LARGE SCALE SEA-AIR ENERGY FLUXES
AND
GLOBAL SEA SURFACE TEMPERATURE FLUCTUATIONS
by
Jane Hsiung Wojcik
A.B., Barnard College, Columbia University
(1974)
M.S., Massachusetts Institute of Technology
(1978)
Submitted to the Department of
Earth, Atmospheric and Planetary Sciences
in Partial Fulfilment of the Requirement of the
Degree of
DOCTOR OF PHILOSOPHY
at the
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
01983, Massachusetts Institute of Technology
Signature of Author
Department ef'Earth, Atmos heric, and
er, 1983
Planetary Scie
Certified by:
Professor Reginald E. Newell
Thesis Supervisor
Accepted by:
Professor Theodore R. Madden
Chairman, Departmental Committee
on Graduate Students
LARGE SCALE SEA-AIR ENERGY FLUXES
AND
GLOBAL SEA SURFACE TEMPERATURE FLUCTUATIONS
by
Jane Hsiung Wojcik
Submitted to the Department of Earth, Atmospheric,
and Planetary Sciences in December, 1983 in partial
requirements for the Degree of Doctor of Philosophy
ABSTRACT
A newly available Consolidated Data Set (CDS) from the U.S. Navy's Fleet
Numerical Weather Central in Monterey, California is utilized to
investigate large scale energy fluxes at the sea-air interface and
global sea surface temperature fluctuations.
Sea surface temperature
data from January, 1949 to December, 1979 were extracted from the data
set along with air temperature, sea level pressure, dew point
temperature, wind speed, wind direction, and cloud cover. Five degree
latitude by five degree longitude spatial averaging and monthly temporal
averaging were applied to the parameters in the data set for the purpose
of studying long term large scale fluctuations. The statistical
properties of global sea surface temperature are documented through its
long term annual and monthly means and variances and frequency
distributions.
The heat balance of the global ocean surface layer is
calculated using bulk flux formulations.
Estimates of oceanic meridional energy transport for the Pacific, the
Atlantic and the Indian oceans are made using calculated annual mean
surface energy fluxes. The results show a northward transport at all
latitudes in the Atlantic Ocean; a poleward transport in both
hemispheres centered around 10'S in the Pacific Ocean with a northward
transport south of 25"S, and a southward transport at all latitudes in
the Indian Ocean.
A hypothesis is made on the possible relationship
between the cooling of the sea surface temperature in the Northern
Hemisphere oceans during 1965-1979 and the large latent heat loss in the
Indian Ocean during the same period.
Characterization of nonseasonal global SST variations is made through
empirical orthogonal function (EOF) analysis.
The first mode is the
so-called El Nino mode with a warm eastern tropical Pacific together
with a cold north central Pacific.
The second mode shows a cooling
trend in the northern hemispheric oceans. Nonseasonal fluctuations of
SST at two key regions of the Pacific Ocean (the eastern tropical and
north central regions in the first global EOF) are investigated further
through autoregressive modeling. It is found that a first order model
is adequate to explain variations in the north central Pacific while a
second order model is needed for regions in the eastern tropical
Pacific. Results from EOF analysis on the nonseasonal component of the
net heat flux, the incoming solar radiation and the latent heat flux
show that the variation in the net energy flux is completely dominated
by the variation in the latent heat flux. The first EOF time series of
the net energy flux shows a cooling trend and the first EOF time series
of the incoming radiation resembles the time series of the El Nino mode.
Relationships between nonseasonal SST and other nonseasonal sea surface
parameters are explored briefly. The variation in air temperature
follows closely with that of contemporaneous sea surface temperature.
The nonseasonal variation in net energy flux (mostly from the latent
heat flux) correlates negatively with SST anomalies while a positive
correlation is obtained between the finite difference form of 3(ASST)/8t
and the anomalies of the net energy flux.
Thesis Supervisor: Reginald E. Newell
: Professor of Meteorology
Title
This thesis is dedicated to
my parents Teh-shu Hsiung and Shiu-fong Hsieh
and to
my husband Michael Wojcik
TABLE OF CONTENTS
ABSTRACT - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -2
DEDICATION - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -4
TABLE OF CONTENTS - - - - - - - - - - - - - - - - - - - - - - - - - - 5
LIST OF FIGURES - - - - - - - - --- - - - - - - - - - - - - - - - - - 7
LIST OF APPENDIX FIGURES - - - - - - - - - - - - - - - - - - - - - - 12
LIST OF TABLES - - - - - - - - - - - - - - - - - - - - - - - - - - - 13
I. INTRODUCTION - - - - - - - - - - - - - - - - - - - - - - - - - - -14
II. THE DATA SET - - - - - - - - - - - - - - - - - - - - - - - - - - 20
II.1
11.2
II.3
11.4
11.5
History
Contents
Processing
Data Density
Notation and Definition of Quantities
III. STATISTICAL PROPERTIES OF SEA SURFACE TEMPERATURE - - - - - - - 31
III.1
111.2
III.3
Annual Mean and Variance
Monthly Mean and Variance
Frequency Distribution
IV. ENERGY BUDGET - - - - - - - - - - - - - - - - - - - - - - - - - -45
IV.1
IV.2
IV.3
IV.4
Theory
Sensitivity of Flux Formulations
Results
Error Analysis
V. ESTIMATES OF OCEANIC MERIDIONAL ENERGY TRANSPORT - - - - - - - - 104
V.1
V.2
V.3
V.4
Theory
Computation and Results
Discussion
Differences in Transport between two Periods
VI. NONSEASONAL VARIATIONS OF SST AND ENERGY FLUXES - - - - - - - - - 135
VI.1
VI.2
VI.3
VI.4
EOF Analysis of SST
Statistical Properties of ASST:Autoregressive
Models
EOF Analysis of Nonseasonal Heat Fluxes
Relationship Between Nonseasonal SST and Other
Nonseasonal Parameters
VII.CONCLUSION - - - - - - - - - - - - - - - - - - - - - - - - - - - -190
APPENDICES
A. List of Parameters Available on the Data Set - - - - - - - - -197
B. Problems Associated with 5' by 5' Grid Averaging - - - - - - -199
C. Monthly Mean Maps of Input Meteorological Parameters - - - - -204
D. Empirical Orthogonal Functions and Single Value Decomposition 217
E. Wind Stress Calculation - - - - - - - - - - - - - - - - - - - 223
REFERENCES - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -235
ACKNOWLEDGEMENT - - - - - - - - - - - - - - - - - - - - - - - - - - - 241
BIOGRAPHICAL NOTE-
- - - - - - - - - - - - - - - - - - - - - - - - - -242
LIST OF FIGURES
Figure 2.1
Indian Ocean SST: average number of observations at each
grid square and number of years with observation (January)
Figure 2.2
Same as 2.1 except for Pacific Ocean SST
Figure 2.3
Same as 2.1 except for Atlantic Ocean SST
Figure 2.4
Total number of months with observations at each grid
square for Indian, Pacific and Atlantic oceans
Figure 2.5
Monthly time series of the number of observations
averaged over all grid squares
Figure 3.1
Atlantic Ocean SST: Long term annual mean and standard
deviation
Figure 3.2
Same as 3.1 except for Pacific Ocean SST
Figure 3.3
Same as 3.1 except for Indian Ocean SST
Figure 3.4
Contour plot of global long term annual mean SST
Figure 3.5
Long term monthly mean of SST for January
Figure 3.6
Long term monthly mean of SST for April
Figure 3.7
Long term monthly mean of SST for July
Figure 3.8
Long term monthly mean of SST for October
Figure 3.9
Indian Ocean SST: long term monthly standard deviation
for January and July
Figure 3.10
Same as 3.9 except for Pacific Ocean SST
Figure 3.11
Same as 3.9 except for Atlantic Ocean
Figure 3.12
Typical frequency distribution of SST at selected grid
squares
Figure 3.13
Histograms of frequency distribution of SST and air
temperature for three oceans
Figure 4.1
Frequency distribution histogram of the three oceans for
wind speed, zonal and meridional wind components, dew
point temperature, cloud cover, and drag coefficients
Figure 4.2
Transfer coefficients (Ce) and drag coefficients (Cd)
versus wind speed for seven different stability classes
qs and wind
Figure 4.3
Latent heat flux as a function of qa
speed
Figure 4.4
Outgoing radiation as a function of cloud cover and air
temperature
-
Figures 4.5-4. 8
Long term monthly mean of net heat flux for January,
April, July and October
Figures 4.9-4. 12
Long term monthly mean of incoming solar
radiation for January, April, July and October
Figures 4.13-4 .16
Long term monthly mean of latent heat flux for
January, April, July and October
Figures 4.17-4 .20
Long term monthly mean of outgoing radiation for
January, April, July and October
Figures 4.21-4 .24
Long term monthly mean of sensible heat flux for
January, April, July and October
Figures 4.25-4 .28
Seasonal cycle of heat flux components at selected
grid squares of the three oceans
Figure 4.29
February and August zonal mean SST for the Atlantic and
Pacific Oceans (from Newell et al, 1981)
Figure 4.30
Long term annual mean of net heat flux
Figure 4.31
Long term annual mean of incoming solar radiation
Figure 4.32
Long term annual mean of latent heat flux
Figure 4.33
Long term annual mean of outgoing radiation
Figure 4.34
Long term annual mean of sensible heat flux
Figure 4.35
Long term annual mean of cloud cover
Figure 4.36
Long term annual mean of wind speed
Figure 4.37
Long term annual mean of air-sea temperature difference
Figure 4.38
Long term annual mean of specific humidity difference
Figure 4.39
Long term annual mean of drag coefficient (Ce)
Figure 4.40
Zonal average of heat flux components for the three oceans
Figure 4.41
Zonal average of SST, air, dew point, qs~9ao
Ta-Ts, wind speed, Ce, cloud cover, and wind stress
Figure 4.42
Meridional profile of annual energy budget for all oceans
Figure 5.1
Schematic representation of the heat balance of earthatmosphere-ocean system
Figure 5.2
The net flux divergence for each 5* latitude belt and the
direction of the purposed meridional transport of heat
Figure 5.3
Meridional heat transport for three oceans separately and
combined (positive indicates northward transport)
Figure 6.1
Global nonseasonal SST: The eigenvalues and the associated
sampling errors for the first twenty modes. The
eigenvalues are normalized by the total variance and
therefore can be considered as percentage of variance
explained
Figure 6.2
First nonseasonal SST eigenvector pattern for 1949-1979
(7.6% of total variance explained)
Figure 6.3a
Time series of the first eigenvector patterns for
1949-1979
Figure 6.3b
Same as 6.3a except for two separate periods: 1949-1964
and 1965-1979
Figure 6.3c
Same as 6.3a except for four seasonaly stratified data
Figure 6.4
Standard deviation of SST for the period 1949-1979
Figure 6.5
Correlation coefficients of EOF #1 time series and each
5*
by 5* grid squares
Figure 6.6
Cross correlation between time series of EOF #1 and
selected squares
Figure 6.7
Global SST anomaly patterns for November, 1957 and
November, 1982
Figure 6.8
Global SST anomaly pattern for November, 1982
Figure 6.9
Nonseasonal time series of SST and incoming solar
radiation at two selected grid squares
Figure 6.10
Second nonseasonal SST eigenvector pattern for 1949-1979
(4.29% of total variance explained)
Figure 6.11
Time series of second eigenvector for the period 1949-1979
and for two separate half periods
Figure 6.12
Second nonseasonal SST eigenvector pattern for:
a) 1949-1964 (4.62% of total variance explained),
b) 1965-1979 (5.70% of total variance explained)
Figure 6.13a
Figure 6.13b
Third nonseasonal SST eigenvector pattern for 1949-1979
(3.44% of total variance explained)
Time series of third eigenvector for 1949-1979
Figure 6.14
Autocorrelation functions for the first three eigenvector
time series computed for the entire period and for the two
half periods separately
Figure 6.15
Nonseasonal time series of SST for grid squares at 5*S,
80*W (eastern tropi'cal Pacific) and at 30'N, 165'W (north
central Pacific)
Figure 6.16
Autocorrelation function of nonseasonal SST at eastern
tropical Pacific and north central Pacific
Figure 6.17
Autocorrelation coefficient at lag=l for all grid squares
in the global oceans
Figure 6.18
Residual plots of the first order and second order
autoregressive fit at north central Pacific and eastern
equatorial Pacific
Figure 6.19
Autocorrelation of residual from first and second order
fit for eastern tropical Pacific and north central Pacific
Figure 6.20
Time series plots of the net heat flux anomaly and zonal
wind anomaly at eastern tropical Pacific and north central
Pacific
Figure 6.21
Autocorrelation function of zonal wind anomalies and net
heat flux anomalies at eastern tropical Pacific and north
central Pacific
Figure 6.22a
EOF #1 of net heat flux anomalies and its associated
time series
Figure 6.22b
EOF #1 time series of latent heat flux anomalies
Figure 6.23
EOF #1 of incoming solar radiation anomalies and its
associated time series
Figure 6.24
Scattergrams of surface air temperature vs. surface sea
temperature at four selected grid squares
Figure 6.25
Global map of correlation coefficients between air
temperature and sea temperature
Figure 6.26
Correlation coefficients between anomalies of SST and
net heat flux
Figure 6.27
Correlation coefficients between anomalies of SST and
incoming solar radiation
Figure 6.28
Correlation coefficients between anomalies of SST and
latent heat flux
Figure 6.29
Correlation coefficients between anomalies of SST and
sensible heat flux
Figure 6.30
Correlation coefficients between anomalies of SST and
outgoing radiation flux
Figure 6.31
Correlation coefficients between anomalies of net heat
flux and dT/dt
Figure 6.32
Correlation coefficients between anomalies of SST and
zonal wind stress
Figure 6.33
Correlation coefficients between anomalies of SST and
meridional wind stress
LIST OF APPENDIX FIGURES
each of the marine
Figure A.1
List of possible parameters present in
reports in the consolidated data set
Figure B.1
Time series plots for grid square at 40*N, 60*W of:
a) monthly mean number of observations,
b) monthly mena latitudial position, and
c) monthly mean longitudial position
Figure B.2
Time series plots of SST anomalies at grid 400 N, 60*W
using three different averaging methods:
a) average of anomalies at 25 1* by 1* subsquares,
b) average with respect to 1* by 1* long term monthly
means, and
c) average with respect to 5* by 50 long term monthly
means
Figures C.1-C.4
Long term monthly means of wind speed for January,
April, July and October
Figures C.5-C.8
Long term monthly means of cloud cover for January,
April, July and October
Figures C.9-C.12
Long term monthly means of specific humidity
difference for January, April, July and October
Figures C.13 C.16
Long term monthly means of surface wind for January
April, July and October
Figures C.17-C.20
Long term monthly means of air temperature for
January, April, July and October
Figures C.21-C.24
Long term monthly means of sea level pressure for
January, April, July and October
Figures E.1-E.4
Long term monthly means of zonal wind stress for
January, April, July and October
Figures E.5-E.8
Long term monthly means of meridional wind stress
for January, April, July and October
Figures E.9-E.12
Long term monthly means of wind stress vector for
January, April, July and October
LIST OF TABLES
Table II.1
Summary of CDS source data sets
Table III.1
Range of input parameters
Table IV. 1
Total short wave radiation received at the top of the
atmosphere (from Ledley, 1983)
Table IV.2
Oceanic albedo as a function of month and latitude (from
Payne, 1972)
Table V.1
Heat flux divergence, meridional heat transport and area
of 50 latitude belts for Indian, Pacific and Atlantic
oceans
Table V.2
Total meridional heat transport by all three oceans
Table V.3a
Comparison of estimates of meridional heat
transport for Indian Ocean
Table V.3b
Comparison of estimates of meridional heat
transport for Pacific Ocean
Table V.3c
Comparison of estimates of meridional heat
transport for Atlantic Ocean
Table V.4
Comparison of estimates of meridional heat
transport for all three oceans combined
Table V.5a
Net heat flux estimates for two separate periods(1949-1964
and 1965-1979) and their differences
Table V.5b
Same as Table V.5a except for latent heat flux
Table V.5c
Same as Table V.5a except for incoming solar radiation
Table V.5d
Same as Table V.5a except for sensible heat flux
Table V. 5e
Same as Table V.5a except for outgoing radiation flux
Table V.6
Hypothesis test of the differences between latent heat
flux means from two separate periods in the Indian Ocean
Table VI.1
Percentage of total variance explained for separate EOF
analysis of nonseasonal SST
Table VI.2
Autoregressive model identification using Baysian
Information Criterion
Table VI.3
Percentage of total variance explained of EOF analysis for
nonseasonal net heat flux, nonseasonal incoming solar
radiation and nonseasonal latent heat flux
CHAPTER I. INTRODUCTION
The world's population has been increasing at an alarming rate.
Accompanying this is an increasing demand on our natural resources.
It
is well known that food production is extremely sensitive to weather
fluctuations from year to year.
Consumption of our natural resources
(as heating fuel and for electricity production,
to a large extent, weather dependent.
for example)
is
also,
The scarcity of our limited
supply of natural resources has made it
increasingly important to
understand the problem of interannual variability of the weather and,
eventually, to explore the possibility of making long range forecasts.
The absorption of solar radiation - the ultimate driving force of
the atmosphere - occurs primarily at the earth's surface.
The
atmospheric circulation and climate are inextricably tied to the
energy balance of the earth's land and ocean surfaces.
the ocean on climate is
especially important in
climate forecasting for a number of reasons.
The influence of
the area of long range
First of all, the oceans
cover approximately 72% of the earth's surface.
Secondly, the heat
capacity of the ocean is much greater than that of the atmosphere.
The
ability of the oceans to 'store' information from past fluctuations on a
smaller time scale makes the oceans a potentially promising candidate
for the investigation of climatic forecasting.
The understanding of the
ocean-atmosphere interactions will be a crucial step towards realizing
the future goal of a long range climate forecast.
Wliiwlwliiill
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15
Historically, studies concerning the ocean's role in influencing
the climate had been hampered by a lack of adequate data coverage.
With
recent improvements in collection and archiving historical ship reports
of surface observations,
there has been a tremendous growth in
related to air-sea interactions.
research
One of the most often reported
The
parameters is sea surface temperature (hereby denoted as SST).
conductive heat loss (sensible heat loss) of the ocean to the air is a
function of the temperature difference between the sea and the air.
Latent heat loss to the air is a function of the specific humidity
difference between the air and the sea,
where the specific humidity at
the surface is also a function of the surface temperature.
Ocean
surface temperature is thus one of the main variables in determining the
heat content of the air and its temperature.
It is the most frequently
used parameter in characterizing the fluctuations of the oceanic
surface.
In order to have an understanding of the air temperature
change and hence the climate, we need to have a good understanding of
the variability of the sea surface temperature and the physical factors
that control the observed changes.
Recent diagnostic studies on the interrelationship between the
SST's and the atmosphere have given us new insights into the behavior of
this complex system.
With advancements made in computer technology
and increasingly available data, there have been many articles that
concentrate on empirical studies of the air-sea interaction.
However,
because of the lack of unique or universally agreed on criteria and
procedure for processing data and defining relationships, it is very
difficult to compare and synthesize these studies into a comprehensive
picture.
In addition, most of the works have traditionally concentrated
on specific geographic regions.
The North Pacific and the North
Atlantic have received most of the attention because data coverage in
these areas is most complete.
Due to the complexity of this coupled
system of the oceans and the atmosphere, each having its own time scale
of behavior,
there exist many different
exerts its influence on climate.
that changes in
interpretations of how the ocean
Newell and Weare (1976) have found
the Pacific Ocean SST preceed atmospheric changes.
Frankingnoul and Hasselmann (1977) think the ocean is a low pass filter
of the shorter range atmospheric fluctuations.
Presumably the
difference in these conclusions came about because different regions
and/or different time periods were studied.
Theoretical studies, in trying to simulate the observed behavior
and explain the differences observed in diagnostic studies, have had
limited success.
One can either use a very simple model which does not
always treat the two way feedback mechanisms realistically, or, use
general circulation models (GCM) to simulate observed atmospheric
circulations given a set of anomalous SST's.
studies do not always clarify the picture.
The conclusions from these
Rowntree (1972,1976a,b)
conducted a series of experiments on a GCM using tropical SST anomalies
and found local and remote responses in the atmosphere similar to those
described by Bjerknes (1966).
Kutzbach et al (1977) ),
Others (Chervin and Schneider (1976),
using mid-latitude SST anomalies, have found
little resemblance in the model atmosphere compared to what was
observed.
Most recent studies (Webster (1981) and Pedlosky (1975))
have given us a clue as to why the contradictory conclusions arose.
It
seems that two important
reacts to a change in
factors that determine how the atmosphere
SST are : a) the atmospheric mean state when SST
anomalies are imposed, and b) the location of the SST anomalies.
There are three main causes of variations in
observed SST:
radiative transfer which is a function of the cloudiness; heat exchange
at the ocean surface;
and advective heat transfers from ocean currents,
A clarification of these
both horizontally and vertically.
relationships would be useful in obtaining a more comprehensive theory
of sea-air interaction.
So far most of the work done on the heat and
radiative budget of the oceans is
periods.
Hastenrath and Lamb (1978)
heat budget for the Indian Ocean,
Oceans.
limited to specific regions and
have published an atlas of oceanic
the tropical Atlantic and Pacific
Bunker (1976) has results for the North Atlantic.
and Wyrtki (1965)
have estimates for the North Pacific.
Clark (1965)
Weare et al
(1981) have done calculations for the tropical Pacific.
In addition to modulating climate changes through anamalous SST's,
the oceans play a major role in maintaining the observed climate on
earth.
Because of the sphericity of the earth, high latitudes receive
less radiation than low latitudes.
Without the modifying influence of
the oceans the climate would be more severe than it is today.
The large
heat capacity enables the oceans to store the large amount of radiation
received in the summer and to release it in winter.
The oceans also
assist the atmosphere in transporting the surplus of energy received in
the low latitudes to high latitudes where there is an energy
deficit.
A better knowledge of the exact nature of this oceanic
transport is
important in
understanding how the earth's climate works.
---1
Previous estimates on the magnitudes of the ocean's heat transport
have shown that it is comparable to atmospheric heat transport.
Vonder
Haar and Oort (1073), Newell et al (1974), and Oort and Vonder Haar
(1976) have estimated this parameter as a residual in atmospheric energy
balance. Oceanographers, (Bryan (1962), Bennett (1978), Wunsch (1980),
to name a few,) have also made estimates using direct measurements at
hydrographic stations for specific seasons and years.
Sverdrup (1957),
Budyko (1953), Emig (1967), and Hastenrath (1980,1982) made the
calculation using surface energy balance.
The uncertainty associated
with these estimates, different data base used, and different
computation methods used make it difficult to compare these results to
obtain a global picture of the oceanic transports.
A comprehensive data set covering the global ocean surface for a
period of 1946-1979 became available recently from Fleet Numerical
Weather Central in Monterey, California.
This data set from the Navy
contains ship observations of marine parameters that are needed to
calculate the radiative and heat fluxes at the ocean's surface.
The
completeness of this data set in both space and time provides us the
opportunity to take a new look at the energy balance of the global ocean
surface.
In this study, a survey of global oceanic variability is
performed through the analysis of seasonal and nonseasonal variations of
the sea surface temperature and the components of the energy balances
(incoming and outgoing radiation, sensible and latent heat fluxes) at
the surface of the oceans.
Oceanic meridional energy transport is
estimated for all three oceans using calculated surface energy balance
data and the relationship between the nonseasonal SST and energy fluxes
is explored.
Chapter II of this thesis describes the data set.
The history,
contents, processing and density of observations are discussed.
Chapter
III presents the annual and monthly mean and variance of the global sea
surface temperature.
calculations.
Chapter IV deals with the energy budget
The theory of the energy balance is reviewed and the
results of this calculation presented.
Chapter V presents the estimates
of oceanic meridional transport of energy using data calculated in
Chapter IV.
The theory and method of computation are discussed and
previous estimates reviewed.
The results of oceanic energy transport
for this 31-year data period are presented.
Differences in transports
between two shorter periods are calculated. The results and their
implication on short period climatic changes are discussed.
In Chapter
VI, nonseasonal variation of global SST are characterized through
empirical orthogonal function analysis.
Statistical properties of
nonseasonal SST at key regions of the global ocean are found through
autoregressive modeling.
flux is
The nonseasonal variation of global energy
also examined using empirical orthogonal function analysis.
The
relationships between SST and other nonseasonal parameters such as the
surface air temperature and the components of energy fluxes are
investigated to see how well local energy balance accounts for the
observed SST variations.
Finally, significant results from this study
are summarized in the conclusion.
CHAPTER II
THE DATA SET
The data set used for this study is derived from the Consolidated
Data Set (CDS) prepared by the Navy's Fleet Numerical Weather Central
(FNWC) in Monterey, California.
In this chapter, we briefly describe
the history, the contents, the processing and the density of this
consolidated
II.1
data set.
History
The original purpose of the Navy producing a marine data set was to
obtain synoptic analysis of hourly sea-level pressure data to diagnose
wind fields which are in
Model.
turn used to drive the FNWC Spectral Wave
The model was to be used to produce a 20-year (1956-1975),
6-hourly set of wave fields.
observations
Family-il
The data base of marine surface
in which this input data existed is
(TDF-11) data base.
the so-called Tape Data
However, the format of TDF-11 is such
that it was unsuitable for use in synoptic analysis.
needed to be extracted and reorganized.
major effort in
processing the data,
include all parameters of the TDF-l1
it
The relevant data
Since they were undertaking a
was decided that they would
data for the period 1946-1975.
This would not only satisfy the needs of the wave spectral modelling
study, but would also be useful to future research purposes.
project was started, new TDF-l1
After the
supplemental data and the marine
observations archived by FNWC since 1966 (the so-called 'SPOT' reports)
became available.
In order to form an exceptionally comprehensive data
base, it was decided to consolidate all the above mentioned data sets
into a common format.
The end product of this effort was the
Consolidated Data Set covering a period from January 1946 to January
1980.
11.2
Contents
The basic data categories which were used as input into the CDS
were the TDF-11 and FNWC Spot reports of marine surface observations.
Table II.1 below list the various data sources and periods covered:
Table II.1
Summary of CDS Source Data
Source Data
Period
TDF -11
TDF -11 Supp. A
TDF -11 Supp. B
TDF -OSV
KUNIA-SPOT
NEDN-SPOT
NEDN-SPOT
1946-1968
1968-1972
1973-1975
1946-1970
1966-1970
1970
1971-1979
The basic TDF-11 data was the product of the first monumental
effort made to collect, digitize and organize ships logs of marine
observations into machine readable magnetic tapes.
covered the period from 1946 to 1968.
issued in
This initial effort
Additional data beyond 1968 were
supplemental forms which not only included the post-1968 data
but also some historical data back to 1854.
The TDF-1l
Ocean station
Vessel (OSV) data was maintained as a separate
contained in the basic TDF-1l
file by FNWC and was not
data base supplements.
has been included in this consolidation.
The OSV data also
The FNWC's SPOT data are
archived meteorological data reports collected by FNWC.
The name
'KUNIA' and 'NEDN' are used to distinguish different formats used.
Because of the archiving procedure, tape handling techniques and
reporting inconsistencies, the 'SPOT' data set has become a notoriously
'dirty' data set.
Altogether, approximately 55 million observations
were included in building the CDS data set.
11.3
Processing
The CDS from FNWC consisted of 36 magnetic tapes of 6250 bpi
density containing ship log observations in packed binary format.
The
data set obtained was organized by mardsen squares (10* by 10* square).
Within each mardsen square, data were sorted in ascending order by 1* by
1* subsquares.
For each 1* subsquare, data have been ordered
chronologically over the period 1946-1979.
In the orginal report, up to
43 parameters were recorded including: source, longitude, latitude,
data, time and the marine observations such as wind and sea surface
temperature.
A detailed list of the parameters available within each
report is included in Appendix A.
Of the 43 marine parameters available, 9 were extracted from each
report.
They are: sea-level pressure, air temperature, sea surface
temperature(SST), dew point temperature, wind direction, wind speed,
total cloud amount, low level cloud amount and wet bulb temperature.
In addition, we extracted the associated time and space parameters:
year, month, day, hour, longitude ,and latitude.
In order to have a better handle on this copious amount of data, a
decision was made to perform some averages over space and time so that
the amount of data would be manageable for research purposes.
In
addition, averaging minimizes small-scale noise and data inhomogeneity.
Since we are primarily interested in large-scale, global phenomena of
climatic variations, we decided to take a 5* latitude and 5' longitude
average in space, and a monthly average in time.
Before each averaging,
each parameter was checked for gross errors and duplications.
Duplicate
checking was done by comparing consecutive records for an exact match of
date, location and time, plus one physical parameter.
Due to the
limitation of computer time, a more elaborate duplication procedure was
out of the scope of this project.
Since the Navy has already done some
preliminary processing in checking for duplications and validity ranges
of data parameters,
we believe the final result of averaged data is in
fairly good shape.
11.4
Data Density
The final processed data set consists of data from 65'N to 50'S ( a
total of 1100 5* by 5* squares) for the period January 1949 to December
1979 (a total of 372 months).
504 grid squares are in the Pacific, 312
squares are in the Atlantic and 284 squares are in the Indian Ocean.
The average number of observations per month for each grid square is
calculated and the results for January are presented in Figures 2.1
Indlan Long
a)
d1
20
-20---2,---3'-----40---
I
b) lndidn
10
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45
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Sea.Suraee.TepPrdture
.
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15 1151111111111111111
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Observation(maximum 31 yrs) for Months I sea.urtace..emperature
75
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40
40
50
5
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65
7
75
20
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90
95 100
15 110 115 120 125
130 135 140 145 10
Figure 2.1 Indian Ocean SST: a) Average number of observations,
and b) number of years with observation at each grid
square (January).
through 2.3
A maximum number of observations up to four hundred a
month are found at several places.
ocean station vessels.
These are locations where there were
Included in these figures are the number of
years each grid square had observations in January.
This is an
indication of how complete the time series is in each grid square (31
indicates a complete time series of 31-years.)
Figure 2.4 presents the
total number of months with observations in each square for the 31-year
indi4n
25
2u
Total
33---
217 266 233
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Total Nunber of nonths witi obccrvation- -t each
square for Indian, Pacific and Atlantic oceans
grid
-----------
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(1949-1979)_ -
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44
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of Month
.urer
3J. 35
5
0
-5
10
15
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25
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-30
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e40
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35
Atlantic
Long Tem(1949-1979) Averaged *b.
evng -6.
l
6I---
-j,
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-lu
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1W11111
1
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49 410 s6
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224 149
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s2u 161
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l2 b
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92
8b
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J115
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3
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-
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sen-Surtace.Teap
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Figure 2.3
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to
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Sea..Surgace.Y
-70 -65 -60 -55 -50 -45 -40 -36' -3U -2b -2U -16 -10
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ti
4
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1
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2
10
11
2Q
Same as 2.1 except for Atlantic Ocean SST
period. Here 372 indicates a complete time series.
These figures also
outline the geographical boundaries defined in this study for each
ocean.
It can be seen from Figures 2.1 through 2.4 that there are serious
data gaps for certain regions of the oceans.
In the tropics, except for
16
23
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areas right off coastal regions, data is generally sparse.
This is
There are also voids
especially true in the central tropical Pacific.
in major parts of the southern Atlantic Ocean, southern Indian Ocean,
and southeast Pacific Ocean.
The grid squares with high numbers of
observations seem to lie along the ship routes.
Overall the north
Atlantic and north Pacific have the best coverage.
In addition to variations in number of observations per month in
space, there are large fluctuations in the average number of
observations in the 31-year period as well.
number of observations
Figure 2.5 presents the
averaged over all the available squares for each
of the three oceans as a function of time.
in data density in 1964 and onward.
Note there is
a large jump
Presumably this is from the
infusion of data from various countries under a WMO agreement to collect
and archive marine reports.
(Sources from British Meteorological Office in Bracknell,
is puzzling.
NO.
I
The drop of number of observations in 1970
OF OBSERVATIONS FOR THREE OCEANS
04 5 S
Isf
Z0 .11.6
a
Pacifirc
i
il%i
7.2,
40.-1
1949
1951
1953
1955
Figure 2.5
1957
1967
199
1971
1963
155
1959
151
NO. O OSSERVATIONS/lITH FOR TI'EE OCEANS
1973
191
Average number of observations per month
1977
1979
NOWN1111
1, ,III
ININ
I
II I
III"ININ
III
29
England claim that the data source from the Soviet Union has stopped
since 1970.)
We suspect there are also more recent reports that were
not available when the consolidated data set was prepared.
The 5' by 5* averaging in space presented another problem in
regions where there are strong temperature gradients within the square
(for example the Gulf Stream region).
There would not be any problem if
the observations within each square were evenly distributed.
this was not always the case.
However,
We found instances where there were
significant drifts in the movement of ships during our data period.
In
some squares, the drift was severe enough to introduce an artificial
temporal trend in the data.
Appendix B documents one such particular
square and the efforts that were made to correct this situation.
11.5
Notation and Definition of Data Quantities
It should be pointed out that in all figures presented in this
document negative latitude indicates southern hemisphere and negative
longitude indicates west of the Greenwich Meridian.
Each of the 5' by
5' squares are referred to by the latitude and longitude of its
southeast corner. (i.e. the square denoted by 5 and -30 in the Atlantic
refers to the square from 5'N to 10N and from 30'W to 35'W.)
This
notation will be used throughout this thesis whenever references are
made to any particular grid point.
Several quantities are refered to often in this study and will be
defined here formally:
The long term annual mean for any variable x at any geographical
location i is defined as:
1
N
xi
NeM
M
k=1 j=1
Kijk
where N is the number of years and M the number of months with available
data at i.
The long term monthly mean for any month
1
Xij
=
j
is defined as:
N
-
N
Xijk
k=1
The standard deviation for the annual mean is
1
si =
[
N
M
(xj
-.
N-M
i)2
]1/2
k=1 j=1
and the same quantity for the monthly mean is
sig =
[
1
N
N
k=1
(xijk~Tij) 2 ]1/2
-
The monthly anomaly is defined as the departure from the monthly mean:
X
ijk
~ Xijk
-
xij
CHAPTER III STATISTICAL PROPERTIES OF SST
In this chapter we present some statistical properties of the
global SST field derived from CDS.
The long term annual and monthly
mean and standard deviations of SST are presented.
The histograms of
the global SST and the autocorrelation of SST are also calculated to
give an indication of the nature of the statistical distribution and the
persistence in SST.
III.1
Annual Mean and Variance
To characterize the long term behavior of the SST field, the long
term annual mean and annual standard deviations for the three oceans are
calculated and presented in Figures 3.1 to 3.3
mean SST is presented in Figure 3.4.
.
A plot of the annual
As can be seen in Figure 3.4, the
distribution of the annual SST pattern is latitudinal in general except
for regions where boundary processes such as upwelling and the western
boundary currents dominate.
Although the 5' by 5' resolution is perhaps
too coarse to absolutely define the Gulf Stream and the Kuro-Shio
current,
the
this analysis does show that the temperature gradient in
Gulf Stream is much higher than its counterpart in the Pacific.
see the influence of the Gulf Stream all the way to 60'N.
another important feature.
One can
Upwelling is
The clearest example is along the South
American coast where the 26' isoline bends northward from the 20*S
latitude line over the Pacific to the 5'S latitude line near the
Peruvian coast.
A weaker but still obvious example is the upwelling off
ANNUAL MEAN SST
4
3
r-
2
LONGITUOE
Figure 3.4
Long term (1949-1979) annual mean SST
the African coast.
The western Pacific and the eastern Indian Ocean
along the equator have a large body of >28* temperature, the highest SST
observed.
Other features include the cool California current and
upwelling off Baja California.
Since the annual variance contains seasonal variation, the
variances at extratropical regions are obviously larger than those in
the tropical region (see Figures 3.1 through 3.3).
The largest observed
variance occurs, not surprisingly, in western boundary current regions.
Water influenced by the Kuro-Shio and the Gulf Stream both have standard
deviations larger than 6'C.
The Pacific Ocean contains more grids with
greater than 3*C standard deviations
in mid-latitude than the Atlantic.
33
Atlantic Ocean Long Term
-100 -95
65-.
60---.
55--50--45--40--35--30--25-20--15--10--5--0---5---10---15---20---25---30---35--.40---45--50---
-90
Nean
(1949-1979) Using
New
095 -80 -75 -70 -65 -60 -55 -50
0
0
0
0
0
0
0
0
0
0 . 0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0 123
0
0
0
0
0
0
0
0 174 100
0
0
0
0 250 237
248 251 262 261 263 253
257 264 273 271 272 271
0
0 230 279 279 278
0
0
0 279 277 272
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0. 0
0
-100 -95 -90 -85 -80 -75 -70
0
0
0
0
60
110
213
232
252
269
275
275
0
0
0
0
0
0
0
0
0
0
0
0
-65
0
0
0
0
0
0
0
0
67 66
128 147
218 217
231 229
249 249
265 261
273 270
27627
0 277
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
-60 -55
0
21
47
36
56
139
213
227
246
256
266
274
276
0
0
0
0
0
0
0
136
0
0
0
-50
Filled Data for Atlantic-BST
-45 -40
-35 -30 -25
-20 -15 -10
.5
0
21
52
72
66
146
210
225
243
254
262
269
276
276
0
0
0
0
231
222
209
0
0
0
-45
0
63
75
95
145
177
201
220
235
245
251
260
270
273
274
272
239
261
252
234
0
0
0
0
-35
41
5
10
125
143
166
188
207
219
227
237
255
270
270
264
264
257
245
236
223
193
0
0
0
-20
0
92
109
128
144
160
136
200
207
202
231
254
273
267
260
260
249
238
230
219
190
0
0
0
-15
59
9
108
122
139
154
178
193
0
0
0
0
0
271
254
251
235
224
221
209
191
0
0
0
-5
Atlantic Ocean Long Term Standard Deviation (1949-1979)
0
47
63
96
128
175
205
223
239
250
257
264
275
275
0
0
0
0
237
233
195
0
0
0
-40
0
74
37
108
144
175
196
216
230
241
246
258
269
271
271
272
269
262
244
229
0
0
0
0
-30
Using New
61
13
99
118
143
171
191
212
226
235
243
257
270
272
266
266
262
254
241
225
0
0
0
0
-25
Filled
0
88
111
128
141
160
131
195
200
0
0
0
277
272
256
254
243
232
227
212
190
' 0
0
0
-10
10
72 31
94 93
98 97
121 113
131
0
0 179
136 191
0
0
0
0
0
0
0
0
0
0
0
0
272 275
255 260
246 246
233 224
217 210
214 205
207 199
137 134
0
0
0
0
0
0
0
5
6
90
99
105
0
177
191
0
0
0
0
0
0
275
259
254
223
203
195
193
163
0
0
0
10
15
20
0
0
0
0
0
0
0
0
0
0
117 165
0
0
0
0
0
0
0
0
0
0
- 0
0
0
0
0
0
0
0
0
0
233
0
182
0
172
0
178
0
181 172
0 12
0
0
0
0
15 20
Data for Atlantic.SST
-100 -95 -90 -85 -00 -75 -70 -65 -60 -55 .50 -45 -40 -35 -30 -25 -20 -16 -10
1
S
0
-5
0
5
10
15
20
11111111 20 20 19 2111111111
17 16 13 lb 17 25 2411111111
13 13 13 19 24 32 4111111111
13 19 20 23 30 38 4711111111
20 21 22 24 261111111111111111
23 25 23 211111 40 37 39 42
23 24 22 21 32 33 3311111111
22 21 20 221111111111111111111
19 13
17
19 25 3 2ti 21711
40 34 713911
26
17
271111111111111111111111111111
9 10
1117
251 211111111
10 13 13 15 1
32 1411111111
13 15 20 16 19 20 2211111111
12 14 14 17 18 20 2411111111
5-60--55-50--45--40--35--30--25--20--15--10--5-.
0---5-..
-10--
11111111111111111111111111111111111111111111111111111111
18 17 22 19 17
111111111111111111111111111111111111
111111111111111111111111111111111111 22 22 21 19 18
111111111111111111111111111111111111 28 26 I
21 19
1111111111111111111111
43 55 53 46 38 28 21 20
11111S11111111111111 57 47 50 45 45 37 20 27 27
1111111111111111 61 47 36 31 30 30 30 29 28 27
1111111111111111 26 28 30 30 30 29 23 27 26 2b
35 34 24 25 20 23 23 24 22 22 21 20 20 20
26 21 15 19 15 14 15 14 14 14 14 13 14 14
11111111 11 10 10 10 11 10 10 10 10 11 12 14
-15-~~2 1
111111111111
9 10
9
9
8
9 10 12 12 13
7
6 15
9
S
6
4
5
7
6
11
i
9
-20-26
-25-246
-40---30-W
-S5---35---
13 15 16 15 14 15 17 16 20 21 241111
2
11111111111111111111111111111111111111111111111111 11 90111111111111111111
0111111111111111111
10 1t 10 19 191111
25 11 22 23 23 24 24 24 23 21 19 16 111111
1111111111111111111111111
111111111111111111111111111111111111111111111l111
111111111111111111111111111111111111
35 27 25111111111111
2
25 24 25 22 21 19 1
1
15
13
16
20
23
23
23
20
17
13
14
7
16
10
10
100 -95 -90 -5 -00 -75 -70 -65 -60 -55 -0 -45 -40 -35 -30 -25 -20 -15 -10
Figure 3.1
-5
0
S
10
15
20
Atlantic Ocean SST: Long term annual mean and
standard deviation
The variance in the tropical region varies typically from .7*c to
1.00 C.
The exception is in the eastern tropical Pacific where standard
deviations of 2.70C are observed.
North Africa is also of note.
observed.
The upwelling region off the coast of
Standard deviations as high as 3.10C are
In the Indian Ocean, the Adrian Sea is where the largest
variance (4.1 0C) occurs.
Pacific ocean bona Term
Mean
for PacIfic-53T
(1949-1979)
135 140 145 150 155 160 165 170 175 180-175-170-165-160-155-150-145-140-135-130-12b-120-115-110-105-100 -95 -90 .85 -60 -75 -70
0
0
0
0
0
109
171
225
242
263
200
286
286
287
.5*
-10*
-15*
-20*
-25*
-30*
-35*
-40*
-45*
-50*
0
0
0
0
0
128
169
220
242
267
292
296
297
263
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
116
199
219
244
269
261
284
267
209
0
0
0
0
0
0
0
0
0
0
0
0
0
0
62
96
161
21b
245
270
291
284
296
209
0
0
0
0
0
0
0
0
0
0
0
0
0
0
53
110
191
214
244
271
281
264
268
290
0
0
0
263
247
234
211
181
0
0
0
0
0
44
58
109
179
212
244
270
290
284
28
0
0
0
0
265
246
230
211
179
0
0
0
0
0
52
66
105
178
211
244
268
277
264
289
0
0
0
0
265
243
226
201
174
0
0
0
0
0
55
65
107
177
210
243
266
275
261
297
0
0
0
0
269
242
223
192
171
0
0
0
0
0
57
66
115
176
209
241
263
272
260
296
0
0
0
281
269
247
220
169
168
0
0
0
0
0
57
69
120
174
208
240
261
270
277
0
0
0
0
285
270
247
221
196
177
0
0
0
0
46
53
72
122
173
206
236
256
270
274
0
0
0
0
297
274
249
222
190
173
0
0
0
0
47
60
75
123
171
205
23b
256
267
272
0
0
0
0
296
276
251
219
191
166
0
0
0
0
49
62
73
123
171
204
235
255
264
269
280
278
0
0
287
273
252
222
109
164
0
0
0
0
54
66
92
124
170
204
233
253
261
269
278
277
0
0
285
274
250
220
196
163
0
0
0
0
68
68
95
126
171
204
231
248
257
266
277
273
0
0
284
275
253
221
198
160
0
0
0
0
70
72
99
127
172
204
231
241
251
264
276
273
0
0
282
274
249
221
191
157
0
0
0
0
76
73
94
130
173
202
227
237
249
263
275
0
0
0
290
273
249
216
194
155
0
0
0
0
14
3
98
133
172
199
216
232
245
261
274
0
0
0
276
270
255
221
195
159
0
0
0
0
91
93
104
139
168
192
206
227
241
261
273
0
0
0
273
266
255
225
191
162
0
0
0
0
93
101
111
13V
163
182
199
221
236
261
272
0
0
0
269
265
250
232
191
162
0
0
0
0
0
0
115
131
151
171
192
214
236
263
272
0
0
263
264
262
247
229
193
0
0
0
0
0
0
0
114
119
133
157
18e
211
244
267
271
261
254
259
259
256
240
22?
200
0
0
0
0
0
0
0
0
0
0
169
182
213
254
272
273
257
251
255
255
249
244
228
0
0
0
0
0
0
0
0
0
0
0
0
199
225
265
277
274
255
246
252
248
244
239
0
0
0
0
0
0
0
0
0
0
0
0
0
0
257
272
282
276
253
241
248
242
233
234
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
293
286
277
250
238
243
239
232
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
287
263
278
255
236
242
234
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
275
294
274
261
236
241
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
276
276
264
237
236
0
0
0
0
0
0
0
0
00
0
0
0
0*
0
0
0*
0
0
0
0*
0*
0
0
0*
0
0
0
0
0*
0
0
0
0
0
0*
0*
0
0
0
00
0
0
0
0*
0*
279
0
0
0*
265
234
0
0
0
202
0
0
216 190
0 191 169
0 191 167
0
0'167
0
0
0
0
0
0
0
0
0
0
0
0
.
65.
60
55
50
45
40
35
30
25
20
15
10
5
0
135 140 145 150 155 160 165 170 175 1S0-175-170-165-160-155-150-145-140-135-130-125-120-115-110-105-100 -95 -90 -I5 -80 -75 -70
Pacific ocean Long Term Standard Deviation (1949-19791
for Pacific.S&T
135 140 145 150 155 160 165 170 175 180-175-170-1&5-160-155-150-145-140-135-130-125-120-115-110-105-100 -95 -90 -85 -00 -75 -70
1111160
2111111111111111111111111055
31
32 30
27
28
27 30Q 29
1111111111111111111111111128
29
29111111111111111111111111111111111111111111111111*50
29
29 29
25 27
29
22
34 29
25 23 22
11111111111111111111 37
29
29
27 2311111111111111111111111111111111111111116 45
26 27
26
29
29 29
26 27
26
36
39
37 33 30
111111111111 44
24
151111111111111111111111111111111111111119 40
30
26
32
31
33
33
32
33 33
33 33
43
39 37 35
55 52 49
66 62
161111111111111111111111111111111111111111* 35
22
20
28 25
30
35
35
34 33
35 35 35 35
36 36
40
39
53
44 42
53
16 17
191111111111111111111111111111'11111111* 30
19
27
25
21 20
32 31
29
33
34 34 33
36
36
35 35
36
36
36
36
2711111111111111111111111111111111* 25
15
14
15 20
15
15
15
22
20
17
25
24
23
26
27
25
31
30
29
31
29
30
30
30
251111111111111111111111111111* 20
14
18 21
11 11 11 13
14
13
12 12
16 16
15
17
11 19
17 17
19
17
22
21
10
161111111111111111* 15
19
12
15 14
13
14
12
13 14
11 11 11
12
11
11
12
13 12
12 12
11
11 11
12
11
12
10 11111111111111* 10
7 12
11
9
7
14
12
13
13
11
12
13
9
11
11
12
11
11
10
10
10
11
0
.
I
1
8
5
711111111*
11
11 10
9
10 is
11
9
9 10
9 10
9 10
11
a
9
9111111111111
9
9 11
3
7
7
a
9
0
7 11 1 1
5 1
9 i
1
6 1
13 1211111111111111111111
11 11
711111111111111111I11111111111
1
7
9
9
1211111 111 1711111111111
-5*1 111
111 11711191111112311
1111 111 1114111
1111112111 111 111111111 111111
115111111
1111111211111
-10* 111 111111
29 231111
1411111111
11 12
10
10 It
10
10
9 10
9
9 10
9
9
9
10
9 10
-1591111111111111111111111111111
25 24
121111111111111111
12
11 12
12
11 11 12
11
11
11 12
12 .11
11
16 14
14 14 12
16 16
-20*111111111111
23 24
14
15 1511111111111111111111
14
14
15
15
15 16
17
16 17
17
16
17
17 17
20
19
10 17
-25*111111111111
21
19
19
20
20
19
20
20
21
20
20
20
20
20
19 19 20
20
19
-300111111111111
1
11111111111
24 24
22
22
22 24
22 21
22
23
22 22
21 21 21 24
20
311111111111
24
24 21111111111111111111111111111111111111111
22
22 23
23
22
22
23 23
22 23
22 24
22
23 22
-40*1111111111
135
140 145 150 155 160 165 170 175 10-175-170-165-60-155-15045-140-135-130-125-120-115-110-105-100
Figure 3.2
Pacific Ocean SST:
-95 -90 -65 me0 -75 -70
Long term annual mean and standard deviation
111.2
Monthly Mean and Variance
The long term monthly means of SST are calculated and the results
for one month in each season are illustrated from Figures 3.5 to 3.8
In general,
the variations in higher latitudes are mostly zonal with the
exception of the Gulf Stream region and upwelling areas.
The
longitudinal variation is most evident in the Atlantic ocean.
The mean
temperature gradient in the southwest Pacific and south Indian ocean
stays fairly constant throughout the year.
In the tropical oceans, the
most pronounced feature is the migration of the >28' body of water.
expands from January to April and moves northward in
location changes relatively little
July.
from summer to fall.
It
The
The mean
temperature gradient in the eastern Pacific has large seasonal
variations.
In January, it is at a minimum.
In April, the
intensification starts at the Peruvian coast when the expansion of the
28* C water pushes the gradient southeastward.
about twice that of January.
in the fall.
By July, its value is
The gradient gradually starts decreasing
Similar movement is
observed off the south African coast
in the Atlantic and at the 20*S region in the Indian Ocean.
When the seasonal component is removed by calculating the standard
deviation with respect to individual monthly means,
somewhat from the annual standard deviations.
the scenario changes
Figure 3.9 to
3.11 presents the standard deviations of the three oceans.
Months
January and July are selected to illustrate the standard deviations
representative of the winter and the summer seasons.
In Figures 3.10
and 3.11, the Gulf Stream and the Kuro-Shio still dominate the variance
Filled
Indian Ocean Long Term Mean (1949-1979) Using mew
20
35--30--25--20--15--10--5--0---5---10---15---20---25---30---35---40---45---50--'20
25
30
197
203
0
0
0
0
0
0
0
0
0
0
0
0
185
191
0
0
194
208
0
0
0
0
0
0
0
0
0
0
0
0
210
201
0
0
25
30
Data for Indian.SST
40
45
50
55
60
65
70
75
to
I5
90
211
0
0
215
247 260
0 278
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0 267
0 259
242 241
227 220
195
0
0
0
0
0
0
0
0
0
291
264
0
269
270
272
273
270
258
239
210
0
0
0
0
0
0
0
0
279
267
270
273
273
270
0
250
241
205
0
0
0
0
0
266
0
266
269
269
273
276
274
267
261
251
231
201
0
0
0
0
0
275
267
260
269
275
2R1
281
274
266
257
252
225
0
0
0
0
0
0
0
267
270
276
202
285
203
276
266
258
0
0
0
0
0
0
0
0
0
267
276
282
284
286
2R4
278
266
259
0
0
0
0
0
0
0
0
0
0
279
284
285
285
2R3
275
270
0
0
0
0
0
0
0
0
0
0
0
0
282
280
284
28J
278
267
256
0
0
0
0
0
0
0
0
0
0
263
294
232
284
283
278
268
252
0
0
0
0
0
0
0
0
0
0
281
284
284
284
284
281
269
254
0
0
0
0
0
0
40
45
50
55
60
65
70
75
80
35
90
35
35
95 100 105 110 115 120 125 130 135 140 145 150
0
0
0
0
280
284
285
285
0
280
272
254
229
0
0
0
0
0
0
0
0
0
0
284
288
291
0
279
271
254
231
206
0
0
0
0
0
0
0
0
0
289
286
289
0
281
271
260
226
207
179
0
0
0
0
0
0
0
265
273
279
284
286
282
272
259
233
209
184
0
0
0
0
0
0
252
269
279
201
286
285
284
277
263
241
217
196
166
0
0
0
0
0
250
276
282
285
286
288
283
201
0
0
0
197
179
0
0
0
179
234
264
276
284
2@4
287
0
283
283
0
0
0
0
165
0
0
0
0
0
0
0
0
0
0
200
0
0
0
0
0
244
0
0
0
0
260
0
0
0
0
277
0
0
0
0
284
0
0
0
0
284
0
0
0
285
0
0
0
0
0
0
0
0
281 279 277
0
0
0
0 277
0
'0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
158 156 154 154 150
0
0
0
0
0
0
0
0
- 0
0
95 100 105 110 115 120 125 130 135 140 145 150
Indian Ocean Long Term ftandard Deviation (1949-1979) Using New Filled Data for Indian.SST
20
25
30
35
40
45
50
55
65
60
70
75
80
85
90
95 100 105 110 115 120 125 130 135 140 145 150
1111111111111111
41 1
111111111111111111111111111111111111111111111111
3
2
611111111
3
441111111111111111
31 30111
11111111111111111111111111111111
111111111111211711
37 35 1 11
12
921111111111111111
41
1111111111 23 2511111111
31
9
9
1111111111111111
11
3 10
1111111111111231111111
9
7
81111111111111111
91 1
14
17b
121111111111111
9 10
11111 91111111111111111
11 1
8
9
8
8
13
9
20
18
111111111111111
9 101111411111111
1
10 10
1 8 10
8
8
17 14
1
10
111111111111111116
13 1019171
1111111111111111
16
1
1
7 1
11
1
1
14
13
13
111111111111111
1 1
111111111111111111111111
1
91 19 20 22
13111111111111
1111111131
35--30--10--20--15--IQ--5--0---5------40---
1
20120
-40---
16
11111
116111
1111111111111111
7 111
1Is1
111111111111111111111111
1
20
26
30
35
40
45
Figure 3.3
50
60
12
18 14
141411111111111111
2
171
117
17
411111111111111111111111111111111111111111161
11
711 91111111111111111111111111111111 1111151111111111111111111111111111
2
55
16 17
17I
6
5
70 72
15
90
95 100 105 110 115
120 125 130 135 140 145 150
Indian Ocean SST: Long term annual mean and
standard deviation
pattern of the global ocean although their magnitudes are much smaller
than the annual case (maximum of 2.5%
winter. )
The variances in
is observed in the Kuro-Shio in
upwelling regions of the oceans become
comparable to the western boundary current regions.
There is not a
great deal of difference among the standard deviation of different
months, although summer standard deviations seem to be slightly larger.
The southern hemisphere generally exhibits larger variance than northern
hemisphere at the same latitude.
In general, our long term
statistics of the global sea surface temperature do not show any
unexpected features except for the more extensive coverage in the
Southern Hemisphere.
MONTHLY MEAN SST MON=1
LONGITU OE
Figure 3.5
Long term monthly mean of SST for January
MONTHLY MEAN SST MON=4
-I
LONGITUDE
Figure 3.6
Long term monthly mean of SST for April
MONTHLY MEAN SST MON=7
rc:)
--4
LONGITUDE
Long term monthly mean of SST for July
Figure 3.7
MONTHLY MEAN SST MON=10
60
~DEGC)
40
14
16
30
26
2
-
2
2-~1028
I
NN~
22
168
20
/s
30
~
2220r
-20
-N22
-0
s
-16
I OMrGITilE
Figure 3.8
Long term monthly mean of SST for October
JIdIan Ocean Ponthly Standard Deviation (1949-1979) Using pew Tilled Data for Months I for Indian.S5T
50 55 60 65 70 7S go gS 90 95 100 105 110 115 120 125 130 135 140 145 150
20 25 30 3b 40 4
35---
7
1
20--1510--5-0---5--10---15---20---25---30---35---40---45--.50 ---
1
30
35
40
45
50
55
60
65
70
75
80
35
90
95 100
11
12
6
6
5
91111111111111111
71111111111111111
11
91111111111111111
6
71111111111111111
6
I
41111111111111111
6
7
71111111111111111
6
6
611111111111111
5
I
6
5111111111111111111111111
5
711111111
7
6
7
7
7
611111111
911111111
11
11
111111111111111111111111111111
151111111111111111111111111111
91111111111111111111111111111
9111111111111111111111111
9
15
10
9 11
a
7
S
12
1 1
1 1 1 1
1 1 11 1 1
1
105 110 115 120 125 130 135
11
1
140 145 150
Ocean Monthly Standard Deviation.(1949-1979) Using pew rilled Data for Months 7 for Indian.SST
20
25
30
35
40
45
50
55
60
65
70
75
80
a5
90
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55
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30
IS
90
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Indian Ocean SST: Long term monthly standard
deviation for January and July
111.4 Frequency Distribution
The variance field give us an idea of how variable the oceans are
and the mean field tells us the expected value at any given month.
It
would be of interest to know how the SST is distributed from a
statistical point of view.
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0
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10
15
Atlantic Ocean SST: Long term monthly standard
deviation for January and July
then we would know, given a mean and a standard deviation, how its
anomalies would be distributed for the field.
more than two times
For example, anomalies
its standard deviation should not occur more than
20
4.5% of the time and anomalies three times its standard deviation should
not occur more than .2% of the time if
distributed.
We have calculated histograms for every grid point of the
Bendat and Piersol) to check
ocean and applied the normality test (p.121
whether SST's are normally distributed.
negative.
normally
a given variable is
The result is overwhelmingly
Less than 2% of the total possible 1100 grid squares can be
considered to have a normal distribution and there' is no spatial
coherence to those grid squares that do indicate a normal distribution.
a) Mid
b)
-lotitude
Subtropics
30N, 150w
50N, 175W
90
807060-
504030Z20I-
>10
o
2
I
4
6
8
10
12
14
c) Tropics
5N/170W
90-
16
18
d)
20
22
24
26
28
30
32
Eastern tropics
IOS,
95W
80-
:70 6050403020-
10
262830824
Figure 3.12
32
20
22
24
26
28
Typical frequency distribution of SST at
selected grid squares
The results of the histograms from this analysis are too voluminous
to present completely.
Figure 3.12 illustrates some of the typically
observed distributions of SST.
Figure 3.12a is the typical pattern of
the northernmost high latitude locations.
It is a skewed distribution.
Figure 3.12b is the typical distribution for regions from 20'N to 45'N
in the Pacific and from 25'N to 55*N in the Atlantic.
bimodal distribution.
It is clearly a
Initially, we suspected this might be due to
the
result of the nonstationarity of the time series with two different long
term means for two different periods.
The data set was then divided
into two subsets: 1949-1964 and 1965-1979. Similar results are observed
from both subsets.
In addition, a similar bimodal distribution is also
observed at mid-latitudes in the southern hemisphere.
The monthly mean
maps of SST in Figures 3.5 to 3.8 indicate that in these regions the sea
surface temperatures tend to have a summer mean and a winter mean, even
for the transitional seasons of spring and fall.
conclude that the bimodal structure is
This led us to
from the seasonal cycle at these
latitudes.
In the tropics, the distributions become centered around narrower
temperature ranges.
The exception to this is again in upwelling regions
in the tropics where a more 'squatter' distribution is noted.
In some
squares there is even evidence of another bimodal distribution such as
the one shown in Figure 3.12d.
This type of distribution might be a
result of the frequent occurrence of
El Nino which gives the time
series a secondary peak that is warmer than the mean.
However, the
bimodal structure is not observed in all grid squares in the eastern
tropical boundary region.
(b)
0
x
a
C-3 PACIFIC
INDIAN
E
EEM ATLANTIC
0
-
x
2.
0
10
5
15
25
20
SST IN DEGREES
Figure 3.13
30
0
5
s0
15
20. .
25
AIR TEMPERATURE IN DEGREES
C
Histograms of frequency distribution of SST
and air temperature for three oceans
Frequency histograms of SST for each of the three oceans are
presented in Figure 3.13
.
Together on the same figure is the
frequency histograms of air temperature in the data set.
As can be
seen from the figure, the distributions of SST, and air temperature are
almost identical.
The SST distributions in the Pacific Ocean and the
Indian Ocean both have their maximum at 28C while the Atlantic peaks at
29'C.
One feature worth noting here is that almost no SST (or air
temperature) is observed to be larger than 31*C.
This fits precisely
with the evaporation buffering limit that was proposed by Newell and
Dopplick(1979).
C
CHAPTER IV.
1V.1l
ENERGY BUDGET
Theory
Energy Balance of the Surface Layer
IV.la
The equation governing the change of sea surface temperature can be
derived from the second law of thermodynamics (conservation of enthalpy)
as:
DT
(4.1)
= q
Dt
where T is the sea surface temperature; D()/Dt the total derivative
operator and q the rate of heating.
Expanding this equation further,
we have:
I
3T
--
(4.2)
VT + q
V
at
aT/at is the local time derivative operator.
Here
The term - V - VT
represents the advective processes.
When we consider the sea surface temperature change over a finite
mixed layer of uniform temperature with depth D and over a finite time
period t,
0
t
f
0
the integral form of the above equation can be written as
f (pC
-D
...
) dz dt
at
f
0
f (Qv + Q) dz dt + f
-D
0
t
0
t
aT
0
f Qd dt
-D
(4.3)
where
= water density
p
Cp = specific heat capacity of water
Q
= total energy- transfer across air-sea surface
Qv = horizontal advection of heat into the layer
Qd = vertical flux of heat into the layer at depth D
Theoretically , the local rate of the temperature change over a
finite layer can be estimated from Equation (3.3).
In practice, this is
rarely done because of the following reasons:
1)
3T/3t has to be estimated from finite difference schemes,
2)
Q
has to be inferred from empirical formulas,
3) the depth of the mixing layer D is not well known,
4)
the current data needed to estimate Qv and Qd are not
available directly.
Each of the above factors contributes to the uncertainties of the
estimates. In this study, we will not attempt to specify the individual
terms in equation (2) directly.
perform
However, we do have data available to
a detailed calculation of the second term in the equation - the
total energy flux across the sea and air interface.
It
is
hoped that
from this calculation we will see how much of the local SST change is
accounted for by this term.
IV.lb Energy Flux Formulations
The total energy flux
Q
can be separated into four components:
Qnet" Qin~ Qout~ Qh
-
Ql
(4-4)
Here we are using Qnet to denote the total energy flux. Qin
is the
incoming solar radition; Qout is the outgoing longwave--radiation; Qh
is the sensible heat flux and Q, is the latent heat flux.
The following sections describe the formulations used to estimate each
of the components of the energy transfer fluxes.
The formulas applied by most researchers to calculate sensible and
latent heat fluxes are the so-called bulk formulas:
Qh=Cp Pa CeIvI(Ts-Ta)
(4.5)
Ql=Le Pa Ce vl(qs~qa)
(4.6)
where the meteorological variables are:
Ivl=wind
speed in m/s
Ts =sea surface temperature in deg. K
Ta =air temperature in deg. K
qs =specific humidity corresponding to Ts
qa =specific humidity of air in g/kg
and the constants are:
1
C,=specific heat of air (=1.0048 x 103 J kg-lK- )
Le=latent heat of evaporation (= 2.5008 x 106 J kg- 1 )
Pa=air density in kg/m 3 = (RTa/Ps)
R = ideal gas constant (= 287.04 J kg~K
1
)
ps= sea level pressure in mb
Ce= transfer coefficient; function of
lvi
and (Ts-Ta)
These formulae are finite difference approximations of the equation
for the vertical flux of a property x:
ax
Fx =
Here
Kx
K
-- az
(4.7)
is the eddy transfer coefficient and turbulent exchange is
assumed to be the dominant mechanism affecting the vertical
distribution.
The choice of the transfer coefficient is a perplexing problem.
Budyko (1963) in his estimate of the annual mean energy transfer over
the world ocean used constant transfer coefficients. Bunker (1976)
estimated the energy balance over the North Atlantic ocean using an
update of the transfer coefficients. He determined values of the
coefficients as a function of stability and wind speed from results by
other researchers and data of experiments at sea and in laboratories. He
ignored the difference between the coefficients of latent heat and that
of sensible heat. Since sensible heat flux is an order of magnitude
smaller than latent heat, this difference is negligible. Liu et al
(1977) developed an iterative method for estimating the transfer
coefficients using boundary layer theory.
These are just a few of the available formulations for estimating
the transfer coefficient Ce.
Although the methods of various
estimates of the coefficients are different, the results for most
meteorological conditions are quite similar. We decided to use Bunker's
formulation of Ce as a function of wind speed and atmospheric
stability (defined by the difference between the sea surface temperature
and air temperature.) The coefficients are easily calculated with the
data on hand.
10
01111b
J11161111M
I
11111,111
, AM
1
1.
49
The meteorological data required to calculate the energy fluxes are
lvi, Ts, Ta, qas qs, and ps.
All are available from the
consolidated data set except qs and qa. These are calculated by:
.622
e
e
(4.8)
q =
ps -
.378 e
where e is the saturation vapor pressure. It is computed using a
polynomial approximation as a function of temperature (Lowe, 1977). For
qa, e is calculated using dew point temperature. For qs, e is
calculated using sea surface temperature.
In this study, when Iv
calculated.
is missing, none of the heat fluxes are
When Ta or Ts are missing,
sensible heat flux is
not
calculated. When qa or qs are missing, latent heat flux is not
calculated. When ps is missing, air density is assumed to be 1.2 kg/m3
and ps is set to 1000 mb in the formulation for q.
The outgoing radiative flux is calculated according to the formula:
Qout= 4 eaTa4 (.39 -
.05 /e)-(1 -
aoutC 2 ) + EaTa 3 (TS-Ta)
where
Qout= the outgoing long wave radiation
aoutlfunction of latitude; varying from 1. at the poles
to .5 and equator
C
=emissivity of water (ratio of radiation of the sea to that of
a black body) = .97
a
=
Stefan-Boltzman constant = 5.6697 x 10
C
=
cloud cover in tenths
in watt/m2 *T-4
The notation of meteorological variables are the same as before.
Finding the appropriate formulation for the net radiation received
at the surface is an extremely difficult task.
First of all, one needs
the total radiation (direct and diffuse) received at the ocean surface
under clear sky.
The direct radiation received at the top of the
atmosphere is fairly well known and can be calculated given present day
astronomical parameters and a solar constant.
To estimate the radiation
at the surface, one needs a knowledge of the climatological mean of the
transmissivity of the atmosphere,
and this is
not well known.
Secondly,
the cloudiness affects the amount of the solar radiation received and
its effect is
usually included with an empirical relationship. Thirdly,
the albedo of the ocean surface has to be taken into consideration.
There are uncertainties involved at each stage of the estimation and
there are many formulations available in the literature. For comparison
sake, one would like to use the same formulation used by most other
researchers. Budyko's formulation seemed to be a good choice.
Qin = Qo (-
ainC -
He used values from Berliand's
.38 C 2 ) (1 -
(1960)
A)
(4.10)
estimate as the total radiation
received at the surface under clear sky (Qo),
and a quadratic function
of cloudiness to correct for the effect of clouds. For oceanic albedo A,
he used an empirical estimate of values from .06 to .23 .
Application
of this formulation gave results that are unrealistically low.
example,
in
For
the tropics values of solar radiation received at the
surface are less than 200 watt/m 2 . At the suggestion of Simpson and
Paulson (1979), we used a formulation given by Reed (1977) for
estimating the insolation over the oceanic surface
Qin" Qo (1.-.62C + .0019a)
(1.-A)
(4.11)
Here a is the solar noon altitude (in degrees) and is calculated by
sina = sint sin(23.45 sin(t-82)) + cost cos(23.45 sin(t-82)) (4.12)
where I is the latitude and t is the day of the year. Qo is the total
radiation received at the surface. To estimate Qo, Reed (1977) used a
formulation given by Seckel (1970) which, at low latitudes, should be
the same as the direct radiation at the top of the atmosphere with a
transmissivity of .7 . Since Seckel only gave formulae for low latitudes
and we also need values for high latitudes, we decided to use the direct
radiation received at the top of the atmosphere calculated by Ledley
(1983) using present day astronomical parameters.
We then adjusted this
for the transmissivity of the atmosphere . It took many experiments to
arrive at an appropriate value for the transmissivity of the atmosphere.
Values from .75 to .65 were considered as possible candidates.
The
final selection of .68 is based on the consideration of three
constraints.
First of all, the incoming solar radiation calculated at
the surface using the chosen transmissivity should be comparable with
independent calculations by others.
For this we have used values
presented by Weare (1980) in the tropics and by Bunker (1976) and Clark
(1967)
in
the mid-latitudes.
This comparison ruled out any value
greater than .7 because values of Qin calculated were much too large.
The second constraint considered was Wunsch's estimates of maximum and
minimum transport values at 24'N and 48*N in
(personal communication).
the Atlantic Ocean
He presented a range of 8 to 13 x 1014
watts at 24'N and a range of 1 to 7 x 1014 watts at 48*N.
Transmissivity values greater than and equal to .7 would all give
transport values that are below the minimum values at these latitudes.
The last constraint concerns the transport values at the southern
boundaries.
Since a north to south integration technique was used to
calculate the transport values, the final transport at the southern most
latitude (40*S)
should be in
general agreement with independent
estimates at the same latitude if our values are reasonable.
results from Georgi and Toole (1982)
at 40*S were used.
Transport
They obtained a
transport of -6.67 x 1014 watts at 40*S (negative indicates a
southward transport).
Transport values calculated for three
transmissivity values .7, .68 and .65 gave values of -16.58 x 1014,
-4.37 x 1014 and +18.74 x 1014 respectively.
considerations,
With the above three
a final values of .68 was chosen as the most suitable
value to use.
The values of QO used are presented in Table IV.1 . The oceanic
albedo (A) is
taken from Payne (1972).
It
is
a function of month and
latitude, ranging from .4 around the edges of sea ice to .06 at the
center of the ocean basin (see Table IV.2).
These are climatological
results derived from an experimental study of the albedo of the sea
52a
(d)
C"]
E
EZ
Os-0o
1 6
8
o
e
14
a
W
2D
ZZ
DEW POINT TEMPERATURE IN DEGREES C
IN G/KG
MERIDIONAL WIND (v)
PACIFIC
INDIAN
ATLANTIC
IN m/sec
ZONAL
24
IN m/sec
0
x
WIND SPEED IN
Figure 4.1
M/S
Frequency distribution histogram of the
wind speed, zonal and meridional wind components, dew
point temDerature, cloud cover, and drag coefficients.
26
Table IV.2
Mlar
Apr
'May
Jun
Jul
Aug
Sep
Oct
Nov
Dcc
0.33
0.14
0.10
0.07
0.10
0.08
0.07
0.09
0.07
0.07
0.08
0.07
0.06
0.08
0.09
0.07
0.12
0.11
0.07
0.25
0.10
0.16
0.08
0.11
0.10
0.13
0.13
0.11
0.27
0.08
0.07
0.08
0.08
0.07
0.07
0.44
0.12
0.11
0.09
0.07
0.07
0.06
0.06
0.06
0.06
0.06
0.06
0.06
Jan
Fcb
70N
6ON
5ON
40N
30N
20N
10N
0
0.28
0.11
0.10
0.09
0.07
0.07
0.06
0.41
0.12
0.10
0.09
0.07
z0.06
.0.06
9. 0.06
0.15
0.09
0.08
0.07
0.06
-0.06
-0.06
-0.06
20S
30S
40S
5s
605.
0.06
0.06
0.06
0.06
0.06
2 0.06
0.06
0.06
0.07
0.07
10.06
- 0.06
0.07
0.07
0.08
Latitude
SON
10S
0.06
;, 0.06
Oceanic Albedo
'0.06
0.07
0.07
0.06
0.06
0.06
0.06
0.06
0.06
0.07
0.08
0.06
0.06
0.06
0.06
0.06
0.06
0.07
0.07
0.08
0.09
0.06
0.06
0.06
0.06
0.06
0.06
0.07
0.07
0.09
0.11
0.06
0.06
0.06
0.06
0.06
0.06
0.06
0.07
0.08
0.10
0.07
0.06
0.06
0.06
0.06
0.06
0.06
0.07
0.07
0.08
0.07
0.07
0.06
0.06
0.06
0.06
0.06
0.06
0.07
0.07
0.11
0.10
0.08
0.07
0.06
0.06
0.06
0.06
0.06
0.06
0.08
0.08
0.07
0.06
0.06
0.06
0.06
0.06
0.06
0.07
0.06
0.06
Payne (1972) expressed the albedo as a function of atmospheric
surface.
transmittance and sun altitudes and found that the uncertainty in the
The
measurement of albedo is greater at low sun altitudes (< 20%).
effect of wind (through surface roughness) was found to be small with
decreasing albedo accompanying increasing wind.
Simpson and Paulson
(1979) performed an independent experiment and found that their results
agreed with Payne's.
It should be noted here that both of these
experiments were performed over fairly open ocean and there might be
significantly different ocean albedos along coastal regions,
particularly where there is active marine biosphere.
IV.2
Sensitivity of the Flux Formulations
Once we have made the choice as to which formulations to use for
the flux calculations, it is instructive to understand its sensitivity
with respect to the input data set from which the fluxes will be
computed
.
One should have a good idea of how changes in the input
variables affect the output variables regardless of whether it
is
a real
physical change or an error in observation. For example, in sensible
heat flux calculations, we might want to ask the question of whether a
change of 1 m/sec in wind speed has a greater effect on the heat flux
1011MIAMIUM
than a change of one degree in
sea and air temperature difference
(Ts-Ta)' In most cases because of the nonlinearity of the formulas
used, it is hard to find a definite answer. Nevertheless, we will show
relationships that illustrate the importance of some meteorological
variables in modulating the fluxes.
IV.la Range and variations of the input parameters
The important meteorological variables used in the flux
calculations are wind speed( vt), zonal and meridional components of
wind (u and v) , air and sea temperatures (Ta and Ts), dew point
temperature (Td) and cloud cover (C). The frequency distribution
histograms for these variables are presented in Figures 4.1 and 3.13.
Following is a table listing the range of 90% of their values and the
most frequently occuring value:
Table IV.3
Range of Input Parameters
Variable
Unit
Ta
Ts
Ta-Ts
Td
Qs~Qa
v
u
v
C
*C
'C
'C
'C
g/kg
m/sec
m/sec
m/sec
octal
Range
10
10
-2
4
0
0
-8
-3
0
to
to
to
to
to
to
to
to
to
Most Frequent
31
31
2
26
8
10
8
7
8
27
28
-.5
23
5
6
-4
4
5,6
Month: 1
0.00
0.00
0.00
0.00
0.00
3.52
23.69
52.51
85.08
119.57
154.92
190.40
225.45
259.63
292.55
323.86
353.28
380.53
405.38
427.63
447.12
463.70
477.27
487.78
495.20
499.57
500.97
499. 58
495.70
489.82
482.78
476.21
474.85
486.55
498.07
505.80
509.68
510.15
2
0.00
0.00
0.00
2.71
17.22
44.7-177.26
111.70
146.75
181.65
215.84
248.92
280. 51
310.31
338. 03'
363.44
386.31
406.46
423.72
437.96
449.06
456.96
461.59
462.94
461.02
455.88
447.61
436.35
422.29
405.69
386.97
366.77
346.26
328.50
321.36
323.60
326.08
326.38
3
14.22
17.14
39.22
72.76
108.46
144. 12
179.03
212.76
245.00
275.46
303.88
330.03
353.71
374.72
392.91
408.13
420.27
429.22
434.93
437.35
436.46
432.26
424.79
414.11
400.30
383.47
363.76
341.31
316.31
288. 96
259.49
228.17
195.30
161.30
126.85
94.15
72.49
69.62
4
218.61
218.41
219.18
229.84
251.80
277. 75
303.72
328.50
351.45
372.17
390.39
405.89
418.50
428.08
434.55
437.83
437.90
434.73
428.36
418.82
406.20
390.58
372.09
350.89
327.14
301.03
272.80
242.70
210.99
178.01
144.12
109.81
75.78
43.30
16.41
2.44
0.00
0.00
5
6
7
8
9
423.29
422.90
419.68
413.27
404.89
404. 50
413.96
425.45
436.50
446.00
453.34
458.17
460.24
459.40
455.58
448.75
438.90
426.09
410440
391.94
370.84
347.28
321.46
293.59
263.94
515.71
515.24
511.31
503.50
491.86
476. 53
470.90
473.29
476.91
479.78
480.99
479.99
476.46
470.24
461.22
449. 38'
434.74
417.36
397.36
374.86
350.05
323.12
294.30
263.86
232.10
199.36
166.03
132.57
99.55
67.75
38.34
13.45
0.06
0.00
0.00
0.00
0.00
0.00
479.38
478.94
475.29
468.03
457.21
445. 91
447.05
453.09
459.60
465.02
468.57
469.80
468.41
464.24
457.22
447.30
434.52
418.91
400.59
379.68
356.34
330.76
303.15
273.76
242.88
210.83
177.96
144.70
111.58
79.27
48.77
21.82
3.01
0.00
0.00
0.00
0.00
0.00
324.56
324.26
321.80
318.28
322.71
J38. 00
356.50
374.87
391.92
406.97
419.64
429.65
436.82
441.01
442.15
440.18
435.11
426.94
415.74
401.59
384. 58
364.86
342.58
317.94
291.14
262.42
232.06
200.36
167.67
134.41
101.13
68.60
38.14
13.16
1.40
0.00
0.00
0.00
87.75
90.60
109.45
139.27
172.01
204. 49
235.88
265.74
293.73
319.60
343.11
364.07
382.31
397.68
410.05
419.34
425.46
428.37
428.04
424.48
417.71
407.79
394.79
378.81
359.96
338.45
314.38
287.96
259.41
228.97
196.89
16b. 47
129.07
94.15
59.56
28.51
9.04
6.12
232.80
200.48
167.36
133.91
100.67
68.45
38.48
13.42
1.18
0.00
0.00
0.00
0.00
10
0.00
0.00
5.20
23.18.
53.01
96.80
121.60
156.35
190.46
223.48
255.06
284.90
312.73
338.31
361.43
381.89
399.55
414.24
425.86
434.32
439.56
441.53
440.22
435.65
427.87
416.94
402.97
386.09
366.48
344.33
319.93
293.64
265.99
237.98
212.54
197.50
193.77
193.95
11
0.00
0.00
0.00
0.00
2.37
17.63
44.98
76.83
110.74
145.52
180.39
214.77
248.23
280.38
310.88
339.46
365.84
389.61
411.15
429.71
445.34
457.92
467.38
473.68
476.81
476.81
473.75
467.80
459.17
448.25
435.62
422.33
410.67
408.10
415.34
421.78
425.02
425.40
12
0.00
0.00
0.00
0.00
0.00
0. 19
14.98
41.66
73.07
106.96
142.12
177.72
213.17
247.96
281.69
314.00
344.57
373.12
399.41
423.22
444.'37
462.72
478.15
490.59
500.02
506.46
510.03
510.91
509.43
506.14
502.04
499.18
504.51
520.61
532.94
541.21
545.36
545.85
Lat.
89.50
87.50
82.50
77.50
72.50
67. SOM
62.50
57.50
52.50
47.50
42.50
37.50
32.50
27.50
22.50
17.50
12.50
7.50
2.50
-2.50
-7.50
-12.50
-17.50
-22.50
-27.50
-32.50
-37.50
-42.50
-47.50
-52.50
-57.50
-62.50
-67.50
-72.50
-77.50
-82.50
-87.50
-89.50
Table IV.1
Total short wave radiation received at the top of the atmosphere
(from Ledley, 1983)
The most frequently occuring value for specific humidity difference
is 5g/kg while the same for wind speed is 6 m/sec.
This is true for all
Since these are the two main parameters that make up the
three oceans.
latent heat flux, it is interesting to note that the most observed
values for these two terms make equivalent contributions towards the
magnitude of the latent heat flux.
In higher latitudes, however, the
wind is typically much larger in magnitude than the specific humidity
difference.
This may explain why the distribution is skewed towards
higher values in the distribution of wind speed and towards lower values
in the distribution of specific humidity difference (Figure 4.lc and
4.lg).
An inspection of the variance pattern also shows that the
standard deviations for these two parameter are also about the same in
magnitude, ranging from 1 to 3 g/kg and 1 to 3 m/sec.
The distribution of air-sea temperature difference shows that most
of the time the sea is warmer than the air.
large.
The difference is not very
Few observations have values greater than 3*C (Figure 4.lh).
Together with wind speed, the temperature difference makes up the
sensible heat flux.
The small difference observed is the main reason
for the small calculated values of sensible heat flux.
The standard
deviations of the temperature difference are also about the same as
those of the wind speed (or a little
smaller).
Values with comparable
magnitude to the mean are observed in high latitudes.
The distribution of zonal winds is dominated by the easterly winds
in the tropics.
For the meridional component of the wind, southerly
winds cover a large part of the ocean.
The long suspected bimodal
distribution from the opposing westerlies and easterlies is
in
our calculations.
not present
It
should be pointed out that all the observed peaks in
frequency
distributions are from values observed in the large area covered by the
tropical oceans.
For instance, if the mean humidity difference in the
tropics is 5 g/kg, the peak in the frequency histogram will also be 5
g/kg.
For reference, monthly mean maps from each season for these
parameters are presented in Appendix C.
'IV.2b Energy Budget Fluxes
Let us rewrite the flux formulae in terms of their meteorological
variables:
Sensible Heat (Qh)= constant - f(Jvj, Ta-Ts)
Latent Heat
(Ql)= constant - f(
v,
qa-qs,Ta-Ts)
Incoming Solar(Qin)= f(C) - constant(f(lat,month))
Outgoing Radiation (Qout)
=
f(C,TsTd) and f(TsTa-Ts)
We will discuss each flux terms below.
From Bunker (1976), both sensible and latent heat flux are a
function of the transfer coefficient Ce, which in turn is a function
of the stability and wind speed.
air-sea temperature difference.
Stability is defined as the surface
Figure 4.2 is a plot of Ce versus
wind speed for seven different stability classes.
Ce is greatest
under unstable conditions, decreasing quadratically with wind speed.
Under stable conditions (Ts<Ta), Ce increases quadratically with
wind speed.
The values converge for wind speed above 20 m/sec.
Since Ts-Ta is small (over 95% of the time its value is between
-.2 and .2 *C
,
more than an order of magnitude smaller than the
2.57
unstable
2.0-
1.5
- 5
1.0
-
.5
2
6
3
9 12 15
ws
20
25
30
35
3.C
2.5
2.0
1.5
CC
1.0
.5
-
NOT
4
3
- 3
4
I
2o
'.2
-2to
5 -1.Oto -. 2
6 '.5 to -I.O
<5
7
2
5
Figure 4.2
-T
p
I
I
I
I
I
.
10
15
20
25
30
35
40
45
Transfer coefficients (Ce) and drag coefficients
(Cd) versus wind speed for seven different
stability classes
humidity difference), contribution to the total heat flux from sensible
heat is small.
A graph showing the latent heat flux as a function of
qa-qs and wind speed is presented in Figure 4.3 .
For latent heat
flux, the dependence on wind speed is slightly larger than the
dependence on specific humidity difference. A change of wind speed by
1.0 m/s (from 5 to 6 m/s) will give a 22% change in the flux while a 1
g/kg change (from 5 to 6 g/kg) in specific humidity will give a 20%
change in the flux.
The effects of wind speed on latent heat flux are
more pronounced when the humidity difference is high.
59
LATENT HEAT IN WA TT/M*2
4.3
IL
F igure
8
7
6
5
4
3
2
1
10
9
~1
5
7
-
/
~ I
7
/1.
9
F/I
is~o
'I
too
I
2501
200
50
~
300
1
2.3243
450
400
r
ii
1
350
1
6
7
S
QS-QR IN G/KG
a
9
to
OUTGOING RADIATION
Figure 4.4
L
-%_
I
,_T
7911
/
13
1517' 84
19 -
2176
23
25
~ 68
27-
29-6
I
524
£ 2
4
P
6
7
8
9
CLOUD COVER IN TENTH
Figure 4 .3 Latent heat flux as a function of q
qa and wind speed
Figure 4 .4 Outgoing radiation as a function of cloud cover and air temp.
Once a formula is chosen for incoming radiation, the variation of
this flux is principally from the variation of cloud cover.
Given a
time of the year and the latitude, the solar radiation is then a linear
function of the cloud cover. The outgoing radiative flux consists of two
terms: a black body formulation and a correction term for air-sea
temperature difference.
The black body radiation term is typically an
order of magnitude larger than the second term.
The change in vapor
pressure in the first term contributes little to the flux.
biggest contributors are cloud cover and air temperature.
Its two
Figure 4.4
gives the outgoing radiation flux as a function of cloud cover and air
temperature.
At temperatures below 17* C, the outgoing radiation is
almost solely a function of cloud cover while at higher temperatures the
depence on cloud cover is less pronounced.
Recall from Eq.(4.4), the net energy flux is the sum of the four
fluxes.
Of the four fluxes, Qh is typically an order of magnitude
smaller than Qin and Ql.
Qout is about 25% of that of Qin-
Qnet is then mostly a balance between Qin and Ql. Qin is
determined mostly by QO, the amount of radiation received under
cloudless sky, modified by the amount of cloud cover. Q, is mainly
determined by wind speed and the humidity difference.
Therefore, the
meteorological variables that are most responsible for the net energy
flux balance are the wind speed, cloud cover and the humidity
difference.
To obtain an estimate of the percentage error introduced by the
meteorological parameters, namely wind speed and specific humidity
difference,
we consider the formulation of the latent heat flux,
the
largest contributor to the net surface energy flux.
We may rewrite the flux formula as:
(4.12)
Q, = A -f(V)-V-6q
Here a constant A is used to denote Le pa, V is wind speed, 6q is
the humidity difference at the surface, and f(V) is a function to denote
the dependence of the transfer coefficient (Ce) on wind speed.
Assuming 6q and V are independent, changes in Ql can be related
to changes in V and 6q by the following expression:
8Ql
DQl
3Qi =
-
+ -
dv
av
d(6q)
36q
The magnitude of 3Q1 can be estimated by:
=
1/2
3Qi
aiQ
[(
AV) 2 + (
A6q) 2 ]
3V
(4.13)
36q
From (4.12),
301
f'(V)
1
= Qi -(-
3V
V
+
(4.14)
)
-
f(V)
and
DQ1
Ql
=
(4.15)
-
6q
36q
Substituting (4.14) and (4.15) into (4.13), we have
AV
AQi
=
Ql
()2
_
V
+
(
)2 + (
6q
f'(V)-AV 2 1/2
AV-f'(V)
A(6q)
]
)2 + 2
f(V)
V-f(V)
The transfer coefficient's dependence on wind speed can be approximated
by the following expression:
-V/Vo
f(V) = a-(1-e
)
+ c
f'(V)
as:
This would give us an expression for
f(V)
f'(V)
a/Voe exp(-V/Vo)
f(V)
a(1-exp(-V/VO))+c
With a= .67, c=1.0 and VO=3, this expression satisfies a neutral to
weakly stable atmosphere, a condition that occurs most of the time.
Taking AV to be 1 m/s and A(6q) to be 1 g/kg (these values are
typical standard deviations for V and 6q in the tropics), together with
5 g/kg, we have
V=5 m/s and 6q
(_)2,
=[(..)2,+
2-0.4
1
1.46
5
1/2
(____]
1.46
5
5
Ql
04
1
1
AQ1
.30
If we assume AV to be 2 m/s (a typical standard deviation in the
mid-latitudes), then
AQ1
=
2
[(-)2
5
Q1
0.8
2
+
(_)2
5
+
2-0.4
4
1.46
5
1/2
(______.2
1.46
.50
It should therefore be kept in mind that 30% to 50% are the possible
percentage error in the flux estimates due to uncertainties in the
meteorological parameters.
IV.3
Results
IV.3a Seasonal Means
To see how the seasonal pattern of observed SST is related to the
seasonal patterns of the components of the energy budget, the long term
monthly means of Qnet' Qin) Qout' Qh, and Q, are calculated
and results for one month in each season (January, April, July, and
October) are presented in Figures 4.5 to 4.24 .
In January (Figure 4.5), there is net loss of energy in the
Northern Hemisphere and a net gain of energy in the Southern
Hemisphere.
The regions with the largest loss are the Gulf Stream and
the Kuro-shio region.
By April
(Figure 4.6),
the pattern has changed
In the Northern Hemisphere, the only significant energy
considerably.
There is
loss region is confined to the Gulf Stream in the Atlantic.
energy gain everywhere in the tropics and energy loss south of 20'S.
The maximum energy gain occurs in the North Indian Ocean.
In July
(Figure 4.7), the pattern is the reverse of that in January (Figure 4.7)
- a net gain in
Hemisphere.
the Northern Hemisphere and a net loss in
the Southern
In October (Figure 4.8), the pattern reverses again towards
the direction of the winter pattern.
All the non-latitudinal spatial variation in incoming solar
radiation is from the variation in cloud cover.
The monthly mean maps
of the incoming solar radiation (Figure 4.9 through Figure 4.12)
therefore resemble that of the cloud cover (see Appendix C).
In
January, the distribution in the Northern Hemisphere is mostly zonal.
64
NET HEAT BALANCE MON=1
2
rn
LONG ITUDE
Figure 4.5
Long term monthly mean of net heat flux for
January
NET HEAT FLUX MON=4
Figure 4.6
LONGI TUDE
Long term monthly mean of net heat flux for
April
64a
NET HEAT FLUX MON=7
I-
30
i-
i
i.2
60
90
120
Figure 4.7
i
f
'
i.2
i
i
I
ISOE 180 NiSO 120 90
60
30 N 0E
LONGITUDE
Long term monthly mean of net heat flux for July
NET HEAT FLUX MON=10
Fi eI 4.Lg tyTDE
Figure 4.0' Long term monthly mean of net heat flux for October
INCOMING SOLAR RADIATION MON=1
LONGITUDE
Figure 4.9
Long term monthly mean of incoming solar radiation
for January
INCOMING SOLAR RADIATION MON=4
Figure 4.10
LC!GIT IPF
Long term monthly mean of incoming solar radiation
for April
65a
INCOMING SOLAR RADIATION MON=7
LONGITUDE
Figure 4.11
Long term monthly mean of incoming solar radiation
for July
INCOMING SOLAR RADIATION MON=10
LPOMC TTITUDE
Figure 4.12
Long term monthly mean of incoming solar radiation
for October
66
LATENT HEAT MON=1
C-4j
Figure 4.13
LrC'GiT'JDE
Long term monthly mean of latent heat for January
LATENT HEAT MON=4
LONGITUDE
Figure 4.14
Long term monthly mean of latent heat for April
67
LATENT HEAT MON=7
C
M,
Figure 4.15
LONGITUDE
Long term monthly mean of latent heat for July
LATENT HEAT MON=10
3
m <
rn3
Figure 4.16
I_
OK ITU0F
Long term monthly mean of latent heat for October
68
OUTGOING RADIATION MON=1
LONGITUDE
Figure 4.17
Long term monthly mean of outgoing radiation for
January
OUTGOING RADIATION MON=4
LONGITUDE
Figure 4.13
Long term monthly mean of outgoing radiation for
April
OUTGOING RADIATION MON=?
21
C
M
Figure 4.19
LONGITUDE
mean of outgoing radiation for
monthly
Long term
July
OUTGOING RADIATION MON=10
C
i-n
Figure 4.20
LCNG!T'0JE
Long term monthly mean of outgoing radiation for
October
70
SENSIBLE HEAT MON=1
LONGIT UDE
Figure 4.21
Long term monthly me an of sensible heat for January
SENSIBLE HEAT MON=4
rn
LONGITUOE
Figure 4.22
Long term monthly mean of sensible heat for April
SENSIBLE HEAT MON=7
30
60
Figure 4.23
90
120
1SOE 180 Hi50
120
90
60
de
N
L
LONGITUDE
mean of sensible heat for July
monthly
Long term
SENSIBLE HEAT MON=10
Figure 4.24
LCT'I TU''
Long term monthly mean of sensible heat for October
There is large longitudinal structure in the Southern Hemisphere with
maximum incoming radiation at 20*-30*S.
In April, values at higher
latitudes in both hemispheres are zonally distributed with the maximum
in the equatorial region.
20*-30'N latiude belt.
10*S.
In July, the maximum shifts north to the
In October, the maximum is centered around
There is considerable similarity between the spatial pattern of
mean SST and mean incoming solar radiation, indicating that the solar
energy is the primary driving force responsible for the mean SST
pattern.
There is very little variation in outgoing radiation from season to
Most of the values range from 40 to 50
season (Figures 4.17 to 4.20).
watt/m 2 . The only location where there is any gradient is along the
coast of China where the calculated maximum value is 80 watt/m 2.
There is large seasonal variation in the distribution of latent
heat flux (Figure 4.13 to 4.16).
In January and October, the western
ocean loses a large amount of heat through evaporation while the
upwelling areas show minima.
In April, the area of maximum loss moves
to the central subtropical Pacific and southern Atlantic and southern
Indian Ocean.
Except in parts of the Indian ocean, the same pattern
prevails in July where with the summer Monsoon season, there is a
pronounced latent heat maxima in the Arabian Sea and in the western Bay
of Bengal.
Contrary to latent heat fluxes, the sensible heat (Figures 4.21 to
4.42) has little spatial variation except in January when the warm
western boundary currents in both the Pacific and the Atlantic oceans
set up a large temperature gradient between the cold air in the
atmosphere and the warm ocean.
This, together with the stronger winds
in January, produces a large amount of energy loss through sensible heat
flux.
To compare seasonal cycles of the energy flux components of the
three oceans more closely, plots of seasonal energy flux cycles of
selected grid points are presented from Figure 4.25 through Figure 4.28
.
In Figures 4.25 and 4.26, grid points in the central oceans at
latitudes 45'N, 20*N, 0*,
15*S and 30'S were chosen to demonstrate the
differences (if any) of annual cycles of energy fluxes among three
oceans at the same latitude.
In Figures 4.27 and 4.28, grid points in
the boundary regions of the three oceans were selected.
Along with the
components of energy fluxes, seasonal zonal and meridional wind stress
are also presented to indicate the possible effects of upwelling or
advection.
The grid points presented here are chosen mostly because
they illustrate different characteristics
of energy balance throughout
the year, and also because the number of observations for these squares
are good.
Figure 4.25a and 4.25b shows the energy balance for central north
region (45*N)
in
the Pacific and Atlantic oceans.
substantially more energy loss in
Pacific in the same latitudes.
There is
the north Atlantic than in the north
This is a direct result of much greater
latent heat loss in the Atlantic due to warmer water in the Atlantic
than in
the Pacific at the same latitude.(See Figure 12 in Newell et al
(1981), reproduced here as Figure 4.29.)
In northern hemisphere winter
C)i22
-22-
12-
12-
N
N
32
321
22-
22-
2
4
6
8
10
2 14
16
V
20 22 24 26 28 30
2
81012
Figure 4.29
14 16 18 20 22 2426283
TS (C)
TS ("C)
February and August zonal mean SST for the
Atlantic and Pacific Oceans (From Newell et al,
1981)
months, the latent heat loss in the Atlantic can be three times greater
and has a much larger annual cycle than that in the Pacific. The other
components of the energy balance are comparable
Newell et al (1981)
for these two regions.
have argued that the warmer water in
the Atlantic is
caused by the wind field carrying warm Gulf water further north than in
the Pacific.
The wind stress component shows a more northerly component
in the Atlantic during the first part of the year.
In the Pacific
ocean, the largest latent heat loss and the largest meridional wind
stress occurs in the Northern Hemisphere late fall and early winter.
This suggests that warmer water is carried there during these months and
it gives off large amounts of latent heat.
Warren (1983) recently put forth an argument that the cold water is
responsible for the absence of deep water formation in the North
Pacific.
In a simple salinity budget box model, he demonstrated that
higher salinity in the North Atlantic surface water resulted from higher
evaporation loss through warmer sea surface temperatures.
accord with our result that the latent heat loss is
This is in
much greater in
North Atlantic than in the North Pacific at the same latitude.
denser water with higher salinity in
the
The
the North Atlantic sinks to the
ocean bottom while the fresher surface water in
the North Pacific stays
close to the surface.
In Figures 4.25c,
d,
three oceans are compared.
and e,
central ocean regions at 20'N from
The Pacific and Atlantic profiles are much
more alike than they were at 45*N.
Note this is also the latitude
where the zonal temperature of these two oceans are the same (Figure
4.29).
The grid point in
the Indian Ocean is
from the eastern Arabian
sea and it shows a completely different profile.
It has two peaks in
W1
0
Ia
ill
udklllilondomilg|Ig|M
76
45N/2SN CENTAAL NORTH ATLANTIC
2AN/70E NORTH CENTAAL INOIAN
29N/165N CENTRAL N. PAC.
2N/2SN CENTRAL NORTH ATLANTIC
cca
so6
6
I."
MONTH
3iof
L."
a;
11.9611 8
i
16
."
.6
ttsi
UN
.NORTH
8/?65N CENTRALECUATORIAL PACIFIC
4SN/16S NOAT: CENTRAL PACIFIC
1."4
L
d)
MONTH
1/70E CENTRAL EQUATORIAL INDIAN
ii.
1
a
.
IN I
. I."i
MONTH
1/25N CENTRAL EQUATOAIAL ATLANTIC
e an
4
Z2
a
i
j
i
I
14
MONTH
.6
I."4
MIN I
U
f
PM
MNONTH
NE
g
U
-Net Flux
-M---A
Figure 4.25
.4
L
MONTH
.
.
I
h)N
i
PM
MO--H
.4
NE
(On.,)
olf
-t-A-fr-m
QL
Qout
........
Ti
Q
........
...
T
Seasonal cycle of energy flux components at
selected grid squares
the annual net energy gain: one in the spring and another in the fall.
These are the two seasons when there is the least latent heat loss and
the most incoming solar radiation.
In July, the minimum in heat gain is
associated with the summer monsoon and its stronger winds. In northern
hemisphere winter, the larger latent heat loss is from large humidity
difference between the air and the sea.
in
incoming radiation is
In July and January, a decrease
observed due to enhanced cloudiness.
5.3
t.
Net Flux
)SS/7E
(Clout
Q~Q
T
''''''''
-S4--
-.L
...........
....
SOUTH CENTRAL PACIFIC
0j/t65N
CENTRAL SOUTH INDIAN
ISS/2SW CENTRALSOUTH ATLANTIC
3W3
aMONTH
:ONTH
LN
lxcmpnnsa
11
1
NMn
3SZNCNRLSUHALNI
nrg
yceo
Saoa
Fiue42
-MONTH
IIS6SWSOUTH CENTRAL PACIFIC
353S/73ECENTRAL SOUTU INDIAN
lN
a
MNTH
Ca
Figure 4.26
INN
0
M
.40
La
P.
'**IN
IN N.
M__
ONTH
I.
MONTH
Seasonal cycle of energy flux components at
selected grid squares
At the equator, the seasonal cycle disappears in all oceans as is
evident in Figure 4.25f, g and h.
the Indian Ocean at this latitude.
The monsoon cycle is still present in
The peak in the latent heat in the
Atlantic is from the higher level of zonal wind stress from June to
November.
In the Pacific, the annual variation is again due to
variation in the latent heat flux.
secondary peak in July.
It is greatest in January with a
In the Southern Hemisphere, points along 15'S
and 30*S were selected and presented in Figure 4.26.
At 15*S, the
seasonal cycle is evident again with its variation weakest in the
Pacific where the incoming solar radiation balances all other components
in January.
In the Atlantic and the Indian oceans, the peaks in latent
heat during the southern winter (July) are brought about by increased
Coupled with less solar radiation,
winds.
deficit in
this results in a energy
the winter season for all oceans.
The winds in the
Pacific are weaker but the latent heat loss is comparable in magnitude
with the other oceans. This indicates the specific humidity difference
there is
is
greater than it
for the other two oceans at the same
latitude.
Further south at 30*S,
the seasonal swing is
greater.
Here again,
the profile of latent heat loss follows that of the zonal wind stress.
In the Atlantic and the Indian oceans the seasonal variation in latent
heat brings about a energy surplus in
winter.
the summer and.a deficit in
In the Pacific, latent heat loss stays high throughout the
year, eliminating any significant energy surplus in the Southern
Hemisphere summer months.
hemisphere in
Thus,
for most of the central southern
the Pacific there is
a significant annual energy loss
while in the Atlantic and the Indian oceans there is a balance between
the energy gains in
the summer and energy losses in
the winter.
The outgoing radiation and sensible heat loss stay constant
throughout the year.
Their magnitudes are almost identical for all
three oceans at almost all latitudes in central oceans.
The sensible
heat loss also has a slight annual cycle in the higher latitudes in the
Atlantic and in the Pacific.
The energy balance for western boundary current regions in the
Atlantic and the Pacific are shown in
Figure 4.27a and 4.27b.
regions where maximum energy loss are observed.
Hemisphere winter months,
the warm current
These are
In the Northern
from the south sets up a
tremendous sea-air temperature difference and therefore large amounts of
Net Flux
;x
U
0*
-
--
--
b)
)OUT.
ISS/tiRE SOUTH WESTERN PACIFIC
IIS/1256 CENTRAL EQUATORIAL PAC.
MONT
SS/SIN EASTERN EQUATORIAL PACIFIC
a
d)
Figure 4.27
MONTH
MONTH
MONTH
C)
P
Seasonal cycle of energy flux components at
selected grid squares
sensible heat loss to the air.
The strong winds in the winter together
with high humidity difference bring about latent heat flux in excess of
350 watt/m 2 . The larger northward meridional wind stress in the Atlantic
might also help to advect warmer water further north than in the
Pacific.
This in turn causes larger latent heat loss in the Atlantic
than in the Pacific so that the annual net energy loss is greater in the
northwestern Atlantic than it is in the northwestern Pacific.
mini
EllEN,.
I
80
To contrast the different characteristics in the energy balance
profile between eastern and western coast in the tropical Pacific,
The eastern coast Pacific is a
Figure 4.27c, d,and e are presented.
region where there is large energy gain observed all year.
There is
very little energy loss through evaporation due to weaker winds and
small humidity differences.
In the central equatorial region, there is
a slight energy deficit in May to August.
The higher humidity
difference causes greater latent heat loss and cloudiness decreases the
incoming radiation received.
There is greater meridional wind stress in
the central region than in the eastern region, but the larger latent
heat flux is
mostly from the high humidity difference there.
-Net
-
(One,)
Flux
ISN/ISN
EASTERNATLANTIC
SIN/55E NESTERN
INOIAN
483/125E
*N
.
N
9.84
9.0
.
~
.
~ ~
305/15i
3IN/IISN NORTHEASTERNPACIFIC
MONTH
111
SOUTHEASTERNATLANTIC
--
N-
c
31S/4SN SOUTHWESTERNATLANTIC
3
3
d)
It01
.9.
b)
MONTH
SOUTHEASTERNINDIAN
a
4
a)
Ta
*"-----
out
In the
d)MONTH
Figure 4.28
0)MONTH
M)f
MONTH
Seasonal cycle of energy flux components at
selected grid squares
western equatorial region the wind and the humidity difference are both
greater, therefore, there is a much larger energy deficit in the winter
months.
The difference between the southwestern Atlantic and the
southeastern Atlantic is not as great as the east-west difference
observed in equatorial Pacific (Figure 4.28e and 4.28f).
The zonal wind
stress is greater off the southern African coast than it is off Brazil.
However,
latent heat loss is
greater near Brazil due to warmer sea
water.
Two additional
grid points from the Indian ocean are shown in
Figure 4.28b and 4.28c.
and the other is
is
One is
from the western Indian ocean at 10'N
south of western Australia at 40*S. The point at 10*N
north of the Somali Republic.
is clearly evident.
Here the effect of the summer monsoon
In most of the northern Indian Ocean, there is a
large net heat gain throughout the year similar to the balance shown
here.
Heat balance in the southeastern Indian ocean is
not much different
from the central south Indian ocean (see Figure 4.27d) with the
exception of smaller latent heat loss in the eastern part of the ocean
due to drier air there. The total heat loss is
the central region.
This is
therefore smaller than in
true despite the fact that it
is
further
south and hence receives less incoming radiation.
Two grid points off the eastern coast in the Atlantic and the
Pacific oceans are shown in Figure 4.27a and 4.27d .
Sahara desert in
California coast.
the Cape Verde Island region,
One is off the
the other is
off the Baja
The eastern subtropical Atlantic is a major heat gain
area.
Maximum annual heat gain is observed there.
where major upwelling is observed.
This is a region
Under the influence of the
Bermuda-Azore high, lack of clouds due to the subsidence allows
radiation close to 300 watt/m 2 to come through.
The cool water also
keeps the dew point depression small, hence less latent heat loss.
Similar mechanisms operate in the eastern Pacific region.
IV.3b Annual Mean Fluxes
In this section we present the results of the 31-year annual means
of the heating terms and the pertinent meteorological parameters used to
calculate these means.
Ultimately we would like to see how much of the
observed SST pattern is explained by the net energy flux.
ANNUAL HEAT BALANCE
30 60
2
120
isoE lao~ W190
2
0
6
0 WoE
600'
6
so
40-f
-~
20-
~
~
~
L7~
14
/~.
S10"
so5
~2
\2
14-'*
10
%4.
LONGITUDE
Figure 4.30
Long term annual mean of net energy flux
The annual net energy balance (Qnet) is
presented in Figure
In general, there is a net surplus of energy in the equatorial
4.30.
Pacific region, most of the Indian Ocean,
Atlantic Ocean.
and in
the eastern tropical
The largest energy surplus occurs in the upwelling
region along the South American coast, and in a small region off eastern
Africa.
The Gulf Stream and the Kuro-Shio are the two regions where
there are large energy losses to the atmosphere, the Gulf Stream having
the largest of the two.
There are small areas of energy gain north of
these western boundary currents, and a positive strip exists along the
coast of North America where the cool California current travels.
Similarly, energy gain is observed along the upwelling region off the
African coast.
There are calculated energy losses in the Pacific and
Indian oceans south of 20*S.
Most of the balances in the south Atlantic
are probably too small to be significantly different from zero.
In
general , there is a nice gross relationship between observed SST
patterns and the net energy balance:
Areas with warm currents give off
energy to the atmosphere and areas with cool water (such as upwelling
regions) take in energy from the atmosphere.
To see which component is
responsible for this net energy pattern, we present the annual mean
values of Qin, Qout'Ql
and
Qh separately in Figures 4.31
through 4.34
Incoming solar radiation is the largest energy input into the
oceans.
The long term mean annual pattern shows that most of the Indian
and tropical Pacific oceans are dominated by values greater than 200
watt/m 2 .
The Atlantic has a smaller tropical region with the same
11=1
M
ANNUAL MEAN OF INCOMING RADIATION
LONGITUDE
Figure 4.31 Long term annual mean of incoming radiation
ANNUHL MEAN OUTGOING RADIATION
Figure 4.32
LONGITUDE
Long term annual mean of outgoing radiation
values.
The deviation between the zero line and the 180 watt/m
2
line
comes from the interplay between other components of the total flux.
Since all of the variation in the incoming solar radiation comes from
the cloudiness data, one would expect the annual mean cloud cover to
explain most of the observed distribution of absorption of incoming
Figure 4.35 illustrates the annual mean pattern of
solar radiation.
cloudiness. One can clearly see the similarity of annual mean cloud
cover to that of the incoming solar radiation. The absorption is
where the mean cloud cover is
low and vice versa.
outgoing radiative flux from long wave
Another radiative flux is
radiation (Figure 4.32).
high
This term is a function of air temperature,
cloud cover and humidity.
The magnitude of this term is
about 25% of
the incoming solar radiation and its latitudinal variation is much less
pronounced than other components of the energy budget.
worth noting is
in
that the mean value of outgoing radiative flux is
the North Pacific than it
latitude.
One feature
is
in
less
the North Atlantic at the same
Presumably this is due to the surface water being colder in
the North Pacific than it
is
in
the North Atlantic (see Figure 4.29).
Of the two heat fluxes (latent
and sensible),
overwhelmingly the dominant flux (Figure 4.33).
net energy is
latent heat is
One might say that the
mostly a balance between the incoming radiation and the
latent heat flux.
The largest evaporative
loss regions are the Indian
Ocean, the subtropical western Pacific, the Gulf Stream and the
southwestern Atlantic.
Regions where there is a minimum of evaporative
ANNUAL MEAN LATENT HEAT FLUX
LONG ITUDE
Figure 4.33
Long term annual mean of latent heat flux
ANNUAL MEAN SENSIBLE HEAT FLUX
Figure 4.34
LONGITUDE Long term annual mean of sensible heat flux
loss are also areas of large net heating.
where there is cooler surface water.
These are mostly regions
Three factors contribute to the
calculation of latent heat flux: wind speed, specific humidity
difference and the bulk transfer coefficient(Ce).
value of Ce is shown in Figure 4.36 .
1.6.
Spatially, Ce does not vary much.
The annual mean
The values vary from 1.1 to
The area with the most
variation is the area above Australia where the lowest Ce is
observed.
The low value of Ce explains why low latent heat flux is
observed there.
Off the south American coast, the low value of Ce
also contributes to the low latent heat flux.
Humidity difference and wind speed are about equally important in
the variation of latent heat flux.
a product of these two fields.
Figures 4.37 and 4.38 .
pattern of temperature:
where they are cold.
in low latitudes.
The latent heat flux is essentially
Their annual mean patterns are shown in
The humidity difference roughly follows the
it
is
high where the oceans are warm and low
The wind speeds are greater in high latitudes than
There are minima along regions of upwelling and in
the north Indian Ocean.
In general, there is a negative correlation
between wind speed and the humidity difference.
The wind is strong
where the humidity difference is low and vice versa.
The sensible heat flux is the smallest of all terms contributing to
the net heating term (Figure 4.34).
Its maximum is the same in
magnitude as the mean of the outgoing radiation (about 50 watt/m 2 ).
This is
observed in the regions of western boundary currents.
The
spatial pattern shows little or no variations outside the boundary
currents.
Like latent heat, sensible heat flux is a product of three
88
ANNUPe_ MEAN CLOUD COVER
L'I ITUDE
Figure 4.35
Long term annual mean of cloud cover
ANNUAL MEAN WIND SPEED
21
r-(
LONG ITUDEE
Figure 4.36
Long term annual mean of wind speed
ANNUAL MEAN
AIR - SEA
21
rT1
C
Figure 4.37
LONGITUDE
Long term annual mean of air-sea temperature diff.
ANNUAL MEAN OF QS - QA
04
C
Figure 4.38
LC'G ITUDE
Long term annual mean of specific humidity difference
90
ANNUAL MEAN CE
6
5
4
21
r-4
1T1
LONGITUDE
Figure 4.39
Long term annual mean drag coefficient (Ce)
terms: Ce, wind speed and air-sea temperature difference.
The annual
mean pattern of air and sea temperature difference is illustrated in
Figure 4.39 . Clearly the spatial variation can be attributed mostly to
that of air-sea temperature difference.
Note the only regions where the
sea is cooler than the air are in areas of intense upwelling.
Zonal averages of all three oceans are computed for each of the
terms that make up the net energy term and these are presented in Figure
4.40.
The same quantity is also calculated for the meteorological
variables that contributes to these fluxes.
They are presented in
Figure 4.41. There is an obvious inverse relationship between Qin and
cloud cover. The zone of ITCZ is visible at 5'N and it has a
corresponding local minimum for Qin at that latitude.
Q, is a
ANNUAL MERIDIONAL PROFLE FOR
3 OCEANS
220
200
18C
0I
160
140
-%
120
/O
100
80
I
-60
%
0
ode
40
Iii
OUT
%J~~%
420
0-
ONET
0-
0O
60
Figure 4.40
50
40
30
20
10 EO
10
20
30
40
50
Zonal average of energy flux components for the
three oceans
product of the profiles for Ce, wind speed and humidity difference
with a minimum at 5*S and 45*N.
Profiles of Qh follow that of air-sea
temperature difference with a minimum around 45*N.
little or no latitudinal variation.
Qout exhibits
The latitudinal profile of Qnet
has a local maximum at 45'N and a local minimum at 35'N.
from the variation in Ql.
The minimum in
This is
mostly
Qin around 5'N and the
minimum in Ql at 5*S gave Qnet its variations in the tropics.
Comparing these profiles to that of SST, one can see clearly latitudinal
zones where large dynamical processes are necessary in order to explain
the observed profile of SST.
There is almost a symmetry of SST profiles
around the equator (The actual maximum is skewed slightly to 5*N.)
1111A
Z - o5
o a.
to
-
-
30
1F
C
Ur
4s
..
-6S80-
IR-.
0.1
-4
01
speedT
wind
Ta-Ts,
The
~ ~
~
~
Figumreidi onalflso
~
~
ara
oceanssepartely wrenprstessnFgr
~
C*
T prflTfQe
n
lodcoe,
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t5S and lack thI ymti
ofnergyir bdew
.2
oithe three
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teudesfile onrthaof a0'Simumh atndiandOceacks soth
upu
ofy5'mandnort
pop15*S tintheaifi oeanandtsouth orde to' unrt the
dynaticcn
Clearly, if no latitudinal trend is observed, there should be a
transport of energy from the surplus regions to regions with a deficit.
With the constraint imposed on by the configuration of the ocean basins,
FOR 3 OCEANS
MERIDIONAL PROFILE OF ANNUAL HEAT BUDGET
PACIFIC
INDIAN
N EQ S 20
LATITUDE
40
60
Figure 4.42
-
-
22 0
s
220,
20
-
NET HEAT (Onet )
LATENT HEAT ( L)
SENSIBLE HEAT (OH,
RADIATION (O0UT)
- OUTGOING
INCOMING RADIATION (QIN)
40
20 N EQ S
LATITUDE
20
40
ATLANTIC
r
60
40
20 N EQ 5
LATITUDE
20
Meridional profile of annual energy budget for
the the three oceans
this would imply a northward transport in the Atlantic; a southward
transport in the Indian; a northward transport in the northern Pacific
and a southward transport in parts of the south Pacific.
The
calculation of this energy transport will be discussed in
detail in
Chapter V.
IV.3c
Comparison with Other Results
In this section we will compare our calculations of annual mean
energy budget terms with those of other researchers.
It is extremely
difficult to make a straightforward comparison of various estimates due
to several reasons:
usually different.
First of all the data processing criterion are
Secondly, different formulae are used to derive the
same quantity.
Thirdly, the spatial and temporal resolution of the
calculations vary.
However, it is often instructive to compare
estimates of the same quality to see how variations from the above
mentioned sources contribute to the differences observed.
We will
restrict our comparisons to those estimates that have the same data
sources and whose method of computation are closest to ours. Namely,
studies that use ship observations and make the calculations with bulk
formulae.
Hastenrath and Lamb (1978,
1979)
have published an atlas of
oceanic energy budgets for the Indian Ocean,
the eastern Pacific oceans.
Atlantic and Clark (1965)
300,
a)
North
the tropical Atlantic and
Bunker (1976) has results for the North
has estimates for the North Pacific. Weare et
b)
Pacific
North
Atlantic
, 160W
I
Figure 4.43
2
3
4
5
6
7 8 9
MONTH
10
Comparison of seasonal cycle of net energy flux
estimates for a) North Pacific, and b) North
Atlantic
11
12
al (1980) has also published values for the tropical Pacific. We will
compare results region by region.
In the North Atlantic,
Bunker's estimate.
our net energy term agrees fairly well with
The long term monthly mean values of Qnet at two
grid squares in the North Atlantic are presented in Figure 4.43b.
The
zero line that divides the surplus area from the deficit coincide almost
exactly but the magnitudes of the net energy flux are different,
Bunker's estimate
especially in the Northern Hemisphere winter seasons.
in regions of maximum energy loss in the Gulf Stream are approximately
10% higher than ours.
The same discrrepancy is
found (not
upwelling regions where there is a maximum energy gain.
shown) in
His values for
the sensible heat flux is about 5 watt/m2 higher in regions of maximum
loss (again in the Gulf Stream.)
Radiative fluxes and latent heat
fluxes also exhibit the same general distribution pattern, but our
values are about 10% higher than his.
These differences could be
attributed to the fact that he calculated individual fluxes from each
observation and then applied monthly averages to the fluxes whereas we
computed our fluxes from monthly averaged variables.
It is pleasing to
see that our error estimate of about 10% (Chapter IV.4) verifies in
comparison here.
In the north Pacific, our results are most comparable with Clark's
(1967) estimate.
Comparison of long term monthly means are presented
for two representative squares are given in Figure 4.43a.
Again, there
are differences observed between the two estimates of the net energy
flux.
The agreement is
higher latitudes.
than his.
This is
much better at subtropical region than that at
In general,
our estimate of net heat loss is
higher
a direct consequence of the fact that our estimates
- l~
M1IM111l11
ih~HI
l
o= lM
i
ln
lI
llll~lmill
l
1111''
4llN,
of the latent heat flux is higher than his.
His latent heat has a
constant transfer coefficient (Ce) while ours is a function of wind
With higher wind speed in the winter at higher
and stability.
latitudes,
INDIAN
0)
O-
OCEAN
- 45-55E
ION
100
clE 50
S0
-50
X
10S-20S, IIOE-120E
0
10
z -5
UJ
4
A
z -54
10O
TROPICAL
b)
3
2
I
4
5
6
9
8
7
TROPICAL ATLANTIC
c)
PACIFIC
0- 5N1,10W
O0S , 85W
00 %
0-5S
O,95W
--
i
23
4
5
6
Figure 4.44
7
lI 12
10
8
9
10
11 12 1
2
-
3
30-35W
This study
astenrato and Lanb (1978 ,1979)
Wooe it al. (1980)
-
4
5
6
7
8
9
10
1I
12
Comparison of net energy flux estimates for
the tropical oceans: a) Indian Ocean, b) Pacific
Ocean and c) Atlantic Ocean
this can cause a significant difference in
flux.
the estimate of latent heat
Our incoming radiation estimates are also different due to
different formulae used.
Clark used Budyko's formulation while in this
Estimates of sensible heat and
study we used Reed's formulation.
outgoing radiation are in better agreement.
In the tropical region, our results are directly comparable with
those of Weare et al (1980)
and Hastenrath and Lamb (1978,
In
1979).
our net energy term agree well with
the Pacific Ocean (Figure 4.44b),
Weare's estimate although our maximum energy gain is
about 10% lower.
However, it is higher than Hastenrath and Lamb's estimate (1978). In the
Indian Ocean (Figure 4.44a), our results differ from Hastenrath and
Lamb's estimate with ours generally higher than theirs, and in some
areas the differences are quite significant.
(Figure 4.44c),
our net heat flux is
and Hasterath and Lamb's estimate.
again in
In the tropical Atlantic
between Weare's estimate
As for other components of the
energy budget (not shown), our incoming solar radiation is low compared
with Weare's (-
10%)
and high compared with Hastenrath's
(w 5%).
Our
longwave radiation compares well with Hastenrath and Lamb but Weare has
values =10% lower.
Our latent heat values are,
again, higher than
Hastenrath's in general. The exception is in regions of maximum
evaporative loss, where it agrees well with his.
Weare's estimate is
greater than both ours and Hastenrath's estimates.
As can be seen, significant discrepancies exist among various
estimates of the same quantity.
Comparison among them does not tell us
whether one estimate is better than others.
Rather, it serves the
purpose of giving us an idea of how variable some of these quantities
11111111111
WWI
Basically all of the estimates are made from the same set of
can be.
ship observations - some have better coverage than others.
The
differences are from different data periods, different processing
methods, and different methods of computation.
The general feature of
all estimates agree in spite of the differences observed in magnitudes.
Error Analysis
IV.4
IV.4a On monthly fluxes
No energy budget calculations are complete without an analysis of
In addition to errors associated with meteorological
errors.
parameters, there are four major areas that may cause additional errors
in our flux computations:
1) Inadequacy of the bulk flux formulae as an approximation to the
true fluxes,
2) Observation, reporting, and archiving problems,
3) Bias from inadquate data sampling, both spatially and
temporally.
4) Calculation of the monthly mean fluxes from monthly averaged
input variables.
We will address these four problems separately in the following
sections.
The amount of uncertainty of calculated fluxes associated from
using bulk flux formulas is hard to assess.
There is a serious lack of
verification of fluxes calculated over open ocean.
In addition, marine
reports do not give sufficient information on the condition over the
lower atmosphere and/or the upper ocean necessary for more detailed
calculation of the fluxes. The determination of the transfer
coefficients is a derived empirical relationship from data which may or
may not be suitable for all areas of the ocean.
one study to another,
Their values vary from
sometimes differing by as much as a factor of
two. As can be seen from the previous section on sensitivity of the flux
formulas,
a factor of two change in
the transfer coefficients can cause
a factor of two change in the heat fluxes.
The transfer coefficient is
especially important for latent heat flux because it is one of the most
Radiative fluxes,
important components in the total energy budget.
espcially the incoming shortwave radiation, also suffer from
uncertainties in their formulation. Simpson and Paulson (1979) compared
some mid-ocean observations of atmospheric radiation to the calculated
fluxes using various available formulations and suggested that Reed's
(1979) formula is probably the most suitable one to use.
Compared with
observation results, they obtained an error of 6% with Reed's
formulation and an error of 1% with Berliand's formulation for the
longwave radiation.
Even with perfect observational data and the best
available formulation, we probably have an uncertainty of accuracy in
the range of 10%.
2
at high
This translates to be about 10 watt/m
2
latitudes and about 20 watt/m in low latitudes. It should be noted that
errors associated with formulations are fixed for all regions and all
times and are therefore time invariant.
This means that this systematic
error will not affect comparison studies among different areas of the
ocean or among different time periods.
However,
associated with long term mean calculations.
it
will dominate errors
100
The second source from which error may arise is from sampling
errors associated with observation,
example,
reporting and archiving method.
take latent heat flux and radiative flux.
For
Since latent heat is
a function of Ce and wind speed and Ce is a function of wind speed,
an error in wind speed observation could give substantially different
results in the latent heat flux calculation.
Weare and Strub (1981)
have estimated that a 1 m/s error would lead to about a 1% error in the
variance of the latent heat flux estimation. Similarly, since radiative
flux is a function of cloud cover, and ships observations of cloud cover
have been shown to be less reliable than other parameters (Bunker,1976),
the error introduced here may be a serious one.
Presumably this type of
error is random and will decrease with increasing number of
observations.
Averaging over space and time increases the number of
observations and therefore long term means over large areas of the ocean
should be relatively free of this type of error.
However, it would
dominate the fluctuations on a short term time scale.
Weare and Strub (1981)
have done a detailed study of the error
associated with sampling bias from inadequate sampling both spatially
and temporally.
By this we mean the error introduced from an uneven
sampling throughout the month and from a narrow ship route within the
five by five degree grid square.
in time and in space.
This type of error varies greatly both
For instance, in areas where there is a large
gradient within the grid area, a narrow ship route could introduce a
large bias (See Appendix B).
In areas where there are large diurnal
101
variations, the time of the day a report is taken becomes critical.
In
regions of frequent cyclonic activity, a large number of observations is
necessary to capture the large fluxes over short periods of time
associated with storm activities .
Weare and Strub (1981) gave an
estimate of about 10% of the longer term mean being affected by this
bias and a much greater percentage for individual monthly means.
Finally, we should consider errors introduced from calculating
monthly mean fluxes from monthly mean meteorological variables rather
than calculating the fluxes from individual observations and then
averaging the fluxes.
This type of error arises from the fact that the
flux formulas are non-linear in nature and the error is
high when the
variables in the formula are highly correlated on a daily basis. Clark
(1965)
computed monthly averaged flux values both ways: first daily
values were averaged over the number of days, secondly the variables
were averaged and the flux terms computed
He found a difference in
from these averaged values.
the long term monthly mean flux between the two
methods of 10% to 17% for the net energy flux, with the largest
contribution from sensible heat flux and latent heat flux.
This is due
to the fact that daily values of surface wind, Ts-Ta and qs-qa
are strongly correlated.
Weare and Strub (1981) did a similar study on
latent heat flux and radiative flux and found similar results.
Esbensen
and Reynolds (1981) in a more recent work using boundary-layer
similarity theory for the formulation of the transfer coefficients,
obtained a relative error of approximately 10% for sensible and latent
heat fluxes.
It should be noted that all of the estimates on the
MIN11bill
11,161
102
difference of two types of methods of calculation are based on
mid-latitude areas. This is because these are the only regions where
there are sufficient frequency of daily observations to enable this type
of comparison studies.
There is reason to believe, however, that
similar results should be obtained in tropical regions where the Bowen
ratio (ratio of sensible heat to latent heat) is small and the wind
speeds are also lower.
IV.4b On annual mean estimates
As mentioned before, in taking the long term mean averaged over a
31-year period, most of the error is
probably from systematic sources.
Two of the major systematic errors are from the bias in data
observations and from bias from flux formulations.
As mentioned in
the
previous section, 10%-20% may be a reasonable estimate for errors
arising from the methods of calculation for Qin and Ql.
accuracy of Qout is
observations.
hard to estimate in
The
the absence of published
Although the magnitude of Qout is small compared to
Qin and Q1 , it is comparable to the magnitude of Qnetsmall and any error associated with it
Qh is
probably will not alter Qnet
significantly.
Experiments with various formulations for Qin
and Ql have
shown that Qin is the most sensitive component of the four.
Ql, on
the other hand, is quite insensitive to any reasonable estimates of Ce
(in
the annual mean.)
Weare et al (1981)
have made estimates for
significance level of various terms for the tropical Pacific region.
They found a 95% confidence level for solar, infrared and latent heat
103
fluxes to be 29,14, and 39 watt/m
fluxes are normally distributed.
2
respectively if one assumes these
They also indicated that this would
correspond to a 49 watt/m 2 as the 95% confidence level for Qnet'
Because our fields in the high latitudes have different means and
standard deviations, we cannot apply these error estimates to our
findings directly.
However, our error in the tropical region will
probably be around the same range as their estimates.
In higher
latitudes, the values would be larger due to larger standard deviations
of these fluxes.
We should note here that the approximately 20% error mentioned in
this section is in addition to the large errors (30% to 50%) associated
with uncertainties in the meteorological parameters discussed in section
IV.2b.
If we assume these two errors are independent, then the total
error associated with the flux estimates is anywhere from
((.2)2+(.3)2)1/2=.34
to ((.2)2+(.5)2)1/2 =.54, or from 34% to 54%.
In the worst case, the total error can be as large as 70% (20%+50%).
104
CHAPTER V. OCEANIC MERIDIONAL ENERGY TRANSPORT
In this chapter, we will present estimates of oceanic meridional
transport of energy using the surface energy balance method. The theory
and method used will be discussed first and the results will be
presented.
V.1
Theory
We may write the energy equation of the earth-atmosphere system as
Rnet= Rin- Rout: Sn + Sc + So + Sa + Div(Fa + F0 )
where
Rnet= net radiation received at the top of the atmosphere
Rin = radiation received at the top of the atmosphere
Rout= radiation lost at the top of the atmosphere
S
= storage terms
F
= flux terms
Div = horizontal divergence
Subscripts are
o
= ocean
a
= atmosphere
n
= land
c
= ice
Figure 5.1 (adopted from Newell et al (1981)) illustrates this balance
schematically.
105
RNET
in
Rout
Div (Fa)
SA
Qin
S t
Figure 5.1
-
Div (F 0 )
Schematic representation of the energy balance of
the earth-atmospheric system
In the annual mean, as long as no long term temperature change is
observed, the storage terms vanish and the energy balance equation
becomes:
Rnet= Div (Fa + FO)
In other words, there must be a transport of energy from areas with
a surplus of energy to areas with a deficit of energy.
accomplished by either the atmosphere or by the oceans.
This can be
The role that
the ocean plays in maintaining the temperature field relative to that of
the atmosphere is
one of the critical problems in
present climate and its potential changes.
understanding the
The various mechanisms that
accomplish this transport may be summarized into the following
categories: (Chiu,1978)
I
0010EIIIEIWNIE-O
M
106
1) transport associated with the net meridional volume flow.
2) transport associated with the mean meridional cell.
3) transport associated with the horizontal gyres.
4) transport associated with Ekman drift
5) transport associated with eddy motions in the ocean.
Considerable literature has been collected on the estimate of energy
transport accomplished by the oceans.
Generally, the methods used to
estimate this transport can be separated into three categories: the
residual method, direct estimates, and the surface energy balance
method.
The following sections describe briefly each method and the
results from various estimates.
One way to compute the oceanic transport is from the residuals in
balancing the energy atmosphere-ocean system.
The ocean flux is
calculated as the difference between the net radiation at the top of the
atmosphere and the atmospheric flux, i.e.
Div F0 = Rnet - Div Fa
Vonder Haar and Oort (1973) applied this method to the Northern
Hemisphere and found a northward transport at all northern latitudes.
Using the same method, Newell et al (1974) calculated the flux from 90'N
to 30'S and found a poleward transport in both hemispheres.
The maximum
transport is found to be at 30' in both hemispheres.
The errors associated with the residual method are large because
the residual is the difference between two large terms.
In addition,
107
the transport for individual oceans cannot be resolved from this
approach.
However, it does give us an estimate of the relative
magnitude of the oceanic transport compared to the transport by the
atmosphere
The oceanic transport of energy can be calculated directly.
This
is done by vertically integrating the meridional velocity and
temperature fields.
However, due to a lack of continuous measurements
of the variables needed for the calculation, this method has only been
applied to particular areas with oceanographic stations and for limited
time periods.
Bryan (1962) and Bennett (1978) have made direct
estimates of energy transport using hydrographic data from 12 sections
taken within the period from March to October.
Their results indicate
that there is a northward transport in both hemispheres in the Atlantic,
a southward transport in both hemispheres in the Pacific, and a
northward transport in the southern Indian Ocean.
Roemmich (1981),
Wunsch (1980) and Fu (1981) applied an inverse method to estimate the
transport in
the Atlantic Ocean and found northward transport in
Atlantic ocean in both hemispheres.
the
They also found small southward
transport in the southern Pacific Ocean.
The disadvantage of direct estimates is that the time periods and
locations for which data are available to make such an estimate are
limited.
It is hard to infer an
average
or two years data for a given season.
value of transport from one
Without a knowledge of seasonal
variability and the interannual variability of the transport, it is
,i
il llil Wli
Nil
n
o in
kilillkiill
108
difficult to compare results from direct estimates to the annual mean
values inferred from both the residual method and surface energy balance
method.
However,
these estimates do give us a feeling of the possible
ranges of oceanic transports for certain locations.
The surface energy balance method uses, as the name implies,
balance at the surface of the ocean-atmosphere interface.
From Figure
5.1, the balance at the surface of the ocean can be written as
Qnet
=
So
+ Div F0
=
Qin
-
Qout
-
Ql
-
Qh
The notation used here are the same as before:
Qnet =
Qin
net energy flux at the ocean surface
= radiation received at the surface
Qout = radiation lost at the surface
Q,
= latent heat flux
Qh
= sensible heat flux
Again, in the long term mean, So vanishes as long as no long term
temperature change is observed.
We would then have
Qnet= Div F0
The above equation indicates that the annual mean net energy
balance at the ocean surface can be used as an estimate of the oceanic
flux divergence.
The meridional energy transport could then be
109
calculated using Green's theorem by integrating the energy flux
divergence with respect to area.
to be assumed.
to
An appropriate boundary condition has
The most common assumption (and perhaps the safest) is
assume the flux vanishes at the northern or the southern boundary of
the ocean basin.
Sverdrup(1957) did the first calculation of oceanic energy
transport using this method.
Bryan (1962) used Budyko's (1956) data and
made similar calculations. Emig (1967) recalculated the oceanic
transport using updated values of Qnet from Budyko (1963).
The
results from these studies generally indicate a poleward transport of
energy in both hemispheres with a maximum at 30*N in the Northern
Hemisphere and 20*S in the Southern Hemisphere.
Hastenrath (1980)
performed an updated calculation using satellite measurements of
radiation at the top of the atmosphere and estimated the transports for
individual oceans.
In the Pacific, the energy transport is directly
from the tropics into both hemispheres. In the Atlantic, it is northward
in all latitudes, including the Southern Hemisphere. In the Indian
Ocean, it is directed southward in all latitudes.
He found a maximum
transport at 30'N and 25' S for all oceans combined.
The disadvantage
of using this balance method is that it is essentially an estimate of
flux divergence as the difference between the two largest components of
the energy budgets, namely Qin and Ql.
this may be large.
The error associated with
In addition, only the long term annual mean value of
the transport can be calculated since only in the long term can one
safely assume that the storage term is zero.
One would need additional
subsurface data to calculate the seasonal variations of the flux values.
110
V.2
Computation and Results
In this section we present the estimates of oceanic energy
transport from our annual mean net energy flux at the oceanic surface
using the surface energy balance method.
The annual mean net energy
balance (or equivalently, the energy flux divergence) from the previous
chapter is integrated to yield the energy transport across each 5'
latitude circle.
For each ocean, the net energy transport across each
5* latitude band is computed by multiplying the appropriate annual mean
flux divergence (Qnet) and the corresponding ocean area in that
latitude belt.
This value is then integrated to yield the transport
across that latitude.
The integration can be done from either the
northern boundary or the southern boundary depending on which boundary
condition is available.
To illustrate how transport across each latitude is calculated, we
take the transport across 65'N in
the Atlantic Ocean as an example.
Since we do not have flux divergence data for the southern end of the
ocean basin, we will perform the integration from the north to the
south.
In this case, we need a boundary condition at 70'N.
assume a flux of zero at 70'N and if
If we
no long term change for that
latitude belt is observed, then the deficit of .54 x 1014 watts (Table
V.1) for the 65*-70'N belt must be made up from a transport of the same
magnitude from the south (since no energy flux is
north).
65*N.
transported from the
So a northward transport of .54 x 1014 watts is
At 60'N,
to take care of the total deficit
obtained for
in these two five
111
degree latitude belts,
the deficit of 1.02 x 1014 watt must be added
to the flux at 65*N to give us a net northward flux of 1.56 x 1014
watts across 60*N.
This process is repeated for all latitudes.
The transport for the Indian Ocean and the Pacific Ocean is
calculated in the same way.
We assume a zero net flux at 30*N in the
Indian Ocean and a zero net flux at 60'N in
is performed from north to south.
the Pacific.
The integration
The presence of continents in
northern boundaries makes it relatively safe to assume a zero flux for
the northern boundary conditions.
from south to north.
Of course, one could also integrate
Since we only have data down to 40'S and reliable
energy transport flux across this latitude is not easily obtained, we
choose to use a north to south integration.
calculated
The transport values are
for each 5* latitude for each oceans.
This transport value,
the flux divergence and the area for each of the latitude belts in each
ocean are presented in Table V.1.
The total transport accomplished by
all three oceans combined is also computed by assuming a zero flux
across the 70*N latitude.
presented in Table V.2.
The results for this computation are
To help ease the digestion of the data, the net
flux divergence (weighted by the area) for each 5*
each ocean is
presented schematically in
latitude belt and for
Figure 5.2 . The calculated
transport directions at selected latitudes are indicated by arrows.
Figure 5.3 presents a plot of the estimated meridional energy transport
for each ocean and for all oceans combined.
Our results indicate a northward transport at all latitudes in the
Atlantic with a maximum of 9 x 1014 watts at 20*N.
The Pacific Ocean
transports energy northward north of 10'S and southward from 10'S to
I
112
TABLE V.1 Annual Mean Heat Flux and Heat Transport
*Error bars on the flux estimates are approximately 35% to 70%
Flux
Area
Atlantic Ocean
Pacific Ocean
Indian Ocean
Lat.
F*A
watt
m2
watt
Trsprt
watt
/m2*
1012
1012
1014
Area
F*A
watt
m2
watt
Trsprt
watt
Flux
watt
Area
m2
F*A ITrsprt
watt
watt
/m2*
101 2
1012
1014
/m2*
1012
1012
Flux
1014
72.5
0.0-54
67.5
-50.2
1.07
62.5
-59.4
1.72 -102
-54.5
2.2
-39.1
1.98
-86
-25.1
2.3
-58
-32.2
3.18 -102
54
A
57.5
-11.2
2.37
-27
52.5
-0.4
3.54
-1
47.5
5.8
4.31
25
42.5
-17.0
5.10
-87
37.5
-54.2
5.24
-284
32.5
-46.5
5.83
-271
6.29
-143.
7.08
-91
7.80
-71
8.71
-30
9.15
-15
9.22
337
7.95
502
Al
56
-120
27
28.
90
13.1
.93
22.5
22.4
1.76
17.5
45.5
3.10
12.5
43.8
3.94
7.5
42.3
4.68
N2.5
60.6
4.41
17.5
1.1
4.98
22.5
-12.5
4.21
27.5
-27.1
4.23
32.5
-23.6
5.0
-22.8
.12.7
-12.9
39
.51-9.1
141
.92.
-3.4
173
-3 .65.
-1.6
198
.63
36.5
267
.30
63.2
290
-11.20.-1
26.5
248
-13
.685.3
120
-14 .88
-7.4
5
. -.
-14.93 -18.3
-53
:-14 .40 --27.5
-115
.25.-3
-13
-27.8
-118
37.5
-32.8
6.0
-197
7.5
12.5
53.9
40.6
19.7
5.38
6.1
6.08
_
07.
--
_-
-
7.
05
-37
8.
72
5.4
4.51
24
5.5
4.23
23
14.9
3.9
58
29.2
2.8
82
9.09
-8. 85
8. 62
9 .95-
-
-
-
---
-
_-
3.75
152
66.7
3.37
225
24.0
2.86
69
8.4
3.02
25
43.3
8.
04
7.
22
5.70
-6 .58-.5--3.
7.93
210
8.11
43
8.22
-61
45
2. 76
.54
.97.
.-.
..-.
-
.
7.97
-146
7.66
-211
7.19
-200
-
..-
-
---.-.
-
13.7
2.94
40
20.1
3.25
65
15.9
3.55
56
0.3
3.61
1
2.
1.
-
1
-
--
6.66
-
5
.21
-167
89
_
-21.5
6 881
8
46
90
.21-
-
51
2. 11
.36
-
-
-
1 .10
-25.1
I-10 . 101
4.53
-9.80
_
.
-8.1
9 50L
_
___-12
-
45-
-8 .79-
_-5
S2.5
-
- -
3.51 -167
,88-
_______-1
_______-8
22
-32.7
6
12
62
3.58 -183
3 . 74 -_--
0A.0
27.5
3.
_5.
-51.0
__
76
-4. 20
03
______
___
2.
-82
3.82
1
1
'
l.-
113
TABLE V.2 Total Oceanic Heat Transport
Error bars are approximately 34% to 70%
Lat.
Flux
watt
Area
M2
/m2*
1012
F*A
watt
1012
67.5
-50.2
1.07
62.5
-44.4
2.3
-102
57.5
-32.1
4.57
-147
52.5
-17.4
47.5
TrsF rt
wat t
4
101
n
0.0-
-54
54
5&
01
3.
_______
5.52
-96
-6.9
6.61
-46
42.5
-23.9
8.28
-198
37.5
-46.5
10.03
-466
32.5
-35.5
10.71
-380
27.5
-11.3
11.74
22.5
-0.6
13.40
-8
17.5
9.4
15.13
142
12.5
14.8
16.55
242
7.5
17.5
16.63
291
N2.5
45.0
17.38
782
S2.5
60.3
16.73
1009
7.5
31.4
16.89
530
12.5
11.2
17.21
193
17.5
-0.6
16.14
-10
22.5
-8.1
15.45
-125
27.5
-15.9
15.44
-245
32.5
-18.9
15.83
-299
37.5
-27.5
16.48
-453
-3. 99.
__
-. 45.
6.4
09-
_11.
-14. .89
______
-133
-16. .2216.
-14.
88-
12..46-
.551..73.36-
______-8.
_
_
_-13.
66.
-15..59-15. 49-
-14, .24
____
'11. .79.-8..80.
-4 27-
142.5
1
_
I
I
I
IIIWI
-
11.
,
114
10 E 180 Wjs0
20
90
6
0
9a
120
30 W o E
60
707
10
60
6
Watt
-.
5-.-86
585
-1.0 2
AZ-~
+.25
-. 87
5-
1.83
-
2-84
-
-
- 2.71
1-67/
.37
9
7D 3
-:0
rM
21
90-
40
-
1
- .0
1.98,12.67
u
2.90
2.48
I 1.20 1
1.0 5 115
-. 53
-1.15
1.18
-l.97
A-
.24
.I.s
- 1.43
- .30
.15
+3.37 +5.02
+2.10
-+ .43
e' -. 6-1
- 1.46
- 2.1li
- 2.00
.
-1.67
-
.58
*.92
1.52
105
-
n2.25
-
.69
.25
.40
- .65
-01
U
- .82
-
50415
61
60
'/0
30
60
990
Figure 5.2
25*S.
120
150 E 180 Wise
120
90
60
.30
W 0 E /I
The net energy flux divergenece for each
5' latitude belt and the direction of the
purposed meridional transport of energy
South of 25'S, the transport becomes northward again.
The
maximum northward transport is at 5*N with a magnitude of 10 X 1014
watts.
In the Indian Ocean, the transport is southward for all
4
latitudes with a maximum of 15 X 101 watts at 20'S.
When data for
all three oceans are combined, the total oceanic energy transport is
northward in the Northern Hemisphere and southward in the Southern
Hemisphere with a maximum of 16 x 1014 watts at 25'N and 16 x 1014
watts at 150 S.
115
For comparison purposes, the results of the oceanic energy
transport from this study and other estimates are presented together in
Table V.3 for each of the three oceans separately and in Table V.4 for
MERIDIONAL
HEAT
TRANSPORT
LATITUDE
Figure 5.3
Meridional energy transport for three oceans
separately and combined
116
all oceans combined.
Two estimates under one study represent estimates
using different assumptions and usually imply the possible ranges of the
transport values.
For example, the two estimates from Bennett(1978) are
the ranges using different width assumption for the western boundary
current.
Georgi and Toole (1982) obtained different estimates using
different reference levels.
TABLE V.3c Comparison of Various Estimates for Atlantic Ocean
Meridional Heat Transport in 1014 Watts
Latitude
This
Study*
Hastenrath
1980,1982
Fu
1982
Bunker
1976
Bennett
1978
Bryan Wunsch Roemmich
1981
1962 1980
1.8
60N
1.56
2.6,2.6
50N
3.62
4.1
40N
5.22
6.3
0.
7.
36N
8.72
25N
9.09
15N
8.62
1ON
8.04
0
5.70
10S
2.76
15S
2.51
8.6,7.3
20S
2.11
5.4
25S
1.46
30S
.90
40S
15.5,10.7
12.
13,6
15.8,11.1
4.2, 1.8
8.2
6.6
14.4, 9.8
3.9
11.5, 6.9
8.3,5.4
3.9
3,6.5
3.
1.6,1.8
4.
4.1
7.7
1.71
8.
9.7
30N
32S
7.5
1.7,.67(Georgi & Toole, 1982)
*Errors on these estimates are from 34% to 70%
12.
117
V.3
Discussion
As can be seen from Figure 5.3, the nature of the transport differs
remarkably for the three oceans.
The Atlantic ocean as a whole loses
energy and needs to have energy imported from other oceans in order to
maintain its temperature.
There is significant energy loss in the
mid-latitudes of the north Atlantic,
influence of the Gulf Stream.
particularly at latitudes under the
Although the energy surplus area in the
tropical region has one of the largest values per square meter,
total area with this surplus is small.
energy for the tropical
region is
the
Therefore, the total available
not large enough to make up for the
energy loss in the Northern Hemisphere. Hence the estimated energy
transport is northward at all latitudes of the Atlantic Ocean.
The most estimates of energy transport exist for the Atlantic Ocean
(Table V.3c).
It is also where most of the estimates are in agreement
with each other.
In Bunker (1976) and Hastenrath (1980,1982),estimates
are obtained by surface energy balance methods. The Hastenrath 1982
estimate is an update of his 1980 estimate using a different boundary
condition at 30*N.
Lamb (1981)
data set as Hastenrath's.
made transport estimates using the same
He also made estimates of the annual
variation of meridional heat transport in the Atlantic Ocean with the
addition of subsurface data and found that from November to December the
transport is
southward,
Roemmich (1981),
opposite to that for the rest of the year.
Wunsch (1980)
obtained using inverse methods.
Hall (1980)
and Bennett (1978)
hydrographic data .
and Fu (1981)
The
data are direct estimates
Results from Bryan (1962),
Bryden and
are also direct estimates using
Wunsch (personal communication) has calculated the
maximum and minimum values of energy transport using linear programming
4111111
1111
118
techniques.
He found a range of 8-13 x 1014 watt for the energy
transport at 24*N and a range of 1-7 x 1014 watts at 48'N.
estimates fall within this range.
Most
In the Southern Hemisphere, the
magnitudes of various estimates are quite variable although the
directions are the same.
others.
Our estimates are uniformly lower than
This is probably due to the assumed boundary condition of zero
flux across 70'N.
Aagaard and Greisman (1975) have estimated the energy
budget for the Arctic Basin and found a s'mall transport northward into
the Basin from the Atlantic Ocean.
Hastenrath (1980,1982)
1014 watts at 66.5'N as his boundary condition.
used a 1 x
With a correction of
the northern boundary value at 70'N , our values would be in better
agreements with others.
1.7 x 1014 watts is
Note,
however,
our final flux across 40'S of
in good agreement with values from Georgi and
Toole (1982) where they estimated the energy and fresh water balance for
the Antarctic circumpolar current.
Energy Transport in the Indian Ocean is the opposite of that in the
Atlantic.
The direction of the transport is southward in all
latitudes.
With the exception of higher latitudes in the Southern
Hemisphere,
most of the Indian Ocean has a surplus of energy.
TABLE V.3a. Comparison of Various Estimates for Indian Ocean
Meridional Heat Transport in 1014 Watts
This
Study*
Hastenrath
1982
-8.30
-4.8
15S
-14.88
-7.7
30S
-13.25
-4.9
Latitude
0
Georgi &
Toole 1982
4.6-6.4,
15.5-17.6
32S
40S
Bennett
1978
-10.10
-8.77,-6.35
The
119
excess energy cannot be transported northward into the continent and if
we assume not much energy is
transported laterally into the Pacific
Ocean, then the excess energy has to be transported southward.
The
deficit in the Southern Hemisphere is much smaller than the energy
surplus at the northern ocean so that the Indian Ocean as a whole
exports energy to other areas of the oceans.
Our estimates of a southward transport in the Indian Ocean is in
agreement with Hastenrath's estimate but the magnitude of our estimate
is about twice as large. (See Table V.3a)
Part of this difference is
from the way our Pacific Ocean and Indian Ocean is divided.
Both our
estimate and Hastenrath's estimate differ from those obtained by direct
estimate by Bennett (1978).
transport at 32*S.
He obtained a significant northward
This difference may indicate that there are large
interannual variations in the energy balance in the southern Indian
Ocean.
Again, our southward flux of approximately 10 x 1014 watts
agrees rather well with estimates of Georgi and Toole (1981) of 9 x
1014 watts at 40*S.
Energy transport in the Pacific ocean is more complicated and more
uncertain than in the other two oceans.
The tropical Pacific ocean,
especially the eastern part, has the largest observed energy surplus.
Together with the large area covered by the tropical Pacific Ocean, this
region has the highest surplus energy of any latitude belt.
However,
because of the Kuro-shio current, the north Pacific requires a large
amount of energy to be imported to make up for the large energy loss
there.
With no significant transport from the Bering Strait (Aagaard
120
TABLE V.3b. Comparison of Various Estimates for Pacific Ocean
Meridional Heat Transport in 1014 Watts
Latitude
60N
This
Study*
Hastenrath
1982
Bennett
1978
Bryan
1962
Georgi &
Toole 1982
Wunsch
1983
Roemmich
1980
-1.8+2.2
-2.5
-.3+3.5
-2.
.1
0
-12.
32N
30N
6.45
11.4
0
6.58
-2.3
20S
-.36
-20.7
-11.6,-1.7
28S
30S
3.21
-19.2
40S
6.88
-18.0
0.4, -8.9
-1.5, 4.2
43S
*Errors on these estimates are from 34% to 70%
and Greisman, 1975), the transport in the north Pacific would have to be
northward.
The region between 40'N-50'N has a small surplus of energy
but it is not large enough to change the direction of the transport.
Also any other reasonable boundary condition at 60'N (other than the
zero value used) would not alter the direction in the Northern
Hemisphere.
Higher latitudes in the Southern Hemisphere also experience
a large energy loss and energy also has to be imported to maintain the
temperature field.
The surplus energy in the tropics can either be
transported north and/or south.
The energy surplus in the tropical
Pacific from this calculation is
not large enough to take care of all
the energy deficits in both hemispheres.
Therefore in our estimates
there is a northward transport in the higher southern latitudes.
121
The Pacific Ocean is also the place where there are large
differences
among the results from various estimates (Table V.3b).
Most
estimates, with the exception of Hanstenrath (1982) have small energy
transports for the southern Pacific Ocean.
Wunsch et al (1983) have
some estimates indicating a small transport northward at 43'S.
and Toole (1982)
also found a small northward flux at 40*S.
Georgi
It should
be noted that all the discrepancy amongst various estimates in the
southern Pacific may indicate that it
is
a region that is
highly
variable and that the transport may be too small to have a definite
TABLE V.4
Comparison of Various Estimates for World Oceans
Meridional Heat Transport in 1014 Watts
Latitude
This
Study*
70N
0.0
60N
1.56
50N
3.99
10.±7
40N
6.43
30N
14.89
20N
Hastenrath Oort & Von
Vonder Haar
1982
der Haar 1976 & Oort 1973
Emig
1967
-1.±4
+1.
0.
-2.±5
1.
Newell Atmo.
et al. Newell
-.48
14.5
1.84
0.
27.1
11.
4.38
6.29
32.4
18.±12
21.
6.98
15.5
30.
20.±15
25.
9.74
20.8
23.2
16.30
29.±17
34.
8.58
18.4
16.4
ION
12.46
11.±19
19.
.42
9.2
8.2
0
1.73
-7.±21
3.
-13.59 -1.45
-1.4
10S
-13.66
20S
-15.49
30S
-11.79
40S
-4.27
2.5
22.5
1.0
-25.0
-9.69
-12.6
-20.0
-27.87 -16.9
-21.3
-17.5
-25.43 -23.2
-24.7
-17.29
*Errors on these estimates are from 34% to 70%
hiilll Il
ll
l
i
H
.
122
direction.
As a matter of fact,
the tropical regions are the most
sensitive to perturbations in our solar radiation estimation and the
amount of surplus energy in the tropical region is crucial to the
transport in the Southern Hemisphere.
1014 watts across 40'S seems large.
Our estimate of approximately 7 x
Part of this is due to the fact
that we only have data for the western part of the higher southern
latitudes in our estimates for the latitudial mean.
The southeastern
Pacific would presumably have smaller deficits
(since the water is
colder there) and inclusion of all the area in
these latitudes would
bring our transport values down.
When three oceans are taken together as a whole, the transport
becomes northward in the Northern Hemisphere and southward in the
Southern Hemisphere with a maximum at 20'N and 15'S (Table V.4).
The
direction of our estimates agree with those of Hastenrath but the
magnitudes are different.
In both hemispheres, our estimates are
smaller than his and the latitudes where the maximums occur are slightly
different.
Our northern hemisphere estimates agree fairly well with
those made by Emig (1978)
using Budyko's flux data.
are higher than ours in the Southern Hemisphere.
Again,
her values
Newell et al (1974)
obtained the oceanic transport value using the residual method.
Their
transport values are about twice ours in the Northern Hemisphere
mid-latitudes and higher latitudes in the Southern Hemisphere.
The
agreement is much better for the subtropical regions and for the
tropics.
Estimates of the atmospheric transport from Newell et al is
also presented in Table V.4 .
As can be seen, energy transport
accomplished by the atmosphere is
in
the mid-latitudes,
much greater than those by the oceans
especially in
the North Hemisphere where it
is
123
In regions
about twice to five times the oceanic energy transport.
between 30*N and 30*S,
summary,
In
the transport values much more comparable.
our results indicate a northward transport at all
latitudes in the Atlantic with a maximum of about 9 x 1014 watts at
25*N.
It
The Atlantic Ocean as a whole experiences a net energy deficit.
to maintain its
would require transport from other ocean areas
temperature field.
The Indian Ocean transports energy southward in all
and it has a energy
latitudes with a maximum of 15 x 1014 watts at 20'S
surplus for this 31-year period.
It needs to export energy to other
areas to avoid a increase in its temperature field.
The Pacific
transports energy northward in the Northern Hemisphere with a maximum of
10 x 1014 watts around 5-15'N.
The data coverage in the South Pacific
is too sparse to make any definite statements on transports there.
It
should be pointed out here that the error bars on these
estimates due to uncertainties in the fluxes can be large.
One might
want to ask the question of whether there would be a significant
in the transport estimates with the possible errors.
more or less systematic change in
question is
all latitudes,
that in the Indian Ocean,
change
If we consider a
the answer to that
the North Pacific and the North
Atlantic, the direction of the transport will remain the same (the
magnitudes of the transport will obviously change with a change in the
flux estimates) while the transport estimates in
the South Pacific and
the South Atlantic would have a different direction as well as a
different magnitude from the estimates presented.
reminded of a point Wunsch (1980) stressed.
We should perhaps be
In his opinion, due to the
large error bars associated with estimates from bulk formulas,
there is
no real discrepancy among various estimates and that any agreements
found are fortuitous.
... M .....
ww
fi""'
124
One should also be careful when comparing annual mean estimates
from bulk formulas to direct estimates. This is because direct estimates
do not give us a true average transport.
In addition, we do not yet have
a good enough knowledge of the seasonal or interannual variation of the
transport value to make a good comparison.
To obtain long term mean
estimates, bulk formulas, although inadquate are the only viable means
so far.
In this study, it is the first time global data coverage is
available to estimate the oceanic transports.
With net energy flux data
availabe only in limited regions,
one has to assume a boundary condition
that is crucial to the transport.
The importance of correct boundary
conditions, as evident in Hastenrath's case when he needed to update his
transport values due to incorrect boundary condition used at 30'N,
becomes a smaller problem when data is available up to the northern
boundary of the ocean basin as we have in this study.
V.4
Difference in Transport between Two Periods
In our EOF analysis of non-seasonal SST, we found a cooling trend
in the North Atlantic and in the North Pacific (Chapter VI.1 ).
The
time series associated with this pattern indicated that most of the
cooling occured in the 1965-1979 period.
In order to investigate the
pattern of the cooling further, we performed the EOF analysis for two
periods separately: one from 1949 to 1964 and another from 1965 to
1979.
We found the cooling to be most evident in the latter period.
The pattern tells us that the strongest cooling occured along 30-40'N in
the Pacific and along 40-45'N in the Atlantic - both at the northern
edge of the warm western boundary current (Figure 6.6).
Note there is
also slight warming in the Southern Hemisphere in both oceans.
125
In order to investigate the underlying cause for this cooling
further,
we calculated
the annual mean values of the four components of
the energy budget separately for these two periods.
know whether there is
these two periods.
We would like to
any significant difference among the means for
If there is, we need to know which components are
responsible for the differences as well as where these differences
occur.
The annual mean energy balance for the periods 1949-1964 and
1965-1979 are calculated separately.
The values are then zonally
averaged to produce zonal means for each ocean.
The results for both
periods and their differences is presented in Table V.5.
Each
component of the energy balance are presented separately for each
ocean.
The number of grids that made up the zonal means are also
presented in Table V.5a.
This table indicates that because of the poor
data coverage in the first period, it is impossible to compare the
results from the two periods for some latitudes.
For instance, the
difference between the two periods is artificially high in the 5-10*S
latitude belt in the Pacific. This is primarily due to the fact that
most of the central and western Pacific have virtually no useable data
in the first period.
A brief inspection of the differences tells us there is negligible
difference in Qouts Qh and Qin
Ql accounts for most of the
differences shown in the net energy budget (Qnet-
Referring to Table
V.5b, we can see that the biggest difference occurs in the Indian
Ocean.
It has a much larger energy surplus in the first period than in
the second period.
126
TABLE V.5a
Difference in Net Heat Flux
Units in watt/m2
Latitude
Indian Ocean
Pacific Ocean
Atlantic Ocean
1949-1964 1965-1979 Diff. 1949-1964 1965-1979 Diff. 1949-1964 1965-1979 Diff.
65N
-37(5)
-50(11)
13
60
-55(12)
-62(14)
7
-53(15)
-53(15)
0
55
-26( 8)
50
-10(14)
4(18)
-6
-43(14)
-33(14)
-10
45
5(18)
9(20)
-4
-28(14)
-22(14)
-6
40
-19(22)
-13(22)
-38(19)
-26(18)
-12
35
-60(22)
-48(22)
-12
-55(18)
-47(18)
-8
30
-50(23)
-41(23)
-10
-35(15)
-31(15)
-4
-5(18
-11(18)
6
-5(16)
-21
6
25
29( 6)
2( 9)
27
-30(24)
-17(24)
-13
20
29( 8)
8( 8)
21
-20(25)
-6(25)
-14
7(17)
4(17)
3
15
51(15)
39(16)
12
-15(28)
-3(28)
-12
7(15)
4(15)
3
10
47(18)
40(18)
7
-8(29)
1(29)
-9
16(14)
14(14)
2
5N
48(17)
36(17)
12
-6(30)
2(30)
-4
22( 8)
33(13)
-11
0
69(18)
53(18)
16
35(26)
36(30)
0
41( 9)
46(13)
-5
5S
65(17)
46(22)
19
90(11)
63(26)
27
68( 9)
67(10)
1
10
59(20)
31(22)
28
43(13)
26(26)
17
22(10)
28(10)
6
15
42(21)
10(22)
32
9(26)
5(22)
4
7(11)
9(11)
-2
20
8(15)
-7(20)
15
-12(26)
-4(28)
-8
16(10)
15(11)
1
25
-9(13)
-18(18)
11
-18(24)
-16(28)
-2
28(10)
16(13)
12
30
-20(15)
-32(17)
12
-26(21)
-26(220
0
8(10)
16(13)
12
35
-22(20)
-26(24)
4
-35(20)
-21(10)
-14
2(15)
0(15)
2
40
-34(12)
-32(26)
-2
-29(18)
-22(18)
7(13)
-23(16)
30
-7
i
127
TABLE V.5b
Difference in Latent Heat Flux
Units in watt/m2
Atlantic Ocean
Pacific Ocean
Indian Ocean
Latitude
1949-1964 1965-1979 Diff. 1949-1964 1965-1979 Diff. 1949-1964 1965-1979 Diff.
65N
54
54
0
60
67
70
-3
55
60
39
21
80
73
7
50
51
39
12
82
70
12
45
49
47
2
81
75
6
40
78
73
5
104
93
11
35
125
115
10
136
127
7
30
137
129
8
136
132
4
25
124
136
-12
138
129
7
129
131
-2
20
122
138
-16
149
136
13
135
134
1
15
113
121
-7
155
146
9
145
145
0
10
119
123
-4
154
145
9
140
140
0
113
120
-7
139
133
6
118
110
8
0
90
99
-9
111
112
-1
107
102
5
5S
90
103
-13
71
102
-31
98
96
2
10
100
119
-19
113
129
-16
131
127
5
15
119
142
-23
139
140
-1
132
130
2
20
141
153
-13
146
138
8
116
120
-4
25
141
150
-9
140
137
8
116
120
-4
30
132
142
-10
133
133
0
108
101
7
35
114
199
-5
125
115
10
100
100
0
40S
109
108
1
108
103
5
102
107
-5
5N
128
TABLE V.5c
Difference in Incoming Radiation
Units in watt/m 2
Atlantic Ocean
Pacific Ocean
Indian Ocean
Latitude
1949-1964 1965-1979 Diff. 1949-1964 1965-1979 Diff. 1949-1964 1965-1979 Diff.
65N
76
69
7
60
82
80
2
55
97
86
11
92
90
2
50
98
94
4
103
101
2
45
106
104
2
116
114
2
40
121
120
1
141
140
1
35
139
138
1
160
158
1
30
158
157
1
175
172
3
25
218
202
16
178
176
2
194
189
5
20
209
218
-4
194
192
2
205
202
3
15
214
210
4
206
200
0
212
209
3
10
215
213
2
262
260
2
212
209
3
5N
209
206
3
188
188
0
198
197
1
0
208
204
4
204
202
2
202
200
2
SS
204
201
3
213
219
-6
217
214
3
10
207
203
4
210
211
-1
208
207
-1
15
212
208
4
205
202
3
197
197
0
20
207
207
0
196
195
1
193
191
2
25
200
200
0
186
185
1
189
186
3
30
181
181
0
174
174
0
178
179
-1
35
165
165
0
161
160
1
165
162
3
40
145
146
-1
147
146
1
169
148
21
129
TABLE V.5d
Difference in Sensible Heat Flux
Units in watt/m2
Latitude
Indian Ocean
Pacific Ocean
Atlantic Ocean
1949-1964 1965-1979 Diff. 1949-1964 1965-1979 Diff. 1949-1964 1965-1979 Diff.
65N
26
29
-3
60
27
29
-2
55
21
21
0
25
25
0
50
12
13
-1
20
19
1
45
8
8
0
15
13
2
40
16
14
2
19
17
2
35
21
19
2
19
17
2
30
17
15
2
14
12
2
25
9
9
0
12
10
2
10
10
0
20
7
8
-1
10
8
2
8
8
0
15
3
3
0
9
7
2
6
6
0
10
3
3
0
9
7
2
5
5
0
5N
2
4
2
11
9
2
8
6
2
0
3
4
1
8
7
1
7
5
2
5S
3
5
2
3
5
-2
2
2
0
10
3
6
3
4
6
-2
4
4
0
15
2
6
4
9
8
1
6
5
1
20
5
7
-2
11
9
2
5
5
0
25
7
9
-2
12
11
1
5
5
0
30
16
11
5
14
12
2
7
6
1
35
12
12
0
15
12
3
8
9
-1
40
13
13
0
15
13
2
13
13
0
- -
HIM101611
,,1'11
IN11",
IN
I,
130
TABLE V.5e
Difference in Outgoing Radiation
Units in watt/n 2
Atlantic Ocean
Pacific Ocean
Indian Ocean
Latitude
1949-1964 1965-1979 Diff. 1949-1964 1965-1979 Diff. 1949-1964 1965-1979 Diff.
65N
43
43
0
60
47
47
0
55
46
43
3
46
46
0
50
40
41
-1
47
46
1
45
41
41
0
49
48
1
40
48
47
1
58
57
1
35
54
53
1
61
60
1
30
57
55
2
61
60
1
25
58
56
2
57
56
1
60
60
0
20
52
54
-2
56
54
2
57
57
0
15
49
48
1
52
51
1
55
55
0
10
47
47
0
49
48
1
51
51
0
5N
46
46
0
46
45
1
50
48
2
0
46
47
-1
49
48
1
49
48
1
5S
45
47
-2
51
50
1
49
50
-1
10
46
48
-2
51
50
1
51
52
-1
15
48
50
-2
52
50
2
52
52
0
20
53
55
-2
53
52
1
52
53
-1
25
57
59
-2
56
55
1
53
54
-1
30
59
60
-1
57
57
0
56
56
0
35
59
60
-1
58
56
2
56
55
1
40
56
56
0
56
54
2
57
54
3
131
one might
Having found the regions with the largest difference,
want to check and see if
truly significant.
latent heat flux is
the difference observed in
If the standard deviations for this area is high,
then the difference shown may be part of the natural random
fluctuation.
The significance test can be done by a simple hypothesis
One would
testing the difference of the means for these two periods.
have to make sure the frequency of ship observations for these two
periods are not drastically different
in
areas compared.
Four
representative grids with similar number of observation per month for
the two periods are chosen and the hypothesis that there is
difference between the means is tested.
is
no real
The results imply that there
a significant difference and are given in Table V.6.
Most of the
other areas with similar differences are presumably also significiant if
we believe that this pattern of difference is a large scale phenomenon.
TABLE V.6
Hypothesis Testing of Difference in Latent Heat Flux
Units in watt/m2
Latent Heat
Latent Heat
1965 -
1949 -
1979
Xi + X2
1964
Sl/Ni+S2/Nz
N1
X2
S2
N2
49
180
112
63
175
3.8
117
48
180
103
57
180
2.5
115E/10N
136
44
180
118
51
180
3.6
120E/15N
138
56
180
125
53
180
2.3
Location
X1
40E/20S
135
45E/20S
S1
Reject the hypothesis y, = P2 if Z > 1.625 at 5% significance level.
p, and P2 are the population mean for these two periods, X, and X 2
are the sample means, Si and S2 are the sample standard deviations,
and Ni and N2 are the number of observations.
Mlmi1i", "
I'LIA111
li,
132
In the calculation of the annual mean values, most of the uncertainties
arise from the formulation of the fluxes or from fixed bias in ship
observations.
This systematic error should disappear when one compares
the difference between two values calculated using the same
formulation.
If we are sure that random errors do not override the
differences, we can place more confidence in interpreting the results of
the differences.
From the results presented in the previous section, it
seems that the difference in our latent heat estimates between these two
periods are indeed significant in the Indian Ocean (where the largest
differences are observed).
We will be speculative and infer a little
further on the possible relationship between this difference in the net
energy flux and the cooling of the sea surface in the Northern
Hemisphere.
If we consider the first period as a base year where not much
cooling occured and assume that most of the cooling occurred in the
second period,
there must be a larger Qnet in the first period than
in the second period.
However, the only place that has such a
significant difference is in the Indian Ocean.
The two areas where the
major cooling occurred (the North Pacific and the North Atlantic)
actually have a slightly smaller surface loss in the second period than
in the first.
In the previous section we deduced that the Atlantic transports
energy northward, the Pacific transports energy in both directions, and
the Indian Ocean transports energy southward.
From this we can offer
the following explanation of the Northern Hemisphere cooling:
During
the first period, the surplus in the Indian Ocean not only made up for
133
the deficit in the southern Indian Ocean, but it also supplied energy
northward to the Atlantic to maintain its temperature.
The Pacific
Ocean, on the other hand, must have relied on the tropical ocean to
maintain the temperature in the Northern Hemisphere.
The south Pacific
takes some energy from the tropical region and some from latitudes south
Due to the larger latent heat loss, the energy surplus in the
of 40*S.
Indian Ocean is not as great during the second period.
There may be
just enough energy surplus to make up for the deficit in the southern
part of the Indian Ocean.
The southern Atlantic ocean normally gets a
northward influx of energy from the southern oceans.
It would therefore
not experience this expected input of surplus energy from the Inidan
Ocean.
The northern Atlantic ocean, not having enough energy from the
southern ocean, cooled in response to this net loss of energy.
The
tropical Pacific probably transported its energy surplus entirely
southward when no energy was imported from the 40*S or higher
latitudes.
to a deficit
The northern part of the ocean therefore cools in response
that is
not quite made up by the usual transport from the
tropical region.
The above argument is based on qualitative reasoning given the
estimated SST and energy flux variations.
We have not estimated the
actual magnitudes of the transports for these two periods because the
assumption that the storage term vanishes in
the long term mean probably
requires a time period larger than the 15-year period we have here.
More data, especially storage information using subsurface data are
needed to have a better understanding of the observed behavior of long
term SST variations.
The differences of the fluxes between the two
periods shown in this section does illustrate the importance of the time
0111ki
I,
Al
M1
134
period used when estimating energy transport values.
We have assumed in
the previous section that 31 years is a long enough period for the
storage term to be neglected.
It is entirely possible that a different
31 year period might give us different transport values.
One needs more
careful assessment as to exactly how long a period is required to
neglect the storage term and to use the net surface flux as a valid
estimate for the oceanic flux divergence.
135
CHAPTER VI. NONSEASONAL VARIATIONS OF SST
VI.1 EOF Analysis of SST
VI.la
The Analysis
The method used to characterize the nonseasonal variation of global
SST is commonly referred to as empirical orthogonal function (EOF).
This technique decomposes the time series at geographical
locations into
separate space and time functions that are orthogonal to each other.
The functions are the eigenvectors of the variance-covariance
the original data field.
matrix of
This method was pioneered for use in
meteorology by Lorenz (1956) and by Gilman (1957).
In this study, the
theorm of singular value decomposition (SVD) is used to find the
eigenvectors and the associated eigenvalues.
single value decomposition is
EOF.
different
The calculation of the
from that of the conventional
No covariance matrix needs to be constructed explicitly for SVD.
Rasmussen et al (1981) have applied this method to surface temperatures
of the United States,
and pointed out the advantages
of its use over the
conventional calculation of eigenvectors from the covariance matrix.
It is more accurate than most matrix inversions, especially when the
data is highly correlated.
In cases where the number of grid points in
space exceeds the length of. the time series (as
is
the case here when
876 grid points are available over a period of 372 months), considerable
computer time and storage requirement can be saved.
The numerical
method used here follows that of Businger and Goulb (1969).
Further
"I'AN1111,111il',"
,
, 1MW,
136
information on single value decomposition may be obtained from the text
by Goulb and Reinsch (1970).
A brief derivation of EOF and SVD and the
relationship between the two are given in Appendix C.
Using long
term monthly mean SST's of the 1949-1979 period (see Chapter III), the
monthly anomalies with respect to the monthly means were computed.
monthly anomalies at 876 grid square were used.
372
234 grid squares were
eliminated from the original 1100 grid squares due to excessive number
of months without data.
Data for November and December of 1977 are
deleted because there are large areas with no data for these two
months.
Interpolated values between October, 1977 and January, 1978
were used instead.
VI.lb The main results
After performing the analysis on the SST anomaly data set, one
needs to find out whether the eigenvectors obtained are physically
meaningful.
First of all, there is the problem of degeneracy where the
consecutive eigenvectors may not be independent of each other and the
'true' eigenvector may be a linear combination of the calculated
eigenvectors.
Secondly, one needs to know whether the eigenvectors are
sufficiently different from random noise.
Two separate formulae are
used to determne whether the eigenvalues are distinct and significantly
different from random noise.
The first method is to apply a formula
derived by Kendall (1980) to estimate the sample error assocaited with
each eigenvalue.
North et al (1982) recommended using the same
procedure recently.
The formula used is:
3X = X -(2/N)1/2
(6.1)
137
where N is the number of independent time samples used to calculate the
EOF.
If the sampling error for a particular eigenvalue A is larger than
the spacing between A and a neighboring eigenvalue, then the eigenvector
associated with A will not be distinguishable from its neighboring
eigenvectors.
The first twenty eigenvalues and their sample errors are
illustrated in Figure 6.1.
The sample errors for the first five
eigenvalues all show values smaller than the spacing between their
neighboring values.
8
1949 -1979
7
6
z
.J
0
z
0:
< 4
IA-3
z
C-
0
Figure 6.1
5
10
NUMBER
15
OF MODES
The eigenvalues and the associated sampling
errors for the first twenty modes of the
nonseasonal SST EOF analysis.
19111
... ..OWSONSONOM
138
In the second method,
we use one of the testing procedures suggested by
Preisendorfer and Barnett
in the data.
(1977)
to separate the noise from the signal
The procedure chosen involves calculating the
autocorrelation function of the time series of a particular EOF and
forming the 'Q-statistic':
k
r2(.E)
Q = 1
9=1
(6.2)
var[r(.E)]
where r(k) is the sample autocorrlation at lag k.
The Q-value is used
to perform a X-square test against the hypothesis that the time series
is a random sample from a Gaussian population.
The Q-statistic of the
first ten time series associated with the first ten eigenvectors are
calculated.
Their values are all exceedingly large, indicating a
strong non-noise signal in these modes.
To further test the significance and the stability of the principal
eigenvectors, eigenvector analysis was performed on various partitioning
of the 31-year data set.
The data was first divided into two separate
15-year periods, one from 1949 to 1964 and another from 1965 to 1979.
The first period denotes a period where the number of observations per
month was small compare to the second period.
Seasonally stratified
data (December-February, March-May, June-August, Septermber-November)
were also used to see if the principal patterns (modes) are different
from season to season.
The fraction of variance explained by the first
five eigenvectors are given in Table VI.1 for the various combinations
analyzed.
The sample error (X)
for the eigenvalues of the smaller
139
TABLE VI.1 Percentage of Variance Explained for Separate EOF Analysis
Dec-Feb
Mar-May June-Aug Sept-Nov
# 1949-1979 1949-1964 1965-1979 1949-1979 1949-1979 1949-1979 1949-1979
1
7.67
9.42
8.26
10.42
8.96
7.90
9.53
2
4.29
4.62
5.78
5.50
4.59
6.06
5.76
3
3.44
4.05
3.49
4.73
4.18
4.28
4.44
4
2.84
3.53
3.37
4.50
4.02
3.90
3.79
5
2.37
2.90
3.07
3.49
3.58
3.69
3.11
partitioned data sets may not be small enough to render the modes higher
than three to be independent of each other.
Therefore,
we will limit
our discussion to the first three modes of the EOF analysis
(which are
clearly distinct from each other) in the following sections.
VI.lc
Discussion
A. The First Mode (The El Nino Mode)
The first eigenvector pattern is shown in Figure 6.2.
This pattern
explains between 7.7 and 10.4% of the total variance of the global SST
field.
As can be seen from Figure 6.2,
this mode is
the first eignevector found by Weare el al (1976)
almost identical to
for a data set
covering the Pacific Ocean alone from 20'S to 55'N but omitting the
western tropical Pacific.
This was termed the El Nino mode because of
the presence of the warm body of water in the eastern equatorial
140
75
90
i20E
Figure 6.2
Pacific.
WO
543m *0
i~d Vo
135 1Zo lO
90
75
60
45
30'
First nonseasonal SST eigenvector pattern for
1949-1979 (7.67% of total variance explained)
When temperatures are high in the eastern equatorial Pacific,
they are also high in the tropical Atlantic, the tropical Indian and
north eastern Pacific.
At the same time, they are low in the north
middle latitude and the western Pacific.
We should point out here that
the name El Nino may be misleading because both studies show a large
region in the mid-latitude central Pacific to be an integral part of
this mode,
as noted by Weare el al (1976).
Time series of the first
eigenvector is presented in Figure 6.3a for the analysis covering
1949-1979.
It has been shown that an eigenvector analysis of zonal mean SST
data evaluated for the global oceans (Chiu and Newell, 1983) is also
dominated by this mode.
The El Nino is strongly related to the Southern
Oscillation and to subsequent tropical troposphere free air tempeature
changes (Newell and Weare, 1976a,b and Walker (1923,1932)).
Kidson
(1975) has shown by eigenvector analysis that the Southern Oscillation
explains the largest fraction of the variance of the nonseasonal global
pressure field.
It seem reasonable to find this El Nino mode also
dominates the variability of the global SST pattern.
141
TIME
SERIES
OF
EOF #1
21.
L16 .356. 87.
8-
W
-1.
3-
I I
949
I
51
I
53
*
I
.
55
I
57
.
I
59
a
I
61
.
I
63
.
I
65
.
I
67
.
I
69
a
I a
71
I
73
I
a
75
1949-1964 EOF #1 TIME SERIES AND 1965-1979 EOF *1 TIME
a
I
a
77
SERIES
16
Li.
0
0 6,
C/)
W
C-.
Figure 6.3
Time series of the first eigenvector patterns for
a) 1949-1979 and b) 1949-1964 and 1965-1979
The first mode obtained from various partitioning of the data set
are very similar to the one obtained from the entire period.
There are
minor differences, mostly in the Atlantic and the Indian Ocean. This
indicates that perhaps these regions are not dominated by the El Nino
mode.
The time series for the two half periods separately show the
same fluctuations as the time series for the whole data set, as
1979
111,
11
HIM
, '111111111
19111,
mill
142
illustrated in Figure 6.3b.
Even though the error bar of this analysis
is increased due to decreased sample size for the two half periods, this
mode is still separated from the second mode (as indicated in Figure
6.1).
Time series of the first mode from the four seasonally stratified
analysis are presented in Figure 6.3c.
The global pattern of the
eigenvectors are essentially the same as before.
the same characteristics
The time series show
as Figure 6.3a but with different relative
amplitude of the extremes.
TIME SERIES OF SEASONAL EOF ANALYSIS OF GLOBAL SST ANOMALY
224
174
u124
w
0
0
-
-
74
C" 24
W-26
C,,
-76
E-126
-476
49
53
57
73
65 69
61
WINTER EOF # I
77
SPRING
EOF *1
22'
174 -
f 124
8
12
74
(w-
7 4-2 4--
W 24
-1
nc-26
-26
2 -76
-76
~-126
-126
-176
Figure 6.3c
49
53
57
6I
At UTUMN
65 69 73
EOF #1
77
Time series of first eigenvectors for seasonally
stratified analysis.
143
Note that the fraction of variance explained by the first mode is
smaller than the 23% obtained by Weare el al (1976).
to the addition of the rest of the global ocean.
This is mostly due
This addition of the
Atlantic Ocean, the Indian Ocean, and the tropical western Pacific has
apparently increased the variance without a proportional increase in the
signal.
Since we have calculated the eigenvector analysis on the
nonseasonal anomalies without first normalizing them according to their
standard deviations, one might wonder whether the eigenvectors are
merely a result of the regions with high variance.
The standard
deviations based on the entire nonseasonal data set are shown in Figure
6.4.
We can see that the equatorial Pacific dominance of the first
eigenvector is not simply due to standard deviations of SST being larger
than elsewhere.
There are large values in the vicinity of the
Kuro-Shio and Gulf Stream.
A situation that also prevails if standard
deviations for separate months are considered.(See Chapter III.)
Figure 6.4
Standard deviation of SST for the period 1949-1979
11'.
41o0iiiW11114
144
In order to investigate the relationship between the El Nino mode
and other areas of the ocean, the correlation coefficient between the
time series of the first EOF and the time series of SST anomalies in
The global pattern of this
each 5* by 5' grid region was calculated.
correlation coefficient, shown in Figure 6.5, is quite similar to that
of the first eigenvector, but the relative values are different.
For
example, the tropical Indian Ocean and the tropical Atlantic Ocean are
quite highly correlated with the first EOF time series, whereas in the
eigenvector pattern itself these areas show relatively low weight.
0
E 45
60
90
75
105
120
15
150
65 E
10
W 165
150
135
ORRELATION COEFFICIENT WITH EOF *1
TIME SERIES
120
..
75
90
120
Figure 6.5
EI
0
-
0
___44
1
60
a W
5
00-50AO
a
45
30
45
60
_.2 50
25
OE
75
90
105
4
135
IS0
5E60W165
I50
105
35
120
05
9C
75
60
45
30
065W
i
Correlation coefficients of EOF #1 time series
and each 5' by 5' grid squares
Cross-correlation were performed between EOF #1 time series and
selected points over the global ocean to see if the contemporary
correlations found in Figure 6.5 are the maximum correlations if all
lags are considered.
The results are displayed in
Figure 6.6 for
squares that are significantly related to El Nino variations.
The
correlation between this mode and tropical Atlantic have their maximum
at three month lag and the same is true for tropical Indian Ocean.
In
both cases, the eastern tropical Pacific leads the temperatures in other
"I11 - I - I-
145
tropical areas.
There is also a high positive contemporary correlation
between areas off the north American coast and contemporarious negative
correlation with the north central Pacific (this is to be expected
from the pattern of the first eigenvector.)
The exact lag at which peak
correlation occurs between tropical oceans varies slightly depending on
which grid points are used, but the general result,
evident in all
squares considered, is that the tropical Atlantic and Indian lags the
eastern tropical Pacific.
The matrix of the correlation coefficients between zonal mean
temperatures in the three separate oceans has been presented by Newell
and Chiu (1981) and shows high values between the tropical Pacific and
tropical Indian Ocean.
The coherence between the nonseasonal SST
variation in the tropical Atlantic and eastern tropical Pacific has
previously been pointed out by Covey and Hastenrath (1978) and
Hastenrath (1978).
As for the physical link between the regions, they
suggested that the trade wind appear to be stronger or weaker in both
regions at the same time,
and the increased wind stress and
evaporational loss occur at the same time in these regions.
Thus a
general finding from Figure 6.5 is that the tropical oceans vary in
phase.
It has been known since Walker's early work (Walker, 1932) that the
Indian Ocean temperatures vary with an index of the Southern
Oscillation.
Newell (1979) and Weare (1979) pointed out that the
physical reasons for the temperature changes are different in the Indian
Ocean and the equatorial Pacific.
The eastern equatorial Pacific is
146
CROSS
CORRELATION
BETWEEN
EOF
#1 AND SELECTED
SOUARES
Cross correlation between time series of EOF #1
and selected grid squares
Figure 6.6
colder due to enhanced upwelling from higher than average pressure in
the south-east Pacific
On the other hand,
the water over the norther a
Indian Ocean is colder due to enhanced cloud cover from lower than
average
pressure, and therefore less radiation available to heat the
ocean (see Newell (loc cit); Weare (loc cit); Hastenrath and Wu (1982)
and Newell et al (1982)).
Empirical orthogonal functions were calculated for nonseasonal
variations in incoming solar radiation (see Chapter VI.3).
The first
eigenvector is a time series whose behavior is similar to the El Nino
mode.
The pattern of the first eigenvector shows large positive values
in the eastern and western tropical Pacific, North Indian Ocean and
tropical Atlantic.
This indicates that the physical parameters that
link the SST in tropical oceans during El Nino episodes might be the
variations in cloudiness.
147
While the first EOF pattern in
the Pacific closely mirrors
individual situations with the eastern equatorial Pacific out of phase
with the central North Pacific, the other parts of the global ocean do
not follow a unique pattern linKed to El Nino.
If actual monthly
anomaly patterns are examined, it is seen that for the same conditions
in the eastern equatorial Pacific there are quite different conditions
in the Gulf Stream region off the northeastern United States.
Figures
6.7 and 6.8 illustrate the behavior of global ocean temperature
anomalies during El Nino episodes in 1957,
1982.
1972 and more recently, in
The only consistent pattern in these episodes of El Nino is the
north central Pacific and eastern tropical Pacific oscillation.
Figure 6.7
Global SST anomaly pattern for November, 1957
and for November, 1972
wou
ilil ,,I
I'd
1,11,11
Mid
INN
1111',
,,
148
120
150
180
E
150
W
1
90
W
30
60
E
0
of-
SST ANOMALY (C)
NOVEMBER 1982
N
0
-I
00
-I
0
0
0
0
0
3D0
0
0
-0t
2
0
0
120
150
1I0
E
Figure 6.8
W
150
120
90
30
60
W
E
0
Global SST anomaly pattern for November, 1982
Since the north central Pacific and eastern tropical Pacific
oscillation is
the strongest
feature in
all El Nino episodes,
one might
want to rise the question as to why the water of the central North
Pacific are cold while the equatorial water are warm.
There are three
possible reasons: there could be oceanic energy loss due to increase
evaporation from enhanced northerly flow; there could be weaker
advection of warm water from the south from a weaker subtropical gyre;
and there could be reduced solar radiation reaching the sea surface from
more cloud cover.
The first hypothesis is supported by Kidson (1975).
He showed that
when the eastern equatorial Pacific was warm the middle latitude
north-south pressure gradients were enhanced in both hemispheres.
One
could argue that either stronger winds produced greater evaporational
cooling in the central mid-latitudes or carried drier air to the ocean
149
there, which would have the same effect. Correlation studies between
anamolous SST and anamalous zonal wind tends to support this hypothesis
(see Chapter VI.4).
A significant negative relationship was found at the
northern branch of the subtropical gyre suggesting that colder SST is
associated with stronger wind.
There is
little
data on ocean current velocities to test the second
hypothesis, although Reiter (1978) has suggested that the Pacific gyre
is modulated by trade wind changes and these would operate to produce
colder water at the equator and warmer water at 30'N at the same time.
The third hypothesis is
that the subtropical gyres are weaker in
the El Nino mode as suggested by Newell et al (1982).
Computation of
solar energy flux at the surface using observed mean monthly cloud
amounts obtained from the same data set has been made and this flux has
been correlated with SST anomalies (see Chapter VI.4b).
There are
regions of significant positive correlation in the North Central Pacific
The solar flux at the
suggesting that more cloud cover lowers the SST.
surface and the actual SST anomalies are shown for 30'N/165*W and
0*/80*W in Figure 6.9.
The correlation between this flux and SST is
0.41 (with a maximum of .61
in
the summer season)
the association between the curves is evident.
equatorial Pacific,
the association is
coefficient is -0.02).
in some periods.
at 30'N and 165*W and
For the eastern
not so clear (the correlation
Changes in the parameters are clearly related
1957 is a good example.
A similar check of the
evaporation anomalies shows no significant correlation between SST and
111NJIW11111*111101110
1110.
14,11101111111110
1101
150
UWN/SS E.TROPI:AL PACIFIC
-I I
5
I
.55
.56
.57
171 .55
'59
'61
INCOMING RADIRTION
-
6
4IS11~1
.67
.64
61
.7
.71
'7Z
73
77
'74 576
16lH/3IN NORTH CENTRAL PACIFIC - INCOMING RADIATION
4V
II
I
7
1
I
I
S
T1zui.
MfII
11
65
I
677
16
I
N
It 71 7
73
74
71
7
7
1N/SS EASTERN TROPICAL PACIFIC
.
49
'4
'51
'59
43
51A4
5
'56
'57
'59
'59
'69
't
.67
.5
6
.1
'6
71
1
7'
74 3
'75
'76
77
74 '76
'76
77 '1
74
168/3IN NORTH CENTRAL PACIFIC
*
I
11
1
1
4 '55
'6
Figure 6.9
'by
l
'as
'Go
6S
3
'
I
9la"
.
61
75 .7 1 79
71
Nonseasonal time series of SST and incoming solar
radiation at two selected grid squares
evaporation in mid-latitudes. Hence the third possibility, that enhanced
cloudiness explains the lower sea temperature in the middle latitude
seems the most likely explaination.
Another point evident from Figure
6.9 is that enhanced solar flux is sometimes associated with warmer
water in the tropics.
It has been argued that the warm water is
generally a response to decreased upwelling with solar radiation
supplying a constant heat source (Newell et al,1982).
If there is
increased solar flux at the same time as decreased upwelling, as
apparently occurred in 1957, the positive anomalies would be expected to
be sharp.
Further studies need to be made of factors controlling
cloudiness change.
151
Figure 6.10
Second nonseasonal SST eigenvector pattern for
1949-1979 (4.29% of the total variance explained)
B. The Second Mode (The Cooling Mode)
The second eigenvector is shown in Figure 6.10 with the associated
time series shown in Figure 6.11a.
Large positive values occur in the
north Atlantic, north Pacific, the Mediterranean and the eastern
equatorial Indian Ocean.
They are negative values in the eastern
equatorial Pacific, the south Atlantic, south Pacific and a good part of
the western Indian Ocean.
The second mode from the eigenvalue analysis
of the two separate half periods shown somewhat different patterns
A substantial negative region appearing in the the west
(Figure 6.12).
Atlantic at 40-50'N and in the subtropical north Pacific in 1949-1964.
Positive values in the northeast and southwest Indian Ocean were
enhanced and positive values appeared in the western equatorial region.
The 1965-1979 period, however, yielded a similar pattern to that for the
1949-1979 period.
6.11b.
It
is
The time series of this mode is shown in Figure
apparent that the cooling trend occurred mostly in
second half of the 31-year period.
The pattern from the eigenvectors
shows that the north Atlantic and the north Pacific dominated the
cooling.
the
This cooling trend was also evident in a previous
1,
152
TIME SERIES OF EOF #2
20
L' 15
w
0
- 10
U)
i5
w
WC0
U)
w-5
77
69
71
73
75
59
61 ~ 63
65
67
53
55
57
1949 51
SERIES
TIME
#2
EOF
-1979
1965
ANDSERIES
TIME
1949- 1964 EOF #2
1979
-20
10-
--5-
-15-
1949
51
53
55
Figure 6.11
57
59
61
63
5
6"{
69
71
73
75
77
1979
Time series of second eigenvector for the periods
a) 1949-1979 and b) 1949-1964 and 1965-1979
investigation of zonal mean SST changes (Newell and Hsiung,1979), in the
third non-seasonal eigenvector of the Pacific SST reported by Weare et
al (1976) and the first non-seasonal eigenvector of the Atlantic SST
reported by Weare (1977).
This interpretation also leads to the
inference that the south Atlantic and part of the south Pacific are
warming at the same time that the northern oceans are cooling.
153
av
ia
r*
1
90
105
Figure 6.12
120
135
50
165 E 80 W 15
50
15
120
105
75
90
60
45
30
15W
Second nonseasonal SST eigenvector pattern for
a) 1949-1979 (4.62% of total variance explained)
b) 1965-1979 (5.70% of total variance explained)
The observed cooling is intriguing and calls for an explanation.
Is
this an effect of the Mt. Agung volcanic eruption of 1963 or is this
just another natural mode of variation of the ocean ?
One could safely
rule out the argument of bucket versus engine intake method as an
explanation of this trend because the data set covers a period which we
believe is free of this bias.
engine intake took place in
Most of the conversion from bucket to
the mid-1940's.
At any rate,
engine intake method would have given us a warming trend,
the cooling trend observed.
the switch to
rather than
Douglas et al (1982), in a recent
contribution, reported that the cooling SST trends between the 1947-1966
and 1969-1980 periods are matched by 700 mb height changes in the
Pacific sector.
They make a good case for a relationship between SST
154
and 700 mb height - a relationship that has been frequently pointed out
In a previous paper on global SST (Newell and Hsiung, 1979),
by Namias.
a cooling trend was also found to be present in the north Atlantic (as
Boer and Higuchi
found by others; see for example Kukla et al, 1977).
(1980) also showed that the zonal mean 1000-700 mb thickness
(geopotential difference) of the polar cap showed a cooling trend after
Douglas et al ascribe the cooling to stronger winds, and greater
1964.
than normal southward Ekman drift, at least for the winter season.
C. The Third Mode
The third eigenvector (Figure 6.13) shows a general sign
alternation between the northern hemisphere and the southern hemisphere
60
30 E 45
90
75
120
105
50
35
00 W 165
65
15
30
45
60
0
60
45SST 20EOF
45
75
90
05
-40 0
I3,. 1949-1979.60T
*3.1949-I979
20040
0
3
15
-- 080
0-
20
-
1-
s.
-0
E
45
60
75
90
105
135
120
150
~
40-
60
<
-r
40
.'-o
20
\_40
o0
30
-40
0
-
0
0
- -26
-00
30
165 E
TIME
180
W 165
SERIES
120059
135
150
OF
EOF
7
75
o
"
30
604
/
5W
#3
U' 10
to5
0
C,5
-5
-t0
1949
51
Figure
53
6.13
nonseasonal
a)Third
(3.44%
1949-1979
and
b)
time
series
of
of
69
67
65
63
61
59
57
55
SST
eigenvector
the
total
the
71
73
for
pattern
variance
eigenvector
77
75
explained)
1979
155
in the Atlantic, and a general east-west sign change in both the north
and south Pacific.
The latter is
not present
for the 1949-1964 period.
The third global mode seems to reflect a shorter-term fluctuation
of some type as well as trends, making the interpretation complex and
difficult.
Once the data is divided into two to try to examine the
trends separately, the error bars on the eigenvalues increase to the
point where the third and fourth modes may not be resolved.
We
therefore do not pursue this further.
Autocorrelation functions were computed from the eigenvector time
series for the entire period and for the two halves separately in order
to provide further information on the differences in
(Figure 6.14).
the patterns
For the first eigenvector, the period 1965-1979
exhibites a typical recent El Nino characteristic and the 1949-1964
results seem to reflect the fact that the rather large event, the 1957
El Nino dominated the period.
The second eigenvector time series shows
unmistakeable evidence of a trend occuring in the second half and
dominating the entire period.
Autocorrelations for the third
eigenvector show evidence of a trend in the 1949-1964 period.
VI.2
Statistical Properties of ASST: Autoregressive Models
The time series of SST anomaly at the two centers of action of our
first global EOF analysis - the north central Pacific (NCP) and the
eastern tropical Pacific (ETP) - are investigated next in more detail.
We examine how SST anomalies in these two key regions behave.
m.II.il ~lI
156
blank page
157
1949 -1964
1949-1979
U:
W
0 0.8 0
,.......... .....
I.
0.8
0.8
z
06-
0.6
0.6
C
0.4
0.4
0.4
C
0.2-
0.2:
0.2
0.1-
0.1
0 - -0.1
0.1
-0.1
0
-0.3
0C
I
6
-0.I
-0.3
-0.5
16
21
26 31
-0.3
I
36
16
11
16
21
26
31
LAG IN MONTHS OF EOF
1.0 .
.
,
.
. . , . . . ,
,
, . ....
1965-1979
1.0
,,....,..,..
I.U ,,,,, ...
..
0
36
6
-1
16
2
26
31
36
*1
t.0.
,,,..
S0
z
0.48'
0.6
-- 04
0.2-
0.4
0.2
02
0.1
0.1
o -0.1
0
-0.
-0.1
C
1
0.6
OA
0.1
-0.I
-0.3
6
il
16
21
26
31
.0.3
1
36
6
11
16
21
26
31
LAG IN MONTHS OF EOF
36
-0.51.
I
.. . ..
6
11
.
16
21
26
31
36
6
16
21
26
31
36
*2
If-.
0.8
0.60.4-
Q2
-0.1-
-0.3.
-0.3
I 6 I1 6 21 26 31 36
LAG IN MONTHS OF EOF *3
I
II
Figure
Figure 6.14
Autocorrelation functions for the first three
eigenvector time series computed for the entire
period and for the two half periods separately
158
13 bZ 3
54
55
'56 5
7
58
'59
'65
'61
"r
'62
i
6
~6
SST RNOMALY AT CR10 0117
49
53
St
bZ
'53
54
155
56 *57
Figure 6.15
'5
'5
69I
'61
'i f
i 61I
1 67
6 I
73
71
72
73
71,
75
71
'7?
73
7
71
76
77
7
W
7
7
30N 165*W
6
1
7
'G.
.69
1
7
7
Nonseasonal time series of SST
at 5*S, 80'W and 30*N, 165'W
The time series plots at two representative grid points from NCP
In ETP, the grid point at 5*S and
and ETP are presented in Figure 6.15.
80*W is selected and in NCP the grid point at 30*N and 165*W is
selected.
The time series at ETP mimic the time series of the first EOF
- the El Nino mode.
that in
the NCP.
The amplitude of the fluctuations is larger than
The anomaly in ETP also seem to have more high
frequency component than that in the NCP. The difference observed in the
behavior of SST anomaly at these two areas can perhaps best be explained
by the observed mean mixing layer depth at these two areas.
Mixing
depth at NCP has a large seasonal variation ranging from as deep as 300
meter in
the winter to about 50 meter in the summer time, while at
tropical regions the mixing depth is
shallow (ranging from 10 to 50
meters) all year round (Levitus,1982).
The energy that is required to
change the temperature of the layer is larger when it is deep than when
159
it
is
shallow.
Therefore,
we observed the slow-varying SST anomaly in
NCP while the adjustment in
the tropics is
much faster.
During episodes
of El Nino, however, the behavior of SST anomaly in eastern tropical
regions seems to switch to a different mode - one that is more similar
to SST anomalies in the NCP region.
thermocline during El Nino is
As expected, the observed
also much deeper than usual (Wyrtki,
1975).
VI.2a
Autoregressive model fitting
Here we assume that the two time series considered in the previous
section can be represented as autoregressive processes for some unknown
order p.
A pth order autoregressive process
(Box and Jenkins,
1976)
denoted by AR(P) can be expressed as
f
*k (xt-k
-
y)
=
(6.3)
at, t=p+l,p+2,...
k=0
with $0 = 1, y the mean, and the other autoregressive coefficients
#k,
k=1,2,.. .p being the unkown parameters to be estimated from the
time series.
In (6.3), it is required that the at's constitute a
white noise process with zero mean and constant variance.
more complicated process can also be considered.
Of course,
Nevertheless,
low-order autoregressive models are adequate to explain these time
series and it is easier to interpret these simple models physically.
One good way to estimate the order of the autoregressive model for
the time series is to examine the autocorrelation functions.
The
autocorrelation function for these two points are estimated from the
time series by:
II'M
1
, iWIN
101111j,
160
(6.4)
rk=
bo
where
1 N-k
bk = -
N
t=1
(xt ~
(t+k
(6.5)
- ~)
Here x is the mean for the time series xi, i=1,2,...N.
The results
are presented in Figures 6.16. As can be seen, these two autocorrelation
plots indicate that the SST anomalies for these two regions are probably
the results of different mechanisms: NCP exhibits an autocorrelation
function that is similar to a first order autoregressive process while
the ETP has the characteristics of a second order process (see Box and
Jenkins,1976).
Autocorrelation funchon
of ASST
Log in months
Figure 6.16
Autocorrelation function of nonseasonal SST at
eastern tropical Paciic and north central Pacific
161
Autocorrelations
of SST anomalies were also calculated for the
global ocean and the coefficients at lag=l are presented in Figure
6.17.
This coefficient is
the parameter estimate of a simple Markov
process and gives an indication of how persistent the SST anomaly is.
Note both north central and eastern tropical Pacific are areas with high
persistence, but the behavior of their autocorrelation function are
quite different in higher lags.
Figure 6.17 also indicates that the SST
anomalies are much more persistent in the northern hemisphere than in
the tropics or in the southern hemisphere (with the exception of
upwelling regions in the tropics.)
autocorrelation
levels.
This is the opposite of the
function of the air temperature anomalies at higher
Newell et al (1983)
have found that
for air temperature
AUTOCORRELATION OF SST AT LAG=1
5060
33
20
20
to'1
N
0
C-:
CD
I
*0
LONGITUDE
Figure 6.17
Autocorrelation coefficient at lag=l
162
fluctuations the areas with highest persistence (as measured by the
tropical regions and decreasing towards
autocorrelation at lag=l) are in
higher latitudes.
To determine the optimal order of an autoregressive model for these
SST fluctuations, we calculated the autoregressive coefficient of orders
from one to five using Yule-Walker recursive method (see Box and
Jenkins, 1976, p.8 2 ) and used the Bayesian information criterion (BIC)
suggested by Katz (1982) to select the appropriate order of an
autoregressive fit to the time series.
The procedure requires that all
possible orders p, p= 0,1,...,p be fitted to the data.
Then the value
of p is selected that minimizes the quantity
BIC(P) = N-ln[a
2
(p)] + (p+l)-ln[N], p=0,1,...p
(6.6)
where
N
a2 (p)
a2 (p)
(6.7)
N-p-1
Here a2 (p) is an unbiased estimator of the white noise variance for an
AR(P) process and can be calculated by:
M
02
1
( P)
_
N
-
[Xt
-
At(P)] 2
(6.8)
N-p-1 t=1
where xt(p) denotes the fitted value of xt obtained by substituting
the estimated autoregressive coefficients. Thus, the first term on the
right hand side of (6.6) can be thought of as a measure of how well an
AR(P) process fits the data and the second term on the right hand side
163
of (6.6)
is
estimated.
a penalty function for the p+l parameters that needs to be
The results of the criterion testing for models AR(1) to
AR(5) are calculated and the results presented in Table VI.2 together
with the parameter estimates for each model.
There are other test selection rules available such as Akike's
However, the BIC procedure is more
information criterion (AIC).
parsimonious and would select as low order a model as possible.
can see,
a first order autoregressive
for the north central Pacific,
model gives the best fit.
As we
For the eastern tropical Pacific, a second
order proved to give the best fit.
TABLE VI.2 Autoregressive Model Identification
Baysian Information Criterion
North Central Pacific(30'N/165'W)
Model
Order
1
2
3
4
5
*Minimum
Parameter
Estimates
.67
.644,.038
.641,0.010,.075
.639,-O.Ol,
.055,.031
.637,-.014,.056
-.010,.064
BIC
Eastern Tropical Pacific(5*S/80*W)
Model
Order
Parameter
Estimates
1339.0*
1
.64
1342.0
2
.52,.187
1341.6
3
.517,.178,.017
1343.7
4
1343.8
5
.517,.178,
.017,-.001
.517,.177,.008
.028,.052
BIC
1725.7
1699.9*
1700.9
1702.3
1703.2
164
As an additional check, the order of autoregressive models can be
obtained from looking at the residuals from the selected order.
residuals are plotted in Figure 6.18.
The
The autocorrelation function of
the residuals from a first order fit and a second order fit for both NCP
and ETP are calculated to see if additional information can be gained.
The results are presented in Figure 6.19.
For NCP, the residual for a
first order and a second order fit are similar and close to the
autocorrelation of a white noise process.
Figure 6.18
For ETP, the residual from a
Residual plots of the first order and second
order fit for eastern tropical Pacific and north
central Pacific
165
Autocorrelation of residuals from ist to 2nd
9
-
Eastern
-
tropical
North centrol
.8-
order
Pacific
Pacific
.6-
.5-
Ist
order
.3.2 -
-.2 3L
2nd order
23
5
10
15
Log
Figure 6.19
20
25
30
in months
Autocorrelation of residual from first and second
order fit for eastern tropical Pacific and north
central Pacific
first order fit clearly shows a non-white noise behavior, suggesting a
higher order fit is desirable. When a second order model is applied, the
residuals show a behavior much more similar to that of a white noise
series.
VI.2b
Discussion
Having identified the order of the autoregressive model for SST
fluctuations at two key regions in the Pacific, we might want to ask
ourselves what kind of physical mechanisms are operating to give us the
results we observed.
In this section, we investigate the possibility of
some physical parameters as candidates for the parameters in the
statistical models proposed in the previous section.
The autoregressive equation of any given order is the finite
difference
form of a differential
equation of the same order.
For a
166
first order autoregressive model, we have the equivalent differential
equation of the form:
dX
-
+ AX
Y
(6.9)
dt
where Y is a white noise forcing function.
If Y is not a white noise
but instead is forced by another white noise, Z, then we have
dY
dt
+ BY = Z
(6.10)
substituting (6.7) into (6.8), we have
d2 X
-
dX
+ (A+B)-- + AB-X = Z
dt
(6.11)
dt
which is the equivalent of a second order autoregressive equation.
Frankingoul (1978) has shown that the observed SST anomaly in the
North Pacific can be explained using a first order model forced by the
anomalous net heat flux, the heat flux being a white noise process
(i.e. Y).
In the eastern tropical Pacific, the process is more
complex. We showed in the previous section that it
model rather than a simple first order.
is
a second order
It would probably be modeled
better by equation (6.11) rather than (6.7).
The forcing function Y, be
it the wind or another paramter, should be a parameter that is in turn
forced by another white noise process.
The zonal wind anomaly and the
anomaly of net heat fluxes can be considered as possible candidates
the forcing functions Y and Z.
wind
for
Figure 6.20 gives a plot of the zonal
and net heat flux anomalies at these two regions.
The zonal wind
167
anomaly at NCP show a higher amplitude and frequency fluctuation than
those at ETP.
The anomalies for the net heat fluxes, however, seems to
exhibit similar characteristics in both regions.
Autocorrelation functions for these anomaly time series are
calculated to determine whether they are indeed similar to the behavior
of a white noise time series.
We applied the test suggested by Box and
Pierce (1970) in their studies of the residual of ARIMA time series by
forming the Q-statistics (see Eq. 6.2). The statistic
distributed as a
X2 variate with k degree of freedom.
Q
is approximately
Applying a X2
test to the autocorrelation functions of zonal wind anomalies and the
net heat flux anomalies, we found that zonal wind anomalies at both
regions is a random noise time series at 99% confidence level.
Figure 6.20
The same
Time series plots of the net heat flux anomaly
and zonal wind anomaly at eastern tropical
Pacific and north central Pacific
0111011111111111
INIA111i
168
is
The heat flux anomaly at ETP
true for the heat flux anomaly in NCP.
however,
shows non-random behavior according to the Q-statistic test and
resembles a first order autoregressive process.
In summary,
the above results show that the SST anomaly in ETP is
the result of a more complex dynamic than that in NCP.
can be explained
While the latter
fairly well by a first order model forced by a random
noise time series, SST anomalies in ETP would require one order higher
model to explain its fluctuations.
For SST anomalies in the north
central region in the Pacific, a simple first order model forced by the
zonal wind anomalies would be sufficient to explain its variations.
For
the eastern tropical Pacific, a possible scenario to explain its SST
Since the net heat
fluctuations may be in the form of equation 6.11.
flux anomaly in ETP has more structure to it than a simple random noise
--.----
o stelrn tropical Pacific
North central Pacific
2
-Z
onoaoamas
wind
Autocorelation function of zonal
Aotocorrelton
'L 450
Figure 6.21
t
function of not
heet
(out anomnalies
15
20O
Log in months
25
' 32~
Autocorrelation function of zonal wind anomalies
and net heat flux anomalies at eastern tropical
Pacific and north central Pacific
169
series, it might be a possible forcing function for SST (as Y in
Eq.6.10). This is in turn forced by the white noise function of the
zonal wind at the same area.
Of course, the forcing functions could be
other parameters that satisfy the required statistical properties rather
than the net flux and zonal wind anomalies considered here.
It should be noted that here we are only considering linear models
of different orders.
Presumably the process that involved the
interaction between the atmosphere and the ocean is a highly non-linear
process and could be a lot more complex than the model we are proposing
here.
VI.3
Empirical Orthogonal Functions of Heat Flux Anomalies
In order to characterize the non-seasonal variations of components
of the heat fluxes, we performed an EOF analysis on the anomalies of the
net heat flux and two of its major components:
the incoming radiation
and the latent heat flux.
VI.3a
Data and Analysis
The analysis procedure used to calculate the EOF is identical to
that used on SST anomalies (see Chapter VI.la).
There were numerous
months with missing data in the calculated flux data (especially the net
heat flux) due to missing input parameters.
Efforts were made to retain
the maximum amount of available data and a preliminary run was done
using all 1110 grid points in the 31-year data period.
Missing values
"IN
111W
170
were replaced by zeros (meaning zero departures from the monthly
means).
This method of filling in missing data would be justified if
there is sufficient signal in the nonseasonal data set so that the
variation introduced by the artificial zero anomalies would appear in
higher modes of the EOF analysis.
missing data in
Unfortunately, there was so much
the grid points for the first half of our data set
(1949-1964) that the principal eigenvectors from this preliminary
analysis were merely measures of variations in the number of
observations missing.
In view of the results from this preliminary
analysis, another EOF analysis was made using only data from 1965-1979
period and grid squares with incomplete time series were deleted from
the analysis altogether.
Although this reduction has eliminated many
valuable grid squares in the central tropical Pacific and a good part of
Indian Ocean,
there are still
enough data to give us an approximate
picture of what process, if any, dominates the nonseasonal variations in
heat flux components.
VI.3b
Results and Discussion
As stated in the previous section, EOF analysis was applied to
Qnett
Qin, and
Ql.
The percentage of total variance explained
by the first five components of EOF are listed in Table 6.3 below.
171
TABLE VI.3. Percentage of Total Variance Explained
Mode
Qnet
Qin
3.3115
2.2456
1.9636
1.8550
1.7881
5.0857
2.8830
2.8131
2.2607
2.1624
1
2
3
4
5
Ql
5.6787
2.7949
2.5008
2.2634
2.0637
To see whether the eigenvalues from the EOF analysis are sufficiently
separated from each other, we calculated the sampling error bar
associated with the first five eigenvalues for the three EOF analyses.
The
The method used is the same as those described in Chapter VI.la.
first mode from all three EOF analyses are distinct from the other
modes.
Beyond the first eigenvalue, the eigenvalues were too close to
be clearly separated from each other.
The time series and the pattern
of the first mode from Qnet are shown in Figure 6.22. The same for
Qin are shown in Figure 6.23.
The time series from Ql is shown in
Figure 6.22 together with the first time series from QnetThe time series from the first eigenvector of Qnet shows an
unmistakable trend in
the period 1965-1979.
Since the eigenvector
pattern shows that most of the ocean has a negative weight, the trend in
the time series should therefore be interpreted as being an upward trend
- that there is more flux available in the latter half of the period.
The exact opposite behavior was obtained in the time series of the first
eigenvector of latent heat flux anomalies.
shown here because it
is
identical
The pattern itself is not
to that of the net heat flux.
Again,
172
EOF #1 NET HEAT BUDGET
LONGITUDE
U)
E-v r
TiME
#A.-.
r
SEIE
OF NET
HEAT
-
FLUX
-
\~v~
1
EOF
0
-SC
__________
63
64
65
TIME IN YERR
'
66
67
'
6
69N
IV
IV0
I
'
7w2
7
-
7-
7
- 50
0
1-50
Fivure 6.22 a) F.Op #1 of net heat flux anomalies
b) Time series of net heat flux anomalies EOF #1
c) Time series of latent heat flux anoraalies EOF #1
173
INCOMING RADIRTION EOF #1
LONGITUOE
1-50
Figure 6.23 EOF #1 of incoming solar radiation anomalies and its
associated time series
''.Ii
l
m e
llk 1,11
ni1
-----
174
the negative sign in the pattern of the first eigenvector indicates that
there is more latent heat loss in the first half of this analysis period
than the second half.
The identical fluctuations observed in the first
eigenvectors of the net heat flux and the latent heat flux shows clearly
that the nonseasonal variations in Qnet is completely dominated by
variations from latent heat flux.
Although the other components do
contribute to the seasonal variation of the net flux, they play very
small parts in modulating the nonseasonal variation.
Recall in our EOF analysis of global SST anomalies from Chapter
VI.la, the second major mode of nonseasonal variation was a cooling
trend.
The trend for the variations in latent heat revealed in this
analysis is also a downward one.
The implication here is that the
variation in latent heat is controlled by variations in SST: the warmer
the water, the more latent heat released to the atmosphere and vice
versa.
The result from an EOF analysis of Qin is intriguing.
series associated with the first eigenvector
behavior that is
(Figure 6.23)
The time
exhibits a
very similar to the behavior of the SST El Nino mode.
The first EOF pattern in the same figure displays large positive weights
in most of the tropical ocean except the central tropical Pacific.
The
largest values occurred off the coast of China and also in southwestern
Pacific.
This discovery may help us in understanding the reason why
tropical oceans vary together during El Nino events.
principal mode of nonseasonal variation in
Here we found the
incoming radiation is
also
associated with El Nino, supporting the theory proposed in Chapter VI.lc
that cloud cover change is
tropical oceans together.
a major factor that ties the variations in
175
VI.4
Relationship between Nonseasonal SST and Other Nonseasonal
Parameters
VI.4a Surface Sea and Air Temperatures
The relationship between the sea surface temperature and the
surface air temperature (SAT) could give us an idea of how closely the
upper ocean and the lower atmosphere are linked together.
Here we
present the results of relating contemporaneous sea and air temperatures
over the global ocean. The results are based on the monthly anomalies
from the long term monthly means.
90 20
AIR-SEA CORRELATION
o E teo Wiso 12
~0~ 60
0
3
\7
ZI
(.5
~
I
~5
LONGITUDE
Figure 6.24
Global map of correlation coefficients between
air temperature and sea temperature
176
There are substantial spatial variations in the relationship
between sea and air temperature.
Figure 6.24 shows a spatial
distribution of the correlation coefficients between air and sea
temperature variations.
The correlations are generally very high (only
a small part of the ocean has values below .5).
Figure 6.25
illustrates their relationship through scattergrams of four selected
squares with different correlation coefficients ranging from .22 to .8.
For some areas, the relationship is a very well defined straight line
the scatter is more or less random.
Figure 6.25
The seasonal variation of this
Scattergrams of surface air temperature vs.
surface sea temperature at four selected grid
squares
177
relationship (not shown) reveals that the correlation is highest in the
summer season.
This may be from the fact that other processes in winter
(stronger advection, for example) may have hampered the thermal
communication in the winter while the relatively quiet summer months
allow more thermal communication between the upper ocean and lower
atmosphere.
One special feature worth noting in Figure 6.24 is that in the
Pacific the coefficients increase
from west to east while in
Atlantic they decrease from west to east.
the
One would expect the western
boundaries of the ocean basins to behave the same way.
Cayan (1980)
observed the same pattern in a similar analysis for the North Pacific
and North Atlantic.
He claims that this difference might arise from
different processing procedures done on the Atlantic and Pacific data.
Since our data processing procedure is identical for all oceans, the
The
above argument cannot be invoked to explain the difference.
autocorrelation study on the persistence of SST shows a map of the
autocorrelation at lag=l (see Figure 6.17).
A surprising similarity is
found between the areas with high autocorrelation coefficients and areas
with high correlation coefficients between SST and SAT.
It seems
plausible that regions where SST anomalies have a larger time scale
(large persistence) would have more 'time' to communicate with (or
influence) the air above, therefore higher correlations are observed in
regions with high persistence.
One other feature worth noting is
that
in the eastern tropical upwelling regions of both the Pacific and the
Atlantic, high correlation coefficients are also observed.
Again, these
ujl,1
lul~
lol
lll alMMI
IMmloMMMMh
ili in
"ANIg
I1ilil0
, , i ,u
n,
II
1,
Wm
111,
178
regions also show high autocorrelation of SST at lag=l.
However,
as was
shown in the previous section, the statistical nature of the nonseasonal
SST between the northern ocean and the eastern tropical ocean is very
different despite the fact that both area possess high autocorrelation
at lag equal to 1. The results here seem to indicate that the strength
of the correlation between air and sea temperatures is related only to
the correlation between consecutive SST anomalies (i.e. the degree of
persistence) regardless of other characteristics of the SST time series.
VI.4b Relationship between SST anomalies and Heat flux Anomalies
Anomalies of global SST and anomalies of components of heat fluxes
are correlated to see if the observed SST departures from monthly means
can be explained by that of the heat fluxes.
Maps of the correlation
coefficients between anomalies of SST, Qnett Q9
Qh are presented in Figures 6.26 to 6.30.
Qins Qout, and
These coefficients are
significantly different from 0 at the 95% confidence level if they are
larger than .20.
This is calculated using a fairly conservative
estimate of a time scale of 4 months to reduce the number of degrees of
freedom from N to an 'effective' degree of freedom of N/4. (See Davis,
1976)
The most striking result from the correlation map between SST and
are
Qnet is that all the significant correlation coefficients
negative.
This indicates that larger heat loss to the atmosphere is
associated with high SST anomalies.
Intuitively one would expect the
opposite: that the SST would be lower if more heat is lost to the
179
atmosphere.
The association between AQnet and ASST is the strongest
in the tropical oceans, especially in central Pacific where the highest
SST are observed.
Minimum correlation occur in the mid-latitudes along
25*N to 45'N.
The correlation map between anomalous latent heat and anomalous SST
changes is almost identical to that in the previous Figure 6.26.
suggests that the nonseasonal fluctuation in
dominated by the fluctuation in
This
the net heat flux is
the latent heat flux,
as was evident in
Chapter VI.3 through EOF analysis of the flux components.
Again, we
have high latent heat associated with high SST.
The outgoing radiation flux is a function of SST and the humidity
of the air.
Therefore it is not surprising to find that the highest
correlation between
Qout and SST occurrs where the SST is the warmest
- namely the western and central tropical Pacific. Variations in
sensible heat flux are from the wind and the sea-air temperature
difference.
Areas with strong positive correlations with SST are areas
where the variation in SST dominates over the variation in the wind
since anomalous wind speed is not significantly correlated with SST.
Conversely, areas with low correlation imply that the variation in the
wind there dominates over the variation in SST.
It is then not
surprising to find that the maximum correlation between SST and Qh
occur in regions of weaker winds.
Nonseasonal variation in the incoming
solar radiation is solely from the the variation in cloud cover.
The
only place with a significant correlation between Qin and SST is
located between latitude 20'N and 45'N in the central ocean and the
180
relationship is a positive one, meaning more cloud is associated with
colder SST.
There is a strong seasonal variation in the relationship
between cloud cover and SST.
The correlation coefficient, when
calculated separately for each of the four seasons, shows the strongest
relationship in the summer (maximum .61) and weakest in winter.
This
finding is somewhat contrary to expectations based on physical
principal.
One would expect to see the dependence being stronger in
winter when there is more variation in the amount of cloud cover due to
higher baroclinic activities.
It should be noted that regions with
maximum correlation between Qin and SST are also regions where a
minimum correlation between latent heat and SST are found.
Lag correlation up to 30 month were also calculated to see if there
is a delay in the reponse of anomalous SST to the net surface flux
anomalies.
For a strip in the center of the subtropical gyre,
significant positive correlation is found when the Qnet leads SST by
one month (coefficients of .28 to .31).
This is the same region where
there is little or no contemporary relationship between AQnet and
ASST.
Elsewhere the negative correlations drop off after the zero
lag.
This result implies that for a given area, there is a delay of
about one month for ASST to respond to changes in the surface heat flux.
To further investigate the role of Q in affecting the observed
changes in SST, we calculated the finite difference form of the term
aT/at, taking the difference of SST anomalies in month i+l from SST
anomalies in month i.
This field is then correlated with anomalous Q.
The results (Figure 6.31)
show a highly significant positive
181
correlation with the maximum at the equatoral eastern Pacific between 0
and 10'S and 70'W to 130*W.
In the Atlantic ocean, regions of maximum
are off the coast of Africa in the tropics.
in
This reveals that changes
surface heat flux affect the rate at which the SST anomaly is
changing rather than the SST anomaly itself.
Correlation coefficients were also calculated between the wind
stress anomalies and SST anomalies to see how advection or upwelling
influences the changes in SST.
The formulation of the wind stress is
described and the results presented in Appendix E.
The relationship
between the zonal component of the anomalous wind stress and ASST found
in the tropics is hard to interpret (See Figure 6.32).
There is a
significant negative correlation between the two in the eastern tropical
Pacific with a maximum of .44 around 110*W in the equatorial region.
Intuitively one would expect that when the wind is more easterly
(negative anomaly of Tx ) more upwelling would occur and SST would be
colder (negative anomaly of SST), resulting in a positive correlation.
A negative relationship indicates that when the wind is stronger, the
SST is warmer, a counter-intuitive relationship.
However, the above
argument is only applicable to regions close to the coast where
upwelling is a major factor in controlling the SST variations.
A
negative coefficient would lead one to argue that a stronger easterly
wind stress brings about a larger advection of warm water from the
equator through the Coriolis force in the southern hemisphere and
therefore resulting in warmer SST. (Of course, the relationship could
also work the other way around - that warmer SST brings about a stronger
easterly although this is hard to explain physically.)
182
Significant negative correlation of ATX and ASST are also found
in the north central oceanic region.
This implies that weaker
westerlies (negative T) are associated with warmer SST (positive
ASST) and stronger westerlies associated with colder SST.
This could be
accomplished through cold water advection: stronger westerlies in the
northern hemisphere would advect colder water from the north and make
the SST colder.
Seasonal variation in the correlation coefficients show
that this relationship is strongest in winter - the season when the mean
SST gradient is the greatest in mid-latitudes.
Results of the same
study in the Atlantic ocean supports the above argument.
There are
significant negative correlations along the path where the mean SST
gradient is greatest, indicating that advection is the link between
Tx and ASST. In the tropical Atlantic, positive coefficients are found
along the coastal squares off Gabon, south of the Gulf of Guinea.
Negative correlations are found in the tropical mid-ocean.
When ASST is correlated with the anomalous meridional component of
the wind stress (Ty), the only areas with significant correlations are
in the eastern tropical oceans and the maximum correlation coefficient
obtained is .44 (Figure 6.33).
This is found in the equatorial tropical
Pacific at 5'S from 100'W to 110*W.
A similar relationship is found in
the Guinea Basin in the Atlantic Ocean.
One would expect the
coefficient to be negative in sign right along the coastal regions,
since more northward wind would bring about more upwelling (in the
southern hemisphere) and hence colder temperature.
Advection from
higher latitudes would give a negative coefficient in the southern
183
hemisphere where the significant relationships are found.
Further
investigations in more detail are needed to explain the results obtained
here.
The following points summarize the results obtained in this
section:
- On the whole SST in the tropical oceans correlates much better
with the heat fluxes than the middle latitude regions.
relationship is
The maximum
found between the latent heat flux and SST.
The
positive coefficients indicate that warmer SST causes more latent heat
to be released to the atmosphere,
rather than colder SST resulting from
a larger heat loss.
- The only region where there is a significant relationship between
the ASST and AQin is
in
the middle latitudes between 30*N and 40'N.
The sign of the coefficients indicates that more cloudiness leads to
colder SST.
- A significant positive correlation is found between AQnet and
3ASST/9t in the eastern tropical regions.
This implies that the net
heat loss does affect the rate of change of ASST, but only in the
tropical regions.
- Negative correlations between ASST and ATx are found in two
regions: the central mid-latitudes and eastern tropical Pacific
indicating that colder temperature are associated with higher
westerlies anomalies.
This is an effect of cold water advection.
184
- The only place where significant correlation exists between ASST
and
ATy
is again the eastern tropical Pacific.
The sign indicates
stronger northward wind is associated with warmer temperature.
Note that the two key regions found in
our EOF #1 of nonseasonal
SST (Chapter VI.1) seem to be the regions where most of the significant
correlations are found.
This would imply that these are two areas with
the strongest non-random signal and their SST variations are more
readily explained with the given data we have while the dynamics
associated with other parts of the ocean are more complex (or more
random in nature) and needs further information to explain the observed
variations.
Weare (1983) in a recent study analyzed the interannual variation
in net heating at the surface of the tropical Pacific Ocean.
general, his results agree with ours.
In
He found anomalously high heating
to be associated with colder water in the tropical region.
He also
concentrated the analysis on composited El Nino periods and found the
greater than average heating of the ocean occured prior to periods of El
Nino through the correlation of 8ASST/3t with AQnet.
No literature is
found on the nonseasonal relationship between SST and heat fluxes for
other parts of the ocean.
It should be pointed out that the correlation studies done in this
section are based on unsmoothed raw time series using all available
months.
It is not clear whether similar results would be obtained if we
concentrated only on time periods associated with one particular
185
phenomenon such as El Nino.
Spatial averaging with a given area and the
application of a low-pass filter to remove the high frequency noise may
give different results.
Nevertheless, this is intended as a preliminary
study to guide further research in the area of nonseasonal SST
fluctuations, therefore no preselected space or time averages are used.
The results, although crude, do give us an indication as to how ASST
behaves in relation to the parameters studied.
..WIllN....
Illlitill
1.ilolllelu..
acoins.,
ilulleillInlliitiinimi,
i.1lu.i.
I1.iliWll
186
SEA-NET HEAT BALANCE CORRELATION
bj
9k
it3
1b3L 1dl
W150
120
90
60
36
WI E
LONGITUDE
Figure 6.26
Correlation coefficients between anomalies of
SST and. net heat flux
SEA-INCOMING RADIATION CORRELATION
qk.NrTT~inr
Figure 6.27
Correlation coefficients between anomalies of
SST and incoming solar radiation
187
SEA-LATENT HEAT CORRELATION
LONGITUDE
Figure 6.28
Correlation coefficients between anomalies of
SST and latent heat flux
SEA-SENSIBLE HEAT CORRELATION
2
Cc
rn
I-nMrTIIDE
Figure 6.29
Correlation coefficients between anomalies of
SST and sensible heat flux
188
SEA-OUTGOING RADIATION CORRELATION
r-4
2,
0
LONGITUDE
Figure 6.30
Correlation coefficients between anomalies of
SST and outgoing radiation flux
Correlation bet. Onet and dT/dt
21
C=
r'ii
180 W150
LONGITUDE
Figure 6.31
Correlation coefficients between anomalies of
net heat flux and dT/dt
189
CORRELATION BETWEEN SST AND TAUx
r-
Figure 6.32
LONGITUDE
Correlation coefficients between anomalies of
SST and zonal wind stress
CORRELAT[ON BET. SST AND TAUy
r-
LONGITUDE
Figure 6.33
Correlation coefficients between anomalies of
SST and meridional wind stress
190
CHAPTER VII.
SUMMARY AND CONCLUSION
A newly available 31-year consolidated data set that spans from
January, 1949 to December, 1979 was used to investigate the observed
fluctuations of global sea surface temperature.
In particular, the
energy flux at the interface between the ocean and the atmosphere was
calculated using surface observations from the data set.
of this thesis is two fold:
The purpose
first of all, we would like to have a
complete documentation of the global seasonal-nonseasonal variation of
the sea surface temperature and the components of the surface heat
flux... Secondly, we wanted to see what role the oceans play in
maintaining the climate of the earth by calculating the meridional
transport of heat by the oceans.
Specific conclusions and salient features from the calculations are
summarized as follows:
1) The heat balance at the global ocean surface is calculated using
bulk formulas.
Of the four components that make up the net heat
balance, the incoming solar radiation and the latent heat flux are the
largest contributors. There is a large latitudinal variation in the
incoming solar radiation with a maximum of 220 watt/m
2
near the equator
and a minimum of 80 watt/m 2 at 60'N in the annual mean.
latent heat flux is
more evenly distributed spatially with a maximum of
180 watt/m 2 in the Gulf Stream and a minimum of 40 watt/m
southern oceans.
The annual mean
The sensible heat flux is
2
in the
about one quarter of the
191
latent heat flux in magnitude and the outgoing radiation is around a
half to a third of the latent heat flux.
2) In the annual mean there is a net loss of heat in regions of the
2
western boundary currents (up to 140 watt/m in the Gulf Stream). The
upwelling regions in both the Atlantic and the Pacific have the maximum
2
found at eastern tropical
heat gain with approximately 100 watt/m
Pacific.
The northern Indian Ocean also has a substantial heat gain.
3) Ocean transport of heat in the meridional direction is estimated
using annual mean net heat flux calculated.
This is based on the
theory that in the long term there must be a balance of surface heat
components if no long term changes are observed.
A northward transport
is found at all latitudes in the Atlantic with a maximum of 1.0 x 1015
watts at 30*N.
In the Indian Ocean, the transport is southward at all
latitudes with a maximum of 1.5 x 1015 watt at 20*S.
The Pacific
transports heat northwards north of 10'S with a maximum of 1.0 x 1015
watt at 10'N. There is a small southward transport between 25*S and 10*S
in the Pacific. The transport becomes northward again in the extreme
southern Pacific Ocean.
The transport at the southern Pacific Ocean is
most uncertain due to the sparse data available in that region.
When
all three oceans are taken as a whole, there is a northward transport
north of 15'S and a southward transport south of 15'S.
The maximum
northward transport is 1.6 x 1015 watt at 25'N and the maximum southward
transport is
1.5 x 1015 watt at 15'S.
The reader should be reminded
here that the uncertainty associated with these estimates can be fairly
large.
192
4) The annual mean heat flux difference between periods 1965-1979
and 1949-1964 was calculated.
Significant differences were found for
the Indian ocean where there was considerably greater latent heat loss
in the 1965-1979 period than in the 1949-1964 period. There might be a
possible link between this observed extra loss of heat in the Indian
Ocean and the cooling of the north Pacific and north Atlantic.
This
link could be accomplished through less available heat transport
southward in the Indian ocean and thus less availabe heat to be
transported into the Northern Hemisphere of the Atlantic and Pacific
oceans.
To say anything more specific concerning the nature of the
difference in heat transport, one would need transport values for these
two separated periods. Unfortunately, 15 years may not be sufficiently
long enough a period to calculate the specific transport values under
the assumptions made using the surface energy balance method.
5) Global nonseasonal variation in SST is characterized through an
analysis of empirical orthogonal functions.
The first global mode is
very similar to the El Nino mode found for the Pacific Ocean alone.
This mode consist of an oscillation between the warm eastern tropical
Pacific and the cold north central Pacific.
Other areas of the global
ocean have little or no correlation with this mode.
The tropical
regions in the Atlantic Ocean and the Indian Ocean are the only areas
that vary concomitantly with the tropical region in the eastern
Pacific.
mode.
The North Atlantic seems to be completely detached from this
Physical mechanisms that connect this oscillation between remote
193
regions in the north central and eastern tropical regions in the Pacific
Ocean are examined.
One possible explanation is
that the warm tropical
ocean induces a stronger Hadley cell and this in turn strengthens the
westerlies. This would bring about more cloudiness, and therefore
cooling of sea surface temperature in the mid-latitudes.
6) The second mode of the global nonseasonal SST EOF analysis
indicates a cooling trend in the north Pacific and in the north
Atlantic. This cooling is especially evident in the northern branch of
the subtropical gyres in both oceans.
The cooling is more pronounced in
the second half of the data period (1965-1979). The reason for this
cooling is puzzling.
The onset of the cooling in 1964 suggest that it
may be related to the Mount Agung eruption in 1963.
hard to verify this theory from one incident.
However, it is
If there indeed is a
relationship between the two, further examination of volcano related
cooling needs to be updated with the recent El Chichon explosion in
1982.
7)
Nonseasonal
SST fluctuations at two key regions,
the eastern
tropical and north central Pacific depicted in the global EOF analysis,
are investigated in further detail through autoregressive modeling
approach.
It is found that the SST anomaly in the eastern tropical
Pacific exhibits a more complex character than that in the north central
Pacific.
A simple first order autoregressive model (a Markov process)
is sufficient for the north central region While a higher order (second
Ail
u1
i
j
illllIlhu
i
a
194
order)
is more desirable for the SST fluctuations in
the eastern
tropical region.
8) EOF analysis were also performed on the nonseasonal net heat
flux and two of its major components: the incoming solar radiation and
the latent heat flux.
Limited area and time were used for this EOF
analysis due to excessive missing values in certain areas of the
oceans.
It is found that the nonseasonal net heat flux variation is
almost identical to that of the latent heat flux.
The only significant
mode for both the net heat flux and latent heat flux anomalies is the
first mode which explains about 5% of the total variance.
The time
series associated with the first EOF mode of the net heat flux indicates
a significant upward trend.
This means that less latent heat was lost
to the atmosphere in the second period due to the cooler SST observed.
The first mode of the incoming solar radiation has a time series that
resembles the time series of the El Nino mode.
This may be an
indication of the proposed relationship between the cloudiness change
and the El Nino pattern observed in the first EOF of SST anomalies.
9) Correlation studies were carried out between global SST
anomalies and components of the heat flux anomalies. It is found that
SST anomalies are positively correlated with net heat flux.
This means
that a warmer SST is associated with a larger net heat loss and a colder
SST with a smaller heat loss. Similar relationships are found between
latent heat flux anomalies and SST anomalies (i.e. warmer SST induces
m llllll,
M Mil 26k all
I
il
iu
lllk
195
larger latent heat loss).
This implies that it is the SST anomalies
that determines the amount of heat loss to the atmosphere rather than
the net surface heat available determining the SST.
The tropical SST
anomalies show the best correlation with all components of the heat
fluxes except the incoming solar radiation.
Here the only region that
exhibits a relationship between changes in cloud cover and SST is the
north central Pacific.
10) The net heat flux does have an effect on the month to month
change of SST anomalies. This is evident in the correlation between net
flux anomalies and the finite difference form of
this effect is most pronounced in the tropics.
a(ASST)/at.
Again,
The overall results
indicate that the SST anomaly determines the anamalous heat loss to the
atmosphere mostly through latent heat.
This net heat anomaly,
in
turn,
modifies the month to month change of the SST anomaly.
To summarize, we have presented results from two major areas of
investigation in
this thesis.
One is
a detailed documentation of the
global seasonal and nonseasonal variations of the sea surface
temperature and the components of the surface heat fluxes.
the calculation of oceanic meridional-heat transport
The other is
for the three
oceans individually and combined.
We have not attempted to specify all possible factors that
contribute to sea surface temperature fluctuations.
The inadequacy of
empirical formulas, the lack of current data to account for the
196
advective effects and a lack of subsurface data are major factors that
make the task extremely difficult,
if
not impossible.
We have shown
that nonseasonal sea surface temperature anomalies are related to the
heat flux anomalies through preliminary correlation studies.
Further
more detailed studies would add tremendously to our understanding of sea
surface temperature fluctuations:
variations of SST on a smaller scale
both in time and in space; relationships between parameters for specific
events and periods are just two the possible areas that need to be
investigated.
Our estimates of the oceanic meridional heat transport use the most
complete coverage of global heat flux data.
However, the transport
estimates using the surface balance method do not permit us to estimate
the interannual variations of the heat transport.
Heat storage in the
subsurface layer would be needed on an interannual variations basis.
A
knowledge of this subsurface variability would help us a great deal in
describing factors that control SST changes.
We should mention as a
last note that although there are many parameters we cannot calculate
due to the limitation of our data set, there are still a great many more
studies one can perform using this data set.
in
The complete coverage both
space and time, and the surface parameters available makes this data
set a tremendous research aid in realizing the long term goal of climate
forecasting.
197
APPENDIX A. LIST OF PARAMETERS AVAILABLE ON THE DATA SET
For reference, Table A.l lists the parameters available on each of
the marine observations in the Consolidated Data Set.
In this thesis,
nine meteorological parameters are extracted from the list for the
necessary calculations.
They are: sea-level pressure, sea surface
temperature, air temperature, wind direction, wind speed, total cloud
cover, lower cloud cover, dew point temperature, and wet bulb
temperature.
Figure A.1
PARAM
2
3
4.
5
6
7
8
9
9
10
11
12
13
14
15
16
17
18
.
-19
20
21
22
23
- 24
25
26
27
28
29
30
31
32
32
33
34
35
36
37
38
39
40
41
42
PARAM NAME
SOURCE
LATITUDE
LONGITUOE
CLASSIFICATION
SHIP DIR
SHIP VFLDCITY
PRESSURE
AIR TEMP
SEA TEMP
SEA TEMIP
.DE4 POINT TEMP
PRESSURE CH.ANGE
INDICATOR
WAVE PERIOD
WAVE HEIGHT
SWELL PERIOD
SWELL HEIGHT
SWELL DIqECTIO
WINO DIRECTION
WIN O SPEEU
CLOUD AHT
PAST W.EATHER
TOTAL AMT LO
LO CLOUD TYPE
HID CLOUD TYPE
HI CLOUQ TYPE
CLOUD HEIGHT
PRESENT 4EATHER
VISIBILITY
ERR3R INDICATOR
DSV
ICE TYPE
ICE THICKNESS
ICE THICKNESS
ICE ACCRETION
SIG CLOUD AHT
SIG 'CLOUD TYPE.
SIG CLOUD HEIGJT
AIR-SEA TEMP 0IF
YEAR
MON TH
DAY
HOUR
SHIP 10
WET BULR
FNWC
CODE
LAT
LOqG
C
KDSD
KV 3
KPPD
KDlY
KSEA
KSEA
KOEW
HASP
IN)
LPA
LH4
KP4
KH4
K04
LFir
mW.
NL.
LC
MC
LH
LWd
KVV
ICE Tr
ICE
ICE
KRAL
KS IG C
KSIGT
KSE3
CI
LT3S
NYrAR
JH3JR
SHIP
MARINE CONSOLIDATED DATA SUBSET
PARAMETER SJM4ARY
BITStWO)
59
58-48
47-36
35-34
33-30
29-26
25-15
14-4.
59-54
3-0
53-47
46-37
36-35
34-30
29-24
23-20
19-14
13-7
6-0
59-53
52-49
48-4544-41
40-37
36-33
.32-29
28-25
24-18
17-14
13
12
1.1-9
8-0
59
58-56
55-50
49-42
41-30
29-24
23-14
13-10
9-5
4-0
TOTAL BITS
()
(1)
(1)
(i.
(1)
(1)
(1)
(1)
(t)
(2)
(2)
(2)
(2)
(2)
(2)
(2)
11'
12
2
4
4
1±
11
4
'6
7
10
2
5
.6
,4
6
7
7
7
4
4
4
4
(2)
(2)
(2)
(3)
(3)
(3)
(3)
(3)
(3)
-4
(3)
4
(3)
4
7
(3)
4
(3)
(3)
(3)
(3)
3.
(3)
9
(4)
(4)
3
(4)
6
(4)
8
(4)
12
.6'
(4)
(4)
.
10
(4)
4
(4)
5
(4)
.59-24 (5)
(5)
23- 0
36
.24
REF (1)
TOF-1t SURIFA"
%IARI9e OBSERVATION--(REVi.E
+--PARAMETER CROSSES WOR BOUDOARIES.
43
REHAIKS
,
0=TOF-118 i=FNWZ SPOT
+/- .90 TO NEAREST TE4THl SOUTH IS COMIP
+/-'180 TO NEAREST TENTIf WEST IS COMD
REF CtL), P.s'
KNOTS/S
TOF-11. P'±0-q000: SPOT
0OULO t00
RANGEI -60 TO 55 OEG C*Lo
RANGEt -8 TO 50 DEG O1
SAHE AS ABOVE
RfjNGEI -60 TO 40 DEG C
RcEF (1), P. 12
*10, ADO TO PP 3NLY'
REF CL), P. 10, WHOLE SEC
RANGE: 0 TO 63, HALF m1ErERS
RE-F (1), P. 10e WHOLE SEc
RANGE: 0 TO 631 HALF METERS
RANGE: 0 TO 73 ZIT CO01PA3%S, 01G/5
RANGE: 0 TO 73 3T C04IPASS, OEr'G/5 .
M*ET ERS/SECONO
0
REF (Lis Ps..7
SANE
AS ABOVE
Ps 6
RE:' W1t
REF (t.)l Ps 7
REF (i)v Ps 7
OREF (t)., P. a
(1.), P. 9
REF
Rc01 1),P.1
(1) g.P (I
*REF
REF (L ).0P v 2
W-,. P. 2
REF
R
* FLAGS ERROR IN IEPORT0-5
REF (i),
P. 11
WHELE DEG C
01-31
00-2f
REF (I, P. 13
REF (t), P.
SEPT A196T)
W
199
APPENDIX B.
PROBLEM ASSOCIATED WITH 5* BY 5' GRID SPACE AVERAGING
In this appendix we illustrate the problem associated with taking
5*
latitude by 5'
longitude averaging
for certain regions of the ocean
and the method used to correct the problem.
Figure B.1 presents time series plots of the monthly mean number of
observations(B.la), the monthly mean latitudial position of the
observations(B.lb), and the monthly mean longitudinal position(B.lc) at
40*N and 60'W (the square from 40'N to 45*N and from 60*W to 65'W).
From the plot of the mean latitudinal position shown in
Figure B.lb,
can clearly see the drift of the ship's movement within this 5'
square in time.
one
by 5*
The monthly mean position is fairly constant around
41N to 42*N from 1949 to 1961.
From 1961 on, it started to move
northwards and by 1979, the mean position is around 43*N to 44*N. As to
the reason for this northward movement of ship tracks,
one hypothesis is
that with better equipment to handle possible ice conditions in
ocean during the latter period,
shorter northern route.
the
ships were able to take advantage of the
Ordinarily the mean temperature gradient does
not vary much within a 50 by 5' square and variations in ship movement
would not have much effect on averaged temperatures.
location,
however,
is
This particular
right on the track of the path where the Gulf
Stream leaves the east coast of North America and bends northwards.
Large temperature gradients are observed here.
A mean latitude
difference of 2 degrees would result in a mean monthly temperature
difference up to 6* C.
Figure B.2 illustrates the monthly
I ---Imm
1110116
200
mean SST anomalies obtained from three different
Figure B.2c is
averaging methods.
the anomaly calculated using long term monthly means from
5* by 5' square monthly values.
There is a marked trend in this time
What
series, corresponding closely to the time series in Figure B.1b.
we are interested in knowing is how much of this trend is real and how
much of it
an artificial result of the ship's northward movement?
is
Figure B.2a is the average of 25 1* by 1' subsquares (within this 5' by
5* square) time series of SST anomalies with respect to 1
term monthly means.
series for the 5'
taking the 5*
This can be considered the 'true' anomaly time
by 5* square.
by 5*
by 1* long
Figure B.2b is the anomaly obtained by
SST time series and
subtracting the respective
1* by
1* long term monthly means according to the mean monthly latitudinal
position for any given month.
This was intended as a quick correction
to compensate for the latitudinal movement of the ship's position.
It
could be calculated much faster than calculating 25 1* by 1* averages of
SST time series.
However,
the result
from this shortcut does not seem
to be a true indication of the average anomalous condition for the
square.
This is
probably due to the large standard deviations of the
mean latitudinal positions for each month.
Faced with this problem in our data set, we decided to check the
mean latitudial positions for grid squares located in areas with large
temperature gradients for significant drifts similar to the one
presented.
Several more grid square were spotted with the same problem
although none of them was as severe as the example illustrated.
Either
the drift in position was not as significant or the temperature gradient
201
was not as large.
Most of the time,
the correction of taking an average
of the 25 1* by 1* subsquares merely reduced the amplitudes of the
anomaly time series.
All together, a total of 16 grid squares were
corrected for the Atlantic Ocean and a total of 17 squares were
corrected for the Pacific Ocean..
The only other parameter besides SST that was influenced by this
drift is air temperature.
This is to be expected since variations in
air temperature follow closely with that of the sea surface
temperature.
If we have no reason to suspect the atmospheric
temperature gradient to be excessively large in the western boundary
region, then this is a good example to verify the thesis that it is the
ocean that controls the air temperature directly above it rather than
the other way around.
.WWWAMM"NAMMIUMN
11111%
202
Figure B.l
Time series plots for grid square at 400 N, 600 W
1715.a
1501.5
z o1288.0
z
asa
40
434.0
=
220.5
-651.8
S-62.1
-- 63.0
z
-63.3
-63.5
1949
c
1951
1953
1955
Figure B.lc)
1957
1959
1961
1963
1965
1967
1969
1971
MONTHLY MEAN LONGITUDE POSITION FOR GRID AT 40N/60W4
1973
1975
1977
1979
203
Figure B.2 .Time series plots of SST anomalies at 40 N, 60 W
2.2
-0.6 -
-0.2
-1.6
1949
1951
1953
1955
1959
1961
1963
1965
1967
1969
1971
AVERAGE SST ANOMALY FOR 25 1 BY 1 DEG. SQUARES-
1957
--
-
1973
1975
1977
1979
4.9
3.7
SM
cc
ii
-2
2.4
b.
SS
.
AN.L
SE IE
F.
. ..
S AR
BY .5 .DEG...
.. .Y. .EAN
.T
0-1.4
-1.
-3.9.
1949
1951
1953
1955
C
1957
1959
1961
1963
1965
1967
1969
1971
1973
1975
1977
1972
SST ANOMALY SERIES FOR 5 BY 5 DEG. SQUARE W.R.T. 1 BY 1 MEANS
3.8a
'I 2
1
1
2.6
-3.
o-1.15
94
cn
-.
95
15
15
91
SSzNML
O
16
95
97
Y5SUAEWRT
.z
16
91'193
Y5MAS
17
97
Ii
'',flII j911
111lik
,,,Illi.
.111111
204
APPENDIX C. LONG TERM MONTHLY MEANS OF RELATED METEOROLOGICAL PARAMETERS
For reference, contour plots of long term monthly means of January,
April, July and October are presented in this appendix for the following
parameters:
-Wind speed (Figures Cl-C4)
-Cloud cover (Figures C5-c8)
-Specific humidity difference (Figures C9-C12)
-Surface wind (Figures C13-C16)
-Air temperature (Figures C17-C20)
-Sea level pressure (Figures C21-C24)
205
MONTHLY MEAN WIND SPEED MON=1
LONGITUDE
Fibure C.1
Long tern January means of wind speed
MONTHLY MEAN WIND SPEED MON=4
r-
cI
LONGITUDE
Figure C.2
Long tern April m-eans of wind speed
ON
01111
206
MONTHLY MERN WINO SPEED MON=7
61
51
41
31
21
r-~
rn
c
1
21
31
41
LONGITUDE
Figure C.3
Long term July means of wind speed
MONTHLY MEAN WIND SPEED MON=10
LONGITUDE
Figure C.4
Long term October means of wind speed
207
MONTHLY MEAN CLOUD COVER MON=1
I-
-'
0-
LONGITUDE
Figure C.5
Long term January means of cloud cover
MONTHLY MEAN CLOUD COVER MON=4
r-
-M
C
0
LONGITUDE
Figure C.6
Long term April means of cloud cover
1111k
il
-
|- |
|,
208
MONTHLY MEAN CLOUD COVER MON=7
2i
m
M1
<
LONGITUDE
Figure C.7
Long term July means of cloud cover
MONTHLY MEAN CLOUD COVER MON=10
2:
M4
Fimure C.8
LONGITUDE
Long term October means of cloud cover
209
SPECIFIC HUMIDITY DIFF MEAN MON=l
r-
LONGITUDE
Figure C.9 Long term January means of specific auid.iisy cifference
SPECIFIC HUMIDITY DIFF MEAN MON=4
LONGITUDE
Figure C.10
Long term April means of specific humidity difference
w1hillw1glon
IN111"
210
SPECIFIC HUMIDITY DIFF MEAN MON=7
LONGITUDE
Figure C.11
Long term July means of specific humidity difference
SPECIFIC HUMIDITY DIFF MEAN MON=10
Figure C.12
LONGITUDE
Long term October means of specific humidity difference
211
MEAN WIND FIELD MON=1
\\\,
.su
\\\\\\\\\-%
- Jii
s.
ae
rN/o
ry2
20
1
~t'
i
i '
%
40
i
A
140
30
60
90
120
150 E 180 NISO
120
Figure C.13
90
60
30
N 0 t
-
LONGITUDE
Long term January aeaus of surface wind
MEAN WIND FIELD MON=4
30 40 2o 2
W .1\
23.~~
SOE
soWio12o
I lilu
\\\\\\%n
'%
%
4
-9.'~~
T\A\\\
r\\
,*-rI
\ 1
,
-1\
%...-
fl\
\ \
n~~%.an
go 60
3o W o E
& TV "AXI I2PI/ V
n
i%%A litik-11ezi:-
MIs
I
30
60
Figure C.14
90
120
150
I 'I
I
I
I
I
180 N150
120
LONGITUDE
90
60
Long term April neans of surface wind
30
W 0E
~
4
I'll,
1
M =Nlk,,
IV
212
MEAN WIND FIELD MON=7
I~~~ I/
30
//
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/
,
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{
2010
n
/
I
20
4
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u
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30
Sol'
30
60
90
Figure C.15
120
50
180 WiSO
120
LONGITUDE
90
60
30
0
Long term July means of surface wind
MEAN WIND FIELD MON=10
607
60
fill
INk,
ZI
50-
1
40
//
/////////
9
30
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30
/
60
Figure C.16
/
90
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I/
120
ISOE
!,
,
120
180 WiSO
LONGITUDE
-
90
60
Long term October means of surface wind
-
30
W0
E
213
MONTHLY MEAN AIR MON=1
-1
LONGITUDE
Long term Junary means of air temperature
Figure C.17
MONTHLY MEAN AIR MON=4
30-
20
-
126i
it
1 28
20
30
-
24-
1
16
9
2-0-
8
16181
12
150E
10
180
isO
120
90
60
33
LONGITUDE
Figure C.18
Long term April means of air temperature
W 0E
wwnn flh
w11UW1i1w1k11w1
wwwN
-
ww
214
MONTHLY MEAN AIR MON=7
Figure C.19
Long term July means of air temperature
MONTHLY MEAN A[R MON=t0
20
4
-
16
'
-
--
16
- - 12
:!~E
fNGITilDE
means of air temperature
October
term
Long
I
Figure C.20
215
MONTHLY MEAN SLP
-4j
P,
4
LONGITUDE
Figure C.21
Long term January means of sea level pressure
MONTHLY MEAN SLP MON=4
LONGITUDE
Fiaure C.22
Long term April means of sea -level pressure
.... NOONNMdwml
li,
216
MONTHLY MEAN SLP MON=7
-II
C
D
1016
1020,
30
60
'
90
120
-'
.-
1020
1016
150 E 180 WiSO
120
90
50
kJ
LONGITUDE
Figure C.23
Long term July means of sea level pressure
MONTHLY MEAN SLP MON=10
r-
Figure C.24
LONGITUDE
Long term October means of sea level pressure
217
APPENDIX D.
EMPIRICAL ORTHOGONAL FUNCTIONS AND SINGLE VALUE
DECOMPOSITION
Very often in meteorology we have a set of n number of observations
for p number of variables.
When n and p are large,
the amount of
information contained in the data set can be overwhelming.
orthogonal function analysis
Empirical
offers a method to 'reduce' the data set
to a manageable number of eigenvectors while maintaining the maximum
amount of information.
The eigenvectors are orthogonal to each other
and can be considered as weights for each of the p variables.
Associated with each vector is
a time series that describes the
variation of the particular vector in time. So in addition to the
reduction of the data set, EOF analysis conveniently separates the data
set into a space component and a time component.
To calculate the
empirical orthogonal functions of a large data set requires the
construction of the variance-covariance matrix. If the number of
variables in the data set p is large, this can be a tremendous amount of
computation, even for a high speed computer.
Single value decomposition
is also a technique that decomposes a matrix. It separates any given
matrix into products of matrices, one of which is a single-valued
diagonal matrix.
In this appendix we will show how SVD are related to
the EOF analysis and how one could avoid calculating the p by p
covariance matrix to obtain the empirical orthogonal functions.
If
the
we denote by xij the deviation of the ith observed value of
jth variable from its mean xj where
218
I
--
xj
n
I
kj
n k=1
Store our deviations into a nxp matrix X:
X21- --.
xlp
X2p
Xnl-----
Xnp
x1l .............
then each of the columns of X gives the n observed deviation time series
from the mean of the
jth variable.
In empirical orthogonal function analysis, we assume the existence
of two matrices Y and Z such that the matrix X can be factorized into:
(D.1)
X = Z*Y
with the following constraints:
y.y' = I
(D.2)
Z'-Z = D
(D.3)
where Y is a pxp matrix, I is a pxp identity matrix, Z is a nxp matrix
and D is
a pxp diagonal matrix.
Here we are using a capital letter to
denote a matrix and a prime to denote the transpose of a matrix.
One
can think the p columns of Z as the time components with length n and
the columns of Y as the space components with size p.
From (D.1) we have
X' = Y'-Z'
Using (D.4)
and (D.1)
we obtain the following:
(D.4)
219
X'X = Y'Z'ZY = Y'DY
(D.5)
With the property of orthogonality of the matrix Y, equation (D.5) can
be written as
Y(X'X)Y' = D
(D.6)
From (D.6) we see that the matrix Y whose existence we merely assumed is
an orthogonal matrix that can be used to diagonalize the product matrix
XX'.
The matrix Z can be computed using (D.1) as:
Z' = XY'
(D.7)
The problem of finding the matrix Y such that equation (D.6) holds
is
known in
linear algebra as the eigenvalue-eigenvector
problem
turns out that the rows of Y (or equivalently, the columns of Y')
the eigenvectors of the matrix (X'X)
It
are
and the corresponding diagonal
elements of D are the associated eigenvalues.
One can deduce from matrix algebra that in
(D.6)
Tr(X'X) = Tr(D)
where Tr(A) denotes the trace of matrix A (trace being the sum of the
In other words, the sum of the eigenvalues di,
diagonal elements).
i=1,
2,...,p is equal to the total variance of the p variables (since
from the definition of X the product X'X is the variance-covariance
matrix.)
The fraction
di
ri
i=1,2,..,p
=9
p
Idj
j=1
Alo
l
WIi
lll
, i, II
il
li
ib i1ilil MI
lld ileE
lil1liiili
1ellul
Ik ""
iM
o '111a1W11
lllil
l la
M
l 1.ll
1ll'lll
i
11Mi
Wn11lu
220
is the ratio of the variance of the ith eigenvalue to the total
variance.
We can think of ri as the percentage of variance
'explained'
eigenvalue.
by the ith vector that is
associated with the ith
If we rearrange the order of the eigenvalues in decreasing
order of magnitude, then the first k components will account for K
percent of the total variance where
k
ri
K =
i=1
Depending on the particular data field, we could have K close to 1. for
a k much smaller than p,
our original number of variables.
Thus the p
variables are effectively reduced to k components and in these k
components we have an optimal description of the data field using the
least number of components.
In single value decomposition, one is interested in decomposing a
given matrix into a single-valued matrix (i.e. a diagonal matrix).
example,
For
given the matrix X, we want to find a matrix S such that
x = U.S-v'
(D.8)
Here S is a pxp diagonal matrix, u is a nxp matrix and v is a pxp
matrix.
In addition, we require
From (D.8)
U'u = I
(D.9)
V'V = I
(D.10)
we have
X' = V-S'-U'
and
(D.1l)
221
X'X = VS'U'-USV' = VS2 V'
(D.12)
Rewriting (D.12) using (D.10):
V'X'XV = S2
(D.13)
Equation (D.13) is the equivalent of (D.6) except now the matrix V'
is
the matrix that diagonalizes the product matrix X'X and the diagonal
elements of S2 are the eigenvalues of X'X.
The equivalent of Z is the
product U -S.
So far we have shown the equivalence of the matrix V and Y.
They
are both eigenvectors of the matrix X'X - which is nothing other than
the variance-covariance of X if X is a matrix consisted of deviations.
The advantage of SVD comes from the fact that one can also form the
product XX'
such that
XX' = USV'-VS'U' = US2 U'
(D.14)
Again the above equation is
U'(XX')U = S2
(D.15)
We can see that the rows of the matrix U' are the eigenvectors of XX'
and the diagonal elements of S2 are the eigenvalues.
If in our matrix
X n is smaller than p (recall n is the number of observations and p the
number of variables), then the size of the product XX' (nxn) would be
much smaller than the size of the product X'X (pxp).
It is therefore
much more efficient to calculate U first and then calculate V from the
relationship in (D.8) to obtain the required Y matrix of an EOF
analysis.
M nlimillllilliwillleli.
111
MMnIM
11
222
In summary, to find the eigenvector Y in EOF analysis, one can form
XX'
first. Calculate its eigenvector U' and from (D.8)
(which is equivalent to Y.).
find the matrix V
This approach can be a considerable
saving in both computing space and time, especially if p is much larger
than n.
223
APPENDIX E.
E.1
WIND STRESS CALCULATIONS
Wind Stress
The bulk aerodynamic formulas used for the zonal and meridional
component of wind stress calculations are
Tx =
Pa Cdlv u
Ty = Pa Cdlvi v
(E.1)
Here u and v are the zonal and meridional components of wind,
wind speed,
Pa is
The development
the air density,
and Cd is
-
is the
the drag coefficient.
of these formulas are from the same equation of vertical
flux as the heat fluxes(see Eq.4.7).
controversial
lv
The specification of Cd is
some use a specified constant and some treat it as the
same coefficient as the transfer coefficient for the heat fluxes. For
the sake of consistency, we used Bunker's (1976) table of Cd as a
function of atmospheric stability and wind speed.
wind speed is
conditions.
This dependence on
illustrated in Figure 4.1b for various stability
The formulation of wind stress calculations indicate that
they are strongly dependent
on wind speed because the drag coefficient
Cd is a function of wind speed as well as the formulas themselves.
low wind speed (say less than 10 m/s),
At
the dependence of stress on
stability becomes as great as the dependence on wind speed.
Contours of the long term monthly means of zonal wind stress for
one month of each of the four seasons
(months January, April,
October) are presented in Figures E.1 to E.4.
July and
The circulation that is
MIN110filluilwill"
'i LWA
224
responsible for the subtropical gyres in the north Pacific and north
Atlantic is clearly evident in Figure E.1.
There is a lack of such well
defined feature in the same season in the southern hemisphere(see Figure
E.3.)
The northern hemisphere circulation weakens and moves northwards
as the season progresses towards summer.
In July (Figure E.3), the
maximum wind stress in the global ocean is the large scale monsoon wind
in the Arabian Sea west of India.
The southern hemisphere circulation
becomes more noticeable but the strength is weaker than that observed in
the northern hemisphere at the same latitudes.
Notice that the
movement of the zero wind stress line over the year is greater in the
Atlantic than it is in the Pacific.
Long term monthly means for the same months of the meridional
component of the wind stress are presented in Figures E.5 to E.8.
The
maximum northward wind is observed in high northern latitudes in
winter. In most areas of the ocean, the magnitude of the meridional wind
stress is generally much less than that of the zonal wind stress
indicating a more east-west orientation of the surface wind.
reference,
For
the vectorial representation of the wind stress fields are
presented in Figures E.9 to E.12.
Our results agree well with respect to the zero line contour when
compared to Hellerman's (1967, 1968) estimates of wind stress.
maximum values are typically 10% larger than ours.
His
The best agreement
is found in the North Atlantic and the North Pacific while the worse
agreement is in the Southern Hemisphere where his values are much higher
than ours,
especially the zonal component of the wind stress.
Weare and
225
Strub (1980) made estimates for the tropical Pacific from 30'N to 30*S.
The magnitudes of our zonal wind stress in the Southern Hemisphere agree
better with their values.
226
blank page
227
ZONAL WIND STRESS MON=1
C
Mn
LONGITUDE
Figure E.1
Long terL January
n
of zonal wind stress
ZONAL WIND STRESS MON=4
CC)
M,
LONGITUDE
Figure E.2 Long term April means of zonal wind stress
228
ZONAL WINO STRESSMON=7
2
r-
L'"'' IT'.'E
Figure E.3
Long term July means of zonal wind stress
ZONAL WIND STRESMON=10
20
S10
M
LONGITUDE
Figure E.4
Long term October means of zonal wind stress
229
MERIDIONAL WIND STRESSMON=1
LONGITUDE
Figure E.5 Long term January means of meridional wind stress
MERIDIONAL WIND STRESS MON=4
LONGITUDE
Figure E.6 Long term April means of meridional wind stress
230
MERIDIONRL WINO STRESS MON=7
LONGITUDE
Figure E.7
Long term July means of meridional wind stress
MERIDIONRL WIND STRESS MON=10
LCrI TL'DE
Figure E.8
Long term October means of meridional vind stress
231
WIND STRESS MON=1
r-Di
eowo:o/
\
\\
s
\
r
\\...
5o
30
150E 180 WISO
120
90
60
120
60
90
30
W OE
LONGITUDE
Long term monthly means of wind stress vector for
January
WIND STRESS MON=4
N E
W
E
Figure E.9
-. c,
tE9 NEUTON/NMu.2
ILk
-
7
{
//P
f
/J
I
.I//////
.V
-A
30
60
Figure E.10
90
1H
/
-
//SH
120
120
WiSO
LONGITUDE
150 E 180
90
60
30
W 0E
Long term monthly means of wind stress vector for
April
232
W[ND STRESS MON=7
1o6L
90
io E 180 Wiso
12 0
120
90
e1
-E
0-
60
30 HoE
I
1 ti
16
-o
11% 14I kv
60
-P
ff
V
3
S,"
-/i
\\\
Y
90
60
Figure E.11
60
\50 E 180 His0
120
90
30 H 0
LONGITUDE
Long term montn.Ly means of wind stress vector
for July
90
120
WIND STRESS MON=10
2
c-
LONGITUDE
Figure E.12
Long term monthly means of wind stress vector
for October
233
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239
ACKNOWLEDGEMENT
I would like to express my sincere thanks to my thesis supervisor,
Professor Reginal E. Newell.
This thesis would not have been possible
without his constant guidence and encouragement.
His cheerful
disposition and his enthusiasm in this work have been a constant source
of inspiration throughout the preparation of this thesis.
I thank members of my thesis committee: Professors Ron Prinn, Ed
Lorenz and Erik Mollo-Christiansen for their constructive criticisms.
Special thanks goes to Professor Mollo-Christiansen for his generosity
in given me computer time on his PDP 11/60.
The thesis would have taken
a lot longer without his assistance.
I like to thank my husband, Michael Wojcik, for putting up with me
while this thesis was being done.
His encouragement and support were
always there when I most needed it.
In addition, his painstaking
proofreading of my thesis is greatly appreciated.
Members on the 15th floor deserve special mention in their
supporting roles during the preparation of my thesis.
They have offered
their time and encouragement when I needed it.
Initial process of the data set was done at Group 28 at Lincoln
Laboratory on their DEC VAX/780.
Their support for student research on
the computer made this thesis work possible.
generated graphs in
Kole.
All the non-computer
the thesis were done by the steady hands of Isabelle
This work was done under support from the Department of Energy
contract DE-AC02-76EV12195.
240
BIOGRAPHICAL NOTE
I was born on June 28, 1952 in Taiwan, China.
My family came to
the United States in 1965 when my father was assigned to the United
Nations.
I became a naturalized citizen in 1975.
I graduated from
Barnard College in 1974, majoring in mathematics and geology.
to work at Meteorology Research,
Inc.
for a year as a meteorologist and
came to Massachusetts Institute of Technology in
work in Meteorology.
I went
1976 for my graduate
After an M.S. in meteorology, I took a two-year
leave of absence and worked as a mathematican programmer at Pacific Gas
and Electric Company.
I came back to MIT in 1980 to continue my
studying towards a Ph.D. degree in meteorology.
Wojcik in July, 1980.
I married Michael A.