AN ABSTRACT OF THE THESIS OF
Robert Lawrence Swanson for the Master of Science in Oceanography
(Degree)
(Name)
(Major)
Date thesis is presented
Title Tidal Prediction, and the Variation of the Observed Tide
from the Predicted Tide at Newport, Oregon
Abstract approved
Redacted for privacy
.(Major Professor)
A tidal and sea level survey was begun in Yaquina Bay, Oregon,
on 8 May, 1964. A continuous recording tide gage was installed at
the pier of the Oregon State University Marine Science Center.
An harmonic analysis of the observed data was made, and the
major tidal constants were compared with those published by the
Coast and Geodetic Survey. A program was written for the IBM 1410
computer, so that the tide could be predicted at any time using the
tidal constants for the Newport area. An investigation of the
"meteorological tide" was made by comparison of the predicted and
observed tides. River stage, sea level variation, barometric pres-
sure, and wind were considered.
Lastly, a comparison was made between the predicted tide at
Newport and the predicted maxima and minima of the tide at Newport
as determined using the Coast and Geodetic Surveyts tide table.
TIDAL PREDICTION, AND THE VARIATION OF THE OBSERVED
TIDE FROM THE PREDICTED TIDE AT NEWPORT, OREGON
by
ROBERT LAWRENCE SWANSON
A THESIS
submitted to
OREGON STATE UNIVERSITY
in partial fulfillment of
the requirements for the
degree of
MASTER OF SCIENCE
JUNE 1965
APPROVED:
Redacted for Privacy
Prossor of Oceanography
In Charge of Major
Redacted for Privacy
Head of Dep artmOanography
Redacted for Privacy
Dean of Graduate School
Date thesis is presented
Typed by Marcia Ten Eyck
ACKNOW LEDGE MENT
I would like to express my deep appreciation to Doctor June G.
Pattullo and Doctor Wayne V. Burt for supplying the financial assistance and equipment needed for this project. Special acknowledge-
ment is due to Doctor Pattullo, my major professor, and an authority
on sea level fluctuation. She was a great inspiration to me, and with-
out her encouragement and assistance the project would never have
been successful.
I wish to extend my gratitude to Doctor Donald Guthrie, who
devoted much of his valuable time serving as a statistical consultant,
and to Mrs. Susan Borden, for assistance in programming for the
computer.
Also, I am greatly indebted to Mr. Richard Easley and Mr.
Curtis Collins for their aid. They spent many days in the cold and
rain of the winter months helping to install the stilling well for the
tide gage. My further thanks to them for taking time to mark the
marigram and wind the clock whenever they were in the vicinity.
Lastly, thanks to my wife, Dana. She not only aided in reducing
the data, but ably assisted throughout the project, including holding
the rod while the levels were run. Her company was also appreciated. on all the weekly trips to Newport.
TABLE OF CONTENTS
Page
INTRODUCTION .......................
TIDE GAGE INSTALLATION ................
1
3
REDUCTION OF DATA ...................
6
COMPARISON OF PREDICTED AND OBSERVED TIDE
9
.
.
THE METEOROLOGICAL TIDE ...............
ADEQUACY OF THE PREDICTED TIDE AS PUBLISHED
IN THE TIDE TABLES ...................
39
...............
48
SUMMARY AND CONCLUSIONS
BIBLIOGRAPHY
................... .
.
.
APPENDIX
I
II
III
IV
V
VI
VII
VIII
IX
X
XI
XII
Hourly heights observed .............
Observed high and low tides ...........
Levels ......................
Tidal constants to be used in IBM 1410 program
Stencil sums ...................
Fortran listing ..................
Hourly heights prediction ............
Tide curves ....................
Meteorological data ...............
Sea
level data ...................
High and low tides for Newport predicted from
the tide table ...................
High and low tides for Humboldt Bay as recorded
in the tide tables .................
51
53
57
60
6Z
65
67
69
73
89
9Z
94
97
LIST OF FIGURES
Page
Figure
1
Chart indicating tide gage location .......
4
Z
Symbols used in harmonic analysis ......
11
3
Graph for determining component of wind along
4
Graph for obtaining deviation in water level
5
Graph of high and low tide at Newport, Oregon,
vs. Humboldt Bay California ......... 44-45
a NE-SW direction ...............
due to barometric pressure and wind ....,
38
LIST OF TABLES
Table
Page
I
Harmonic constants ................
II
Results of the paired t-test for the difference
inmean sea level .................
III
Corrections for sea level, barometric pressure,
and wind applied to the observed tide and com-
pared to the predicted tide ............
IV
V
Computations for paired t-test for predicted
maxima and minima at Newport versus
Humboldt Bay ...................
Data from least squares analysis of the predicted maxima and minima at Newport using the
IBM 14Z0 versus the Predicted Maxima and
Minima at Humboldt Bay .............
VI
Computations for paired t-test for observed
times of maxima and minima at Newport versus
predicted times at Newport as predicted in the
tide tables .....................
19
34-37
40
42
47
TIDAL PREDICTION, AND THE VARIATION OF THE OBSERVED
TIDE FROM THE PREDICTED TIDE AT NEWPORT, OREGON
INTRODUCTION
An interest in a tidal study on Yaquina Bay was encouraged for
two primary reasons. Other than the Coast and Geodetic Survey
primary tide station at Astoria, there were no known permanent recording gages anywhere on the Oregon coast. Second, members of
the Oceanography Department had heard numerous complaints as to
the accuracy of the published tide data in Yaquina Bay.
The author interviewed several local residents and asked if they
had occasion to use the tide tables, and if so, how much faith they
had in the predictions. A fisherman commented that he never paid
much attention to the heights, but the predicted times of high and low
water did not appear to be correct. An owner of a small boat marina
stated that he had been around Newport for several years and could
not remember when the predicted values were correct. He said that
when the marina was dredged in order to accomodate small boats at
the lowest tides of the year, the basin was left dry shortly thereafter.
Also, at the site of the Oregon State University Marine Science
Center, a proposed pipe line, to be laid on the basis of the highest
high water, was found to be inundated quite frequently.
Partly because of these inquiries, a project was begun to test
the adequacy of the predicted tidal heights. A tide gage was installed
on the pier at the Oregon State Jniversity Marine Science Center,
and a continuous record of the water level was made, beginning in
the latter part of April, 1964.
From the observed data for the first usable month of observations the following studies were made:
1.
An estimate of the tidal constituents was made from the
observed data, and the results were compared with constituents furnished by the Coast and Geodetic Survey.
2,
Since hourly heights of the tide are not published for New-
port, values were computed for the same period as the ob-
served data, and the results were compared with the observed heights.
3.
The difference between the predicted and observed tide was
analyzed to see if "meteorological tides" could be the cause.
4.
A comparison was made between the predicted tide at New-
port and the estimated predicted tide as based on the tide
at Humboldt Bay, Caiifornia. (The Coast and Geodetic Sur-
vey predictions for Newport maxima and minima are referred to HumboJdt Bay.
3
TIDE GAGE INSTALLATION
The tide gage was mounted on the west side of a piling on the
west end of the pier at the Oregon State University Marine Science
Center (Figure 1). The site was chosen because the current sweeps
around the embayment from the east end of the pier, bringing large
logs from the lumber mills that are up river. Since construction of
the pier in the latter part of 1963 many cross bracings on the pier
have been destroyed by the logs. At the site chosen, there has been
no damage by such debris.
The float well is a twenty foot section of poly-vynil-chloride
pipe with a 9
inch inner diameter. We were not permitted to
drive nails into the piling, in order to prevent deterioration insofar
as possible. Consequently, galvinized iron straps three inches wide
and
inch thick were used to secure the float well to the piling.
Three inch laminated plywood blocks were used to fill the space
between the piling and the float well. The laminated blocks were
used to prevent the float well and piling from crushing the blocks
when tension was taken on the bolted straps.
The bottom of the well is a piece of one-half inch fiber glass.
The intake for the water in the fiber glass is one inch in diameter.
All wooden parts are covered with a marine paint to prevent
destruction by the marine environment.
4
Figure 1. Chart indicating tide gage location.
3'W
Newport
8 'N
N
Tide
OSU
Marine
Science Center
124°O2'
5
The tide gage is a float type Stevens Water Level Recorder,
Type A 35, made by Leupold Stevens Instruments, Incorporated, of
Portland, Oregon.
The scale is 1:10, or, one centimeter of height on the record
corresponds to ten centimeters of float movement. The time scale
is 9. 6 inches equals one day. The clock is weight driven, and
mounted as specified in the instructions. (The feasibility of using
an electric clock is being considered.
A porcelain enameled iron gage, marked in meters, is located
on another piling visible from the location of the automatic tide gage.
This is used to make height comparisons with the automatic tide
gage, and to establish a reference to mean lower low water.
Tide notes (time, height, and weather) have been marked inter-
mittently on the record, for the purpose of reducing the data to a
usable form.
REDUCTION OF DATA
The marigram was recorded in the metric system at a scale
of 1:10.
To obtain absolute heights above lower low water, the
record was marked weekly with the staff reading. The changes in
height at the staff, as recorded in the weekly tide note, corresponded to the changes in height as recorded by the gage. This agreement
indicated that the height scale on the gage remained constant during
the period of study.
Time was also marked in the tide note on the chart. The clock
on the gage ran slowly, as indicated on the time scale of the man-
gram. A linear correction was applied to the time scale as needed
to coincide with the time marks. The source of time used was the
Pacific Northwest Bell Telephone Company; their time is checked
with the Greenwich time kept by the Navy in Washington, D. C.
A continuous record of the sea water level was read for hourly
heights beginning 8 May, 1964, at 0000 hours, and continuing for
twenty-nine days, through Z400, 5 June, 1964.
Hourly heights were
recorded to the nearest centimeter; two centimeters was the smallest graduation on the height scale.
Time was recorded originally
in daylight saving time, estimated to the nearest minute, where
fifteen minute intervals were the smallest marked intervals on the
time scale.
7
The water level was converted to feet, and the time to Pacific
Standard Time, to make the data conform with that of the available
published tide data.
In order to compare the predicted values to the observed values,
it was necessary to convert the observed data to the same reference
plane as the predicted values. The reference level used was mean
lower low water.
To reduce the data to mean lower low water, a line of levels
was continued, from a line run by the County Engineer, to the staff.
A loop was run, and the levels checked within the usually allowable
error of 0. 003 feet. A wye level was used, along with a Philadel-
phia rod, for running the level loop.
A temporary bench mark had been installed for the construction
of the Oregon State Marine Science Center.
The mark had been
established at an elevation of 17. 00 feet above mean lQwer low water.
Levels were run on 3 July, 1964, from this mark to a nail located
on the staff at 3. 6 meters, or 11.812 feet. The mean difference in
elevation for the two runs between the bench mark and the spike was
10. 0005 feet; so the nail was actually at an elevation of 6. 9995 feet
above mean lower low water. This means that the staff zero was
4. 812 feet below mean lower low water. Consequently, 4. 8 feet
were subtracted from the observed readings in order that the data
be referred to mean lower low water. A copy of the leveling data
is in the Appendix Ill.
These changes in the original data put it into a form which is
easy to analyze with the tidal information available.
COMPARISON OF PREDICTED AND OBSERVED TIDE
The tidal predictions that are published for Newport, Oregon
are a corrected version of the more completely predicted values of
the tide at Humboldt Bay, Ca1ifo:ia, Constant corrections for Newport are applied to the times and heights at high and low water. As
a result, the rise and fall of the water level at Newport is only
approximated.
It is possible, however, to predict the tide at Newport with a
much greater accuracy if an harmonic analysis is performed on the
data that reflect conditions that exist at Newport. An harmonic
analysis is a method of separating a complex periodic function into
several simple sinusoidal curves. On revamping the curves, an
harmonic prediction of the tide can be obtained at any time, since
the amplitudes and phases of the simple "constituent" curves have
been determined. The equation for the height of the tide at any
time can be represented as:
h=Ho+Acos(at+a)+Bcos(bt+P)+---+Zcos(zt+).
The symbols are as follows:
height of tide,
Ho = height of the mean water level above the datum used,
A cos (at + a) = tidal constituent,
A, B, etc. = amplitudes of the constituents,
The term in brackets is the phase of the constituent,
a, b, etc. = the constituent speed in degrees per hour,
t time,
a, 3, etc. initial phase when t = 0; the initial phase depends
upon t and the locality in which one is interested (Schureman,
h
1941).
10
In the equilibrium theory of tides, the water is considered to
respond directly to the tide producing forces. This is not quite rep-
resentative of the real earth, however, since such things as friction,
inertia, and the distribution of the land masses are not considered.
In actuality there is a time difference between the equilibrium tide
and the observed tide.
This lag in each of the constituents is called the epoch. The
epoch and the amplitude of each constituent are called the harmonic
constants of the constituent. These are the values which are of
interest in the harmonic analysis and prediction of the tide.
A better idea of the symbols and what they mean can be seen
in Figure 2. Let A cos (at + a) be one of the constituents of the
tide curve caused by a force M. The time t = T is the time at which
there is an interest in the height of the tide caused by M. The point
M is when the equilibrium tide would equal the maximum height or
the amplitude, A. However, the actual tide lags behind the force by
the epoch
ic.
The term (Vo + u) is the "equilibrium argument.
This gives the phase of the argument at time T and is referred
from M.
The term a is the phase of the argument from t = 0.
From the figure, it can be seen that a = (Vo + u) +
(-.}c)
where -K
is the explement of J(Schureman, 1941).
The Coast and Geodetic Survey did a tidal survey at Newport
in 1933 and 1934.
The length of that series was 369 days. The
H.W.
II
Time
Figure Z. Symbols used in harmonic analysis.
12
tidal constituents for Newport were computed from this data. These
constants are listed in the Appendix IV. Another series of observations was run in 1953, and agreement, according to the Coast and
Geodetic Survey, was very good.
From the twenty-nine day series run in May and June, 1964, it
was desired to check the constants, to see if there had been any
change in the past eleven years. A twenty-nine day series, however,
is not nearly as good for determining the constants as a 369 day
series. In fact, only a few of the major constants can be computed
from the twenty-nine day series, as most of the constants are
masked, due to the presence of other constituents having periods
which are approximately of the same period.
The problem in the harmonic analysis is finding a way to sep-
arate the different constituents so that the constants might be determined. Consider a tide that only has two constituents. The series
can be divided into periods equal to the period of one of the constituents. These periods can then be divided into equal time inter-
vals called constituent hours. This will leave the effect of the constituent being investigated alone, while the effect due to the other
constituents will be averaged out.
In the case of the solar constituent the observations are divided
into periods of twenty-four hours. This is then divided into twenty-
four equal periods, or constituent hours. If the tide at each zero
13
hour for the entire length of observation is recorded, the solar
tide will always be the same. The effect of the other constituent
will be different at successive zero solar hours. Therefore, if all
the tidal heights at zero hours are summed and averaged, the ave
rage will approximate the effect of the solar tide alone at zero hours.
This procedure is done for each hour of the solar day, and the hourly
heights due to the solar tide will be determined. The same method
is used to separate the other constituents.
It is more convenient, however, if only the solar time is used
for analysis. For example, a lunar day lasts twenty-four hours and
fifty minutes in solar time. Instead of picking lunar hours off the
observed tide curve equal to one hour, two minutes, and five sec-
onds, it is easier to work with only solar hours. In this case there
are approximately twenty-five solar hours to twenty-four lunar
hours, so that to stay in solar time, once a day two solar hours are
designated to a specific lunar hour (Dronkers, 1964). To simplify
this approximation technique "stencils" have been devised. The
method is discussed in detain in Schureman (1941). Mean constituent hourly heights are found by dividing the hourly sums by the
length of the tidal series.
The stencil sums and mean constituent hourly heights for the
present sample are in Appendix V. Over this series the following
components were computed: M1, M2, Sz, K1, and 01. These
14
computations were done before the data were reduced to mean
lower low water.
The method used is called, "A Twelve-Ordinate Scheme of Harmonic Analysis of Tidal Heights, Neglecting Harmonics Above the
Third. " The method makes use of the constituent hourly heights
that were computed from the stencil sums.
Assume:
Y(x)=Y=a1sinx + a2sinZx + a3sin3x + b0 + b1cosx + b2cosZx + b3cos3x
where, instead of using the hourly heights Y0, Y1, Y2,
Y3- - -
already found, the heights at intervals of two hours are used;
that is Y0, Y2, Y4, Y6, Y8, Y10, Y, Y14, Y16, Y18, Y, Y
in the first notation. For convenience adopt the following new
notation for these twelve hourly heights: Y0, Y1, Y2, Y3---Y11
and compute the coefficients from the following equations,
letting x
whereT' = 0, 1, 2, ----11 =
r,
=
a=l £
11
11
6=0
b0=i
12
Ysin nTrL
Ycos nnL
6
11
Y(..
.= 0
15
However, the work of computing can be reduced by using
a suitable combination of these equations, II, III, and IV, and
equation I for y, as follows:
First, equations II, III, and IV for the coefficients b0, b3, and
a3 reduce to
(Y0+Y1+Y2+Y3+Y4+Y5+Y6+Y7+Y8+Y9+Y10+Y1 i)
b0 =
(1)
b3 =! (Y0 - Y2 + Y4 - Y6 + Y8 - Y10),
(2)
- Y11).
(3:)
- Y7 +
(Y1 - Y3 +
a3 =
Next, we have, by putting x successively equal to 90° and
2700 in equation (I) above,
= b0 - b2 + a1 - a3
Y9
whence
=
b0
Y3
-
-
b2
Y9
=
-
a1
+
2(a1
-
a3)
a3),
and therefore a1 =1 (Y3 - Y9) + a.
2
(5)
Next, putting x equal to 0° and 1800 in (I), we have
= b0 + b1 + b2 + b3)
- b1 + b2
Y6 = b
whence Y0 -
and therefore
b3)
(6)
2 (b1 + b3)
(Y0 - Y6) - b3.
(7)
Equations (4) anc (6) now give
b2 =
(Y0 -
+ Y6 - Y9).
(8)
16
Also,
16
a =1 {Y0sinO° + Y1sin3O° + Y2sin6O° + Y3sin9O0
+ Y4sinl2O° + Y5sinl5O° + Y6sinl8O° + Y7sinZlO°
+ Y8siriZ4O° + Y9s1n270° + Y10sin300° + Y11sin330°}
=!
{(Y3-Y9)o. 86602(Y2+Y4- Y8-Y10)+O.500(Y1+'- Y,'-Y11)1
II, which reduces
0. 1443 (Y1+Y2-Y4-Y5+Y7+Y8-Y10-Y11).
a2 can be computed directly from equation
to a2
=
Thus equations (1) to (8) give the coefficients a1,a3,b0,b1,
b2 and b3 merely by averaging the observed ordinates
YO, Yl___Yll.
The coefficients in equation (I) may be positive or negative,
and the equation can be changed into the following form:
+ A1 cos(x-'1) + A2 cos (Zx-) + A3 cos (3x-3),
Y
where A1
a12
=
b12,
+
A2
are the amplitudes, and
+ b22 and A3 =a32 + b32
=
tan
1
1
tan
1
'3=tan -1 -a3
are the constant phase angles
1
(University of California).
A sample calculation for the M constants is as follows:
The stencil means for y1, i
Yl
yO
8. 96
6
8.92
YZ
=
0, 1, 2,
6. 29
5. 93
8. 10
y7
y8
y9
6.16
5.81
8.06
---, 11 in feet are:
y5
Y3
and
10. 57 11. 03
y10
y11
10.75
11.26
17
=
8.487
a1
=
-0.023
b1
=
0.063
b2
=
0.430
a2
=
-2.802
A1
=
b
0
A2
M11= 0. 063 ft.
M2'= 2.835 ft.
The amplitudes of the constants vary periodically, due to the
variation of the moon's orbit to the plane of the earth's equator.
This variation is called the obliquity; it has a period of 18. 6 years.
In order to convert the computed amplitude to the mean amplitude
as recorded in the Appendix IV, it is necessary to correct for the
obliquity. This is done by using a node factor, f, which is defined
as the ratio of the true obliquity to the mean. This factor is printed
The
in Table 14 of Schureman (1941) for the middle of each year.
factors used to convert M1' and M to
and M2 for 1964 are
1/1. 166 and 1/1. 001. Therefore, M1 and M2 equal 0.054 feet and
2.832 feet respectively.
The phase ang1ehas to be corrected for the 'tequilibrium
argument" in order to convert the angle'to K
(See Appendix IV
for identification of symbols. ) This argument is called
(V0
+ u)
where the subscript o refers to the beginning of the series, in this
case 8 May. The argument is an astronomical argument.
For M2,
= 278. 73
The value of local
+
from the formula tan -
(V0
+ u)
69. 680,
j
-2.802
0.43
therefore
local (V + u) = 278. 730 + 69. 68°= 348, 41°.
Table I contains the values computed for the five constants,
along with the values computed from the data in 1933 and 1934.
There is very good agreement, especially in the amplitudes. The
phase angles agree only fairly well, but this is excusable, since a
small change in "a" or "b" will cause a relatively large change
in
.
Since the comparison of the two sets of constants revealed good
agreement, I decided to use all of the constants furnished by the
Coast and Geodetic Survey to reconstruct computed hourly heights
of the tide for the period for which there were observations. In
this manner a good comparison between the observed and predicted
tide could be made. The formula for the height of the tide at any
time can be rewritten in the form:
h = Ho +fH cos (at
+ a.)
where all the symbols have the same meaning as before, except
that H is the constituent amplitude and f the node factor (Schureman,
1941).
A program for the IBM 1410 computer was written. The time
was reckoned from 0000 hours, 1 January, 1964, and the program
19
TABLE I
Harmonic Constants
1964 Data
Constant
Amplitude
ft.
f
Mean
Amplitude
1933-1934 Data
Mean
Amplitude
ft.
ft.
M1
0. 063
1/1. 166
0. 054
0. 046
M2
2.835
1/1.001
2.832
2.778
S2
0. 680
1. 000
0. 680
0. 728
K1
1.450
1/1.011
1.434
1.386
01
0.735
1/1.018
0.722
0.843
(V0+u)°
jO
ITo
M1
357.28
168. 10
165.38
94.6
M2
278.73
69.68
348.41
346.9
8. 06
0. 34
14. 8
S2
9. 58
K1
340.26
483.31
103.97
116.3
156.33
310.38
100.41
99,9
-
20
was started at time t = 3072 hours, which corresponds to 0000
hours 8 May, 1964. The program ran through
3768 hours on
5 June, 1964. In order that the formula above be valid for the be-
ginning of the year the following substitutions had to be made to
compute a:
- pL- I= at +
(1/s +
u) - K,= at + Greenwich
or Greenwich
(V0
+ u)
(V0 +
u) -
K=a
where the new symbols are:
S = west longitude in degrees of time meridian used at
the tide station (120. 00 W)
L
west longitude in degrees, of station for which
predictions are desired (124. 03° W)
p
1 when referring to diurnal constituents
p = 2 when referring to semidiurnal constituents, etc.
The arguments used for the IBM 1410 computer are in the
Appendix IV. Appendix VI contains the FORTRAN LISTING.
In the program, the term, at, is incremented as at, at + a, at
+ Za,
etc., rather than the computation being done by changing t by an
hour. This operation is done at statement 5+5 and statement 7, by
making use of the identities cos (a+b) = cos a cos b - sin a sin b
and sin (a+b) = sin a cos b + cos a sin b.
computer time approximately in half.
This operation cut the
21
After the hourly heights were computed they were tabulated to
the nearest tenth of a foot (see Appendix VII). The values were
plotted, along with corresponding observed tidal values (Appendix
VIII).
The two curves fit quite well. On several days, in fact,
there is hardly any noticeable discrepancy. However, it is necessary and interesting to investigate the discreparcy that does exist.
22
THE METEOROLOGICAL TIDE
The relationship between the observed tide and the predicted
tide appears to be quite clGse. There is no indication that the time
of maxima and minima differs between the two over the month.
However, the difference in heights certainly causes me to believe
that the prediction is not an adequate approxImatior of the actual
water level. Possibly the difference is caused by the rneteorological
tide. ' The umeteoroiogical tides's generally are considered to be
caused by variations in temperature, barometric pressure, and
wind (Schureman, 1941).
In this
papers
variation in sea level and
river stage will also be included in the 'meteorological tide.'
Newport is located at the mouth of the Yaquina River. Conse-
quently, the stage of the river plays a part in the variation of the
tide. There are, however, no published data on the stage of the
Yaquina River below Mill Creek. Mill Creek has a drainage area
of only 4. 08 square miles, and consequently is of little use. Also,
the Geological Survey has stated that there are no unpublished stream
flow data on the Yaquina River (U. S. Geological Survey, personal
communication).
The drainage area at the mouth is only 270 square
miles. The best estimate of the stage of the river is from an exam-
ination of the rainfall data. Since there is no runoff from melting
snow in the area, the excess runoff over groundwater flow must be
23
due to precipitation. The precipitation record, as well as other
meteorological data for the time of observations, are contained in
Appendix IX.
From 8 May through 5 June there were only 1. 42 inches of rain.
Most of this water was probably consumed by surface storage, in-
filtration, and interception (Linsley, Kohier and Paulhus, 1949).
Consequently, river stage will be neglected in considering an effect
on the tide during this period.
The formula for computing the height of tide contains the term
Ho, which is the difference between mean water level and the datum
to which the gage records are referred. At Newport, mean lower
low water was 4. 16 feet below mean sea level (U. S. Coast and
Geodetic Survey, 1959). The term Ho, however, is not constant,
but varies throughout the year.
Deviations of sea level from mean sea level for the year have
been calculated and published for approximately twenty-five years
at Crescent City, California, and Neah Bay, WasJ4rigton
(Union
Godsique et Gophysique Internationale, 1959, and 1963). From
these deviations, an estimate of the expected sea level at Newport
during the observations could be obtained.
A statistical analysis, called the t - test on paired observation,
was performed on the data. To use these data in this test, the mean
sea level for the year was used as the control, and sea level for a
24
particular month was subtracted from the yearly mean. This gives
a series of deviations from the mean. The hypothesis is that the
mean of the deviations is zero, or that there is no difference between
the yearly sea level value and the sea level during the month used.
In order that this test be applicable, it must be assumed that the
sample is random and drawn from a normal distribution. These
assumptions seem to be essentially fulfilled, since all available observations have been used, and the samples are errors which tend to
follow the normal distribution (Li, 1957).
The sea level data used
are listed in the Appendix X. The test is explained below in the case
of Crescent City during the month of May.
= 0, the hypothesis is that the mean of the deviations is 0.
n
= sample size, in this case twenty-six years of data were
examined.
= -6. 19 feet, the sum of the deviations of the twenty-six
years from the mean.
=
(y)2
= -0. 2381 feet, the average of the deviations.
= 38. 3161 feet2, the sum of the deviations squared.
= 1.4737 feet2.
= 2. 0535, the sum of the individual observations squared.
ss
=y2 (y)2
= 0. 5798 feet2
= n-i = 25, degrees of freedom.
25
S2
2
n
=
= 0 0232 feet2.
= 0. 00089 feet2.
= 0. 0298 feet, estimate of the sample standard deviation.
-40
The t- statistic is t =
= -7. 99. At the 95% level of sig-
I-
nificance the critical regions are -2. 060 < <+ 2. 060 for
= 25.
This indicates that at the 95% level of significance, the value -7. 99
lies inside the critical region, and that the test of hypothesis that
= 0 should be rejected. In other words, the sea level in May
is not the same as mean sea level for the year.
The 95% confidence interval for the average difference of sea
level in May from the yearly mean is:
-t.o25
+t.o25
-0. 2381 - 2.060 (0. 0Z98)q-O. 02381 + 2.060 (0. 0298)
-0. 2995 ft<-I-< -0. 1767 ft
Table II includes the t-statistic, critical region, mean difference,
and confidence intervals listed for Crescent City, California, and
Neah Bay, Washington, for May and June.
From the mean difference for the months of May and June an
estimate of the difference in mean sea level for the period of obser-
vation can be made. A linear relationship of the difference in sea
TABLE II
Results of the Paired t-Test for the Difference in Mean Sea Level
T-
Place
Stat-
Month istic
Critical
Region
Mean
Diff.
Confidence
Tnt.
Crescent May -7.99 -Z.O6Ot<+.O6O -O.Z381 -O.Z995<14<-O.l767
City
Neah
Bay
June -9.78 -Z.060<t<+Z.060 -0.2319 -O.Z807<.(-O.183J
May
-6.28 -2.069<t<+2.069 -0.2800 -O.37l9<-0.188l
June
-7.57 -2.069<t<+2.069 -0.3135 -0.3987<-O.2283
27
level to latitude was assumed between Crescent City (
A 124. 20° W) and Neah Bay
(
(4)
41. 75° N,,
48. 37° N, A 124. 62° W). Newport
44. 62° N, A 124. 03° W) then had a mean difference of -0. 27 feet
for the period covering the twenty-nine days of the observation.
This difference accounts for most of the difference between the predicted and observed values (Pillsbury, 1940).
However, the difference between the predicted and observed
values is not constant. I felt that the remaining deviation might be
due to barometric pressure and the wind. Another statistical test
was applied, this time to the difference between the predicted tide
and the observed tide corrected for sea level. A correlation coefficient between the difference in water level and the combined effect
of pressure and wind was computed, to determine whether the
changes in water level were related significantly to the combined
effects of both meteorological factors.
The mechanics of the computation are much the same as those
for the paired t - test. The only new terms for computing the multiple correlation coefficient r, are
SP y2 and SFxz . The
subscripts x, y, and z stand for water level deviation, barometric
pressure, and wind respectively. The quantity SF is similar to SS
and is defined as:
SP
=
xy
=
sp
xz
=
xz
n
Values of the variables taken at 0000 hours and 1200 hours
throughout the observations were used to compute the correlation
coefficient.
Weather data for the period of observation are given in Appendix IX. In order to simplify the computation, the following adjust-
ments were made to the data:
1) The barometric pressure as recorded was reduced by
the amount 29. 80 inches. The difference was then
multiplied by 100. As an example, the value 29. 90
inches would be used in the computation as 10. This
does not alter the computation in any way.
2) The wind was assumed to move water only along the
axis of the bay. The entrance to the bay lies roughly
in a northeast-southwest direction, so only components
of the wind in this direction were considered to effect
the water level. Wind blowing from the southwest was
taken as positive, and a wind from the northeast as
negative. The wind was converted from the Beaufort
Scale to nautical miles per hour before the component
was taken. Figure 3 gives the wind component in knots
in terms of the Beaufort Scale.
Figure 3. Graph for determining component of wind along a NE-SW direction.
W
SW
NW
N
NE
indic ate
e aufort
to knots.
NJ
'C
30
The multiple correlation coefficient is defined as r
i-r2=
where jAI
a11
where:
IAI
1A221
SPxy
SPxy SSy
SSx
=
2
SPxz
SPyz
SPxz SPyz SSz
a
A221
=
SSx
=
SSy
SSyz
SPyz SSz
(Anderson, 1958).
Therefore
1
- r
10.0735414. 1622
2
r
(5. 2684) (36926803. 6745)
=
0.694
The 95% level of significance was used with n-k degrees of freedom.
Since there are three variables (waterlevel, pressure and wind)
and 57 observations, k = 3, n = 57 and n-k = 54 degrees of freedom.
The critical value for the correlation coefficient with n-k
54 is
0.328, which is less than 0.694. This indicates that there is a very
good correlation between the fluctuation of the predicted tide from
the observed tide, and the pressure and the wind
(Owen, 1962).
Therefore, an estimate of the change in water level can be made
knowing the wind and pressure. The estimate' can be made using an
equation of the form:
x=c+By(y-)+Bz(z-
)
31
where
x = deviation from the predicted tide in feet, caused by
barometric pressure and wind.
= average deviation as computed from the data, in feet.
y = observed barometric pressure converted as mentioned
before.
= mean barometric pressure as computed.
z
component of wind along the northeast-southwest
direction.
= average wind as computed.
By = regression coefficient on the water level deviation
due to barometric pressure.
Bz = regression coefficient on the water level deviation
due to wind.
The regression coefficient is computed from the relationship:
(By, Bz) = Al2 (A22)
Al2 = (SPxy, SPxz)
(A221)
=
J__
A22
SSx
-SPyz
SSz
A22
-SPyz
-SPyz
SSy
A22
-SPyz
A22
SSy
A22
32
SSz+ SPxy (..SPyz
And By = SPxy (-)
A22
A22
+ SPxy (i)
Bz = SPxy (- SPyz
A22
A22
By = 0. 0131
Bz = -0.0143
Therefore
Ax = 0. 195 + 0.0131 (y - 25. 982) - 0.0143 (z - 3.921)
The equation can now be converted so that the barometric pressure
can be inserted.
25.982in. + 29. 8Oin.= 30.06 inches of mercury
100
By
=
0.0131
ft.of water
= 1.31 ft./inch of mercury
inches mercury
100
The equation can now be written
AX
(It) 0. 195 ft
+ 1.31
in.
(y-30. O6iri)-0. 01.43 ft(z-3.92 knot)
knot
where the value of Ax should be subtracted from the predicted tide
in order to obtain the observed.
The regression coefficient for pressure indicates that for a
change in one inch of mercury of the barometer there is a change of
15. 72 inches in the water level. Actually the relationship should be:
L water level = - fm
A mercury level
where f?m is the density of mercury and,..° the density of the water
33
(Proudman, 1963). The slope in this equation is approximately
- 13,6 gJcm
1. 02 gjcm.
or -13.3. The difference between the actual slope
and the computed is small, but there is certainly an indication that
forces (evidently of smaller magnitude) other than the pressure are
influencing water levels. In the portion of this simplified equation
concerning wind (-0. 0143 ft/knot (z - 3. 92 knot)) it should be noticed
that for a zero change in water level an observed value of wind has
to be of the magnitude of four nautical miles per hour. This also
confirms the previous statement that other phenomena are important
in affecting sea level.
The empirical equation is applied on the high and low waters for
a portion of the series of observations. The weather conditions
closest to the times of high and low waters are arguments. Sea
level is also included. The corrected values of the observed tide
are tabulated in Table III and also plotted on the graphs in Appendix
VIII.
The maximum and minimum values fit quite well after the
above corrections are applied. Figure 4 can be used to obtain
directly the corrections for wind and pressure to be entered into
the equation.
Table III. Corrections for Sea Level, Barometric Pressure, and Wind Applied to the Observed Tide
and Compared to the Predicted Tide. High Tide Only.
Observed
Date
May8
Hour
0935
2210
Tide
ft.
5.8
ft.
+0.27
7. 1
1028
2240
6.2
1108
2320
6.5
1220
2353
12
9
Sea
Level
Correction
Constant
Pressure
ft.
+0.20
ft.
+0.25
+0. 22
+0.26
Wind
ft.
0.06
0.06
-0.01
Corrected
Tide
ft.
Predicted
Tide
ft.
6.6
6.5
7.8
6.9
8.5
6.9
7. 9
0. 24
+0. 06
+0.32
0.03
+0.06
7.3
9.0
7.2
8.8
6.6
8,7
+0. 18
+0.01
+0.06
+0.06
9.2
7. 3
7. 4
1314
6.8
-0.10
-0.13
7.0
7.4
13
0033
1400
9.0
6.8
-0.01
+0.08
0.04
0.06
9.5
7.4
9.2
7.3
14
0117
1456
8.8
6.6
+0.05
+0.07
+0.06
+0.06
9.4
7.2
7.1
0210
1602
8.5
-0.04
-0. 24
+0.06
+0.06
9.0
8.8
6.9
0310
8. 4
6. 9
0. 36
-0. 29
-0. 21
+0. 06
8. 3
8. 2
6. 8
10
11
15
16
1715
7. 7
8, 2
+0. 32
6. 6
0. 27
+0. 20
6. 9
7. 1
8. 4
9.2
9.1
Date
Hour
May 17 0408
18
.ft..
1815
7.5
6.5
0523
6.7
1 925
19
Table Ill Continued. High Tide Only.
Observed
Correction
Sea
Tide
Constant
Level
Pressure
Wind
0630
2015
ft.
+0. 27
ft.
+0. 20
6. 6
6.3
7. 1
+0. 27
+0. 20
ft.
-0. 09
ft.
0. 06
Corrected
Tide
ft.
7. 9
Predicted
Tide
ft.
7. 5
-0.13
7.0
6.7
+0.09
+0.03
0.06
7.3
6.9
0.00
-0.08
+0.14
+0.06
7. 5
6.9
6.4
+0.13
+0. 06
7. 2
6. 9
7. 2
'.7'
Table III Continued. Corrections for Sea Level, Barometric Pressure, and Wind Applied to the Observed
Tide and Compared to the Predicted Tide. Low Tide Only.
Observed
Date
May 8
9
10
11
12
13
Hour
0330
1535
15
16
ft.
0.8
-0. 2
Sea
Level
ft.
0. 27
Correction
Constant
Pressure
ft.
+0. 20
ft.
0. 18
+0. 25
0416
1617
-0.3
-0. 1
0. 25
0502
1653
-1. 4
0.2
+0.08
+0.32
0547
1740
-2. 2
+0. 45
0645
1829
-2. 6
0726
-0.08
Wind
ft.
+0.06
+0.06
Corrected
Tide
ft.
1.5
0. 6
Predicted
Tide
ft.
1T7
1.0
+0.06
-0.03
0.1
0.6
0.6
0. 06
0.06
-0.8
1.0
-0. 4
1.1
1.3
+0.18
+0.06
-0. 03
-1. 3
-1. 2
-0. 09
-0.01
-0. 29
+0.06
-2. 5
-1. 8
-3.0
1.6
+0.08
0.06
-2.4
2. 2
-2.0
2.4
0818
2005
-3.0
+0.05
+0.06
-2.4
-2.1
0910
2102
-2. 5
1010
2220
-1.5
3.2
1915
14
Tide
0.7
1.3
+0. 12
2. 1
2.8
+0.27
+0.20
+0.06
1.4
1.8
1.6
2.0
+0. 05
+0. 06
-0.08
-0.30
+0. 06
-2. 1
-1. 8
-0.32
-1.10
-0.22
+0.06
-1.6
3.6
-1.3
3.4
-0. 10
+0.06
2. 7
3.0
2. 8
3.2
0'
Table III Continued. Low Tide Only.
Observed
Date
May 17
.Jiour
1108
2330
Tide
ft.
-1.1
3.0
18
1215
-0.6
19
0055
1305
0. 0
Sea
Level
ft.
+0. 27
2.6
-i-U. 27
Correction
Constant
Pressure
ft.
ft.
+0. 20
+0.12
0. 20
Wind
ft
Corrected
Tide
ft.
Predicted
Tide
ft.
+0.10
-0. 22
+0.06
-0.7
3.6
-0.6
3.4
0.07
0.06
0.0
0,0
-0.08
+0.14
3.1
0. 2
3.1.
0. 12
-0. 38
0. 5
-3
Figure 4. Graph for obtaining deviation in water level due to barometric pressure and wind.
29.70
80
90
30.00
I
I
10
20
Barometric Pressure in inches of Mercury
30
30.40
).5
I
). 4
Use graph to obtain values of 1. 31 (y-30. 06) for pressure and -0. 0143 (z-3. 921) for
wind to substitute in the equation.
1'
X should be subtracted from the predicted value to
obtain observed water level.
'C
3
C
tX = 0.195 + 1.31. (y-30.06)-0.0143(z-3. 921)
0 2
CD
0
0.2
\?.'
1
0
0.1
,.
$
0
1
0
CD
CD
CD
.-
C)
).1
CD
-0. 1
).2
-0. 2
-0. 3
). 3
c
4
I
I
C)
I
2
4
I
I
I
R
1(1
I
1.
14
I
i;
SW-NE Component of Wind Velocity in Knots (SW positive)
1R
20
22
-0. 4
i
CD
CD
39
ADEQUACY OF THE PREDICTED TIDE AS
PUBLISHED IN THE TIDE TABLES
The predicted tide (Section I) has been computed from data
collected at Yaquina Bay, Newport, Oregon. However, the tide
tables published by the Coast and Geodetic Survey do not include predictions for Newport computed from known parameters for each constituent. Instead, the tide tables contain corrections for time and
height of tide, which are added to the detailed prediction for Humboldt
Bay, California, These corrections are:
Time:
Height:
High Water:
Low Water:
+ 13 minutes
+ 12 minutes
High Water:
+ 1.6
Low Water:
+ 0. 1
(IJ. S. Coast and Geodetic Survey, 1964).
It seen-is reasonable to ask whether these corrected values for Humbolcit Bay are an adequate estimate of the more elaborate method of
redicting the tide at Newport.
Again the paired t - test was used. The predicted values were
paired with the corresponding corrected Humboldt values (Appendix
XI).
Separate tests were run on the high tides and low tides. The
important computations are in Table IV.
As indicated in the table, the difference for both highs and lows
was significant. A least squares analysis was then run on the data,
again using separate tests for the high waters and low waters, The
TABLE IV
CompUtatb0
for Paired tTest for Predicted Maxima and Minima at Newport verSuS
Humboldt Bay.
High Tide
56
55
10.5
0.188
2.281
4147X10
74x10
6.91
Z.004
41
test was run comparing the uncorrected values at Humboldt Bay with
the values of the actual prediction at Newport. The computed values
are contained in Table V.
The correlation coefficients for the high
and low waters are both 0. 98. The test of significance can be made
at the 95% level using the following formula:
on
r Jn-2
(Li, 1957).
Taking r in both the case of the highs and of the lows to be 0.
0. 98 Ts6-2
1- 0. 96
The critical region at the
) 2.
0049.
95%
0. 98 (7. 35)
98:
= 36. 0
0. 2
significance level is: - 2. 0049 ' t
Therefore the value of r is significantly different from
zero, and there is a linear correlation between the predicted values
at Humboldt Bay and the values at Newport. A value of r
1 indicates
that there is a perfect linear relationship between the two arguments.
An estimate of the line of regression takes the form of:
=
where
rx
+ B (x -
= the estimated predicted tide at Newport (feet)
= the mean of the predicted values used at Newport in
the regression analysis (feet)
B = regression coefficient or the slope of the line
(feet/feet)
TABLE V
Data from Least Squares Analysis of the Predicted Maxima and Minima
at Newport using the IBM 1420 versus the Predicted Maxima and Minima
at Humboldt Bay.
ft.
SSy
ft.
2
ft.
High Tide
7. 139
46. 514
5. 355
Low Tide
1. 205
161. 908
0. 925
SPxy
SxSSy
yx
+B(x-i)
SSx
SPxy
ft. 2
37.880
41. 098
1. 085
145. 042
1. 105
131.28
B=SPxy/SSx
43
x = the predicted value at Humboldt Bay (feet)
= the mean of the predicted values used in the
regression analysis at Humboldt Bay (feet).
On substituting the computed values into the equation the
estimates are:
High tide at Newport in feet:
V High = 7. 139 + 1. 085 (x
or
V
- 5.355)
High = 1. 085x: + 1. 329.
Low tide at Newport in feet:
V
Low = 1. 205 + 1. 105 (x - 0. 9250)
Low = 1. 105x + 0. 183
Consequently the constant corrections published in the tide tables
do not give an adequate estimate of the predicted tide at Newport.
A graph for these equations is contained in Figure 5. This graph
enables one to obtain directly the estimate of the predicted values
of the tide at Newport from the data published on Humboldt Bay. The
equation should be a better estimate than the constant corrections
published in the tide table.
By inspection of the tide curves in Appendix VIII, one can see
that the periods appear to be in good agreement. A t - test,
however, was run on the observed times and those indicated in the
44
9. 0
0
0-4
a)
z
-4-,
7.0
5. 0
4.0
5.0
6.0
7.0
8.0
Ht. in ft. at Humboldt Bay
Figure 5.
Graph of high tide at Newport, Oregon,
vs. Humboldt Bay, California.
4.0
3.0
2.0
z
1.0
-1.0
-2. 0
-3. 0
LLJ±
-3.0 -2,0 -1.0
I
0,0
I
1.0
2.0
3.0 4.0
Ht. in ft. at Humboldt Bay
Figure 5 Continued. Graph of low tide at Newport, Oregon,
vs. Humboldt Bay, California.
46
tide table. The results are in Table VI. The t - statistic indicated
that the difference between the predicted times of high and low waters
using the tide table and the observed times differed by only a tenth
of an hour.
TABLE VI
Computations for Paired t-Test for Observed Times of Maxima and Minima at
Newport versus Predicted Times at Newport as Predicted in the Tide Tables.
st/n2
n
)
hr.
hr.
High Times
56
55
6. 1
0. 109
2. 47
45x103
804x106
3.89
2.004
Low Times
56
55
2. 9
0. 052
0. 98
18x103
321x106
2.89
2.004
SS
hr.
s
hr.
2
hr.
t
t (55)
0. 05
SUMMARY AND CONCLUSIONS
Analyses and conclusions given in this paper have been based
on a series of tidal observations that lasted twenty-nine days.
Certainly this is a very short period of time on which to draw conclusions. However, it was felt to be an adequate sample, since the
analysis of observed data for May, 1964, yielded major tidal con-
stants that were the same as those computed from the 1933 and 1934
data collected by the Coast and Geodetic Survey.
A computer program for the IBM 1410 computer was written
in order to predict the height of the tide at any time. These predicted values were accepted as the basis for a comparison with the
observed tide. They can also be used for predicting sea levels for
any future period.
The differences between the predicted tide and the observed
tide were found to be reasonably explained as "meteorological tide."
River stage, sea level fluctuatior, wind, and pressure were investigated as the major causes of the "meteorological tide. " River
stage was felt not to be effective in these data, but it certainly in-
fluences water level in many cases. Ambient sea level fluctuations
effect local levels. Local wind and barometric pressure also cause
significant fluctuations in water level.
49
A correction that could be subtracted from the predicted values
to obtain an approximation for the observed water level is:
x ft
0. 195ft + 1.31 (barometric pressure in inches - 30. 06)
- 0. 0143 (component of wind along NE, SW direction in knots
- 3.92 ).
When sea level fluctuation, wind and pressure effects are sub-
tracted from the observed tide, the adjusted observed tide fits quite
well with the predicted. As a result the values predicted using the
IBM 1410 are felt to be an accurate estimate of the tide.
Lastly, the published tide tables do not give the tidal pre-
dictions for Newport itself, but give constants to add to the values
published for Humbolt Bay, California. A least squares analysis
was performed in order to find a better estimate for corrections to
be applied. The results are as follows:
High water at Newport (feet)
1. 085 (high tide Humbolt Bay
in feet) + 1. 329 feet
Low water at Newport (feet) = 1. 105 (low water Humbolt Bay
in feet) + 0. 183 feet
A t - test was also run on the times of tide corrected as mdicated in the tide table and the observed. The test indicated a significant difference between the two values, but only a difference of
a tenth of an hour or six minutes. This does not seem to be sig-
nificant at the present time.
50
The purpose of the study was to examine the tides near Newport,
Oregon. One conclusion is that the knowledge of the tidal fluctuations
is not adequate.
Newport is now the site of the Oregon State University Marine
Science Center, and an accurate prediction, in which hourly heights
may be obtained, is certainly information that should be available to
the ever growing science of oceanography. This, however, is not
the only reason for having better tide records available. Compared
to the east coast, the available tide data are quite sparse. For
example, in a north-south direction of 15°25' of latitude, there are
only seven stations on this coast which have daily predictions.
Three of these stations are in California and two are in Puget Sound.
This leaves only two stations covering the coasts of Washington and
Oregon. One of these is Astoria, which is effected greatly by the
Columbia River.
it is my
belief that a Coast and Geodetic Survey primary tide
station should be located somewhere inthe 270 mile gap between
Humboldt Bay and Astoria. Since there is an oceanographic center
in Newport, this new location might reasonably be located at this
facility.
51
BIBLIOGRAPHY
1.
Anderson, T. W. An introduction to multivariate statistical
analysis. New York, John Wiley and Sons, 1958. 374 p.
2.
Defant, Albert. Physical oceanography. vol.
Pergarnon Press, 1961. 598 p.
3.
Dronkers, J. 3. Tidal computations in rivers and coastal
waters. Amsterdam, North Holland, 1964. 518 p.
4.
Li, Jerome C. R. Introduction to statistical inference.
Ann Arbor, Edwards Brothers, 1957. 568 p.
5.
Linsley, Ray K., Jr., Max A. Kohier and Joseph L. H.
2.
New York,
Paulhus. Applied hydrology. New York, McGraw-Hill., 1949.
689
p.
6.
Owen, D. B. Handbook of statistical tables. Reading,
Addison-Wesley, 1962. 580 p.
7.
Pillsbury, George B. Tidal hydraulics. Washington, D. C.,
United States Government Printing Office, 1940. 283 p.
8.
Proudman, J. Dynamical oceanography. Liverpool, Methuen,
9.
Sanderson, Roy B., District Engineer, Geological Survey,
Portland. Oct. 13, 1964. Personal communication.
1963. 409 p.
10.
Schureman, Paul. Manual of harmonic analysis and prediction
of tides. Washington, D. C., United States Government
Printing Office, 1941. 317 p.
11.
Union Ge'ode'sique et Ge'ophysique Internationale. Monthly and
12.
annual mean heights of sea level for the period of the international geophysical year 1957 to 1958. Liverpool, 1959. 65 p.
(As sodation dt Oceanographic Physique Publication Scientifique
no. 20)
Union Godsique et Gophysique Internationale. Monthly and
annual mean heights of sea level 1959 to 1961. Paris, June,
1963. 59 p. (Assodation dtOceanographie Physique Publication
Scientifique no. 24)
52
13.
University of California, Scripps Institute of Oceanography.
A 12-ordinate scheme of harmonic analysis of tidal heights,
neglecting harmonics above the third. Unpublished lecture
supplement. 3 mimeographed sheets.
14.
U. S. Coast and Geodetic Survey. The difference between
elevations based on the geodeticl level net and elevations
based on mean lower low water ... Washington, D. C.,
July 20, 1959, 1 sheet.
15.
U. S. Coast and Geodetic Survey. Tides: Recapitulation of
results, Newport, Oregon, 1933-1934. Washington, D.C.,
1944j 1 sheet.
16.
U. S. Coast and Geodetic Survey. Manual of tide observations.
Washington, D. C., 1941. 92 p.
17.
U. S. Coast and Geodetic Survey. Tide tables: High and low
water predictions, west coast of North and South America,
including the Hawaiian Islands, 1964. Washington, D. C.,
1964.
18.
224 p.
U. S. Weather Bureau. Climatological data. Oregon.
vol. 70, 1964.
APPENDICES
53
APPENDIX I
Hourly Heights Observed
OSTJ Marine Science Center, 1964
Time Meridian: 120° W
Height datum is MLLWwhichis 4.8 ft. above staff zero.
Hour
0
1
2
8
9
10
4.4
5.4
6.6
3. 1
1. 7
10
0.9
0.9
1.3
2.5
3.7
4.8
5.6
5.7
Noon
3. 8
3
4
5
6
7
8
9
11
13
14
15
16
17
18
19
20
21
22
23
5.0
2.2
0. 9
0.0
-0.
1
0.6
1.9
3.6
5. 0
6. 4
7. 1
6. 4
3. 9
2. 1
5. 0
-0.3
0.0
-0.6
-1.4
-0.8
0.6
0.9
2.2
3.8
5.1
6.0
5.9
5. 0
3.7
2. 2
0.8
0. 0
0.2
1.2
2.8
4. 6
6. 2
7. 4
7. 6
3.2
1.1
0.4
2.1
3.9
5.4
6.4
6. 2
5.2
3. 7
May
11
12
7..8
8.7
4.6
2.2
0.0
-1.8
-2.2
6.3
4.1
1.7
Feet
6. 4
14
8.7
7.8
7.7
5.9
3.5
1.0
8.4
8. 8
8. 7
7.2
5.2
2.9
0.3
0.2
2.1
4.0
5.6
-0.8
-2.3
-2.5
-1.3
0.6
2.6
4.5
-1.4
-2.8
-2.6
-1.4
6.2
7.0
(5.8)
4.4
5.4
3.8
2.4
1.4
1.4
6.3
6.6
3.7
2.4
5.0
3.8
2.7
-1.4
6. 5
5. 0
2.2
0.7
0.2
0.8
2.0
0.9
0.8
1.6
7. 1
8. 1
4. 9
6. 7
8. 3
3. 7
5. 6
7. 9
13
3.6
2. 1
3. 1
6. 2
6. 6
2. 4
4. 0
5. 8
7. 4
0.5
2.4
4. 5
6. 8
5. 1
1.6
2. 0
3. 1
4. 6
6. 3
-1.9
-3.0
-2.5
-1.1
0.6
2. 6
5. 9
6. 0
2. 1
2. 6
3. 6
4. 9
54
APPENDIX I Continued
Ma
16
Hour
17
18
19
20
21
eet
0
6. 4
5. 2
4. 0
3. 1
7.8
2. 9
5.0
4. 2
2
8.4
8.0
6.6
4.8
-0.3
-1.1
-0.6
0.2
1.6
3.2
4.6
5.9
3.5
4.3
5.3
6.2
6.6
6.5
5.6
4.4
3.0
1.4
0.1
-0.5
-0.2
0.7
2.0
3.4
4.8
2.6
3.0
3.9
4.8
5.5
6.2
6.2
5.5
4.5
3.2
1.7
0.6
0.1
0.4
1.2
2.5
4.0
2.6
2.3
2.5
3.3
4.3
5.2
5.9
6.3
5.7
4.8
3.7
2.4
1.4
0.8
1.0
1.8
3.1
3.0
6.1
6.6
7.7
8.4
7.9
6.7
5.0
3.0
1.0
-0.7
-1.5
-1.0
0.2
1.7
3.4
4.9
6.2
6.8
3. 6
1
5. 2
6. 4
6. 5
5. 9
4.1
5. 4
19
5.6
4. 6
3. 4
20
6.3
6.6
6.5
6.0
3. 3
4. 6
4.9
5. 6
6. 5
21
2.8
7. 1
3.8
7. 0
6. 3
22
23
4.6
5.8
6.7
3. 2
7.3
3. 3
7.1
3. 7
4. 8
3.9
5. 9
3.3
6. 7
7. 1
3. 1
3.8
4.8
5. 6
6. 2
3
4
5
6
7
8
9
10
11
Noon
13
14
15
16
17
18
2.6
0.2
-1.7
-2.5
-1.9
-0.7
1.0
2.8
4.6
6.0
6.6
6.1
7.0
7.5
7.2
6.2
4.7
2.9
1.1
1.8
1.2
1.5
2.3
3.4
4.5
5.4
5.8
5.4
4.4
3.2
2.0
1.0
0.7
1.1
APPENDIX I Continued
22
May
23
Hour
24
25
26
27
28
Feet
5.8
4.3
6.4
5.0
6.7
5.5
7.4
6.4
8.0
1
5.0
3.5
2
7.5
7.5
7.6
2. 1
2. 6
3. 3
3. 9
5. 1
6. 8
1.1
1.5
0.0
-0.8
-0.5
2.1
11
0.9
0.5
1.0
2.0
3.3
4.4
5.4
5.9
5.5
6. 3
3
Noon
3.3
4.6
5.5
0.4
-1.1
-1.4
-0.8
0.5
2.1
3.6
4.9
3.3
1.4
-0.2
-1.2
-0.9
0.0
1.5
3.2
4.6
4.8
2.9
1.0
-0.5
-1.2
-0.6
0.6
2.1
3.7
4. 6
5.5
3.8
1.9
0.0
-1.1
-1.3
-0.4
0.9
2.4
5. 5
5. 7
5. 8
5. 1
4. 0
3. 5
4.4
5. 9
13
5. 1
5. 7
14
15
16
17
6.4
6. 0
2. 2
5. 2
3. 3
4. 1
4. 8
6. 0
1.3
2.2
6. 3
3.8
5. 9
5.1
2. 7
4. 1
18
2.7
1.8
2.0
2.0
3.2
2.7
19
4. 1
1.5
1.5
2.3
3.5
2. 7
2. 6
20
5.6
6.8
3. 0
4.8
4.0
3.7
3.8
5.6
4.8
3.8
3.0
2.9
3.4
5.7
1. 0
2.9
1.9
1.4
4.3
3.4
2.9
3.0
6. 3
5. 4
5. 2
5. 0
4. 4
3. 7
7. 4
7. 3
6. 6
6. 4
6. 3
5. 4
4. 7
6. 9
7. 4
7. 3
7. 4
7. 4
6. 6
5. 7
0
4
5
6
7
8
9
10
21
22
23
1.6
0.0
-0.2
0.4
1.5
3.0
4.4
5.4
5.9
0.4
1.8
5. 1
56
APPENDIX I Continued
1-lour
0
1
2
3
4
5
6
7
8
9
10
11
Noon
13
14
15
16
17
18
19
20
21
22
23
May
29
30
6. 7
6. 0
7. 0
6. 0
4. 6
7. 1
7.3
2.9
1.1
-0.5
-1.3
-1.0
0.0
1.4
2.9
4.3
5.4
5.9
5. 6
6.9
6. 4
5. 3
3.8
2.2
0.5
-0.8
-1.1
-0.5
31
5. 4
6.3
6. 9
6. 8
6. 1
4.9
3.5
1.9
0.4
-0.4
-0.4
(0.6) 0.2
1
Feet
4. 6
5.5
6. 2
6. 6
6. 3
5.6
4.5
3.1
1.7
0.4
-0.2
3.4
4.8
5.6
2.7
4.0
5.1
0.1
0.7
1.8
3.0
4.3
5.3
5.8
6.0
<2.0>
1.3
2
3. 9
4.4
5. 1
5. 9
6. 2
6.0
5.2
4.2
3.0
3. 5
3. 4
3. 8
4. 6
4. 0
3. 6
3. 6
4. 0
4. 7
5. 5
4. 7
4. 0
3. 4
4. 1
5. 1
5.2
5.8
6.0
5.6
4.8
3.7
6.8
3. 1
4. 1
3. 6
3. 6
2. 0
2. 2
2. 8
3. 7
4. 4
6.6
6. 1
3.4
3. 1
6.0
5. 9
5.4
5.7
3. 6
4.4
5. 3
4.7
5.8
3. 2
2.9
5.1
4. 7
4.0
4. 0
4. 7
5. 3
5
5.5
4. 1
3.3
3. 1
3.4
4
2.2
3.4
1.8
0.6
0.1
0.3
1.0
5. 8
4.9
3
5.1
4.1
3.0
1.9
1.0
0.5
0.7
1.5
2.6
5. 9
5. 3
June
4. 7
3. 9
6. 1
6. 4
5. 8
4. 9
4. 1
2.7
1.7
1.1
1.3
2.0
2.6
3.6
4.6
5.5
5.9
5.5
4.8
3.7
2.6
1.6
1.2
1.5
3. 1
2. 4
5. 7
5. 1
7. 2
6. 8
5. 8
4. 8
3.7
6.5
7. 6
7. 8
7. 1
6. 0
57
APPENDIX II
Observed High and Low Tides
OSU Marine Science Center
Time Meridian 120° W.
Height Datum is MLLW
Date
May
Time
Highs
hrs. mm.
Ht.
ft.
Lows
Ht.
ft.
Time
hrs. mm.
0935
2210
5.8
0330
1535
1028
2240
6.2
7. 7
0416
1617
-0.3
1108
2320
6.5
8. 2
0502
-1.4
1220
2353
8. 7
6.6
0547
1740
-2.2
12
1314
6.8
0645
1829
-2.6
13
0033
1400
9.0
6.8
0726
1915
-3.0
0117
1456
8.8
6. 6
0818
2005
-3.0
15
0210
1602
8.5
6.6
0910
2102
-2.5
16
0310
1715
8.4
6.9
1010
2220
-1.5
17
0408
1815
7.5
6. 5
1108
2330
-1.1
0523
1925
6. 7
6. 6
1215
-0. 6
8
10
11
14
7. 1
1653
0.8
-0.2
-0. 1
0. 2
0. 7
1.3
1.6
2. 1
2.8
3.2
3. 0
APPENDIX II Continued
Highs
Date
May
Time
hrs. mm.
Ht,
ft.
Time
Lows
hrs. mm.
Ht.
ft.
19
0630
2015
6, 3
7. 1
0055
1305
2. 6
0. 0
20
0800
2050
6.3
7. 3
0210
1410
2.2
0900
2129
5.8
7.3
0315
1455
1.2
0. 7
22
1000
2205
5.9
7.4
0357
1546
0.5
1.0
23
1100
2234
5.9
7.5
0445
1629
-0.3
24
1140
2305
5.8
7.3
0515
1703
-0.9
25
1225
2335
5.9
7.6
0550
1735
-1.4
1300
6.4
0625
1800
-1.3
0005
1347
8.0
6. 3
0700
1843
-1.2
0035
1420
7.7
6.0
0737
1924
-1.5
0108
7.3
5.9
0823
1950
-1.4
7. 1
0852
2037
-1. 1
21
27
28
1505
Ii1
0145
1555
5.9
0. 7
1.4
1.4
1.9
2. 7
2. 9
2.9
3. 1
3.3
59
APPENDIX II Continued
Date
May
Time
Highs
hrs. mm.
Ht.
ft.
Lows
Time
hrs. mm.
Ht.
ft.
0225
1632
7. 0
5.9
0946
2132
-0. 6
0305
1727
6.6
6.0
1008
2244
-0.2
2
0415
1817
6.2
6.2
1117
0.1
3
0520
1915
5.9
6.7
0102
1210
3. 1
0645
2005
6.0
7.2
0113
1315
2.9
0805
2030
5.9
0220
1355
1.9
31
June
1
4
5
7. 9
3.5
3.5
0.4
1.1
1. 1
APPENDIX III
Levels, To Refer Tide Record to Mean Lower Low Water
Levels Run July 3, 1964
Nail in tide staff
at3.60m
=
1l.8lZft
12.992
BS
HI
28. 804
FS
-
TP
5.014
19. 790
BS+ 4.975
HI
FS
-
TP
24.765
4.998
19. 767
BS+ 4.123
23. 890
MI
FS
-
TP
BS
HI
Fire Plug
+
FS
-
TP
20. 990
BS
+
F'S
-
I-Il
Spike = 17. 000 ft.
above MLLW
Fire Plug
TP
BS
HI
+
FS
-
TP
BS
HI
F'S
TP
5.930
17.960
5.975
23.935
2.945
+
-
3.759
24. 749
2.938
21.811
2.941
24. 752
3.762
20. 990
2.726
23.716
2.858
20. 858
BS+ 3.701
24. 559
HI
FS
TP
-
4.756
19.803
BS+ 5.150
HI
Nail in tide staff
at 3. 60 m
FS
-
24. 953
13. 144
11.809
61
APPENDIX III Continued
Determination of staff zero below mean lower low
water
I
-
=
44.
Nail is 17. 000 ft. -10. 0005 ft.= 6. 9995 ft. above MLLW
6.9995 ft above MLLW
3.60 m.= 11.812 ft.on staff
Staff Zero = 6.9995.ft. -11.812 ft,= -4.8125
All observations referenced to the tide staff are
4. 812 ft.higher than the corresponding reading at mean
lower low water.
APPENDIX IV
Tidal Constants to be used in IBM 1410 Program
IBM Card Col. No...
Cornponent
K1
K2
L2
M1
M2
M3
M4
M6
M2
N2
ZN2
Source
Smaller lunar elliptic
Luni-solar diurnal
Luni-solarsemi-diurnal
Smaller lunar elliptic
Smaller lunar elliptic
Principal Lunar
Lunar terdiurnal term
Lunar quarter diurnal term
Lunar sixth diurnal term
Lunar eighth diurnal term
Larger lunar elliptic
Lunarelliptic second order
Principal lunar diurnal
01
00
Lunar diurnal term
P1
Principal solar diurnal
Larger lunar elliptic
2ç
Lunar diurnal term
R2
Solar semi-diurnal term
S1
Solar diurnal term
S2
Principal solar
S4
Solar quarter diurnal term
S6
Solar sixth diurnal term
T2
Larger solar elliptic
Smaller
lunar evectional
2
ii 2
Variational
Larger lunar evectional
Lunar diurnal terms
1-5
11-15
H ft.
0.067
K°
124.5
116.3
12.3
356.8
94.6
346.9
1. 386
0.190
0.062
0.046
2. 778
0. 014
0. 044
0.021
0.006
0. 566
0.075
0.843
0.036
0.426
0. 141
0. 022
0.066
0.029
0. 728
0. 005
0.001
0.043
0.019
0.043
0.110
0.032
18
P
1
1
2
2
1
2
19.4
3
115. 3
4
291.4
194.6
6
8
2
2
323. 0
299.1
99.9
132. 7
110.5
93.3
83. 5
14.8
258.4
14.8
249. 1
245.6
14.8
359.8
340. 9
326.2
92.8
1.
1
1
1
1
2
1
2
4
6
2
2
2
2
1
20-26
a(°/solar hour)
15.58544
15. 04107
30.08214
29. 52848
14. 49669
28. 98410
43. 47616
57. 96821
86. 95231
115. 9364
28. 43973
27. 89535
13. 94304
16. 13910
14. 95893
13. 39866
12. 85429
30.04107
15. 00000
30. 00000
60. 00000
90.00000
29. 95893
29. 45563
27. 96821
28. 51258
13. 47151
30-34 38-42
Greenwich
(V0 + u)°
I
53.7
0. 9
181.6
1.025
1.011
1.008
194. 4
30?. 6
1. 200
1. 166
293. 3
260. 0
1.002
1.003
1.004
1.005
326.7
310.0
226.6
269. 8
213.0
329.8
204.0
350.3
272.9
216. 1
177. 4
180.0
0.0
0. 0
0.0
2. 6
121.0
295. 4
352.3
355. 4
1.001
1. 001
1.001
1.018
1.053
1.000
1.018
1. 018
1.000
1.000
1.000
1. 000
1.000
1. 000
1.001
1.001
1.001
1.018
(Defant, 1961)
(Schureman, 1941)
C'
63
APPENDIX IV, Continued
Explanation of
The quantity
(V0
(V0
+ u)
+ u) is called the equilibrium argument of a
constituent at the time t = 0. The time t = 0 is most often taken as
0000 hours on 1 January of the year for which there is an interest
in the tide.
V = the uniformly varying portion of the argument, and refers
to the initial epoch. It depends on the rotation of the earth
and the mean motion of the moon in its orbit.
u = a slow variation, due to changes in the longitude of the
moon's node; (the moon's node being the intersection of the
ecliptic and the projection of the moon's orbit). The node
moves westward and had a period of 18. 6 years. The value
of u is taken for the middle of the year under consideration
and is considered constant for the year. (Dronkers, 1964)
Values of
(V0
+ u) for Greenwich for the beginning of each
calendar year are tabulated in Table 15 of Schureman (1941).
local (V 0+ u) = Greenwich
(V0
+ u)_pL +
15
where p = 1 when referring to diurnal constituents
p = 2 when referring to semidiurnal constituents, etc.
L = west longitude in degrees, of station for which predictions are desired (124. 03° W).
64
APPENDIX IV Continued
S = west longitude in degrees of time meridian used at
the tide station (laO. 000 W).
a = speed in degrees per solar hour for the constituent of
intere st.
A sample calculation is as follows (from Tables 15, 16, 17 of
Schureman, 1941):
For M2: Greenwich
local
(V0
(V0
3Z6. 7 °
+ u) for January, 1964
for 1 May of each year
= 314.22 0
for 8 May of a leap year
=
+ u) = Greenwich
(V0
+ u)-pL +
164. 950
805. 87°
15
= 805. 87° -(2)(124. 03°) + (28. 984°/hr)(120.00)
15°/hr
65
APPENDIX V
Stencil Sums
Hour
0
1
2
3
4
5
6
7
8
9
10
11
Constituent
M
S
259. 7
301.3
293.2
278.3
259.0
237.4
217.2
202.7
194.0
193.4
199.4
209.0
219.0
219.4
176.0
162.8
178.0
191.2
234.8
271.6
306.4
324.5
320.0
283.4
258. 7
226.8
223.5
227.3
242.6
247.3
255.6
256.9
256.2
266.0
281.9
268.3
273.6
240.8
243.6
231.2
218.9
227.1
229.9
247.3
251.4
250.6
260.6
235.7
272.8
286.5
265.3
275.0
233.4
2174
303.2
307.3
209.8
233. 7
294. 5
249. 8
259. 9
21
22
337. 9
297. 2
20
23
300.9
3a8.7
297.8
0
308.6
282.7
263.7
243.4
225.2
210.8
202.8
201.9
207.1
215.3
222.2
12
13
14
15
16
17
18
19
215.5
178.6
160.3
168.4
197.3
K
228. 9
234.6
238.8
240. 1
317. 1
227. 7
231. 1
237. 6
249. 5
298. 7
266. 8
233. 8
228. 9
238. 4
.
APPENDIX V Continued
Mean Constituent Hourly Heights
M
Hour Divisor
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
29
29
28
29
30
28
29
29
29
29
29
28
29
30
29
29
29
29
29
30
28
29
30
29
Ht.
ft.
8.96
7.57
S
Divisor
Ht.
ft.
29
10.39
6. 29
5. 61
5. 93
10. 11
9. 60
8. 93
8. 19
6.83
7.49
8. 10
6. 99
6. 69
9.. 37
10.. 57
6.67
6.88
7.21
7.55
11. 19
11.03
10.12
8. 92
7. 18
6. 16
7. 89
8. 09
8. 23
5.53
8.28
5. 81
8. 30
6.80
8.40
8.61
8.96
8. 06
9.82
10.75
11.33
11.26
10.27
Constituent
29
9.41
9.88
10.25
10.46
K
Divisor
30
30
29
29
29
29
29
29
29
29
29
29
29
29
29
28
29
29
29
29
29
28
29
29
Ht.
ft.
10.57
10.29
9. 75
9. 09
8. 39
7.77
7. 27
6. 99
6.96
7. 14
7.42
7.66
7. 85
7. 97
7. 97
7.82
7. 83
7.93
8. 19
8.60
9. 15
9.82
10.30
10.60
0
Divisor
29
29
28
30
29
29
29
28
29
30
29
30
29
28
29
29
30
29
28
29
29
29
30
28
Ht.
ft.
7.82
7. 71
8. 12
8. 09
8. 53
8.81
8. 86
9. 15
9. 17
9.40
9.25
9.12
9. 20
8. 83
8. 67
8.64
8. 69
8. 13
8. 35
7.89
8.05
7.50
7.95
7.49
67
APPENDIX VI
FORTRAN LISTING
For the Prediction of Hourly Heights of the Tide Using
Twenty-seven Tidal Constants
DIMENSIONH (27), XK(27), A(27), P(27), V(27), F(27),AL(27),L(2)
DIMENSIONCARG(27), DELC(27), DELS(27), SARG(27)
10 FORMAT(2A5,SF1O.0)
11
FORMAT(F5. 3, FlO. 1, F3. 0, 3F8. 3)
12 FORMAT(13H1INITIAL TIME, 2A5/ I)
13 FORMAT(17, 112. 4)
14 FORMAT(1H1)
15 FORMAT(1H, 14, 5E15. 5)
1
READ(1, l0)L(l),L(2), TI, TEND, 5, XL, HO
READ(l, ll)(-I), XK(I), P(I), A(I), V(I), F(I), 1=1, 27)
WRITE(3, l2)L(l), L(2)
9
8
2
D021=l, 27
PK=A(I)*S*. 0666666_P(i)*XL-XK(I)
AL(I)= V(I)+PK
ARG=A(I)*TI+AL(I)
ARG=ARG-360.
IF (ARG-360.)8,8,9
X=ARG*. 0174533
DELC(I)=COS(A(I)*. 0174533)
DELS(I)=SIN(A(I)*. 0174533)
CARG(I)=CO5(X)
F (I) = 1(I) *H(I)
SARG(I)=SIN(X)
LINE=O
T=TI
3
N= 0
SUM=HO
4
D041=l, 27
SUM=SUM-FF(I)*CARG(I)
5
WRITE(3, 13)N, SUM
IF(LINE. EQ. 45)GOTO6
T=T+1.
LINE= LINE+ 1
N=N+1
IF(T. GT. TEND)STOP
D071=1, 27
X=CARG(I)
7
CARG(I)=DELC(I)*X-DELS(I)*SARG(I)
SARG(I)=DELC(I)*SARG(I)+DELS(I)*X
APPENDIX VI Continued
6
GOTO3
LINE=O
WRITE(3, 14)
GOTO5
END
Explanation of Tidal Terms in the
FORTRAN Listing
Tidal Notation
a
p
Greenwich
f
a
(V0 +u)
Initial Time
Ending Time
S
L
Ho
FORTRAN Notation
XK
A
P
V
F
AL
TI
TEND
S
XL
1-10
Note the card columns used for the data cards are indicated in
the table containing the tidal constituents.
APPENDIX VII
Hourly Heights Prediction Using IBM 1410 Computer
OSTJ Marine Science Center, 1964
Time Meridian: 1200 W
Height datum is MLLW
Hour
0
1
2
3
4
5
6
7
8
9
10
11
Noon
13
14
15
16
17
18
19
20
21
22
23
8
9
10
5. 2
3. 8
6. 2
4. 6
7.4
2.5
1.8
1.8
2.9
1.5
0.7
0.8
1.8
3.2
2.5
3.5
4.7
5.8
6.5
6.5
5.9
4. 7
3. 3
4. 8
1. 1
1.9
1.2
1.3
2.3
4.7
1.9
1.0
1.8
3.1
4. 7
6. 3
7. 4
7.8
7. 4
6.1
6.9
6.9
6.1
3.2
3. 9
5. 6
7. 2
8.2
8. 3
5. 8
3.8
1.8
0.3
-0.4
0.0
1.3
3.0
4.8
6.4
7.2
7.1
6. 2
4.8
3.2
1.9
1.3
1.7
3. 0
4. 8
6. 6
8. 1
8. 8
May
11
12
13
14
8. 5
7. 2
9. 2
8. 5
9. 1
9. 2
8.4
Feet
5.2
2.9
0.7
-0.8
-1.2
-0.6
1. 0
3.0
5.0
6.6
7.4
7. 2
6.2
4. 7
3.1
2.0
1.6
2. 3
3. 8
5. 7
7. 5
8. 8
6.8
4.5
2.0
-0.2
-1.6
-1.8
-0.8
1.0
3.1
5.2
6.8
7. 4
7.1
6. 1
4.6
3.1
2.2
8.2
6.3
3.8
1.2
-0.9
-2.0
-2. 0
-0.8
-2. 1
1.1
-1.8
-0.5
6. 8
5. 4
3.3
5.4
7.3
7.0
5.9
4.5
3.2
2. 1
3. 0
4. 6
2. 5
2. 6
3. 6
8. 1
6. 9
6.4
9. 1
8.9
7.7
5.7
3.2
0.7
-1.1
5.2
1.4
3.5
6.7
7. 1
6.7
5.7
4.5
3. 4
2. 8
3. 1
4. 1
5. 6
APPENDIX VII Continued
I
Hour
0
1
2
3
4
5
6
7
8
9
10
11
Noon
13
14
15
16
17
18
19
20
21
22
23
J
7. 1
8. 3
8.8
8.4
7. 1
5. 1
16
17
5. 7
7. 0
4. 4
5. 4
7. 8
6. 6
7. 6
7. 2
7.9
8.3
1.7
3.6
5.4
4.7
2.7
0.7
-0.7
-1.3
-0.8
0.4
2.0
3.8
6.9
6.5
6.4
6.7
2.8
0.6
6.5
7.3
6.1
May
18
19
20
21
3. 5
4. 1
3. 3
3. 2
3. 7
2. 9
4. 6
3. 2
5. 1
5. 8
3. 5
2. 2
2. 9
Feet
4.9
5.8
6. 5
6. 9
6.6
5.8
4.5
3.0
1.5
0.4
0.0
0.3
3.6
4.2
6.3
6.2
5.7
2.6
2.9
4. 4
1.3
0.9
0.5
0.8
5.3
5.9
6.0
5.7
4.8
3.6
2.3
1.3
1.0
5.4
6.4
4.1
5.5
3.0
4.4
2.2
3.5
3.6
3.2
5.7
4.7
3.8
6.5
5.8
4.9
6.9
6.7
6.0
6.8
7.1
6.9
6.3
7.2
7.4
4.4
3.6
3.5
4.0
4.9
-1.1
-1.8
-1.4
-0.1
6. 5
5. 6
4.5
3. 4
5. 3
6. 4
3. 4
4.6
2.8
1.1
-0.2
-0.6
-0.3
0.8
2.3
3. 9
6. 7
4. 0
2. 6
6. 5
5. 0
4.6
3.3
2.0
1. 7
5. 8
6. 0
1. 3
4. 9
7. 0
5.9
2.3
1.9
3.9
4.9
5.7
6.0
5.8
5.0
3.8
2.6
1.7
1.4
1.8
2.7
4. 1
5.6
6.8
7.6
7. 6
6.9
71
APPENDIX VII Continued
May
22
Hour
23
24
25
26
27
28
Feet
0
5. 6
6. 5
7. 3
7. 8
4.0
8. 1
4.9
8. 0
7. 7
1
5.9
6.7
7.4
2
7.8
2. 5
7.9
3. 2
4. 1
5. 0
6. 0
3
1.5
1.2
1.6
6. 7
1.6
0.7
0.6
1.2
2.3
7. 2
2.2
0.7
0.1
0.2
3.1
1.2
5.0
0.0
-0.4
0. 1
3. 7
1.3
5.0
5.9
6.3
2.4
4.0
5.4
6.2
2.8
4.4
5.7
-0.2
-0.8
-0.4
0.8
2.3
4.0
5.9
4.1
2.2
0.5
1. 1
4.1
2.1
0.4
-0.5
-0.5
0.3
1.7
3.4
4.9
4
5
6
7
8
9
10
11
2.4
3.6
4.9
5.8
6.1
5.9
3.1
1.2
-0. 5
-0. 7
0.0
1.4
2.9
Noon
5. 0
5. 9
6. 3
6. 4
6. 0
13
5. 4
3. 9
5. 0
5. 9
6. 3
6. 4
14
6. 2
5. 7
2. 7
3. 8
4. 9
5. 7
6. 2
15
16
17
1.9
2.7
6. 4
3.7
6. 3
4.7
6.2
2. 1
2. 8
3. 6
2.3
2.2
2.4
5. 1
5. 7
2.8
5.4
4.4
3.5
6.0
1. 8
18
4.2
4.9
3. 4
3. 0
2. 7
2. 7
3. 0
3. 4
4. 0
4. 5
19
4. 8
4. 2
3. 7
3. 3
3. 1
20
3. 2
3. 5
6. 3
5. 6
5. 0
4. 4
4. 0
3. 6
21
3. 5
7. 4
7. 0
6. 4
5. 8
22
23
5. 2
4. 6
4. 2
7. 9
7. 9
7. 6
7. 0
6. 5
5. 8
5. 2
7. 6
8. 0
8. 1
7. 9
7. 5
7. 0
6. 4
72
APPENDIX VII Continued
May
29
30
Hour
June
I
31
J
1
2
3
4
5
3.6
3.2
3.4
Feet
0
7.3
6.6
5.9
5.1
4.2
1
7. 7
7. 3
6. 7
5. 9
4. 9
3. 8
7.5
2. 9
2. 4
2
7.5
7.1
6.5
5.6
4.5
3.2
2.0
3
6. 6
7. 0
7. 1
6. 8
6. 2
5. 2
3. 8
2. 3
4
5. 1
5. 9
6. 5
6. 7
6. 4
5. 7
4. 6
3.3
1.5
0.1
-0.6
-0.4
3. 0
5
5.3
3.7
2.2
0.8
0.0
6.2
5.5
6.0
5.9
5.3
4.3
3.2
5.3
5.7
5.8
5.3
4.5
3.4
2.3
1.4
3.9
4.9
5.6
5.8
5.5
4.8
3.7
2.6
10
0. 6
11
Noon
2.0
3.5
4.3
2.6
1.0
-0.1
-0.4
0.0
1.2
2.6
13
4. 9
4. 0
3. 1
14
15
16
17
18
19
5.8
6.2
5.2
5.9
4.4
5.4
5.9
4.7
3.3
1.9
0.8
0.2
0.3
1.0
2.2
3.5
4.7
6. 0
6. 1
6. 0
5.4
5.8
6.0
4. 6
5. 2
4. 0
20
21
22
23
6
7
8
9
-0. 1
0.5
1.7
4.4
3.2
1.9
0.9
0.5
0.7
1.5
2.7
2. 0
1.2
0.8
1. 1
1. 1
1. 7
4.0
2.0
3.2
1.4
2.4
1.4
1.8
5. 7
5. 1
4. 5
3. 7
2. 9
6.1
6.0
5.6
5.1
4.3
5. 7
6. 1
6. 4
6. 4
6. 2
5. 7
4. 5
5. 1
5. 7
6. 2
6. 7
7. 0
6. 9
3. 6
4. 0
4. 5
5. 1
5. 7
6. 5
7. 2
7. 6
3.9
4.6
3.8
4.2
4.0
3.9
4.4
4.0
5.0
4.3
5.8
4.9
6.7
5.8
7.6
6.9
5. 7
5. 0
4. 3
3. 9
3. 7
4. 0
4. 6
5. 6
APPENDIX VIII
Tide Curves 8 May to 5 June, 1964
Time in Hours
C
CD
rt
I-i.
-
CD
CD
-z
lime in hours
APPENDIX VIII Continued
10
CD
I.-.
cJq
CD
CD
Cl.
L'J
-z
-4
Time in hours
APPENDIX VIII Continued
10
CD
I-'.
I-a.
CD
CD
-2
-4
Time in hours
-4
0'
APPENDIX VIII Continued
10
CD
I-"
CD
CD
-z
-4
Time in hours
-J
-1
CD
I-..
y
-2
CD
CD
-2
0,
8
A
TTTT F
--
6
4
2
0
CD
-2
I-.
CD
CD
6
4
2
0
-z
-J
'0
8
A flflflwt...,-
6
4
2
0
CD
I-..
h
8
CD
CD
rt
6
4
2
0
Time in hours
APPENDIX VIII Continued
(D
I-.
Gq
(D
CD
Time in hours
I-
8
APPENDIX VIII Continued
6
4
2
0
CD
I-"
CD
4
Time in hours
CD
cjq
-z
CD
q
I-..
CD
CD
8
-2
-z
c-p.
-
I-i.
CD
CD
c-f
-2
Time in hours
8
APPENDIX VIII Continued
6
4
z
0
CD
I-"
I-..
CD
CD
6
4
a
0
Time in hours
3
June
APPENDIX VIII Continued
CD
CD
CD
Time in hours
APPENDIX IX
Daily Precipitation
Newport, Oregon, 1964
Date
May
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
June
22
23
24
25
26
27
28
29
30
31
1
2
3
4
5
Precipitation
inches
0.26
trace
0.00
0.07
0.16
0.00
0.04
0.02
trace
0.00
0.04
0.11
0.07
0.00
0.00
trace
0.00
0.00
trace
0.48
0.12
trace
0.00
0.02
0.00
0.00
0.00
0.00
0.00
trace
trace
0. 07
0.02
0.00
0.39
0.08
(U. S. Weather Bureau, 1964)
APPENDIX IX Continued
Barometric Pressure
Inches of Mercury
Date
May, 1964
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
June, 1964
1
2
3
4
5
0000
0400
0800
1200
1600
2000
30. 15
30. 23
30.20
30. 25
30. 26
30.26
30.25
30.30
30.20
29.98
missed
30. 25
30. 26
30. 28
30. 20
30. 14
30.24
30.30
30.07
30. 00
30. 12
30.40
30.02
30.26
30.24
29.99
30. 26
30. 05
30. 10
30. 05
29. 79
29. 98
30. 14
30. 05
30. 00
30. 10
30. 10
30. 03
29. 78
29. 99
30. 13
30. 05
30. 00
30. 12
30. 10
30. 00
29. 78
30. 14
30. 11
30. 06
30. 04
30. 12
30. 10
29. 93
29. 82
30. 15
30. 11
30. 06
30. 12
30. 12
30. 06
30. 00
30. 08
30. 04
30. 08
30. 12
30. 00
30.00
30. 17
30. 08
29. 94
30. 15
30. 18
30. 08
29. 92
30. 12
30. 04
30. 18
30. 18
29. 82
30. 02
30. 15
30. 18
30. 08
29. 94
29. 90
30. 00
29. 89
30. 02
29. 80
29. 82
30.23
30.20
29. 90
29. 96
missed
29.94
29.91
30.30
30.22
29. 89
29.85
29.88
30.00
30. 12
30. 11
29.88
29. 84
30. 16
30. 11
30. 00
30. 15
30.31
30.05
30. 15
30. 10
29.83
29. 90
30. 16
30.08
30. 00
30.23
30. 09
29. 85
30. 03
30. 18
30. 13
30. 06
30. 00
30. 09
29. 98
30. 18
30. 02
29. 90
30. 03
30. 17
30. 10
29. 98
29. 95
30.24
30.21
29. 90
30. 00
30. 00
30. 00
30. 00
30. 01
29. 99
29. 96
29. 85
29. 90
29. 92
29. 94
30.31
29.88
29.92
30.30
30.20
29.86
29.92
30. 10
30. 04
30. 24
30. 02
29. 95
30. 10
30. 18
30. 16
29. 98
29. 94
29.84 missed
29.88
29.90
91
APPENDIX IX Continued
Wind Direction and Force
(Force is in Beaufort Scale)
Date
May, 1964
8
9
10
ii
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
June, 1964
1
2
3
4
5
0000
0400
0800
1200
1600
2000
NWZ
NW1
SW2
SW4
NWZ
SW6
NW1
SWZ
SW4
NW2
SW6
NW1
SWZ
SW2
NW3
W3
calm
NW3
NW5
NWZ
NW3
SW5
NWZ
N3
SW7
SW3
NW3
NWZ
NWZ
NW3
SW5
SW6
NW2
N3
SW7
SW3
NW3
NWZ
calm
calm
calm
calm
calm
NE3
NE3
calm
NW3
calm
calm
SW1
calm
EZ
calm
NW6
calm
calm
NZ
SWS
NW4
NW1
calm
calm
calm
SW3
missed
calm
calm
calm
calm
SW6
SE2
SE1
calm
calm
5W6
calm
NW4
SW4
SW1
NW5
NW5
SW5
SW5
NW3
NWZ
SW7
NW3
NW3
NW5
N2
SW3
N2
calm
calm
NNW6
NW5
SW4
SW3
SW3
NW5
NW3
NW1
SW7
SW6
SWS
SW5
SW3
SW5
SW4
SW3
NNW5
NW2
SWZ
SW3
Ni
NW2
SW4
calm
SW1
calm
NNW5
NW2
SWZ
Ni
calm
calm
missed
calm
NW4
NW5
NW3
SW4
NW1
NW1
SW7
NW3
NW4
NW4
NNW6
NW5
SW6
SW3
SW3
N5
NW2
calm
SW3
NW1
SW1
NW4
calm
W2
NW2
NW6
SW4
calm
calm
W2
NWZ
NWZ
NW2
NW3
NW3
SW5
SW2
NE3
N5
NW1
calm
SW4
SE3
missed
calm
SW1
92
APPENDIX X
Sea Level Data
Crescent City, California
Year
1933
1934
1935
1936
1937
1938
1939
1940
1941
1942
1943
1944
1945
1946
1947
1948
1949
1950
1951
1952
1953
1954
1955
1956
1957
1958
1959
1960
May
ft.
June
Mean for Year
7. 08
7. 37
7. 09
7. 19
7. 20
7. 16
7. 51
7.33
7. 19
7. 08
7. 18
7. 50
ft.
7.49
7.19
7.48
7. 14
7. 28
7.30
7.60
7.34
6.97
7.31
7.35
7. 38
7. 33
6.98
7.37
7. 34
7.26
7. 19
6.85
7. 38
7. 48
7. 30
7. 01
7. 16
7.35
7. 13
7.38
7.28
missing
missing
7. 16
7. 29
7. 33
ft.
7. 46
7.49
7.46
7.49
7.37
7.65
7.80
7.48
7.51
7.48
7.46
7. 51
7.47
7.20
7.52
7.44
7.60
7.28
7. 53
7. 33
7. 12
7. 15
7. 27
7. 19
7. 40
7. 11
7. 22
7. 62
7.42
7.32
7. 37
7. 51
7. 65
7.40
7.41
(Union Godsique et Gophysique
Internationale, 1959, 1963)
93
APPENDIX X Continued
Sea Level Data
Neah Bay, Washington
Year
1935
1936
1937
1938
1939
1940
1941
1942
1943
1944
1945
1946
1947
1948
1949
1950
1951
1952
1953
1954
1955
1956
1957
1958
1959
1960
Mean for Year
May
ft.
June
ft.
.6. 01
6. 18
6. 58
6. 12
6. 01
6. 30
6. 18
6. 25
6. 47
6. 72
6. 79
6. 60
6. 49
6.51
6.40
6.00
6. 24
6. 38
6. 59
6.46
6. 04
6.17
6.50
6. 18
6.13
6. 67
6.40
5. 96
missing
6. 09
6.49
6. 12
5.87
6. 15
6.47
6. 22
6. 17
6.52
6.71
6.5].
5.91
6.14
6. 08
6.41
6.42
6. 36
6. 15
6. 21
6. 15
6. 17
6. 44
5,94
6. 30
6. 15
6. 41
6. 28
5.98
ft.
6.49
6.60
6.46
6.46
6. 51
6.51
6.48
6. 59
6.45
6. 63
6. 56
6.62
6. 64
6.34
6.40
missing
6. 70
missing
6.45
(Union Godsique et Gophysique
internationale, 1959. 1963)
94
APPENDIX XI
High and Low Tides for Newport
Predicted from the Tide Table
High
Time
Low
ft.
Time
hrs. mm.
Ht.
ft.
0.7
Ht.
Date
May
hrs. mm.
8
0921
2152
6.5
7.7
0333
1526
1021
2226
6.6
0421
1608
0.5
1117
2301
6.7
0506
1651
-0.3
1213
2339
6.8
0551
1733
1.O
1. 6
1308
6.8
0637
1817
-1.4
0725
1904
-1.7
2.4
0815
1955
-1.7
0908
2053
-1.5
-1. 1
9
10
11
12
8. 1
8. 5
8. 7
1.3
1. 0
1. 2
2.0
0019
1404
8.8
0102
1503
8.7
0147
1605
8,4
0240
7.9
1711
6. 5
1004
2203
0340
1816
7.4
6.6
1105
2326
-0.7
18
0452
1915
6.9
6.8
1206
-0.3
19
0613
2006
6.4
0053
1306
2.7
13
14
15
16
17
6. 7
6. 6
6. 5
7. 0
2. 7
3. 0
3. 1
3. 1
0. 2
95
APPENDIX XI Continued
Low
High
Time
Ht.
Time
hrs. mm.
Ht.
ft.
Date
hrs. mm.
20
0738
2049
6. 1
0210
2. 1
7. 3
1401
0. 6
21
0853
2126
6.0
7.5
0312
1451
1.5
1.0
22
0958
2159
6. 0
0403
1535
0. 9
23
1055
6. 1
2229
7.8
0446
1615
0.3
1.8
24
1145
2258
6. 1
0525
1653
-0. 1
25
1230
2327
6.2
7.8
0600
-0.5
2.4
26
131.3
6. 1
2355
7. 8
27
1355
6. 1
28
0024
1437
7. 7
0054
7. 6
May
ft.
7.7
7.8
6. 1
1728
1.4
2.2
0635
1802
-0. 7
0709
1836
-0. 7
0743
1910
-0. 7
-0.6
3.3
2. 7
2.9
3.2
1521
6.0
0819
1947
30
0129
1607
7 4
6.0
0859
2031
-0. 5
31
0208
1655
7. 2
0941
2126
-0. 3
29
6.0
3.4
3.4
96
APPENDIX XI Continued
Time
Low
Ht.
ft.
Time
Ht.
ft.
hrs. mm.
0257
1742
6. 9
1026
2234
-0. 1
2
0354
1827
6. 6
6.4
1114
2353
0.2
3
0506
6.
1204
0.4
1909
6.
0627
1949
5. 9
7. 2
0110
1254
2.4
0748
2027
5. 8
7. 7
0215
1345
1.6
Date
June
1
5
hrs. mLi.
6.1
a
3. 3
3. 0
7
0. 7
1. 1
97
APPENDIX XII
Bay
High and Low Tides for Humboldt
Tables
as Recorded in the Tide
Time Meridian 120° W.
Height Datum is MLLW
Highs
Time
hrs. mm.
Date
Lows
Time
hrs. mm.
Ht.
ft.
Ht.
ft.
1.2
May 8
0908
2139
4.9
6.1
0321
1514
9
1008
2213
5.0
6.5
0409
1556
10
1104
2248
5. 1
6.9
0454
1639
11
1200
2326
5. 2
0539
7. 1
1721
12
1255
5.2
0625
1805
13
0006
7.2
5.1
0713
1852
-1.8
2.3
14
0049
1450
7.1
5.0
0803
1943
-1.8
2.6
15
0134
1552
6.8
4.9
0856
2041
-1.6
2.9
16
0227
1658
6.3
4.9
0952
2151
-1.2
3.0
17
0327
1803
5. 8
-0. 8
5.0
1053
2314
3.0
18
0439
1902
5.3
5.2
1154
-0.4
1351
0.6
0.4
0.9
-0.4
1. 1
-1. 1
1. 5
-1.5
1.9
APPENDIX XII Continued
Lows
Time
hrs. mm.
Highs
Time
Ht.
Date
hTs. mm.
ft.
May 19
0600
1953
4. 8
20
0725
2036
4.5
21
0840
2113
22
Ht.
ft.
0041
1254
2. 6
0158
1349
2.0
4.4
5.9
0300
1439
1.4
0.9
0945
2146
4.4
6.1
0351
1523
0.8
1.3
1042
2216
4. 5
0434
0. 2
23
6.2
1603
1.7
24
1132
2245
4.5
-0.2
6. 2
0513
1641
25
1217
2314
4.6
6.2
0548
1716
-0.6
2.3
26
1300
2342
4. 5
0623
1750
-0. 8
27
1342
4. 5
0657
1824
-0.8
2.8
28
0011
1424
6.1
0731
1858
-0.8
29
0041
1508
6.0
0807
1935
-0.7
3.2
30
0116
1554
5.8
4.4
0847
2019
-0.6
3.3
31
0155
1642
5.6
4.4
0929
2114
-0.4
3.3
5.4
5. 7
6.2
4. 5
4.4
0. 1
0. 5
2. 1
2.6
3. 1
APPENDIX XII Continued
Highs
Ht.
Time
hrs. mm. ft.
Date
June
1
0244
1729
Time
Lows
hrs. mm.
Ht.
ft.
-0.2
5. 3
1014
2222
5. 0
4,8
1102
2341
2.9
4.5
3.2
0. 1
a
0341
1814
3
0453
1856
4. 6
1152
0.3
0614
4.3
0058
1242
2.
0.
1936
0735
2014
5. 1
5.
6
4. 2
6. 1
0203
1333
3
6
1.5
1. 0
(U. S. Coast and Geodetic Survey,
1964)