Pumped well

Analytical Versus Numerical Estimates of 

Water-Level Declines Caused by Pumping,

and a Case Study of the Iao Aquifer, 

Maui, Hawaii

U.S. Department of the Interior

U.S. Geological Survey

Water-Resources Investigations Report 00-4244

 Water table with no pumping Water table with no pumping

 Water table from analytical model with pumping

 Water table from 2-D numerical model with pumping

Water table from analytical model with pumping

Water table from 2-D numerical model with pumping
Analytical Versus Numerical Estimates of WaterLevel Declines Caused by Pumping, and a Case

Study of the Iao Aquifer, Maui, Hawaii

By Delwyn S. Oki and William Meyer

U.S. GEOLOGICAL SURVEY

Water-Resources Investigations Report 00-4244

Honolulu, Hawaii

2001
U.S. DEPARTMENT OF THE INTERIOR

BRUCE BABBITT, Secretary

U.S. GEOLOGICAL SURVEY

Charles G. Groat, 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
Contents iii

CONTENTS

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

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

Geohydrologic Setting of the Hawaiian Islands . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

Hydrologic Effects of Withdrawal From a Ground-Water System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

Calculation of Sustainable Yield Using the Robust Analytical Model (RAM) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

Comparisons Between RAM and One-Dimensional Numerical Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

Zero Ground-Water Withdrawals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

Ground-Water Withdrawals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

Comparisons Between RAM and Two-Dimensional Numerical Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

Zero Ground-Water Withdrawals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

Ground-Water Withdrawals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

Case Study of the Iao Aquifer, Maui. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

Geohydrologic Setting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

Ground-Water Withdrawals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

Measured Water Levels and Comparisons with RAM-Predicted Equilibrium Heads . . . . . . . . . . . . . . . . . . . . . . . . . 19

Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

References Cited . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

Appendix: Description of RAM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

Dupuit Assumption . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

Ghyben-Herzberg Relation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

One-Dimensional Analytical Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

FIGURES

1. Schematic cross section of the regional ground-water flow system of the Iao aquifer, Maui, Hawaii . . . . . . . 4

2–7. Diagrams showing:

2. Vertical cross section of the one- and two-dimensional numerical-model grids . . . . . . . . . . . . . . . . . . . . 9

3. Model-calculated steady-state water levels from an analytical model (RAM) and from one-dimensional

numerical models for conditions of zero withdrawal and withdrawal of 50 percent of the total recharge

to the aquifer for selected caprock confining unit vertical hydraulic-conductivity values:

(A) 15 feet per day; (B) 0.15 feet per day; (C) 0.075 feet per day. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

4. Model-calculated steady-state water levels from an analytical model (RAM) and from one-dimensional

numerical models for conditions of zero withdrawal and withdrawal of 75 percent of the total recharge

to the aquifer for selected caprock confining unit vertical hydraulic-conductivity values:

(A) 15 feet per day; (B) 0.15 feet per day; (C) 0.075 feet per day . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

5. Model-calculated ratios (from a two-dimensional numerical ground-water flow model) of steady-state

water levels for withdrawal conditions (he) to steady-state predevelopment water levels (h0) in the

unconfined part of the aquifer for the case of withdrawing, from a well near the inland extent of the

aquifer, 50 percent of the total ground-water recharge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

6. Model-calculated ratios (from a two-dimensional numerical ground-water flow model) of steady-state

water levels for withdrawal conditions (he) to steady-state predevelopment water levels (h0) in the

unconfined part of the aquifer for the case of withdrawing, from a well near the middle of the

unconfined part of the aquifer, 50 percent of the total ground-water recharge . . . . . . . . . . . . . . . . . . . . 17
iv Analytical Versus Numerical Estimates of Water-Level Declines, and a Case Study of the Iao Aquifer, Maui, Hawaii

7. Model-calculated ratios (from a two-dimensional numerical ground-water flow model) of steady-state

water levels for withdrawal conditions (he) to steady-state predevelopment water levels (h0) in the

unconfined part of the aquifer for the case of withdrawing, from a well near the seaward extent

of the unconfined part of the aquifer, 50 percent of the total ground-water recharge . . . . . . . . . . . . . . . 18

8–9. Maps showing:

8. Selected wells in the Iao aquifer, Maui, Hawaii . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

9. Surficial geology of the Iao aquifer area, Maui, Hawaii . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

10–12. Graphs of:

10. Water levels at shaft 33 during 1996–98, Iao aquifer, Maui, Hawaii . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

11. Water levels at Mokuhau well field, Iao aquifer, Maui, Hawaii . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

12. Water levels at Waiehu deep monitor well and test holes B and E, departure of backward-looking

12-month moving average rainfall from the long-term average rainfall for Waiehu Camp rain gage,

and monthly mean total withdrawal from the Iao aquifer prior to 1999, Maui, Hawaii . . . . . . . . . . . . . 25

13. Map showing water-level declines in the flank flows of Wailuku Basalt between April 1977 and April

1997 for the northern part of the Iao aquifer, Maui, Hawaii . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

TABLES

1. Ratios of sustainable yield to recharge used by the State of Hawaii Commission on Water Resource

Management for aquifers in Hawaii . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

2. Values of leakance for coastal discharge areas in Hawaii . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

3. Differences between model-calculated water levels from RAM and the numerical models at selected sites . . . . . 14

4. State numbers and names of selected wells in the Iao aquifer, Maui, Hawaii . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

5. Annual ground-water withdrawal from the Iao aquifer, Maui, Hawaii . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

6. Measured water levels and RAM-predicted equilibrium head (he) at selected wells, Iao aquifer, Maui, Hawaii . 28

Conversion Factors

Multiply By To obtain

foot (ft) 0.3048 meter

foot per day (ft/d) 0.3048 meter per day

million gallons per day (Mgal/d) 0.04381 cubic meter per second
Abstract 1

Abstract

Comparisons were made between modelcalculated water levels from a one-dimensional

analytical model referred to as RAM (Robust Analytical Model) and those from numerical groundwater flow models using a sharp-interface model

code. RAM incorporates the horizontal-flow

assumption and the Ghyben-Herzberg relation to

represent flow in a one-dimensional unconfined

aquifer that contains a body of freshwater floating

on denser saltwater. RAM does not account for the

presence of a low-permeability coastal confining

unit (caprock), which impedes the discharge of

fresh ground water from the aquifer to the ocean,

nor for the spatial distribution of ground-water

withdrawals from wells, which is significant

because water-level declines are greatest in the

vicinity of withdrawal wells. Numerical groundwater flow models can readily account for discharge through a coastal confining unit and for the

spatial distribution of ground-water withdrawals

from wells.

For a given aquifer hydraulic-conductivity

value, recharge rate, and withdrawal rate, modelcalculated steady-state water-level declines from

RAM can be significantly less than those from

numerical ground-water flow models. The differences between model-calculated water-level

declines from RAM and those from numerical

models are partly dependent on the hydraulic properties of the aquifer systemand the spatial distribution of ground-water withdrawals from wells.

RAM invariably predicts the greatest water-level

declines at the inland extent of the aquifer where

the freshwater body is thickest and the potential for

saltwater intrusion is lowest. For cases in which a

low-permeability confining unit overlies the aquifer near the coast, however, water-level declines

calculated from numerical models may exceed

those from RAM even at the inland extent of the

aquifer.

Since 1990, RAM has been used by the State

of Hawaii Commission on Water Resource Management for establishing sustainable-yield values

for the State’s aquifers. Data from the Iao aquifer,

which lies on the northeastern flank of the West

Maui Volcano and which is confined near the coast

by caprock, are now available to evaluate the predictive capability of RAM for this system. In 1995

and 1996, withdrawal fromthe Iao aquifer reached

the 20 million gallon per day sustainable-yield

value derived using RAM. However, even before

1996, water levels in the aquifer had declined significantly below those predicted by RAM, and continued to decline in 1997. To halt the decline of

water levels and to preclude the intrusion of saltwater into the four major well fields in the aquifer,

it was necessary to reduce withdrawal from the

aquifer system below the sustainable-yield value

derived using RAM.

In the Iao aquifer, the decline of measured

water levels below those predicted by RAM is consistent with the results of the numerical model analysis. Relative to model-calculated water-level

declines from numerical ground-water flow models, (1) RAM underestimates water-level declines

Analytical Versus Numerical Estimates of Water-Level

Declines Caused by Pumping, and a Case Study of the

Iao Aquifer, Maui, Hawaii

By Delwyn S. Oki and William Meyer
2 Analytical Versus Numerical Estimates of Water-Level Declines, and a Case Study of the Iao Aquifer, Maui, Hawaii

in areas where a low-permeability confining unit

exists, and (2) RAM underestimates water-level

declines in the vicinity of withdrawal wells.

INTRODUCTION

A one-dimensional analytical model of groundwater flow, known as the Robust Analytical Model

(RAM) (Mink, 1980), is a commonly used tool for estimating sustainable-yield values for aquifer systems in

Hawaii. Sustainable yield, as defined by the State of

Hawaii, refers to “the maximum rate at which water

may be withdrawn from a water source without impairing the utility or quality of the water source...” (State of

Hawaii, 1987). The definition “unequivocally incorporates infinite time as a fundamental condition” of the

sustainable-yield estimate (State of Hawaii, 1992,

p. 98). In Hawaii, the most common limitation on the

rate of withdrawal froman aquifer is the upward movement (into wells) of the brackish-water transition zone

between freshwater and saltwater. To preclude saltwater intrusion at a given location, it is necessary to

maintain a sufficient water level at that location. Estimates of sustainable yield, therefore, require accurate

estimates of the water levels in a ground-water system

for a given distribution and rate of ground-water withdrawal.

To estimate the amount of water available from a

ground-water system on a long-term basis, water-level

declines and the changes in the magnitude and distribution of recharge or discharge within the system caused

by withdrawals need to be estimated. These factors are,

in turn, dependent on: (1) the hydraulic properties of the

system, (2) boundary conditions (hydrogeologic features at the physical limits of the system), and (3) the

positioning of development (wells) within the system

(Bredehoeft and others, 1982).

RAM does not account for aquifer boundary conditions that commonly exist in Hawaii, nor for the spatial distribution of ground-water withdrawals from

wells (RAM is one dimensional). Implicit in the use of

RAM are the assumptions that (1) sustainable yield can

be estimated without accounting for aquifer boundary

conditions, aquifer geometry, and the spatial distribution of hydraulic properties of the system, and (2) sustainable yield is an intrinsic property of an aquifer

independent of the locations of wells and rates of withdrawal from wells.

One of the more important boundary conditions

that RAM cannot represent is a low-permeability confining unit that exists over the volcanic-rock aquifers

near and beyond the shoreline in many areas of the State

(see, for example, Hunt, 1996; Meyer and Presley,

2000). Among the volcanic-rock aquifers that are overlain by a low-permeability confining unit are the two

most important aquifers in the State, the Pearl Harbor

aquifer on Oahu and the Iao aquifer on Maui. [For the

purposes of this report, the Iao aquifer system, as delineated by State Commission on Water Resource Management (CWRM), is referred to as the Iao aquifer

although it is recognized that the Iao aquifer system is

part of a regional ground-water flow system.] The confining unit is formed by a wedge-shaped layer of terrestrial or marine sediments of relatively low permeability

and is referred to as caprock in Hawaii. A caprock

impedes the discharge of freshwater from the aquifer to

the ocean and is an important control on the ultimate

water-level decline caused by ground-water withdrawals from the aquifer.

In 1995 and 1996, withdrawal fromthe Iao aquifer

reached the sustainable-yield value derived using

RAM. However, even before 1996, water levels in the

aquifer had declined significantly below those predicted

by RAM, and were still declining in 1997. As a result,

withdrawal from the aquifer was reduced below the

sustainable-yield value derived using RAM to halt the

decline of water levels and preclude the intrusion of

saltwater into the four major well fields in the aquifer.

Purpose and scope.--The purpose of this report is

to describe (1) comparisons between model-calculated

water levels from RAM and those from numerical

ground-water flow models that account for appropriate

aquifer boundary conditions and spatially distributed

withdrawals, and (2) a case study of the Iao aquifer,

Maui, where water levels have declined below altitudes

predicted by RAM. A site-specific numerical groundwater flow model of the Iao aquifer was not developed

for this study. Rather, generic one- and two-dimensional numerical ground-water flow models were used

to simulate water-level declines for highly permeable

aquifers overlain by caprock near the coast. All numerical models used a sharp-interface code (Essaid, 1990)

that simulates flow in ground-water systems containing

freshwater and saltwater.
Geohydrologic Setting of the Hawaiian Islands 3

GEOHYDROLOGIC SETTING OF THE

HAWAIIAN ISLANDS

The main islands of Hawaii consist of one or more

volcanoes that were formed by submarine and subaerial

eruptions. During the principal stage of volcano building, called the shield stage, thousands of lava flows

emanate froma central caldera and fromtwo to three rift

zones that extend outward from the caldera. Magma

may cool and solidify beneath the surface of the volcano

and formthin, dense, massive, nearly vertical sheets of

intrusive rock known as dikes. Within and near the

caldera and rift zones, lava flows are intruded by

numerous dikes. Outside the zone containing dikes, lava

flows extend to the ocean without intrusions. These latter flows are commonly referred to as flank flows in

Hawaii. In many coastal areas of the State, lava flows

are overlain by sedimentary deposits that form a confining unit, called caprock, above the volcanic-rock aquifer.

In qualitative terms, permeability describes the

ease with which fluid can move through a porous rock

(see, for example, Domenico and Schwartz, 1990). Permeability of dike-free volcanic rocks in Hawaii is

highly variable, depending to some degree on the thickness of individual lava flows and the extent of weathering that individual flows have undergone. Hydraulic

conductivity is a quantitative measure of the capacity of

a rock to transmit water. The horizontal hydraulic conductivity of the dike-free volcanic rocks of central Oahu

and western Hawaii generally is high (on the order of

1,000 ft/d or more) (Hunt, 1996; Oki, 1999), whereas

the horizontal hydraulic conductivity of the volcanic

rocks of eastern Kauai and northeastern Maui generally

is low (on the order of 1 ft/d or less) (Izuka and Gingerich, 1998; Gingerich, 1998; Gingerich, 1999). The low

hydraulic conductivity of volcanic rocks of eastern

Kauai and northeastern Maui may partly be caused by

the presence of dikes.

Ground-water recharge rates in Hawaii vary

greatly and are dependent on factors such as soil properties, land cover, and rates of rainfall, evaporation, and

runoff. In southern Oahu, recharge has been estimated

to range fromabout 16 to 21 Mgal/d per mile of aquifer

width (measured parallel to the coast), depending on

land-use conditions (Giambelluca, 1986). In drier areas,

such as the western part of the island of Hawaii (Oki and

others, 1999), recharge may be as low as 3 Mgal/d per

mile of aquifer width.

Fresh ground water in the Hawaiian islands is

found mainly as: (1) a freshwater-lens system (with

water levels commonly less than a few tens of feet

above sea level) consisting of a lens-shaped body of

freshwater floating on and displacing saltwater within

dike-free volcanic rocks, (2) dike-impounded water

(with water levels that are tens to thousands of feet

above sea level) where overall permeability is low due

to the presence of dikes, and (3) as perched water. The

principal source of fresh ground water for domestic use

in the Hawaiian islands is fromfreshwater-lens systems

within the highly permeable dike-free parts of volcanicrock aquifers, such as the Pearl Harbor aquifer on Oahu

and the Iao aquifer on Maui.

Where the permeability of dike-free volcanic rocks

is relatively high (hydraulic-conductivity values greater

than about 1,000 ft/d), predevelopment water levels in

the freshwater-lens systemgenerally are less than 50 ft

above sea level. Where the permeability of the dike-free

volcanic rocks is relatively low (hydraulic-conductivity

values less than about 1 ft/d), predevelopment water

levels can range from several hundred to several thousands of feet above sea level, forming a vertically extensive freshwater-lens system.

The general movement of fresh ground water is

from mountainous interior areas to coastal discharge

areas (fig. 1). Ground water discharges into the ocean or

streams or by evapotranspiration near the shoreline.

Near coastal discharge areas, movement of fresh ground

water in a freshwater-lens system is predominantly

upward and across the layered sequence of lava flows

and the caprock, where it exists.

HYDROLOGIC EFFECTS OF

WITHDRAWAL FROM A GROUND-WATER

SYSTEM

The effects of withdrawal on water levels and discharge can be understood most readily by considering a

simple, finite ground-water flow system in which the

only source of recharge is fromprecipitation and all discharge is to the ocean. If the rate of recharge to this

ground-water system remains unchanged over time, and

if there are no ground-water withdrawals, a predevelopment equilibrium or steady-state condition will eventually be reached in which ground-water levels do not

vary with time and the rate of discharge from the system

is equal to the rate of recharge.
4 Analytical Versus Numerical Estimates of Water-Level Declines, and a Case Study of the Iao Aquifer, Maui, Hawaii

0 2,000

4x VERTICAL EXAGGERATION

4,000 FEET

FEET

4,0003,5003,0002,5002,0001,5001,000

500

SEA

LEVEL

-500

-1,000-1,500

VOLCANIC ROCKSSEDIMENTARY DEPOSITSGENERALIZED DIRECTION OF GROUND-WATER FLOWWATER TABLEDIKES

Ocean

saltwater

freshwater

transition zone transition zone

EXPLANATION

Dike-impounded

ground water

Boundary between dike-impounded 

ground water and freshwater-lens system

Figure 1. Schematic cross section of the regional ground-water flow system of the Iao aquifer, Maui, Hawaii.
Hydrologic Effects of Withdrawal From a Ground-Water System 5

When withdrawal froma well begins, water is initially removed from aquifer storage in the vicinity of the

well, and water levels in the vicinity of the well begin to

decline. If withdrawal fromthe well continues at a constant rate, the zone over which water levels decline

expands outward from the well as additional water is

removed from storage. Water-level decline is greatest at

the withdrawal site and decreases outward fromthe well

forming what is known as a cone of depression. The

cone of depression eventually reaches an area where

water is discharging to the ocean. As water levels

decline near the discharge area, the rate of discharge to

the ocean decreases. If and when the reduction of discharge rate to the ocean is equal to the rate of withdrawal, a new steady-state condition is reached and

water levels cease to decline further. The magnitude of

the ultimate water-level decline caused by withdrawal is

affected by factors including (1) the rate of withdrawal,

(2) the hydraulic properties of the aquifer system, and

(3) the location of the withdrawal site relative to the discharge boundary of the system. These factors are briefly

described in the following paragraphs.

Rate of withdrawal.--All other factors being equal,

higher rates of withdrawal cause greater water-level

declines than lower rates of withdrawal. This is intuitively clear considering that for a withdrawal rate of

zero water levels will not decline, and that for a small

but positive withdrawal rate water levels will decline to

some extent.

Hydraulic properties of the aquifer system.--The

hydraulic properties at the discharge boundary of the

system have an effect on the magnitude of the ultimate

water-level decline caused by withdrawal. The lower

the permeability of the coastal confining unit, the

greater is the water-level decline at the discharge

boundary necessary to reduce an equal amount of discharge from the system. This is explained by first considering the case of injecting rather than withdrawing

water from a system. Assuming that water is injected at

a steady rate for a period sufficiently long to reach

steady-state conditions, water levels at the discharge

boundary increase to a greater extent (relative to the

pre-injection, steady-state condition) the lower the permeability of the confining unit at the discharge boundary because greater hydraulic head is required to force

an equal amount of discharge through a low-permeability confining unit than a high-permeability unit.

(Hydraulic head at a given point is commonly measured

by water levels in wells that are open to the aquifer only

at that point.) Thus, to return back to the original, preinjection, steady-state condition following the cessation

of injection, the lower the permeability of the confining

unit the greater is the water-level decline at the discharge boundary necessary to reduce an equal amount

of discharge from the system.

Location of the withdrawal site.--The location of

the withdrawal site relative to the discharge boundary

has an effect on the magnitude of the water-level

decline at the withdrawal site. Consider the case of a

one-dimensional, finite aquifer system that is in a

steady-state condition prior to any withdrawal. Steady

withdrawal from a well at the inland extent of the discharge boundary will cause water levels to decline to a

new steady-state level at which the reduction of discharge rate is equal to the withdrawal rate. Because the

cone of depression caused by withdrawal froma well is

deepest at the well, water-level declines decrease inland

from the well. Consider next the case of a well withdrawing at the same rate as in the previous case but

located at the inland extent of an identical one-dimensional aquifer system. All other factors being equal,

withdrawal froma well at the inland extent of the aquifer will cause water levels to decline at the discharge

boundary, and at the inland extent of the discharge

boundary, to the same level as in the previous case

because steady-state discharge to the ocean is the same

in both cases. As in the previous case, water-level

declines are greatest at the withdrawal site and, therefore, water-level declines increase from the inland

extent of the discharge boundary toward the well. Thus,

the water-level decline at an inland withdrawal site is

greater than the water-level decline at a withdrawal site

near the discharge boundary, all other factors being

equal.

In most situations, the source of water derived

fromwells is fromdecreased ground-water storage and

decreased ground-water discharge. In the above discussion, ground-water discharge was limited to the ocean,

which is sometimes the case in Hawaii. However, in

some ground-water systems (including those in

Hawaii), discharge may be to streams and surface-water

bodies other than the ocean, or by evapotranspiration

from plants that have roots extending to ground water.

Thus, withdrawal froma well may cause a reduction of

discharge to streams and other surface-water bodies, or

decreased evapotranspiration by plants if the water table

is lowered below the level of the roots. In addition, the

source of water derived from wells may be from
6 Analytical Versus Numerical Estimates of Water-Level Declines, and a Case Study of the Iao Aquifer, Maui, Hawaii

increased recharge. For example, reduction of groundwater levels by withdrawal may induce flow from a

stream into the ground-water system or may increase

recharge by capturing water that was originally runoff

when water levels were at or near the surface.

The hydrologic analysis of a ground-water system

generally requires construction of a numerical groundwater flow model. If appropriately constructed, a

numerical model can represent the complex relations

among the inflows, outflows, changes in storage, movement of water in the system, and other important features.

CALCULATION OF SUSTAINABLE YIELD

USING THE ROBUST ANALYTICAL

MODEL (RAM)

The one-dimensional RAM used by CWRM to

estimate sustainable yield in Hawaii incorporates the

horizontal-flow assumption (see, for example, Bear,

1972) and the Ghyben-Herzberg relation and is

described in detail in the appendix. By the assumptions

used to derive RAM (Mink, 1980), for any location in

the aquifer, the ratio of the hydraulic head squared to the

total flow rate through the aquifer is constant. Thus, the

following relation is assumed to be true:

h0

2

/Q0 = he

2

/Qe, (1)

where, h0 = hydraulic head [L], relative to mean sea

level, at location x for flow rate Q0,

Q0 = steady-state rate of flow through aquifer

for predevelopment conditions

[L3

/T],

he = hydraulic head [L], relative to mean sea

level, at location x for flow rate Qe,

Qe = steady-state rate of flow (less

withdrawals from wells or shafts)

through aquifer for development

conditions [L3

/T], and

x = Cartesian coordinate [L].

Calculation of sustainable yield using RAM

involves pre-selection of the steady-state water level

that will occur if ground water is withdrawn at a rate

equal to the sustainable yield. This water level is

referred to as the equilibriumhead (he). For the desired

equilibrium head, he, CWRM defines the sustainable

yield, D, as the difference between the predevelopment

rate of flow through the aquifer minus the reduced rate

of flow through the aquifer following development:

D = Q0 − Qe. (2)

Combining equations (1) and (2), and defining I to

be equal to Q0 yields:

D/I = 1 − (he/h0)

2

. (3)

Equation (3) represents the model (RAM) commonly used to set sustainable yield in Hawaii. To apply

this equation, predevelopment values for h0 and I must

be known or estimated, and some desired minimum

equilibrium head, he, must be established. In many

areas, values for h0 are poorly known and must therefore be estimated. The value for I is generally equated

to the recharge froma water budget of predevelopment

conditions. The value for he is selected to preserve the

quality of water produced at steady-state conditions

(State of Hawaii, 1992, p. B3).

In Hawaii, RAM is used for all freshwater-lens

systems and in areas where dike-impounded water is

dominant or extends to the coast (State of Hawaii, 1992,

p. 120). According to the State Water Resources Protection Plan, where the initial head, h0, in the aquifer was

low, the ratio he:h0 must be large and the ratio D:I must

be small (State of Hawaii, 1992, p. B3). Also according

to the State Water Resources Protection Plan, the ratio

he:h0 “used to obtain sustainable yield is based on experience with known aquifers, such as those of Honolulu

and southern Oahu” (State of Hawaii, 1992, p. B4). Values of he:h0 and D:I used by CWRM for given values of

h0 are shown in table 1.

Limitations of RAM.--One of the major limitations of RAM for use in estimating sustainable yield in

Hawaii is the inability of the model to account for the

caprock, which creates resistance to vertical discharge

of ground water fromthe aquifer to the ocean. The overall vertical hydraulic conductivity of dike-free volcanic

rocks (including weathered zones) and the caprock is

generally one to four orders of magnitude less than the

horizontal hydraulic conductivity of the dike-free volcanic rocks. Thus, the resistance to vertical discharge of

ground water to the ocean is much greater per unit area

than the resistance to horizontal ground-water flow in

the aquifer. The rate of vertical discharge is proportional to the overall vertical hydraulic conductivity of

the volcanic rocks and caprock divided by the thickness
Comparisons Between RAM and One-Dimensional Numerical Models 7

of these two rock units. The ratio of vertical hydraulic

conductivity to thickness is known as leakance:

L = Kv /B (4)

where, L = leakance [1/T],

Kv = overall vertical hydraulic conductivity of

the rocks where vertical discharge

occurs [L/T], and

B= overall rock thickness over which

vertical discharge occurs [L].

RAM does not account for the concept of leakance

although leakance is “all important” in controlling the

response of ground-water systems to stresses (Bredehoeft and Hall, 1995). Leakance is important because

for withdrawal to be sustained in most areas of Hawaii,

natural discharge into the ocean must be reduced by an

amount equal or nearly equal to withdrawal. The

smaller the value of leakance (or the greater the resistance to the diversion of water to wells), the greater is

the water-level decline necessary to reduce an equal

amount of natural discharge, and the greater the waterlevel decline in the well or wells. Because RAM does

not account for the presence of a caprock and the concept of leakance, RAM cannot accurately predict waterlevel declines associated with withdrawals in many

Hawaiian ground-water systems due to this limitation

alone.

In addition to its inability to represent a caprock,

RAM cannot account for spatially distributed withdrawals fromwells and the spatial distribution of waterlevel declines, which are greatest in the vicinity of withdrawal wells. As will be shown in the following sections, the one-dimensional RAM invariably predicts the

greatest water-level declines at the inland extent of the

aquifer where the freshwater lens is thickest and the

potential for saltwater intrusion is lowest.

Because RAM is a one-dimensional model, it cannot accurately account for the spatial distribution of

recharge. RAM assumes that all recharge enters the

ground-water flow system at the inland extent of the

system. Furthermore, because RAM is a one-dimensional model, it cannot adequately account for the

geometry of the ground-water flow system. RAM also

cannot account for the spatial variability of aquifer

hydraulic properties, which affects the distribution of

water-level declines caused by withdrawals.

In the following sections of this report, modelcalculated water-level declines from RAM are compared with model-calculated water-level declines from

one- and two-dimensional numerical ground-water

flow models. One-dimensional numerical models are

used to demonstrate the importance of the caprock on

the hydrologic response of the ground-water system to

withdrawals, and two-dimensional (areal) numerical

models are used to demonstrate the importance of representing the spatial distribution of ground-water withdrawals from wells. (By addressing the spatial

distribution of withdrawals, the two-dimensional models also indirectly address the importance of properly

representing the spatial distribution of recharge.)

COMPARISONS BETWEEN RAM AND

ONE-DIMENSIONAL NUMERICAL

MODELS

A simple one-dimensional ground-water flow system was used to compare model-calculated water levels

from RAM with steady-state water levels from sharpinterface numerical ground-water flow models. The

numerical code used was SHARP (Essaid, 1990), which

simulates flow in ground-water systems containing

freshwater and saltwater and treats freshwater and saltwater as immiscible fluids separated by a sharp interTable 1. Ratios of sustainable yield to recharge used by the State of Hawaii Commission on Water Resource

Management for aquifers in Hawaii (State of Hawaii, 1990)

Initial head, h0,

in feet above sea level

Ratio of equilibrium head to

initial head, he:h0

Ratio of sustainable yield to

recharge, D:I

4–10 0.75 0.44

11–15 0.70 0.51

16–20 0.65 0.58

21–25 0.60 0.64

>26 0.50 0.75
8 Analytical Versus Numerical Estimates of Water-Level Declines, and a Case Study of the Iao Aquifer, Maui, Hawaii

face. The ground-water flow system was assumed to

consist of an aquifer that is unconfined inland and that

is confined by a caprock near the shore and offshore.

The numerical model grid used to represent the flow

systemconsists of 44 cells; each cell is 2,000 ft long and

extends to a depth of 6,000 ft below sea level (fig. 2).

Recharge to the system was assumed to be a constant value of 20 Mgal/d per mile of aquifer width and

enter the systemat the inland extent of the aquifer. The

restriction that recharge enter the system at the inland

extent of the aquifer is necessary because RAM cannot

represent spatially varying recharge.

The horizontal hydraulic conductivity of the aquifer was assumed to be a constant value of 1,500 ft/d,

corresponding to a highly permeable volcanic-rock

aquifer. The analysis was restricted to highly permeable

volcanic-rock aquifers because vertical head gradients

are expected to be small in magnitude relative to vertical head gradients in poorly permeable aquifers. Both

RAM and the numerical models used in this study

assume that flow is horizontal, a condition which is less

likely to occur in poorly permeable aquifers.

The confining unit that overlies the aquifer near the

coast is represented in the numerical models as a seaward-thickening wedge of coastal sedimentary deposits

that is 40 ft thick at the inland extent of the confining

unit and 1,000 ft thick at the shore (fig. 2). Offshore, the

caprock is assumed to have a constant thickness of

1,000 ft. Discharge through the caprock is assumed to

be in the vertical direction. Three different values of

caprock vertical hydraulic conductivity were tested

with numerical models: 15, 0.15, and 0.075 ft/d. The

vertical hydraulic-conductivity value of 0.15 ft/d is representative of the Pearl Harbor aquifer of southern Oahu

(Souza and Voss, 1987). The range of leakance values

represented in the one-dimensional numerical models is

about 0.000075 (=0.075/1,000) to 0.375 (=15/40) feet

per day per foot. The range of leakance values tested is

consistent with the range of values estimated for Hawaiian ground-water flow systems (table 2).

Discharge from the aquifer to the ocean was modeled as a head-dependent discharge boundary condition.

The rate of freshwater discharge is assumed to be linearly related to the leakance and head in the aquifer

according to the equation:

Q = LAc(h − h′) (5)

where, Q = rate of discharge fromthe aquifer [L3

/T],

L = confining unit leakance, [1/T],

Ac = plan area of confining unit [L2

],

h = hydraulic head in the aquifer [L], relative

to mean sea level, at the discharge

boundary, and

h′ = hydraulic head above the confining unit

[L], relative to mean sea level.

For onshore areas, h′ was assumed to be equal to

zero. For offshore areas, h′ was assigned a value corresponding to the freshwater-equivalent head of the saltwater column overlying the ocean floor within the cell.

The freshwater-equivalent head, measured relative to a

mean sea level datum, was computed from the equation:

h′ = –Z/40, (6)

where Z is the altitude of the ocean floor.

Zero Ground-Water Withdrawals

For zero ground-water withdrawals, model-calculated steady-state water levels from the numerical models were 6.3, 30.6, and 52.5 ft above sea level at the

seaward extent of the unconfined part of the systemfor

caprock vertical hydraulic-conductivity values of 15,

0.15, and 0.075 ft/d, respectively (figs. 3 and 4). Lower

vertical hydraulic-conductivity values for the caprock

result in a greater resistance to discharge and higher

water levels.

In the absence of ground-water withdrawals, an

analytical equation (see equation a4 in the appendix)

that forms the basis of RAM can be used to compute the

steady-state water-table profile in a one-dimensional

aquifer if the water level is known at the seaward extent

of the unconfined part of the aquifer. To allow for direct

comparisons between the analytical equation and

numerical models, the water level at the seaward extent

of the unconfined part of the aquifer for the analytical

equation was assigned the same value as the corresponding water level from the numerical model. Thus,

in the analytical equation, the water level at the seaward

extent of the unconfined part of the aquifer was

assigned values of 6.3, 30.6, and 52.5 ft above sea level

for the three different cases, corresponding to the three

caprock vertical hydraulic-conductivity values tested

with the numerical models. For zero ground-water withdrawals, the model-calculated water-table profiles from

the numerical models are in close agreement with the
Comparisons Between RAM and One-Dimensional Numerical Models 9 10 11 12 13 14 15 16 17 18 1 2 3 4 5 6 7 8 9 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44

Sea Level

FEET

1,000

-1,000-2,000-3,000-4,000-5,000-6,000

Coastline

Seaward extent of r unconfined aquife

and inland extent

of caprock

Confining unit (caprock)

No-flow boundary cell

No-flow boundary cell

0 10,000 20,000 FEET

Horizontal Scale

CELL NUMBER

Figure 2. Vertical cross section of the one- and two-dimensional numerical-model grids. Model cells 2 to 15 of the one-dimensional model grid (corresponding to rows 2 to 15 of the two-dimensional model grid) are unconfined, water-table cells. Model cells16 to 43 of the one-dimensional model grid (corresponding to rows 16 to 43 of the two-dimensional model grid) are head-dependent discharge cells. All model cells are 2,000 feet long. Recharge is introduced into model cell 2 of the one-dimensional modelgrid (row 2 for the two-dimensional model grid). For the one-dimensional model, pumping is simulated from cells 2, 9, or 15, corresponding to pumping from near the inland extent, middle, or seaward extent, respectively, of the unconfined part of the aquifer.
10 Analytical Versus Numerical Estimates of Water-Level Declines, and a Case Study of the Iao Aquifer, Maui, Hawaii

water-table profiles fromthe analytical equation (figs. 3

and 4).

Ground-Water Withdrawals

For ground-water systems in Hawaii with a lowpermeability coastal confining unit, predevelopment

water levels generally ranged from about 10 to 40 ft

above sea level. For these systems, CWRM assumes

that at least 50 percent of the total ground-water

recharge to the aquifer can be withdrawn (table 1). For

systems with predevelopment water levels greater than

26 ft above sea level, CWRM assumes that as much as

75 percent of the total recharge to the aquifer can be

withdrawn (table 1). Thus, the one-dimensional numerical models were used to simulate steady-state water

levels that result fromwithdrawing 50 percent (fig. 3) or

75 percent (fig. 4) of the recharge to the aquifer.

Water-table profiles were simulated for each of

three caprock vertical hydraulic-conductivity values

(0.075, 0.15, and 15 ft/d) and for each of three different

locations of withdrawal (at the inland extent of the

unconfined part of the aquifer, near the middle of the

unconfined part of the aquifer, and near the seaward

extent of the unconfined part of the aquifer). The seaward extent of the unconfined part of the aquifer is the

same as the inland extent of the caprock discharge

boundary. In a one-dimensional model, withdrawal is

implicitly assumed to occur uniformly along the entire

width of the aquifer. In the numerical model, the simulated withdrawal was restricted to the freshwater part of

the system; that is, no saltwater was withdrawn. Results

from this study are consistent with results from published numerical models, which have shown that leakance is one of the major factors controlling the

response of ground-water systems to natural or imposed

stresses in Hawaii (Underwood and others, 1995; Oki,

1997; Oki, 1998).

The model-calculated water-table profiles from the

numerical models (figs. 3 and 4) indicate that, for a

given withdrawal rate and location, lower values of

caprock vertical hydraulic conductivity cause greater

water-level declines relative to predevelopment (zero

withdrawal) conditions. As described previously, the

lower the value of caprock vertical hydraulic conductivity (or leakance), the greater is the steady-state waterlevel decline needed to reduce an equal amount of natural discharge (see the section “Hydrologic Effects of

Withdrawal from a Ground-Water System”).

The model-calculated water-table profiles (figs. 3

and 4) from the numerical models also indicate that for

a given value of caprock vertical hydraulic conductivity

and withdrawal rate (1) the water-level declines at the

inland extent of the discharge boundary (caprock) are

the same regardless of where the withdrawal site is

located inland from the caprock, and (2) water-level

declines at withdrawal sites are greater for inland withdrawal sites than for withdrawal sites near the caprock.

These results are consistent with the expected response

of a ground-water systemto withdrawal (see the section

“Hydrologic Effects of Withdrawal from a GroundWater System”).

RAM also was used to compute the water-table

profiles that would result if either 50 or 75 percent of the

total 20 Mgal/d per mile recharge was withdrawn (figs.

3 and 4). By the assumptions of RAM, all ground-water

withdrawals are assumed to occur at the inland extent of

the aquifer because withdrawals are represented as a

reduction in recharge. RAM predicts that if 50 percent

of the recharge is withdrawn, then the resulting steadystate water levels are uniformly 0.707 (equal to the

square root of 0.5) multiplied by the predevelopment

a

Leakance is dependent on the thickness of the confining unit and is therefore spatially variable.

Table 2. Values of leakance for coastal discharge areas in Hawaii

Area

Leakance

(feet per day per foot) Reference

Oahu, northern 0.00007–1a Oki, 1998

Oahu, southern 0.00001–0.03a Oki, 1998

Oahu, southeastern 0.0004–0.03a Eyre and others, 1986

Molokai, northern 0.1 Oki, 1997

Molokai, southern 0.001–0.3a Oki, 1997

Hawaii, northwestern 0.01–0.1 Underwood and others, 1995

Hawaii, western 0.05 Oki, 1999
Comparisons Between RAM and One-Dimensional Numerical Models 11 0 5,000 10,000 15,000 20,000 25,000 30,000 0 5,000 10,000 15,000 DISTANCE FROM INLAND EXTENT OF CAPROCK, IN FEET 20,000 25,000 30,000 0 5,000 10,000 15,000 20,000 25,000 30,000

0

605040302010

-10

-5

5

0

10

-100-200-300-400

0

400300200100

MODEL-CALCULATED

WATER LEVEL, 

IN FEET ABOVE SEA LEVEL

DIFFERENCE IN

MODEL-CALCULATED 

WATER LEVELS FROM

AN ANALYTICAL 

MODEL AND

 NUMERICAL MODELS, 

IN FEET

DIFFERENCE IN

MODEL-CALCULATED 

INTERFACE ALTITUDES FROM

AN ANALYTICAL 

MODEL AND

NUMERICAL MODELS, IN FEET

Caprock vertical hydraulic conductivity of 15 feet per day Caprock vertical hydraulic conductivity of 0.15 feet per day Caprock vertical hydraulic conductivity of 0.075 feet per day

ABC

EXPLANATION

ZERO WITHDRAWAL 10 MGAL/D PER MILE WITHDRAWAL (50 PERCENT OF RECHARGE)

ANALYTICAL MODELNUMERICAL MODEL

ANALYTICAL MODEL, WITHDRAWAL AT INLAND EXTENT OF SYTSEMNUMERICAL MODEL, WITHDRAWAL AT SEAWARD EXTENT OF UNCONFINED AQUIFERNUMERICAL MODEL, WITHDRAWAL NEAR MIDDLE OF UNCONFINED AQUIFERNUMERICAL MODEL, WITHDRAWAL AT INLAND EXTENT OF SYSTEM

Shaded where the analytical 

model (RAM) predicts higher

water levels than the numerical 

models

Shaded where the analytical 

model (RAM) predicts deeper

interface altitudes than the 

numerical models

Figure 3. Model-calculated steady-state water levels from an analytical model (RAM) and from one-dimensional numerical models forconditions of zero withdrawal and withdrawal of 50 percent of the total recharge to the aquifer for selected caprock confining unit verticalhydraulic-conductivity values: (A) 15 feet per day; (B) 0.15 feet per day; (C) 0.075 feet per day. Also shown are the differences between themodel-calculated water levels (and interface altitudes) from the analytical model and one-dimensional numerical models for withdrawalconditions. Aquifer hydraulic conductivity is 1,500 feet per day, and ground-water recharge is 20 million gallons per day per mile of aquiferwidth. All recharge enters the system at the inland extent of the aquifer.
12 Analytical Versus Numerical Estimates of Water-Level Declines, and a Case Study of the Iao Aquifer, Maui, Hawaii 0 5,000 10,000 15,000 20,000 25,000 30,000 0 5,000 10,000 15,000 20,000 25,000 30,000 0 5,000 10,000 15,000 20,000 25,000 30,000

0

605040302010

-10

-5

5

0

10

-100-200-300-400

0

400300200100

Caprock vertical hydraulic conductivity of 15 feet per day Caprock vertical hydraulic conductivity of 0.15 feet per day Caprock vertical hydraulic conductivity of 0.075 feet per day

EXPLANATION

ZERO WITHDRAWAL 15 MGAL/D PER MILE WITHDRAWAL (75 PERCENT OF RECHARGE)

ANALYTICAL MODELNUMERICAL MODEL

ANALYTICAL MODEL, WITHDRAWAL AT INLAND EXTENT OF SYSTEMNUMERICAL MODEL, WITHDRAWAL AT SEAWARD EXTENT OF UNCONFINED AQUIFERNUMERICAL MODEL, WITHDRAWAL NEAR MIDDLE OF UNCONFINED AQUIFERNUMERICAL MODEL, WITHDRAWAL AT INLAND EXTENT OF SYSTEM

ABC

DISTANCE FROM INLAND EXTENT OF CAPROCK, IN FEET

Shaded where the analytical 

model (RAM) predicts higher

water levels than the numerical 

models

Shaded where the analytical 

model (RAM) predicts deeper

interface altitudes than the 

numerical models

MODEL-CALCULATED

WATER LEVEL, 

IN FEET ABOVE SEA LEVEL

DIFFERENCE IN

MODEL-CALCULATED 

WATER LEVELS FROM

AN ANALYTICAL 

MODEL AND

 NUMERICAL MODELS, 

IN FEET

DIFFERENCE IN

MODEL-CALCULATED 

INTERFACE ALTITUDES FROM

AN ANALYTICAL 

MODEL AND

NUMERICAL MODELS, IN FEET

Figure 4. Model-calculated steady-state water levels from an analytical model (RAM) and from one-dimensional numerical modelsfor conditions of zero withdrawal and withdrawal of 75 percent of the total recharge to the aquifer for selected caprock confining unitvertical hydraulic-conductivity values: (A) 15 feet per day; (B) 0.15 feet per day; (C) 0.075 feet per day. Also shown are the differencesbetween the model-calculated water levels (and interface altitudes) from the analytical model and one-dimensional numerical modelsfor withdrawal conditions. Aquifer hydraulic conductivity is 1,500 feet per day, and ground-water recharge is 20 million gallons per dayper mile of aquifer width. All recharge enters the system at the inland extent of the aquifer.
Comparisons Between RAM and One-Dimensional Numerical Models 13

steady-state water levels (see equation 3). Similarly,

RAM predicts that if 75 percent of the recharge is withdrawn, then the resulting steady-state water levels are

uniformly 0.5 (equal to the square root of 0.25) multiplied by the predevelopment steady-state water levels

(see equation 3).

Model results indicate that for the case of an aquifer overlain by a coastal caprock with a high vertical

hydraulic conductivity (15 ft/d), (1) the modelcalculated water-table profile from RAM is almost

identical to the model-calculated water-table profile

from a one-dimensional numerical model if withdrawal

in the numerical model is represented at the inland

extent of the aquifer, and (2) model-calculated water

levels from RAM are generally lower than or at the

same altitude as model-calculated water levels from a

one-dimensional numerical model if withdrawal in the

numerical model is from sites other than at the inland

extent of the aquifer (figs. 3A and 4A; table 3). As

described previously, withdrawal sites closer to the discharge boundary are expected to cause smaller waterlevel declines than sites farther from the discharge

boundary, all other factors being equal (see the section

“Hydrologic Effects of Withdrawal from a GroundWater System”).

For lower values of caprock vertical hydraulic conductivity (0.075 and 0.15 ft/d), the model-calculated

water levels fromRAM are higher than those fromonedimensional numerical models at the site of withdrawal

represented in the numerical models (figs. 3B and C,

and 4B and C). For the case of withdrawing 50 percent

of the recharge from an aquifer overlain by a caprock

with a vertical hydraulic conductivity of 0.15 ft/d,

model-calculated water levels from RAM are higher

than those from the numerical models at the withdrawal

site by 3.2 ft (withdrawal at inland extent of aquifer) to

4.1 ft (withdrawal at inland extent of caprock) (fig. 3B

and C; table 3). For the case of withdrawing 75 percent

of the recharge from an aquifer overlain by a caprock

with a vertical hydraulic conductivity of 0.15 ft/d,

model-calculated water levels from RAM are higher

than those from the numerical models at the withdrawal

site by 3.9 ft (withdrawal at inland extent of aquifer) to

5.0 ft (withdrawal at inland extent of caprock) (fig. 4B

and C; table 3). At the site of withdrawal in an aquifer

overlain by a low-permeability coastal caprock, the difference in model-calculated water levels from RAM

and the numerical models increases with increasing rate

of withdrawal. This result indicates that properly

accounting for the hydrologic effects of a lowpermeability caprock on water levels at the withdrawal

site becomes increasingly important as the withdrawal

rate increases.

For caprock vertical hydraulic-conductivity values

of 0.075 and 0.15 ft/d, the maximum difference between

model-calculated water levels from RAM and the

numerical models is at the inland extent of the caprock

(figs. 3B and C, and 4B and C). For the case of withdrawing 50 percent of the recharge, model-calculated

water levels from RAM are higher than those from the

numerical models at the inland extent of the caprock by

4.1 and 7.3 ft for caprock vertical hydraulic conductivity values of 0.15 and 0.075 ft/d, respectively (table 3).

The differences in model-calculated water levels

from RAM and the numerical models result from the

inability of RAM to adequately account for the hydrologic effects of a coastal confining unit. Because RAM

assumes that discharge from the system is not impeded

by a coastal confining unit, RAM tends to underestimate steady-state water-level declines caused by withdrawals for cases in which a low-permeability confining

unit is present.

The Ghyben-Herzberg relation (see appendix)

indicates that for every foot of water-level decline, the

position of the freshwater-saltwater interface will rise

by 40 ft. Except for cases in which water is withdrawn

from the inland extent of an aquifer without a lowpermeability coastal caprock, model-calculated waterlevel declines (and interface rises) fromRAM and from

numerical models generally differ (figs. 3 and 4). RAM

predicts that the interface beneath sites of withdrawal

will rise to a lesser extent than indicated by one-dimensional numerical models representing aquifers that are

confined by a low-permeability caprock (figs. 3B and

C, and 4B and C). For the case of withdrawing 50 percent of the recharge from an aquifer overlain by a

caprock with a vertical hydraulic conductivity value of

0.15 ft/d, model-calculated water levels from RAM are

higher than those from the numerical models at the

withdrawal site by 3.2 to 4.1 ft. Thus, at the withdrawal

site, the corresponding freshwater-saltwater interface

position predicted by RAM is 128 to 164 ft deeper than

indicated by the numerical models (fig. 3B). In Hawaii,

management practices have generally assumed that it is

desirable, where possible, to maintain about a 100 ft

zone of freshwater between the bottomof a withdrawal

well and the top of the brackish-water transition zone
14 Analytical Versus Numerical Estimates of Water-Level Declines, and a Case Study of the Iao Aquifer, Maui, Hawaii

(Mink and others, 1988). Therefore, underestimating

water-level declines by a few feet is significant and

could lead to saltwater intrusion into some wells.

COMPARISONS BETWEEN RAM AND

TWO-DIMENSIONAL NUMERICAL

MODELS

Although RAM is a one-dimensional model,

steady-state water levels fromtwo-dimensional (areal),

sharp-interface numerical ground-water flow models

also were compared with water levels from RAM. The

numerical code SHARP (Essaid, 1990) also was used

for the two-dimensional models. The geometry of the

two-dimensional ground-water flow system was the

same as the one-dimensional system described previously, except that the two-dimensional system was discretized perpendicular to the coastline. The numerical

model grid used to represent the flow system consists of

1,188 square cells, each 2,000 ft long by 2,000 ft wide,

arranged in a rectangular array with 44 rows and 27 columns. As with the one-dimensional system, the horizontal hydraulic conductivity of the aquifer was

a

Positive differences indicate that the water level predicted by RAM is greater than the water level predicted by the numerical model. For the twodimensional numerical model, differences were computed along a line through the well, and perpendicular to the coast.

b

Kv is the vertical hydraulic conductivity of the caprock confining unit.

Table 3. Differences between model-calculated water levels from RAM and the numerical models at selected sites

Location of withdrawal

well in the unconfined

part of the aquifer

Difference between water levels predicted

by RAM and the numerical model at

different locations in the unconfined part

of the aquifer, in feeta

Numerical model

Seaward

extent Middle

Inland

extent

50 percent of recharge withdrawn

One-dimensional model, Kv = 0.075 feet per dayb seaward extent 7.3 5.4 3.6

middle 7.3 7.0 5.0

inland extent 7.3 7.0 6.7

One-dimensional model, Kv = 0.15 feet per dayb seaward extent 4.1 1.3 -1.0

middle 4.1 3.6 0.8

inland extent 4.1 3.6 3.2

One-dimensional model, Kv = 15 feet per dayb seaward extent -0.1 -3.9 -5.9

middle 0.0 0.0 -3.4

inland extent 0.0 0.0 0.0

Two-dimensional model, Kv = 0.15 feet per dayb seaward extent 11.5 1.7 -1.0

middle 4.6 9.3 1.3

inland extent 4.2 4.2 11.1

75 percent of recharge withdrawn

One-dimensional model, Kv = 0.075 feet per dayb seaward extent 9.2 5.1 1.4

middle 9.2 8.7 4.3

inland extent 9.2 8.7 8.2

One-dimensional model, Kv = 0.15 feet per dayb seaward extent 5.0 -0.6 -4.6

middle 5.0 4.4 -1.2

inland extent 5.0 4.4 3.9

One-dimensional model, Kv = 15 feet per dayb seaward extent -0.3 -6.8 -10.2

middle -0.1 0.0 -6.2

inland extent -0.1 0.0 0.0
Comparisons Between RAM and Two-Dimensional Numerical Models 15

assumed to be a constant value of 1,500 ft/d, and the

recharge to the system was assumed to be a constant

value of 20 Mgal/d per mile of aquifer width and uniformly enter the system at the inland extent of the aquifer. The coastal confining unit in the two-dimensional

system was represented using the same geometry as in

the one-dimensional system. The caprock vertical

hydraulic-conductivity value tested with the twodimensional system was 0.15 ft/d, which is a reasonable

value for low-permeability coastal sedimentary deposits.

Zero Ground-Water Withdrawals

For zero ground-water withdrawals, the model-calculated water level at the seaward extent of the unconfined part of the systemwas 30.6 ft above sea level for

the numerical model. The water level at the seaward

extent of the unconfined part of the aquifer for the analytical equation (equation a4) was assigned the same

value of 30.6 ft above sea level. The water-table profiles

from the analytical equation and numerical model were

in close agreement. Although the numerical model is

discretized in two dimensions (areally), the flow field

for this case is one-dimensional because recharge is

introduced uniformly along the width of the aquifer at

the inland extent of the system. Thus, the water-table

profile is identical to the profile from the one-dimensional numerical model without withdrawals (fig. 3B).

Ground-Water Withdrawals

Unlike in a one-dimensional model in which withdrawal is implicitly assumed to occur uniformly along

the entire width of the aquifer, in a two-dimensional

(areal) model withdrawal can be nonuniformly distributed at individual sites in the aquifer. Water-table profiles were simulated for each of three different sites of

withdrawal: at the inland extent of the unconfined part

of the aquifer (fig. 5), near the middle of the unconfined

part of the aquifer (fig. 6), and near the seaward extent

of the unconfined part of the aquifer (fig. 7). Each of the

individual withdrawal sites represented in the twodimensional system was placed along the centerline

(perpendicular to the coast) of the aquifer. The numerical models were used to simulate steady-state water levels that result fromwithdrawing 50 percent of the total

ground-water recharge to the aquifer.

Although RAM predicts that the ratio of development heads to predevelopment heads (he:h0) is 0.707 at

all locations if 50 percent of the recharge is withdrawn,

results from the two-dimensional numerical models

indicate that for a caprock vertical hydraulic-conductivity value of 0.15 ft/d, the ratio he:h0 is (1) spatially variable, (2) less than 0.5 near the sites of withdrawal,

where maintaining higher water levels is generally most

important, (3) less than 0.707 for all locations if water

is withdrawn at a site that is inland from the middle of

the unconfined part of the aquifer, and (4) equal to

0.707 only along a single line in the aquifer (in plan

view) if water is withdrawn near the seaward extent of

the unconfined part of the aquifer (fig. 7).

Model results indicate that water levels fromRAM

are as much as 11.5 ft higher than water levels from a

two-dimensional numerical model at the site of withdrawal (table 3). Thus, on the basis of the GhybenHerzberg relation, RAM predicts that the position of the

freshwater-saltwater interface is as much as 460 ft

deeper than indicated by the two-dimensional numerical model. Spatially, the differences between modelcalculated water levels from RAM and model-calculated water levels from the numerical models are greatest in the most critical areas, which are near the sites of

withdrawal. The inability of RAM to adequately

account for the spatial distribution of withdrawals (or

recharge) is a major limitation of RAM.

It should be noted that the simulated water-level

decline in a numerical-model cell may be much less

than the actual decline at the withdrawal well because

the simulated water-level decline represents the average

decline over an entire cell rather than the maximum at a

given point. In addition, the actual water-level decline

in the immediate vicinity of partially penetrating withdrawal wells may be much greater than simulated with

the numerical model because a single-layer numerical

model cannot account for vertical head gradients in the

aquifer. On the other hand, because a single-layer

numerical model cannot account for vertical flow, the

numerical model may overestimate the rise in position

of the freshwater-saltwater interface caused by withdrawal from a partially penetrating well, especially for

highly anisotropic aquifers in which the vertical hydraulic conductivity is several orders of magnitude less than

the horizontal hydraulic conductivity.
16 Analytical Versus Numerical Estimates of Water-Level Declines, and a Case Study of the Iao Aquifer, Maui, Hawaii

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

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

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

COLUMN

ROW

NO-FLOW BOUNDARY CELL

HEAD-DEPENDENT DISCHARGE CELL

UNCONFINED, WATER-TABLE CELL

LINE OF EQUAL he:h0 RATIO

WELL THAT WITHDRAWS 50 PERCENT OF THE

 TOTAL RECHARGE TO THE AQUIFER

EXPLANATION

COASTLINE

LANDWARD

DIRECTION

SEAWARD

DIRECTION

024 6 x 1,000 FEET

0.575

0.575

0.600

0.600

0.625

0.625

0.650

0.650

0.550

0.525

0.500

well

Figure 5. Model-calculated ratios (from a two-dimensional numerical ground-water flow model) of steady-state

water levels for withdrawal conditions (he) to steady-state predevelopment water levels (h0) in the unconfined

part of the aquifer for the case of withdrawing, from a well near the inland extent of the aquifer, 50 percent of the

total ground-water recharge. Recharge enters the system uniformly at the inland extent of the aquifer at the rate

of 20 million gallons per day per mile of width. The horizontal hydraulic conductivity of the aquifer is 1,500 feet

per day, and the vertical hydraulic conductivity of the caprock confining unit is 0.15 feet per day.
Comparisons Between RAM and Two-Dimensional Numerical Models 17

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

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

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

COLUMN

ROW

NO-FLOW BOUNDARY CELL

HEAD-DEPENDENT DISCHARGE CELL

UNCONFINED, WATER-TABLE CELL

LINE OF EQUAL he:h0 RATIO

WELL THAT WITHDRAWS 50 PERCENT OF THE

 TOTAL RECHARGE TO THE AQUIFER

EXPLANATION

COASTLINE

LANDWARD

DIRECTION

SEAWARD

DIRECTION

024 6 x 1,000 FEET

well

0.550

0.500

0.650

0.675

0.625

0.600

0.575

0.525

Figure 6. Model-calculated ratios (from a two-dimensional numerical ground-water flow model) of

steady-state water levels for withdrawal conditions (he) to steady-state predevelopment water levels (h0)

in the unconfined part of the aquifer for the case of withdrawing, from a well near the middle of the

unconfined part of the aquifer, 50 percent of the total ground-water recharge. Recharge enters the system uniformly at the inland extent of the aquifer at the rate of 20 million gallons per day per mile of width.

The horizontal hydraulic conductivity of the aquifer is 1,500 feet per day, and the vertical hydraulic conductivity of the caprock confining unit is 0.15 feet per day.
18 Analytical Versus Numerical Estimates of Water-Level Declines, and a Case Study of the Iao Aquifer, Maui, Hawaii

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

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23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

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

COLUMN

ROW

NO-FLOW BOUNDARY CELL

HEAD-DEPENDENT DISCHARGE CELL

UNCONFINED, WATER-TABLE CELL

LINE OF EQUAL he:h0 RATIO

WELL THAT WITHDRAWS 50 PERCENT OF THE

 TOTAL RECHARGE TO THE AQUIFER

EXPLANATION

COASTLINE

LANDWARD

DIRECTION

SEAWARD

DIRECTION

024 6 x 1,000 FEET

well

Line (he /h0 = 0.707) where the RAM and the

numerical model predict the same steady-state water levels

0.725

0.700

0.675

0.650

0.625

0.600

0.575

0.550

0.525

0.500

0.707

Figure 7. Model-calculated ratios (from a two-dimensional numerical ground-water flow model) of

steady-state water levels for withdrawal conditions (he) to steady-state predevelopment water levels (h0)

in the unconfined part of the aquifer for the case of withdrawing, from a well near the seaward extent of

the unconfined part of the aquifer, 50 percent of the total ground-water recharge. Recharge enters the

system uniformly at the inland extent of the aquifer at the rate of 20 million gallons per day per mile of

width. The horizontal hydraulic conductivity of the aquifer is 1,500 feet per day, and the vertical hydraulic

conductivity of the caprock confining unit is 0.15 feet per day.
Case Study of the Iao Aquifer, Maui 19

CASE STUDY OF THE IAO AQUIFER, MAUI

The Iao aquifer lies on the northeastern flank of the

West Maui Volcano. As delineated by CWRM, the

aquifer system extends from the mountainous crest of

the volcano to the ocean (fig. 8). The aquifer system is

the main source of domestic water for Maui, accounting

for about 76 percent of the water supplied by the Maui

County Department of Water Supply (DWS) on the

island in 1998 (Meyer and Presley, 2000).

Geohydrologic Setting

This section describes the major features of the

geohydrologic setting of the Iao aquifer area. Meyer and

Presley (2000) provide a more detailed description.

The West Maui Volcano has a central caldera and

two main rift zones that trend in northwestern and

southeastern directions from the caldera (fig. 9). Thousands of dikes exist within the rift zones of West Maui

Volcano, with the number of dikes increasing toward

the caldera and with depth. Additional dikes exist outside the general trends of the rift zones, creating a radial

pattern of dikes emanating from the caldera (Macdonald

and others, 1983). Thousands of lava flows emanated

fromvents in and near the caldera and rift zones. Volcanic rocks in the Iao aquifer consist mainly of the shieldstage Wailuku Basalt, which is overlain in places by the

Honolua Volcanics (Stearns and Macdonald, 1942;

Langenheim and Clague, 1987). The dike-free flank

flows of the Wailuku Basalt are generally thin-bedded

and highly permeable and extend to depths far below

sea level. Volcanic rocks in the Iao aquifer are overlain

by sedimentary deposits near the coast (fig. 9).

The general movement of ground water in the Iao

aquifer is from the dike-impounded ground-water systemnear the mountainous interior toward the ocean (fig.

1). Dike-impounded ground water occurs at levels as

high as 2,000 ft above sea level. A freshwater-lens system exists within the dike-free volcanic rocks that

extend beyond the dike-impounded system. Water levels measured in wells in the freshwater-lens system of

the dike-free volcanic rocks have been as high as 37 ft

above sea level (Meyer and Presley, 2000). In the Iao

aquifer, the less-permeable sedimentary deposits that

overlie the Wailuku Basalt near the shoreline form a

confining unit that impedes the discharge of water from

the volcanic-rock aquifer into the ocean.

Ground-Water Withdrawals

Four major well fields (shaft 33, Mokuhau,

Waiehu Heights, and Waihee) are in the part of the Iao

aquifer containing a freshwater lens, and the Kepaniwai

well field is in the upgradient area containing dikeimpounded water (fig. 8; table 4). The freshwater lens is

the main source of water from the Iao aquifer. Major

withdrawal of ground water fromthe part of the aquifer

containing a freshwater lens began in 1948 at shaft 33

(fig. 8). Water from shaft 33 was originally used for

agricultural purposes. The Mokuhau well field was constructed in 1953 for domestic supply. Two additional

well fields were constructed in the late 1970’s (Waiehu

Heights in 1977 and Waihee in 1979) and the remaining

well field, Kepaniwai, was first used in 1977. Water

fromall of these well fields is presently (1999) used for

domestic supply. Nearly all of the water presently withdrawn from the aquifer is from these five well fields

operated by the Maui DWS.

In 1990, the sustainable yield of the Iao aquifer

was set at 20 Mgal/d by CWRM (State of Hawaii,

1990). The sustainable-yield value (D) was derived

assuming a predevelopment recharge rate (I) of 31.57

Mgal/d and a ratio of D:I equal to 0.64 (Mink, 1995).

The D:I ratio is obtained from table 1 with a predevelopment head (h0) of 25 ft. Average annual withdrawal

in 1990 was 17.31 Mgal/d, a value that was approached

once before in 1975 (table 5). Average withdrawal rates

increased steadily between 1985 and 1990, however,

and this increase continued through 1995 when withdrawal peaked at 20.50 Mgal/d. The average rate of

increase from 1985 through 1995 was 0.86 Mgal/d per

year. Average 1996 withdrawal was 20.35 Mgal/d,

about equal to the 1995 rate. Withdrawal was reduced to

19.10 Mgal/d in 1997 and to 17.90 Mgal/d in 1998

(table 5).

Measured Water Levels and Comparisons with

RAM-Predicted Equilibrium Heads

The use of RAM by CWRM for estimating

sustainable-yield values for the State’s aquifers is relatively recent (1990). Data fromthe Iao aquifer are now

available that allow an evaluation of the model’s predictive capability for the aquifer.
20 Analytical Versus Numerical Estimates of Water-Level Declines, and a Case Study of the Iao Aquifer, Maui, Hawaii

P A C I F I C

O C E A N

Iao-Waikapu Ditch

Waihee

Spreckels

Ditch

Ditch

Maniania Ditch

North Waiehu

Stream

South Waiehu Stream

Waiehu Stream

Iao

Stream

20o54'

20o

52'

20o

56'

156o 156 30' o 156 32' o34'

Waihee

Waiehu

Wailuku

Waikapu

0

0

1 2 MILES

1 2 KILOMETERS

EXPLANATION

IAO AQUIFER STUDY-AREA BOUNDARY

DITCH OR TUNNEL

INFERRED BOUNDARY BETWEEN DIKE-IMPOUNDED GROUND

WATER AND FRESHWATER-LENS SYSTEM (modified from Yamanaga and Huxel, 1970)

WITHDRAWAL WELL OR WELL FIELD AND NAME

WELL FIELD WITH WITHDRAWAL AND WATER-LEVEL OBSERVATION WELLS 

 AND NAME

WATER-LEVEL OBSERVATION WELL AND NAME

RAIN GAGE AND STATE NUMBER

DIKE-IMPOUNDED

GROUND WATER

FRESHWATERLENS SYSTEM

MAUI

Area

of map

Pacific Ocean

Test 

hole E

Test 

hole 15D

Test 

hole B

Waiehu deep 

monitor well and 

Test hole D

484

484

Test 

hole B

Shaft 33

Shaft 33

Mokuhau

Waihee

Waihee Waiehu

Heights

Kepaniwai

Base modified from U.S. Geological Survey

digital data, 1:24,000, 1983, Albers equal area 

projection, standard parallels 20°35' and 21°00', 

central meridian 156°20'

Figure 8. Selected wells in the Iao aquifer, Maui, Hawaii.
Case Study of the Iao Aquifer, Maui 21

0

0

1 2 MILES

1 2 KILOMETERS

P A C I F I C

O C E A N

Waihee Waihee

Wailuku

Waikapu

Puu

Kukui

Waiehu

Waikapu

EXPLANATION

SEDIMENTARY DEPOSITS

 Unconsolidated deposits, 

 chiefly younger alluvium 

 Calcareous sand dunes

 Consolidated earthy deposits, 

 chiefly older alluvium

VOLCANIC ROCKS

 Honolua Volcanics

 Wailuku Basalt

CONES, VENTS, DOMES, CRATERS, BOSSES, AND DIKES

 Cones or domes of Honolua Volcanics

 Pit craters

 Bosses of Wailuku Basalt

 Dikes of either Wailuku Basalt or Honolua Volcanics

 Dikes, where too numerous to show individually

 Axis of rift zone (from Macdonald and others, 1983)

 Caldera boundary, dotted where concealed, dashed where inferred

INFERRED BOUNDARY BETWEEN-DIKE IMPOUNDED 

 GROUND WATER AND FRESHWATER-LENS SYSTEM

STUDY-AREA BOUNDARY

Base modified from U.S. Geological Survey

digital data, 1:24,000, 1983, Albers equal area 

projection, standard parallels 20°35' and 21°00', 

central meridian 156°20'

156°34'

21°56'

21°54'

21°52'

156°32' 156°30'

Figure 9. Surficial geology of the Iao aquifer area, Maui, Hawaii (modified from Stearns and Macdonald, 1942 and

Langenheim and Clague, 1987).
22 Analytical Versus Numerical Estimates of Water-Level Declines, and a Case Study of the Iao Aquifer, Maui, Hawaii

Water-level data of most interest for this discussion are from the 1990’s, when total withdrawal

increased and reached (in 1995 and 1996) the sustainable-yield value used by CWRM. Water levels near

shaft 33 were measured intermittently from 1940

through 1970. After 1970, water levels were not measured until 1996 when measurements were made in one

of the unused wells at shaft 33 (fig. 10). Water levels at

and near Mokuhau well field were measured from 1951

to 1979. After 1979, water levels were not measured

until 1998 when measurements were made in one of the

unused wells in the Mokuhau well field (fig. 11) (Meyer

and Presley, 2000). Water levels near Waihee and

Waiehu Heights well fields can be inferred fromwaterlevel measurements made at the nearby Waiehu deep

monitor well and at test holes B, D, and E (fig. 12)

(Meyer and Presley, 2000). Given their locations (fig.

8), water levels in the Waiehu deep monitor well and

test holes B and D can be considered representative of

water levels at Waihee well field, and water levels at

test holes B and E can be considered representative of

those at Waiehu Heights well field.

Changes in water levels in observation wells in the

area of Waiehu Heights and Waihee well fields indicate

that water levels in the Iao aquifer respond to changes

in withdrawals, rainfall, and recharge from irrigation.

Between April 1977 and April 1997, water levels

declined by about 6 ft near these wells (from about 15

to 16 ft above sea level in April 1977 to about 9 to 10 ft

above sea level in April 1997) (fig. 13). During this

period, withdrawals from the Waiehu Heights and

Waihee well fields increased and recharge from irrigation decreased. Withdrawals at the Waiehu Heights and

Waihee well fields started in 1977 and 1979, respectively. In addition, because of changes in irrigation

practices, changes in types of crops grown, and reduction in agricultural acreage, estimated recharge from

irrigation decreased from17 Mgal/d during 1926–79, to

6 Mgal/d during 1980–85, to 2 Mgal/d during 1986–95

(Shade, 1997). The water-level declines (fig. 12) were

not continuous, however, indicating that water levels

are influenced by a factor or factors in addition to

increased withdrawals from the Waiehu Heights and

Waihee well fields and decreased recharge from irrigation. During the 1980’s, water levels rose above 1977

and 1979 water levels because of reduced withdrawals

fromthe Mokuhau well field and shaft 33 and variations

in rainfall. Between 1977 and 1991, trends in water levels in the vicinity of the two well fields correlate closely

to the 12-month departure of rainfall from mean rainfall

(Meyer and Presley, 2000) (fig. 12). From 1992

onward, however, there is little correlation between

rainfall and water levels. Average water levels declined

from 1990 through 1996, in apparent response to

increased withdrawals from the aquifer between 1990

and 1996. Although withdrawal was reduced in 1997,

water levels continued to decline through 1997. Further

reduction of withdrawal in 1998 resulted in a slight

increase in water levels. Changes in rainfall would be

expected to affect water levels, but the effect of withdrawal on water levels is more significant than the

effect of recent (1990–98) changes in rainfall. Average

1998 water levels are about 10 ft above sea level at all

of the well fields.

The RAM-predicted equilibriumheads, he, associated with the 20 Mgal/d value of sustainable yield used

by CWRM can be determined in two ways: (1) by using

a

Well also used for vertical salinity-profile information.

Table 4. State numbers and names of selected wells in the Iao aquifer, Maui, Hawaii

State well

number Well name Use of well

5330-05 Shaft 33 withdrawal and water-level observation

5330-07 Test hole 15D water-level observation

5330-09 to -11 Mokuhau withdrawal and water-level observation

5332-05 Kepaniwai withdrawal

5430-01, -02 Waiehu Heights withdrawal

5430-03 Test hole E water-level observation

5430-04 Test hole D water-level observation

5430-05 Waiehu deep monitor water-level observationa

5431-01 Test hole B water-level observation

5431-02 to -04 Waihee withdrawal
Case Study of the Iao Aquifer, Maui 23

Table 5. Annual ground-water withdrawal from the Iao aquifer, Maui, Hawaii

[Values in million gallons per day, or percentage where noted; --, not applicable; data from Maui Department of Water Supply and unpublished data from

Wailuku Sugar Co. in U.S. Geological Survey well files, Honolulu]

Well field Domestic

(percentage

Year of total)

Waiehu

Heights Waihee Kepaniwai Mokuhau Shaft 33 Total Domestic

1948 -- -- -- -- 2.00 2.00 0.00 0.0

1949 -- -- -- -- 1.99 1.99 0.00 0.0

1950 -- -- -- -- 1.77 1.77 0.00 0.0

1951 -- -- -- -- 3.70 3.70 0.00 0.0

1952 -- -- -- -- 3.05 3.05 0.00 0.0

1953 -- -- -- -- 9.77 9.77 0.00 0.0

1954 -- -- -- -- 6.11 6.11 0.00 0.0

1955 -- -- -- 1.10 1.31 2.41 1.10 45.6

1956 -- -- -- 0.66 0.83 1.49 0.66 44.3

1957 -- -- -- 1.19 6.12 7.31 1.19 16.3

1958 -- -- -- 1.22 0.67 1.89 1.22 64.6

1959 -- -- -- 1.43 4.15 5.58 1.43 25.6

1960 -- -- -- 1.59 5.65 7.24 1.59 22.0

1961 -- -- -- 2.25 5.64 7.89 2.25 28.5

1962 -- -- -- 2.04 7.97 10.01 2.04 20.4

1963 -- -- -- 2.06 0.85 2.91 2.06 70.8

1964 -- -- -- 2.79 6.00 8.79 2.79 31.7

1965 -- -- -- 2.67 4.68 7.35 2.67 36.3

1966 -- -- -- 3.12 4.69 7.81 3.12 39.9

1967 -- -- -- 2.91 3.08 5.99 2.91 48.6

1968 -- -- -- 2.88 6.28 9.16 2.88 31.4

1969 -- -- -- 3.61 1.18 4.79 3.61 75.4

1970 -- -- -- 3.98 5.08 9.06 3.98 43.9

1971 -- -- -- 4.34 11.65 15.99 4.34 27.1

1972 -- -- -- 4.66 9.45 14.11 4.66 33.0

1973 -- -- -- 5.16 8.11 13.27 5.16 38.9

1974 -- -- -- 5.44 9.11 14.55 5.44 37.4

1975 -- -- -- 6.40 10.56 16.96 6.40 37.7

1976 -- -- -- 6.69 6.37 13.06 6.69 51.2

1977 0.38 -- 0.04 8.10 6.39 14.91 8.52 57.1

1978 0.46 -- 0.01 8.29 3.14 11.90 8.76 73.6

1979 0.48 1.37 0.02 6.51 3.29 11.67 8.38 71.8

1980 0.48 6.15 0.02 3.05 0.00 9.70 9.70 100.0

1981 0.59 4.87 0.03 5.80 1.18 12.47 11.29 90.5

1982 0.49 5.20 0.007 4.60 0.00 10.30 10.30 100.0

1983 0.34 5.39 0.14 5.82 0.00 11.69 11.69 100.0

1984 0.29 5.41 0.11 6.39 0.37 12.57 12.20 97.1

1985 0.18 5.12 0.03 6.52 0.00 11.85 11.85 100.0

1986 0.27 6.63 0.003 6.42 0.00 13.32 13.32 100.0

1987 0.34 8.53 0.003 5.11 0.00 13.98 13.98 100.0

1988 0.35 8.06 0.00 6.71 0.00 15.12 15.12 100.0

1989 0.51 7.34 0.00 7.49 0.00 15.34 15.34 100.0

1990 0.92 8.66 0.07 7.66 0.00 17.31 17.31 100.0

1991 1.96 8.22 1.03 5.72 1.90 18.83 18.83 100.0

1992 1.08 7.96 0.82 3.17 5.10 18.13 18.13 100.0

1993 1.51 7.24 0.49 3.60 5.56 18.40 18.40 100.0

1994 1.20 8.15 0.45 6.49 2.91 19.20 19.20 100.0

1995 1.71 7.92 0.49 4.92 5.46 20.50 20.50 100.0

1996 1.56 8.22 0.28 5.13 5.16 20.35 20.35 100.0

1997 1.23 8.94 0.80 6.29 1.84 19.10 19.10 100.0

1998 0.23 9.11 0.51 3.21 4.84 17.90 17.90 100.0
24 Analytical Versus Numerical Estimates of Water-Level Declines, and a Case Study of the Iao Aquifer, Maui, Hawaii

J F M A M J J A S O N D J F M A M J J A S O N D J F M A M J J A S O N D

1996 1997 1998

8

18

9

10

11

12

13

14

15

16

17

MONTHLY MEAN WATER LEVEL, IN FEET ABOVE MEAN SEA LEVEL

RAM-predicted equilibrium head, he = 14 ft (assuming he:h0 ratio of 0.5 from table 1)

RAM-predicted equilibrium head, he = 17 ft (assuming he:h0 ratio of 0.6 from equation 3)

5

30

10

15

20

25

WATER LEVEL, IN FEET ABOVE MEAN SEA LEVEL

1950 1952 1954 1956 1958 1960 1962 1964 1966 1968 1970 1972 1974 1976 1978 1980 1982 1984 1986 1988 1990 1992 1994 1996 1998 2000

Pumps 1 (5330-10) and 2 (5330-09)

Pump 2 (5330-09)

Test hole 15D (5330-07)

RAM-predicted equilibrium head, he = 14 ft

Figure 11. Water levels at Mokuhau well field, Iao aquifer, Maui, Hawaii.

Figure 10. Water levels at shaft 33 during 1996–98, Iao aquifer, Maui, Hawaii.
Case Study of the Iao Aquifer, Maui 25

DEPARTURE OF 12-MONTH

MOVING AVERAGE RAINFALL, 

IN PERCENT

MONTHLY WITHDRAWAL,

IN MILLION GALLONS

PER DAY

-100

150

-50

0

50

100

0

28

4

8

12

16

20

24

1976 1978 1980 1982 1984 1986 1988 1990 1992 1994 1996 1998 2000

Test hole B (5431-01)

Test hole D (5430-04) and Waiehu deep monitor well (5430-05)

Test hole E (5430-03) 

Iao aquifer withdrawal

Waiehu Camp (station 484)

WATER LEVEL, IN FEET ABOVE MEAN SEA LEVEL

minimum water level 7.84 ft measured October 1996

minimum water level 9.65 ft measured October 1996

minimum water level 9.01 ft measured October 1996

RAM-predicted equilibrium head, he = 15 ft

RAM-predicted equilibrium head, he = 15 ft

RAM-predicted equilibrium head, he = 15 ft

24

8

12

16

20

22

6

10

14

18

22

6

10

14

18

Figure 12. Water levels at Waiehu deep monitor well and test holes B and E, departure of backward-looking 12-month moving average rainfall from the long-term average rainfall for Waiehu

Camp rain gage, and monthly mean total withdrawal from the Iao aquifer prior to 1999, Maui,

Hawaii. (Unpublished rainfall data from Commission on Water Resource Management.)
26 Analytical Versus Numerical Estimates of Water-Level Declines, and a Case Study of the Iao Aquifer, Maui, Hawaii

P A C I F I C

O C E A N

?

?

?

?

?

?

?

?

?

?

2 Waiehu Strea m

Iao

Stream

Waihee

Waiehu

Wailuku

Waikapu

0

0

1 MILE

1 KILOMETER

DIKEIMPOUNDED

GROUND

WATER FRESHWATER-LENS

SYSTEM

AREA UNDERLAIN BY 

 CONFINED FRESH GROUND 

 WATER IN THE WAILUKU 

 BASALT

LINE OF EQUAL WATER-LEVEL

 DECLINE--Contour interval 

 is one foot. Dashed where 

 appoximately located. Datum is 

 mean sea level.

APPROXIMATE SEAWARD 

 EXTENT OF FRESHWATER IN 

 WAILUKU BASALT FOR 

 PREDEVELOPMENT 

 CONDITIONS

BOUNDARY BETWEEN 

 UNCONFINED AND CONFINED

 WATER IN THE WAILUKU

 BASALT

INFERRED BOUNDARY 

 BETWEEN DIKE-IMPOUNDED 

 GROUND WATER AND 

 FRESHWATER-LENS 

 SYSTEM (modified from 

 Yamanaga and Huxel, 1970)

STUDY-AREA (IAO AQUIFER)

 BOUNDARY

WITHDRAWAL WELL OR WELL 

 FIELD AND NAME

WELL FIELD WITH WITHDRAWAL 

 AND WATER-LEVEL 

 OBSERVATION WELLS AND 

 NAME

WATER-LEVEL OBSERVATION 

 WELL AND NAME

EXPLANATION

Kahului

Bay

20°56'

20°54'

20°52'

156°32' 156°30'

Waihee Waiehu

Heights

Kepaniwai

Test 

hole E

Test hole

15D

Test 

hole B

Waiehu deep 

monitor well

and Test hole D 

Shaft 33

Waihee

Test 

hole B

Shaft 33

Mokuhau

2

3

4

5

6

Base modified from U.S. Geological Survey

digital data, 1:24,000, 1983, Albers equal area 

projection, standard parallels 20°35' and 21°00', 

central meridian 156°20'

Waihee River

Waikapu Stream

MAUI

Area

of map

Pacific Ocean

Figure 13. Map showing water-level declines in the flank flows of Wailuku Basalt between April 1977 and April 1997

for the northern part of the Iao aquifer, Maui, Hawaii.
Case Study of the Iao Aquifer, Maui 27

equation 3, or (2) by using ratios of he:h0 from table 1.

Using equation 3 and assuming D and I values of 20

Mgal/d and 31.57 Mgal/d (Mink, 1995), respectively,

the ratio he:h0 is computed to be 0.6 for the Iao aquifer.

Predevelopment heads averaged 28.5 ft above sea level

near shaft 33 and 24 ft above sea level near the Mokuhau well field. Thus, using a ratio for he:h0 of 0.6, the

RAM-predicted equilibrium heads are about 17 ft and

14 ft for the shaft 33 and Mokuhau well fields, respectively (table 6). No information exists for predevelopment heads at the Waiehu Heights and Waihee well

fields, although Yamanaga and Huxel (1970) suggest

that they might have been about 25 ft above sea level.

For a predevelopment head of 25 ft above sea level, and

a ratio of he:h0 of 0.6, the RAM-predicted equilibrium

head for the Waiehu Heights and Waihee well fields is

15 ft above sea level.

For a predevelopment head of 28.5 ft above sea

level at shaft 33, the ratio of he:h0 from table 1 is 0.5.

Thus, on the basis of ratios of he:h0 from table 1, the

equilibriumhead for shaft 33 is estimated to be about 14

ft, which is lower than the 17-ft value previously calculated using equation 3. At the Mokuhau, Waiehu

Heights, and Waihee well fields, predevelopment heads

ranged fromabout 24 to 25 ft above sea level. Thus, the

ratio of he:h0 from table 1 for these well sites is 0.6,

which is the same value calculated using equation 3.

In 1995 and 1996, withdrawal fromthe Iao aquifer

reached the sustainable-yield value derived using

RAM. However, by 1996 or earlier, water levels at shaft

33 and Waiehu Heights (represented with water levels

from test holes B and E) were below RAM-predicted

equilibrium heads. Water levels at Waihee well field

(represented with water levels from the Waiehu deep

monitor well and test hole B) also were below the

RAM-predicted equilibrium head and were at an altitude that potentially could have resulted in saltwater

intrusion. No water-level data were available for Mokuhau well field in 1996. CWRM held hearings on the status of the aquifer and in April 1997 concluded that

“current pumpage rates in current locations cannot be

sustained in the long term” (State of Hawaii, 1997, p. 4).

Although the decline in water levels ceased prior to

1999, average 1998 water levels were still below RAMpredicted equilibrium heads for shaft 33, Mokuhau,

Waihee, and Waiehu Heights well fields. At their lowest altitudes prior to 1999, water levels were 5 to 7 ft

below RAM-predicted equilibrium heads for Waihee

and Waiehu Heights well fields, and about 5 ft below

the 14-ft RAM-predicted equilibriumhead for shaft 33.

Water-level data for Mokuhau well field were not available until 1998 when the average water level was about

4 ft below the RAM-predicted equilibriumhead for this

well field (table 6).

Water levels in the Iao aquifer continued to decline

when withdrawal was at the sustainable-yield value

determined from RAM. The ultimate decline that would

have occurred if withdrawal was permitted to remain at

20 Mgal/d cannot be estimated from available data. The

rise in the position of the brackish-water transition zone

generally will not occur immediately following a

decline in water level. Rather, the change in position of

the transition zone will generally lag behind the change

in water level (see, for example, Essaid, 1986). Thus,

the ultimate rise in the transition zone that would have

occurred if withdrawal was permitted to remain at 20

Mgal/d also cannot be estimated from available data.

However, even with average 1998 withdrawal at about

18 Mgal/d, water levels were probably still below

acceptable long-termvalues to preclude saltwater intrusion at some of the well fields (Meyer and Presley,

2000).

Although uncertainty associated with the recharge

estimate and predevelopment water levels contributes

to uncertainty in the equilibrium heads predicted by

RAM, the decline of water levels below those predicted

by RAM in the vicinity of the well fields in the Iao aquifer is consistent with the results of the preceding numerical model analysis that demonstrate (1) the effect of a

caprock on water-level declines caused by withdrawals,

and (2) the importance of representing the distribution

of withdrawals in an aquifer. The field setting for the

Iao aquifer is similar to that shown in figure 7, and

although the model does not simulate the Iao aquifer,

model results provide insight to why water levels in the

Iao aquifer fell below equilibrium heads predicted by

RAM. Water availability in the Iao aquifer can be best

understood by constructing a numerical model of the

ground-water flow system. The data needs, required

expertise, and development time are much greater for

constructing a numerical model than for using RAM.

Although construction of a numerical model is more

costly than simply using RAM, a numerical model will

lead to an improved understanding of the ground-water

system and better management decisions.
28 Analytical Versus Numerical Estimates of Water-Level Declines, and a Case Study of the Iao Aquifer, Maui, Hawaii

SUMMARY

Sustainable yield, as defined by the State of

Hawaii, refers to “the maximum rate at which water

may be withdrawn from a water source without impairing the utility or quality of the water source...” (State of

Hawaii, 1987). In Hawaii, sustainable-yield values for a

given aquifer system are commonly determined from a

one-dimensional analytical model of ground-water flow

known as the Robust Analytical Model (RAM). The

analytical model incorporates the horizontal-flow

assumption and the Ghyben-Herzberg relation to represent flow in an unconfined aquifer that contains a body

of freshwater floating on saltwater.

RAM does not account for aquifer-system boundary conditions that commonly exist in Hawaii, nor for

the spatial distribution of ground-water withdrawals

fromwells (RAM is one dimensional). Therefore RAM

cannot accurately predict water-level declines associated with withdrawals except under the most restrictive

situations.

Two of the State’s most important aquifers, the

Pearl Harbor aquifer on Oahu and the Iao aquifer on

Maui, are overlain by coastal sedimentary deposits

known as caprock. A caprock impedes the discharge of

freshwater from the aquifer to the ocean and is an

important control on the ultimate water-level decline

caused by ground-water withdrawals from the aquifer.

For areas where a caprock exists, water-level declines

predicted by RAM generally are less than those indicated by numerical ground-water flow models that

incorporate this boundary condition. This, in turn, indicates that management of these ground-water systems

using a sustainable-yield value determined from RAM

could result in some existing or future well fields ultimately being intruded by saltwater.

In addition to its inability to represent a caprock,

RAM cannot account for spatially distributed withdrawals fromwells, which is significant because waterlevel declines are greatest in the vicinity of withdrawal

wells. The one-dimensional RAM invariably predicts

the greatest water-level declines at the inland extent of

the aquifer where the freshwater lens is thickest and the

potential for saltwater intrusion is lowest.

The use of RAM by the Hawaii Commission on

Water Resource Management (CWRM) for establishing the sustainable yield of the State’s aquifers is relatively recent. Data from the Iao aquifer, which lies on

Table 6. Measured water levels and RAM-predicted equilibrium head (he) at selected wells, Iao aquifer, Maui, Hawaii

RAM-predicted equilibrium head, he (feet) Average

measured

water level

(feet)

Total

withdrawal

from Iao

aquifer

Well (Mgal/d)

he estimated from

he:h0 ratios in

table 1

he estimated from

equation 3 Year

Waiehu monitor 15 15 13 1992 18.12

12 1994 19.2

10 1997 19.12

10.5 1998 17.89

Test hole B 15 15 13 1992 18.12

12 1993 18.41

9 1997 19.12

10 1998 17.89

Test hole E 15 15 13 1994 19.2

12 1996 20.4

10.5 1997 19.12

12.5 1998 17.89

Shaft 33 14 17 10 1996 20.4

10.5 1998 17.89

Mokuhau 14 14 10.5 1998 17.89
References Cited 29

the northeastern flank of the West Maui Volcano and

which is confined near the coast by a caprock, are now

available to evaluate the predictive capability of RAM

for this aquifer. In 1995 and 1996, withdrawal reached

the sustainable-yield value derived using RAM (State of

Hawaii, 1990). However, even before 1996, water levels in the aquifer had declined significantly below those

predicted by RAM and were still declining in 1997. As

a result, it was necessary to reduce withdrawal fromthe

aquifer below the sustainable-yield value derived using

RAM in order to halt the continuing decline of water

levels and to preclude the ultimate intrusion of saltwater

into the four major well fields in the aquifer.

Although uncertainty associated with the recharge

estimate and predevelopment water levels contributes

to uncertainty in the equilibrium heads predicted by

RAM, the decline of water levels below those predicted

by RAM in the Iao aquifer is consistent with the results

of the numerical model analysis that demonstrate (1) the

effect of a caprock on water-level declines caused by

withdrawals, and (2) the importance of representing the

distribution of withdrawals in an aquifer. Water availability in the Iao aquifer can be best understood by constructing a numerical model of the ground-water flow

system.

REFERENCES CITED

Bear, Jacob, 1972, Dynamics of fluids in porous media: New

York, American Elsevier, 764 p.

Bredehoeft, J.D., Papadopulous, S.S., and Cooper, H.H.,

1982, Groundwater: the water-budget myth, in U.S.

National Research Council, Scientific basis of waterresource management: Washington, D.C., National

Academy Press, p. 51–57.

Bredehoeft, J.D., and Hall, Phil, 1995, Ground-water models:

Ground Water, v. 33, no. 4., p. 530–531.

Domenico, P.A., and Schwartz, F.W., 1990, Physical and

chemical hydrogeology, New York, John Wiley & Sons,

Inc., 824 p.

Essaid, H.I., 1986, A comparison of the coupled fresh watersalt water flow and the Ghyben-Herzberg sharp interface

approaches to modeling of transient behavior in coastal

aquifer systems: Journal of Hydrology, v. 86, no. 1/2,

p. 169–193.

Essaid, H.I., 1990, The computer model SHARP, a quasithree-dimensional finite-difference model to simulate

freshwater and saltwater flow in layered coastal aquifer

systems: U.S. Geological Survey Water-Resources

Investigations Report 90-4130, 181 p.

Eyre, Paul, Ewart, Charles, and Shade, Patricia, 1986,

Hydrology of the leeward aquifers, southeast Oahu,

Hawaii: U.S. Geological Survey Water-Resources Investigations Report 85-4270, 75 p.

Giambelluca, T.W., 1986, Land-use effects on the water balance of a tropical island: National Geographic Research,

v. 2, no. 2, p. 125–151.

Gingerich, S.B., 1998, Numerical modelling of vertically

extensive groundwater bodies in Maui, Hawaii: an alternative to perched aquifers: International Association of

Hydrological Sciences Publication no. 253, p. 167–174.

Gingerich, S.B., 1999, Estimating transmissivity and storage

properties from aquifer tests in the Southern Lihue

Basin, Kauai, Hawaii: U.S. Geological Survey WaterResources Investigations Report 99-4066, 33 p.

Hunt, C.D., Jr., 1996, Geohydrology of the island of Oahu,

Hawaii: U.S. Geological Survey Professional Paper

1412-B, 54 p.

Izuka, S.K., and Gingerich, S.B., 1998, Ground water in the

Southern Lihue Basin, Kauai, Hawaii: U.S. Geological

Survey Water-Resources Investigations Report 98-4031,

71 p.

Langenheim, V.A.M., and Clague, D.A., 1987, The Hawaiian-Emperor volcanic chain, part II, stratigraphic framework of volcanic rocks of the Hawaiian Islands, chap. 1

of Decker, R.W., Wright, T.L., and Stauffer, P.H., eds.,

Volcanism in Hawaii: U.S. Geological Survey Professional Paper 1350, v. 1, p. 55–84.

Macdonald, G.A., Abbott, A.T., and Peterson, F.L., 1983,

Volcanoes in the sea: The geology of Hawaii (2d ed.):

Honolulu, Hawaii, University of Hawaii Press, 517 p.

Meyer, William, and Presley, T.K., 2000, The response of the

Iao aquifer to ground-water development, rainfall, and

land-use practices between 1940 and 1998, island of

Maui, Hawaii: U.S. Geological Survey Water-Resources

Investigations Report 00-4223, 60 p.

Mink, J.F., 1980, State of the groundwater resources of southern Oahu, Honolulu Board of Water Supply, 83 p.

Mink, J.F., Yuen, G.A.L., and Chang, J.Y.C., 1988, Review

and re-evaluation of groundwater conditions in the Pearl

Harbor groundwater control area Oahu, Hawaii: State of

Hawaii Department of Land and Natural Resources,

Report R-78, 95 p. plus appendixes.

Mink, J.F., 1995, Sustainable yields, Maui and Molokai: letter dated September 9, 1995 to Rae M. Loui, State of

Hawaii Commission on Water Resource Management,

2 p.

Oki, D.S., 1997, Geohydrology and numerical simulation of

the ground-water flow systemof Molokai, Hawaii: U.S.
30 Analytical Versus Numerical Estimates of Water-Level Declines, and a Case Study of the Iao Aquifer, Maui, Hawaii

Geological Survey Water-Resources Investigations

Report 97-4176, 62 p.

Oki, D.S., 1998, Geohydrology of the central Oahu, Hawaii,

ground-water flow system and numerical simulation of

the effects of additional pumping: U.S. Geological Survey Water-Resources Investigations Report 97-4276,

132 p.

Oki, D.S., 1999, Geohydrology and numerical simulation of

the ground-water flow systemof Kona, island of Hawaii:

U.S. Geological Survey Water-Resources Investigations

Report 99-4073, 70 p.

Oki, D.S., Tribble, G.W., Souza, W.R., and Bolke, E.L.,

1999, Ground-water resources in Kaloko-Honokohau

National Historical Park, island of Hawaii, Hawaii, and

numerical simulation of the effects of ground-water

withdrawals: U.S. Geological Survey Water-Resources

Investigations Report 99-4070, 49 p.

Shade, P.J., 1997, Water budget for the Iao area, island of

Maui, Hawaii: U.S. Geological Survey Water-Resources

Investigations Report 97-4244, 25 p.

Souza, W.R., and Voss, C.I., 1987, Analysis of an anisotropic

coastal aquifer system using variable-density flow and

solute transport simulation: Journal of Hydrology, v. 92,

p. 17–41.

State of Hawaii, 1987, State water code: Hawaii Revised Statutes, Chapter 174C.

State of Hawaii, 1990, Water resources protection plan, volumes I and II, June 1990: Commission on Water

Resource Management, Department of Land and Natural

Resources, variously paged.

State of Hawaii, 1992, Water resources protection plan, volumes I and II, review draft, March 1992: Commission on

Water Resource Management, Department of Land and

Natural Resources, 313 p. plus appendixes.

State of Hawaii, 1997, Recommendation on the designation

of the Iao aquifer system as a ground water management

area: Staff submittal for the meeting of the Commission

on Water Resource Management, April 16, 1997,

Wailuku, Maui, 7 p. plus exhibits.

Stearns, H.T., and Macdonald, G.A., 1942, Geology and

ground-water resources of the island of Maui, Hawaii:

Hawaii Division of Hydrography Bulletin 7, 344 p.

Underwood, M.R., Meyer, William, and Souza, W.R., 1995,

Ground-water availability from the Hawi aquifer in the

Kohala area, Hawaii: U.S. Geological Survey WaterResources Investigations Report 95-4113, 57 p.

Yamanaga, George, and Huxel, C.J., Jr., 1970, Preliminary

report on the water resources of the Wailuku area, Maui:

State of Hawaii Department of Land and Natural

Resources, Division of Water and Land Development,

Circular C61, 43 p.

APPENDIX: DESCRIPTION OF RAM

The one-dimensional Robust Analytical Model

(RAM) (Mink, 1980) used by CWRM to estimate sustainable yield incorporates the Dupuit assumption of

horizontal flow (see, for example, Bear, 1972) and the

Ghyben-Herzberg relation. The steady-state model is

described and derived in this appendix.

Dupuit Assumption

For ground-water flow systems with small watertable slopes, an approximate solution for flow in an

unconfined aquifer can be derived. The assumption of

small water-table slope is equivalent to assuming that

equipotential surfaces are vertical and flow is essentially horizontal, or to assuming that a hydrostatic pressure distribution exists (Bear, 1972, p. 361). This is

known as the Dupuit assumption. With the Dupuit

assumption, variations in velocity and pressure in the

vertical direction are neglected and, thus, two-dimensional flow in a vertical cross section can be approximated by one-dimensional flow in the horizontal

direction.

In general, ground-water flow in an unconfined

aquifer is three dimensional. If ground-water flow is

first assumed to be adequately represented by flow in a

two-dimensional vertical cross section, and if the horizontal-flow assumption is then used, the original threedimensional flow system can be approximated by a onedimensional system.

Ghyben-Herzberg Relation

In Hawaii, fresh ground water commonly occurs as

a lens-shaped body of freshwater floating on denser,

underlying saltwater derived from the ocean. A brackish-water transition zone of varying thickness exists

between the freshwater and underlying saltwater. The

transition zone is created by mixing of saltwater with

seaward flowing freshwater.

For areas where the brackish-water transition zone

is thin, the Ghyben-Herzberg relation can be used to

estimate the thickness of the freshwater lens. If the specific gravities of freshwater and saltwater are assumed

to be 1.000 and 1.025, respectively, then the GhybenHerzberg relation predicts that every foot of freshwater

above sea level must be balanced by 40 ft of freshwater

below sea level. The Ghyben-Herzberg relation is valid
Appendix: Description of RAM31

for hydrostatic conditions. For dynamic conditions, the

Ghyben-Herzberg relation tends to underestimate freshwater-lens thickness near the discharge zone and overestimate lens thickness near the recharge zone.

One-Dimensional Analytical Equation

The flow rate in a porous medium is proportional

to the cross-sectional area of flow and the hydraulic gradient, and can be described by Darcy’s law. For onedimensional steady-state flow, Darcy’s law can be written as:

Q = –K i A, (a1)

where, Q = rate of flow [L3/T],

K = hydraulic conductivity [L/T],

i = hydraulic gradient [L/L], and

A = cross-sectional area of flow [L2

].

The constant of proportionality in Darcy’s law is

the hydraulic conductivity, K, which is related to the

properties of the porous medium and the fluid. The

hydraulic conductivity is a quantitative measure of the

capacity of a rock to transmit water. For one-dimensional flow, the hydraulic gradient is given by:

i = dh/dx,

where, h = hydraulic head [L] measured relative to

mean sea level,

x = Cartesian coordinate [L], and

dh/dx = derivative of h with respect to x.

Flow is in the direction of decreasing hydraulic

head, which accounts for the negative sign in equation

a1. The cross-sectional area of flow at any section is

given by:

A = 41hw,

where, w = width of section [L], and

41h = height of section from the GhybenHerzberg relation [L].

Thus, Darcy’s law can be expressed as:

Q = –K (dh/dx) (41hw). (a2)

Rearranging terms yields:

–[Q/(41Kw)] dx = h dh. (a3)

Integration of equation (a3) yields:

–[Q/(41Kw)] (x2–x1) = 0.5(h2

2

 – h1

2

). (a4)

If h1 = 0 at x1 = 0, then from equation (a4), h as a

function of x can be written as:

h2 = –[2Q/(41Kw)] x. (a5)

Equation (a5) forms the basis of RAM. Equation

(a5) can be rearranged as:

h2/Q = –2x/(41Kw). (a6)

For any given location, x, the right hand side of

equation (a6) is a constant and, thus, the ratio of h2

/Q is

a constant:

h0

2

/Q0 = he

2

/Qe, (a7)

where, h0 = hydraulic head [L] at location x for

flow rate Q0,

Q0 = steady-state rate of flow through

aquifer for predevelopment

conditions [L3

/T],

he = hydraulic head [L] at location x for

flow rate Qe, and

Qe = steady-state rate of flow (less

withdrawals from wells or shafts)

through aquifer for development

conditions [L3

/T].

For some desired equilibrium head, he, CWRM

defines the sustainable yield, D, as the difference

between the predevelopment rate of flow through the

aquifer minus the reduced rate of flow through the aquifer following development:

D = Q0 − Qe. (a8)

Combining equations (a7) and (a8), and letting

Q0 = I yields:

D/I = 1 − (he/h0)

2

. (a9)

Equation (a9) represents the model (RAM) used by

CWRM to set sustainable yield in Hawaii. To apply this

equation, predevelopment values for h0 and I must be

known. After establishing some desired minimum equilibrium head, he, equation (a9) is used by CWRM to

estimate the sustainable yield of an aquifer. For example, if the desired equilibriumhead is 60 percent of the

predevelopment head (he/h0 = 0.6), then D/I = 1 –

(0.6)2

, or D/I = 0.64. Thus, RAM estimates that the

sustainable yield, D, is 64 percent of the predevelopment flow rate, I, in the aquifer for this case.