Measurements of thermal structure off Southern California with the Nel thermistor chain

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RESEARCH REPORT 4
REPORT 1130
28 AUGUST 1962 0

OSLL jA0d9y/T A

MEASUREMENTS OF THERMAL STRUCTURE
OFF SOUTHERN CALIFORNIA
WITH THE NEL THERMISTOR CHAIN

E. C. LaFond and A. T. Moore

U.S. NAVY ELECTRONICS LABORATORY, SAN DIEGO, CALIFORNIA

A BUREAU OF SHIPS LABORATORY

art

THE PROBLEM

Investigate oceanographic factors pertinent to the behaviour of
underwater sound and to surface and subsurface navigation.
Specifically, study the thermal structure of the upper sea layers
by use of the towed thermistor chain.

RESULTS

1. The average slopes, autocorrelation, and power spectra of
the isotherms obtained with the NEL thermistor chain on the dif-
ferent "legs'' of a deep-water cruise show that many internal
waves are of very long period. The spectra appear to be continu-
ous at very low frequencies and to possess minor peaks at higher
frequencies (1/20 to 1/3 cycle per minute).

2. These studies further indicate a probable shoreward move-
ment of the dominant internal waves.

3. The records of circular tows with the chain establish that the
thermal structure is complex. Although the circular paths fol-
lowed were too small to clearly demonstrate significant motion in
any particular direction, the data obtained do reveal that wave
crests and troughs of a generally similar type were crossed in all
directions of tow.

RECOMMENDATIONS

1. Continue development of the thermistor chain to improve the
quality, accuracy, and reliability of the data.

2. Make detailed studies of the thermocline and its associated

internal waves by use of the chain. Include studies of the effects
on the thermocline of islands, shoals, coastal configurations,

We Onem A AHA

301

tides, currents, upwelling, river runoff, water mass boundaries,
storms, and seasons. Particularly, acquire more data on the
direction and speed of internal waves.

3. Procure electronic equipment to provide digital tape records
of temperature-depth or isotherm -depth data and still retain the
present analog recording system. Use the digital tape with avail-
able large-scale computers for detailed statistical analyses of the
isotherm data where applicable.

ADMINISTRATIVE INFORMATION

Work was performed under S-R004 03 01, Task 0580 (NEL
L4-4) (previously listed as Task 0539 (NEL L4-1)) by members of
the Marine Environment Division. This report covers the period
1 July 1961 to June 1962. It was approved for publication 28
August 1962. The authors wish to express appreciation to O. S.
Lee who led the cruise on which the data for this report were col-
lected and to G. H. Curl and EK. E. Gossard for reviewing this
report.

CONTENTS

INTRODUCTION ... page 7
EQUIPMENT... 7
OBSERVATIONS AND DATA ... 10
Offshore Section ... 10
Alongshore Section ... 12
Onshore Section... lo
Isotherms and Internal Waves ... 15
ISOTHERM DEPTH VARIABILITY... 18
Differences in Depth Values... 18
Autocorrelation of Depth Values... 24

Power Spectrum of Depth Values... 28

DIRECTION OF PROPAGATION OF INTERNAL WAVES...

SUMMARY AND CONCLUSIONS ... 41
REFERENCES ... 44

35

ILLUSTRATIONS

oNnoan Fe WO DY EF

10

id

12

13

14

15

16

17

18

Thermistor chain hoist on USS MARYSVILLE... page 8
Track of USS MARYSVILLE on cruise 2... 9

Isotherm data from leg one of cruise 2 (250-550 feet) ... 11
Isotherm data from leg two of cruise 2 (100-300 feet) ...13
Isotherm data from leg two of cruise 2 (400-600 feet) ...14
Isotherm data from leg three of cruise 2 (100-300 feet)... 16

Isotherm data from leg three of cruise 2 (450 and 650 feet)... 17

Frequency distribution of differences in depth between half-
minute or 304 ft spaced readings of 9°C isotherm, leg one,
GuUUISe Zooo BO

Frequency distribution of differences in depth between half-
minute or 304 ft spaced readings of 14°C and 9°C isotherm,
leg two, cruise2... 21

Frequency distribution of differences in depth between half-
minute or 304 ft spaced readings of 16°C and 9°C isotherm,
leg three, cruise 2... 22

Approximate slopes of isothermal surfaces measured in deep
and shallow water... 23

Autocorrelation computed from successive half-minute
interval readings of the depth of 9°C isotherm, leg one,
GQawigse Zsoo 29

Autocorrelation computed from successive half-minute
interval readings of the depth of 14°C isotherm, leg two,
cruise 2... 20

Autocorrelation computed from successive half-minute
interval readings of the depth of 9°C isotherm, leg two,
CiMUISS Aoon BS

Autocorrelation computed from successive half-minute
interval readings of the depth of 16°C isotherm, leg three,
GUMS Zoon BO

Autocorrelation computed from successive half-minute
interval readings of the depth of 9°C isotherm, leg three,
GUNS Boss Be

Power spectrum computed from successive half-minute
interval readings of depth of 9°C isotherm, leg one,

cruise 2... 30

Power spectrum computed from successive half-minute
interval readings of depth of 9°C isotherm, leg two,

CHongse Acco Bll

ILLUSTRATIONS (Continued)

19

20

21

22

23

24

25

26

Power spectrum computed from successive half-minute
interval readings of depth of 9°C isotherm, leg three,

cruise 2... 32

Power spectrum computed from successive half-minute
interval readings of depth of 14°C isotherm, leg two,

CmUNISE Booo BS

Power spectrum computed from successive half-minute
interval readings of depth of 16°C isotherm, leg three,
cruise 2... 34

Schematic of the relative motions of ship with chain (C)
moving at 6 knots and the dominant wave crests moving

at 1.5 knots... 37

Frequency factor of the relative direction of ship and internal
wave motion using the speed of 6 knots for ship and 1.5 knots
for waves... 38

Vertical temperature structure resulting from four circular
tows with the thermistor chain. The same depth intervals on
the four 2-mile-diameter tows are arranged together for
comparison ... 39

Vertical temperature structure resulting from two circular
tows with the thermistor chain. The same depth intervals on
the two 6-mile-diameter tows are arranged together for
comparison ... 40

Three-dimensional construction of the 9°C isothermal surface
based on two repeated 6-mile-diameter tows with the thermis-
tor chain (vertical scale equals about 200 times

horizontal) ...42

INTRODUCTION

The U.S. Navy Electronics Laboratory thermistor chain was
obtained in 1961.’ (See list of references at end of report. ) With
the new thermistor chain it has become possible to measure verti-
cal sections of the temperature structure from the surface down to
800 feet. USS MARYSVILLE (EPC E(R) 857), from which the chain
is operated, is capable of steaming anywhere in the oceans (fig. 1).

The first cruise with the thermistor chain was made in June
1961 in order to test the equipment over the nearby San Diego
r—]
Trough. The results of this cruise have already been reported.

The second cruise, the subject of the present report, was
made between 10 and 14 July 1961 off Southern California. The
purpose was to investigate the nature of internal waves in the deep
ocean regions. The ship's course was three-directional, consist-
ing of a run of about 12 hours directly offshore, another of 12
hours parallel to shore, and a third of 12 hours directly toward
shore (fig. 2). In addition to this course, four circles of 2-mile
diameter and two of 6-mile diameter were traversed in an at-
tempt to determine the direction of internal-wave propagation
from the doppler effect created through changing the direction of
tow.

EQUIPMENT

The oceanographic chain hoist, ’~ the thermistor chain, and
the drum on which the chain is wound are large and rugged, weigh-
ing 37,500 pounds. The chain is composed of flat links about 1
foot long, 10 inches wide, and 1 inch thick. At the end of the
chain is a 2300-pound streamlined weight, called a ''fish, "' to hold
it down.

About 100 pairs of insulated electrical leads fit through
grooves inside the flat links. Every 27 feet the electrical wires
connect with the temperature sensors, or thermistor beads.

‘ATTIASAUVIN SSN UO JSToOY UTeYyO IO}STULIEeyT, “T oan8t 7

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10

The upper ends of the electrical leads connect with a re-
corder located in the ship's laboratory. Signals from the beads
are scanned electronically every 10 to 12 seconds, and lines show-
ing the depths of isotherms are printed on 19-inch-wide tape.

This procedure is equivalent to lowering a bathythermograph
every 100 to 120 feet at a ship's speed of 6 knots. Also printed on
the same tape are the depth of the fish at the end of the chain,
which is the maximum depth of observation, and the temperature
of the sea surface.

With the new thermistor chain it is possible to lower a
string of temperature sensors into the water and then cruise
ahead with the string vertically suspended from the fantail. Since
elements are sensing from the surface down to about 800 feet
while the ship is moving through the water horizontally, two di-
mensions of coverage, depth and distance, are achieved.

OBSERVATIONS AND DATA

Offshore Section

On 11 July 1961 USS MARYSVILLE towed the chain from
near San Diego in a southwesterly direction (247°). Some of the
temperature data collected on this line from point A on figure 2,
31°52'N, 119°13'W (0500 on 11 July), to the end of this leg of the
cruise, point B, 31°22'N, 120°41'W (1830 on 11 July), are pre-
sented in figure 3. The incompleteness of the shallow part of the
record is due to malfunction of some of the shallow thermal sen-
sors. However, the 9°C isotherm was correctly recorded for the
whole of this traverse. In the figure, the vertical temperature
record between 250 and 550 feet is divided into three connecting
parts (WX, XY, and YZ). The nearshore point is W (correspond-
ing to A in fig. 2) and the farthest offshore point is Z (correspond-
ing to B in fig. 2). The horizontal scale may be considered as
either time or distance, and these scales are marked between the
sections.

eta
ik wy ela Brn . nena
a” wont

AY

miles

May an

teeth a ae

Figure 3. Isotherm data from leg one of cruise 2 (250-550 feet).

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12

Because of the rapid scanning rate, the isotherms are near-
ly continuous. The part of this record nearest shore (WX) con-
tains the 8°, 9°, and 10°C isotherms and shows the descending or
deepening trend of the isotherms in an offshore direction. The
other two parts (XY and YZ) also contain three to four isotherms.
These isotherms dip to the right.

It is apparent that none of the isotherms is horizontal, and
that they fluctuate up and down in a short distance or interval of
time. The thermocline or thermal structure, in general, is
rough. The detail shown in figure 3 cannot be obtained by bathy-
thermograph lowerings or with other instruments.

Alongshore Section

From point B, 31°22'N, 120°41'W, the chain was towed in a
southeasterly direction (154°) parallel to the continental shelf.
This traverse started at 1830 on 11 July and ended at 0700 on 12
July at point C, 30°10'N, 120°00'W. Some of the temperature
data collected on this leg are presented in figures 4 and 5. In
both figures the record is broken into three connecting parts, as
in figure 3, with WX the farthest north and YZ the most southerly.

Figure 4 covers the depth range from 100 to 300 feet with
isotherms from 12° to 17°C, and includes the main thermocline.
The isotherms are more nearly horizontal than for the offshore
leg, and the surface becomes warmer in the more southerly sec-
tions. Figure 5 covers the depth range 400 to 600 feet, where
only the 9° and 10°C isotherms were found. In both figures it is
again evident that the depths of isotherms change over short dis-
tances.

Figure 4.

Wnt Sees ea ey

Isotherm data from leg two of cruise 2 (100-300 feet).

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4

13

: Pace (despot i
fr NN Co teas AAA way Canal

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Figure 5. Isotherm data from leg two of cruise 2 (400-600 feet).

14

Onshore Section

The temperature records for the shoreward tow from 1900
on 12 July to 0730 on 13 July are similarly presented in figures
6 and 7. This leg of the cruise started at point C, 30°15'N,
120°01'W, and ended at point D, 30°58'N, 118°31'W. Isotherms
12° to 16°C are present in the 100-to-300 foot record, which is
also broken up into three connecting parts. The apparent temper-
ature inversion in the 14°C isotherm that results in closed iso-
therms around 200 feet in the XY and YZ sections appeared to be
caused by malfunction of a thermistor. In the deeper section,
running from 450 to 650 feet, the 9° and sometimes the 10°C iso-
_therms are present.

lsotherms and Internal Waves

The nature of the vertical changes in the isotherms in deep
water has not been investigated in such detail before. Likewise,
the cause of vertical oscillations has not been established. It is
possible, but not likely, that these changes in temperature are
balanced by changes in salinity, and thus that the density surfaces
are level. Another possibility is that the vertical temperature
changes are merely the result of standing waves in the thermo-
cline. Eckart,* referring to Vaisala,” points out that a given den-
sity boundary may have its own normal oscillating frequency, the
Vaisala frequency. Still another possibility is that strong winds
may create convection cells in the upper layers of the sea, the
circulation of which causes the thermocline to be lowered more in
one area than another. There is, however, reason to believe that
the vertical variations observed with distance in the isotherms
are caused by internal waves moving in one or more directions.
Evidence to support the latter explanation lies in the fact that, at
all anchor stations where repeated measurements have been made,
the isotherms show vertical fluctuations with reference to time.
The progressive nature of these oscillations in shallow water has
been proved by results obtained off anchored ships and at the NEL
Oceanographic Research Tower.® In this report, therefore, the
oscillations are assumed to move as progressive internal waves.

15

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, ea Rey ote, Fh, mI Sie
aa dies ee e 2 gi
BER or Sw

pi Lal gah had

L Me

cl «

Saye, Mn

‘ Prd
Ce eae

Sy

weraryac’ RONEN

Tp ae nn,

Figure 6. Isotherm data from leg three of cruise 2 (100-300 feet).

16

Figure 7. Isotherm data from leg three of cruise 2 (450 and 650 feet).

17

18

The detailed recording of isotherm depths indicates the
complicated character of the thermal structure of the seas. It
also emphasizes that the ocean is probably a complex body, not
only as regards temperature, but also as regards chemical, bio-
logical, and other aspects.

ISOTHERM DEPTH VARIABILITY

Changes in sea temperature at the surface and at various
depths may be attributed to any of several factors, among which
are the advection of water of different temperature into an area,
radiation from the sun, mixing by the wind, tidal currents, inter-
nal waves, and others. ” Since all the factors simultaneously
exert influence, it is difficult to sort out their individual effects.

It is equally difficult to adequately describe the structure and vari-
ability of the sea temperature.

Several investigators have made studies of the variability of
surface and internal temperatures. ” * 7% 1. Others have devel-
oped methods for the statistical analysis of physical properties
applicable to sea temperature variability.’ 1*1*1>* In this re-
port three approaches to the study of isotherm depth variability
are used: (1) differences in depth values; (2) autocorrelation of
depth values; and (3) power spectrum of depth values.

Differences in Depth Values

The depths of isotherms were scaled from the original rec-
ord (figs. 3 - 7) at half-minute intervals. The isotherms chosen
were 9°C for all legs, 14°C for the alongshore leg, and 16°C for
the onshore leg. The depth differences from point to point along
the isotherms were determined from the formula

My ee =p;

where

1=k=N

The quantities 4; and X i+ are depths (feet) of a given iso-
therm at the beginning and end of the 7 th distance (or time inter-
val) along the track, Y; is the depth difference (feet), and V is

the total number of readings in a given series. When the isotherm

becomes deeper with distance run, the difference is negative.

From the speed of the ship and depth differences, approxi-
mate slopes can be obtained. Ata speed of 6 knots, the ship trav-
eled 304 feet in each half-minute interval; therefore, dividing the
depth differences by 304 feet gives the slope of the isothermal
surface in the direction of the ship's motion. This slope can also
be expressed by the angle of which the slope is the tangent. How-
ever, it must be pointed out that the slopes measured by this
method are influenced by the wave motion, that is, the vertical
change of isotherm depth caused by wave motion that takes place
in half a minute. Thus, exact slopes cannot be acquired; however,
this method yields the best approximation yet obtained of the
slopes of isothermal surfaces in the deep ocean.

At least 1500 observations of isotherm depth were made on
each leg of the cruise. The frequency distributions of depth
changes and slopes for each selected isotherm on each leg of the
cruise are shown in figures 8, 9, and 10. Half-minute depth
changes as great as plus or minus 30 feet were observed in the
9°C isotherm on the offshore run (fig. 8), corresponding to an
angle of 5°38'. Twenty-six per cent of adjacent half-minute read-
ings showed depth changes less than 1 foot. However, 50 per cent
of the slopes observed on this leg were less than 25 minutes from
the horizontal, as indicated by the vertical lines in the figure.

On the alongshore leg (figs. 9A and 9B) nearly all half-minute
depth changes were less than 15 feet. For the 14°C isotherm, 50
per cent of the depth changes in 304 feet were less than 1. 2 feet,
corresponding to a slope of 14 minutes from the horizontal. The
9°C isotherm had a somewhat broader distribution of slopes, but
the distribution was narrower than for the same isotherm on the
offshore leg. Here 50 per cent of the slopes fell within 21 minutes
(fig. 9B).

tg)

SLOPE IN DEGREES
UP 6° 5° ae Be om 1° o° 1° 2° 3° 4° 5° DOWN

9°C ISOTHERM

i)
(e)

PERCENT OF OBSERVATIONS
(e)

DEPTH CHANGE (FT.)

Figure 8. Frequency distribution of differences in depth between half-minute
or 304 ft spaced readings of 9°C isotherm, leg one, cruise 2.

The vertical depth and slope changes of the two chosen iso-
therms on the shoreward leg are shown in figure 10. The fre-
quency distribution for the 16°C isotherm is sharply peaked and

- narrower than for any other record. The 9°C isotherm also has a
narrower slope distribution than in the two previous directions of
tow, with 50 per cent of observations falling within 15 minutes.

The distribution of isothermal slopes may be useful in de-
termining the propagation direction of the dominant internal waves.
When the ship is running counter to the waves the slopes should be
steeper, and when the waves are running in other directions the
slopes should be less. The diagrams show that the slopes were
more gentle on the last two legs of the cruise (figs. 9B and 10B)
than on the first leg, for similar isotherms (9°C). Thus, it may
be inferred that the waves were moving more in the shoreward
direction than the other two directions sampled (see later discus-
sion under Direction of Propagation). However, it must again be
pointed out that not all the isotherm depth readings were simul-
taneous. The depths are actually depths of encounter and thus
these slopes may not necessarily be the true ones.

PERCENT OF OBSERVATIONS

SLOPE IN DEGREES
1° i

UP 6° Sm a 3° 2° o° 2° 3m 4° 5° DOWN

30

14°C ISOTHERM

20

(A)
10
)
30
9°C ISOTHERM
20
(B)

) -10 -20 -30
DEPTH CHANGE (FT.)

Figure 9. Frequency distribution of differences in depth between half-minute
or 304 ft spaced readings of 14°C and 9°C isotherm, leg two, cruise 2.

21

PERCENT OF OBSERVATIONS

22

SLOPE IN DEGREES
30 uP 6° 5e 4° 3 2a 1° o° Ie 2° Sh 4° 5° DOWN

16°C ISOTHERM

20

(A)
10
to)
30

9°C ISOTHERM

20

(B)

+30 +20 ene Oo -10 -20 -30
DEPTH CHANGE (FT.)

Figure 10. - Frequency distribution of differences in depth between half-minute
or 304 ft spaced readings of 16°C and 9°C isotherm, leg three, cruise 2.

ACCUMULATED PERCENT

Figure 11. Approximate slopes of isothermal surfaces measured in deep and

A similar study was made of the approximate slope of iso-

thermal surfaces from the NEL Oceanographic Research Tower

100

80

60

40

oO | ° 2° 3° 4

off Mission Beach, California. Ht Here, the approximate slope was
obtained by means of a continuous depth recording of a single iso-
therm in the thermocline made with an isotherm follower. '~ The
computation of slopes with the isotherm-follower record, as the
internal waves pass the fixed point (tower) in 60 feet of water, is
based on an average wave speed of 0.31 knot. Waves moving
faster than 0.31 knot would give steeper slopes than actually exist,
and slower moving waves more gentle slopes. This effect has a
tendency to give a little wider distribution of slopes, but the aver-
age should be close to the true value. The slopes (accumulative
frequencies) detected by this method are shown in figure 11 to-
gether with similar curves for the 14° and 16°C isotherm slopes
obtained from the data of figures 9A and 10A. ee

Although the two methods of obtaining slopes are not the
same, nor the results wholly accurate, a comparison of the curves
based on large samples (10, 000 at the tower, 3000 in deep water)

Oo 0: e ect
= SSS — omy
—_— : :

SLOPE OF ISOTHERM

shallow water.

23

24.

shows that the accumulative per cent of small angles of the deep
water isotherms (from the traverses at right angles) is significant-
ly greater than for similar isotherms in shallow water. It is
therefore reasonable to assume that the shallow water internal
waves in the thermocline are considerably steeper than those 180
miles farther out to sea. This difference indicates that the inter-
nal waves peak as they move into shallow water.

Autocorrelation of Depth Values

Another approach to the problem of subsurface temperature
variability is by means of autocorrelation coefficients. ~ By
using the same half-minute isotherm-depth data, autocorrelations
were computed for each leg of the cruise and each selected iso-
therm. Elements of successive pairs of points (depth of an iso-
therm) at equal but overlapping time intervals were correlated
with each other, and the process repeated for each time interval,
increasing by half-minute steps from a half-minute to 250 minutes.
Autocorrelation, *} , was computed for increasing intervals, ) ,
of 304 feet (half-minute), using the expression:

IN = Wek I=

A
Gi) SS eae I Oe ae
fe 9 OU ee Pye 0

fiy=

M=i [aa |e fe, len Tie
GEN 3 I = paeG EMD Besa] 2 ea

where 4 =0, 1, 2, .... 500 lag intervals and WV is the total num-
ber of depth readings in each leg. The computed autocorrelations
based on about 1500 depth readings (sample length, 750 minutes)
and lag length variable from 0 to 500 steps (0 to 250 minutes) are
shown in figures 12 through 16.

Figure 12 gives the results of the autocorrelation of the half-
minute sampling rate for the depth of the 9°C isotherm of offshore
traverse, leg 1. The correlation is positive throughout.

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27

28

Autocorrelation of depth of the 14°C isotherm in the along-
shore traverse, leg two (fig. 13), showed a positive correlation
for lag intervals of a half-minute up to about 90 minutes (9 miles).
After 100-minute intervals, the correlation remained negative for
over 6-hour intervals. By comparison, the deeper 9°C isotherm
(fig. 14) gave a positive correlation for only 45 minutes, followed
by a negative correlation for about 2 hours, after which the cor-
relation again became slightly positive. This comparison indi-
cates that any dominant cycles in the 14°C isotherm are of longer
period than those in the 9°C isotherm.

The results of the same correlation for the depths of the 16°
and 9°C isotherms, measured on the shoreward traverse, leg three
of the cruise, are given in figures15and16. The depth correlation
for the 16°C isotherm remained positive for over 2 hours whereas
that for the 9°C isotherm remained positive for 6 hours. Here the
dominant cycles are much longer than the period of computation.

If the values of & remain positive, the long periods dominate
the spectrum which may be broad or narrow. In all cases the
major waves are of long period because the correlation does not
reach a maximum negative value for 220 and 90 minutes (figs. 13
and 14) and greater than 250 minutes for the data shown (figs. 12
and 16). The time interval to maximum negative value is half a
wave period. The minimum wave periods, then, for the most sig-
nificant correlations are for the 9°C alongshore waves and amount
to 180 minutes or 18 miles. The wave periods for the onshore and
offshore data runs are greater than 500 minutes or 50 miles. In
all cases the short-period waves are not consistent enough to out-
weigh the long-period ones, by this comparison.

Power Spectrum of Depth Values

The third method of representing variability is by the power
spectrum. ©’ *’’’ The power spectrum [U/(j;) is given by the
Fourier transform of the autocorrelation, . It is the energy per
unit bandwidth and thus designed to emphasize the dominant

frequencies, since the amplitudes are squared. The smoothed
power spectrum values were obtained as follows:

il A=n-l
(hy =— Lec + RA) + cos) cos —
Lei it

where 7 =0, 1, 2, 3.... m index number of frequency (actual
frequencies are given by h/(2A t)
cycles/min, At =1/2 min), and

NK =05 ty 25 Basco pm US Wee Leys iniouanloyene

The power spectrum [/(h) was converted to units of vari-
ance per cycle per minute by multiplying by 2nAt where A? is the
time interval between depth samples and is equal to 0.5 minute.

The results of the computation are shown in figures 17
through 21. The power spectrum of the 9°C-isotherm depth on
the offshore leg is plotted in figure 17. The importance of the
power spectrum lies in the peaks in the curve which indicate fre-
quencies (or periods) in the original data which may have been
obscured by "background noise." Significant is the fact that this
power spectrum has a large number of peaks ranging in periods
from 3.2 to 13.5 minutes which corresponds to 0.3 and 1.3 miles,
but none of these is especially dominant. The greatest power is
in the low frequencies which show no peaks. There are, however,
several high frequency peaks but there is no dominant one.

Similar computations of power spectrum of the 9°C-isotherm
depth (fig. 18) on the alongshore leg show a number of peaks with
periods of 3.0 to 21.3 minutes (0.3 to 2.1 miles).

The power spectrum for 9°C of the onshore traverse (fig. 19)
shows only a low frequency peak at 14.7 minutes (1.5 miles) and
quite weak higher frequency peaks. In comparison, the offshore
9° spectrum has higher power in all frequencies (by a factor of 10
or more) than that for the alongshore or onshore examples.

A similar comparison can be made between the alongshore
14°C isotherm power spectrum and that for the onshore 16°C iso-
therm. The power spectrum for the 14°C isotherm in the

30

POWER PER BANDWIDTH, FT°/CPM

fo} 05 10 AS -20 2

FREQUENCY, CPM

Figure 17. Power spectrum computed from successive half-
minute interval readings of depth of 9°C isotherm, leg one,
eruise 2.

35

Wd9/514

¢

HLOIMGNV€ Yad YAMOd

FREQUENCY, CPM

Power spectrum computed from successive half-

minute interval readings of depth of 9°C isotherm, leg two,

Figure 18.
eruise 2.

31

32

1,000,000

POWER PER BANDWIDTH, FT“/CPM

FREQUENCY, CPM

Figure 19. Power spectrum computed from successive half-
minute interval readings of depth of 9°C isotherm, leg three,
cruise 2.

= 10,000
a
oO
~

(aN) 5,000
(=
L
8
=
a)

= 1,000
z
q

a 500
ac
WwW
a
(ag
=

5 100
a

50

10

5

|

(0)

FREQUENCY, CPM

Figure 20. Power spectrum computed from successive half-
minute interval readings of depth of 14°C isotherm, leg two,
cruise 2.

33

34

POWER PER BANDWIDTH, FT-/CPM

FREQUENCY, CPM

Figure 21. Power spectrum computed from successive half-
minute interval readings of depth of 16°C isotherm, leg three,
cruise 2.

alongshore traverse shows few peaks. The two lower frequency
peaks (fig. 20) are for 10.0 and 19. 2-minute periods (or 1.0 and
1.9 miles), which are relatively long periods when compared to
the 9°C isotherms.

The power spectrum computed for the 16°C isotherm for the
onshore leg shows low peaks which occur between 3. 2 and 22. 2
minutes (0.3 to 2.2 miles) (fig. 21).

2N 1

The degree of freedom v=—~ - 3° When using 1500 depth
sample values and 150 lags, v = 19.5. From reference 12, the
ratio of measured to average value falls between 0.54 and 1.60 for
a 90 per cent confidence limit.

Thus the 7. 2 minute period peak of the offshore 9°C isotherm
depth (fig. 17) has a ratio to background of 58 to 31 or 1.87 which
is significant, whereas the onshore 14.7 minute period peak shown
in figure 19 has a ratio of 1.65 which is barely outside the 90 per
cent confidence limit.

The difference in power spectrum, if caused by a dominant
internal wave moving in one direction, sheds some light on which
way the waves are moving. The greatest power is concentrated in
the long-period fluctuations at the beginning of the spectrum.

Comparing the power spectra with the corresponding auto-
correlation curves indicates that when the autocorrelation curve is
irregular the power spectrum shows a greater number of peaks.
However, any possible wavelength shown on a correlation curve is
at the low frequency end of the power spectrum diagram.

DIRECTION OF PROPAGATION |
OF INTERNAL WAVES

Little is known of the propagation direction of internal waves
in deep water. It is reasonable, however, to assume that internal
waves do propagate in one or, more likely, many directions.
Since the ship is moving at 6 knots with reference to the sea

35

36

surface, and the internal waves are moving in unknown directions,
it is difficult to establish definite structures of the thermocline or
its movements. However, some qualitative assessment of the
dominant direction of propagation can be made.

It was indicated earlier that the slopes of the isothermal
surfaces might assist in determining the direction of internal-
wave motion. In addition, the autocorrelation and power spectrum
indicate a shoreward direction. Furthermore, a doppler effect
may be obtained by towing in different directions.

If the ship with the chain is anchored, the wave trains will
move past and be recorded in accordance with their true frequen-
cies. If the chain is towed in a direction parallel to the "crests"
of long-crested waves, that is 90 or 270° to their direction of
propagation, the true frequency should again be recorded. How-
ever, if the chain is towed in any other direction relative to the
waves, their true frequencies will not be recorded. In other
words, the recorded frequency of waves will depend on the rela-
tive directions of ship and waves and their relative speeds.

If some arbitrary speed is assumed for the waves, such as
1.5 knots, and the ship's speed is 6 knots (fig. 22), a frequency
factor can be computed for all relative directions of ship and
waves (fig. 23). Under these conditions the frequency factor
should be three times normal when the chain is towed in a direc-
tion with waves and five times when being towed counter to the
waves. When a towing is conducted in a relative direction of
75°31' and 284°29', no waves should be encountered if the fronts
are long and parallel, and if the waves are of constant period.
Unfortunately the waves are not so uniform, but it is believed that
there may be dominant waves that would be revealed by the doppler
effect. Thus, to test the directionality of internal waves, an ex-
periment was arranged (at position E, fig. 2, near 30°19'N,
120°03'W) whereby the direction of tow was changed 6 degrees
every minute. In this way the ship made a complete 2-mile-
diameter circle in 1 hour. Four such circles were made; the re-
corded isotherms are presented in figure 24. In addition, two
larger circles of 6-mile diameter were traversed in a similar
fashion; the resulting data are presented in figure 25.

6.0 KNOTS

1.5 KNOTS 1.5 KNOTS
oth. “ERR
sit aH
‘EE ' ee
HEE Hi too a
hs, +BY fe é se,
270° denen enema Pensa e seen n a 50°
Poae sai B
fs = Hh aff
eee He if oe
|
Hb “oR am § Su? Giiiiittis
Fe | |
|
ns ee 9 =
|
|
|
|

180°

Figure 22. Schematic of the relative motions of ship with chain (C)
moving at 6 knots and the dominant wave crests moving at 1.5 knots.

37

FREQUENCY FACTOR

38

EE —————
90° 180° 270"
RELATIVE DIRECTION OF SHIP AND WAVES

360°

Figure 23. Frequency factor of the relative direction of ship and internal wave
motion using the speed of 6 knots for ship and 1.5 knots for waves.

The records from the four 2-mile-diameter tracks (I, UH,
III, and IV, fig. 24) are arranged one above the other for compari-
son. In each case the record is broken down into four depth in-
tervals, going from left to right inthe figure. The horizontal
scale is the direction of tow in each case. However, the nature of
the waves at all directions of tow fails to indicate any wavelength
that is specific for a particular direction of tow.

A similar depth-direction (distance) presentation of iso-
therms is used for the 6-mile-diameter record (fig. 25).

The significant point is that there are vertical fluctuations
in all directions of tow for both the 2- and 6-mile tracks. Visual
inspection reveals no dominant wave heights in any direction nor
any obvious change in frequency. The duration of tow in any direc-
tion by this small circle technique is too small for reliable anal-
ysis, but the occurrence of internal waves at any direction of tow
demonstrates that waves are not parallel in lines. ‘In fact, they
must be in the form of irregular bumps and depressions, so that
any direction of traverse will cross a high and low thermal sur-
face feature.

In the sharp parts of the thermocline there is a good corres-
pondence in the vertical traverse of adjacent isotherms, but this
correlation deteriorates when the vertical gradients become weak.

‘UOSTIVAUIOD TOF Tay{e80} pesueIAIV 91 SMO} JOJOUILIP-s]IUI-Z INOF oY} UO STBALOIUT YAdep sues OTL
"ULCYO IOJSTULTEYY oY} YIM SMO} IB[NOATO INO} wo} BuIy{Nser ornjons13}s o1nzereduils [eoIIEeA “PZ VANSLT

anes Bae my

J 5001

098 =~ OBI

39

"UOSTIVAULOD TOF 19080} poSuUvAIE 91B SMO} 1OJOULLIP-s]IWI-9 OMY OY} UO STeATEqUI YIdep oUTeS OY,
‘ULBYO TOISTULIOY OY} YIM SMO} TB[NOATO OMY WOT] SUTA[NSer oANjONAIS sinyereduie, [eoTEA “Gz aINSIyT

- A, v
els é i dl” aoe

40

This implies that the waves must have different modes and fre-
quencies and are probably moving in different directions.

The establishment of the characteristics of internal waves
and three-dimensional isothermal surfaces by use of the chain is
not as difficult as might be supposed. If the waves are moving
one-fourth as fast as the ship, the results can be treated as spatial
distributions rather than as time variations. In the specific case
cited above, the distortion would be in error by only 25 per cent
at the most, and would become less with increased relative speeds
and by towing in directions nearly normal to the directions of
propagation of the dominant wave.

It is therefore possible to construct a fairly reliable repre-
sentation of internal waves and isothermal surfaces by considering
their space distributions at a given time.

If we consider, for example, the depth of the 9°C isotherm
recorded during the two circular traverses (fig. 25) of 6-mile
diameter, assume a ship drift of 0.5 knot down the coast, and dis-
regard the wave propagation and time of traverse, an approxima-
tion of a three-dimensional representation of the 9°C isothermal
surface can be constructed (fig. 26). This artist's conception,
based on the isotherm depths for the two circles, appears to be a
rough irregular pattern similar to the sea surface or a mountain
range.

SUMMARY AND CONCLUSIONS

With the thermistor chain it has been possible to record a
two-dimensional picture of the thermal structure. In addition, by
towing the chain in rectangular and circular paths, an attempt has
been made to gain knowledge of the spatial changes in isotherm
depth and the direction of propagation of internal waves.

The record of the rectangular tow, away from, parallel to,
and toward shore, was analyzed by computing the isotherm depth
differences at half-minute intervals. These were used to study

41

42

Figure 26. Three-dimensional construction of the 9°C isothermal surface
based on two repeated 6-mile-diameter tows with the thermistor chain (vertical
scale equals about 200 times horizontal).

isothermal surface slopes, and to compute autocorrelations and
power spectra. From the results obtained it was concluded that
many significant waves are of very long period. These analyses
further indicated that there is probably a shoreward movement in
the dominant waves. —

The records of circular tows showed that the thermal struc-
ture is very complex. The circles were too small to clearly dem-
onstrate significant motion in any direction. The data did reveal
that wave crests and troughs of a generally similar type were
crossed in all directions of tow. Thus, the isothermal surfaces
are very complex and vary in all directions.

43

44

REFERENCES

Io

10.

Navy Electronics Laboratory Report 1114, The USNEL
Thermistor Chain, by E. C. LaFond, 20 June 1962

LaFond, E.C., 'Two-Dimensional Oceanography, '’ Bureau of
Ships Journal, v.10, p.3-5, December 1961

Richardson, W. S. and Hubbard, C. J., "The Contouring
Temperature Recorder, '' Deep Sea Research, v.6, p. 239-244,
1959-1960

Eckart, C. H., Hydrodynamics of Oceans and Atmospheres,
Pergamon Press, 1960

Vaisala, V., 'Uber die Wirkung der Windschwankungen auf
die Pilot Beobachtungen, "' Societas Scientiarum Fennica,
Commentationes Physico-Mathematicae II, v.19, p.37, 1925

Lee, O. S., "Observations on Internal Waves in Shallow
Water,'’ Limnology and Oceanography, v.6, p. 312-321,
July 1961

LaFond, E. C., "Factors Affecting Vertical Temperature
Gradients in the Upper Layers of the Sea," Scientific Monthly,
v.78, p. 243-253, April 1954

LaFond, E. C. and Moore, A. T., "Short Period Variations
in Sea Water Temperatures, "' Indian Journal of Meteorology
and Geophysics, v.11, p.163-166, April 1960

Roden, G. I. and Groves, G. W., "On Statistical Prediction
of Ocean Temperatures, "' Journal of Geophysical Research,
v.65, p. 249-263, January 1960

Pierson, W. J. and Marks, W., ''The Power Spectrum
Analysis of Ocean-Wave Records, '' American Geophysical
Union. Transactions, v.33, p.834-844, December 1952

REFERENCES (Continued)

11. Roden, G. I., "Spectral Analysis of a Sea-Surface Tempera-
ture and Atmospheric Pressure Record off Southern
California," Journal of Marine Research, v.16, p. 90-95,
1957-1958

12. Navy Electronics Laboratory Report 831, Information Recov-

ery from Finite-Sample Fluctuation Data, by C. A. Potter,
26 February 1958

13. Tukey, J. W., ''The Sampling Theory of Power Spectrum
Estimates, "' p. 47-67 in Woods Hole Oceanographic Institution,
Symposium on Applications of Autocorrelation Analysis to
Physical Problems, 13-14 June 1949

14. New York University Meteorology and Oceanography Depart-
ment, A Study of Wave Forecasting Methods and of the Height
of a Fully Developed Sea on the Basis of Some Wave Records

Obtained by the O.W.S. WEATHER EXPLORER During a

Storm at Sea, by W. J. Pierson, June 1959

15. Navy Electronics Laboratory Technical Memorandum 296,
Cross Spectrum Analysis with Certain Applications to
Geophysical and Electromagnetic Problems, by E. E. Gossard,
9 July 1958

16. Mode, E. B., Elements of Statistics, 2d ed., p. 246, 328,
Prentice-Hall, 1951

17.. LaFond, E. C., "Oceanographic Tower," Bureau of Ships
Journal, v.9, p. 21-22, April 1960

18. LaFond, E. C., ''The Isotherm Follower, '' Journal of Marine
Research, v.19, p.33-39, 1961

19. LaFond, E. C., ''Temperature Structure of the Upper Layers
of the Sea and its Variation with Time, "' Symposium on
Temperature, its Measurement and Control in Science and
Industry, Third. Proceedings (In Press)

45

46

REFERENCES (Continued)

20. Navy Electronics Laboratory Report 937, Slicks and Temper-
ature Structure in the Sea, by E. C. LaFond, 2 November 1959

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