STATISTICAL RELATIONS BETWEEN SALINITY,
TEMPERATURE AND SPEED OF SOUND IN THE
UPPER OCEAN
Harry Augustus Seymour
NAVAL POSTGRADUATE SCHOOL
Monterey, California
THESIS
STATISTICAL RELATIONS
BETWEEN SALINITY, TEMPERATURE
AND
SPEED OF SOUND IN THE UPPER
OCEAN
by
Harry Augustus Seymour, Jr
Thesis
Advisor :
H.
Medwin
Thesis
Co- Advisor: N.
E.
Boston
March 1972
Approved faon. pubtic -icXeoie; dU&Ubutlon wnZimutzd.
Statistical Relations
Between Salinity, Temperature
and Speed of Sound in the Upper Ocean
by
Harry Augustus Seymour, Jr.
Lieutenant, United States Navy
B.S., United States Naval Academy, 1965
Submitted in partial fulfillment of the
requirements for the degree of
MASTER OF SCIENCE IN OCEANOGRAPHY
from the
NAVAL POSTGRADUATE SCHOOL
March 1972
ABSTRACT
In situ measurements of salinity and temperature fluctu-
ations at depths to 14 meters indicate distinct dependences
at different times of the day. The variance of the salinity
fluctuations decreased with increasing depth, but was greater
just after sunrise than just prior to sunset. The variance
of the temperature fluctuations decreased with increasing
depth just prior to sunset, but increased with depth immedi-
ately after sunrise. The correlation length of the sound
index of refraction was calculated by using the variance of
the sound velocity fluctuations, and the variance of sound
amplitude modulation in the theory of Mintzer. This analysis
shows that micros tructure patch size increases approximately
linearly with depth. The power spectral densities of the
salinity, temperature and sound velocity fluctuations show
peaks of energy corresponding to dominant ocean wave
frequencies .
TABLE OF CONTENTS
I. INTRODUCTION 11
A. HISTORY 11
B. SIGNIFICANCE OF PROBLEM 12
C. OBJECTIVES OF THIS RESEARCH 13
II. EXPERIMENTAL PROCEDURE 14
A. OCEANOGRAPHIC ENVIRONMENT 14
1. Location 14
2. Time of Year 14
3. Meteorological, Oceanographic ,
and Biological Conditions at
Time of Project 14
B. EQUIPMENT USED DURING EXPERIMENT 16
1. Bissett-Berman STD Model 9006 .... 16
2. Thermistors (3) 18
3. Ramsay Corporation Mark I SVTD .... 18
4. Wave Height Sensors 18
5. Particle Velocity Sensor 19
6. High Pass Filter #1 - Krohn-Hite
Model 3340 19
7. Band Pass Filter #2 - Krohn-Hite
Model 330-A 19
8. Band Pass Filter #3 - Velocimeter . . 19
9. Amplifier #1: Preston Scientific
Model 830 0 xwb 19
10. Amplifier #2: Preston Scientific
Model 830 0 xwb 19
11. Amplifier #3: Hewlett-Packard
Model 2470 19
12. Amplifier = 4: Hewlett-Packard
Model 24 70 19
3
13. Amplifier #5: Hewlett-Packard
Model 2470 20
14. Amplifier #6: Hewlett-Packard
Model 2470 20
15. Sangamo Magnetic Tape Recorder
Model 3500 20
C. EXPERIMENTAL CONFIGURATION 20
1. Schematics 20
2. Geometry of Sensors 24
III. DATA CUMULATION AND RUN DESCRIPTION 29
IV. DATA REDUCTION 30
A. INTRODUCTION 30
B. MAGNETIC TAPE TO STRIP-CHART RECORDING . . 30
C. ANALOG TO DIGITAL TAPE 32
D. CONVERSION OF TAPED DIGITAL DATA
TO DATA CARDS 32
V. DATA ANALYSIS 34
A. INTRODUCTION 34
B. STATISTICAL PROGRAMMING 34
C. STATISTICAL ANALYSIS 36
1. Introduction 36
2. Variance of Oceanographic
Fluctuations 36
3. Variance of Temperature
Fluctuations 37
4. Variance of Salinity Fluctuations . . 43
5. Probability Density Function
Results 44
6. Normalized Autocorrelation Function . 44
7. Pover Spectral Density 44
VI. PARAMETRIC INTERRELATIONS BETWEEN SALINITY,
TEMPERATURE, AND SOUND VELOCITY 4 8
A. INTRODUCTION 48
B. DERIVATION OF THEORETICAL SOUND
VELOCITY VARIANCE FROM WILSON'S
EQUATION 4 8
1. Wilson's Equation 48
2. Computation of Variance 4 8
3. Dropping the Term, var (T2), as
Negligible Yields the Final Result . 4 8
VII. CONCLUSIONS 52
VIII. RECOMMENDATIONS FOR FURTHER STUDY ...... 53
APPENDIX A GENERAL DESCRIPTION OF BISSETT-BERMAN
MODEL 9006 SALINITY, TEMPERATURE AND
DEPTH MONITORING SYSTEM 54
APPENDIX B DATA CUMULATION AND RUN DESCRIPTION . . 56
COMPUTER OUTPUT 59
COMPUTER PROGRAM A 97
COMPUTER PROGRAM B 10 3
BIBLIOGRAPHY 104
INITIAL DISTRIBUTION LIST 106
FORM DD 1473 10 8
LIST OF TABLES
I. Values of Variance as Computed From Power
Spectral Densities 38
II. Values of Variance as Computed Directly
From Time Series Data 38
III. Values of Salinity as Determined From
Nansen Cast Samples 58
LIST OF FIGURES
1. NUC Oceanographic Research Tower 15
2. Bathythermograph Traces 17
3. Bissett-Berman STD Flow Diagram 21
4. Ramsay Sound Velocimeter Flow Diagram .... 22
5. Thermistor Flow Diagram 23
6. Geometrical Relationships Between Sensors . . 25
7. Geometrical Separations Between Oceanographic
Sensors and Acoustic Source 26
8. Bissett-Berman STD Model 9006 27
9. STD Relationship With Other Sensors 27
10. STD and Other Sensors 2 8
11. STD and Other Sensors 2 8
12. Representative Oceanographic Fluctuations . . 31
13. Plot of Temperature Variance Versus Time
of Day 40
14. Plot of Salinity Variance Versus Time
of Day 41
15. Plot of Sound Velocity Variance Versus
Time of Day 42
16. Salinity Histogram 45
17. Sound Velocity Histogram 46
18. Temporal Correlation of Thermistor 1
Run 3 59
19. Temporal Correlation of Thermistor 2
Run 3 60
20. Temporal Correlation of Salinity Run 3 . . . . 61
21. Temporal Correlation of Thermistor 2
Run 4 62
22. Temporal Correlation of Salinity Run 4 . . . . 63
23. Temporal Correlation of Sound Velocity
Run 4 64
24. Temporal Correlation of Thermistor 1
Run 5 65
25. Temporal Correlation of Thermistor 2
Run 5 66
26. Temporal Correlation of Salinity Run 5 . . . . 67
27. Temporal Correlation of Sound Velocity
Run 5 68
28. Temporal Correlation of Thermistor 1
Run 6 69
29. Temporal Correlation of Salinity Run 6 . . . . 70
30. Temporal Correlation of Sound Velocity
Run 6 71
31. Temporal Correlation of Thermistor 1
Run 8 72
32. Temporal Correlation of Salinity Run 8 . . . . 73
33. Temporal Correlation of Sound Velocity
Run 8 74
34. Temporal Correlation of Thermistor 1
Run 9 75
35. Temporal Correlation of Salinity Run 9 . . . . 76
36. Temporal Correlation of Thermistor 1
Run 10 77
37. Temporal Correlation of Salinity Run 10 . . . 78
38. Power Spectral Density of Thermistor 1
Run 3 79
39. Power Spectral Density of Thermistor 2
Run 3 80
40. Power Spectral Density of Salinity Run 3 . . . 81
41. Power Spectral Density of Thermistor 2
Run 4 4 82
42. Power Spectral Density of Salinity Run 4 . . . . 83
X
43. Power Spectral Density of Sound Velocity
Run 4 84
44. Power Spectral Density of Thermistor 1
Run 5 85
45. Power Spectral Density of Thermistor 2
Run 5 86
46. Power Spectral Density of Salinity' Run 5 . . . 87
47. Power Spectral Density of Sound Velocity
Run 5 88
48. Power Spectral Density of Thermistor 1
Run 6 89
49. Power Spectral Density of Salinity Run 6 . . . 90
50. Power Spectral Density of Sound Velocity
Run 6 91
51. Power Spectral Density of Thermistor 1
Run 8 92
52. Power Spectral Density of Sound Velocity
Run 8 93
53. Power Spectral Density of Thermistor 1
Run 9 94
54. Power Spectral Density of Thermistor 1
Run 10 9 5
55. Power Spectral Density of Salinity Run 10 . . 9 6
ACKNOWLEDGEMENT
The author wishes to express his appreciation to his two
thesis advisors Dr. Herman Medwin and Dr. Noel E. Boston for
their guidance and assistance throughout the project.
The author would also like to thank LCDR Gail Griswold
of the Pt. Mugu Oceanographic Detachment, Mr. Dana Maberry
of the Naval Postgraduate School, and Mr. Dale Good of the
Naval Undersea Research and Development Center all of whom
played integral roles necessary to the successful completion
of the project.
The author would also like to acknowledge the support of
the Navy Ship Systems Command, as well as the Office of
Naval Research which funded the project under ONR Contract
P.O. 2-0012.
Finally, but not to the least degree, the author would
like to thank his wife for the many hours she spent typing
the several drafts of this manuscript.
10
I. INTRODUCTION
A. HISTORY
The study of sound propagation in the ocean and the ef-
fects of oceanographic parameters (particularly temperature)
on it has been the subject of considerable research since
early World War II. Wilson [Ref. 1] formulated an equation
describing the relationships between sound velocity, tem-
perature and pressure in distilled water, and then extended
his work to an oceanic regime by utilizing filtered seawater
diluted with distilled water to obtain desired salinity
dependence [Ref. 2], Since Wilson's efforts in this field,
many investigators have attempted to revise the sound speed
equation with newer techniques and theory. The reasons for
revised formulations included, among others, the use of new
type velocimeters [Ref. 3] the suspicion that standard sea
water did not maintain a standard salinity to sound speed
relationship [Ref. 4] , the desire to obtain simpler expres-
sions, and the use of a more realistic range of values for
the oceanographic parameters [Ref. 5] .
While these investigations into the parametrical rela-
tionships to sound velocity were proceeding, other investi-
gators attempted to measure the magnitude of the fluctuations
of the important parameters affecting sound propagation in
seawater. Liebermann [Ref. 6] studied the effects of tem-
perature inhomogeneities on sound propagation. He found that
thermal inhomogeneities do have an effect on the scattering,
11
intensity, and refraction of the sound transmission. Shon-
ting [Ref. 7] also measured the thermal micros tructure, his
results indicating the importance and magnitudes of tempera-
ture fluctuations in the ocean environment.
B. SIGNIFICANCE OF PROBLEM
The characteristics of sound propagation in a deep ocean
environment (defined in this paper as the depth below the
thermocline) are well known and predictable. This is due
to the fact that in the deep water regime the fluctuations
of temperature and salinity are minor. As a result of this
predictability, sound is used properly and constructively
in deep waters. For the United States Navy this specifically
relates to optimum usage of sound in the field of anti-
submarine warfare.
However the propagation of sound in the shallow ocean
environment and in the near surface region is not as pre-
dictable, and as a result seriously hinders the user and
the planner in their efforts to utilize sound to its best
advantage. The near surface region usually plays a part in
long range propagation of sound.
Sound velocity amplitude and phase in the region between
sound source and sound receiver change in the near surface
regions. They change due to small scale variations in oceano-
graphic parameters including possibly the presence of micro-
bubbles and organic content in the regime.
12
C. OBJECTIVES OF THIS RESEARCH
The main motivation in this research was to statistically
describe the oceanic parameters of temperature and salinity,
and to relate their statistics to the statistics of sound
velocity in a near surface environment. It was hoped to ob-
tain enough data to enable one to draw conclusions concern-
ing the variation of the fluctuations with respect to depth
and time of day. If such concrete conclusions could be
reached in the near surface region, then the users of sound
either in oceanographic research or in present anti-submarine
warfare would be afforded new tools with which to update the
state-of-the-art in sound use and understanding.
13
II. EXPERIMENTAL PROCEDURE
A. OCEANOGRAPHIC ENVIRONMENT
1. Location
Due to its advantageous location of being rigidly
fixed in a shallow water environment the N.U.C. Oceano-
graphic Research Tower, approximately one mile off Mission
Beach, California, was chosen as the location for the pro-
ject. It allows for continuous data accumulation and
monitoring as well as some analysis in a near laboratory
controlled environment.
Figure 1 is an illustration of the tower. It is
fixed by supporting pins driven 63 feet into the ocean
floor. Electrical power is supplied from shore thereby
guaranteeing stable voltage and frequency. The tov/er is
located in 60 feet (18 m) of water with a sandy bottom
and is free of water traffic most of the time. The upper
level of the two level tower was the location for elec-
tronic support equipment. The lower was for handling
equipment.
2. Time of Year
The experiment was conducted from the afternoon of
21 October 19 71 through the morning of 22 October 19 71.
3. Meteorological, Oceanographic , and Biological
Conditions at Time of Project
a. Weather State: clear to light haze
b. Wind: 21 October - 300-320 from 7 to 9 kts
22 October - 065-110 from 2 to 8 kts
14
FIGURE 1. NUC Oceanographic Research Tower
15
c. Wind Waves: 0 to h ft from crest to trough
d. Swell: 2 ft from Northwest
e. Bubbles: 1 square foot in vicinity of tower
stanchions during all runs. During run #4 bubbles were
present on the surface in patches of size 20 ft by 2 ft
near vicinity of tower.
f. Biologies
(•*-) Seaweed. Small amount of sea grass on
surface during run #4.
(2) Animal Life . Seal in vicinity during run
#6, porpoise and seals in vicinity during runs 7 and 8.
g. Temperature Structure: thermocline varied from
depths between 40 ft to 60 ft below the surface (see
Fig. 2)
h. Salinity: Nansen Cast results, as determined
from Hytech model 621 salinometer, found in Table III.
B. EQUIPMENT USED DURING EXPERIMENT
1. Bissett-Berman STD Model 9006
a. Temperature Sensor
(1) Time Constant: 0.35 sec
(2) Output: 0 - 10 mv DC
(3) Temperature Range Used: 14 - 19° C
(4) Accuracy: ±0.02° C
b. Salinity Sensor
(1) Time Constant: 0.35 sec
(2) Output: 0 - 10 mv DC
16
Temperature (°F)
Temperature (°F)
5 8 59 60 61 62 6:
10--
20--
<D
<D
Cm
a
•H
+j
cu
0)
a
30--
64
58 59 60 61 62 63 64
H 1 1 1 H-+
10--
20"
-P
<a
a)
fa
c
•H
+j
a
0)
Q
30--
40--
50--
40--
50-
60-L I
0800 22 Oct 1971
6 0-
0900 22 Oct 1971
FIGURE 2. Bathythermograph Traces
17
(3) Salinity Range Used: 37.5 - 39 .'5 ppt
(before correction)
(4) Accuracy: ±0.0 3 ppt
c. Detailed Description Found in Appendix A
2. Thermistors (3)
a. Time Constant: 150 milliseconds
b. Output: .0553 volts per °C
c. Temperature Range: Thermistors nulled using
Wheats tone Bridge Circuit prior to start of each run.
d. For further description see NPS thesis of LCDR
Duchock, March 19 72.
3. Ramsay Corporation Mark I SVTD
a. Time Constant: 160 microseconds
b. Output: 0 - 10 v DC
c. Sound Velocity Range: 140 0 - 160 0 m/sec
d. Accuracy: +.01 m/sec
e. For further description see NPS thesis of LCDR
Duchock, March 19 72.
4. Wave Height Sensors
a. Baylor Wave Profile Recorder System
(1) Output: 50 millivolts per foot of height
(2) Accuracy: 1% or reading
(3) For further description see NPS thesis of
LT Bordy, March 19 72.
b. Interstate Electronics Corporation Pressure Wave
Gauge
(1) Output: .25 v/psi
18
(2) Accuracy: 2% of reading
5. Particle Velocity Sensor
a. Engineering Physics Company Electromagnetic
Current Meter
(1) Output: variable voltage per meter/second
(2) Accuracy: 1% of full scale reading
b. For further description see NPS thesis of LT
Bordy, March 19 72.
6. High Pass Filter #1 - Krohn-Hite Model 3340
a. Gain: OdB
b. High Pass Filter Cutoff: 0.01 HZ
7. Band Pass Filter #2 - Krohn-Hite Model 330 -A
a. Gain: OdB
b. Low Pass Cutoff: 0.0 2 HZ
High Pass Cutoff: 2000 HZ
8. Band Pass Filter #3 - Velocimeter
a. Gain: OdB
b. Low Pass Cutoff: 0.0 2 HZ
High Pass Cutoff: 20 00 HZ
9. Amplifier #1: Preston Scientific Model 8300 xwb
a. Gain: 500
10. Amplifier #2: Preston Scientific Model 8300 xwb
a. Gain: 1
11. Amplifier #3: Hewlett-Packard Model 2470
a. Gain: 30
12. Amplifier #4: Hewlett-Packard Model 24 70
a. Gain: 100
19
13. Amplifier #5; Hewlett-Packard Model 2470
a. Gain: 100
14. Amplifier #6: Hewlett-Packard Model 24 70
a. Gain: varied 100-300
15 . Sangamo Magnetic Tape Recorder Model 3500
a. 14 channel with 11 channels allocated for
oceanographic parameter data were utilized.
b. Channel Allocation:
(1
(2
(3
(4
(5
(6
(7*
(8
(9
(10
(11
(12
(13
(14
Ramsay Temperature Sensor (not used)
Ramsay Velocimeter
Bissett-Berman Salinometer
Turbulent Velocity (horizontal component)
Turbulent Velocity (vertical component)
Baylor Wave Height
Sound Amplitude Modulation
Pressure Wave Height
Thermistor #1
Bissett-Berman Temperature (not used)
Thermistor #2
Thermistor #3
Sound Phase Modulation
Voice (not used)
C. EXPERIMENTAL CONFIGURATION
1. Schematics
a. Bissett-Berman STD - See Fig. 3
b. Ramsay Velocimeter - See Fig. 4
c. Temperature Thermistors - See Fig. 5
20
Under Water
Sensors
Discriminators
Panel
Meters
Filter #1
Amplifier #1
Salinity Output
to Recorder
Filter #2
Amplifier #2
Temperature
Output
to Recorder
FIGURE 3. Bissett-Berman STD Flow Diagram.
21
Ramsay
Velocimeter
Filter #3
Amplifier #3
Sound Velocity
Output
to Recorder
FIGURE 4. Ramsay Sound Velocimeter Flow Diagram,
22
Thermistors
Wheatstone
Bridge
Circuit
Amplifiers
Temperature
Output
to Recorder
FIGURE 5. Thermistor Flow Diagram,
23
2. Geometry of Sensors
The sensors' geometric relationships were deemed to
be of major importance in view of potential acoustical and
physical interferences which could have had an adverse ef-
fect on the experimental results. In addition to the attempt
to describe the oceanic regime in terms of the oceanic
parameters two acousticians simultaneously conducted ex-
periments related to sound amplitude modulation, sound
dispersion, and phase fluctuations. (See NPS thesis of
LCDR W. J. Smith, Jr., December 1971 and thesis of LCDR
Juergen Rautmann, December 19 71.)
In order to reduce the effects of mutual interfer-
ence between the sensors especially in the path of sound
propagation between hydrophone and receiver, a physical
separation of the sensors was mandatory. The geometrical
separations between the sensors as shown in Figs. 6, 7 were
used. Photographs of the Bissett-Berman STD and the geo-
metrical relationships of the other sensors to it appear
in Figs. 8-11.
24
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FIGURE 8.
Bisset-Berman
STD Model 9006
FIGURE 9.
STD Relationship
With Other Sensors.
27
FIGURE 10.
STD and
Other Sensors
FIGURE 11.
STD and
Other Sensors.
28
III. DATA COLLECTION AND RUN DESCRIPTION
Data collection and run description will be found on page 56 under
Appendix B.
29
IV. DATA REDUCTION
A. INTRODUCTION
The analog data were recorded for each run on the
Sangamo Model 3500 magnetic tape recorder operated at a
speed of 1 7/8 ips using FM electronics. The recorded
data were then transferred to a Brush Mark 200 Strip-Chart
recorder. In some instances, in order to produce better
resolution, the recorded data were transferred to a Brush
Mark 2 Strip-Chart recorder through a Krohn-Hite Model
3340 filter set on low pass-max flat (see Fig. 12) . The
printed analog data were converted to digital data on
magnetic tape using the Fleet Numerical Weather Central,
Point Pinos , California tracing digitizer. The taped data
were transferred to punched IBM data cards compatible for
statistical analysis on an IBM 360-67 digital computer.
B. MAGNETIC TAPE TO STRIP-CHART RECORDING
The recorder playback speed was seven and one half
inches per second, which is an increase of four times over
the data collection speed. The strip-chart recorder was
run at a speed of five millimeters per second. The speed
differentials between the record, playback, and strip-chart
phases were programmed in the IBM program used for data
analysis. The sensitivity setting on the strip-chart re-
corder was important for data presentation and analysis.
The sensitivity settings varied from run to run and with
30
3X
unity fluctuations ruN6 4.3 meters 0354
H 1 1 1 1 1 1 I 1 1 1 1 1 1 1 1 1 1 h
H 1 H
H 1 — h
idnJCTTJATTO hIS R UN 6 ' 4.3 'm E T E R S 03 54 2 2 OCT
—I — l — l — l — l — I — i — (- — I — l — l — l — I — I — i 1 I 1 — l —
TT7T
5TOUND VELOCITY FLUCfUAT TONS TruN V 4^mETERS 0354 22 OCT 1971
H i h
H \ — h
H 1 h
FIGURE 12. Representative Oceanographic Fluctuations.
31
each parameter. The settings used can be found in
Appendix B.
C. ANALOG TO DIGITAL TAPE
In order to utilize the IBM 360 computer to determine
the statistics of the fluctuations , the analog data on the
strip-chart record had to be converted to digital form. In
order to effect the conversion use was made of the Calma
tracing digitizer at Fleet Numerical Weather Central's
Point Pinos, California facility. The tracing digitizer
transfers analog data to digital data on magnetic tape at
a sampling rate of 100 samples per inch in both the x and
y directions . The length of each run analyzed amounted to
approximately the first nineteen minutes of the run while
the number of data points varied depending upon the posi-
tioning of the strip chart on the digitizer. It was im-
portant for future correlations that the tracing of all
parameters began at the same starting point. This was
ensured by starting at the sharp line transient signaling
the start of a particular run.
D. CONVERSION OF TAPED DIGITAL DATA TO DATA CARDS
Conversion of taped digital data to a form compatible
for use on the IBM 360 Digital Computer, i.e. data card
form, was accomplished using Fleet Numerical Weather
Central's Computer Facility. Fourteen data points were
recorded on each IBM card. The number of data points per
32
run varied depending on the positioning of the strip chart
on the Calma Plotter at Point Pinos , but the average run
produced approximately 5400 data points.
33
V. DATA ANALYSIS
A. INTRODUCTION
Attention was focused entirely on analysis of the
statistics of the fluctuating parameters. Two arguments
led to this method of analysis: first of all, the statis-
tics of the oceanographic variables are important in deter-
mining the statistics of sound propagation. Since the
major objective of the experiment was to define the medium
in order to determine its effect upon the propagation of
sound the statistical method of analysis was the natural
approach. The second reason for using statistics as the
major tool for analysis was due to the relatively wide
separation between sensors which was required to prevent
instrumental interactions. In order to enable one to dis-
cuss the interrelationships between spaced sensors it was
necessary either to correct for the lack of idential point
location or to consider the statistical relations, assum-
ing that the medium was statistically homogeneous in the
region of the sensors. The latter is the easier choice.
B. STATISTICAL PROGRAMMING
The programs used in the data analysis appear in
Appendix C .
Program A analyzed the data for mean, variance, normal-
ized autocorrelation function, and power spectral density.
The standard Blackman-Tukey method was used to compute
power spectral density with a Parzen window as the spectral
34
window. Program A was modified to compute variance by two
methods. The first method calculated variance by integra-
ing the power spectral density. A subroutine (aver) was
then added to calculate variance directly from the time
series data.
Program B was used to output data from which a histogram
could be plotted of the number of times a particular value
of a parameter occurred versus the value of that parameter.
In utilizing program A several important inputs were
necessary:
NTS : number of data points
MLAG: number of time lags =10% (NTS)
DT : time increment in seconds/sample. This parameter
took into account the different driving speeds of the strip-
chart recorder, playback and record modes of the tape re-
corder, and the analog-to-digital digitizer.
DT =•
inch 100 samples
(5/4 mm/sec) ( ) ( )
25.4mm inch
= 0.2032 sec/sample
1
Af : frequency increment =
2 MLAG (DT)
FBHZ : lowest frequency
FEHZ : highest frequency = Nyquist Frequency
1
FEHZ = = 2.46 HZ
2(.2032)
Calibration factor: variable on each run
35
The raw data on the IBM cards had the units of inches.
The calibration factor converted inches to volts per milli-
meter by incorporating the Brush recorder sensitivity set-
ting into the program input thereby giving the data units
of volts per inch. When each data point was multiplied by
the calibration factor the results produced were in voltage
units .
# volts 25.4 millimeters volts
C.F. = ( ) = "X"
millimeter inch inch
C. STATISTICAL ANALYSIS
1. introduction
In order to convert the program output in volts to
the correct oceanographic units and values, conversion
factors for sensor voltage sensitivities, amplification
factors and filter gains were used. On location monitoring
of the data combined with post-experimental review in-
dicated some runs higher in quality and accuracy than
others. For such reasons runs 3,4,5,6,7,9,10 were analyzed
for salinity and temperature, and runs 4,5,6,8 for sound
velocity. The conversion factors used were:
thermistors: 5.5 3 v/°C
salinity: 2.5v/%.
m
sound velocity: 1.5 v/
sec
2. Variances of Oceanographic Fluctuations
The values of the variances of the oceanographic
parameters as computed by integrating the power spectral
densities are indicated in Table I.
36
The values of the variances of the oceanographic
parameters as computed directly from the time series data
are listed in Table II.
It was noted that there was only a very slight dif-
ference between the values of variance computed by both
methods. However the variances used in subsequent analysis
were those computed directly from the data thereby ensuring
a higher degree of accuracy. Additionally all subsequent
analysis was performed using temperature data measured by
thermistor #1 since the quality of the fluctuating signal
from that sensor was the best and most consistent throughout
all runs. (Thermistor #2 data used during run 4 since
thermistor 2 was operating reliably at that time) . Figures
13-15 are graphical displays of variances versus time of day
with depths at which runs were made noted in parentheses.
A survey of the literature indicates that this ex-
periment was unique in its attempt to establish statistical
relationships between the described oceanographic parameters.
As a result little direct comparison with previous results
is possible.
3. Variance of Temperature Fluctuations
Two past investigators have studied temperature fluc-
tuations in the near surface region on approximately the same
time scale as was used in this experiment. Shonting used a
double-beaded thermistor manufactured by Fenwall Electronics,
Inc., Framingham, Massachusetts, to observe thermal micro-
structure. He conducted his measurements in the Bahamas in
37
Run
Time
Depth
Sound Vel.
Variance
Temp #1
Variance
Temp #2
Variance
Salinity
Variance
3
21 OCT
1616
9.0m
.0187(°C)2
.0121(°C) 2
.0016 (%.) 2
4
1648
13.9m
.0294(M/S) 2
.0167
_
.0013
5
1728
6.9m
.0003
.0230
.0002
.0023
6
22 OCT
0354
4. 3m
.0072
.0052
.0044
8
0650
9. 5m
.0023
.0013
.0110
9
0725
14.6m
.0076
.0065
10
0802
7. 8m
.0017
.0002
TABLE I
Run
Time
Depth
Sound Vel.
Variance
Temp #1
Variance
Temp #2
Variance
Salinity
Variance
3
21 OCT
1616
9. 0m
,0143 (°C) 2
.0093(°C) 2
.0 016(%.) 2
4
1648
13.9m
.0293(M/S) 2
.0129
_
.0012
5
1728
6.9m
.0003
.0184
.0002
.0023
6
,
22 OCT
0354
, —
4 . 3m
.0072
.0042
.0041
8
0650
9. 5m
.0021
.0010
.0111
9
0725
14.6m
i — "
.0059
.0059
10
0802
7.8m
.0013
—
.0002
TABLE II
38
August 19 67. Analysis of his measurements taken between
1323-1400 indicated representative values of variance of
approximately 25 x 10" 6 (°C) 2 at two meters depth and ap-
proximately 72 x 10""8 (°C) 2 at 20 meters, a decrease of two
orders of magnitude with depth down to 20 meters. Although
the variance was much greater in the present experiment
than in Shonting's, there was in the late afternoon period
a one order of magnitude decrease in temperature variance
with depth down to approximately 15 meters.
Liebermann also recorded temperature fluctuations in
the near surface region at a depth of 50 meters. A rough
calculation of variance from Liebermann' s Fig. 1, which was
given as a representative temperature record for July and
August (time of day unreported) for the continental waters
from Southern California to Alaska, resulted in a variance
of approximately 17 x 10~4(°C)2. This figure is somewhat
closer to data of Fig. 13 but the lack of time of day in-
formation and depth dependence prevents conclusions from
being drawn.
Due to the maximum temperature gradient being effected
just prior to sunset the strongest fluctuations of tempera-
ture were noticed at all depths at that time. The variance
decreased with increasing depth. However in the short
period just after sunrise the temperature fluctuations were
noticed to increase with depth. Sagar [Ref. 8] quotes, from
a personal communication, Deacon, of the National Institute
; hav is same si
39
FIGURE 13.
Plot of Temperature
Variance Versus Time
of Day (Depth in
Parentheses) .
c
•H
Q)
O
C
<TJ
■ft
U
>
020 T
018
O (6.9M
.016
014
""
O (9m)
u
w .012
010
008
006
.004
.002
O (13.9m)
O (14.6m)
O (4.3m)
(9.5m)
O ° (7.8m)
H
4-
+
■4
1600 1700
0400 0500 0600 0700 0800 0900
21 Oct
Sunset 1805
22 Oct
Sunrise 0703
Time of Day by Hour
40
c
d)
o
c
to
•H
CO
>
012
Oil
010
009 -
008
007
006
005 "■
004 t
003 ■*
,002 ■"
.001 ■■
FIGURE 14.
Plot of Salinity
Variance Versus Time
of Day (Depth in
Parentheses) .
O (9.5m)
O (4.3m)
O (6.9m)
O (9m)
O (13.9m)
I 1-
O (14.6m)
4-
O (7.8m)
H 1 1
1600 1700
21 Oct
Sunset 1805
0400 0500 0600 0700 0800 0900
22 Oct
Sunrise 0703
Time of Day by Hour
41
FIGURE 15.
C
•H
Q)
U
C
rd
•H
>
45 T
40 "
35 "
— .30 f
u
Q)
03
\
g .25 +
20 "
15 "
10 "
05 "
O (6.9m)
O (9m)
O (13.9m)
Plot of Sound Velocity
Variance Versus Time
of Day (Depth in
Parentheses) .
0
O (4.3m)
O (14.6m)
f-
4
(9.5m)
H 1 h
O (7.8m)
-i
1600 1700
0400 0500 0600 0700 0800 0900
21 Oct
Sunset 1805
22 Oct
Sunrise 0703
Time of Day by Hour
42
This behavior could possibly have been caused by the "con-
vective lag" phenomenon. James [Ref. 9] describes this
behavior as occurring in the early morning just after sun-
rise. Insolation increases to the point where it is equal
to the outgoing heat loss from the water. However heat
loss occurs exclusively at the surface, with consequential
continued cooling of the surface. As insolation increases
in the hours just after sunrise, surface cooling continues
while the lower levels are slowly heated. Eventually, of
course, the lag is overcome and surface heating begins
causing growth of small cells with large fluctuations near
the surface and large cells of small fluctuations at greater
depths, as described by Deacon.
4. Variance of Salinity Fluctuations
The analysis of the plots of salinity variance versus
time showed a decrease in salinity fluctuations with depth
during the late afternoon period. The fluctuations were
smaller during the period just prior to sunset than just
after sunrise (assuming that the 7.8m reading is in error) .
The decrease in variance of salinity with increasing depth
in the late afternoon was expected since a stronger salinity
gradient would exist in the surface layer where evaporation
was initiated. However, it is speculated that convective
mixing caused a more nearly isohaline condition to exist in
the water column by sunset than existed just after sunrise
thereby accounting for the difference in magnitudes of
variances at those two times of the day.
43
In the section "Parametric Interrelations Between
Salinity, Temperature, and Sound Velocity" the theoretical
calculation of sound velocity variance is discussed, and
further analysis of the difference between theoretical and
experimental results is made.
5. Probability Density Function Results
Salinity and sound velocity information were put into
Program B in order to establish the type of distribution of
the populations sampled. In all cases the distributions were
Gaussian in nature. Figures 16 and 17 are examples of the
distributions .
6. Normalized Autocorrelation Function
The normalized autocorrelation functions of the oceano-
graphic parameters (see Appendix D) indicated a long correla-
tion time for temperature data thereby indicating relatively
well mixed thermal structure. Conversely the relatively low
degree of correlation for both salinity and sound velocity
indicated an inhomogeneous medium with respect to those two
parameters . The peaks and troughs found on the salinity and
sound velocity autocorrelation plots indicated the presence
of patches of higher and lower salinity water as well as
patchy areas of water yielding higher and lower values of
sound velocity.
7. Power Spectral Density
Plots were made of power spectral densities of salin-
ity, temperature, and sound velocity fluctuations (see
Appendix E) .
44
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46
The nature of the plots indicated peaks of "energy"
centered about frequencies of 0.17 and 0.08 Hertz. This
coincided with the dominant wave frequencies existing at
the time of the experiment.
47
VI. PARAMETRIC INTERRELATIONS- BETWEEN SALINITY/ TEMPERATURE,
AND SOUND VELOCITY
A. INTRODUCTION
With hopes of shedding light on possible heretofore un-
known variables capable of affecting sound velocity a com-
parison was made between sound velocity variance derived
from Wilson's sound speed equation and that measured experi-
mentally with the Ramsay Velocimeter.
B. DERIVATION OF THEORETICAL SOUND VELOCITY VARIANCE FROM
WILSON'S EQUATION
1. Wilson's Equation
C (t) = 1449.2 + 4.623 T (t) - .0546 T2 (t)
+ 1.391 (S (t) - 35)
2. Computation of Variance
var C = 0 + (4.623) 2 var T - (.0546) 2 var (T2)
+ (1.391)2 var (S)
3. Dropping the Term, var (T2), as Negligible Yields
the Final Result
var C = 21.372 var T + 1.9 35 var S
The utilization of the above formula yielded the
following results, with the velocimeter results shown for
comparison:
48
RUN
3
4
5
6
8
9
10
VARIANCE Ctf^ry
.3095 (m/sec) 2
.2770 (m/sec.)2
.3979 (m/sec)2
.09 68 (m/sec)2
.0437 (m/sec)2
.1371 (m/sec)2
.0273 (m/sec)2
VARIANCE C
velocimeter
.0293 (m/sec)2
.0003 (m/sec)2
.0072 (m/sec)2
.0021 (m/sec)2
It was hoped that the results would indicate a theo-
retical variance slightly smaller than experimental variance
thereby implying the presence of other parameters such as
bubble presence to which the 3 MHz acoustic velocimeter
would have been insensitive. However, as seen above, the
experimental variance was much smaller than that calculated
from the variances of temperature and salinity. Analysis
of the wide discrepency led to the conclusion that since
all sensors appeared to have operated in an optimum manner,
and salinity and temperature signals were strong and yielded
good results, the sound velocity signal was suspect. The
signal had been filtered and amplified and conceivably could
have been altered, or else a mistake made in the data re-
duction settings . In order to determine which values of the
variance of sound velocity should be used for the remainder
of the analysis a final check of the results of both methods
was conducted. Part of the experiment involved the measure-
ment of sound amplitude modulation (see NPS thesis of LCDR
49
W. J. Smith, Jr., December 1971). Stone and Mintzer [Ref.
10] define the coefficient of variation (CV) as:
AP
CV
Pi2
where AP is the variation of the acoustic pressure relative
to the mean value P. In his experiment LCDR Smith measured
cr which he shows is related to CV by:
s J
(CV) 2 = 40 crs2
Chernov [Ref. 11] formulated the relationship:
(CV) 2 = n/tTU2 Kq2 aL
where ,
2ir
K0 = —
X
X = acoustical wave length
y2 = variance of sound velocity
a = correlation length (Gaussian correlation function
assumed)
L = distance between transducer and receiver
This relationship combined with the measured values of CV
and sound velocity variance, allowed for the calculation of
the correlation length:
RUN DEPTH a (from var C., ^ ) a (from var C_v . )
(m) (cm) rneory (cm) expt
5 6.9 175.0 2.699 x 10 5
3 9.3 157.5
4 13.9 452.5 4279.9
50
The values of "a" calculated from velocimeter data are un-
reasonably large. For this reason the theoretical sound
velocity variances are used throughout the remainder of the
analysis. A graphical plot of theoretical sound velocity
variances versus time of day with depths in parentheses are
shown in Fig. 15.
It is interesting to observe that Skudrzyk [Ref. 12]
also found patch sizes, which increased approximately
linearly with depth in approximatley the same manner as
shown above. However, Skudrzyk' s patch sizes were much
larger than reported here, probably due to his acoustic
range being much greater than in this experiment.
51
VII. CONCLUSIONS
A. Although the near surface regime is one of complex and
high variability, several conclusions can be made:
1. Temperature fluctuations decrease with depth during
the period just prior to sunset.
2. Temperature fluctuations increase with depth just
after sunrise, but are smaller in magnitude than the
fluctuations just prior to sunset.
3. Salinity fluctuations decrease with depth but are
larger in magnitude in the period after sunrise.
4. Sound velocity fluctuations normally follow the
trend of temperature variations. However, the im-
portance of salinity fluctuations cannot be neglected.
In one instance the salinity fluctuations had as much
an effect on sound velocity fluctuations as did tem-
perature fluctuations .
5. The maximum energy spectra of salinity and temper-
ature fluctuations occurred at frequencies that agreed
with dominant surface wave frequencies.
6. The sizes of patches of sound velocity fluctuations
were calculated from the statistics of sound amplitude,
temperature and salinity fluctuations. The implied
patch sizes increased approximately linearly with in-
creasing depth.
52
VIII. RECOMMENDATIONS FOR FURTHER STUDY
A. While the medium was described in terms of temperature
and salinity, a major question remains, "Are there other
variables that could affect the propagation of sound in
sea water?" In order to best achieve an answer to this
question one should ensure that a correct experimental
value of sound velocity is measured for comparison with
sound velocity computed theoretically. LCDR Smith's and
Rautmann's thesis work indicated the presence of bubbles
in the medium that could have a marked affect on sound
velocity.
B. In order to complete the description of the medium, an
analysis of the size of the "patches" of temperature and
salinity should be performed by use of arrays of sensors .
Application of knowledge of the drift velocity, in addition
to the procedures used in the present experiment, would
also enable patch size determination.
53
APPENDIX A
GENERAL DESCRIPTION OF BISSETT-BERMAN MODEL 9006 SALINITY,
TEMPERATURE AND DEPTH MEASURING SYSTEM [Ref. 13]
The model 9 006 STD is comprised of underwater sensors
and deck equipment whose functions are to furnish power to
the sensors and process data received from same.
In situ measurement of salinity is determined by measur-
ing conductivity, temperature and pressure. An inductively-
coupled sensor enables detection of conductivity, which is
also compensated for temperature and pressure effects,
thereby producing an output totally dependent upon salinity
The output shifts the frequency of a PARALOC signal pro-
viding an FM analog of salinity.
The temperature sensor uses a platinum resistance
thermometer and a PARALOC which provides an FM analog of
temperature .
The depth sensor utilized a pressure transducer into
which is incorporated a strain-gauge bridge circuit. The
changes in resistance are converted to a frequency analog
in the PARALOC.
The signal mixer receives and regulates power from the
deck equipment and sends it onto the underwater sensors.
It then multiplexes and amplified the FM signals from the
sensor and sends them to the deck equipment.
The distribution amplifier amplifies the FM signal
from the underwater units, and separates data signals from
54
the DC power which enters the distribution amplifier from
the power supply rack.
Each underwater sensor has a separate discriminator
which separates the mixed data signal into an individual
channel for recording availability. The discriminator
filters the desired signal and rejects others. The accepted
signal is amplified, squared, and converted to a 10 millivolt
DC level which is the output of the recorder. Dial readouts
enable continual monitoring of this signal.
The Power Supply is a model 86 0 0 and provides a constant
voltage of 26.5 volt DC to the deck units, and a constant
current of 150 milliamps at a maximum of 140 volts DC to the
underwater units. The underwater rack is stainless steel.
The sensors and mixer are mounted in individual shock-
absorbent brackets .
A single conductor cable provides for physical connec-
tion between sensors and deck equipment.
55
APPENDIX B
DATA CUMULATION AND RUN DESCRIPTION
The output DC voltage from the oceanographic sensors
was recorded on the Sangamo magnetic tape recorder as
explained in "Experimental Configuration" section. The
runs during which data were collected are described below
RUN
DEPTH
DATE
START TIME
STOP TIME
1
4. 3m
21
Oct
1419
1429
2
4.2m
21
Oct
1530
1550
3
9.0m
21
Oct
1616
16 36
4
13.9m
21
Oct
1648
1708
5
6.9m
21
Oct
1728
1748
6
4.3m
22
Oct
0354
0448
7
4.3m
22
Oct
0546
0622
8
9.5m
22
Oct
0650
0715
9
14.6m
22
Oct
0725
0749
10
7. 8m
22
Oct
0802
0821
11
8.2m
22
Oct
0832
0852
12
5. 7m
22
Oct
0929
0945
Run 3
salinity
thermistor 1
thermistor 2
SENSITIVITY SETTINGS
50 millivolts/millimeter
100 millivolts/millimeter
100 millivolts/millimeter
Run 4
salinity 50 millivolts/millimeter
thermistor 2 100 millivolts/millimeter
sound velocity 50 millivolts/millimeter
56
Run 5
salinity
thermistor 1
thermistor 2
sound velocity
Run 6
salinity
thermistor 1
sound velocity
Run 8
salinity
thermistor 1
sound velocity
Run 9
salinity
thermistor 1
Run 10
salinity
thermistor 1
50 millivolts/millimeter
100 millivolts/millimeter
50 millivolts/millimeter
20 millivolts/millimeter
50 millivolts/millimeter
10 0 millivolts/millimeter
50 millivolts/millimeter
100 millivolts/millimeter
100 millivolts/millimeter
100 millivolts/millimeter
100 millivolts/millimeter
100 millivolts/millimeter
50 millivolts/millimeter
100 mi Hi volts /millimeter
In addition to Bissett-Berman salinity measurements,
Nansen casts were taken during each run in order to monitor
the calibration correction which had to be applied to the
dial readout of the base value of salinity (see Table III) .
The correction factor was (-) 5.1 ppt. While this was a
high correction factor, pre-experiment checks on the STD
led to the assumption that the system was operating correctly
in the measurement of fluctuations and was consequently used
for that purpose.
57
Run
Depth
(Meters)
Time
Date
Salinity
(%)
2
4.2
1530
21 Oct
33.520
3
9.0
1636
21 Oct
33.512
6
4.3
0357
22 Oct
33.506
6
4.3
0410
22 Oct
33.478
6
4.3
0425
22 Oct
33.489
6
4.3
0442
22 Oct
33.484
7
4.3
0552
22 Oct
33.506
7
4.3
0559
22 Oct
33.480
8
9.5
0654
22 Oct
33.459
8
9.5
0659
22 Oct
3 3.43 8
8
9.5
0715
22 Oct
33.471
9
14.6
0725
22 Oct
3 3 . 4 6 q
10
7.8
0810
22 Oct
33.455
10
7.8
0817
22 Oct
33.463
11
8.2
0839
22 Oct
33.453
11
8.2
0852
22 Oct
33.455
12
5.7
0934
22 Oct
33.440
TABLE III
58
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FIGURE 24.
Temporal Correlatior
Thermistor 1 Run 5
6.9m 1728 21 Oct
Correlation Coef. (1^
Versus Time Lag
(0-40 Seconds) .
,
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FIGURE 27.
Temporal Correlation
Sound Velocity Run 5
6.9m 1728 21 Oct
Correlation Coef. (Max 1.0)
Versus Time Lag
(0-40 Seconds) .
•
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Sound Velocity Run 6
4.3m 0354 22 Oct
Correlation Coef. (Max 1.0)
Versus Time Lag
(0-40 Seconds) .
I
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14.6m 0725
Correlatio:
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(0-40 Seco:
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FIGURE 38.
Power Spectral Density
Thermistor 1 Run 3
9.0m 1616 21 Oct
Spectrum ((°C)2/HZ)
Versus Frequency (0-2.5
HZ) .
1 " -t
nc,
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0
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TV
iwV. .
v v/ v ■ v- V- W "\.'.'-Vv-^-,
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79
•
FIGURE 39.
Power Spectral Density
Thermistor 2 Run 3
9.0
m 1616 21 Oct
ctrum ((°C)2/HZ) —
Spe
Versus Freque
ncy (0-2.5
HZ) .
_
j
_______■___
:j5
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80
13
pa:
Cll
FIGURE 40.
Power Spectral Density-
Salinity Run 3
9.0m 1616 21 Oct
Spectrum (° / 0 0) 2 /HZ)
Versus Frequency (0-2.5 HZ)
A
Vf\JUil»
Wr
i_^JU
81
FIGURE 41.
Power Spectral Density
Thermistor 2 Run 4
13.9m 1648 21 Oct
Spectrum ((°C)2/HZ)
Versus Frequency (0-2.5 HZ)
J2 J
:ij
ft
\
v%
\ A
ft
i
-r-53— ?j
fw
v v
82
— V
!Ji3
^\
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w<
F
FIGURE 42.
BT3
Power Spectral Density
Salinity Run 4
13.9m 1648 21 Oct
Spectrum ((°/0o)2/HZ)
Versus Frequency (0-2.5 HZ)
iWUi
<TV
vV
P/i
inJV\
83
izt
1313
313
FIGURE 43.
?.15
Power Spectral Density
Sound Velocity Run 4
13.9m 1648 21 Oct
Spectrum (.(m/sec) 2/HZ)
Versus Frequency (0-2.5 HZ)
84
FIGURE 44.
Power Spectral Density
Thermistor 1 Run 5
6. 9m
Spec
Vers
1728 21 0
trum ((°/0
us Frequen
ct
0)2/HZ)
cy (0-2.5
HZ) .
-
1 - -
b jt.
-t i n
."-J
3i:
:js
1
I
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\
X
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yw vYvVx
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WvN
■'V V-*V^v-^"-
85
. ... . _, , ....
FIGURE 45.
Power Spectral Density
-i
Thermistor 2 Run 5
V
r
9m 1728 21 Oct
0 ■
Spectrum ((°C)2/HZ)
n
Versus Frequ
lency (0-2.
5 HZ) .
— i
£ ■
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86
FIGURE 46.
Power Spectral Density
Salinity Run 5
6.9m 1728 21 Oct
Spectrum ((°/oo)2/HZ)
Versus Frequency (0-2.5
HZ)
%\\,L
»•'>•■ 'W
87
FIGURE 47.
Power Spectral Density
Sound Velocity Run 5
6.9m 1728 21 Oct
Spectrum ( (m/sec) 2/HZ)
Versus Frequency (0-2.5
HZ)
V.
\A
X
>
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-88
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MIFUM
FIGURE 48.
Power Spectral Density
Thermistor 1 Run 6
4.3m 0354 22 Oct
Spectrum ( (°C) 2/HZ)
Versus Frequency (0-2.5 HZ)
J! i if,
! S r i i' I
31::
i 1 1
t-y- -';•-• 'v'l' , ■- — prVirifr'
,lji
-;t-
I <
89
a
o
lis p:o
FIGURE 49.
Power Spectral Density
Salinity Run 6
4.3m 0354 22 Oct
Spectrum ((°/oo)2/HZ)
Versus Frequency (0-2.5 HZ)
i'liUf./lAA (!
mi
■A
»#W
90
91
FIGURE 51.
Power Spectral Density
Thermistor 1 Run 8
9.5m 0650 22 Oct
Spectrum ((°C)2/HZ)
Versus Frequency (0-2.5 HZ)
I \« ■
92
i:i
-s*-
",i
.if?
FIGURE 52.
|D1.'.
r
Power Spectral Density
Sound Velocity Run 8
9.5m 0650 22 Oct
Spectrum ( (m/sec) 2/HZ)
Versus Frequency (0-2.5 HZ)
~f
<*v
•a
V u' i
93
n
t !
rt
*rr
FIGURE 53.
Power Spectral Density
Thermistor 1 Run 9
14.6m 072S 22 Oct
Spectrum ((°C)2/HZ)
Versus Frequency (0-2.5 HZ)
4-
N'i
'■ . • i :' >
; i
:V / ;i '. >
1 i' "».',:
_)
» f *.
94
I
V:
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l Y
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n>
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11 «'V\
i
Jl
P
fT
FIGURE 54.
Power Spectral Density
Thermistor 1 Run 10
7.8m 0802 -22 Oct
Spectrum ((°C)2/HZ)
Versus Frequency (0-2.5 HZ).
[■ItJ/tf
95
p:-'~
A
^T
r<
FIGURE 55.
Power Spectral Density
Salinity Run 10
7.8m 0802 22 Oct
Spectrum (<%o>2/HZ)
Versus Frequency (0-2.5 HZ)
J i / i « A i
ii V*' -- v « f '
f
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BIBLIOGRAPHY
1. Wilson, W. D., "Speed of Sound in Distilled Water as a
Function of Temperature and Pressure," The Journal
of the Acoustical Society of America, v. 31, p.
1067 - 1072, August 1959.
2. Wilson, W. D., "Speed of Sound in Sea Water as a Function
of Temperature, Pressure, and Salinity," The Journal
of the Acoustical Society of America, v. 32, p.
641 - 644, June 1960.
3. Mackenzie, K. V., "A Decade of Experience with Veloci-
meters , " The Journal of the Acoustical Society of
America, vT 50 , p. 1321 - 1332, November 1971.
4. Del Grosso, V. A., "Sound Speed in Pure Water and Sea
Water," The Journal of the Acoustical Society of
America , v. 47, p. 947 - 949, March 1970.
5. Leroy, C. C., "Development of Simple Equations for
Accurate and More Realistic Calculation of the Speed
of Sound in Seawater , " The Journal of the Acoustical
Society of America, v. 46, p. 216 - 226, June 1968.
6. Liebermann, L. , "The Effect of Temperature Inhomogeneities
in the Ocean on the Propagation of Sound," The Journal
of the Acoustical Society of America, v. 23, p. 563 -
570, September 1951.
7. Kadis, A. L. and Shonting, D. H. , "The Thermiprobe. A
System for Measuring Thermal Micros tructure in the
Sea," Instrument Society of America, Marine Sciences
Instrumentation , v. 4, p. 652 - 660, Plenum Press,
1968.
8. Sagar, F. H., "Acoustic Intensity Fluctuations and Tem-
perature Micros tructure in the Sea," Journal
Accoustical Society of America, v. 32, p. 112 - 121,
January 19 60 .
9. James, R. W., Ocean Thermal Structure Forecasting,
p. 105, U.S. Government Printing Office, 1966.
10. Mintzer, D. and Stone, R. G., "Transition Regime for
Acoustic Fluctuations in a Randomly Inhomogeneous
Medium," Journal Acoustical Society of America,
v. 38, p. 84 3 - 846, November 19 65. ""
11,
Chernov, L. S., Wave Propagation in a Random Medium,
McGraw - Hill, 1960.
104
19 Skudrzvk E. J., "Thermal Micros tructure in the Sea and
12. Skudrzyk^E.^.,^ to sound Level Fluctuations ,-
Chapter 12, underwater Acoustics V M Albers , ed. ,
p. 199 - 233, Plenum Press, New York, l9bJ.
c •*.*, tt t Tr Amplitude Modulation of an Acoustic
bnKed S tageTT^vaTTPostgra^^ , Monterey,
1971.
14 Rautmann J., Sound nf.pPrSion and Phase Fluctuations
14. Rautanann^ g^fr- acBany MS I'heBiB, Uiixled States Naval
Postgraduate School, Monterey, 19 71.
1R Duchock C. J., The Measurement and Correlation of
^ound vkocitv »ntf Temperature- ^y^txons ' ear
■the Sea Surface, MS Thesis, United States Naval
Postgraduate School, Monterey, 19 72.
16 Bordv M. W., Spectral Measurement of Water Particle
16 " B°T%iovhtlks^ez Waves, MS Thesis, United SLaLes
Naval Postgraduate School, Monterey, 19 72.
105
INITIAL DISTRIBUTION LIST
No. of Copies
1. Defense Documentation Center 2
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2. Library, Code 0212 2
Naval Postgraduate School
Monterey, California 9 39 40
3. Oceanographer of the Navy 1
The Madison Building
732 N. Washington Street
Alexandria, Virginia 22217
4. Department of Oceanography 3
Naval Postgraduate School
Monterey, California 9 39 40
5. Commander, Navy Ship Systems Command 1
Code 901
Department of the Navy
Washington, D. C. 20 30 5
6. Dr. Ned A. Ostenso 1
Deputy Director
Code 4 80 D
Ocean Science and Technology Division
Office of Naval Research
Arlington, Virginia 22217
7. Dr. Albert D. Kirwan, Jr. 1
Program Director/Physical Oceanography
Code 4 81
Ocean Science and Technology Division
Office of Naval Research
Arlington, Virginia 22217
8. LCDR Jon W. Carlmark (USN) 1
Project Office
Code 4 85
Ocean Science and Technology Division
Office of Naval Research
Arlington, Virginia 22217
9. Professor H. Medwin, Code 61 (thesis advisor) 5
Department of Physics
Naval Postgraduate School
Monterey, California 9 39 40
106
10. Dr. Noel E. Boston, Code 58 (thesis advisor) 3
Department of Oceanography
Naval Postgraduate School
Monterey, California 9 39 40
11. LT Harry A. Seymour, Jr. (USN) 2
USS FORTIFY (MSO-446)
FPO San Francisco 96601
12. Mr. William E. Smith 2
Department of Physics
Naval Postgraduate School
Monterey, California 9 3940
13. Professor David Mintzer 1
Technological Institute
Northwestern University
Evanston, Illinois 60201
14. Dr. E. B. Thornton, Code 58 3
Department of Oceanography
Naval Postgraduate School
Monterey, California 9 39 40
107
Security Classification
DOCUMENT CONTROL DATA -R&D
-Serurily CfMsHiC.Hon of title, body of abstr.c, and ,na>„n„ gnnoMTion n.u.st be enfer,* vvben th. ove,.» reporr I, f f.„,,„g-)
"'. origin* ting ACTIVITY (Corporale author)
Naval Postgraduate School
Monterey, California 93940
2a.»EPORT SECURITY CLASSIFICATION
Unclassified
2b. GROUP
3 REPORT TITLE
Statistical Relations Between Salinity, Temperature and Speed of
Sound in the Upper Ocean
« DESCRIPTIVE NOTES (Type 01 report and.inclusive dates)
Master's Thp.sis: March 1972
5. au THORI5I (First name, middle initial, last name)
Harry Augustus Seymour, Jr.
6- REPOR T D A TE
March 1972
Sa. CONTRACT OR GRANT NO.
6. PROJEC T NO.
7M. TOTAL NO. OF PASES
i09_
76. NO. OF REFS
16
9a. ORIGINATOR'S REPORT NUMBER(S)
9b. OTHER REPORT NO(S) (Any other numbers that may be assigned
this report)
10. DISTRIBUTION STATEMENT
App
roved for public release; distribution unlimited
11. SUPPLEMENTARY NOTES
12. SPONSORING MILITARY ACTIVITY
Naval Postgraduate School
Monterey, California 93940
13. ABSTR AC T
In situ measurements of salinity and temperature fluctuations at
depthi to~T4 meters indicate distinct dependences at different times
of the day. The variance of the salinity fluctuations decreased with
increasing depth, but was greater just after sunrise than just prior
to sunset. The variance of the temperature fluctuations decreased
with increasing depth just prior to sunset, but increased with depth
immediately after sunrise. The correlation length of the sound index
of refraction was calculated by using the variance of the sound
velocity fluctuations, and the variance of sound amplitude modulation
in the theory of Mintzer. This analysis shows that microstructure
patch size increases approximately linearly with depth. The power
spectral densities of the salinity, temperature and sound velocity
fluctuations show peaks of energy corresponding to dominant ocean
wave frequencies.
FORM
i nov esl^T / O
S/N 0101 -807-681 1
DD
(PAGE 1)
108
Security Classification
A-31408
Security Classification
KEY WO R O $
Salinity
Temperature
Sound Velocity
Variance
Correlation Length
Power Spectral Density
Temporal Correlation
DD
FORM
I NO V 68
1473
(BACK)
S/N 0101-807-6821
109
Security Classification
A-3M09
'/ JUt 73
'bOOT 7 4
13 AUG79
9 I
I
_2600U
^Z 6 ♦; O fl 9
Thesis
S423
c.l
TH
s1
133852
Seymour
Statistical rela-
tions between salinity,
temperature and speed
of sound in the upper
ocean.
7 JUL 73
*CT 74
13 AUG79
J U I 8 I
s*m
Thesis
S423
c.l
133852
Seymour
Statistical rela-
tions between salinity,
temperature and speed
of sound in the upper
ocean.
thesS423
^2Sl:^t,0nsbe^een salmi
ty.
3 2768 001 94515 7
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