ot Columbia Gniversity
in the Cityol PewPork

Hudson Laboratories
“ Dobbs Ferry, N.Y.

TECHNICAL REPORT No. 90

Temperature Measurements
In the Ocean Near Eleuthera

by T. Arase

Se

° \b

Contract N6-ONR-27135

TO

SyGQ)

Asc?

CU-112-50-ONR-271-Phys.

Columbia University
Hudson Laboratories
Dobbs Ferry, N.Y.

R. A. Frosch
Director

Technical Report No. 90

TEMPERATURE MEASUREMENTS IN THE OCEAN NEAR ELEUTHERA

by
T. Arase

September 15, 1960

This report consists Copy No. foes
of 21 pages. of 100 copies.

This work was supported by the Office of Naval Research,
under Contract N6-ONR-27135.

Reproduction in whole or
in part is permitted for any purpose of the United States
government,

ABSTRACT

Temperature records have been obtained at depths
of 130, 150, 170, 190, and 250 ft from five buoys in-
itially separated from one ancther by six miles. Each
record had a duration of about one day and records for
three successive days were taken. These records have heen
analyzed for autocorrelation and power spectrum. The
power spectrum for a typical record is (180 £°)geg?/eph
in the frequency range from 0.5 to 12 cph. No lines were
observed in the spectrum, showing that the temperature re-
cord cannot be synthesized by a linear combination of

a few simple harmonic waves.

INTRODUCTION

This report descvzibes the results of the second of a series of
experiments v.hich are being conducted with the tvofold aim of obtaining
extended temperature measurements in the ocean and of diveloping reli-
able equipment for such measuvements. Temperature measuvements are
impovtant in understanding such features of near-su~face ocean behavior
as internal waves or surface sound channel propagation,

Early experinents have quite often led to the conclusion that
the observed temperatuve fluctuations could be described as a simple
harmonic wave o~ as a combination of a few such waves Usually these
analyses have been pe-formed on data of inadequate duration o~ with im-
propevly designed instvuments.

More recent experiments, of adequate time duration, show markedly
different zesults. The first, Operation STANDSTILL, utilizing BT's taken
every half-hour for 25 days from an anchoved ship, finds peaks at periods
of one and five days in the power grrecine 2 The second, utilizing data
taken by thermistors placed on the ocean bottom near Bermuda, for many
months, finds a spect7um which decveases monotonically with frequency as

-3 3 . a s Sle
ft as vell as evidence for the existence of a peak at the principal

lunar tide and a peak at O 5 cycles per none. 8

The experiment described here is for data of one day's duration
taken at two-minute intervals and hence yields information on the power
spectra of the temperature fluctuations to a higher» frequency range than

given in the references cited in Footnotes 1 and 2.

2 Brown, Corton. and Simpson, Power Spectrum Analysis of Internal Waves
f-om Operation STANDSTILL (U. S. Navy Hyd-ographic Office, 1955),

Technical Report TR-26

Hauzwitz, Storimel, and Munk, On the thermal unrest in the ocean. In
Rossby Memorial Volume (Rockefelle> Institute P~ess, New York, 1959).

THE EXPERIMENT

The experiment was conducted from the R/V GERDA during the period
August 11 to 14, 1957, approximately 15 miles off the coast of Eleuthera
Island, BWI. Figures 1 (a-c) show the tracks of the five buoys which sup-
ported the thermometers. Each buoy consisted of a spar buoy from which
were suspended four thermometer units and one temperature-pressure unit.
Figure 2 illustrates the geometry employed.

Each thermometer unit consisted of an open-aperture camera which
photographed a mercury-in-glass thermometer illuminated at approximately
two-minute intervals. The motive power for the film drive as well as the
timing of the illumination was supplied by a 24-hour clock. Standard ther-
mometers calibrated to 0.1°C were enclosed in a well to protect them from
hydrostatic pressure. Good thermal contact between the thermometer and the
well was secured by filling the well with water. The time constant for the
complete unit was of the order of 1 to 2 minutes.

On the first morning, the five buoys were launched six miles apart
and allowed to drift. The next morning, the thermometer units were retrieved
and replaced with another set of thermometer units and similarly on the
third day. Hence the final result is a set of one-day thermometer records
from five buoys at four depths. Due to various difficulties with the appa-
ratus, usable data was obtained from only 36 of the 60 units launched. Of
these, 29 records were processed for autocorrelation and power spectrum

analysis.
RESULTS

A. Temperature Records

The temperature records are typically fairly irregular functions of
time with some short sections being oscillatory, with a vague hint of a daily
or semidaily period, and with root-mean-square fluctuations in the order of

0.3°C. No obvious correlations of the temperature fluctuations exist with

itn
til
H

OPERATION 6l
RUN |

FROM 1130 6/10/57
TO 1007 4/II/57

0947 8/il
0350
2300

BUOY I 4/47

ELEUTHERA
ISLAND

PALMETTO PT.

Figure la

76°
OPERATION 6I 1
RUN 2

1015 6/12 +
HOO 6/2
FROM 0947 °/\i/57
TO 124€ 38/12/57 2400
KAS 8/12
25° 30
+ —_______—__1_1 4 1
127
6/1 1
BUOY II
2332 ]
2137 1
1248 |

BUOY Iv T

ELEUTHERA ere
ISLAND

PALMETTO PT.

76°

OPERATION 6l

RUN 3
0835 a/13
23408 0922 6/13
’ 2320
2035
2045
x\ 005 (IY)
BUOY TI af ioist/ }'*29
00 6/I2

2247% BUOY II

2122
Nee Ww

45 8/12
na

FROM ©0900 8/12/37
TO 10 8/13/57

110 8/i3
2205

BUOY Y
1248 6/I2

ELEUTHERA
\. 1SLAND

PALMETTO POINT

25° 30

GEOMETRY OF
THERMOMETER UNITS

SPAR BUOY
w/ LIGHT AND
RADAR REFLECTOR

I30' THERMOMETER UNIT

I50' THERMOMETER UNIT

170' THERMOMETER UNIT

1I90' THERMOMETER UNIT

250' THERMOMETER
PRESSURE UNIT

WEIGHT

Figure 2

~(R —

regard to either local tides or times though one might expect to find them
present. However the presence of these effects may be determined only by
records of much greater time duration. We shall separate the discussions
of the temperature records by classifying them as to day, buoy, and depth
at which taken. Table I gives the figures illustrating the three temper-

ature record categories

TABLE I
DAY BUOY DEPTH
Fig. 3 same same different
Fig. 4 same different same
Fig. 5 different same same

Records taken on the same day at various depths at the same buoy
(see Fig. 3) generally have the same characteristics, that is, if the
temperature increases at one depth, it increases at all depths. The magni-
tude of the temperature change is different for the different depths, being
greatest for the unit at the depth where BT's indicated a large change in
temperature with depth.

Records taken on the same day at different buoys, and at the same
depth are illustrated in Fig. 4. We note that there are no obvious corre-
lations between these records. From Fig. 1(a), we see that the tracks of the
buoys range from northerly to northwesterly with slightly differing speeds.

Table II gives the spacing of the buoys at various times after launching.

TABLE II

Spacing of buoys in miles at various times during the first day's vun

TIME
BUOY At launching 2000 2400 0400
- 6 5-3/4 5-1/2 6
2 12 11 10-1/4 8-3/4
: 6 7 7-1/4 7-1/2
5

The mean temperature observed at each unit during four-hour periods

is given in Table III.

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pKa euHOe Tis ides tere

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Vite a es ee rE BA ae CRSs2 UU eT I eM

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Kt MEG) Rid Re RE EERE Sl wait
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NEE = . i i
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0 > ne | ti Ee
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7 i
Mikron usteras? poieyh. LPH ih PR Re) Cen My ik. Beh

; hee eS ea a ee

LOW HIGH LOW HIGH LOW
TIDE TIDE TIDE TIDE TIDE

1357 2006 0224 0830 1435

SUNSET

BE?

28°

TEMPERATURE (C°)

26°

Figure 3. Temperature records for the first day, Buoy 5, at various depths.

HIGH LOW HIGH LOW HIGH
TIDE TIDE TIDE TIDE TIDE

0830 1435 2046 0257 0906

28° cooo BUOY |
cx00 BUOY 4

aire

a
anh So

a aa atch

TEMPERATURE (C°)

26°

Figure 4, Temperature records for the second day, Buoys 1 and 4, at 170 ft.

HIGH LOW HIGH LOW HIGH
TIDE TIDE TIDE TIDE TIDE
0906 151 2115 0329 0940

29° SUNSET THIRD RUN SUNRISE
= 8-12 8-13
iS}
W °
Wi 28
=)
—
Ps
°o
Ms BY
a
=
uJ
F 26° THIRD RUN
SECOND RUN
1435 2046 0257 0906
LOW HIGH LOW HIGH
TIDE TIDE TIDE TIDE
8 - Il SECOND RUN

Figure 5. Temperature records for second and third runs, Buoy 1, at 170 ft.

mwa

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TABLE III

Four-hour average temperatures in °C observed at 150-ft depth
at various times during the first day's run

TIME
BUOY 2000 2400 0400
1 27.7 PAS U 27.75
2 28.25 28.0 28.2
4 27.75 27.75 27.95
) 27.6 27.65 28.25

Comparing the entries in this table, we see that the greatest
average temperature difference for a given separation is that between
Buoys 1 and 2 at 2000 hr, of magnitude 0.1°C per mile. This difference
is small in comparison to the difference in average temperature at dif-
ferent depths at the same buoy on this day, which averaged 0.1°C for
5 ft. Thus, there is a factor of about 1000 in the ratio of horizontal
to vertical average temperature differences. Part of this ratio can be
accounted for if the depths of these units differed by several feet. This
may have been due to differential stretchage, tangling, or slippage of the
suspension points on the Manila rope to which all the units were connected.
However, every effort had been made prior to the launching to make the
buoys identical in construction.

Records obtained on successive days at the same buoy and depth are
illustrated in Fig. 5. Note that they appear to share the same general char-
acter. These records will be further analyzed and illustrated in the next

section.

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B. Correlation and Spectrum Analysis
Autocorrelation and power spectrum computations were carried out

on all records according to the methods of Tukey, ‘>

who gives formulae
for the digital computation of these quantities for data obtained at equal
time intervals. The formulae are summarized below.

Let the N+l numbers

A OSS aL

be the time series taken at time intervals At , with zero mean. The
quantity corresponding to the autocorrelation function is the mean lagged

product

C == X X E-On Ane Siegen

The raw spectral density estimate is formed by

m-1]
agli SLs
Ve = ne(c, + 2 2 oe cos a + Ch cos | _

which is the estimate of the two-sided spectral density at the frequency

ie = (r/2mAt) Peaw Ok Mee 2ee 2 em

This process of obtaining spectral density estimates is analogous to ob-
taining the power spectrum of electrical signals by determining the strength
of the signal transmitted by various bandpass filters. Just as these filters
respond to components of the signal whose frequencies lie outside the main
passband and at a side lobe, so the raw spectral density estimate gives an
erroneous reading for signals at the side lobes of the effective passband for
this computation. Several procedures are available for reducing this error
by reducing the amplitude of the side lobe response. We have used the pro-

cedure known as hanning, which reduces the maximum side lobe response to

3 R. B. Blackman and J. W. Tukey, The Measurement of Power Spectra

(Dover Publications, New York, 1958).

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2 percent of the main passband. The result of applying the hanning pro-
cedure yields the refined spectral density estimates. Further details
are given in the reference cited in Footnote 4.

In this method of calculating the power spectrum, error may be
introduced by aliasing, which is serious because its presence cannot be
detected in the final result. Aliasing (also known as spectrum folding)

arises from the fact that the data is taken at discrete time intervals

At . The highest frequency at which spectral density estimates can be
made is the Nyquist frequency fy = (at)! If appreciable power is
present at frequencies greater than f, , they will appear at the fre-

N
quencies

For example, Fig. 6 shows how the aliased spectrum of the form faa will

appear. Hence, in the design of the experiment, one must insure that the
upper frequency cutoff of the measuring instruments is less than fy
Alternately, the data may be lowpass filtered by digital computation before
the spectrum analysis is performed. An example of aliasing is shown in the
experimental data taken by BI's in Fig. 9, discussed later.

Some typical results of the autocorrelation computation are given
in Fig. 7. For zero delay, the value of the autocorrelation is the vari-
ance of the record. For the three records shown, this varies by a factor
of four, which is typical of the range of values obtained for all the units.
The autocorrelation decreases with delay time at differing rates, reaching
zero most quickly fo: the second day while remaining large for the third
day. It is tempting to interpret the autocorrelation in terms of the re-
sults for known functions. For example, if the time series were composed
of a set of random numbers, then the autocorrelation should be a delta

function. Again, if the time series were a cosine function,then the auto-

4 T. Arase, A Guide to the Usage of Power Spectrum Calculations According

to the Methods of Tukey (Columbia University, Hudson Laboratories, 1960),
Technical Memorandum-to-File No. 47.

siilke

EFFECT OF SPECTRUM FOLDING

ORIGINAL SPECTRUM, f 2

SPECTRUM AFTER FOLDING
ABOUT f=/7

FREQ

Figure 6

10
Sie
oO
©
WW
a
05
) (3
(e) 1.0 25
DELAY TIME (HR)
Figure 7.

The temperature records of mean
lagged products for three successive days,
Buoy 2, at a depth of 150 ft.

ola

wot

correlation should also be a cosine function. Hence, one might conjecture
that the oscillatory portion represented by the autocorrelation for the
second day is indeed due to a periodic component in the time series. Simi-
larly, the time in which the autocorrelation decreases to some small
number is a measure of the correlation time for the phenomena beyond which
the time series is uncorrelated. However, a study of the time series does
not appear to support these conjectures. In no case can one point out the
differences in the time series which would account for the differences in
their autocorrelations. It is not a function which one can compute mentally.
Suffice it to say that it is useful as an intermediate step in the computa-
tion of the power spectrum, except for certain exceptional cases.

The power spectra corresponding to the autocorrelations previously
discussed are given in Fig. 8. The very interesting result is obtained
that the power spectra all have the same form within the error associated
with the results. There are slight differences but these reflect large
differences in the autocorrelation. For example, at 0 frequency the auto-
correlation which decreased slowest has the highest value, exceeding by an
order of magnitude the results of the other two. Again, the autocorrelation
with one oscillatory cycle shows peaks in its spectrum. These peaks, however,
are within the errors to be associated with the computation (shown as the
error bar) and hence must be ignored. The overwhelming similarity is in the
form of the power spectra, for, excluding the data obtained at frequencies
less than 1 cycle per hour as reflecting errors due to the finite sample
time, and cxcluding the data at the highest frequency as perhaps being in-
Sake by the response time of the thermometers, the power spectra follow
the f

at the same buoy and at the same time; it applies also to data obtained at

law as indicated. This is true for data obtained at various depths

the same depth at different buoys; and the data shown is data obtained at the
same depth, at the same buoy, and on successive days.

Power spectra representing the extremes of those calculated were
plotted with those of the bottomed thermistors at Bermda ‘=? (see Fig. 9).

The difference in slope between the thermistor data and the thermometer data

13

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°¢2/CPH FOR 50 METERS

-2
10 a
m
o
Ls
“~
oO
Uv
ac
10-5
SECOND DAY
ERROR IN SPEC -
TRUM ESTIMATES
(Ome
10-5
0 4 8 12
CYCLES / HOUR
Figure 8. Spectral density estimates for
the temperature records of three success-
ive days, Buoy 2, at 150 ft.
Onl) Gn
a
uJ
|
WwW
Ol =
{e)
°
wo
-3
10 5
we
ze
lo-4 6
~“
Nn
>
Og?

0 | 1.0 2.0
CYCLES PER HOUR

Figure 9. Comparison of power spectra of
temperature fluctuations obtained by ther-
mistors at Bermuda2 (dotted lines) and by
thermometer units at Eleuthera (solid
lines). The corresponding estimates of
error are given by the error bars.

Eyes

AND PRESENT DATA

— nll ill iad a 7 ey. Scshaeel

{ ‘ be 3 Me ;

= -
oe mes ls
5
, 7
s ‘ aintinrent
“
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i
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¢)
i Lfeel pe fv
ae
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¢ + a hk
i : it Sy
fy ; \
Wa Pus
2 fn it ea ene i

is evident even for this frequency range. What is more important is that
the orders of magnitude of the power spectra from these two experiments
are similar, The data of 50 m is puzzling because it is so much lower in
level than that of 500 m. This difference was explicitly pointed out in
Reference 2.

The power spectra of the temperature at 150-ft depth as obtained
by BT’s taken during the course of the three days, every half-hour, is
also plotted in this figure. Here again the order of magnitude and the
rate of falloff are similar to the data of 500 m. The rise at 1 cycle
per hour is due to aliasing, which shows that the BT responds to temper-
ature changes at a greater rate than it cought to for observations taken
at this slow rate.

A second important result shown in Fig. 8 is the absence of lines
of any sort in the power spectra. Essentially this means that this data
is not susceptible to interpretation as being composed of a si:ple har-
monic temperature wave or even as a combination of a few simple harmonic
waves. This is quite different from the results obtained by early experi-
menters who reported the frequency and wavelength of the simple harmonic
waves with which they reconstructed the experimental temperature record.
Perhaps the temperature records are analogous to sea surface records, which

are describable only by their power spectra and by statistical measures.

CONCLUSIONS

For the data obtained in this set of one-day observations, spread
over 24 miles horizontally and 120 ft vertically, the power spectra of the
temperature “hojimtinns have been found to obey the fe law in the fre-
quency range from 0.5 to 12 cycles per hour. No lines have been observed
in the spectra. These results differ from those of early experimenters.
However, they cannot be considered to be at varia:ce with the data reported
in the references cited in Footnotes 1 and 2 bocause the frequency range

covcred differs so widely.

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icin Tis

toatl ah

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Additional experiments are planned to extend the recording time
so that such a comparison can be made, An experiment has been completed
in the Bermuda area, but the longest record obtained of the temperature
was less than two days. A power spectra analysis of this data is in

progvess.

ACKNOWLEDGMENTS

Captain Kou Walter and the crew of the R/V GERDA weve of great
help in the conduct of this experiment, Tom Farrell designed the ther-
mometer units. Tom Kelly was responsible for the maintenance, launching,

and vecovery of the thermometer units.

“is

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copies 65-66

Commanding Officex and Director

U. S. Naval Underviater Ordnance Station

Newport, Rhode Island
copy 67

Director

Applied Physics Laboratory
University of Washington
Seattle, Washington

copy 68

Director

Ordnance Research Laboratory
Pennsylvania State University
University Park, Pennsylvania
via

Production Representative
Ordnance Research Laboratory
University Park, Pennsylvania
copy 69

Commanding Officer

Naval Air Development Unit

U. S. Naval Air Station

South Weymouth, Massachusetts
copies 70-71

Superintendent

U. S. Naval Post Graduate School
Monterey, California-

copies 72-73

Chief. Bureau of Naval Weapons (RUDC-252)
Navy Department

Washington 25, D. C,

copies 74-75

December 1960

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