SPECTRAL ANALYSIS OF THE
ENERGY EXCHANGE AT OWS NOVEMBER

Kevin Merle Rabe

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Spectral Analysis of the
Energy Exchange at OWS NOVEMBER

by

Kevin Merle Rabe

March 1975

Thesis Advisor:

R. H. Bourke

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Spectral Analysis of the Energy
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March 1975

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Kevin Merle Rabe

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Spectral Analysis
OWS November
Heat Budget
Sea-Surface Temperature

20. ABSTRACT (Continue on reveree elde 11 neceeeery end Identity by block number)

Oceanographi c and meteorological data from Ocean Weather
Station (OWS) NOVEMBER were analyzed by statistical and
spectral methods in order to describe the nature and perio-
dicities of the air-ocean energy exchange. Salinity data
from 1968 through 1970 were compared with daily observed
parameters commonly associated with changes in the salinity.
Regression analysis showed surface salinity to be highly

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20. Abstract (continued)

correlated with surface pressure which is interpreted as the
surface salinity responding to a baroclinic transport. At
this location none of the classical parameters usually
associated with fluctuations in the surface salinity were
highly correlated.

Twenty-four years (1947-1970) of daily averaged,
observed cl imatol ogi cal values, as well as heat exchange
terms computed from them, were compared with the sea-surface
temperature time series and spectrally analyzed. The
spectral analysis yielded spectral density, phase and
coherence functions indicating the response of surface
temperature to the heat exchange terms. From these it was
evident that at the yearly cycle the net heat exchange, whi ch
is shown to be equal to the horizontal heat advection, is
of the same order of importance as solar radiation in its
effect on the fluctuation of sea-surface temperature.

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Spectral Analysis of the
Energy Exchange at OWS NOVEMBER

by

Kevi n Merl e ,Rabe

Environmental Prediction Research Facility

B.A. , University of Washington, 1970

B.S., University of Washington, 1970

Submitted in partial fulfillment of the
requirements for the degree of

MASTER OF SCIENCE IN OCEANOGRAPHY

from the

NAVAL POSTGRADUATE SCHOOL
March 1975

i

library

2WS£

ABSTRACT

Oceanographi c and meteorological data from Ocean Weather
Station (OWS) NOVEMBER were analyzed by statistical and
spectral methods in order to describe the nature and perio-
dicities of the air-ocean energy exchange. Salinity data
from 1968 through 1970 were compared with daily observed
parameters commonly associated with changes in the salinity.
Regression analysis showed surface salinity to be highly
correlated with surface pressure which is interpreted as the
surface salinity responding to a baroclinic transport. At
this location none of the classical parameters usually
associated with fluctuations in the surface salinity were
highly correlated.

Twenty-four years (1947-1970) of daily averaged,
observed cl imatol ogi cal values, as well as heat exchange
terms computed from them, were compared with the sea-surface
temperature time series and spectrally analyzed. The
spectral analysis yielded spectral density, phase and
coherence functions indicating the response of surface
temperature to the heat exchange terms. From these it was
evident that at the yearly cycle the net heat exchange, whi ch
is shown to be equal to the horizontal heat advection, is
of the same order of importance as solar radiation in its
effect on the fluctuation of sea-surface temperature.

TABLE OF CONTENTS

I. INTRODUCTION - - 12

A. OBJECTIVE 12

B. REVIEW OF THE LITERATURE -- 14

1. The Subtropic Region 14

2. Surface Circulation 16

3. The Subarctic Transition Zone 16

4. Average Annual Heat Balance 20

5. Surface and Subsurface

Temperature Anomalies 21

6. Recent Studies of Pacific Air-Sea
Interactions 23

II. TREATMENT OF THE DATA - 26

A. SOURCES 26

B. TREATMENT OF THE DATA TIME SERIES 26

C. THE HEAT BUDGET EQUATIONS 27

D. COMPUTATION OF PRECIPITATION 31

E. COMPUTATION OF THE ENERGY SPECTRUM r 33

F. COMPUTATION OF THE CROSS-SPECTRAL DENSIY 34

G. COMPUTATION OF THE COHERENCE FUNCTION 35

H. COMPUTATION OF THE PHASE ANGLE -- 36

III. RESULTS 38

A. REGRESSION ANALYSIS 38

B. SPECTRAL ANALYSIS - --- 46

IV. CONCLUSIONS 75

APPENDIX A - THE AUTOCORRELATION FUNCTIONS 77

APPENDIX B - FIFTEEN-YEAR TIME SERIES SEGMENTS 95

LIST OF REFERENCES 102

INITIAL DISTRIBUTION LIST -105

LIST OF TABLES

I. Correlation coefficients by season, resulting
from a linear regression analysis of surface
temperature, surface salinity, and 50 meter
temperature data, 1968 through 1970 44

II. Correlation coefficients, all parameters

vs surface salinity 45

III. Contribution of the yearly cycle to the

total variance 47

IV. Spectral results for the solar radiation,
sea-surface temperature, and cloud cover
at the yearly cycle 48

V. Months of maximum and minimum value for the

surface temperature and the heat budget terms 52

VI. Spectral results for the back radiation and

related parameters at the yearly cycle 53

VII. Spectral results for tne heat of evaporation

and related parameters at the yearly cycle 60

VIII. Spectral results for the convective heat vs

the SST at the yearly cycle 69

IX. Spectral results for the net radiation and

related parameters at the yearly cycle 70

LIST OF FIGURES.

1. Oceanographi c climatic regions of the North
Pacific Ocean showing the location of Ocean

Weather Station November at 30° north, 140° west -- 15

2. Winter surface circulation patterns for the

North Pacific Ocean 17

3. Summer surface circulation patterns for

the North Pacific Ocean 18

4. Monthly means of the observed surface
temperatures, 1968 through 1970 and Robinson's

(1971) long-term monthly means 39

5. Total monthly meridional transport between 135°
and 145° west at 30° north during 1969 and 1970.
Positive northward, negative southward 40

6. Monthly means of observed surface salinity,

1968 through 1970 - 42

7. Monthly temperature and salinity modal points
resulting from the bivariate analysis of the

data, 1968 through 1970 - 43

8. Spectral density, coherence and phase for

the SST vs the solar radiation 49

9. Spectral density, coherence and phase for

the SST vs cloud cover 50

10. Spectral density, coherence and phase for

the solar radiation vs cloud cover 51

11. Spectral density, coherence and phase for

the SST vs the back radiation 55

12. Spectral density, coherence and phase for

the SST vs air temperature 56

13. Spectral density, coherence and phase for

the SST vs the air-sea temperature difference 57

14. Spectral density, coherence and phase for

the SST vs the vapor pressure of the air 58

15. Spectral density, coherence and phase for

the back radiation vs cloud cover 59

16. Spectral density, coherence and phase for

the SST vs the heat of evaporation 62

17. Spectral density, coherence and phase for

the SST vs the vapor pressure difference 63

18. Spectral density, coherence and phase for

the SST vs the wind speed 64

19. Spectral density, coherence and phase for

the SST vs the wind speed squared 65

20. Spectral density, coherence and phase for

the SST vs the evaporation 66

21. Spectral density, coherence and phase for

the SST vs the convective heat 68

22. Spectral density, coherence and phase for

the SST vs the net radiation 71

23. Spectral density, coherence and phase for

the SST vs the surface pressure 73

24. Spectral density, coherence and phase for

the net radiation vs the surface pressure 74

LIST OF SYMBOLS

SST

PS

W

W2

E

P

Ta

Tw
CL

ew

ea

CD
S

QS

QB

QE

QC

QN

Sea-surface temperature (°C)

Surface pressure (mb)

Wind speed (m sec" )

Wind speed squared

Evaporation (cm)

Precipitation (cm)

Air temperature (°C)

Water temperature (°C)

Cloud cover, in tenths of sky covered

Vapor pressure over water (mb)

Vapor pressure of the air (mb)

The drag coefficient

Salinity (°/00)

-2 - 1
Solar radiation (cal cm day )

-2 - 1
Back radiation (cal cm day )

-2 - 1
Heat of evaporation (cal cm day )

- 2 - 1
Convective heat (cal cm day )

-2 - 1
Net radiation (cal cm day )

10

ACKNOWLEDGMENTS

The author wishes to thank Dr. Robert Bourke for his
assistance and guidance, both during the course of this
research and the preparation of this thesis, and also, Dr.
Dale Leipper and Dr. Edward Thornton for their constructive
review of the text. Thanks are also extended to various
personnel at both the Environmental Prediction Research
Facility and Fleet Numerical Weather Central through whose
assistance the opportunity to conduct this research was made
possible. They are: Captain G. D. Hamilton, past Commanding
Officer at EPRF, Captain R. C. Sherar, present Commanding
Officer, Dr. Taivo Laevastu, my immediate supervisor, and
Captain C. Barteau, formerly Chief of Development at FNWC.

11

I. INTRODUCTION

A. OBJECTIVE

Sea-surface temperature is one of the most important
parameters in any study of air-sea interaction. Anomalies
of this parameter, measured over periods of a week to
several months, have been linked to gross atmospheric
effects. However, few studies have investigated the time
response of the sea-surface temperature over long periods
to those factors which govern its fluctuations.

Until the more recent decades such a study would have
been limited by both instrumentation and general paucity
of data. This resulted in reliance upon monthly or annual
means to describe the state of the ocean. The advent of the
ocean weather station program in the 1940's, and recently,
the use of satellites has greatly increased the amount and
frequency of data available to the researcher. Also, the
advent of high speed computers has made the use of time
series analysis routines relatively easy and inexpensive to
use .

The past limitations made statistical studies of changes
of surface temperature on time scales of a day or less,
difficult. However, daily fluctuations can be quite inform-
ative. If advection is ignored, the sea-surface temperature
at OWS NOVEMBER was found to fluctuate primarily in response
to the day to day changes in air temperature, the amount of

12

insolation, wind-wave mixing, and the amount of cloud cover
as well as the elevation of the sun. The magnitude of
these diurnal fluctuations can be as large as the monthly
fluctuations.

Sea-surface temperature fluctuations are important in
many oceanographi c parameters, such as the stability of the
water column. This, in turn, is of great consequence in
sound propagation. Anomalies of sea-surface temperature,
likewise, have been linked to climatic variations over the
ocean.

The salinity is important in that it affects the
density of sea water. Thus, it affects both vertical
stability and sound propagation. Together with the water
temperature, one can infer transport characteristics of a
region based on water mass analysis.

This study examines changes occurring at the surface
of the ocean over time scales varying from one day to
several years. The two parameters of primary interest are
the sea-surface temperature and surface salinity. The area
of study is Ocean Weather Station (OWS) NOVEMBER located at
30° North and 140° West. The data used are synoptic data
collected by the United States Coast Guard at this position.
The data are of two types: hydrographic Nansen cast data and
shipboard meteorological observations.

The thesis is organized to first present correlations
of the primary parameters versus various meteorological
parameters. These correlations provide an indication of

13

those parameters which can be used as predictors for the
sea-surface temperature and salinity.

Secondly, a spectral analysis of the data is made.
From this, the synoptic atmospheric mechanisms which cause
the fluctuations of the sea-surface temperature are identi-
fied. Periods of high spectral energy, along with their
corresponding phase and coherence relationships are examined
to gain insight into the time scales associated with each
mechanism.

B. REVIEW OF THE LITERATURE
1 . The Subtropic Region

Ocean Weather Station NOVEMBER, located at 30°
North and 140° West, lies within what Tully (1964) defines
as the Pacific Subtropical Region. Figure 1 shows its
location in comparison to other major features of the North
Pacific Ocean. The region is characterized by three dominant
conditions: an excess of evaporation over precipitation
throughout the year, the occurrence of convective mixing,
and seasonal heating and cooling patterns which result in a
pronounced seasonal thermocline.

The excess of evaporation over precipitation (E-P),
has a distinct effect on the other two traits. Tully (1964)
estimated E-P to be approximately 80 cm" yr in the vicinity
of OWS NOVEMBER. This leads to a removal of fresh water
from the surface and acts as a driving force for the con-
vective mixing. This mixing then contributes to the erosion
of the seasonal thermocline.

14

15

2 . Surface Circulation

The subtropical region of the Pacific is dominated
by the Pacific Gyre. Figures 2 and 3 show graphically how
the gyre varies seasonally both in location and intensity.
In the winter the gyre's axis is displaced northward; in
summer it is shifted approximately 100 n mi southward and
intensifies by approximately 0.2 kt. Throughout the year
the current speed ranges from 0.1 to 0.3 kt. Hansen (1973)
hypothesized that this intensification occasionally results
in the advection of large volumes of cold subarctic water
into the area surrounding 0WS NOVEMBER, specifically during
the period of 1968 through 1970.

3. The Subarctic Transition Zone

The North Pacific Gyre, linked with the Subarctic
Gyre, is also involved in the formation of a transition zone
which bounds the subtropical region to the north. Roden
(1970) first described the subarctic transition zone as an
area characterized by large temperature and salinity gradients
and low hydrostatic stabilities. This oceanic front defines
the boundary between the subtropical and subarctic water
masses, varying in location between 30° and 40° North.
Subsequent articles by Roden (1971, 1972) further described
this zone in the North Pacific.

The transition zone is largely maintained by the
surface wind stress. Its northern boundary is characterized
by the subarctic water mass, resulting in temperature

16

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inversions, gravitational instabilities, a complicated sound
velocity structure, and a disappearance of the subarctic
halocline. It appears to lie in the area of 40N to 45N
latitude throughout the year.

The southern boundary lies in the area of 30N to
32N, depending upon the season, and is displaced to the
north more in the winter months. It is characterized by
sharp temperature gradients in the thermocline and vertical
instabilities in the mixed, upper layers. A salinity minimum
is a common occurrence at this boundary. Also, around 30N
there is a transition toward the higher salinities and
higher temperatures of the subtropical water mass with
salinities greater than 35°/00 and a strong halocline located
at a depth between 50 m and 100 m.

Thus, the transition zone is defined by a deep
salinity minimum, at approximately 500 m and a concurrent
sound velocity minimum of less than 1480 m sec- . There is
apparently both a seasonal and yearly variation in the posi-
tion of the boundary (Seckel, 1968). Both the salinity
minimum and sound velocity minimum rise as one goes further
to the north. Roden (1970) also examined both barotropic
and baroclinic motion in the transition zone and found that
they rarely exceeded 5 cm sec" .

As the transition zone approaches North America,
it turns to the southeast and becomes associated with the
heat and salt flux divergence zones noted by Roden (1971)

19

in the area of OWS NOVEMBER. These are related to flux
divergencies which are linked to the presence of horizontal
advection of salinity as has been noted by Hansen (1973).
4. Average Annual Heat Balance

Based upon an examination of the annual heat
balance of the North Pacific Ocean and the prevalent circu-
lation patterns, Wyrtki (1965) determined that there is a
small amount of heat gain in the vicinity of OWS NOVEMBER.

On the average, he estimated this gain to be approximately

- 1 -2

25 ly day (where a langley, ly, = 1 ca 1 cm ).

Seckel (1970) computed the heat balance for the
area of OWS NOVEMBER during the Trade Wind Zone Pilot Study
His studies showed that the average net radiation computed
on a daily basis was approximately 3 ly day" .

In a more recent study, Dorman (1974) studied 20
years of the heat balance at OWS NOVEMBER and separated it
into two decades, 1951 through 1960 and 1961 through 1970.
He found the two decades had distinctly separable heat
balances, with the first decade having a deficit of
90 ly day" and the second a 40 ly day" deficit. These
results were based on three-hourly meteorological observa-
tions. Dorman ascribed this difference to the change in
climatic regimes described by Namias (1970, 1971), which
resulted in displacement of cooler waters in the North
Central Pacific by warmer water, beginning approximately in
1961.

20

5 . Surface and Subsurface Temperature Anomalies

The sea-surface temperature and its anomalies have
been widely studied in their relationships to both oceano-
graphic and meteorological forecasting. Emphasis has also
been placed on subsurface temperature anomalies. Beland
(1971) illustrated their considerable importance to the flow
of energy between the sea and the atmosphere. Bernstein
(1974) used subsurface temperature measurements in the trade
wind region northeast of Hawaii to identify mesoscale eddies
drifting westward.

Namias (1971) in his study of an anomalous warming
of the northeastern Pacific from May to June 1968, found the
anomaly extended to a depth of 122 m. The warming, as a
whole, was attributed to increased insolation and horizontal
convergence of surface waters with its associated down-
welling. The warming was identified with the development
and maintenance of a Pacific anticyclone in June of 1968.
The depth of the anomaly was attributed to bulk heating and
downward advection of the warmer surface waters.

Clark (1972) concluded that both advection and
non-advecti ve processes are vital in determining the nature
of surface temperature anomalies. He hypothesized that
advection is the more important process in the winter and
spring seasons, while the non-advecti ve processes dominate
in the summer and fall.

21

Beland (1971) in his study of the North Pacific,
observed that about 50% of the near-surface temperature
anomalies extended to at least 100 m depth. Most of these
were negative anomalies in the months of March and April,
apparently due to the distribution of heat throughout the
upper layer by convective mixing. Positive anomalies were
more common in December through February and were confined
to the upper 30 m. Whereas the negative anomalies were of
a magnitude of 1.0°C or more, the positive anomalies were
generally less than 1.0°C.

Finally, Favorite and McClain (1973) reported that
they could observe an orderly trans-Pacific movement of
areas of anomalously warm and cold surface waters. These
features were found to be quasi -permanent and apparently
move around the North Pacific gyre, approximately 180 degrees
out of phase and with periods of 5 to 6 years. These
anomalies have been shown to have a great influence on the
weather conditions off the west coasts of Canada and the
United States, as shown by Namias and Born (1970).

From the above it can be noted that temperature
anomalies, both surface and subsurface, and whether temporary
or periodic, inhabit the region around 0WS NOVEMBER, and in
all probability, affect the location of the subarctic
transition zone and the heat balance through the process of
advection .

22

6 . Recent Studies of Pacific Air-Sea Interactions
In recent years there have been three studies
of the air-sea relationships at or around OWS NOVEMBER by
different researchers using three different methods. Taken
as a whole, they provide a logical progression, resulting
in the methods utilized in this study. The first of these
studies was carried out by Seckel and Yong in 1970, using
harmonic analysis to study temperature and salinity fluctua-
tions at Koko Head, Hawaii, and Christmas Island. Hansen
(1973) used regression methods to study surface and
subsurface temperatures and salinities at OWS NOVEMBER.
Dorman (1974) used a spectral approach on time series of
meteorological values at OWS NOVEMBER, dividing the time
series into two ten-year decades. Since each of these
studies utilized a different approach, each will be described
in some detail here.

Seckel and Yong (1970) utilized temperatures and
salinities measured at two points in the North Central
Pacific; Koko Head, Hawaii, beginning in 1956 and running
through 1969, and Christmas Island, beginning in 1954 and
continuing through 1969. Their hypothesis was that
fluctuations in the temperature and salinity time series
reflected air-sea interaction processes (heat exchange, E-P)
and oceanographic processes (advection, diffusion, etc.).
Their approach used a Fourier series to provide a least
squares fit to the observed values, which was done for each
year of the available data. This approach expressed the

23

temperature and salinity as a function of time. Phase
angles and coefficients for each year of salinity and temper-
ature data from both locations were computed and tabulated.

The results at Koko Head showed seasonal varia-
bility in the salinity, but not the temperature series. At
both locations the annual cycle (n=l) was the dominant cycle
Also of note were the 60- and 52-day cycles, ascribed by the
authors to the presence of large geostrophic eddies. The
Christmas Island results were quite similar except that they
lacked evidence of the eddy- induced seasonal variations.

The next major method was a regression analysis
used by Hansen (1973) in his study of temperature and
salinity fluctuations at the surface, 50 m, and 200 m at
OWS NOVEMBER. His data were for 1968 through 1970 and
consisted of daily hydrographic records. Deterministic
approaches showed that the temperature system was seasonal
so the data were divided into four seasonal records,
February to April, etc., in three month segments correspond-
ing to Spring, Summer, etc. Regressions were then computed
with the surface salinity, and 50 m and 200 m temperatures
being regressed against the surface temperatures.

Most of the results showed little correlation,
except occasionally during the spring and fall transition
periods. Only a very poor correlation was found between the
surface salinity and the surface temperature. From this, it

24

was concluded that these seasonal correlations were due to
the advection of water by the shifting of the subarctic
transition zone.

The final approach was that utilized by Dorman
(1974) who computed spectra for surface wind speed, air
pressure, sea temperature, air temperature and dew-point
temperature for the 10-year period 1961 through 1970.
Spectra were also computed for each of the four seasons.
From this it was found that the energy peaked significantly
at the annual, diurnal and semi-diurnal periods. Variances
were largest in the winter season and smallest in the
summer season, except for the sea-surface temperature which
had its largest variance in the spring and the smallest in
the winter. The maximum spectral density, for all variables ,
was at the annual period. From the annual period the
spectral densities followed a decrease to the shorter periods,
where significant spikes at the diurnal and semi-diurnal
periods were noted in many of the spectra.

25

II. TREATMENT OF THE DATA

A. SOURCES

The cl imatol ogi cal data used in this study were taken
from the NWRC, Asheville data file of ocean weather station
observations. These observations were begun at OWS NOVEMBER
in 1947 and have continued to the present. The observations
were taken e\/ery three hours, except for some short periods
when all or only some of the observations were not taken for
some parameters. The data extracted included the sea-surface
temperature, air temperature, wind speed, surface pressure,
cloud amount and the present weather codes for 1947 through
1970.

The salinity data used in this study came from the NODC
hydrocast data. Since July 1966, the U.S. Coast Guard has
conducted a continuing program of collecting Nansen cast
data at OWS NOVEMBER. The surface salinity data for 1968
through 1970 was utilized in one segment of this study.

B. TREATMENT OF THE DATA TIME SERIES

Daily surface salinity values from 1968 though 1970
were extracted from the NODC data set and any gaps in the
series were linearly interpolated. The daily salinity values
were then included with surface pressure, evaporation, solar
radiation, heat of evaporation, and wind speed, all taken
directly from or computed from the Asheville data set. To
this was added the calculated values of precipitation and

26

the evaporation minus precipitation terms to form a three-
year time series which was then used in the regression
analysis segment of this study.

The Asheville meteorological data were used primarily
to create the 24-year (1947-1970) time series used in the
spectral analysis segment of this study. The values of SST,
air temperature, cloud amount, air-sea temperature difference,
the saturated vapor pressure of the air, the vapor pressure
over the water, wind speed, surface pressure and wind speed
squared were extracted or computed for ewery three hours
and then converted into daily average values and these were
the values utilized in all the spectral analyses. For the
cloud amount parameter, only daylight observations were used.
From these data sets the heat budget terms were computed on
a daily basis. For the occasional gaps in the data, linear
interpolations were made.

C. THE HEAT BUDGET EQUATIONS

Empirically derived formulas were used to create the
heat flux data for this study. The heat budget equation
utilized excludes the effects of heat gained or lost by
ocean currents :

HEAT CHANGE = HEAT INCOMING - HEAT LOSSES
QN = QS - QE - QB - QC

(1)

27

where QN is the measured heat change, i.e., the heat gained
or lost by the water due to the exchange processes. On the
right-hand side of the equation, QS is the incident solar
radiation, QB is the effective back radiation, QE is the
heat of evaporation and QC is the conduction of sensible
heat. Each of these terms will be described in detail below
as to their formulation.

The equation used for QS is an improved version of that
described by Seckel (1970). The basic form is:

QS = Q0K

where

(2)

Q = A + A, cos<j> + B, sin* + Ap cos2<}> + B2 sin2<}> (3)

From the Smithsonian Tables (List, 1951), utilizing a
transmission coefficient of 0.7, the above terms can be
computed as follows for latitude 30N:

A

i

A

A,

B,

32.65 + 674.76 cosi

19.88 + 397.26 cos (£+90) =

6.75 + 224.38 sin i

1 .32 + 16.10 sin 2(x-45) =

1 .04 + 29.76 cos 2(5,-5) =

551 .7

(4)

-178.7

(5)

105.4

(6)

- 9.4

(7)

18.1

(8)

where :

l is the latitude

t is the time of the year in days

C is the cloudiness in tenths, ranging from 0 to 1, and

28

*

2 7T

365

(t-21)

(9)

The cloud factor correction utilized was one for
cumulus type clouds (Seckel, personal communication):

K = 1 .0 - 0.012C - 0.363C

(10)

An albedo factor of 0.95 was utilized.

The new equation results in values approximately one-
fourth to one-third greater than previously estimated.

The effective back radiation, QB, is a Berlyand
expression utilized by Seckel (1970):

QB = 1.14 (10)"7 (273.16 + T ,)4

w

(11)

(0.39 - 0.05 fe~) (1 - 0.6CT)

a

+ 4.58 (10)"7 (273.16 + T )3

<Tw - V

where T is the sea-surface temperature in degrees C. It

w r a

utilizes a cloud coefficient of 0.6 and neglects latitudinal
variation.

QE, the heat of evaporation depends upon the difference
between the saturation vapor pressure over the sea at the
sea-surface temperature and the vapor pressure of the air
above the sea surface:

QE = 3767 Cn (0.98 e -e ) W
D w a '

(12)

29

where:

e is the vapor pressure of the air (mb)
a

e is the saturation vapor pressure over water
at sea-surface temperature (mb)

CD is the drag coefficient

-1

W is the wind speed (m sec" )

Whereas Seckel utilized a varying drag coefficient, this

_3
study utilized a constant drag coefficient of 1.3 x 10

As in Seckel's study, the vapor pressure difference was

multiplied by 0.98 to account for the salt effect.

The final heat balance term is the conduction of

sensible heat, QC:

QC = 4 (Tw-Ta) W

(13)

where :

T, is the sea-surface temperature (C)
w r

T is the air temperature (C)
a

W is the wind speed (m sec" )

It can be seen readily that QC is dependent upon two factors,
the air-sea temperature difference and the wind speed. It
is usually the smallest of all the heat exchange terms. As
with Seckel's study, a conduction factor of 4.0 is used.

The above equations were those used to create the five
heat flux time series used in this study. QS was computed
using only the daylight cloudiness observations, night

30

values being ignored. A daily value for each day was
calculated for the span of 1947 through 1970. They were
compared with Seckel's (1970) results to guarantee their
accuracy, where possible. The utilization of the newer QS
formula resulted in higher values for this term than he
reported and correspondingly more positive values of QN.

D. COMPUTATION OF PRECIPITATION

In relation to the study of the surface salinity at
OWS NOVEMBER, it was vital to have some measurement of E-P,
the evaporation-precipitation term. The evaporation was
readily available, having been calculated from the data
already available. However, no direct measurement of pre-
cipitation is made routinely at ocean weather stations.
To gain a measure of the precipitation, Tucker's (1961)
method was used. Elliot and Reed (1973) applied this method
along the Pacific Northwest Coast with good results. This
approach is based on the current weather code which gives a
numerical value to the type of weather being observed at
three hour intervals; this yields an estimation of the amount
of rainfall. The amount of rainfall was based on the amount
of precipitation observed for a similar weather code at a
land station where actual rainfall measurements were avail-
able. Based on a frequency analysis for all the codes and
the measured rainfall, Tucker was able to fit a numerical
system of equations to the prediction of precipitation,
using only the weather code as an input.

31

In Tucker's system all codes less than 50 are rejected
since they contribute no appreciable amount of precipitation.
The codes used had values ranging from 50 to 99. Each of
these codes is associated with a term made up of some combi-
nation of three rainfall parameters. These are x, associated
with light, continuous rainfall; y, associated with moderate,
continuous rainfall; and z, which is a measure of heavy,
continuous rain. These three parameters satisfy the follow-
ing criteria:

y = nx mm where 1 <n<5
z = my mm where l<m<3
z = 10 mm (in 3 h r )

For this study x was set equal to 1.85, y = 5.66, and
z = 8.13, the same values as derived by Tucker from his
frequency distributions of the codes recorded and the actual
rainfall at land stations. Thus, the amount of rainfall,
in millimeters, associated with each current weather code
can be determined from one of the above, or a combination or
ratio of these terms. For example, weather code 64, which
is "rain, not freezing, intermittent, but heavy at the time
of observation", is described by the term z/2. Likewise,

code 84, "showers of rain and snow mixed, moderate to heavy",

v + z
is represented by the formula, ^j- .

32

For the purposes of this study, the precipitation was
calculated every three hours and then summed to obtain the
total precipitation for that particular day. This was then
subracted from the evaporation term for that day to yield
the E-P time series for 1968 through 1970.

E. COMPUTATION OF THE ENERGY SPECTRUM

The covariance function, R (x), of a time series of

A A

random data is a measure of the general dependence of the
values of the data at one time, t, with the values at
another time, t+x. The covariance equation in integral form

is :

Rxx<^

= lim I x (t) x (t+x) dt

(14)

This yields the average of the product of the value of a
data point, x(t), with that of x(t+x), a point at some
lagged time increment, x. As T approaches infinity, the
resulting average product approaches the exact auto-
covariance function.

Since this data forms a finite data set, a lag window
is applied to the covariance function. The Parzen window
used in this analysis is defined as:

P(x) = l-6(x/Tm)2 + 6(x/Tm)3 x = 0,1,2 --- 1J2 (15)

= (1-tx/T.))

= 0

x = T /2 + 1 , ---T (16)
m m v '

= T.

m

(17)

33

where T is the lag and T is the total lag time. This
window has the desirable effect of minimizing any numerical
instability due to side lobe resonance (Bendat and Piersol,
1971).

The energy -density spectrum is obtained by Fourier
transforming the covariance function. The form of the
energy-density spectrum, corrected by the Parzen window is:

/

Sxx(f) = P(t) Rxx(t) e"12nfTdT <18)

with f being a specific frequency. The energy-density
spectrum is the statistical estimate of the energy-density
distribution for the frequency bands forming the total
spectrum.

F. COMPUTATION OF THE CROSS-SPECTRAL DENSITY

When comparing two-time series of the same length and
time interval, the cross-covari ance function similar to the
covariance function, is used. For a given lag time interval,
t, it has the form:

T

Rxy(x) = lim 7 / x (t)y (t+x) dt' (19)

T-*-°° o

Because the data sets are records of finite length, the
Parzen lag window is applied. Thus, similar to the covariance
function and the spectral density, the cross-spectral density
is the Fourier transform of the Parzen window lagged, cross-
covari ance function.

34

The cross-spectral density is a non-zero function
having real and imaginary parts of the form:

Sxy(f) = / P(t) Sxy(x) e-i27TfT d

(20)

which can be expressed in terms of its real and imaginary
parts :

S (f) = C (f) - 1Q (f)

where C (f), the real co-spectrum, is given by:
xy

(21)

Cxy(f) = 2 f [Sxy(x) + Sxy(-x)] cos (2irfx) dx (22)

and the imaginary quadrature spectrum, QYV (f)

xy

Qxy(f) = 2 / [Sxy(x) ■ Sxy("x)] sin (2llfT) dx (23)
o

G. COMPUTATION OF THE COHERENCE FUNCTION

The coherence function, for two records x and y, is a
measure of the statistical dependence of two series. The
coherence is defined as:

2 [S (f)]
xy

xx v ' yy '

(24)

where :

0 < Y (f) <T.

xy

35

o

If Y w(f) = 1» f°r a^ frequencies, then the two records
xy

are totally coherent and statistically dependent. If

Y (f) = 0 for all frequencies, then the x and y records

xy

are totally independent. For intermediate range coherences

three conclusions may be inferred concerning the two records
(Bendat and Piersol, 1966); (1) the systems are non-linear,
(2) noise is present in the measurements, or (3) the output
response is due to more than one input function. It should
be noted that this is the coherence squared, but will here-
after be referred to as the coherence.

H. COMPUTATION OF THE PHASE ANGLE

The average angular difference by which the cross-
correlated points in y(t) lead their corresponding components
of x(t) is called the cross-spectral phase angle, e xv(f)-
It is computed from the co- and quad-spectra by:

exy(f) = arctan [Qxy(f ) / Cxy(f)] (25)

Since this study deals with a time step of one day, the
phase angles can be converted to a lag in days from:

e (f) * 0.01745
L(days) = -^ (26)

f*2TT

When either the value of the phase angle (measured in
degrees) or the lag time (in days) is positive, then y(t)
lags behind x(t) by that amount; if the value is negative,
then x(t) lags behind y(t).

36

In the computations involved in this study there were
8766 data points. A standard lag of 876, 10% of the total
time series, was used. The 90% confidence interval for the
energy densities was computed by the formula:

r - £3.7
M

(27)

when N = 8716, M = 876.

The limits were found from tables to be:

a = 24.075

b = 52.192
where a and b are the values which when subtracted and
added, respectively, to the value of the spectral energy
density result in the lower and upper 90% confidence limits

37

III. RESULTS

A. REGRESSION ANALYSIS

The regression analysis phase of this study was limited
to the three-year time series of the NODC hydrocast data due
to the desire to utilize the salinity data present in this
data set alone. The period covered was from 1968 through
1970, the same time span of data analyzed by Hansen (1973).
At this point it is appropriate to visually inspect the
surface temperature and salinity data sets in a determinis-
tic approach.

Figure 4 shows the monthly means of the sea-surface
temperature for 1968 through 1970 compared to Robinson's
(1971) twenty-year long-term monthly means. A characteristic
annual cycle is evident in all three years as well as the
long-term mean. The only major difference from the long-
term mean is a persistent cold anomaly which is present in
the spring of all three years.

The year 1968 was the most anomalous, being both colder
in March and April and warmer for the balance of the year.
Nam i as (1971) attributed this to bulk heating, advection
and mixing. The year 1969 was more normal, except for an
anomalous cooling in the summer, attributed by Roden (1970)
to a southward displacement of the transition zone. This
has been supported by Wickett and Thompson (1971a, 1971b)
whose meridional transport data, Figure 5, shows a transport

38

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40

of cooler water equatorward during April through October,
1969. Except for the spring months, 1970 was more typical
to the long-term mean than the preceding two years.

Figure 6 shows the monthly means of surface salinity
for 1968 through 1970. The most obvious fact from this
figure is that the salinity shows evidence of having a
semi-annual periodicity. In addition to this, there is the
feature in 1970 of a reduction in the salinity, possibly due
to the advection of abnormally fresh, cool subarctic water,
indicating an equatorward shift in the subarctic transition
zone .

As stated previously, Hansen (1973) did much work on
the same data series. Figure 7 is the result of his
bivariate analysis of the monthly mean surface temperatures
and salinities. It shows that the temperature follows four
phases, namely the seasonal phases of summer, autumn, winter
and spring, with autumn and spring appearing as transitional
phases. Hansen also performed a regression test. of the
seasonal surface temperature versus the surface salinity and
also the temperature at 50 m. The correlation coefficients
are given in Table I. For most cases the correlations were
poor, especially between the surface salinity and the surface
temperature. The only good correlations occurred during the
transition periods when both the surface temperature and
salinity were responding to the changes of the annual cycle.

41

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23

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20

19 —

18

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r

MAR

1

34.8 35.0 35.2 35.4

SALINITY

35.6

35.8

Figure 7. Monthly Temperature and Salinity Modal Points
Resulting from the Bivariate Analysis of the
Data, 1968 through 1970 (from Hansen, 1973).

43

Table I

Correlation coefficients, by season, resulting from a linear
regression analysis of surface temperature, surface salinity,
and 50 meter temperature data, 1968 through 1970 (from
Hansen, 1973).

Winter
Warmi ng
Summer
Cooling

1968

1969

1970

Mean

Sfc

50 m

Sfc

50 m

Sfc

50 m

Sfc

50m

Sal

Temp

Sal

Temp

Sal

Temp

Sal

Temp

0.61

0.58

0.61

0.56

0.77

0.42

0.66

0.52

0.59

0.90

0.77

0.70

-0.11

0.67

0.42

0.75

-0.28 0.31 0.16 0.40 -0.05 -0.29 -0.05 0.14
0.57 0.88 0.84 0.98 -0.01 0.96 0.47 0.94

Since the surface salinity and temperature were
obviously responding to different causal parameters, a
further regression analysis was performed. The surface
salinity was regressed against many of the classical para-
meters associated with its fluctuations. In this instance,
there were seven variables chosen; the vapor pressure
difference, E-P, the heat of evaporation, the wind speed,
evaporation, precipitation and surface pressure. No separa-
tion into seasons was made, all computations being made as a
three-year series of daily average observations.

The results of the regression study are shown in Table II
Two major observations are apparent from this study. First,
the standard parameters often associated with a change in
salinity, especially E-P, showed very little correlation with
the surface salinity. However, this is quite reasonable

44

Table II

Correlation coefficients, all parameters vs surface salinity

PARAMETER

1968

e -e

w a

.094

E-P

.045

QE

.028

W

-.030

PS

.830

E

.034

P

-.030

1969
.043
.151
.161
.163
.803
.166
-.019

1970

.097

-.016

-.001

-.043

.803

.004

.028

considering the location of OWS NOVEMBER with its year round
excess of evaporation over precipitation. The other major
observation is that only one parameter is consistently
highly correlated, i.e., the surface pressure.

This latter fact could mean that the changes in the
surface salinity are largely due to an advective process,
as is supported by the fact that the other no n -conservative
terms associated with the air-sea interface have such poor
correlation coefficients. This suggests that the changes in
the surface salinity are related to some geostrophic process,
most likely an advection of water from the subarctic region,
corresponding to a southward shift of the transition zone.

45

B. SPECTRAL ANALYSIS

The major thrust of this study was to use spectral
analysis as a means of numerically describing the inter-
actions at the air-sea interface at OWS NOVEMBER. Specifi-
cally, it was to identify those meteorological parameters
most closely associated with fluctuations in the sea-surface
temperature. Since this latter term has a dominant annual
cycle and most of the other parameters were compared with
this term, the results presented here will primarily be
those for the yearly cycle. The logic of this is further
demonstrated by comparing the percentages of the variance
explained by the yearly cycle for the different terms. The
percentages shown in Table III were calculated from the
energy-density functions which were produced for each time
series. This function is a measure of the variance contained
at that frequency. To compute the variance contributed by
the yearly cycle a bandwidth was specified by those frequencies
for which the value of the energy-density function decreased
to less than half the value at the yearly cycle.

From Table III it can be seen that 86% of the total
variance of the sea-surface temperature is explained by the
yearly cycle alone. For this reason, even though the
spectral results were computed for frequencies as short as
the monthly cycle, the emphasis of this study was placed on
the yearly cycle. Also, since the major areas of interest
were the correlations with the heat budget terms, each of

46

these is discussed describing its influence on the sea-
surface temperature. In addition, the contributing effects
of the parameters involved in the computation of that heat
flux term will be discussed.

Table III
Contribution of the yearly cycle to the total variance explained

Parameter

SST

T

Tw " Ta

w
ea

Vea

E (evaporation)

W

w2

CI (cloud cover)

PS

QS

QB

QE

QC

QN

% of Total Variance

86

80

20

86

46

14

34

8

9

7

8

70

87

11

17

42

47

The first heat budget term to be examined is the solar
radiation, QS, which like the surface temperature exhibits
a strong annual periodicity. From Tabe III, it can be seen
that 70% of the total variance of this term is explained by
the annual cycle. The term which primarily controls the
variation of QS is the cloud cover, CI, and in Table IV the
spectral results for the yearly cycle are given for the
interactions of the SST and CI with QS. Along with a
correlation of the cloud cover with the SST, the complete
spectral results are shown in Figures 8, 9, and 10. Figures
A-l, A-2, and A-3 of Appendix A show the respective auto-
correlation functions and Figures B-l and B-2 of Appendix B
illustrate 15-year segments of the 24-year time series of
the SST and QS.

As would be expected, Table IV shows that the solar
radiation is strongly coherent with the SST at the yearly
cycle. However, there is a lag of almost 60 days, which
cannot be explained by the cloud cover correlation with its
low coherence and therefore dubious lag time. Also, there
is a strong coherence at the semi-annual cycle, which appears
to reflect the effect of the cloud cover as seen in Figure 10

Table IV

Spectral results for the solar radiation,
SST and cloud cover at the yearly cycle.

Parameter
Codes

QS vs SST

QS vs CI

Coherence Phase

(degrees )

.94567
.85236

60.0
126.2

Lag
(days)

-58.5

122.0

48

y

09
ZI

uJ

CI

•y

o
cc

UJ

z:

G".

UJ

CI

.J

350 175 143

_J L_|

77

(Days^1)

0.007
0.013
0.020
0.034

TIME

(DAYS)

143

77

37

29

O.OOQ

0.007

0.013

0.020

0.077

SST

29 TIME(DAYS)

0.034 ffDAYS"')

LD

UJ

X

O

LJ

0.000

0.007

0.013

0.020

0.027

TIME(DAYS)

0.034 f (DAYS'1)

cr

C.

[ r\

1

-^ I

\\

/| J

\ir- 1

-

"^

vM/

\l'\ || c!

/

W

H

/

?J'l

Figure 8. Spectral density, coherence and phase for
the SST vs the solar radiation.

49

F ,
(Days-1)

TIME

(Days)

0.007 =

143

0.013 =

77

0.020 =

37

0.034 =

29

0.000

SST

0.007

0.013

0.020

0.027

TIME(DAYS)

0.034 f(DAYS~')

350

l

0.000

175 143

— L_ I

77

0.007

0.013

50

37

0.020

0.027

TIME(DAYS)

29
0.034 f (DAYS')

\t

Figure 9. Spectral density, coherence and phase for
the SST vs cloud cover.

50

(Days-1)

0.007
0.013
0.020
0.034

TIME
(Days)

143
77
37
29

0.000

350
i

175 143

—I—I

77

0.007

0.013

50

-+-

0.020

37

0.027

29

TIME(DAYS)

0.034 f(DAYS-')

0.000

350

_J

175 143

— 1_! —

77

0.007

0.013

50

37

0.020

0.027

29

TIME (DAYS)

0.034 f(DAYS"')

Figure 10. Spectral density, coherence and phase for
the solar radiation vs cloud cover.

51

This rather large lag is equally evident in Table V
which shows the months in which SST and the heat transfer
terms achieve their maximum and minimum values. Along with
Figures B-l and B-2, it can be seen that the surface
temperature is a maximum during September and at a minimum
during March. However, the solar radiation peaks in August
and is a minimum in January. This is approximately the 58
day lag shown in Table IV. This lag can be explained by the
fact that the solar radiation is absorbed and transferred
throughout the upper mixed layers of the water column. Thus,
a lag of two months exists before the total effects of the
solar radiation are represented by a warming or cooling of
the surface temperature.

Table V

Months of maximum and minimum value for the
surface temperature and the heat budget term.

Parameter
SST
QS
QE
QB

QC

QN

Minimum
March
January
May
July/January
August
December

Maximum

September
August/September

November
March/November

March

June

52

In Figures 8, 9, and 10 there are also noticeable peaks
at the six month cycle and three month cycle. These results
are thought to be, for the most part, artifacts of the yearly
cycle and are relatively small when compared to the yearly
value; yet, as mentioned before, several show evidence of
bei ng real .

The major result of this portion of the study is that
the use of the new formula for QS results in significantly,
higher estimates of this term than previously calculated.
Fluctuations in solar radiation precede those of the surface
temperature by approximately two months and thus the solar
radiation is a good predictor of the surface temperature,
as would be expected.

The back radiation, QB , represents the loss of heat
energy as long-wave radiation. It is strongly dependent
upon the surface temperature and the vapor pressure of the
atmosphere. Table VI summarizes the results for the yearly
cycle of QB and associated terms with the surface temperature

Table VI

Spectral results for the back radiation and
related parameters at the yearly cycle.

QB vs

SST

.59755

121 .8

119.0

T vs
a

SST

.98800

- 6.0

- 5.9

VTa

vs SST

.67194

-49.1

-47.9

eo vs
a

SST

.98815

- 6.4

- 6.2

QB vs

CI

.37565

-82.9

-78.1

53

From Table III it was found that about 87% of the total
variance of the back radiation was contained in the yearly
cycle; yet, Table VI shows only a slight coherence between
the SST and QB for the yearly cycle and a large dubious lag
value. This can be explained by examining the interactions
involved. The back radiation term decreases as the SST
increases due to the effect of the humidity in the atmosphere
directly above the surface. Thus, over the yearly cycle,
QB would ideally be 180 degrees out of phase with the surface
temperature. However, the back radiation is also decreased
by an increase in the cloud coverage. Thus, the condition
illustrated by Figure B-3 and Table V may be seen where QB
is shown to have two maxima and minima on roughly a semi-
annual basis. From Figure A-4 it may be seen that this
feature is superimposed over a larger annual cycle which
explains the high percentage of the variance contained by the
yearly cycle.

The complete spectral results for the above correlations
are given in Figures 11 through 15. From Figure 11 it is
seen that QB has two peaks, one at the yearly cycle and
another lesser one at one-half the yearly cycle. Of the
related parameters, only the air temperature and the vapor
pressure of the air are highly correlated and then at only
the yearly cycle. The air-sea temperature difference is only
mildly correlated at the yearly cycle and its associated lag
is highly suspect for that reason. The air-sea temperature

54

(Days'1)

TIME
(Days)

0.007
0.013
0.020
0.034

143
77
37
29

350 175 143

_l L_| —

77

0.000

0.007

0.013

50

37

0.020

0.027

SST

29 TIME(DAYS)

0.034 f (DAYS'1)

0.000

350 175 143

_J i I

77

0.007

0.013

50

37

0.020

0.027

29

TIME(DAYS)

0.034 f(DAYS-')

Figure 11. Spectral density, coherence and phase for
the SST vs the back radiation.

55

(Days'1)

0.007
0.013
0.020
0.034

TIME
(Days)

143
77
37
29

0.000

0.007

0.013

0.020

0.027

TIME(DAYS)

0.034 f (DAYS'* )

0.000

350
_l

175 143

77

0.007

0.013

50

0.020

37

0.027

29 TIME(DAYS)

0.034 f(DAYS-')

Figure 12. Spectral density, coherence and phase for
the SST vs air temperature.

56

(Days'1)

0.007
0.013
0.020
0.034

TIME
(Days)

143
77
37
29

0.000

0.007

0.013

0.020

0.027

TIME(DAYS)

0.034 f (DAYS'1)

•S

0.000

350 175 143

_J l_J

0.007

77

0.013

50

0.020

37

0.027

29 TIME(DAYS)

0.034 HDAYS*1)

Figure 13. Spectral density, coherence and phase for

the SST vs the air-sea temperature difference

57

350
_l

175 143

I I

77

F
(Days

0.007
0.013
0.020
0.034

TIME
(Days)

143
77
37
29

SST

50

37

29 TIME(DAYS)

0.000

0.007

0.013

0.020

0.027

0.034 f(DAYSH)

0.000

0.007

0.013

0.020

0.027

TIME(DAYS)

0.034 f (DAYS'1)

<a

Figure 14. Spectral density, coherence and phase for the
SST vs the vapor pressure of the air.

58

(Days'1)

TIME
(Days)

0.007
0.013
0.020
0.034

143
77
37
29

QB

0.000

350 175 143

_l L_J

77

0.007

0.013

50

37

0.020

0.027

29

TIME (DAYS)

0.034 f(DAY5-')

350 175 143

J L

TIME(DAYS)

0.034 f (DAYS'1)

C- ZZ"-

Figure 15. Spectral density, coherence and phase for the
back radiation vs cloud cover.

59

difference demonstrates a coherence at the 70-day cycle.
Also the back radiation and cloud cover show evidence of
this possible seasonal coherence.

The major conclusion to be drawn from this part of the
study is that the back radiation is semi-annual with an
underlying yearly cycle. As a predictor for the surface
temperature, the back radiation is poorly associated with
fluctuations in SST.

The next heat budget term examined was the heat of
evaporation, QE. Only 11% of the total variance of QE is
explained by the yearly cycle which in itself means that QE
is a poor predictor of the surface temperature. This is
verified by Table VII which shows only a moderate coherence
for QE and the SST at the yearly cycle. This lessens the
credibility of the large lag shown; also from Table V it can
be seen that the actual lag is more of the nature of two
months. Additionally the lag is positive which means that
fluctuations of QE follow those of the SST.

Table VII

Spectral results for the heat of evaporation
and related parameters at the yearly cycle.

Parameter
Codes

QE vs SST

e -e vs SST
w a

W vs SST
W2 vs SST
E vs SST

Coherence

.84783
.86425
.95593
.95512
.81722

Phase
(degrees )

97.5

22.8

138.1

135.4

76.9

Lag
(days)

95.0

22.3

135.4

132.0

74.9

60

Whereas QE is only weakly correlated with the SST at
the annual cycle, the wind speed and wind speed squared are
highly correlated to the SST with large positive lags
(approximately 4 months). These would seem to explain much
of the lag in QE when they are coupled with the vapor
pressure difference. QE is a transfer mechanism of the form

QE = - A

3f

e 3z

(28)

where :

Ao is the eddy coefficient for water vapor

is the humidity gradient above the sea surface.

e

9f

az

Both of these are highly dependent upon the wind speed.
Even though the vapor pressure difference and evaporation
are weakly correlated to the SST, they combine with the wind
speed to produce the low coherence and large lag for QE.

Figures 16 through 20 give the complete spectral results
for the correlations shown. Being computed from the surface
temperature, e and SST are naturally perfectly correlated
and is not included. The yearly cycle dominates in all
except for QE, the vapor pressure difference and the evapora-
tion, as would be expected. Both the wind speed and wind
speed squared show a definite coherence at about the 80-day
cycle. The autocorrelation functions are found in Figures
A-9 through A-13 and a 15-year plot of QE and its anomaly
is shown in Figure B-4.

61

i-i j rn

en

(Days'1)

0.007
0.013
0.020
0.034

TIME
(Days)

143
77
37
29

350 175 143

-J L_J

0.000

0.007

77

0.013

50

0.020

37

0.027

SST

29 TIME(DAYS)

0.034 f(DAYS-')

0.000

0.007

0.013

0.020

0.027

TIME(DAYS)

0.034 f (DAYS'1)

Figure 16. Spectral density, coherence and phase for the
SST vs the heat of evaporation.

62

(Days"1)

0.007
0.013
0.020
0.034

TIME
(Days)
HT3

77

37

29

0.000

e -e
w a

SST

0.007

0.013

0.020

0.027

29 TIME(DAYS)

0.034 HDAYS-1)

0.000

0.007

0.013

0.020

0.027

29 TIME (DAYS)

0.034 f(DAYS-')

Figure 17

Spectral density, coherence and phase for the
SST vs the vapor pressure difference.

63

(Days"1 )

TIME
(Days)

0.007
0.013
0.020
0.034

143
77
37
29

0.000

SST

0.007

0.013

0.020

0.027

TIME(DAYS)
0.034 f (DAYS'1)

0.000

0.007

0.013

0.020

0.027

TIME(DAYS)
0.034 f(DAYS-')

n. C3<i

Figure 18

Spectral density, coherence and phase for the
SST vs the wind speed.

64

(Days'1)

TIME
(Days)

0.007
0.013
0.020
0.034

143
77
37
29

350
_J

175 143

I I

77

0.000

0.007

0.013

50

37

0.020

0.027

SST

29 TIME(DAYS)

0.034 f (DAYS'1)

CD

O Q

0.000

0.007

0.013

0.020

0.027

TIME(DAYS)

0.034 f(DAYS-')

0. J34

Figure 19. Spectral density, coherence and phase for the
SST vs the wind speed squared.

65

F

(Days

0.007
0.013
0.020
0.034

TIME
(Days)

143
77
37
29

SST

0 000

0.007

0013

0.020

0.027

TIME(DAYS)

0.C34 fiDAYS"')

0.000

0.007

0.013

0.020

0.027

TIME(DAYS)
0.034 f (DAYS'1)

Figure 20

0.024

Spectral density, coherence and phase for the
SST vs the evaporation.

66

The heat of conduction, Q C , is the smallest of the heat
flux terms and only 17% of its total variance is explained
by the yearly cycle. From Table VIII it can be seen that
this term also has an unusually large lag, approximately
130 days, and the lowest coherence of any of the heat budget
terms with the surface temperature. From Figure 21 it can
be seen that QC is nearly of the form of white noise with
no distinct periodicities. This is confirmed by Figure B-5
which shows that QC is constantly small and contains few
anomalies of note.

Like QE, QC is a flux term of the form

«c ■ -Ah It

(29)

wnere

A^ is the eddy coefficient of heat conduction, and
is the temperature gradient of the air overlying

kh

3Z

the sea surface

For an area of the nature of OWS NOVEMBER, dominated by
fairly constant temperature patterns for both the air and
the ocean, it can be seen that this term would be expected
to be fairly constant. It does contain quite a deal of
energy in cycles other than the annual and shows evidence
of good coherence at the semi-annual, seasonal and monthly
peri odi ci ti es .

67

l)J m

(Days"1)

0.007
0.013
0.020
0.034

TIME
(Days)

143
77
37
29

QC

350

i

175 143

_JL_1

77

0.000

0.007

0.013

50

37

0.020

0.027

SST

29 TIME(DAYS)

0.034 f(DAYS-')

0.000

0.007

0.013

0.020

0.027

TIME(DAYS)
f (DAYS"')

c ::?

CC27

n. ?,'/■

n

c-j ,

Figure 21

Spectral density, coherence and phase for the
SST vs the convective heat.

68

TABLE VIII.

Spectral results for the convective
heat vs the SST at the yearly cycle

Parameter
Codes

QC vs SST

Coherence
.75694

Phase
(degrees )

134.1

Lag
(days)

130.7

The final heat budget term, the net heat transfer, QN ,
is perhaps the most interesting of the heat equation terms,
representing the gain or loss of heat by the water column.
To this point, the advective and local heat exchange terms
have been ignored. However, since the values for the net
radiation computed from Equation (1) did not result in zero
values, then it is evident that these terms have to be
considered. If QN is then viewed as a combination of the
advective heat term and the local generation of heat it takes
on the form:

QN = Qy + QQ

where

Q is the advection of heat by currents, and
Q is the local heat generated.

Over the annual cycle QQ = 0; therefore, QN must be
representative of only the advection term. This is supported
by the fact that for the entire 24-year period QN was found
to have a slope of only 0.003 which signifies that no long
term generation of heat has occurred.

69

From Tables III and IX it can be seen that the net heat
exchange is dominated by the annual cycle and is highly
coherent with the surface temperature at this period.
Forty-two percent of the total variance is explained by the
yearly cycle, which allows for some seasonal effects and
Figure 22 shows some evidence of high coherence at the
semi-annual and seasonal cycles. The lag is confirmed by
both Table V and Figure B-6. Much of this lag is undoubtedly
due to the effect of the 58-day lag of the solar radiation
and the balance by the other heat budget terms. In addition,
the lag of QN and the surface pressure, considered here
because of the previously noted high correlation of pressure
with the surface salinity, may also contribute to the lag of
QN and SST.

TABLE IX

Spectral results for the net radiation
and related parameters at the yearly cycle

Parameter
Codes

QN vs SST

PS vs SST

QN vs PS

Coherence
Squared

.97954

.79993

.79250

Phase
(degrees )

- 76.7
-120.6

- 46.9

Lag
(days)

- 74.8
-118.6

- 45.3

70

LU n
CD

F

(Days

1

TIME
(Days)

0.007
0.013
0.020
0.034

143
77
37
29

QN

350

i

0.000

175 143

-H—

0.007

77

0.013

50

37

0.020

0.027

SST

29 TIME(DAYS)

0.034 f (DAYS'')

0.000

350
_l

175 143

_!_!

77

0.007

0.013

50

0.020

37

0.027

29 TIME(DAYS)

0.034 f (DAYS')

Figure 22

0-034

Spectral density, coherence and phase for the
SST vs the net radiation.

71

Figures 22 through 24 give thecomplete spectral
results for the net heat exchange, the surface temperature,
and the surface pressure correlated versus each other. In
all three instances the yearly peak dominates.

The major result of this segment is that the new solar
radiation formula results in larger positive values of QN.
Secondly, for the yearly cycle QN is a measure of heat
advection and at OWS NOVEMBER this advection is of nearly
equal importance as the solar radiation as an influence on
the surface temperature. The negative lag makes QN a fairly
good predictor of the surface temperature, even though much
of the variance of the net heat exchange is contained in the
seasonal cycles. The surface pressure seems to be less
correlated with the surface temperature than it is with the
salinity.

Mery little has been mentioned about the autocorrela-
tions; however, White (1974) has used this function in the
study of SST and baroclinic transport anomalies.. He found
an apparent 5-year periodicity in the SST anomalies in the
vicinity of OWS NOVEMBER. This cycle was attributed to
deeper anomalous features in the baroclinic structure.

72

11

z:

uj T
en

>•

o

UJ

z:

i

Ld
Li_ N

in '

D

350 175 143

_J i_l_

F
(Days

1

0.007
0.013
0.020
0.034

TIME
(Days)

143
77
37
29

PS

SST

29 TIME(DAYS)

0.000

0.007

0.013

0.020

0.027

0.034 f(DAYSM)

21

LU
QC
LiJ
X

LJ

U_;

j_
Q.

29 TIME(DAYS)

0.034 f(DAYS-')

Figure 23. Spectral density, coherence and phase for the
SST vs the surface pressure.

73

y

z:

LU

CD

>

O

C£
UJ

ZI

(Days'1)

0.007
0.013
0.020
0.034

TIME
(Pays)

143
77
37
29

cc

Cl

go
o

0.000

350
_J

175 143

i I

77

0.007

0.013

50

0.020

37

0.027

29

TIME(DAYS)

0.034 f(DAYSH)

O

z:

cr

Li J

X.

cr

3.-

TIME(DAYS)
0.034 f (DAYS'1)

Figure 24. Spectral density, coherence and phase for the
net radiation vs the surface pressure.

74

IV. CONCLUSIONS

The aim of this study was to use the tools of spectral
analysis and other statistical approaches to describe the
interactions of the air-sea interface at OWS NOVEMBER,
specifically as to finding those parameters most closely
associated with fluctuations of the daily average surface
temperature and surface salinity.

The results of this research showed that:

1. The surface salinity from 1968 through 1970 was
shown through regression analysis to be poorly correlated
with the parameters traditionally associated with changes
in the observed salinity. The evaporation, evaporation
minus precipitation, and precipitation were found to have
little correlation with fluctuations in surface salinity.
These terms are non-conservative terms associated with the
air-sea interface and their low correlation coefficients
would appear to negate their importance in controlling the
surface salinity at this location in the Pacific.

2. The surface pressure was found to be the most
strongly correlated of all the parameters regressed against
the surface salinity. It was therefore hypothesized that
this represents the presence of a movement of a baroclinic
system of cooler water from the subarctic region into the
vicinity of OWS NOVEMBER, corresponding to a shift southward
of the transition zone.

75

3. For the yearly cycle, it was shown that the net
radiation is a measure of the advection present and that
this advection is of nearly equal magnitude as the solar
radi ati on .

4. The new formula for the solar radiation leads to
values for this term approximately 20 to 30 percent higher
than previously computed. In turn, this leads to much
larger positive values of the net heat exchange term and
larger positive anomalies for both terms.

5. From the spectral analyses it was found that all
the 24-year time series were dominated by the yearly cycle;
except for the back radiation, cloud cover, wind speed and
wind speed squared series which showed evidence of semi-
annual and seasonal cycles as well.

6. As predictors of the surface temperature, the
solar radiation and advection in the form of the net heat
exchange term were the only terms of suitable phase and
coherence at the yearly cycle to be valid. The o.ther heat
transfer terms seems to have less effect upon fluctuations
of the surface temperature. Several of the observed para-
meters, such as the air temperature, were also highly
coherent and, on the whole, had smaller lags associated with
them.

76

Fij

3ure

A-

-1

A-

-2

A-

-3

A-

•4

A-

■5

A-

-6

A-

■7

A-

•8

A-

■9

A-

•10

A-

■11

A-

•12

A-

•13

A-

•14

A-

•15

A-

•16

A-

■17

APPENDIX A

THE AUTOCORRELATION FUNCTIONS

Page

Autocorrelation curves for the SST

and the solar radiation, QS 78

Autocorrelation curves for the SST

and cloud coverage 79

Autocorrelation curves for the cloud

coverage and the solar radiation 80

Autocorrelation curves for the SST

and the back radiation 81

Autocorrelation curves for the SST

and the air temperature 82

Autocorrelation curves for the SST

and the air-sea temperature difference 83

Autocorrelation curves for the SST

and the vapor pressure of the air 84

Autocorrelation curves for the

back radiation and cloud cover 85

Autocorrelation curves for the SST

and the heat of evaporation 86

Autocorrelation curves for the SST

and the vapor pressure difference 87

Autocorrelation curves for the SST

and the wind speed 88

Autocorrelation curves for the SST

and the wind speed squared 89

Autocorrelation curves for the SST

and evaporation 90

Autocorrelation curves for the SST

and the convective heat 91

Autocorrelation curves for the SST

and the net radiation 92

Autocorrelation curves for the SST

and surface pressure 93

Autocorrelation curves for the net

radiation and the surface pressure 94

77

/I

03 SST

« QS

Figure A-l

Autocorrelation curves for the SST and the solar
radiation, QS (abscissa is given in hundreds
of days ) .

78

^^^jL^%^4

■W^f^

■■■■. _ LA^V...

CI

312

SST

Figure A-2. Autocorrelation curves for the SST and cloud

coverage (abscissa is given in hundreds of days)

79

( >
I

!

V

CI

o:o

Ux QS

Figure A-3

Autocorrelation curves for the cloud coverage
and the solar radiation (abscissa is given in
hundreds of days ) .

80

M SST

Figure A-4

Autocorrelation curves for the SST and the back
radiation (abscissa is given in hundreds of days)

81

Figure A-5

Autocorrelation curves for the SST and the air
temperature (abscissa is given in hundreds of days)

82

Figure A-6

Autocorrelation curves for the SST and the
air-sea temperature difference (abscissa is
given in hundreds of days.).

83

Figure A-7

Autocorrelation curves for the SST and the vapor
pressure of the air (abscissa is given in
hundreds of days ) .

84

D
0

thft

Mk

QB

Figure A-8

Autocorrelation curves for the back radiation
and cloud cover (abscissa is given in hundreds
of days ) .

85

-i
o J

Figure A-9

Autocorrelation curves for the SST and the heat
of evaporation (abscissa is given in hundreds
of days ) .

86

Figure A-l 0

Autocorrelation curves for the SST and the vapor
pressure difference (abscissa is given in
hundreds of days ) .

87

CM

O

o

N
O

o
o
o

010

SST

Figure A - 11

Autocorrelation curves for the SST and the
wind speed (abscissa is given in hundreds
of days ) .

88

IT

SST

Figure A- 12

Autocorrelation curves for the SST and the
wind speed squared (abscissa is given in
hundreds of days).

89

Old

a SST

Fi gure A-l 3

Autocorrelation curves for the SST and
evaporation (abscissa is given in hundreds
of days).

90

»

a

^
n

o

H
O

s SST

Figure A- 14

Autocorrelation curves for the SST and the
convective heat (abscissa is given in hundreds
of days ) .

91

Figure A- 15

Autocorrelation curves for the SST and the net
radiation (abscissa is given in hundreds of
days) .

92

a

■t

CD

^^^k «

PS

0:0

ra SST

1

Figure A- 16

Autocorrelation curves for the SST and surface
pressure (abscissa is given in hundreds of days)

93

^ ^>A>

Fi gure A-l 7

Autocorrelation curves for the net radiation
and the surface pressure (abscissa is given
in hundreds of days ) .

94

APPENDIX B
FIFTEEN-YEAR TIME SERIES SEGMENTS

Fi gure Page

B-l Fifteen-year time series of the

surface temperature and its anomaly 96

B-2 Fifteen-year time series of the

solar radiation and its anomaly 97

B-3 Fifteen-year time series of the

back radiation and its anomaly 98

B-4 Fifteen-year time series of the

heat of evaporation and its anomaly 99

B-5 Fifteen-year time series of the

convective heat and its anomaly 100

B-6 Fifteen-year time series of the

net radiation and its anomaly 101

95

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LIST OF REFERENCES

1. Beland, C.L., 1971: Sea surface and related subsurface
temperature anomalies at several positions in the
Northwest Pacific Ocean. Master's Thesis, Naval
Postgraduate School , Monterey.

2. Bendat, J.S. and Piersol, A.G., 1971
Analysis and Measurement Procedures.
New York.

Random Data:
Wi 1 ey Intersci ence ,

3.

4.

5.

Bernstein, R.L., 1974: Mesoscale ocean eddies in the
North Pacific: Westward Propagation. Science, v. 183
(4120): 71-72.

Clark, N.E., 1972: Specification of Sea Surface
Temperature Anomaly Patterns in the Eastern North
Pacific. J. Phys. Oceanogr. v. 2(3): 391-404.

Dorman, C.E. , 1974
oceanograph i c data

Analysis of meteorological and
from ocean station vessel N

(30N 140W
Corval 1 is

Phd. Thesis, Oregon State University,

6.

Elliot, W.P. and Reed, R.K., 1973
off the Pacific Northwest Coast.
V. 78(6): 941-948.

Oceanic rainfall
Geophys . Res .

7. Favorite, F. and D.R. McLain, 1973: Coherence in
Transpacific Movements of Positive and Negative
Anomalies of Sea-Surface Temperature 1953-60, Nature ,
v. 244, pp 139-143.

8. Hansen, D.E., 1973: A study of surface, 50 meter and
200 meter temperature and salinity fluctuations at
Ocean Weather November, 1968-1970. Master's Thesis,
Naval Postgraduate School, Monterey.

9. Husby, D.M., 1968: Oceanographi c observations North
Pacific Ocean Station November. CG 373-18.

10. Husby, D.M., 1969: Oceanographi c Observations North
Pacific Ocean Station November. CG 373-26.

11. List, Robert J., 1951: Smithsonian Meteorological
Tab! es . Smithsonian Mi seel. Collect., Washington, D.C.
1951.

102

12. Namias, J., 1970: Macroscale variations in sea-surface
temperatures in the North Pacific. J. Geophys. Res.

V. 75(3): 565-582.

13. Namias, J. and R.M. Born, 1970: Temporal coherence in
North Pacific sea-surface temperature patterns.

J. Geophys. Res. , v. 75(30): 5952-5955.

14. Namias, J., 1971: The 1968-69 winter as an outgrowth
of sea and air coupling during antecedent seasons.

J. Phys. Oceanogr. v. 1(2): 65-81.

15. National Oceanographi c Data Center, 1972: Ocean Weather
Station November Data, Washington, D.C.

16. Robinson, M.K., 1971: Atlas of monthly mean sea surface'
subsurface temperature and depth of the top of the
thermocline North Pacific Ocean. Fleet Numerical
Weather Central .

17. Roden, G.I., 1970: Aspects of the Mid-Pacific
Transition Zone. J. Geophys. Res. , v. 75(6): 1097-1109.

18. Roden, G.I., 1971: Aspects of the transition zone in
the Northeastern Pacific. J. Geophys. Res . , v . 76(15):
3462-3475.

19. Roden, G.I., 1972: Temperature and salinity fronts at
the boundaries of the subarctic-subtropical transition
zone in the Western Pacific. J . Geophys . Res . ,

V. 77(36): 7175-7187.

20. Seckel , G.R., 1968: A time sequence oceanographi c
investigation in the North Pacific trade wind zone.
Trans. Amer. Geophys. Union, v. 49:377-387.

21. Seckel, G.R. and Marion Y.Y. Yong: 1970: Harmonic
functions for sea-surface temperatures and salinities,
Koko Head, Oahu, 1956-69, and sea-surface temperatures,
Christmas Island, 1954-69. Fishery Bulletin, v. 69(1):
1970.

22. Seckel, G.R., 1970: The trade wind zone oceanography
pilot study part VIII: sea-level meteorological
properties and heat exchange processes July 1963 to
June 1965. U.S. Fish and Wildlife Service, Special
Scientific Report-Fisheries No. 612, U . S . D . of I .

103

23. Tucker, G.B., 1961: Precipitation over the North
Atlantic Ocean. Quart. J. Roy. Meteor. Soc, v.
87:147-158.

24. Tully, J. P., 1964: Oceanographi c regions and assessment
of temperature structure in the seasonal zone of the
North Pacific Ocean. J. Fish. Res. Bd. of Canada ,

V. 21(5): 941-970.

25. U.S. Dept. of Commerce, 1961: CI i matol ogi cal and
oceanographi c atlas for mariners, North Pacific Ocean.
U.S. Department of the Navy, Office of Climatology and
Oceanographi c Analysis Division.

26.

White, W.B., 1974: SST anomaly development and changes
in the general circulation in the upper ocean.
NORPAX Highlight, pp. 3-6.

27

Wickett , W. P. , and J
computations for the
Fish. Res. Bd.

A. Thomson, 1971: Transport

North Pacific Ocean, 1970.
Canada, Tech. Rep. No. 238.

28. Wickett, W.P., and J. A. Thomson, 1971: Transport
computations for the North Pacific Ocean, 1969.
Fish. Res. Bd. Canada, Tech. Rep. No. 239.

29. Wyrtki, K., 1965: The average heat balance of the
North Pacific Ocean and its relation to ocean
circulation. J . Geophys . Res . , v. 70(18): 4547-4559

104

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Thesis

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