The effect of the accounting sequence in the bud-
get is indicated by a comparison of the actual evapo-
transpiration and recharge values from method I which
favors ground-water recharge and method II which
favors actual evapotranspiration. The mean ground-
water recharge value for method I (7,214 Mgal/mo), is
about 69 percent greater than for method II (4,264
Mgal/mo). The monthly actual evapotranspiration val-
ues for method II are greater than the actual evapotrans-
piration values for method I by an average of about 43
percent for the mean.

A comparison of the method II actual evapotrans-
piration and pan evaporation values indicates the degree
to which evapotranspiration can be overestimated in a
water budget that uses an estimate of maximum evapo-
transpiration, such as pan evaporation, rather than cal-
culating some actual evapotranspiration value. The
method II accounting sequence favors ET rather than
ground-water recharge. From December through
March, the AE and pan values are similar. However, as
rainfall decreases from April through October, there is
not enough water to meet the evaporative demand.
Thus, pan values consistently exceed AE values by as
much as 9 times in June.

The seasonality in evapotranspiration and recharge
can also be described in proportion to rainfall (table 4).
The direct runoff-rainfall ratio average is 16 percent.
The slight variability throughout the year, is a conse-
quence of the lack of data and of the runoff estimation
method. Actual evapotranspiration varies from about 31
to 49 percent of rainfall from November through April
(winter) and increases to 65 to 92 percent during the
summer months from May through October. The con-
verse relation for recharge shows recharge occurring at
31 to 47 percent of rainfall in the winter and at about 8
to 17 percent of rainfall from May through October.

Because the values in table 3 are a compilation of
the water budgets calculated for any location on the
island, the water budget for a smaller area (table 5)
shows the variations that can occur and are masked at

the island scale. A large part of the island’s ground-
water development is from the Kualapuu aquifer-sys-
tem area (figs. 3 and 5). The area is 18 mi? and receives
an average amount of rainfall for the island (fig. 6) with
a mean of 1,181 Mgal/mo (39 Mgal/d). The direct run-
off is 11.5 percent of rainfall at 136 Mgal/mo (about 4.5
Mgal/d). The calculated mean actual evapotranspira-
tion, 696 Mgal/mo, is 59 percent of rainfall and mean
ground-water recharge, 349 Mgal/mo, is about 30 per-
cent of rainfall. Compared with the island-wide ratios
(table 4), these ratios describe a relatively dry area
where ground-water recharge is significant during the
wet winter months and negligible during the summer.
The magnitude of the effect of the two accounting
methods is indicated where the method II actual evapo-
transpiration exceeds rainfall in May and June drawing
down the volume in soil storage to zero throughout the
summer months, and causing zero ground-water
recharge in these same months. The ground-water
recharge values calculated by the two methods provide
a range of data with which to test conceptual models of
the ground-water flow system in the area.

Comparison with results of previous study.--
Water-budget results from this study and a previous
investigation are presented by aquifer-system areas
(fig. 5) in tables 6 and 7. The presentation highlights
the comparative magnitude of the effects of assump-
tions made in the water-budget calculations on the
water-budget results. The water budget by the State of
Hawaii (1990) is somewhat similar to the results of the
water-budget accounting method III in this report in
that it calculates a significant proportion of evapo-
transpiration in all areas of the island. The State budget
assumes evapotranspiration occurs at a maximum,
potential rate which emphasizes evapotranspiration and
reduces ground-water recharge. The effect of assuming
potential evapotranspiration rather than calculating an
actual evapotranspiration volume is most apparent in
Kawela where the State evapotranspiration estimate, 32
Mgal/d, is about twice that estimated by the average
value in the present study, 20 Mgal/d. Similarly, the

Table 4. Monthly water-budget ratios for natural conditions, Molokai, Hawaii
[Values using average of methods I and II in percent; AE, actual evapotranspiration; sum of monthly ratios may not equal 100 due to rounding and amount

of water in soil storage]

Ratio Jan. Feb. Mar. Apr. May June July Aug. Sept. Oct. Nov. Dec. Annual
Direct runofi/rain 15 15 16 17 7 17 7 18 7 Te 16 16 16
AE/rain 31 43 36 49 85 92 68 68 719 65 45 37 50
Recharge/rain 47 45 47 42 17 8 13 13 8 15 31 40 34

Water-Budget Results 17


were chosen with similar mean annual rainfall and soil
properties as those of Molokai. The Oahu data provided
average annual runoff-rainfall ratios for each soil runoff
rating within each rainfall range (table 1). The ratios
were multiplied by the monthly rainfall values to esti-
mate monthly direct runoff values.

Study Area Soils
The soil types have been mapped and digitized and

their characteristics tabulated by the Natural Resources
Conservation Service (Foote and others, 1972) (table 2).

Table 2. Average soil characteristics, Molokai, Hawaii

Values for the soil characteristics of permeability, avail-
able water capacity (a measure of the quantity of water
held in the soil available to plants between field capac-
ity and wilting point), and the root depth presented by
Foote and others (1972) were entered into attribute data
tables associated with the digital soil distribution.

Data that were not available from Foote and others
(1972) were provided by the Natural Resources Conser-
vation Service (Saku Nakamura, written commun.,
1997). The available-water value for each soil series in
table 2 is the central value of the range reported by
Foote and others (1972). The root depth was assumed to

(Data from Foote and others, 1972; and Saku Nakamura, Natural Resources Conservation Service, written commun., 1997]

Available-water Maximum soil- -
Soil series capacity (inch per inch Root depth moisture storage, Permeability
“coil (inches) inches) (inches per hour)
0.13 70 3.17 20-60
0.35 8.0 2.48 0.06-20.0
0.04 6.0 0.24 6.0-20.0
0.12 10.0 115 0.6-2.0
Gullied land . 0.01 2.0 0.02 0.2-6.0
Halawa . 0.13 44.0 572 2.0-6.0
Haleiwa 0.14 48.0 6.72 0.6-2.0
Holomua 0.13 26.0 3.38 0.6-2.0
Hoolehua . 0.07 15.0 2.25 0.6-2.0
Jaucas.... 0.06 13.0 0.78 6.0-20.0
Kahanui ol 18.0 1.98 2.0-6.0
0.20 14.0 28 0.6-2.0
0.12 20.0 2.40 0.06-0.2
0.10 19.0 1.90 2.0-6.0
0.14 18.0 2.52 2.0-6.0
0.13 9.0 1.17 2.0-6.0
Kawaihapai 0.13 54.0 7.02 0.6-6.0
Lahaina... O11 31.0 3.41 0.6-2.0
Lualualei 0.12 30.0 3.60 0.06-0.2
Mala. 0.12 40.0 4.80 0.6-20.0
Marsh 0.27 10.0 2.70 2.0-6.0
Molokai 0.12 15.0 1.80 0.6-2.0
0.10 52.0 5.20 0.2-6.0
0.13 11.0 1.43 2.0-6.0
ol 19.0 2.09 2.0-6.0
0.13 21.0 2.23 2.0-6.0
0.19 15.0 2.85 0.01-20.0
0.08 62.0 4.96 0.06-2.0
0.135 33.0 4.46 0.6-2.0
Rock land 0.14 40 0.56 0.6-2.0
Rock outcrop ... 0.04 0.60 0.02 not applicable
Rough broken land. 0.15 30.0 4.50 0.6-2.0
Rough mountain land. 0.14 25.0 3.38 0.2-6.0
Stony alluvial 0.06 50.0 3.00 2.0-6.0
Stony colluvial 0.10 10.0 1.00 0.6-2.0
Tropaquods. . . 0.22 5.0 1.10 0.01-20.0
Very stony land . 0.09 5.0 0.45 0.06-2.0
Waihuna 0.10 18.0 1.80 06-0.6
Waikapu 0.10 12.0 1.20 0.6-2.0

Water-Budget Model 11


occurrence on the island. Numerous reports describe
various surface- and ground-water development and
transmission projects (Lindgren, 1903; Howell, 1938;
Austin and Stearns, 1954; Hirashima, 1963; Parsons,
Brinckerhoff, Hirota Assoc., 1969). A study containing
water-budget estimates relevant to this investigation
was prepared by the State of Hawaii (1990) for a water-
resources protection plan.

Description of the Study Area

The study area encompasses the entire island of
Molokai, 260.5 mi? (fig. 1). Molokai is the fifth largest
of the Hawaiian islands and is located about 25 mi
southeast of Oahu and 8.5 mi northwest of Maui. The
island is long and narrow, 38 miles by 10 miles, and was
formed by volcanic activity at the East Molokai Vol-
cano and the West Molokai Volcano.

East Molokai.--The peak of East Molokai is at an
altitude of 4,961 ft at Kamakou (fig. 1). Originally, a
large caldera, more than 4 mi across, existed near the
summit of this volcano (Stearns and Macdonald, 1947)
(fig. 2). Streams originate in this area of high rainfall,
and most flow north and east, carving deep valleys into
the north side of the extinct East Molokai Volcano.
Streamflow in the uplands is perennial, fed by ground-
water discharge at springs and by seepage from a high-
level swamp (fig. 1). Some of this streamflow is
diverted through a network of ditches and tunnels to res-
ervoirs for municipal and agricultural supply. Forested
conservation land dominates the uplands and the north
part of East Molokai. East Molokai is undeveloped
except for small communities located along the south-
em shore.

Kalaupapa.--The Kalaupapa Peninsula was
formed from rejuvenated-stage lava at the base of a sea
cliff on the north side of the East Molokai Volcano (fig.
2). This area is isolated from the rest of the island by the
steep cliff and it is here that a settlement for Hansen’s
disease patients has been located since 1865. A well in
the lower Waihanau Stream valley supplies water to the
residents of the area.

Hoolehua Plain.--Lava flows of the East Molokai
Volcano partially buried the eastern flanks of the older
West Molokai Volcano (fig. 2) to form the Hoolehua
Plain (fig. 1). No perennial streams exist in the area but
a reservoir supplied by diverted water from East Molo-
kai is located here. This reservoir and some limited

2 Water Budget for the Island of Molokai, Hawaii

ground-water development in East Molokai (fig. 3) sup-
ply water to meet the agricultural and municipal
demands of the 6,600 residents that live in small com-
munities in the area, in the central town of Kaunakakai,
and along the southern shore of eastern Molokai. Much
of the ground water is developed at wells near Kualapuu
where the 1995 withdrawals totaled 2.49 Mgal/d. Agri-
culture is the predominant land use on the plain. Several
thousand acres of pineapple were once cultivated near
Kualapuu and in western Molokai beginning in the
1920’s. Until 1985 pineapple production was a major
source of employment on the island. Since then,
smaller-scale diversified farms have been established
cultivating coffee, watermelons, and other crops. Much
of this fertile land was allocated to native Hawaiians as
homestead lands by the Hawaiian Homes Commission
Act of 1920.

West Molokai.--To the west of the Hoolehua Plain
the island is much drier and there are no perennial
streams. The peak of the West Molokai Volcano is at an
altitude of 1,430 ft near Puu Nana (fig. 1). Ranching is
the major land-use activity in this relatively barren area.
A resort development along the western coast is sus-
tained by water developed from East Molokai.

Most of the fresh ground water on the island is in
East Molokai and moves from the mountain toward the
ocean. Within the rift zone of the volcano, low-perme-
ability basaltic dikes impede ground-water movement
and impound ground water at high levels. The approxi-
mate location of this high-level water as well as other
ground-water areas was described by Stearns and Mac-
donald (1947) (fig. 4). Freshwater floats on saltwater
near sea level within the more permeable lava flows on
the flank of the volcano. The aquifer is confined in
places along the southern coast by low-permeability
sedimentary deposits (fig. 2), locally known as caprock.

WATER-BUDGET MODEL

Ground-water is replenished by recharge from
rainfall that percolates through and beyond the root
zone in the soil to the subsurface rock. Ground-water
recharge can be estimated using a water-budget model.
The method used in this study for calculating the water
budget is similar to that developed by Thomthwaite
(1948) and Thornthwaite and Mather (1955) and is an
accounting procedure that balances moisture input of
rainfall, and moisture outputs of direct runoff, evapo-


estimate of recharge from the State study is about one- _—_ determined in the State of Hawaii report (1990). A com-
third to half of the average recharge values estimated in _ parison of the monthly and annual rainfall distributions
the present study in several of the areas, including Kah- _in the GIS showed some discrepancies particularly in
anui, Haupu, Waikolu and Wailau. the windward aquifer-system areas of Pelekunu,
Wailau, and Halawa. The sum of the monthly rainfall
values were significantly greater than the mean annual
values, apparently owing to a registration error in the
monthly rainfall GIS data causing the rainfall lines to be

Although the same rainfall data were used for these
two studies, the present study used a monthly rainfall
distribution and the previous study used the annual dis-
tribution. It is not clear how area rainfall values were

Table 5. Monthly water budget for Kualapuu aquifer-system area, Molokai, Hawaii
[Values in million gallons per month; 1, method I; Il, method II]

Water-budget 1
component Jan. Feb. Mar. Apr. May June July Aug. Sept. Oct. Nov. Dec. Mean
ini c : : Ty 1 : Ty , ,

Direct runoff 229 190 208 173 100 51 61 63 47 116 165 227 136

Pan evaporation 743 899 841 1,056 1,802 3,919 3,193 3,148 3,928 1,524 1,065 754 = 1,906

AEI 633 736 697 259-816 381 427 439 340 706 = =—769 638 570

AEII 743, 899 840 987 1,309 118 469 481 360 880 935 751 781

AE average 688 818 768 873 1,063 549 448 = 460 350 793 = 852 694 696

Recharge I 1,120 828 863 653 161 24 42 42 20 181 399 864 433

Recharge II 866 553 754 446 2 0 0 0 0 0 45 501 264

Recharge average 993 691 808 550 82 12 21 21 10 91 222 682 349

EndSS I 367 268 306 223 15 0 0 0 0 4 100 353 136

EndSS II 957 972 975 871 328 0 0 0 0 11 295 798 434

EndSS average 662 620 640 547 172 0 0 0 0 7 197 575 285

Assi +14 -99 +38 -83 -208 -15 0 0 0 +4 +96 = +253 0

Ass II +159 +15 +30 -104 543-328 0 0 0 +11 +284 = +503 0

ASS average +86 -42 +20 -93_-375__—-172 0 0 0 +7 +190 +378 i)

| Mean is sum of January through December values divided by 12; for ASS, mean is sum of January through December values which should equal 0.

Table 6. Water budgets from this study for aquifer-system areas, Molokai, Hawaii
[Mgal/d, million gallons per day; AE, actual evapotranspiration. The difference of rainfall minus runoff, average AE, and average recharge may not equal zero due to
rounding, areas shown in figure 9]

‘Average Method Average Pan

Aquifer- Runoff/ Method! Average Method AE/ Method! Average i} recharge/ evapor-
system Area Rainfall Runoff Rainfall AE AE AE rainfall recharge recharge recharge rainfall ation
area (mi2)_ (Mgal/d) (Mgal/d) (percent) (Mgal/d) (Mgal/d) (Mgal/d) (percent) (Mgal/d) (Mgal/d) (Mgal/d) (percent) (Mgal/d)
Kaluakoi 44.4 43 12 24 31 38 72 12 7 1 16 191
Punakou 34.7 25 3 12 14 18 21 72 8 5 1 20 164
Hoolehua 13.6 18 2 u 10 13 15 72 6 4 1 22 53
Manawainui 25.4 22 2 9 14 16 18 73 6 4 2 18 121
Kualapuu 18.0 39 4 10 20 23 26 59 14 1 9 28 63
Kamiloloa 16.7 27 3 11 13 15 18 56 1 9 7 33 64
Kawela 19.8 37 4 ll 14 20 26 54 19 13 7 35 71
Ualapue 21.7 69 10 14 29 35 42 51 31 24 17 35 66
Waialua 15.0 43 6 14 22 24 27 56 16 13 i 30 47
Kalaupapa 3.5 8 1 13 4 4 5 50 4 3 2 38 ll
Kahanui 6.4 24 3 13 6 9 11 38 14 12 9 50 18
Waikolu 45 25 6 24 6 8 9 32 13 a0 9 44 11
Haupu 2.6 15 3 20 4 5 5 33 8 8 7 53 6
Pelekunu 74 39 6 15 12 14 16 36 21 19 17 49 19
Wailau 13.6 75 13 17 19 24 28 32 42 38 33 51 34
Halawa 13.2 43 17 40 14 16 18 37 12 10 7 23 39
Total 260.5 552 88 225 275 323 237 191 140 978

18 Water Budget for the Island of Molokai, Hawaii


geographic information system (GIS) model. Rainfall
distribution over the island ranges from less than 15
in/yr along the central southern coast to greater than 150
in/yr windward of the East Molokai Volcano crest.
Ground water is replenished by recharge from rainfall
that percolates through and beyond the root zone in the
soil to the subsurface rock. Average monthly ground-
water recharge was estimated from two accounting
methods; one that favors actual evapotranspiration, and
the other favors ground-water recharge.

The average ground-water recharge for the island,
estimated by the water-budget analysis, is 189 Mgal/d
(5,739 Mgal/mo). The average rainfall, direct runoff,
and evapotranspiration are 552 Mgal/d, 89 Mgal/d, and
274 Mgal/d, respectively.

REFERENCES CITED

Austin, H.A.R., and Stearns, H.T., 1954, Methods for devel-
opment and delivery of water for irrigation of Hawaiian
Homes Commission Lands at Hoolehua Island of Molo-
kai: Report to the Hawaii Irrigation Authority, Territory
of Hawaii, 57 p.

Campbell, R.B., Chang, J.H., and Cox, D.C., 1959, Evapo-
transpiration of sugar cane in Hawaii as measured by
infield lysimeters in relation to climate: Proceeding of
the 10th congress of the International Society of Sugar-
cane Technologists, p. 637-649.

Chang, J.H., 1968, Climate and agriculture: Chicago, IIl.,
Aldine Publishing Company, 304 p.

Ekern, P.C., and Chang, J.H., 1985, Pan evaporation: State of
Hawaii, 1894-1983: State of Hawaii, Department of
Land and Natural Resources, Division of Water and
Land Development, Report R74, 171 p.

Foote, D.E., Hill, E.L., Nakamura, Sakuichi, and Stephens,
Floyd, 1972, Soil survey of the islands of Kauai, Oahu,
Maui, Molokai, and Lanai, State of Hawaii: U.S. Depart-
ment of Agriculture, Soil Conservation Service, 232 p.

Giambelluca, T.W., 1983, Water balance of the Pearl Harbor-
Honolulu basin, Hawaii, 1946-1975: University of
Hawaii Water Resources Research Center Technical
Report 151, 151 p.

Giambelluca, T.W., Nullet, M.A., and Schroeder, T.A., 1986,
Rainfall atlas of Hawaii: State of Hawaii, Department of
Land and Natural Resources, Division of Water and
Land Development, Report R76, 267 p.

Hirashima, G.T., 1963, Aspects of ground-water storage and
depletion along the Molokai Irrigation Tunnel, Molokai,
Hawaii: Division of Water and Land Development,

20 Water Budget for the Island of Molokai, Hawaii

Department of Land and Natural Resources, State of
Hawaii, Circular C20, 21 p.

Howell, H., 1938, Final report on water supply studies,
Hawaii, F.P. No. 45, Island of Molokai; Description of
project objectives, estimate of cost: U.S. Bureau of Rec-
lamation, 111 p.

Langbein, W.B., and Iseri, K.T., 1960, General introductions
and hydrologic definitions, U.S. Geological Survey
Water-Supply Paper 1541-A, 29 p.

Langenheim, V.A.M., and Clague, D.A., 1987, The Hawai-
ian-Emperor volcanic chain, Part II: Stratigraphic frame-
work of volcanic rocks of the Hawaiian Islands: chap. 1
of U.S. Geological Survey Professional Paper 1350, v. 1,
p. 55-84.

Lindgren, Waldemar, 1903, The water resources of Molokai,
Hawaiian Islands: U.S. Geological Survey, Water-
Supply and Irrigation Paper No. 77, 62 p.

Mink, J.F., and Lau, L.S., 1992, Aquifer identification and
classification for Molokai: groundwater protection strat-
egy for Hawaii: University of Hawaii, Water Resources
Research Center, Technical Report no. 187, 31 p.

Parsons, Brinckerhoff, Hirota Associates, 1969, Island of
Molokai, Waikolu and Pelekunu valleys, Water
resources feasibility study: Department of Land and Nat-
ural Resources, State of Hawaii.

State of Hawaii, 1990, Water resources protection plan, vol-
umes I and II, Hawaii Water Plan: State of Hawaii, Com-
mission on Water Resource Management.

Stearns, H.T. and Macdonald, G.A., 1947, Geology and
ground-water resources of the island of Molokai,
Hawaii: Bulletin 11, Division of Hydrography, Territory
of Hawaii, 113 p.

Thornthwaite, C.W., 1948, An approach toward a rational
classification of climate: Geographical Review, v. 38,
no. 1, p. 55-94,

Thornthwaite, C.W., and Mather, J.R., 1955, The water bal-
ance: Publications in Climatology, v. 8, no. 1, p. 1-104.

Wahl, K.L., and Wahl, T.L., 1995, Determining the flow of
Comal Springs at New Braunfels, Texas: Proceedings of
Texas Water ‘95, A Component Conference of the First
International Conference on Water Resources Engineer-
ing, American Society of Civil Engineers, August 16—
17, 1995, San Antonio, Tex., p. 77-86.


If Xp = SSrax» OR If X<SSiax, (9)
then Gy = X2 — SSinax then G,, =0
and Xeng = SSmrax- and Xenq = Xp.

where:

SSinax = maximum soil-moisture storage,
Gy = ground-water recharge for the month, and
Xenq = Soil-moisture storage at the end of the month
which becomes the beginning soil-moisture
storage for the next month (SS,,41)-

Ground-Water Recharge

The average recharge for Molokai is calculated to
be 5,739 Mgal/month or 189 Mgal/d for natural condi-
tions. The distribution of ground-water recharge (fig. 8)
is somewhat similar to the distribution of annual rainfall
(fig. 6). Ground-water recharge ranges from less than 1
in/yr at many locations in western Molokai and at some
locations along the southern and eastern shore to 100
in/yr near the eastern Molokai mountain crest. Recharge
during the winter months is considerably more than dur-
ing the summer months (table 3). From November
through April, average recharge ranges from 218
Mgal/d (6,547 Mgal/mo) in November to a high of 427

Table 3. Monthly water budget, Molokai, Hawaii

Mgal/d (13,241 Mgal/mo) in January. During the sum-
mer months average recharge ranges from a low of 17
Mgal/d (513 Mgal/mo) in June to a high of 70 Mgal/d
(2,157 Mgal/mo) in October. The low recharge values
in June and September are directly related to the distinct
low rainfall values for the same months.

WATER-BUDGET RESULTS

The relations between the water-budget compo-
nents for natural conditions for Molokai are summa-
rized in table 3. The water budget shows distinct
variations in rainfall, runoff, evapotranspiration, and
ground-water recharge through the months. The winter
rainfall is generally three times the summer rainfall with
a Similar seasonal pattern for runoff. The average
monthly evapotranspiration values do not vary as dra-
matically through the months because actual evapo-
transpiration is limited in the winter by a decrease in
evaporative energy and in the summer by a lack of
water to meet the evaporative demand. Seasonality in
ground-water recharge is similar to that of rainfall,
although the difference in the average values is more
extreme, with the highest winter (January) recharge vol-
ume being more than 20 times the lowest summer
(June) volume.

{Values in million gallons per month; AE, actual evapotranspiration; SS, soil-moisture storage; I, method I; II, method Il]

Water-budget = jan, Feb. Mar. Apr. «May June July Aug. Sept. Oct. Nov. Dec. Mean!

component
Rainfall 27,816 23,563 26,181 20,647 11,169 6,456 9,080 9,415 7,258 13,988 21,093 24,892 16,801
Direct runoff 4246 3,578 4,203 3,453 1,921 1,113 1,579 1,678 1,212 2,272 3,385 3,987 2,719
Pan evaporation 9,898 12,392 11,455 15,921 30,095 70,649 56,479 51,555 49,055 23,052 14,569 11,656 29,731
AEI 7,530 8,392 7,757 8,317 6971 4,360 5,277 5,421 4,955 7,562 8,062 7,820 6,869
AEIL 9,889 12,045 10,864 12,107 11,970 7,490 7,153 7,399 6,548. 10,696 10,856 10,804 9,818
AE average 8,709 10,218 9,311 10,211 9,471 5,924 6215 6410 5,752 9,129 9,459 9,312 8,343
Recharge I 15,245 12,388 13,713 10,037 3,274 1,025 2,224 2,317 1,092 4,144 8,928 12,185 7,214
Recharge Il 11,236 8,608 10,993 7,182 583 0 8&8 213 0 171 4,164 7,936 4,264
Recharge average 13,241 10,497 12,353 8,610 1,929 513 1,156 1,264 $472,157 6,547 10,059 5,739
EndSS I 2484 1,690 2,198 1038 40 oO 1 1 0 10 727 1,628 818
EndSS I 8,332 7,664 7,787 5,691 2,386 239 «501_-=S««627Ss«138-=—«4975 «3,661 5,828 3,652
EndSS average 5408 4,678 4,992 3,364 1,212 119 249-312, 491-2192 3,725 2,234
Ass +856 -794 4508 -1,160 998-4041 0-1 #10. 4717-4901 0
Assit 42,504 668 +123. -2,096 -3,305 -2,147 4262 +126 © -489-«-+837 «+2686. +2,167 0
ASS average +1683 -730 4314-1628 -2,152 -1,093 +130 463-244-4423 +1701 +1,533 0

' Sum of January through December values divided by 12; for ASS mean is sum of January through December values which should equal 0, any imbalance in

budget is due to rounding

Water-Budget Results 15


transpiration, and ground-water recharge. This budget-
ing method is a coarse representation of the allocation
of water to the continuous processes of soil-wetting and
plant interception of rainfall, runoff in streams, the
return of moisture to the atmosphere by way of evapo-
ration from soil and water surfaces and evapotranspira-
tion by plants, and percolation past the plant root zone
to recharge ground water. The relation of the water-bud-
get components is expressed by:

G=P-R-AE-ASS, (1)
where: G = ground-water recharge,
P = precipitation rainfall,
R = direct runoff,
AE = actual evapotranspiration, and
ASS = change in soil-moisture storage.

In the water-budget model, direct runoff is calcu-
lated as a percentage of rainfall and thus the budgeting
method solves for the remaining components of ground-
water recharge, actual evapotranspiration, and the
change in soil-moisture storage. All the specific condi-
tions including the variety of rainfall intensities, the
instances when evapotranspiration is suppressed
because of rainy, cloudy conditions and 100 percent
humidity, or when the soil is so dry there is no water for
plant evapotranspiration, are not specifically simulated
by the budget using monthly data. The monthly budget
does provide, however, average values of the water-
budget components appropriate for a general assess-
ment of the magnitude of the resource.

Data Requirements

A geographic information system (GIS) model was
created to calculate the monthly water budget by linking
the spatial and quantitative characteristics of the vari-
ables in equation 1. The data requirements for the GIS
water-budget model include spatial distributions of the
rainfall, runoff (streamflow) and associated drainage
area, soil properties, and pan-evaporation. The spatial
data allow the water-budget components to be calcu-
lated and displayed by individual area or any combina-
tion of areas.

The digital map of the shoreline of the study area
was prepared by the National Mapping Division of
USGS from 1:24,000-scale USGS topographic maps
prepared in 1983. The area was subsequently divided
into water-management areas (called “aquifer-system”

areas) defined by the State of Hawaii (1990). The digital
representation of these areas was prepared by and
obtained from the State of Hawaii Department of Health
(fig. 5). These subdivisions allow comparisons with
previous water-budget estimates for the island.

Rainfall

The rainfall distribution in the study area is influ-
enced by an orographic effect caused by the East Molo-
kai Volcano. Rainfall is abundant along the crest of the
East Molokai Volcano and on the windward (north) side
of east Molokai as the prevailing northeast tradewinds
are forced to rise and cool over the mountain mass.
However, the rainfall maximum here is lower than that
found at peaks of similar altitude on other Hawaiian
islands, because the orientation of the crest is approxi-
mately parallel to the tradewind direction (Giambelluca
and others, 1986). In some locations windward of the
mountain crest, the mean annual values are more than
150 in. (Giambelluca and others, 1986) (fig. 6). Rainfall
decreases dramatically towards the southern coast,
where average rainfall is less than 15 in/yr near
Kaunakakai.

Giambelluca and others (1986) prepared 12 maps
showing lines of equal mean monthly rainfall for the
island of Molokai. The maps were compiled from data
collected at 84 stations including a network of five base
stations that had complete records for the base period
from 1931 through 1983. Records from an additional
four stations with long periods of record were used in
their statistical analyses (Giambelluca and others, 1986,
p- 6-12). In the analysis of mean annual rainfall, the
most weight was given to stations with the longest
record. Yet some inconsistencies among nearby stations
remained. Adjustments were made on the basis of the
available data and on knowledge of the rainfall-produc-
ing mechanisms. Thus, there is an element of subjectiv-
ity incorporated into these maps (Giambelluca and
others, 1986). These monthly maps were digitized and
constitute the rainfall data set for the GIS model. The
value assigned to the area between the lines of equal
rainfall is the average value of the bounding lines.

The spatial distribution of rainfall varies from
month to month, and most significantly from winter to
summer months. These data were used in the study area
to calculate mean monthly rainfall volumes that range
froma high of 899 Mgal/d (27,876 Mgal/mo) in January

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6 Water Budget for the Island of Molokai, Haw:


WATER BUDGET FOR THE ISLAND OF MOLOKAI, HAWAII

By Patricia J. Shade

U.S. GEOLOGICAL SURVEY
Water-Resources Investigations Report 97-4155

Prepared in cooperation with the
STATE OF HAWAII

DEPARTMENT OF HAWAIIAN HOME LANDS

a USGS

science for a changing world

Honolulu, Hawaii
1997


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shifted slightly to the north in this area. The monthly
rainfall values were adjusted so that the sum of the
monthly values equals the mean annual rainfall in these
three areas.

Although the aquifer-system areas in figure 5 are
identical in the two studies, it is not known how the
areas were computed in the previous study. The area
discrepancy is about 4 mi’ for both Kawela and Ualapue
systems; however, island-wide, the total area differs by
less than 1 percent.

Limitations of the model.--The GIS water-budget
has several limitations, including the regional nature of
the model, the average characteristic of all input data,
and the monthly time-step of the calculations. For most
of the island, the runoff calculations are regionalized by
applying average relations, determined from soil char-
acteristics and data from another study, over large areas.
The available-water capacity and the calculated maxi-
mum soil-moisture storage of the soil types on Molokai
are important components in the water-budget model,
because they limit ground-water recharge and evapo-
transpiration. The data used to calculate these compo-
nents come from individual soil profiles that are
regionalized for the soil series. All rainfall, direct run-
off, pan evaporation, and soil data are averages that
eliminate the extremes that occur in nature. The error
associated with these average data is likely com-
pounded by the budget accounting with a monthly time

interval. Although monthly water-budget calculations
estimate evapotranspiration more accurately than
assuming the maximum evapotranspiration rate as is
done in annual water-budget calculations, in reality, the
components of the water budget are interacting on the
order of minutes and hours within small areas. Averag-
ing the results of the two methods of monthly calcula-
tions presented in this study attempts to mitigate
possible errors associated with each method. Although
daily, watershed-scale, temporal data could more accu-
rately determine evapotranspiration and ground-water
recharge, these data are not available, and a monthly
budget for the island is the time period the available
data warrant.

SUMMARY AND CONCLUSIONS

A preliminary step in understanding the ground-
water system on the island of Molokai is the calculation
of a water budget. A mean monthly water budget was
developed to estimate ground-water recharge. These
recharge estimates are integral to the understanding of
the ground-water system over time and to the ground-
water availability assessment for Molokai.

The water-budget components are defined season-
ally, through the use of the monthly water budget, and
spatially by geohydrologic areas, through the use of a

Table 7. Water budgets from State of Hawaii (1990) for aquifer-system areas, Molokai, Hawaii
{Mgal/d, million gallons per day; ET, evapotranspiration. The difference of rainfall minus runoff, ET, and recharge may not equal zero due to rounding, areas

shown in figure 9]

Runoff/ ET Recharge/
Aquifer-system Area Rainfall Runoff _—Rainfall ET Rainfall © Recharge —_—Rainfall
area (mi?) (Mgal/d) ___(Mgal/d) (percent) _(MgaV/d) __—(percent) _—(Mgal/d)_—_(percent)
Kaluakoi 48 B z 34 79 7 16
Punakou 35.2 28 2 6 20 1 6 21
Hoolehua 13.8 19 1 3 14 2 4 21
Manawainui 24.6 21 1 6 15 72 5 24
Kualapuu 18.2 34 2 5 25 14 9 21
Kamiloloa 17.2 29 2 6 21 14 7 24
Kawela 237 54 3 6 39 B u 20
Ualapue 17.7 58 6 10 34 58 18 31
Waialua 149 53 6 12 28 53 19 36
Kalaupapa 45 10 1 7 7 B 3 31
Kahanui 55 16 1 8 10 67 4 25
Waikolu 45 18 4 21 9 47 6 33
Haupu 2.6 10 2 20 5 48 3 29
Pelekunu 14 35 10 2 14 40 12 34
Wailau 13.3 62 16 2 25 41 20 32
Halawa 13.9 44 7 15 26 61 10 2B
Total 261.6 534 66 326 144

Summary and Conclusions 19


Water Budget for the Island of Molokai, Hawaii

By Patricia J. Shade

Abstract

Ground-water recharge is estimated from a
monthly water budget calculated using long-term
average rainfall and streamflow data, synthesized
pan-evaporation data, and soil characteristics. The
water-budget components are defined seasonally,
through the use of monthly data, and spatially by
geohydrologic areas, through the use of a geo-
graphic information system model.

The long-term average ground-water recharge
for Molokai was estimated for natural land-use
conditions. The island-wide mean recharge rate for
natural conditions is 189 million gallons per day,
which is 34 percent of rainfall. The island-wide
rainfall, direct runoff, and actual evapotranspira-
tion are 552, 89, and 274 millions gallons per day,
respectively.

INTRODUCTION

Ground-water development on Molokai is becom-
ing increasingly important to meet present and pro-
jected municipal and agricultural demands. Although
rainfall is abundant in the mountainous upland water-
sheds, development in this area is difficult. Ground-
water development has been concentrated at a few spe-
cific areas at lower altitudes closer to the coast. In an
effort to meet the present and future water demand and
to increase knowledge of the ground-water system on
Molokai, the State of Hawaii, Department of Hawaiian
Home Lands entered into a cooperative agreement with
the U.S. Geological Survey (USGS) to study ground-
water availability on the island. The project includes a
water-budget calculation described in this report and

simulation of the ground-water flow system using the
ground-water recharge data provided by the water bud-

get.

Purpose and Scope

The purpose of this report is to describe the calcu-
lation of a mean monthly water budget for natural con-
ditions on the island of Molokai. The island is sparsely
populated and there is little urban development affect-
ing the water-budget components. Recently, diversified
agriculture has expanded after large-scale pineapple
production was discontinued on the island. Island-wide,
the effect of irrigated agriculture on the water budget is
minimal because of the limited areas occupied by agri-
culture.

The availability of monthly mean rainfall distribu-
tion maps for the island was the determining factor for
the time period used in the water-budget calculation.
Because monthly calculations provide an estimate of
actual evapotranspiration and water held in the soil root
zone rather than assuming evapotranspiration occurs at
the maximum rate, the resulting estimates of ground-
water recharge are considered more realistic. Three
water budgets are described that together present a
range of actual evapotranspiration and ground-water
recharge values useful for water-resource management.
The spatial distribution of the water-budget components
by water-management areas is tabulated, and the
ground-water recharge distribution is displayed.

Previous Investigations
Several reports address aspects of the water

resources of the island of Molokai. Stearns and Mac-
donald (1947) described the geology and ground-water

Introduction 1


be at the depth where the soil-profile description
changed from “abundant roots” or “common roots” to
“few roots” or “no roots”. The maximum soil-moisture
storage (SS,yqx) is the product of the root depth and the
available water capacity for the soil type (table 2). A
digital map (fig. 7) of maximum soil-moisture storage
was created for use in the GIS model. The SS,,,, value
is important in the water budget because it is the maxi-
mum limit for evapotranspiration and the limit above
which ground-water recharge occurs.

Pan Evaporation and Potential
Evapotranspiration

Pan evaporation data from class-A evaporating
pans provide an estimate of the potential (maximum)
evapotranspiration. Potential evapotranspiration (PE) is
an estimate of the amount of water that could be evapo-
transpired from a given area, assuming a continuous
water supply. Thus, PE, although influenced by other
factors, is primarily a function of solar radiation energy
(Chang, 1968, p. 131 and Mather, 1978, p. 8). Therefore
in dry, sunny areas, actual evapotranspiration can rarely
occur at the estimated potential rate without irrigation,
because there is a lack of water to satisfy the maximum
demand described by the PE value. For this study, pan
evaporation is assumed to equal potential evapotranspi-
ration on the basis of the results of lysimeter studies in
sugarcane fields (Chang, 1968; Campbell and others,
1959) where the average ratio between potential evapo-
transpiration and pan evaporation was about 1.0.

Pan evaporation data are available at three sites on
Molokai (Ekern and Chang, 1985), one in west Molokai
and two on the Hoolehua Plain. Two of these sites have
a period of record of less than 4 years, but one had 14
years of data. These data indicate high pan evaporation
rates on the uplands of the Hoolehua Plain where it is
dry and windy. Ekern and Chang (1985) found that the
annual pan evaporation rates in this area are 30 to 40
percent greater than that for the open ocean adjacent to
Hawaii, which is 79 in/yr. Thus in the GIS model,
annual pan evaporation was calculated to be 135 per-
cent of 79 in., between the altitudes of 500 and 800 ft on
the Hoolehua Plain. Annual values for the remainder of
the island were estimated on the basis of a rainfall-pan
evaporation relation (eq. 2) established from data avail-
able near the southern part of the island of Hawaii
(Giambelluca and others, 1983; and Ekern and Chang,
1985) for an area with equally varying climatic patterns

12 Water Budget for the Island of Molokai, Hawaii

of dry windy conditions in the lowlands and similar rap-
idly increasing rainfall and cloud cover and lower tem-
peratures with increasing altitude:

Annual Pan Evaporation = 235.16 x Annual Rain°®32 (2)

The annual pan evaporation was distributed
monthly on the basis of a set of monthly factors that
describe the relation between the monthly and annual
rainfall values:

annual pan (x/Rain,,)
y

where x = annual rain/12 and

12
x
y= x Rain,
m=

Pan, =

; (3)

The monthly pan evaporation values are inversely
related to rainfall, decreasing in the wet winter months
and increasing in the dry summer months.

Actual Evapotranspiration and Soil-Moisture
Accounting

Actual evapotranspiration is the quantity of water
evaporated from water, plant, and soil surfaces and tran-
spired by plants. Actual evapotranspiration data from
direct field measurements are not available for Molokai;
however, it is possible to estimate actual evapotranspi-
ration from estimates of pan evaporation and soil data.

The potential evapotranspiration (pan evaporation)
demand in a particular month can not always be met by
the amount of water in soil storage. In such situations
actual evapotranspiration is less than the potential
evapotranspiration. The maximum soil-moisture stor-
age capacity, SS,,,x, is important in the water budget
because it is the limit above which ground-water
recharge occurs and is a determining factor in the calcu-
lation of evapotranspiration. Two water-budget
accounting sequences were used; one that favors
recharge and one that favors evapotranspiration.

The amount of water held in the soil changes from
month to month. To determine an initial soil-moisture
storage value for the water-budget model, three model
Tuns were made using different soil-moisture storage
values for the month of January: SS,yax, half of SSiax>
and zero. The resulting soil-moisture storage values at


the end of December were identical for these three
model runs. Thus, the December values were input for
the initial soil-moisture storage in January for the final
water-budget calculation. The first accounting
sequence, method I, creates the opportunity for excess
soil-moisture to be allocated to ground-water recharge
first, and the second accounting sequence, method II,
allocates excess soil-moisture to evapotranspiration.
The results of the two water-budget accounting proce-
dures were averaged to present a reasonable, although
not overly-conservative estimate of ground-water
recharge.

The following accounting sequence, method I,
favors ground-water recharge. The runoff for the month
is subtracted from the sum of the month’s initial soil-
moisture and rainfall. The remainder is the first interim
soil-moisture storage value (X,), and if this quantity
exceeds SSinax, the excess recharges ground water.
Evapotranspiration is subtracted from the second
interim soil-moisture storage (X) at either the potential
(maximum) evapotranspiration value or at some lesser
actual evapotranspiration value depending on the quan-
tity of water in soil-moisture storage available to meet
the demand. Any water remaining in soil-moisture stor-
age (Xeqq) is carried over to the next month. This
accounting procedure is shown in the following equa-
tions.

X, = SS, +P, —Rys (4)

where:

X, = first interim soil-moisture storage for the month,
SS,n = beginning soil-moisture storage for the month,

P,, = rainfall for the month, and

R,, = munoff for the month.

If X; > SSynax> OR
then G,, = X — SSprax
and Xz = SSmax-

IfX;SSSpax, (5)
then G,, = 0 and X, = Xj.

where:

SSynax = maximum soil-moisture storage,
Gy = ground-water recharge for the month, and
X2 = second interim soil-moisture storage in the
month.

14 Water Budget for the Island of Molokai, Hawaii

If X) 2 PE, OR IfX)<PE,,, (6)
then AE,, = PE, then AE,, = X
and Xeng = X27 — PEp- and Xeng = 0.

where:

AE,,, = actual evapotranspiration for the month,

PE, = potential (maximum) evapotranspiration for the
month, and

Xend = Soil-moisture storage at the end of the month
which becomes the beginning soil-moisture
storage for the next month (SS,,41)-

Method II also begins by subtracting the month’s
runoff from the sum of the month’s initial soil-moisture
and rainfall. The remainder is the first interim soil-
moisture storage. Evapotranspiration is subtracted from
this soil-moisture storage at either the potential evapo-
transpiration value or at some lesser actual evapotrans-
piration value depending on the quantity of water in
soil-moisture storage available to meet the demand.
After evapotranspiration is subtracted from storage, if
the remaining water in storage, second interim soil-
moisture storage, exceeds SS,,4x, the excess recharges
ground water. Any water remaining in soil-moisture
storage is carried over to the next month. This account-
ing procedure is shown in the following equations:

X, = SS,,+ Pi —Ryys O)

where:

X = first interim soil-moisture storage for the month
SS,, = beginning soil-moisture storage for the month,

P,, = rainfall for the month, and

Rim = munoff for the month.

If X; 2 PE,, OR IfX;<PEp, (8)
then AE,, = PE,, then AE,, = X;
and X= X; — PE). and Xz =0.

where:

PE,, = potential (maximum) evapotranspiration for the
month,
AE,, = actual evapotranspiration for the month, and
X, = second interim soil-moisture storage for the
month.


CONTENTS

Abstract
Introduction. .
Purpose and Scope
Previous Investigations. .
Description of the Study Area ...

Water-Budget Model . .
Data Requirements. . .
Rainfall .
Runoff. .
Study Area Soils 11
Pan Evaporation and Potential Evapotranspiration . 12
Actual Evapotranspiration and Soil-Moisture Accounting . 12
Ground-Water Recharge. . . 15
Water-Budget Results 15
Summary and Conclusions . . 19
References Cited 20
FIGURES
1-8. Maps showing:
1. Geographic areas and selected stream-gaging stations, Molokai, Hawaii. 3
2. Generalized geology of Molokai, Hawaii 4
3. Selected wells with ground-water pumpage, east-central Molokai, Hawaii, 1995 5
4. Estimated distribution of the principal modes of ground-water occurrence, Molokai, Hawaii 6
5. Aquifer-system areas, Molokai, Hawaii .. . 8
6. Mean annual rainfall, Molokai, Hawaii. . 9
7. Maximum soil-moisture storage, Molokai, Haw: 13
8. Estimated ground-water recharge, Molokai, Hawaii .. 16
TABLES
1. Direct runoff-rainfall ratios for drainage areas of selected streams, Molokai, Hawaii 10
2. Average soil characteristics, Molokai, Hawaii . ll
3. Monthly water budget, Molokai, Hawaii 15
4. Monthly water-budget ratios for natural conditions, Molokai, Hawaii 17
5. Monthly water budget for Kualapuu aquifer-system area, Molokai, Hawaii 18
6. Water budgets from this study for aquifer-system areas, Molokai, Hawaii 18
7. Water budgets from State of Hawaii (1990) for aquifer-system areas, Molokai, Hawaii 19

Contents iii


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

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

The use of firm, trade, and brand names in this report is for identification purposes
only and does not constitute endorsement by the U.S. Geological Survey.

For additional information write to: Copies of this report can be purchased
from:

District Chief U.S. Geological Survey

U.S. Geological Survey Branch of Information Services

677 Ala Moana Blvd., Suite 415 Box 25286

Honolulu, HI 96813 Denver CO 80225-0286


to alow of 215 Mgal/d (6,456 Mgal/mo) in June. Winter
rainfall ranges from about 703 to 929 Mgal/d (21,093 to
27,876 Mgal/mo) from November through April and in
the summer from about to 215 to 451 Mgal/d (6,456 to
13,988 Mgal/mo) from May through October.

Runoff

Streamflow consists of direct runoff, the water that
flows into stream channels promptly after rainfall, and
base runoff, the part of streamflow that is sustained
through dry weather from discharge of ground water
(Langbein and Iseri, 1960). To avoid the inclusion of
the ground-water component of streamflow, monthly
direct runoff was calculated as the difference between
mean monthly streamflow and mean monthly base run-
off. Daily base runoff was calculated in this study using
an automated base-flow hydrograph separation pro-
gram (BFI) developed by Wahl and Wahl (1995). The
daily streamflow record at each station is divided into
N-day periods for which the BFI model computes a
minimum flow. The appropriate N-value, 3, for each
basin was determined by the point of slope change on
graphs of the BFI index compared with the number of
days in the period. The value for f, the turning point test
factor, was set at 0.9 which indicates that if the mini-
mum flow within a given 3-day period is less than 90
percent of the adjacent minimums, then the central min-
imum is a turning point on the base runoff hydrograph.
The base runoff hydrograph is defined on semilogarith-
mic paper by straight lines connecting all turning points.
The area beneath the hydrograph represents the volume
of base runoff for the period of record. These daily val-
ues were summed for each month and monthly average

base runoff values were calculated for the period of
record.

The drainage basins for Halawa, Pilipililau, and
Waikolu Streams upstream of stream-gaging stations
16400000, 16404200, and 16408000 (fig. 1), respec-
tively, were digitized from USGS 1:24,000-scale topo-
graphic maps (fig. 1). Mean monthly rainfall volumes
for these basins were calculated by overlaying each
basin area with each month’s rainfall distribution in the
GIS model. Monthly direct runoff-rainfall ratios (table
1) were calculated for each of the three basins and these
monthly ratios were multiplied by the mean monthly
rainfall amounts over the respective drainage basin to
compute the monthly direct runoff component of the
water budget for the basins.

For non-perennial stream drainage basins and for
areas where there are no, or only limited, streamflow
data, a second procedure was followed to calculate
direct runoff-rainfall ratios on the basis of soil type and
rainfall. Rainfall in these areas varies greatly, from
more than 150 in/yr at high altitudes in windward areas
to less than 15 in/yr at many locations along the coast.
The runoff-rainfall ratios were developed for three
ranges of annual rainfall (greater than or equal to 100
in., greater than or equal to 50 in. and less than 100 in.,
and less than 50 in.) and for three generalized soil runoff
ratings (rapid, medium, and slow).

Runoff ratings of soils on the island are described
by Foote and others (1972). On the basis of soil texture,
permeability, and slope, soil types have a broad runoff
rating of slow, medium, or rapid. From results of a
water balance computed for the Pearl Harbor area of
Oahu (Giambelluca, 1983), comparable areas on Oahu

Table 1. Direct runoff-rainfall ratios for drainage areas of selected streams, Molokai, Hawaii

[values in percent; see figure | for areas}

Stream Station Jan. Feb. Mar. Apr. May June July Aug. Sept. Oct. Nov. Dec.
Halawa 16400000 60 50 73 71 100 = 100 100 98 1,007 100 73 79
Pilipililau 16404200 22 12 13 16 12 4 5 4 3 7 15 12
Waikolu 16408000 29 25 26 28 28 17 18 24 18 23 23 33

Direct runoff-rainfall ratios for areas outside of above drainage areas
Soil Runoff Rain > 100 in/yr 50 in/yr < Rain < 100 in/yr Rain < 50 in/yr
21 13 11
7 13 ll
not applicable ll ll

10 Water Budget for the Island of Molokai, Hawaii


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Water-Budget Model 13