water diverted by Upper Hämäkua Ditch 

at Alakahi Stream intake has not been systematically measured. The next gaging station downstream along Upper 

Hämäkua Ditch is at 3,020 feet (station 16726000) (fig. 3–A), 

and flow at this location includes water diverted at Koÿiawe 

and Waimä Stream intakes. To estimate the amount of water 

diverted by Upper Hämäkua Ditch at Alakahi Stream intake, 

the relation shown in figure 3–D was developed. In figure 

3–D, discharge in Upper Hämäkua Ditch at 3,020 feet (station 

16726000) is plotted against total discharge upstream from the 

Alakahi ditch intake. The graph shows that discharge in Upper 

Hämäkua Ditch at 3,020 feet is greater than total discharge 

upstream from Alakahi Stream intake on all but one day in 

1999 when total Alakahi Stream discharge is less than or equal 

to about 11.0 ft3/s. This indicates that Upper Hämäkua Ditch 

potentially has the capacity to divert all water at the Alakahi 

Stream intake up to 11.0 ft3/s. This would be logical, given 

that Upper Hämäkua Ditch was estimated to be able to divert 

all water in Kawainui and Kawaiki Streams up to 9.5 ft3/s (see 

paragraphs above), and ditch capacity typically increases in a 

downstream direction as more sources of potential contributing inflow are encountered. 

Unfortunately, estimation of how much water will be 

diverted at Alakahi Stream intake is complicated by the 

additional intakes along Upper Hämäkua Ditch above the next 

downstream ditch-gaging station (16726000). The degree 

by which discharge in Upper Hämäkua Ditch at 3,020 feet 

exceeds total discharge upstream from Alakahi Stream intake 

is an indicator of potential increases in discharge at points 

downstream from the intake, assuming all discharge upstream 

from the intake is being diverted. Potential increases are 

Date

Discharge 

measurement 

(ft3/s)

Net effect of 

diversions by 

UHD (ft3/s)

Estimated 

natural 

discharge 

(ft3/s)

Change in natural 

discharge caused by 

UHD diversions 

(percent)

9/21/2000 26.5 -2.53 29.0 -8.7

1/10/2001 18.6 -0.12 18.7 -0.6

3/8/2001 59.1 -8.54 67.6 -12.6

5/30/2001 21.7 -1.12 22.8 -4.9

9/26/2001 41.5 -8.54 50.0 -17.1

6/26/2003 35.0 -5.97 41.0 -14.6

9/25/2003 22.6 -0.15 22.8 -0.7

10/6/2004 16.2 -0.46 16.7 -2.8

2/25/2005 11.4 -0.15 11.6 -1.3

8/24/2005 28.6 -2.64 31.2 -8.5

Average -- -3.02 -- -7.2

 a

 Site number corresponds to that shown in figure 3-C.

Table 3–B. Effect of diversions by the Upper Hämäkua Ditch on discharge 

measurements made during the period 2000–2005 at Kawainui Stream low-flow 

partial-record site 1a, Island of Hawaiÿi, Hawaiÿi.

[ft3/s, cubic feet per second; UHD, Upper Hämäkua Ditch; --, not computed]
Figure 3–D. Relation between discharge at Upper Hämäkua Ditch (station 16726000) and the total discharge upstream fUpper Hämäkua Ditch intake, Island of Hawaiÿi, Hawaiÿi, water year 1999. 0 5 10 15 20 25 30 35 40 0 10 20 30 40 50 60 70 80 

Line of equality Discharge at which overflow at ditch intake is estimated to begin (11.0 cubic feet per second) Total discharge upstream from Alakahi stream intake, in cubic feet per second

Upper Hämäkua ditch discharge, in cubic feet per second

Figure 3D. Relation between discharge at Upper Hämäkua Ditch (station 16726000) and the total discharge upstream from Alakah

 Ditch intake, Hawai‘i, water year 1999.
 Appendix 3. Accounting for Effects of Diversions at Upper and Lower Hämäkua Ditches 77

represented by the degree to which concurrent discharge data 

points plot above the line of equality in figure 3–D. Potential 

increases follow a very distinct linear pattern up to a point at 

which total discharge upstream from Alakahi Stream intake 

equals about 8.0 ft3/s; beyond that point, the data are quite 

variable. This distinct linear pattern is what would be expected 

when Upper Hämäkua Ditch diverts all the water available 

at Alakahi Stream intake and the intakes encountered before 

reaching ditch-gaging station 16726000 on Upper Hämäkua 

Ditch at 3,020 feet. Following this logic, it could reasonably 

be assumed that Upper Hämäkua Ditch diverts all the water 

upstream at Alakahi Stream intake up to 8.0 ft3/s (assuming 

no ditch losses). In this study, diversion totals at the Alakahi 

ditch intake were not estimated for times when total discharge 

upstream from the intake exceeds 8.0 ft3/s. This will not prove 

to be a significant limitation as there were only two days on 

which discharge measurements were made at downstream 

low-flow partial-record stations that discharge at Alakahi 

Stream intake exceeded this limit. On both of those days, 

discharge upstream from Alakahi Stream intake exceeded the 

maximum potential diversion capacity of 11.0 ft3/s and was 

therefore beyond any reasonable range where diversion totals 

could be estimated.

There is a consistent pattern of increasing discharge in 

Upper Hämäkua Ditch between Alakahi Stream intake and the 

gaging station at 3,020 feet (16726000) (fig. 3–D). The magnitude of this increase can be computed by subtracting concurrent daily mean discharges at the two locations. Data upstream 

from Alakahi Stream intake were computed or estimated 

as discussed above. Data at Upper Hämäkua Ditch gaging 

station at 3,020 feet (16726000) are available through 2004. 

For the balance of the study period (2000–2005), a simple 

linear regression model was used to estimate the increase in 

discharge in the subject reach of the Upper Hämäkua Ditch. 

The regression was developed on the basis of data for 171 

days in 1999 when the combined flow upstream from Alakahi 

Stream ditch intake was 8.0 ft3/s or less, and it excluded 

data for four days when uncharacteristically large gains or 

losses in flow were indicated. The regression takes the form: 

increase in Upper Hämäkua Ditch discharge between Alakahi 

Stream intake and gaging station 16726000 at 3,020 feet = 

1.6001 x discharge (in ft3/s) at Alakahi Stream gaging station 

(16725000) – 0.1707. This model has a correlation coefficient 

of 0.869, which indicates a moderately strong linear relation. 

Upper Hämäkua Ditch gaging station at 3,020 feet 

(16726000) is near the watershed divide between streams that 

drain to the north, into Waipiÿo Valley, and streams that drain to 

the southeast, away from Waipiÿo Valley. Increasing discharge 

in Upper Hämäkua Ditch between Alakahi Stream intake and 

the ditch-gaging station at 3,020 feet (16726000) can therefore 

be attributed to additional diversions from Alakahi, Koÿiawe, 

and Waimä watersheds, which are tributary to Waipiÿo Valley. 

The exact distribution of additional diversions from the three 

watersheds is unknown. In this study, it was estimated that 

the distribution of diversions was directly proportional to the 

percentage of Upper Hämäkua Ditch, for the reach in question, 

located in each of the three watersheds. For the 22,800-foot 

reach of Upper Hämäkua Ditch between Alakahi Stream intake 

and the ditch-gaging station at 3,020 feet (16726000) (Hawaii 

Division of Water and Land Development, 1963), 27 percent 

of the ditch lies in Alakahi watershed, 55 percent in Koÿiawe 

watershed, and 18 percent in Waimä watershed.

At the time that discharge measurements were made at 

the low-flow partial-record station at site 6 on Alakahi Stream 

(table 3–C), natural discharge had been (1) increased by the 

amount of losses from the section of Upper Hämäkua Ditch 

upgradient in the watershed and upstream from Alakahi 

Stream intake, (2) decreased by the amount of water originating from Alakahi Stream and being diverted by Upper 

Hämäkua Ditch at the Alakahi intake, and (3) decreased by 

the amount of diversion taking place along the part of Upper 

Hämäkua Ditch upgradient in the watershed and downstream 

from the Alakahi Stream intake. The magnitude of these diversions and losses were computed, as outlined above, and used 

to estimate what discharge at site 6 would have been under 

natural conditions had Upper Hämäkua Ditch not been active 

in any way (table 3–C). On average, discharge at site 6 was 

reduced by about 1.4 ft3/s, or 7.9 percent, on eight days when 

measurements were made. Note that data were not computed 

for the March 8, 2001, discharge measurement because 

reasonable estimates of diversions at Alakahi Stream intake 

could not be made on that day (see discussion above regarding 

Alakahi ditch intake capacity).

At the time that discharge measurements were made at 

low-flow partial-record stations at sites 15 and 18 on Koÿiawe 

and Waimä Streams, natural discharge had been decreased 

by the amount of diversion taking place along the section of 

Upper Hämäkua Ditch located upgradient in the respective 

watersheds. As noted above, this diversion was estimated to 

be 55 percent of the gain in Upper Hämäkua Ditch discharge 

between Alakahi Stream intake and ditch-gaging station 

16726000 at 3,020 feet (from Koÿiawe watershed) and 18 

percent of the gain from Waimä watershed. The magnitudes 

of these diversions were computed and used to estimate what 

the discharge at sites 15 and 18 would have been under natural 

conditions had Upper Hämäkua Ditch not been active in any 

way (tables 3–D and 3–E). On average, discharge at sites 15 

and 18 was reduced by about 0.8 and 0.2 ft3/s, or 9.3 and 19.8 

percent, respectively, on nine days when measurements were 

made. Note that data at both sites were not computed for the 

September 26, 2001, discharge measurement because reasonable estimates of diversions at Alakahi Stream intake could not 

be made on that day (see discussion above regarding Alakahi 

ditch intake capacity). 

Effects of Diversions by Lower Hämäkua 

Ditch

Lower Hämäkua Ditch diverts water from Kawainui 

Stream (altitude 1,037 feet), Alakahi Stream (altitude 1,030 

feet), and Koÿiawe Stream (altitude 1,000 feet) (U.S. Department of Agriculture, 1999, Mink, 1984). In addition to 
78 Low-Flow Characteristics of Streams Under Natural and Diversion Conditions, Waipiÿo Valley, Island of Hawaiÿi, Hawaiÿi

Date

Discharge 

measurement 

(ft3/s)

Net effect of 

diversions 

by 

UHD (ft3/s)

Estimated 

natural 

discharge 

(ft3/s)

Change in natural 

discharge caused by 

UHD diversions 

(percent)

9/20/2000 17.4 -2.36 19.8 -11.9

1/10/2001 14.1 -0.41 14.5 -2.8

3/8/2001 25.7 -- -- --

5/30/2001 14.2 -0.91 15.1 -6.0

6/26/2003 17.2 -3.16 20.4 -15.5

9/25/2003 14.3 -0.78 15.1 -5.2

10/6/2004 12.5 -0.72 13.2 -5.4

2/25/2005 11.4 -0.19 11.6 -1.6

8/24/2005 13.6 -2.32 15.9 -14.6

Average -- -1.36 -- -7.9

a

 Site number corresponds to that shown in figure 3-C.

Date

Discharge 

measurement 

(ft3/s)

Net effect of 

diversions by 

UHD (ft3/s)

Estimated 

natural 

discharge 

(ft3/s)

Change in natural 

discharge caused by 

UHD diversions 

(percent)

8/8/2000 7.02 -0.92 7.94 -11.6

9/21/2000 7.53 -1.05 8.58 -12.2

1/11/2001 7.28 -0.16 7.44 -2.2

3/9/2001 8.28 +0.11 8.17 +1.3

5/31/2001 7.18 -0.69 7.87 -8.8

9/26/2001 10.5 -- -- --

6/27/2003 8.30 -2.07 10.4 -20.0

9/26/2003 7.52 -0.59 8.11 -7.3

10/7/2004 7.32 -0.35 7.67 -4.6

4/27/2005 7.38 -1.67 9.05 -18.5

Average -- -0.82 -- -9.3

 a Site number corresponds to that shown in figure 3-C.

Table 3–C. Effect of diversions by the Upper Hämäkua Ditch on discharge 

measurements made during the period 2000–2005 at Alakahi Stream low-flow 

partial-record site 6a, Island of Hawaiÿi, Hawaiÿi.

[ft3/s, cubic feet per second; UHD, Upper Hämäkua Ditch; --, not computed]

Table 3–D. Effect of diversions by the Upper Hämäkua Ditch on discharge 

measurements made during the period 2000–2005 at Koÿiawe Stream low-flow 

partial-record site 15a, Island of Hawaiÿi, Hawaiÿi.

[ft3/s, cubic feet per second; UHD, Upper Hämäkua Ditch; --, not computed]
 Appendix 3. Accounting for Effects of Diversions at Upper and Lower Hämäkua Ditches 79

Date

Discharge 

measurement 

(ft3/s)

Net effect of 

diversions by 

UHD (ft3/s)

Estimated 

natural 

discharge 

(ft3/s)

Change in natural 

discharge caused 

by UHD diversions 

(percent)

08/08/2000 0.62 -0.30 0.92 -32.6

09/20/2000 0.61 0.00 0.61 -0.0

01/11/2001 0.69 -0.05 0.74 -6.8

03/09/2001 0.60 +0.04 0.56 +7.1

05/31/2001 0.53 -0.23 0.76 -30.3

09/26/2001 0.86 -- -- --

06/27/2003 0.67 -0.68 1.35 -50.4

09/26/2003 0.67 -0.19 0.86 -22.1

10/07/2004 0.72 -0.11 0.83 -13.3

08/23/2005 0.93 -0.40 1.33 -30.1

Average -- -0.21 -- -19.8

a

 Site number corresponds to that shown in figure 3-C.

Table 3–E. Effect of diversions by the Upper Hämäkua Ditch on discharge 

measurements made during the period 2000–2005 at Waimä Stream low-flow 

partial-record site 18a, Island of Hawaiÿi, Hawaiÿi.

[ft3/s, cubic feet per second; UHD, Upper Hämäkua Ditch; --, not computed]

diversions at the three intakes, Lower Hämäkua Ditch also 

diverts (gains) or loses water at various diffuse and point 

locations along its entire reach. The gaging station on Lower 

Hämäkua Ditch (16732800), upstream from the main weir, 

measures the net amount of water diverted by the ditch from 

tributaries to Wailoa Stream. Discharge measured at station 

16732800 also reflects gains associated with the interception of groundwater by Lower Hämäkua Ditch and losses at 

Hiÿilawe Falls that would discharge into Wailoa Stream at 

points downstream from site 24 (fig. 3–C). Visual observations during the time of the study (2000–2005) indicate that 

the magnitudes of gains and loses were comparable. For this 

analysis, it was assumed that these gains and losses would 

cancel each other out; therefore discharge measured at gaging 

station 16732800 during the study will account for the total 

effects of diversions by Lower Hämäkua Ditch on discharge 

measured at site 24. 

Discharge measurements or gaging station data that 

documented net diversions were available at Lower Hämäkua 

Ditch gaging station 16732800 on five of the nine days that 

discharge measurements were made at low-flow partialrecord station at site 24 (see table 3 in main body of this 

report). Discharge data that documented net diversions at 

gaging station 16732800 on the remaining four days was 

estimated by establishing a simple linear regression model. 

The model was based on estimated discharge data at Upper 

Hämäkua Ditch gaging station 16726000 and measured 

discharge data at Lower Hämäkua Ditch gaging station 

16732800 on the four days for which data were available 

at both stations and discharge measurements were made at 

the low-flow partial-record station at site 24. The regression 

indicated that Lower Hämäkua Ditch discharge (ft3/s) could 

be estimated as 2.313 x Upper Hämäkua Ditch discharge 

(in ft3/s) + 8.776. This model has a correlation coefficient of 

0.918, which indicates a moderately strong linear relation. 

At the time that discharge measurements were made at 

the low-flow partial-record station at site 24 on Wailoa Stream, 

discharge was decreased by diversions to Upper and Lower 

Hämäkua Ditches at upgradient locations. The magnitudes of 

these diversions were computed, as outlined above, and used 

to estimate what discharge at site 24 would have been, under 

natural conditions, had Upper and Lower Hämäkua Ditches 

not been active in any way (table 3-F). On average, discharge 

at site 24 was reduced by diversions of 5.1 ft3/s to Upper 

Hämäkua Ditch and 18.3 ft3/s to Lower Hämäkua Ditch. On 

average, discharge in Wailoa Stream at site 24 (fig. 3–C) was 

reduced by a total of 21.9 percent on the nine days when discharge measurements were made.
80 Low-Flow Characteristics of Streams Under Natural and Diversion Conditions, Waipiÿo Valley, Island of Hawaiÿi, Hawaiÿi

Date

Discharge 

measurement 

(ft3/s)

Net effect of 

diversions by 

UHD (ft3/s)

Net effect of 

diversions by 

LHD (ft3/s)

Estimated 

natural 

discharge 

(ft3/s)

Change in natural 

discharge caused by 

UHD and LHD 

diversions (percent)

09/21/2000 78.3 -6.00 -25.5 110 -28.7

01/10/2001 68.8 -0.75 -11.1 80.7 -14.7

03/09/2001 76.5 -7.40 -25.9 110 -30.3

05/30/2001 73.3 -2.50 -16.2 92.0 -20.3

09/26/2001 103 -14.0 -20.0 137 -24.8

06/27/2003 82.9 -6.90 -19.0 109 -23.8

09/25/2003 84.6 -1.80 -9.8 96.2 -12.1

10/06/2004 69.4 -1.70 -17.0 88.1 -21.2

08/23/2005 95.7 -5.06 -20.5 121 -21.1

Average -- -5.12 -18.3 -- -21.9

a

 Site number corresponds to that shown in figure 3-C.

Table 3–F. Effect of diversions by the Upper and Lower Hämäkua Ditches on discharge 

measurements made during the period 2000–2005 at Wailoa Stream low-flow partial-record 

site 24a, Island of Hawaiÿi, Hawaiÿi.

[ft3/s, cubic feet per second; UHD, Upper Hämäkua Ditch; LHD, Lower Hämäkua Ditch; --, not computed]
82 Low-Flow Characteristics of Streams Under Natural and Diversion Conditions, Waipiÿo Valley, Island of Hawaiÿi, Hawaiÿi 

Menlo Park Publishing Service Center, California

Manuscript approved for publication, January 28, 2011 

Edited by Peter H. Stauffer

Layout by Judy Weathers
 83

Fontaine, R.A.—Low-Flow Characteristics of Streams Under Natural and Diversion Conditions, Waipiÿo Valley, Island of Hawaiÿi, Hawaiÿi—Scientific Investigations Report 2011–5118