Field observations and theoretical analysis of wave set-up on Ala Moana Reef

FIELD OBSERVATIONS
AND
THEORETICAL ANALYSIS OF WAVE SET-UP
ON ALA MOANA REEF
David A. Wentland
Department of Ocean Engineering
University of Hawaii
November 27, 1978
OE 699

DEDICATED
to
RAELEAH CORAL
(Home Grown in Hawaii)

ABSTRACT
As a compliment to work carried out over the past few
years on wave attenuation and set-up on a shallow reef,
field observations of actual wave set-up on the Ala Moana
Reef were conducted.
The observations showed the magnitude of wave set-up
to be small and be in close agreement with the magnitude
of wave set-up predicted by energy dissipation and radia-
tion stress for low energy.
i

I.
TABLE OF CONTENTS
ABSTRACT . . . .
LIST OF FIGURES
LIST OF TABLES .
LIST OF PHOTOGRAPHS
PREFACE
INTRODUCTION
DESCRIPTION OF THE STUDY AREA
I . l Location . . . ..
I . 2 Previous Investigations
I.3 Preview .. . . . . . .
i
iv
vi
vii
viii
1
2
2
2
5
II . INVESTIGATION OF WAVE SET-UP 8
II.l Preparation for Observations 8
II.l.a Constructing the manometers 8
II.l.b Establishing stations for the
project . . . . . . . . . . 15
II.l.c Installing tide gauges 18
II . l.d Observing other parameters
on the reef . . . . . 21
II . 2 Observations on the Reef . 22
II . 2.a Measuring wave set-up along the
transect line . . . . . 22
II . 2 .b Additional measurements . . 22
II.3 Results of Observations 25
II.3.a Have set-up along the transect
line . . . . . . . . . . . . 25
II.3.b Tide gauge results . . . . . 34
II.3.c Mean water level oscillations 34
II.3.d Water level difference inside
and outside Kewalo Basin 42
II.4 Conclusions to the Observations 42
II . 4 . a Errors . . . . . . . 45
II . 4.b Effect of errors 47
III . CALCULATIONS OF THEORETICAL WAVE SET-UP 49
III . l Philosophy . . . . . . . . . . . 49
III . 2 Theoretical Wave Set-up Criteria 49
III.2 . a Radiation Stress . . . . . 49
III . 2.b Wave set-up from radiation stress 56
III . 2 . c Computing wave heights . . . . . . 59
ii

IV.
v.
III.3 Computing Wave Set-up Using Theory
and Observed Wave Data . . . .
COMPARISON OF OBSERVED AND CALCULATED
WAVE SET-UP . . . . . . . . . .
CONCLUSIONS FROH THE WAVE SET-UP PROJECT
V.l Field Observations
V.2 Calculations
ACKNOWLEDGEHENTS
BIBLIOGRAPHY . .
APPENDIX I . . . . . . .
(Data Collected at all Reef Stations,
Sept . 14, 16, 28 and 30, 1978)
APPENDIX II . . . . . . . . . . . . .
(Observations made of Mean Water Level
Differences Just Inside and Outside of
Kewalo Basin)
APPENDIX III . . . . . . . . . . . .
(Tide Chart for September Indicating
when Heasurements were made)
APPENDIX IV . . . . . . . . . . . . . .
(Observations made in Determining Mean
Water Level from Field Hanometers and
Tide Gauges and Referencing to the HLLH
Datum)
APPENDIX V . . . . . . . . . . . .
(Hand and Computer Calculations
Determining the hTave Height of an
Idealized Wave Approaching the
Ala Hoana Reef)
APPENDIX VI . . . . . . . . . .
(Calibration Program used to Obtain
Digital Water Level Data from an
Analog Input)
APPENDIX VII . . . . . . .
(Computer Programs used to
Characteristics and Energy
Spectrum at the Deep ·Hater
Compute vJave
Density
Station)
APPENDIX VIII . . . . . . . . . .
(Instruction Bulletin for the NOAA
Station Tide Gauge)
iii
63
73
75
75
78
80
81
82
107
:_1 2
114
124
138
141
165

Figure
I.l
I.2
I.3
I.4
II.l
II. 2
II.3
II. 4
II.5
II. 6
II.7
III.l
III. 2
III.3
III. 4
III. 5
III . 6
LIST OF FIGURES
Kewalo Basin - Ala Moana Reef Location
Ala Moana Reef with Transect Line
Wave Set-up Measurements from 1976
Comparison of 1978 Stationing with
1976 Stationing .. . . .. . . .
Comparison Test Between a Manometer and
an Electronic Water Level Recorder in
Determining the Mean Water Level . . . .
Comparison of Measured Set-up of
Various Days . . . . . . . . . .
Magnitude of Observed Set-up in
Relation to Tide Level and Location
on the Reef . .
Magnitude of Observed Set-up in
Relation to Tide Level and Location
on the Reef
Wave Set-up over a 22-hour Period
Mean Water Level Oscillations at
Sta. 1 on the Ala Moana Reef
Look at Hagnitude of Seiching and
Boat Waves Inside Kewalo Basin
Momentum Flux in a Stationary Fluid
Momentum Flux in a Progressive Have
Bodily Transport of Momentum across
a Plane
Wave Induced Momentum Flux in the
Vertical Direction .
Balance of Horizontal Momentum for
Waves Entering Shallow Water
Classification of Reef Profile by Zones
iv
3
4
6
7
10
27
29
30
31
43
48
50
51
52
54
56
60

Figure
III.7
III.8
III . 9
III . lO
IV .1
IV .2
Method Used in Calculating Energy
Dissipation and Shoaling . . . .
Determination of the Wave Height
Breaking Coefficient . . . . . .
Criteria Used in Calculating Wave
Heights Considering Energy Losses
Wave Set-up in Zones a & b Considering
Energy Losses . . . . . . . . . .
Comparison of Observed and Calculated
Wave Set-up (Stations 1-5) . . .
Comparison Between Measured and
Computed Wave Set-up for Equal Energy
v
62
65
67
72
76
77

Table
II.l
II. 2
II. 3
II.4
II.5
II. 6
I~.7-ll
II.l2
III.l-4
IV.l
LIST OF TABLES
Manometer Computations for ~nNL .
Electronic Water Level Recorder
Printout . . . . . . . . . . . .
July 1978 Tide Chart Shoviling the
Tide Level on the Day the Manometer
was Tested . . . . . . . . . .
Summary of Wave Set-up Results
Wind Data
Analysis of Data Obtained from
the Deep Water Station . . ..
Readings from the NOAA and Sta. 1
Tide Gauges (August 16-0ct. 13)
10 Minute Record of Manometer Readings
at Sta. 1 (taken every 5 sec.) ...
Calculation of V.Tave Set-up from Hrms .
Comparison of Observed and Calculated
Wave Height and Set-up at Sta. 4 & 5 .
vi
11
13
14
26
32
35
37
44
68
74

Photo
II.l-2
II. 3
II.4
II.5
II. 6
II. 7
LIST OF PHOTOGRAPHS
Photos of 1978 Stations on
Ala Moana Reef
NOAA Tide Gauge
Sta. 1 Pressure Tide Gauge
Reading the Field Hanometer
Measuring Currents and Recording the Data
Gathering Wave Data at the Deep ~Tater
Station . . . . . . . . . . . .
vii
16
19
20
23
24
36

PREFACE
This paper has been developed in three parts. The
first part deals with the observations made on Ala Moana
Reef. Included are the considerations made in attempting
to correctly measure wave set-up, the observations and
conclusions.
Part two is an application of linear wave theory to
determine what the set-up would be using an idealized wave
traveling onto the reef. Models for energy dissipation,
radiation stress and wave set-up are applied.
The final part presents a comparison between observed
values and those calculated and what may be concluded from
these comparisons.
viii

INTRODUCTION
Over the past few years, several faculty and graduate
students from the Ocean Engineering Department, University
of Hawaii, have made detailed field and model studies of
wave set-up on a shallow reef. The intent has been to gain
a better understanding of wave behavior on reef areas (and
subsequently shorelines exposed to reefs) and ultimately
provide information and design criteria for engineers doing
coastal engineering work. In a more general case, extensive
work has been carried out by many investigators world-wide
for wave set-up on a sloping bottom for a plane beach.
In 1976, field observations of wave attenuation and
set-up were carried out along a determined line on the Ala
Moana Reef which fringes part of the coastline of Honolulu,
Hawaii. Wave set-up observations, however, seemed far out
of line with what was determined theoretically and believed
to exist on the reef.
My project was to devise a way of accurately measuring
set-up along the same transect line on the Ala Moana Reef
and compare my findings with results given from model cal-
culations.
1

I. Description of the Study Area
I.l. Location
Ala Moana Reef is located on the south coast of
the island of Oahu between dovmtown Honolulu and .Jaikiki
(Figure I.l). The transect line used in the study is near
the Kewalo Basin (ewa end) of the reef lying nearly perpen-
dicular to the reef length (Figure I.2). The reef flat
along this line is approximately 800 feet wide. An old canal
connecting Kewalo Basin to the Ala 1-Jai Yacht Harbor separates
the reef flat from the shoreline. On the ocean side the reef
gr~dually tapers off to deep water with an approximate slope
of 1:30.
I.2. Previous Investigations
Prior to my study, several investigators looked
at other parameters affecting conditions on the Ala Hoana -
Kewalo Basin Reef. As mentioned earlier, my study evolved
from a need for a second look at the wave set-up on the Ala
Hoana Reef. The first project was a joint effort by Ocean
Engineering faculty, Professor Frans Gerritsen, Dr. Ted Lee,
and graduate students, Larry Brower and Carey Black, under
Sea-Grant funding, to observe wave attenuation and set-up.
Earlier investigations included: a study by Fain (1) on the
theoretical analysis of wave set-up and resulting reef and
jetty currents on Kewalo Reef, a study by Levin (2) on the
circulation patterns on the reef between the Kewalo Harbor
Channel and Ala Moana Park, and a study by Fallon et . al .
2

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(3) on the most effective means of reducing strong jetty
currents in the Kewalo Basin Channel.
I. 3. Preview
The wave set-up results from the 1976 wave set-
up and attenuation project showed set-up/set-down values
for the reef flat ranging from as much as -1 . 50 feet to
+1.00 feet (Figure I.3). Even during extreme high tide
conditions the depth of water over the reef is only 3-4
feet so the ratio of wave set-up to water depth (n/d) seemed
grossly large considering only small wave energy input. The
in~truments used to measure set-up were electronic water
level recorders stationed along the survey line on tripods .
The tripods were placed along the transect line at a distance
possible t o r each 9:iven electrical cable length and sea con-
ditions . Figure (I.4) shows how the positioning of the
stations varied with each experiment. The tripods and water
level recorders were then surveyed with leveling instruments
located on a reef buggy near the center of the reef. The
reef buggy was also exposed to wave action on the reef so
precise leveling was difficult and the tripods themselves
were prone to movement. The mean water level (}~) at each
tripod was then computed from the mean value of the wave
record and referenced to the leveling . To eliminate these
problems, I decided to establish permanent stations on the
reef with precise elevations .
Other considerations for the project were :
5

I-
lL.
0
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0
0
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0
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SYMBOLS
+ AUG 25
X SEP 7
~ SEP 14
't SEP 16
X SEP 23
-~------~r--------+--------4-------~r--------+--~--~4---------+
1
-200.00 -100.00 -0.00 100.00 200.00 300.00 400.00 500.00
DISTANCE FRQM DATUM CfT)
Have induced set-up with probe 5 mean record level as
arbitrary zero, Ala Moana, 1976.
Figure (I.3)
Wave Set-Up Measurements from 1976
6

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7

1) obtain a prolonged record of wave set-up on the
reef in addition to that observed on measurement
days.
2) as best as possible, determine the wave height,
period, direction of wave propagation and current
speed and direction at each station along the
transect line.
3) determine what type of input, in terms of energy
and wave characteristics, was responsible for the
set-up observed.
II. Investigation of Wave Set-Up
II.l. Preparation for Observations
II.l.a. Constructing the manometers
With the considerations just listed as design
criteria, measuring tools were developed for the study. The
use of the electronic water level recorders for determining
wave and energy dissipation along the reef were susceptible
to numerous errors when used to measure wave set-up. The
limited budget for my project was also a considerable con-
straint and a method was needed which would be relatively
simple, inexpensive and yet accurate enough for our needs.
Professor Gerritsen had successfully used manometers to
measure mean water level while in Florida and he suggested
that a manometer be built and used in my project . Using local
supplies and Look Laboratory facilities and resources, a
8

prototype manometer was constructed and then checked to see
how reliable its mean water level results were . The mano-
meter was attached side-by-side to an electronic water
level recording capacitance staff on a tripod (Figure II.l).
The entire unit was then taken onto Ala Moana Reef and
measurements were taken simultaneously fr-om the manometer
and the capacitance staff. Wave heights were on the order
of 1.5 - 2.0 feet. Three ten-minute records were taken
with both the recording interval and valve opening being
adjusted on the manometer for each record . The results
(Tables II . l-2) proved that the manometer gave mean water
level readings in close agreement with those given by the
capacitance staff. Table (II.3) is a tide chart for July
showing the tide variation during the test . For Trial 1
with the valve open 1/8 turn and readings taken every 15
seconds, the MWL readings of the manometer and capacitance
staff varied by 0 . 006 feet. For Trial 2 at 1/4 turn and
10 sec. readings, the values varied by 0 . 002 ft . and for
Trial 3 at l/2 turn and readings taken every 15 sec . , the
values varied by 0 . 030 ft.
In hopes of measuring set-up within 0 . 01 ft ., Trials
1 and 2 were within the degree of accuracy required . Trial
3 showed the largest degree of deviation and a possible
reason for this may have been because at a valve setting of
1/2 turn open, the dampening was reduced to a point where
the rapid water fluctuations inside the manometer made it
9

t
Figure II.l
elc.drur-~c.. ~Ll
1~..... f"t<<>' ~~-"" ---4..
'
0
Comparison Test Between a Manometer and an
Electronic Water Level Recorder in Deter-
mining the Hean vJater Level
, ,- uv~'
( L~. <.. 2. ~ ')
1 MW'-

Time
(min.)
0
1
3
4
5
6
7
8
9
Table (II.l)
Manometer Computations for ~~L
Measurements taken with manometer of MWL
Trial 1
-valve open 1/8
turn
-measurements
every 15 sees.
-10 min. record
if-1
186.25
.25
.125
.125
.50
.25
.25
.25
.50
.375
.375
.50
.375
.50
.50
.625
.625
.75
.625
.75
. 75
.625
.50
.75
.875
.75
.875
.75
.75
.75
.875
.875
187.125
.125
.00
.00
Trial 2
-valve open 1/4
turn
-measurements
every 10 sees.
-10 min. record
112
186.25
.75
.75
187.00
.50
.625
.50
.50
.125
.75
.50
.00
.875
.25
.00
.375
.00
.125
186.75
.875
187.125
186.50
187.00
186.625
.75
187.50
186.75
187.00
11
.00
.125
186.50
.50
.50
187.00
186.50
187.75
.50
.00
185.00
.00
186.50
.00
.125
.50
.50
185.75
186.00
.50
187.00
186.00
.25
.375
185.75
186.50
187.50
.50
186.875
.50
.25
.50
Trial 3
-valve open 1/2
turn
-measurements
every 15 sees.
-10 min. record
#3
184.50
8.75
6.0
6.0
5.75
7.625
6.0
6.25
5.75
7.875
6.125
7.75
8.75
7.50
6.25
5.50
6.0
8.5
8.25
5.875
5.25
5.00
5.875
9.125
5.75
5.0
8.0
7.125
7.0
4.25
5.50
6.75
6.5
4.75
4. 75
4.0

Time
(min.)
10
Table (II.l)
(Continued)
Trial 1 Trial 2
#1
.125
.250
.125
.125
Total 26.5 Total 407
26.5
~
.662 407
bO = 6.783
186.662" 186.783"
:/f-1 186.662-144.0-23.625 19.037"
= 1. 586 I
#2 186.783-144.0-23.625 = 19.158"
= 1. 596 I
#3 186.319-144.0-23.625 = 18.694"
= 1. 558 I
Date Tested: July 13, 1978
10:30 - 11:30
12
Trial 3
#3
5.5
5.875
6.25
5.5
Total= 252.75
252.75
40
186.319"
6.319

~AN IV Gl RELEASE 2.0 MAIN DATE = 78310 15/02/25
~TIONS IN EFFECT* NOTERM,NGID,E6CO!CtSOUFCE,NOLtST,NODECK~LOAO,NOMAP,NOTEST
ry10NS TN E~FECT* NAME= MAIN , liNECNT = 60
rATISTICS* SOURCF STATEMENTS = ?Q , PROGRAM SIZE = 4038
rATISTICS* NO DIAGNOSTICS GENERATED
VS LOADER
3 USED- PPINT,NOMAP,NOLET.CALL,RES , NOTEPM,SIZE=l8432J,NAME=**GO
_ LENGTH
( ADDRESS
F!LF = 1
66C8
87010
CAL I BRATION FILE
MEAN ZERO ELEVATION READING = 807 MEAN 3 FT. ELEVATION PEADING = -821
FILF - 2 H~IAL 1
MEAN INTEGER VALUE = -57 FOUIVALFNT MEAN WATER LEVEL READING - 1 . 592
_ MAX. WATFR LEVEL PFAOING - 3 • .317 MIN. ~ATEP LEVEL READING - 0 . 955
....
~ .._,.
F £LE = 3 TRIAL 2
MEAN TN TEGFR VALUE - -58 EQUIVALENT MEAN WATER LEVEL READING = 1.594
MAX. W>TEP LEVEL READING = 3.582 MIN . WATER LEVEL READING = 0.932
FILF = I+ TRIAL 3
MEAN INTEGEP VALUE -- 55 EQUIVALENT MEAN WATER LEVEL READING - 1. 588
MAX . WATER LEVEL RtADING = 3 . 562 MJN. WATER LEVEL READING = 1 . 023
------------------
/ .
-, A BL G ClL; -z.: )
PAGE 0003
RANGE = 1628 . 0
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........ Hn. MI-. PORTS Hrs. IIIIM.
HANALEI BAY, KAUAI 1 40 KAUNAKAKAI, MOLOKAI 0 09
NAWILIWILI BAY, KAUAI 0 32
PORT ALLEN. KAUAI 0 32 KAHULUI, MAUl 1 48
KlfiEI, MMLAEA BAY,
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HANAUMA BAY, OAHU 0 55
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(

extremely difficult to correctly read the float.
With results proving the reliability of the prototype
manometer, field manometers were built (see pp. 122 and 123
for details) and during subsequent measurement days 15 sec.
interval measurements were taken at a valve opening of
approximately 1/8 - l/4 turn.
II.l.b Establishing stations for the project
During the 1976 field observations, the station-
ing varied, making it necessary to resurvey each station
each time out. Furthermore, it was difficult to compare
nu~erous observed set-up conditions along the reef given
a process which appeared neither constantly increasing nor
decreasing nor linear along the reef flat. With this in
mind, permanent stations were constructed along the transect
line of the reef. Since the reef itself was just over 800
feet wide, the stations were placed every 200 feet. In an
effort to do minimal defacement to the reef flat, the sta-
tions (receptacles for the manometers) were placed in coral
pukas found on the reef and concreted in with hydraulic
cement (Photos II.l-2 and p. 122).
Later, three surveys were carried out to the stations
and their elevations were referenced to a Corps of Engineers'
benchmark near Fisherman's Wharf Restaurant. Two other
stations were established, one in deep water* and one inside
*It was found out later that this station is actually
in intermediate water depth and the labeling merely indicates
it as being offshore from the reef.
15

1-'
0'
Sta. 3
Sta . 2
Sta . 1 with manometer
inserted
The engineers scale
and hammer give an
indication of the
bottom roughness .
Photos (II . l)
Photos of 1978 Stations
on Ala Moana Reef

1-'
-.....)
Sta . 4
Sta. 2
Photos (II . 2)
Photos of 1978
Stations on Ala
Hoana Reef
Sta . 3
Sta . 5

Kewalo Basin. The deepwater station, resurrected from the
previous project, was located in approximately 38 feet of
water and had a fiberglass pole which pivoted on a concrete
pad and could be erected to the water surface. During two
measurement days, an electronic water level recorder was
attached to the pole so the input from the ocean on those
days, in terms of mean energy and wave characteristics,
could be determined.
The Kewalo Harbor station, alongside the NOAA wharf
near the harbor entrance, was installed next to a NOAA tide
ga~ge and also leveled to the Fisherman's Wharf benchmark.
Figure (I.2) shows the location of all seven stations used
during the project.
II.l.c Installing tide gauges
Since the cross-sectional area of the channel
into Kewalo Basin is quite large (4000 ft 2) in comparison
to the basin size (surface area of approx. 800,000 ft
2
), it
was assumed* the water level inside the basin could be used
as the still water tidal level at the transect line approxi-
mately 1/4 mile away. The NOAA tide gauge (Photos II.3) was
monitored from August 16 - October 12, 1978 and provided 15
minute tide level readings over that period.
A second tide gauge (Photos II.4) was installed inside
*Later it was calculated and found to differ at the
most by 1.8 x lo-5 ft. given a 2.0 ft. tidal range over a
period of 12 hours and 25 minutes, well within the degree
of accuracy required.
18

Data recorded
on punchtape
Photos (II.3)
The NOAA Tide Gauge
19
Housing
removed
for check
and visual
reading
Housing and
stilling well

Close up of tide record
The tide gauge and nitrogen cylinder
Photos (II.4)
Station 1 Pressure Tide Gauge
20
The complete unit
inside the housing
Bubbler Orifice
Chamber at Sta. 1

the University of Hawaii facility where the porpoise tanks
are housed. A pressure recording tide gauge, its orifice
nitrogen supply line ran out 500 feet to Station 1 where
it monitored the changes in pressure due to water depth
changes. These pressure changes were recorded on strip
chart paper inside the University of Hawaii facility.
Although problems were encountered with the clock mechanism,
the pressure tide recorder operated from August 16 - Octo-
ber 12, 1978.
The data collected from the two tide gauges provided
a ~oak at wave set-up at Station 1 over an extended duration.
II.l.d Observing other parameters on the reef
The remaining items slated to be observed were
wave characteristics and current.
The wave characteristics included wave height, period
and direction. The manometers sufficed in measuring wave
heights. The scale on each manometer was used to measure
the wave crest and trough as a wave passed by. Wave periods
v1ere determined by timing successive wave crests as they
passed by the manometer. The direction of wave propagation
was measured by compass.
Drogues were built to measure current velocity . A
line attached to the drogue was paid out until a predeter-
mined length was carried away, then the time was recorded.
A compass was used to determine the direction of travel .
A final observation was wind velocity. Data for
21

September was gathered from the National Weather Service
Station for winds recorded at Honolulu International Air-
port during that month.
II.2. Observations on the Reef
II.2.a }1easuring wave set-up along the
transect line
Four days of wave set-up measurements were
made on the reef, September 14, 16, 28 and 30, 1978. The
governing constraint was the large manpower requirement to
conduct a proper day's observation. Professor Gerritsen's
OE . 461 class plus additional friends were recruited to help
conduct measurements. To capitalize on one day's efforts,
two 15-minute wave set-up measurements were conducted on
three of the days. On September 16 and 30 the deep water
station was erected and wave input recorded.
The procedure was to begin with a synchronized 15-
minute record of mean water level at all stations. Following
the first record, wave height, period, direction and current
velocity were determined. A second 15-minute mean water
level record was made in concluding one day's measurements.
The entire set of measurements were recorded on a plexiglas
slate for each station. Photos (II.5-6) illustrate the
activities carried out.
II.2.b Additional measurements
In addition to the four days of wave set-up
measurements, two additional measurements were made.
22

'
Recording a 15 minute
observation of ~~
Photos (II.5)
Reading the Manometer
23
Looking seaward along
the transect line at
Sta . 3
The Hanometer
(visible are the
float, measuring
tape and height
indicator)

N
+:--
Measuring currents with a
shallow water Drogue
Photos (II. 6)
Measuring Currents and
Recording the Data
(Note
the
current
direction
- see the
BioMed
Bldg)
Payi
out
line
One
day's
record
from
Sta . 3

A 10-minute record was taken on October 13 at 5 sec.
intervals at Station 1. The purpose was to determine, if
possible, any oscillatory nature to the set-up on the reef.
A second measurement was made on October 5 to see what
type of elevation difference existed on the immediate sides
of the land mass separating Kewalo Basin from Kewalo-Ala
Moana reef. Two manometers were set on each side of the
narrowest bridge of land approximately 150 feet apart.
11.3. Results of Observations
II.3.a Wave set-up along the reef transect line
Table (II.4) summarizes the results of the four
days of observations. The NOAA station was used as a still
water tidal reference from which set-up at each station was
determined. In a few places, data was not obtained in a
certain category and a bar indicates this. A major disap-
pointment was that the manometer at Station 4 broke before
any measurements could be made on September 30 and no data
was collected there on that day.
Looking at the results, one sees that some degree of
set-up was observed on all days. The magnitude, however,
was never large and at the greatest only 0.25 feet above the
still water tide level. Figure (11.2) shows a comparison
of measured set-up on various days. A trend appears evident
of a set-up increasing from Stations 5-4, decreasing from
4-3 and then increasing again to Station 1. Trial 2 on
25

N
0"
Table (II. 4)
Summary of Wave Set-Up R~sults
Set-Up (ft) Wave Current Wind
Date Sta. MWLl MWL2 l:IMWL He1.ght Perlod D1.rect1.on Speea: 1Jlrectlon · Dlrec. ::;peed
1 1. 86 (ft) (sec) 0-3600 (ft/min) 0-3600 0-360° (Kts)
2 1.85 (magnetic) (magnetic) (mag)
~/14 3 1. 75
4 1. 81
5 1. 73 17 16
DW -
NOAP 1. 61
1 1.4Y l. Y.J 0.46 0.4 21 34 none -
2 1.48 1.88 0.40 0.7 8 15 10 240
~/16 3 1.43 1. 86 0.43 1.2 12 0 & 10 23 270
4 1. 48 1.86 0.38 1.8 12 350
*( ~ ~ >
5 1. 39 1. 90 0.51 "" 2. 5 12 350 & 0 18 19
DW - - - 1.81/1.75 10.92/10.92 330 - -
NOAA 1. 37 1.84 0.47 - -
l 1.41 l. 62 0.21 0.5 10 45 8 L.1.J
2 1.41 1. 59 0.18 1.0 12 30 7 255
9/28 3 1. 36 1.56 0.20 1.0 12 0 & 20 12 267
4 1. 39 1. 56 0.17 1.1 15 10 & 30 ,~~1~ 17)
5 1. 36 1. 53 0.17 2.4 15 20 so 19 15
DW - - - - - - - -
NO~ 1. 30 1. 51 0.21 - - - - -
1 2.04 2.10 0.06 0.7 1:$ 0 1:$ 240
2 2.01 2.06 0.05 1.3 10 40 7 237
9/30 3 1. 98 2.04 0.06 1.5 14 0 & 30 22 281
4 - - - - - - -
?>
5 1. 94 1. 98 0.04 2.7 14 15 ,·~ <? 23 13
DW - - - 1.94~2.44 1~~6~~14.~9 330 - -
NOAA 1.90 1.92 0.02 - -
- - - · ------ -- -- ------ - - -
*The currents at Sta. 4 & 5 were difficult to determine since governed by breaking waves.

.,&
1lt
NATIONAL
12-282
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•)
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')
')
20 Squares to the Inch z. 2.7 4

September 16, however, deviates from this pattern and at
this time remains unexplained. Information from Station 4
on September 30 would have been greatly appreciated. Fig-
ures (11.3-4) show the relation of wave set-up to tide level
and location on the reef. Although wave set-up did vary
from day to day, the water depth above the reef was not an
evident factor. Figure (II.S) also shows set-up over a
22 hour period but again no dependency on water depth is
evident.
Other wave data from the four measurement days showed
the wave heights to continually diminish along the reef.
The wave periods remained fa.ir1y consistent at all stations
and agreed closely with the p~ak periods observed at the deep
water station. Wave direction varied from station to station
indicating continued wave refraction on the reef.
At the shorward stations, the currents were found to
be nearly non-existent or of very small magnitude. At the
more seaward stations, currents were very difficult to
determine due to the mass transport of water shoreward in
the breaking zone. Generally, the currents observed moved
in a westerly direction.
A review of wind data (Table II.S), shows that trade
wind conditions existed throughout the test period so set-
up conditions due to varying wind conditions were not
observed.
A final and important correlation to wave set-up on
28

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Table (II.5)
Wind Data
(as observed at the National rJeather
Service Center-Honolulu Int'l Airport)
(Mag. Heading in Parenthesis)
True Heading
Direction Speed Times other than 12:00
Date Time (0-360°) (Kts) Time Direction S:eeed
Aug. 16 12:00 7 17
17 + 7 18
18 7 17
19 8 15
20 6 12
21 10 18
22 6 19
23 6 15
24 10 13
25 7 13
26 7 17
27 7 15
28 6 12
29 6 15
30 7 19
31 7 23
Sept. 1 6 17
2 6 14
3 9 12
4 6 14
5 8 14
6 7 17
7 7 10
8 8 15
9 6 14
10 7 20
11 6 16
12 5 12
13 12 8
14 6(17) 16 18:00 7(18) 17
15 6 19
16 7(18) 19 18:00 7(18) 19
17 7 9
18 6 15
19 7 18
20 7 18
21 6 16
22 6 16
23 8 18
24 0:00 2 7
4 17 6:00 32 4
32

Table (II.5)
(Continued)
(Mag. Heading in Parenthesis)
True Heading
Direction Speed Times other than 12:00
Date Time (0-360°) (Kts) Time Direction SEeed
Sept. 25 12:00 6 16
26 + 7 15
27 12 13
28 8(19) 15 18 :00 4(15) 8
29 8 10
30 14(25) 12 18:00 8 (19) 15
Oct. 14 22 11
33

the reef transect line comes from data collected at the
deep water station on Sept. 16 and 30 (Figure II.6). Two
15-minute wave records for each day, recorded simultaneously
with the MWL records made on the reef, were recorded by an
electronic capacitance water level staff (Photos II.6).
Transformed into a digital readout at 0.4 seconds, the
water level was checked if Gaussian, wave heights deter-
mined by the zero up-crossing method and checked if Ray-
2
leighian, and such parameters as mean energy (cr ), Hrms,
Hl/3, Tl/3 and an energy density spectrum vere calculated.
A calculation was made to see how much energy was
attributable during the record to low frequency oscillations
under 0.4 cps (periods> 25 seconds). Less than 3.5% of
the total energy was in the range f < 0.04 cps in the energy
spectrum. No detrending for tides was done.
II.3.b Tide gauge results
The two tide gauges, although monitored for
nearly a two month period, provided accurate wave set-up
comparisons for only a two week period. The clock running
the strip chart record for Station 1 ran unevenly and made
nearly 3/4 of the data collected unreliable. Accurate data
though for the two weeks showed set-up at Station 1 to
range between 0.04 and 0.28 feet (Tables II.7-ll).
II.3 .c Mean water level oscillations
The 15-minute record at 5 second intervals on
October 13 (Figure II.6 and Table II.l2) shows an oscillation
34

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recorder
36
Looking towards shore
Photo (II. 7)
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of the M}~. Although the record length was far too short
to determine accurately long term oscillations , it appears
a long period oscillation may be in excess of 10 minutes .
A very evident oscillation of just over one minute was
observed and it had an amplitude of around 0 . 10 feet .
Further investigations of this dynamic set-up would be
advantageous since it would enter as an important factor
to any design criteria accounting for set-up.
II . 3.d Water level difference inside and
outside Kewalo Basin
The measurements taken on October 5 across the
narrow neck of land separating the basin from the reef showed
a set-up of 0 . 09 feet . Set-up between Station 1 and the
one just outside the basin were identical, although over 500
feet apart, indicating the old channel once connecting Kewalo
Basin to Ala Wai Harbor (about 50 feet shoreward of Station
1) and the nearly diminished wave height reaching Station 1
probably prevented any further set-up towards shore .
The mVL in the very southeast corner of the harbor was
0.07 feet higher than that at the NOAA facility. Possible
causes for this difference may have been basin oscillations
affecting the basin corner or a leveling error .
II.4. Conclusions to Observations
The basic conclusion supported throughout the
observations is that the wave set-up along the transect line
of the Ala Moana reef is of small magnitude under the
42

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f'V)
I
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M
<r-
-
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p
-
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<r"
N
-
0
N"-),::)
r-.IN,....N~rJ
-
-
-
P
.
.
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...
::
t-
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cr
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IX>,..,..,r-J
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c
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-

conditions mentioned. The largest set-up observed was 0.28
feet. Currents at the transect line are very weak and are
not believed to contribute to or alleviate set-up. The
wind may affect set-up, but no changes were observed during
the project. The set-up observed is not uniformly increas-
ing along the transect line but rather increasing/decreasing,
possibly due to wave refraction focusing energy to certain
locations.
II.4.a Errors
Given such fine measurements of a barely dis-
cernible condition, it is equally important to keep in mind
the reliability of the collected data. Several factors
bear mentioning:
1) Surveying errors
Although extreme care was taken in leveling all
stations, allowance must be made for possible error. Davis,
Foote and Kelly, in their book, Surveying: Theory and
Practice (4), indicate how maximum surveying error is deter-
mined.
(A) In referencing the stations to the Fisherman's
vlliarf benchmark (classified as excellent surveying), the
1
maximum error ±0.05 (distance in miles)7z. Given a dis-
tance of 1900 feet from Fisherman's 1Vharf to the University
of Hawaii porpoise tanks:
Hax. Error = ±0.05 (~)},z = +0.03 ft.
(B) In surveying out to the reef stations from
45

shore, a distance of 1400 feet and classified as ordinary
surveying:
1400 ~
Nax. Error= +0.1 <m) 2
= +0.05 ft.
(C) In surveying from the shoreline benchmark to
the NOAA station, a distance of 900 feet and classified as
ordinary surveying:
900 ~
Max. Error= +0.1 ~
0) = +O.OL~ ft.
These errors are possible in trying to reference the
stations to a common datum. If one considers only the
comparison between subsequent measurements of set-up, then
surveying error is negated and only reading error need by
considered.
2) Reading error
Probable error (E) in reading a manometer can be
approximately determined from a reading record. Standard
deviation obtained from the readings comprising a record
length would not properly identify reading error since a
fluctuating free surface was recorded. Detrending the set-
up fluctuations would be one way of isolating reading error.
Another approach is to consider the recording device .
A small indicator ring built onto the float indicated what
reading on the manometer scale to record. Its width was
0.005 ft. so an error in one reading may vary ±0.01 ft.
With sixty readings in one record length, however, the
reading error would decrease significantly and be insignifi-
cant in comparison to other probable errors.
46

3) Harbor seiching and boat generated waves
A final factor contributing significantly to the
degree of set-up observed is the readings taken inside
Kewalo Basin. Harbor seiching and boat activity are neces-
sary considerations when assuming the water level inside
Kewalo Basin represents the still water tide level. It is
known that seiching exists within the harbor along with
boat generated waves and these conditions may appear in the
NOAA tide gauge readings. Data collected at the NOAA tide
station over the two month observation was examined for
ev~dence of this.
The tide record from noon September 16 - noon Septem-
ber 17 (Figure II.7) illustrates some of the largest observed
deviations from the expected tide level. The tide gauge
reading at 18:45 on September 16 shows that a reading error
as large as 0.24 ft. is possible. During the four days of
set-up measurements on the reef, a 15 minute record, similar
to those taken on the reef, was taken from the NOAA station
manometer to eliminate, as best as possible, these effects.
In the comparison of water level readings between the
two tide gauges over the two month period, seiching and
boat waves may be present.
II.4.b Effect of errors
In concluding this section, the values used in
this report are, at best, approximations to the set-up
phenomenon observed and in general the magnitude of set-up,
47

..&
~
NATIONAL
12-282
-
:t
·r
.1
-4
-:r:
20
Squares
to
the
Inch
.-->
··r
Ti
i
-1
ft-ITi
~
~
1-
C!.
~
-
~
+·
:q.
fY
I+
--ll
l
1

rather than precise measurements, is what bears signifi-
cance. For all measurements given in this report, a
tolerance of +0.05 ft. must be considered.
III. Calculations of Theoretical Wave Set Up
III.l. Philosophy
Wave set-up on a coast is related to a pheno-
menon described by many as radiation stress. Radiation
stress is defined as the excess flow of momentum due to
the presence of waves.
Momentum is transferred to the deep water in the deep
ocean regime and is largely conserved during wave propaga-
tion until arriving at the coastline. Near the coast, the
flow of momentum in the waves perpendicular to the coast
is responsible for an increase in the mean water level,
defined as wave set-up.
III.2. Theoretical Wave Set-Up Criteria
III.2.a Radiation Stress
Dorrestein (1961), Lundgren (1963), Lonquet-
Higgins and Bowen (1960,1961), Lonquet-Higgins and Stewart
(1964), Battjes (1974) and others have shown how the presence
of water waves in a body of water induces radiation stress.
Lonquet-Higgins and Stewart (5) approached the problem by
considering the conservation of momentum. Beginning with
Newton's Second Law of Motion
F (III.l)
49

and considering a constant mass (m), the mass can be placed
inside the time derivative and then the force term (F)
becomes equal to the time rate of change of momentum.
F = d(mv)
dt (III.2)
This force is a manifestation of the radiation stress.
To apply this concept to waves, first consider an
undisturbed body of water of uniform depth h as shown in
Figure (III.l).
h
r • F /" / F
Figure (III.l)
p
0
r ~ 1
Momentum Flux in a Stationary Fluid
The pressure at any point is equal to the hydrostatic
pressure
p = -pgz (III.3)
Thus the total flux of horizontal momentum across a verti-
cal plane of unit width between the free surface (n) and
the bottom (-h) would be
(III. 4)
where P0
the pressure p in a quiescent fluid. The total
so

flux past an identical plane at a distance x+dx from the
first plane would be the same as Eq. (III.4).
Now consider the momentum flux in the presence of a
simple progressive wave motion described in Figure (III.2).
z=o
2=-h--------------------------------~------------------------
Figure (III.2)
Momentum Flux in a Progressive 'dave
The surface elevation z = n is given by
n = a cos(kx-crt) (III. 5)
where a = wave amplitude, k = 2TI/L (wave number) and a =
2TI/T (angular frequency). Particle velocities from linear
wave theory for a wave propagating in the +x direction are
u si~~ kh cosh k(z+h)cos(kx-crt) (III.6)
v = 0 (III.7)
w a a
sinh kh sinh k(z+h)sin(kx-crt) (III.8)
Considering the flux due to wave action in the x
direction Figure (III.3)
51

x = constant
udt
Figure (III.3)
Bodily Transport of Homentum across a Plane
volume = udtdz (where dy = 1)
mass = pudtdz
and momentum flux (dmv) - pudtdzu - pu2dz
at - dt - (III. 9)
2
In this expression pu represents a bodily transfer
of momentum (pu) at a rate u. Thus the total flux of hori-
zontal momentum across a plane (x=constant) is the combina-
tion of the hydrostatic and bodily transfer momentum flux
terms integrated between the bottom z=-h and the free
surface z=n.
(III.lO)
The symbol Sxx is defined as the excess flow of x
momentum due to the presence of waves in the x direction
and is the principal component of radiation stress. sXX
is equal to the mean value of Eq. (III .10) with respect to
time, minus the mean flux in the absence of waves .
52

sXX
=
f:h(p+pu
2
)dz - f~hp0dz
Developing S further
XX
where
s (1)
XX
sCZ) =
XX
n 2
f_h pu dz
fn pdz
0
Considering linear waves (small wave heights) n ~ O
sCl) =
XX
since the limits of integration are constant
s(2)
XX
= !
0
(p-p )dz
0 ( -h 0
f_h p-p0
)dz
(III.ll)
(III.l2)
(III.l3)
(III.l4)
(III.l5)
(III. 16)
Using the same analogy for wave induced momentum flux
but now in the vertical (z) direction, Figure (III.4)
53

+z
0
z=-h
•
/~
)~,-r~;-r
r ~
l~
l-r
/~
r
~
l ~
/ ~
1 -
1~
1 ~
,-~
~
~ ~
~ ~
~~
1-;
rT
z ~
; ~
)~77
7 771
) ~
!r7
? 7
, ~
? ~
/
or
then
Figure (III . 4)
Wave Induced Momentum Flux
in the Vertical Direction
p+pw2 = p0
- 2
p - Po = -pw
s (2) = J~h( -p~)dz
XX
Combining Eqs. (III.l5 and III.l7) gives
(1) (2) 0 ( 2 2)
Sxx + Sxx = f_hP u -w dz
(III.l7)
(III.l8)
Substituting Eqs. (III.6 and III.8) for u and wand inte-
grating yields
s<l) + s(2)
XX XX
2 2
pa cr h
2 sinh2 kh
Bearing in mind the dispersion equation
2 2 H2
cr gktanh kh and a = ~
s<l) + s(2)
XX XX
2
pgH 2kh
8 sinh 2kh
54
(III.l9)
(III. 20)
(III.21)

Considering the remaining contribution
fn pdz
0
and again applying linear wave theory
where p ~ pg(n-z)
Eq. (III.22) after integrating becomes
2
~
then
2
s = ~ [~ + 2kh ]
xx(total) -~ L sinh 2kh
in deep water (kh >> 1)
2
s = .e_gB_
xx To--
and in shallow water (kh << 1)
sXX
3 2
= Ib pgH
(III.22)
(III.23)
(III. 24)
(III. 25)
(III.26)
Longuet-Higgins and Stewart end by relating S to wave
XX
energy
1 2
E = g- pgH (III. 27)
but for my analysis the wave set-up will be calculated from
the changing wave heights so there is no need to carry this
further.
Other components of radiation stress exist but they
will not be considered in this report.
55

III.2.b Wave set-up from radiation stress
When deep water waves encounter a sloping
beach, they shorten, steepen and eventually break. They
continue their advance shoreward with decreasing amplitude
until all energy is either dissipated or reflected . The
resulting changes in radiation stress lead to changes in
the level of the mean water surface (Longuet-Higgins and
Stewart (5)) .
For steady state conditions, the shoreward flux of
momentum must be independent of the distance from shore .
Th~ momentum balance in a slice of water due to a normally
incident wave is considered (Figure III.S).
F
....-------
s +eK<fi+h)
2
- -+
XX T
dx
< •
-
- --
Balance of Horizontal Momentum for Waves
Entering Shallow Water
n
As shown in Figure (III.S), the water is bounded by
the sloping water surface z=n , the sloping bottom z=-h,
56

and two vertical planes x and x+dx . Assuming the bottom
slope to be small, the momentum flux into the slice at x is
F s + Jn pg(n-z)dz
XX -h
Carrying out the integration for the second term
At x+dx the momentum flux will be increased by
- 2
d/dx[S + l/2pg(n+h) ]dx
X X
(III . 28)
(III . 29)
(III.30)
There is an additional flux of horizontal momentum due to
the shoreward component of the hydrostatic pressure, since
the bottom is sloping
(III. 31)
Looking again at Figure (III.S)
dx = dS cos a
or
dS = dx/cos a
Therefore, the horizontal component of the additional flux
equals
- dx
pg(n+h)---- sin a
cos a
Again, assuming the bottom slope to be small
cos a "' 1
and
sin a"' tan a = dh/dx
57
(III .32)

Eq. (III.32) in terms of h and x becomes
- dh
pg(n+h)dx dx (III. 33)
Summing all flux components in the horizontal momentum
balance
d 1 - 2 - dh
dx[Sxx+zPg(n+h) ]dx - pg(n+h)d:X dx = 0 (III.34)
dS
XX - dn
ax+ pg (n+h)rx = o
or (III.35)
Given again (n <<h), Eq. (III.35) equals
dS
-d~x + pg(h) ~~ = 0 (III.36)
Various models relating wave set-up to radiation stress
have been developed (Gerritsen(6)). Eq. (III.36) is the
basis for each model with additional refinements made for
large set-up, shear stresses and wave induced currents .
Since the set-up observed on the reef was very small
(n <<h), n ~ O is a valid consideration. Shear stresses along
the bottom are also assumed negligible since the currents
measured on the reef were very weak . Wave induced currents
were noticed as wave groups broke on the reef but were not
measured and will be neglected in this study. Eq . (III.36),
without additional refinements, is now related to wave
height and then applied to our situation .
Integrating Eq. (III.36) by dx
~s + pgh ~n = o
XX
58
(III. 37)

or
liS
XX
lin = - pg11
Substituting Eq . (III.24) for SXX
[~ + 2kh ]
L sinh 2kh
(III.38)
(III.39)
The only condition remaining is to determine the wave
height (H) as it travels onto the reef and then the wave
set-up can be calculated.
III . 2.c Computing wave heights
The reef profile can be considered divided
into three zones (Figure III. 6).
Zone a = the region outside the breaker point
Zone b = the region between the breaker point and
the outer edge of the reef flat
Zone c = the region on the reef flat
Assuming an unrefracted wave approaches the reef, several
factors need to be determined:
1) the effect of shoaling
2) the effect of energy losses
Up to the breaking point the wave experiences shoaling and
energy losses in the form of friction. After breaking, the
wave encounters the addition of breaking energy losses up
to the reef flat . On the reef flat the wave experiences
energy losses due to breaking and friction until such time
that breaking disappears, then only friction losses are con-
sidered. Shoaling also continues if the reef is not flat .
59

I
t
Qll<l.~ ("I~ ~~o ..,_..r~ .
'or~.._k:~ls
60

Gerritsen (6) has shown that for linear wave theory
the total rate of energy dissipation is given by
= frictional losses
= breaking losses
frictional factor (determined
empirically)
= breaking dissipation coefficient
(determined empirically)
(III.40)
The rate of energy dissipation due to friction and breaking
reduces the energy flux (F) in the direction of wave propa-
gation to
where
F = E Cgr
(III. 41)
For a sloping bottom, a step function is considered (Figure
III.7) where Eq. (III.41) is integrated over a small hori-
zontal step ~x. The value of the energy speed, Cgr' may be
considered constant over the horizontal step ~ x.
Integrating over a step ~x
~E -l: ~X
t cgr
(III. 42)
Substituting Eq. (III.27) for E
~H2 = H 2 H 2 8 l: ~X
j - j+l = pg tCgr
(III. 43)
61

t
I
IJ . I ij .
d I 6
.
'""'" Co-.Ac:.v.Ad,Y..~ tV'ttrjl
~ koc..t, ~ Rl cN.a a.-
(,2

The effect of shoaling is taken into account at a vertical
step in the step function. The energy flux remains un-
changed, therefore
E.C = E.+lC
J grj J grj+l
Again substituting Eq. (III.27) for E
l/8 pgH.
2
C = 1/8 pgH.+
2
1c
J grj J grj+l
or c
2 grj
Hj C
grj+l
(III. 44)
(III.45)
(III.46)
Combining the effects of energy loss and shoaling and writing
the results in a more general form
I 2 I
2
Cgrj
8 !J.x.
(Hj+l) H L: J (III.47)
j Cgrj+l pg tCgrj+l
The computations are then carried forward to compute Hj+2
I
and Hj+2 in the same manner and so on until the wave energy
is completely dissipated.
From the wave height values determined in this manner,
the wave set-up is calculated using Eq. (III.39).
III.3. Computing Wave Set-Up Using Theory and
Observed Wave Data
The four wave records taken on September 16 and
30 are used in supplying input data to theoretically deter-
mine wave set-up. An idealized wave is assumed to repre-
sent the wave spectra and the root mean square wave height
(H ) is used in determining energy dissipation losses.
rms
63

The wave frequency containing the largest amount of mean
energy is used as the wave period (T). Linear wave theory
assumes T remains unchanged . The averaged still water
depth inside Kewalo Basin is used in determining the depth
of water along the transect line. The friction factor (fw)
and the breaking dissipation coefficient ( s ) used in deter-
mining friction and breaking losses in the energy dissipation
equation (Eq . III.40) were given values computed empirically
by Larry Brower (7) during his investigation of energy
dissipation on the Ala Moana reef. The breaking criteria
coefficient (yb) was determined from a graph by Battjes
(Figure III.8). Some interpolation was done here since
~ tan a
(III. 48)
0
vHo/Lo
where
a = the reef slope
H = the
0
deep water wave height
Lo = the deep water wave length
For our reef profile, the slope of the reef varied and an
approximation of where the breaking first occurred was used
in determining the slope. See Figure (III.9) for f , s ,
w
and yb values used. Initially a hand calculation was done
using the input data from Run 1 on September 16. It was
found that the Hrms did not break as it traveled over the
reef (computations contained in Appendix V). Eventually
the wave energy was dissipated by friction losses on the
64

Date trem ; • heraell
o Ieiiia
•• • ••
~ I o ..
+ lewell el I I
• '"i• .....,
• •
t + •
'·· i ..
•••
0
0
•
01 L,.,..........................-:1:-........--""=".::-'.__..._..............-=.............-~---.....~
1101 0 I U D.l 2
Figure (III.8)
Breaker height-to-depth ratio
- · t
•
After Battjes (1974)
Determination of the Wave Height
Breaking Coefficient ( yb)
65

reef. Professor Gerritsen mentioned that this same problem
occurred when analyzing earlier observations using Hrms so
H113 was used instead. Once the breaking point was deter-
mined using H113 the wave set-up was determined using the
Hrms
Analyzing the energy dissipation equation given a
variably sloping bottom is extremely tedious, so a computer
program developed by H.L. Kaul, a graduate student in Ocean
Engineering, was used. Kaul's program indicated that the
idealized wave broke, during all four runs, from 8-29 feet
se~ward of Station 5. Although in the field the extreme
breaking zone was observed to start at approximately 80-
150 feet seaward of Station 5, the H113 wave is expected
to break closer to Station 5.
Given the results of the wave height changes as the
idealized wave moves shoreward, Tables (III.l-4) show the
computations and values obtained in calculating wave set-up
from Eq. (III.39). Figure (III.lO) shows wave set-up/set-
do'vn in relation to the various runs and positions along
the transect line.
An interesting point to note is that the location of
maximum set-down is near the same location for all four runs
and is approximately 500 feet seaward of Station 5. At the
breaking point, just seaward of Station 1, a small dip in
set-up is observed, then the introduction of breaking
losses beyond that point gives a large increase in set-up .
66

0
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(V)
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(
w
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71.
t--
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3
J
H-+-t+H-H+
~
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d
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I
t!=+-++++
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j
lti
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if
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rrrt
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Gerritsen (6) indicates in his paper that when energy
dissipation is considered in Zone a, the point of minimum
waterlevel is shifted seaward as evidenced by Figure
(III.lO). If energy losses are not considered in Zone a ,
then the maximum set-down is expected at the breaking point .
The computations also showed the idealized wave com-
pletely dissipated approximately 40 feet shoreward of
Station 4. The set-up is considered unchanged beyond that
point.
IV . Comparison of Observed and Calculated Wave Set-Up
Table (IV . l) shows the comparison between wave heights
and set-up as determined from observations and calculations
for Stations 4 and 5. At Station 5 the calculated and
observed wave heights agreed fairly well, the calculated
values being somewhat less. At Station 4 the calculated
wave heights were much less than those observed indicating
the idealized wave experienced much larger energy losses
from Station 5-4 than was observed.
The wave set-up comparisons at Station 5 were in very
close agreement only varying between 0 . 002-0 . 031 ft . As
pointed out in Chapter II, the probable measurement errors
exceed this type of precision , but in general the magnitude
of set-up determined by each method agrees well. An inter-
esting note is that the set-up variation from Run 1 to Run
2 for each day is similar in both methods. As in the wave
73

SeEt. 16
Run 1
Run 2
SeEt 30
Run 1
-...J
Run 2
+'
SeEt. 16
Run 1
Run 2
SeEt. 30
Run 1
Run 2
Table (IV . l)
Comparison of Observed and Calculated Wave Heights
and Set-Up at Stations 4 and 5
Wave Heights Wave Set-Up
Station 4 Station 4
Observed Calculated Observed Calculated
1. 8 ft. 0.45 ft . 0 . 11 ft . 0 . 243 ft .
0.45 0.02 0.178
- 0.45 - 0 . 198
- 0 . 64 - 0.323
Station 5 Station 5
Observed Calculated Observed Calculated
"' 2 . 5 ft. 1. 97 ft. 0.02 ft. 0 . 018 ft .
1. 74 0 . 06 0 . 029
2.7 1. 69 0 . 04 0 . 060
2. 22 0 . 06 0.088

height computations, the set-up computations for Station 4
indicated large energy differences between the two methods.
Figure (IV.l) shows the comparison between observed
and calculated set-up at all stations. Since the idealized
wave was completely dissipated just beyond Station 4, no
change in wave set-up shoreward of that point occurs. In
all runs, the calculated set-up shoreward of Station 5
exceeded that observed.
Gerritsen (6) made a comparison between calculated
set-up from his earlier study and the set-up observed
during the present investigation for two days of almost
equal mean energy (Figure IV.2). Using energy values
observed along the reef in 1976, he found the wave set-up
for the two days to agree in both magnitude and trend.
V. Conclusions from the Wave Set-Up Project
V.l. Field Observations
The first conclusion is that wave set-up on the
Ala Moana reef along our transect line is of small magnitude
for low wave energy input. The set-up measurements observed
during similar conditions by the previous investigation seem
to have been in error.
The trend in set-up (except for that observed on
September 16, Run 2 (Figure II . 2)) indicates an increase
from Station 5 to Station 4, a decrease from Station 4 to
Station 3 and then a continual increase to Station 1. Such
fluctuations (also shown from energy observations made
75

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(rn)
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COMPJTE.O- S'E.PT f4 , 1Cf]C
Oo3---
--
DS T"AN ce_ --7
~ Al-ON G R E:. f...f .S ~A·
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Figure (IV . 2)
Comparison Between Heasured and
Computed Wave Set-Up for Equal Energy
77
·5

Field observations and theoretical analysis of wave set-up on Ala Moana Reef

Field observations and theoretical analysis of wave set-up on Ala Moana Reef

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Field observations and theoretical analysis of wave set-up on Ala Moana Reef