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 Planetary Scie er, 1983

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 Title : Professor of Meteorology 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 History 11.2 Contents II.3 Processing 11.4 Data Density 11.5 Notation and Definition of Quantities

III. STATISTICAL PROPERTIES OF SEA SURFACE TEMPERATURE ------31

III.1 Annual Mean and Variance 111.2 Monthly Mean and Variance III.3 Frequency Distribution

IV. ENERGY BUDGET ------45

IV.1 Theory IV.2 Sensitivity of Flux Formulations IV.3 Results IV.4 Error Analysis

V. ESTIMATES OF OCEANIC MERIDIONAL ENERGY TRANSPORT ------104

V.1 Theory V.2 Computation and Results V.3 Discussion V.4 Differences in Transport between two Periods VI. NONSEASONAL VARIATIONS OF SST AND ENERGY FLUXES ------135

VI.1 EOF Analysis of SST VI.2 Statistical Properties of ASST:Autoregressive Models VI.3 EOF Analysis of Nonseasonal Heat Fluxes VI.4 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 Figure 4.3 Latent heat flux as a function of qa - qs and wind 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 earth- atmosphere-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 Third nonseasonal SST eigenvector pattern for 1949-1979 (3.44% of total variance explained)

Figure 6.13b 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

Figure A.1 List of possible parameters present in each of the marine 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, for example) is also,

to a large extent, weather dependent. 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 influence of

the ocean on climate is especially important in the area of long range

climate forecasting for a number of reasons. 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 ollolli , IWII -milli,III, IIII MINI M1,

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 research

related to air-sea interactions. One of the most often reported

parameters is sea surface temperature (hereby denoted as SST). The

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 interpretations of how the ocean exerts its influence on climate. Newell and Weare (1976) have found that changes in 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. The conclusions from these studies do not always clarify the picture. 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). Others (Chervin and Schneider (1976),

Kutzbach et al (1977) ), 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 factors that determine how the atmosphere reacts to a change in 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, both horizontally and vertically. A clarification of these 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 limited to specific regions and periods. Hastenrath and Lamb (1978) have published an atlas of oceanic heat budget for the Indian Ocean, the tropical Atlantic and Pacific

Oceans. Bunker (1976) has results for the North Atlantic. Clark (1965) and Wyrtki (1965) have estimates for the North Pacific. 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. Chapter IV deals with the energy budget calculations. 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. The nonseasonal variation of global energy flux is 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 data set.

II.1 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 turn used to drive the FNWC Spectral Wave

Model. The model was to be used to produce a 20-year (1956-1975),

6-hourly set of wave fields. The data base of marine surface observations in which this input data existed is the so-called Tape Data

Family-il (TDF-11) data base. However, the format of TDF-11 is such that it was unsuitable for use in synoptic analysis. The relevant data needed to be extracted and reorganized. Since they were undertaking a major effort in processing the data, it was decided that they would include all parameters of the TDF-l1 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. After the project was started, new TDF-l1 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 1946-1968 TDF -11 Supp. A 1968-1972 TDF -11 Supp. B 1973-1975 TDF -OSV 1946-1970 KUNIA-SPOT 1966-1970 NEDN-SPOT 1970 NEDN-SPOT 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. This initial effort covered the period from 1946 to 1968. Additional data beyond 1968 were issued in 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 file by FNWC and was not

contained in the basic TDF-1l data base supplements. The OSV data also

has been included in this consolidation. 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 a) Indlan Long TermltP49-1474) Avero'ed Io.Ot Ubservations 1or MOntha I Sea.Suraee.TepPrdture .

20 d1 3" 35 40 45 50 55 60 65 70 75 40 15 90 95 109 105 11v 115 120 126 130 135 14) 145 150

3%--- 141 60 9 311111111111111111111111111111111111111111111111111111111 23 17211111111111111111 34)--- 013 152 69 2 11 1 1 1 11 11 11 11 1 1 11 11 11 1 11 1 11 1 1 1 11 15 1151111111111111111 25--- 11111111 5t 3311112111 51 39 2 111111111111111111111111111111 2 2 132 2551111111111111111 20--- 11111111 1 11411111111 3 04) 50 241211111111111111111111111111111 51 145 312 21b1111111111111111 15--- 1111111111111111 R1 0 43 80 22 50 26 1 a 1 10 2 1 390 159 420 106 1531111111111111111 I)--- 111I1111111111 77 117 121 01 37 19 52 ti 25 12 8 6 34 103 390 103 46 1351111111111111111 5--- 111111111111111 6 44 23 37 59 6b IN 106 91 37 58 53 230 67 29 19 321111111111111111 0--- 11111111111121 4 30 23 9 22 19 7 16 19 32 27 10 40 76 19 5 9 201111111111111111 -5--- 11111111111111 21 34 lb 12 12 17 28 11 30 19 6 7 2 17 6 7 2 22 9 7 8 9 -10--- 1111111111111t1 23 29 8 V 1 12 16 37 9 9 10 5 13 13 6 12 16 16 19 14 3 12 -I--- 1111111 1 1 46 14 11 5 13 22 to 7 16 14 15 11 6 15 4 10 24 16 6 10 20 11 -20--- 111111 1 32 55 1 17 24 35 6 4 6 8 14 16 16 3 15 7 28 13 1 0 1 2 21 -2,--- 21212111 1 1v 7 12 45 23 3 6 6 7 6 7 8 14 25 14 33 12111111111111111111111111 -3'--- 1111111 bV 55 J3.1 26 7 9 b 8 7 5 6 6 5 5 18 32 38 1111111111111111111111111 --- , '.i6 t) 28 17 14 13 10 9 9 9 10 10 11 11 12 13 19 51 13 2 3 2 2 1 1 -40--- 21 12 1" 9 9 1o 10 , 9 9 9 7 H N 3 9 9 b 7 9 36 42 45 45 39 26 30

I 25 31 3b 40 45 SU 55 611 65 70 75 00 85 90 95 100 105 110 115 120 125 130 135 140 14 150

b) lndidn Long Term(191'-1979) No. of Year alth Observation(maximum 31 yrs) for Months I sea.urtace..emperature 10 25 30 35 40 .5 50 5b 60 6 70 75 @0 85 90 95 100 105 110 115 120 125 130 135 140 145 150

35--- U 22 261 111111 1 1 11 1111111111111111111111111111111117 1 21 191111111111111111 3o --- 2t 22 23 5 11 1 1 1 11 1 1 '11 11 1 1 1 11 11 1 1 11 1 1 1 11 1 11 74 221111111111111111 25 --- 31111111 26 2811111111 31 31 9 2 11 1 11 1 1 1 1 11 1 11 1 1 7 19 27 271111111111111111 2v --- 111110'1 8 2811111111 7 31 3) 2 1 1 1 1 J 1 1 1 1 1 1 1 1 1 1 1 31 1 27 7 1 1 1 1 1 1 1 1 15--- 1111111113111111 29 0 71 31 31 312it 6 21 29 25 16 4 26 31 31 31 311111111111111111 1'--- 11111111111111 31 31 31 31 32 31 3U 31 30 30 2b 26 29 31 31 31 31 311111111111111111 5--- 11111111111j1111 ) 25 1( lb 79 31 31 31 31 31 31 31 30 31 31 31 31 301111111111111111 I--- 12221111 11'1111 19 31 3" 24 24 25 24 27 26 29 29 31 31 31 31 23 25 221111111111111111 -5--- 111111Q1111111 30 31 25 25 74 24 2o 21 29 29 10 18 15 23 17 25 7 19 19 20 20 21 -2r,--- 111l11111111121 30 J 23 22 20 25 27 27 26 24122 22 24 26 25 25 22 24 73 23 17 lb -I5--- 1111111 1 J 30 27 ?3 0 23 729 22 23 25 26 2b 13 25 24 23 70 17 20 -2b 24 21 J0 7 15 24 23 23 26 IN 22 22 24 26 26 26 26 26 18 24 3 0 4 9 25 -7v--- 221I11111 2111 2111141124112112411271126124 91 29111 31111311 311111111111111111 -75--- -41---III1 13 73 23 25 2o 29 lb IA IV 1 18 19 '19 25 25 2b 24 141111111211111111111111111 -"'-- 11.111111 30 29 2b 2', 23 20 20 20 15 17 19 1 19 24 27 25 511111111111111111111111 -3---- 30 30 Y9 25 72 23 24 2? 23 23 23 24 23 23 22 21 24 26 29 25 16 10 9 14 b 4 29 24 72 21 22 71 23 22 21 21 22 23 20 21 21 22 23 23 24 27 26 25 26 25 25 26

2o ?b o 3: 40 40 50 5 62 65 7 75 20 25 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. These are locations where there were

ocean station vessels. 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 Total .urer of Month witn ObservatIon for sea-surtace-Temperature._

2u 25 3J. 35 4U 44 So S5 6v 65 7U 75 9v 95 9u 95 100 105 110 115 120 125 13n 135 140 145 150 30 33--- 217 266 233 2 21111111111111111111111111111111112361111111111111111 --- **- 30 3'--- 276 T.792 6 1 1 11 1 1 1 1 11 3 1 11 1 11 111 1 1 1 1 1 1 11 1 1 1 1 1 11 2 #9S 277111111111111111t 81 200o 319 3241111111111111111 ,--- 2 t 2 t--- 11111111 33-1 13711111111 369p 349 I1l 4511111111111111111111111111111111 -- 20 --- 11111111 87 34t4118311111 112 3721 359 37 1111 11 111 1 111 1111 372 372 32% 321111111111111111 2. 15 lb--- 1111311111131111 341 32 3%A 372 36o 372 372 53 315 354 305 157 6; 312 366 366 372 3721111111111111111 10 1111)13 1111311 357 36i9 372 372 366 371 372 371 364 350 315 296 344 37v 366 366 372 3721111111111111111 --- 1.------s--- 11.11111111tIl 20 304 36h 322 362 365 372 372 372 372 372 372 364 372 372 369 371 3531111111111111111 5 279 277 2571111111111111111 -- 0 - 111111111l11l11 25 35 363 30V 305 30o 295 34% 345 333 314 372 372 372 365 251 -- -5 111111111111l111 34o 366 316 305 317 313 304 304 347 341 244 23-. 197 34h 280 275 90 224 226 211 230 28w 266 164 225 --- -10 -1 111111111131111 j'1 362 277 24b 250 2q6 324 329 302 310 301 265 293 333 324 304 265 2V2 247 292 214 24 --- -15 -15--- 11111111 27 55 354 240 275 218 254 317 333 261 268 295 332 302 194 Joe 262 267 24w 224 22 32 92 291 --- -2n -2'--- 11111111 61 359 363 143 262 327 319 291 716 203 297 297 303 330 290 30v 275 20v 170 37 -- -25 -2%--- 11111*' 153 6 S61iah 32o 31V 230 225 214 213 237 253 75 294 331 303 280 16111111111111111111111111 --- -30 -4.--- 311111. 370 .165 313 307 265 26b .245 231 270 216 22D 229 254 25. 303 331 234 4b111111111111111111111111 40 49 --- -35 -ls--- 370 370 366 294 778 27% 271- 253 253 255 259 264 255 242 2%I 260 741 311 345 308 133 133 131 133 327 32m 3t4 314 -40 -1 --- 340 17a 258 2+5 245 750 25, 244 251 2Sp 26I 264 254 755 251 251 259 26u 27o 333 335 333

11 1111111111 1111111111111 --- -50 -50--- tais ' a-* 11 1)1'1411 ) 1 1! It11311111 Iii111111 1111111138111111111 111111

2L 25 30 35 40 45 Sl 55 60 65 70 75 80 a5 90 95 100 105 110 115 120 125 130 135 140 145 150

Pacific ocean Lona Term mean (1949-1979)_ - for 40-ob-Oes-for-S3T

135 140 145 150 155 160 165 170 175 130-175-170-165-160-155-150-145-140-135-130-125-120-115-110-105-100 -95 -90--85 -30 -7 -70

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 0865 0 0 0 0 0 0 0 0 152 167 171 176 116 79 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0* 60 0 0 0 0 200 196 204 213 193 159 229 255 277 272 316 344 349 353 360 313 0 0 0 0 0 0 0 0 '0 0 0 0* 55 0 0 163 116 220 238 284 331 362 372 372 371 372 372 372 372 367 369 372 372 0 0 - 0 0- 0 0 0 0 0 0 0 0so50 0 0 211 232 358 372 372 372 372 372 371 372 372 372 372 372 372 372 365 370 370 359 0 0 0 0 0 0 0 0 '0 00 45 249 360 366 372 372 372 372 372 372 372 372 372 372 372 372 372 372 372 370 369 350 357 0 0 0 0 0 0 0 0 0 00 40 367 370 372 372 372 372 372 372 372 372 372 372 372 372 372 372 372 372 372 372 344 353 0 0 0 0 0 0 0 0 0 0* 35 372 372 372 372 372 372 372 372 372 372 372 372 372 372 372 372 372 372 372 372 352 360 372 0 0 0 0 0 0 0 0 0* 30 372 372 372 372 372 372 372 372 372 372 372 372 372 371 244 269 372 372 372 369 3b9 368 365 367 0 0 0 0 0 0 0 00 25 372 372 372 371 370 370 371 371 371 371 372 372 372 372 293 296 371 372 372 371 361 346 335 367 372 0 0 0 0 0 0 00 20 372 372 371 372 371 371 370 370 367 353 364 364 363 366 363 340 351 362 363 371 372 371 371 372 372 372 372 366 0 0 0 0* 15 372 372 372 372 363 356 341 301 357 344 348 265 287 333 325 317 340 335 316 332 296 296 317 342 372 372 372 372 372 0 0 0* 10 311 317 305 321 287 29U 334 334 295 235 240 255 310 332 334 336 321 294 332 317 282 299 266 267 298 320 364 372 352 354 0 05 5 262 231 253 304 275 206 209 197 159 147 233 252 328 328 339 323 223 237 315 226 228 241 240 236 275 338 359 372 300 236 0 00 0 -5' 0 0 0 275 200 155 165 121 123 115 146 15 167 136 134 100 143 126 156 234 268 337 351 354 365 359 369 368 371 0 0 -10* 0 0 0 213 262 175 154 137 125 124 156 189 152 128 134 143 18 199 236 343 355 352 355 355 365 363 353 292 369 0 0 -150 0 0 0 278 289 233 261 230 252 289 312 339 259 284 33V 355 345 350 332 326 343 346 359 363 364 321 193 218 283 366 0 -200 0 0 0 265 310 272 233 231 314 346 344 342 351 355 357 330 291 334 348 334 340 359 361 344 308 214 161 153 167 366 355 -25s 0 0 0 257 196 301 346 350 356 350 341 333 332 334 342 339 353 343 326 361 361 354 323 266 162 140 167 177 192 312 346 -300 V 0 0 265 223 368 361 350 357 352 346 340 349 340 347 352 361 360 360 343 323 309 230 0 0 0 0 0 0 201 350 -350 0 0 0 264 260 363 366 359 357 364 361 360 359 354 355 355 335 329 320 309 261 172 0 0 0 0 0 0 0 0 337 -400 0 0 0 263 255 306 303 297 352 340 321 343 339 331 332 323 320 301 255 177 0 0 0 0 0 0 0 0 0 0 279 e456 0 0 0 235 241 223 229 249 264 260 241 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -50 0 0 0 93 120 179 185 205 183 171 157 0 0 0 0 ' 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

135 140 145 150 155 160 165 170 175 180-175-170-165-160-155S-150-145-140-135-130-125-120-115-110-105-100 -95 -90 -95 -40 -75 -70

AelonttC Tol71 nseber of "onth with Osrrvation for Sea-iurtece-Teperature-in-u*Deg.C -100 -_45 -90 -95 -So -75 -70 -65 -CO -55 -S& -45 -6o -33 -30 -25 -20 -lb -10 -9 0 5 10 15 2u

65--- 1111111111111111111311111111 42'.2611111111113 270 324 325'2t3 305 245 151'26v 35411111111 --- 65 6o--- 12s211111111111111111111111l111 34 32;1 277 320 461 35t. 363 '3ju Jon Joe 357 359 35211111111 --- 60 55--- 1111111111111111111 11iti 467 351 30 j31 370 36. 364 364 372 372 37u 357 335 292 2.s1111 --- 55 5.--- j:1h13,a11:1 113'11'1111 306 385 *I. 372 i7d 314 72 3e. 172 371' 37t' 371 359 29311111111 --- 50 D3--- tu il 11111111l.J31 366AS ilal j17. 371 371 372 472 374 .l 372 J7; 37& 3721111111111111111 --- 45 s'--- 11.,1j1a£13l.t 1111!i 374 jld 37; 374 374 371 J74 372 374 372 372 37 374 371111 J71 372 371 328 --- 40 35--- ItA111111111l i17 372 372 j72 J74 372 37; 32 374 372 36' 3au 293 2d J4u 43.1 372 37211111111 --- 35 "--- i1111 atailli 371 371 374 372 374 372 374 372 372 472 362 362 jeu .e. 32t1l11111111311111111 --- 30 2!,--- 371 372 3-.5 345 31 37 372 372 374 372 314 s74 s74 371 Jb* 343 J7u J54111111111111111111111111 --- 25 24 --- 369 371 2.5 a-a 171 37. j7) J72 372 172 372 37k j7' 315 353 355 3571111111111111111131111111111 --- 20 37, 371Y 15 5--- 1111111 J7 7 374 374 37, 374 372 372 37U 374 36'. 37u 372 371111111111111111111111111111 I"---- lIiluil1l:l 3 j J72 371 ill 37A 372 374 371 J3 sww 312 312 371 3741111111111111111111111111111 --- 10 s--- 11&111111111111111111111111 216 240 257 21e 16w 171.374 372 372 372 29v 235 2181111111111111 --- 5 11111111111111111111111111111l111 170 466 281 174 150 372 370 362 372 371 371 174 23111111111 --- 0 ---- 11111111111111111*111111111111111111111111111111 JoS 371 j47 291 2"3 29b 259 223 351 34611111111 --- -5 -1v--- 11411111111111111211111111111111111111112111 4J 37o 342 319 l4 291 240 259 315 31211131111 ---- 10 -- IIj1J1tl,11at t11A1111113111)i31J111111111ll 371 JI3 317 364 Jw 36' j71 361 36d E66 2621111 ---- 15 -29--- 255 157 243 371 37 Jo321111 --- -20 11211,1LIaisilet1111111111111111111111111111143711 365 371 372 -25--- 111111111 31tai131~11111l11 111111 333 312 isi 24t ISo) 135 165 J21 366 371 261 2el 2471111 ---- 25 -J1--- litllILII~l~i, IA,11113111111111111111 371 31.' 27o 295 2.2 261 2V 29'4 30o 355 25h 26. 262 21t --- -30 -35--- AAlAA1 ahattIl t Il1Il11111111 372 366 256 269 241 :,h3 21b 't",JG. 32t 331 35" 371 372 372 - 35 -4u--- l1l*1&1.*.,,,aa,111 1111111111 140 106 197 17( 176 171 1 S 153 *53l S 2t9l 22e 241 231 4.7 34% --- e40

-5u--- 1 t a t t Isa A111131 I**s t I 2.43 304 31 aeIl 13 .. I &11111111 11111 11 111111111111 11111 1111111 1111111111 --- -50 -s0 -95 -90 -63 -60 -7s -70 -65 -60 -55 -50 -4S -40 -), -3,. -2t -2o -15 -1. -5 0 5 -13 i5 2U

Figure 2.4 Total Nunber of nonths witi obccrvation- -t each grid square for Indian, Pacific and Atlantic oceans Atlantic Long Tem(1949-1979) Averaged *b. ot ubservations tor Montna I sen-Surtace.Teap

evng -6. -j, -. -, - -lu -- j eii -bb -6J -. 4 -. 4u -J V3 -2b -20 -16 -10 -6 U b 19 Ib 20

6I--- l ll 3d b11111111y11111111112b 3i 2b233 1111111 1W11111 1 111 Iu-- 519 6 7b 12 6132162 193 511111111 --- 111111 111111111111111 290 2 2 24 1 75 16 71 402 20 --- 11111f1 11 2 2n 51 14 97 IIU 72 71 72 26v 331111 4b--- 112111111111111111111111 2o57 12k 206 162 1Jd 143 14u 153 lb 347 307 469 18b1111311111111 4u--- 1II1111i&1111j 11 247 451 37d 26a 270 111 23V 154 1Su 117 213 211 213 3071111 9b 193 125 29 3I--e 11111111111L111 42 960 310 23v 6e 204 2U7 207 237 26a 191 1b3 1. 409 25b 222 27 25111111111 3U--- 111111I11111111 974 b0i 207 200 i,1 22a 2uj 2qPI. 1 1 7b hb 194 335 3140111111111111111111 26 5 26--- 49 410 s6 244 6-2 a s2u 161 15o 166 163e 112 51 66 6837 22 2321 196 1 o,3 91111 21--- 37 b4 264 464 123 di 469 192 lot 131 2t75 b3 34a4 20 177 32b4 2961111111111111111111111111 131 31bJ011111 16--- 11111111 41 151 224 149 l2 b 111 N 36 22 23 Ia 29 44 10--- 11111111111 9e 261 ini lub 131 69 49 25 12 Id 21 39 401 - 1*41111111111111111 1111 111 169 7 141111111111 2 37 5 Id 3 41 17 10124 93 44 24 1911111111

-45 3..22.1 j- ... 92 6b 3 11 14 14 16101 66 56111 ----... 1 8b6 53 23 5 4 3 2 15 17 19 62541151 -. q-- 111111*1111111111111l 41 18 .5 o6 11 5 4 4 It 19 32 195 23 -36--- 11 43V16 2 4 1 62 ti 6 62 b 6 9 1* 4v 16) ... -- 111111i1111131111J115I 1 3 4 3 3 2 4 4 3 3 4 6 14 6b--- 1111111 111t11112111b112b11118 2137151111131 -73 2-7 -7' -o6 5 %5 -2- I -36 -3u -25 -20 -15 -10 -6 0 6 to 16 2U

Atlantic Long TernlCl949-1979) No3. of Year wltn lnbservationCmaximum 31 yrs) for A4onths 1 Sea..Surgace.Y

-100 -95 -90 -85 -00 -7i -70 -65 -60 -55 -50 -45 -40 -36' -3U -2b -2U -16 -10 -6 0 6 2o is 20

- 1 1111111111111111111111 21 2 1 23 31 2 .2 2 2v 29 31 311111111 56--- 11111u11111111 11111111111 111 7 3u 29 u 31 31 13 145 12--11- 275 26l 1 1 1 1 --- 111111111111111111111111111 31 31 3u 31 '2o 30 2111111112 46--- 1111111111111111111111 31 31 31 31 31 31 31 31 31 31 3111111111111111 4v .-. 1l1111lp1la*,p1111111 31 SI 31 31 31 J1 31 31 31 31 31 31 31 )U1111 31 i1 3%) 26 13- il1111111111II 31 IL J1 31 31 31 31 31 31 31 31 30 21 23 2v 2d 31 3111111111 -5--- 11111U1111111 31 3 1 11 31 31 3 1 31 31 31 J1 31 31 24 23 21111111111111111 2'-- 31 31 ia i8 31 31 31 31 31 31 31 31 30 31 31 31 31 2111331111111 Jo-- ... I 3* 2.. 2a it 31 31 31 31 31. 31 31 31 3U 303 26 011111I1311111 -11--- 11111 3J 11 113 31 31 31 31 31 31 31 31 31-56111111111111111111111111

6--- 1. 7 24 24 C2 1 30 31 31 31 26 22 l.1111111111 lb124 24 14 lb 31 31 27 30 31 1t 21 1911111111 -b...6--- I L I 1* 1*1I1111111111111&1I11111111 11111111 30 31 31 24 25 24 22 17 30 2951111 27 Jo 3v 24 24 24 21 22 2o 2611111111 - - J 26 !j26 30 31 31 31 30 2 26 261111 3U 23 1 2a 3 31 31 31 31 26 251111 29 26 31 ls 15 13 16 29 31 31 21 22 201111 31 2a 21 26 22 23 21 24 27 3G 22 22 22 16 -32--- 30 30 25 26 23 23 2a 21 27 27 29 21 31 .31 31 -4--1 27 ;7 20 19 20 1b 17 15 17 20 21 17 16 23 24 21

111v -9o -vi. 6 -.gu -)!a -7v -66 -aul -66 -63* -46 -40 -36 -3U -25 -2U -16 U 36 2 10 11 2Q

Figure 2.3 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 8 8 8 8 hihi8 8 0 Opal 8C 0 0 0 0 0a o0 0 40 0 hi 0 0 44. 4 a %. w a -A w-000 I. - UOihi 'DohoO0 - 0 i0 O W O= hi hi hi h. hi h. hi

4hihiOQO QQQQQQCQQChied4M hi 0 0 00 C -0 ' W hi h hi%Pp hi hi hi hi hi0 0 Q0 3 *0 n 40 s0LQ wo s 4 hiohii-'C i0 .iihi .0 0 00 4ChiO* Mw w. h% hi hi h. hi h hi h h U C - h U.0 hi ^

00 w*a A was SSS..a. Sc 2 * M~ ~ %- A- en A hi90 .. .. dh 4e i C 4 C hi C .d -P hi hi0h0

* 0 w- 40 h 0* hM 0 0 2 0

, 0 hiaU meC00ahi - 0sa4C O 4 000 000 00 000 alCDC"o00 00 Q0 & -d

4 S ...h.. . m 0 - 0 as m 0000000000000000000000CMtr . e0Me-C * C 40 4.00 000.0 CO. aawwal-a QQ00 0@ hihihihihihis .O4.e@ i.hihihi "*hihihhi as hi -91 00 m 44040aoem-A*0* Mte U.0ee .049 . 4.0OOM iOO 0

M i nh ihiQ QhQ QQhi.h. hihihiQQ hiOiQQh hihiae00000000 hiheih-ihihihihi Q 0s 8 tetatr4.teinMhi O *~ 0* 00440-sin sA M 0 = m a C m40 0 O* ",A260 1him0 0 hihCMomo 4 = U WC CiWm hihihPQhihihiQO hihih"* hi**h*hi***i*ih*i"*ihihi 0.0.M.*0 .* M 0 0do ^*4 4 :

0040es sp4 Masse4e n"**M 0.0 0 0 tf0 000400 000000 0000000=C00 CCOOO hihihihihihio hihihMhi-ihihih*o 0. 0 00 0hi..*db4.QQ O4m0.QJ0M t twe 40 hihihihiQhihiMoohihihMihi*hihihihi*h*ih*ihihi S

0g , a

.OmO~hiO~h0 M"O00000C 000 oem e.i o44 hi hi 00 hi Uhi -. Jt ma hi 004.80 h 0 hi h.i hi hi hi hi h* hi*me .0 w hi hi h .i hi hi h hi 0 C 000004. J=0 e 0M 0 Mse4.s0 m .0494.0ms r4000 b. a o eb asw hi hi hi hi hi hi hi - hi hi hi hi hi hi h"i hi hi *

4.r40 00 00t 000 hm hi hi4-Z hit hih 0 0h 0 i- 000 00 h . 004 ei Mmae10040h 0.0 tr0 o 0 0 0 h0 0w 0 v4. . 0 *9 5 0 hi ,.i hi hi hi hi hi hia hi hi hi hi hi* '"* * 2 0 0s e 0 0UhiC4.4n . w a @ t eeOC . 80044400 s m & M 0 0=0t 0000000t0 tp .sta a %D0 C ooo oooO O a"004i 0 en en ww~aC0e-t 9 'a C hihi hihi&* hi hC** * hi * * * * @O himmo-A.1hiCmA mhiC40 OO 0 0 0 0 0 0 0 0000hi ao O O 4*4s 000sese et nste t 0&* 00000.4000 .00, 0 hi hi hi hi hi hi hi hi hi hi ahi p es 0 e

OOOa "hE% m~Ctoo MMiwi e8*Mh 40C00 00 MOO00 0 0 00t000000

hi&eshi thihis i -. hi hi h .i ** * ** O 0 0 0 a 0 ohi 0 0 000 00 000apa o y04A00000 s tr ot4004.0ta 00 QQOOOC 00Mhi QC MM040 MQ00000 000009Chi0Ahih001 000C000

-. 0 -0M 0000w hi W0W00 hi 000000 S

0 CCOPOnOO-C 0 hi 004000000000000**C * * CO se.e en oohihihihihi**aB .0tr . trta eetr s 0 OO@OOea e hiCeOn a QiO& * *@0*0*0*Q *000Q

Ohi4teh., hieMM* MMtsMte . @0040,.1=00 Qme 000000l0C0*0e 00** **Q00 0Q0 a QOQ~whi hiOhiOQQ hi hi hie0hA h inss . n 00COm 0=4000000000000N00000 Q O 4 QQQ00C0.0Qm00000 00000000 0 hiW~ **e t i iCC4.0 trteMM0. M0Ohse 0 0 0 0 0 0 4p9 hi hi h 00 00 0 0oo0 0 Q OQei * 0O0000O 000' 0000"*00OQQQ 000h 00 00 00 0,000 00 0 QQCQQ&,8ee000*00800000C hihiCMiQQCQ 00000000000QQ S 00000O010h 00= 00ihihhi 000000o000h C0 0 00000000000000 -8 Q S .91 0 areas right off coastal regions, data is generally sparse. This is especially true in the central tropical Pacific. There are also voids 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. Figure 2.5 presents the number of observations averaged over all the available squares for each of the three oceans as a function of time. Note there is a large jump in data density in 1964 and onward. Presumably this is from the infusion of data from various countries under a WMO agreement to collect and archive marine reports. The drop of number of observations in 1970 is puzzling. (Sources from British Meteorological Office in Bracknell,

NO. OF OBSERVATIONS FOR THREE OCEANS

I 0 4 5 S Isf

Z0 .11.6 a Pacifirc i il%i

7.2,

40.-1

1949 1951 1953 1955 1957 1959 151 1963 155 1967 199 1971 1973 191 1977 1979 NO. O OSSERVATIONS/lITH FOR TI'EE OCEANS

Figure 2.5 Average number of observations per month NOWN11111, , II II I ININI II I "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. However, this was not always the case. 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 M xi Kijk NeM k=1 j=1 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 j is defined as:

1 N Xij = - Xijk N k=1

The standard deviation for the annual mean is

1 N M si = [ -. (xj i)2 ]1/2 N-M k=1 j=1 and the same quantity for the monthly mean is

1 N sig = [ - (xijk~Tij) 2 ]1/2 N k=1

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 . A plot of the annual mean SST is presented in Figure 3.4. 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, this analysis does show that the temperature gradient in the

Gulf Stream is much higher than its counterpart in the Pacific. One can see the influence of the Gulf Stream all the way to 60'N. Upwelling is another important feature. 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

2 r-

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 Nean (1949-1979) Using New Filled Data for Atlantic-BST -100 -95 -90 095 -80 -75 -70 -65 -60 -55 -50 -45 -40 -35 -30 -25 -20 -15 -10 .5 0 S 10 15 20 65-. 0 0 0 0 0 0 0 0 0 0 0 0 0 0 61 41 0 0 59 72 31 6 0 0 60---. 0 0 0 0 . 0 0 0 0 0 21 21 47 63 74 13 5 92 88 9 94 93 90 0 0 55--- 0 0 0 0 0 0 0 0 0 47 52 63 75 37 99 10 109 111 108 98 97 99 0 0 50--- 0 0 0 0 0 0 0 0 0 36 72 96 95 108 118 125 128 128 122 121 113 105 0 0 45--- 0 0 0 0 0 0 60 67 66 56 66 128 145 144 143 143 144 141 139 131 0 0 0 0 40--- 0 0 0 0 0 123 110 128 147 139 146 175 177 175 171 166 160 160 154 0 179 177 117 165 35--- 0 0 0 0 174 100 213 218 217 213 210 205 201 196 191 188 136 131 178 136 191 191 0 0 30--- 0 0 0 0 250 237 232 231 229 227 225 223 220 216 212 207 200 195 193 0 0 0 0 0 25-- 248 251 262 261 263 253 252 249 249 246 243 239 235 230 226 219 207 200 0 0 0 0 0 0 20--- 257 264 273 271 272 271 269 265 261 256 254 250 245 241 235 227 202 0 0 0 0 0 0 0 15--- 0 0 230 279 279 278 275 273 270 266 262 257 251 246 243 237 231 0 0 0 0 0 0 0 10--- 0 0 0 279 277 272 275 27627 274 269 264 260 258 257 255 254 0 0 0 0 0 - 0 0 5--- 0 0 0 0 0 0 0 0 277 276 276 275 270 269 270 270 273 277 0 0 0 0 0 0 0--- 0 0 0 0 0 0 0 0 0 0 276 275 273 271 272 270 267 272 271 272 275 275 0 0 -5--- 0 0 0 0 0 0 0 0 0 0 0 0 274 271 266 264 260 256 254 255 260 259 0 0 -10--- 0 0 0 0 0 0 0 0 0 0 0 0 272 272 266 264 260 254 251 246 246 254 0 0 -15--- 0 0 0 0 0 0 0 0 0 0 0 0 239 269 262 257 249 243 235 233 224 223 233 0 -20--- 0 0 0 0 0 0 0 0 0 0 0 0 261 262 254 245 238 232 224 217 210 203 182 0 -25--- 0 0 0 0 0 0 0 0 0 0 231 237 252 244 241 236 230 227 221 214 205 195 172 0 -30--- 0 0 0 0 0 0 0 0 0 0 222 233 234 229 225 223 219 212 209 207 199 193 178 0 -35--- 0 0 0 0 0 0 0 0 0 136 209 195 0 0 0 193 190 190 191 137 134 163 181 172 .40--- 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ' 0 0 0 0 0 0 12 -45-- 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -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 -100 -95 -90 -85 -80 -75 -70 -65 -60 -55 -50 -45 -40 -35 -30 -25 -20 -15 -10 -5 0 5 10 15 20 Atlantic Ocean Long Term Standard Deviation (1949-1979) Using New Filled Data for Atlantic.SST -100 -95 -90 -85 -00 -75 -70 -65 -60 -55 .50 -45 -40 -35 -30 -25 -20 -16 -10 -5 0 5 10 15 20 5-- 11111111111111111111111111111111111111111111111111111111 1 11111111 20 20 19 2111111111 60--- 111111111111111111111111111111111111 18 17 22 19 17 15 17 16 13 lb 17 25 2411111111 55-- 111111111111111111111111111111111111 22 22 21 19 18 13 13 13 13 19 24 32 4111111111 50--- 111111111111111111111111111111111111 28 26 I 21 19 16 13 19 20 23 30 38 4711111111 45--- 1111111111111111111111 43 55 53 46 38 28 21 20 20 20 21 22 24 261111111111111111 40--- 11111S11111111111111 57 47 50 45 45 37 20 27 27 23 23 25 23 211111 40 37 39 42 35--- 1111111111111111 61 47 36 31 30 30 30 29 28 27 23 23 24 22 21 32 33 3311111111 30--- 1111111111111111 26 28 30 30 30 29 23 27 26 2b 23 22 21 20 221111111111111111111 25--- 35 34 24 25 20 23 23 24 22 22 21 20 20 20 20 19 13 20--- 26 21 15 19 15 14 15 14 14 14 14 13 14 14 17 17 15--- 11111111 11 10 10 10 11 10 10 10 10 11 12 14 13 19 10--- 111111111111-15-~~2 1 9 10 9 9 8 9 10 12 12 13 14 1726 27111111111111111111111111111125 3 2ti 21711 40 34 713911 5-. 7 6 15 9 S 7 9 10 1117 251 211111111 0--- 6 4 5 16 10 13 13 15 1 32 1411111111 -5--.. 7 6 10 13 15 20 16 19 20 2211111111 -10-- 11 i 9 10 12 14 14 17 18 20 2411111111 -20-26 13 15 16 15 14 15 17 16 20 21 241111 -40----25-246 11111111111111111111111111111111111111111111111111 11 90111111111111111111011111111111111111110 1t 10 19 191111 2 -30-W 25 11 22 23 23 24 24 24 23 21 19 16 111111 -S5----35--- 111111111111111111111111111111111111 111111111111111111111111111111111111111111111l111 35 27 25111111111111 1111111111111111111111111 2 25 24 25 22 21 19 1 1

100 -95 -90 -5 -00 -75 -70 -65 -60 -55 -0 -45 -40 -35 -30 -25 -20 -15 -10 -5 0 S 10 15 20

Figure 3.1 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. The upwelling region off the coast of

North Africa is also of note. Standard deviations as high as 3.10C are observed. In the Indian Ocean, the Adrian Sea is where the largest variance (4.1 0C) occurs. Pacific ocean bona Term Mean(1949-1979) for PacIfic-53T

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 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 65. 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* 60 0 0 0 0 0 0 0 0 0 0 46 47 49 54 68 70 76 14 91 93 0 0 0 0 0 0 0 0 0 0 0 0* 55 0 0 0 0 0 44 52 55 57 57 53 60 62 66 68 72 73 3 93 101 0 0 0 0 0 0 0 0 0 0 0 0* 50 0 0 0 62 53 58 66 65 66 69 72 75 73 92 95 99 94 98 104 111 115 114 0 0 0 0 0 0 0 0 0 0* 45 109 128 116 96 110 109 105 107 115 120 122 123 123 124 126 127 130 133 139 13V 131 119 0 0 0 0 0 0 0 0 0 0* 40 171 169 199 161 191 179 178 177 176 174 173 171 171 170 171 172 173 172 168 163 151 133 0 0 0 0 0 0 0 0 0 0* 35 225 220 219 21b 214 212 211 210 209 208 206 205 204 204 204 204 202 199 192 182 171 157 169 0 0 0 0 0 0 0 0 0 30 242 242 244 245 244 244 244 243 241 240 236 23b 235 233 231 231 227 216 206 199 192 18e 182 199 0 0 0 0 0 0 0 0* 25 263 267 269 270 271 270 268 266 263 261 256 256 255 253 248 241 237 232 227 221 214 211 213 225 257 0 0 0 0 0 0 0* 20 200 292 261 291 281 290 277 275 272 270 270 267 264 261 257 251 249 245 241 236 236 244 254 265 272 293 287 275 0 0 0 00 15 286 296 284 284 264 284 264 261 260 277 274 272 269 269 266 264 263 261 261 261 263 267 272 277 282 286 263 294 276 0 0 0* 10 286 297 267 296 268 28 289 297 296 0 0 0 280 278 277 276 275 274 273 272 272 271 273 274 276 277 278 274 276 279 0 0* 5 287 263 209 209 290 0 0 0 0 0 0 0 278 277 273 273 0 0 0 0 0 261 257 255 253 250 255 261 264 265 0 0* 0 .5* 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 254 251 246 241 238 236 236 237 234 0 0 -10* 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 263 259 255 252 248 243 242 241 236 202 0 0 -15* 0 0 0 0 0 0 0 281 285 297 296 287 285 284 282 290 276 273 269 264 259 255 248 242 239 234 0 0 216 190 0 -20* 0 0 0 263 265 265 269 269 270 274 276 273 274 275 274 273 270 266 265 262 256 249 244 233 232 0 0 0 0 191 169 -25* 0 0 0 247 246 243 242 247 247 249 251 252 250 253 249 249 255 255 250 247 240 244 239 234 0 0 0 0 0 191 167 -30* 0 0 0 234 230 226 223 220 221 222 219 222 220 221 221 216 221 225 232 229 22? 228 0 0 0 0 0 0 0 0'167 -35* 0 0 0 211 211 201 192 169 196 190 191 109 196 198 191 194 195 191 191 193 200 0 0 0 0 0 0 0 0 0 0 -40* 0 0 0 181 179 174 171 168 177 173 166 164 163 160 157 155 159 162 162 0 0 0 0 0 0 0 0 0 0 0 0 -45* 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 -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

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 1111111111111111111111111128 28 27 30Q 29 27 31 32 30 2111111111111111111111111055 11111111111111111111 37 34 29 25 23 22 22 25 27 29 29 29 29 29 29111111111111111111111111111111111111111111111111*50 111111111111 44 36 39 37 33 30 26 27 26 26 27 26 29 29 29 29 29 27 2311111111111111111111111111111111111111116 45 66 62 55 52 49 43 39 37 35 33 33 32 33 33 33 33 32 31 30 26 24 151111111111111111111111111111111111111119 40 53 53 44 42 40 39 36 36 35 35 35 35 35 35 34 33 30 28 25 22 20 161111111111111111111111111111111111111111* 35 36 36 36 36 36 36 35 35 34 34 33 33 32 31 29 27 25 21 20 19 16 17 191111111111111111111111111111'11111111* 30 30 31 29 30 31 30 29 26 27 25 25 24 23 22 20 17 15 15 15 15 14 15 20 2711111111111111111111111111111111* 25 22 21 19 17 11 19 17 17 17 16 16 15 14 13 12 12 11 11 11 13 14 18 21 30 251111111111111111111111111111* 20 12 12 11 11 11 11 12 12 12 13 12 12 11 11 11 11 11 12 13 14 14 15 14 13 19 12 10 161111111111111111* 15 I 1 8 0 . 10 10 11 11 10 11 12 11 9 11 11 12 13 13 13 14 12 11 9 7 7 12 10 11111111111111* 10 a 9 3 7 7 9 9 11 9111111111111 a 9 9 10 11 9 10 9 10 11 9 9 10 is 11 11 10 711111111* 5 9 9 1 7 711111111111111111I11111111111 11 11 13 1211111111111111111111 1 6 1 9 i 5 1 0 7 11 1 1 -5*1 111111 1111 11711191111112311 111 1114111 1211111 111 1711111111111 -10* 111 111111 1151111111111111211111 1111112111 111 111111111 111111 -1591111111111111111111111111111 10 9 10 9 9 9 9 9 10 10 10 9 10 10 10 It 11 12 1411111111 29 231111 -20*111111111111 16 16 16 14 14 14 12 12 .11 11 11 11 11 12 11 11 12 12 12 11 12 121111111111111111 25 24 -25*111111111111 20 19 10 17 17 17 17 17 16 17 16 17 15 15 15 16 14 14 14 15 1511111111111111111111 23 24 -300111111111111 20 19 19 19 20 20 20 20 20 20 20 20 21 20 20 19 19 19 21 311111111111 20 22 22 21 21 21 24 23 22 21 22 22 22 22 24 24 24 1 11111111111 -40*1111111111 22 23 22 22 23 22 24 23 23 23 22 22 22 22 23 24 24 21111111111111111111111111111111111111111

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 -95 -90 -65 me0 -75 -70

Figure 3.2 Pacific Ocean SST: 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. It

expands from January to April and moves northward in July. The

location changes relatively little from summer to fall. 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. By July, its value is

about twice that of January. The gradient gradually starts decreasing

in the fall. 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, the scenario changes

somewhat from the annual standard deviations. 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 Indian Ocean Long Term Mean (1949-1979) Using mew Filled Data for Indian.SST

20 25 30 35 40 45 50 55 60 65 70 75 to I5 90 95 100 105 110 115 120 125 130 135 140 145 150

35--- 197 194 211 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 30--- 203 208 215 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 179 200 0 0 0 0 25--- 0 0 247 260 0 0 266 275 0 0 0 0 0 0 0 0 0 0 0 0 234 244 0 0 0 0 20--- 0 0 0 278 0 0 0 267 267 267 0 0 0 0 0 0 0 0 252 250 264 260 0 0 0 0 15--- 0 0 0 0 291 0 266 260 270 276 279 0 263 281 280 0 0 265 269 276 276 277 0 0 0 0 10--- 0 0 0 0 264 279 269 269 276 282 284 282 294 284 284 284 289 273 279 282 284 284 0 0 0 0 5--- 0 0 0 0 0 267 269 275 202 284 285 280 232 284 285 288 286 279 201 285 2@4 284 0 0 0 0 0--- 0 0 0 0 269 270 273 2R1 285 286 285 284 284 284 285 291 289 284 286 286 287 285 0 0 0 0 -5--- 0 0 0 0 270 273 276 281 203 2R4 2R3 28J 283 284 0 0 0 286 285 288 0 0 0 0 0 0 -10--- 0 0 0 0 272 273 274 274 276 278 275 278 278 281 280 279 281 282 284 283 283 281 279 277 0 0 -15--- 0 0 0 0 273 270 267 266 266 266 270 267 268 269 272 271 271 272 277 201 283 0 0 277 0 0 -20--- 0 0 0 267 270 0 261 257 258 259 0 256 252 254 254 254 260 259 263 0 0 0 '0 0 0 0 -25--- 0 0 0 259 258 250 251 252 0 0 0 0 0 0 229 231 226 233 241 0 0 0 0 0 0 0 -30--- 0 0 242 241 239 241 231 225 0 0 0 0 0 0 0 206 207 209 217 0 0 0 0 0 0 0 -35--- 185 210 227 220 210 205 201 0 0 0 0 0 0 0 0 0 179 184 196 197 0 0 0 0 0 0 -40--- 191 201 195 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 166 179 165 158 156 154 154 150 -45--- 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 -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

'20 25 30 35 40 45 50 55 60 65 70 75 80 35 90 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 60 65 70 75 80 85 90 95 100 105 110 115 120 125 130 135 140 145 150

35--- 3 3 2 611111111 41 1 111111111111111111111111111111111111111111111111 1111111111111111 30--- 37 35 1 11 111111111111211711 11111111111111111111111111111111 31 30111 441111111111111111 10--- 1111111111 23 2511111111 41 12 921111111111111111 20--- 1111111111111231111111 11 3 10 31 9 9 1111111111111111 15--- 121111111111111 14 17b 91 1 9 7 81111111111111111 IQ--- 111111111111111 20 18 13 9 98 8 8 11 1 9 10 11111 91111111111111111 5--- 111111111111111116 17 14 1 10 1 8 10 8 8 1 10 10 9 101111411111111 0--- 111111111111111 14 13 13 11 1 1 16 1 1 7 1 13 1019171 1111111111111111 -5--- 1111111131 91 19 20 2213111111111111 1 1 1 111111111111111111111111 ---- 1 16 1111111111111111116111 16 17 12 18 14 141411111111111111 -40--- 20120 11111 1Is1 7 111 17I 11 41111111111111111111111111111111111111111116117 117 171 2 -40--- 1111111111111111111111111 2 711 91111111111111111111111111111111 1111151111111111111111111111111111

20 26 30 35 40 45 50 55 60 6 5 70 72 15 90 95 100 105 110 115 120 125 130 135 140 145 150

Figure 3.3 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% is observed in the Kuro-Shio in

winter. ) The variances 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

r-

--c:)4

LONGITUDE Figure 3.7 Long term monthly mean of SST for July MONTHLY MEAN SST MON=10

60 ~DEGC)

40 14

16 30 2 - 26 2

2-~10-

28 I NN~

22

168

20 /s

30 ~ -N22 2220r -0 -20

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 20 25 30 3b 40 4 50 55 60 65 70 7S go gS 90 95 100 105 110 115 120 125 130 135 140 145 150

35--- 7 1 111111111111111111111111111111111111111111111 1111111111111111111111 1111111111111111 30- 7 9 6111111111111111111111111111111111124 91111111111111111 25- 11111111 10 811111111 14 11 1 1 1 11 1 1 1 1 1 1 1 11 1 1 1 1 1 11 11 11 71111111111111111 20--- 111111111111 v111111111 6 6 1011111111111111111111111111111111 13 12 6 91111111111111111 15- 1111111111111111 51111 5 6 6 6 61111 9 7 811111111 16 I 6 6 71111111111111111 10--- 1111111111111111 5 5 5 a. 6 4 4 7 6 I 9 11 8 7 6 6 41111111111111111 5-- 11111111111111111111 6 5 5 6 6 4 4 4 4 4 5 10 8 6 5 6 71111111111111111 0--- 1111111111111111 5 6 7 7 4 I 5 4 6 5 6 5 6 6 6 I 5 611111111111111 -5-- 1111111111111111 8 9 6 7 6 5 4 7 5 7111111111111 7 5 5111111111111111111111111 -10--- 1111111111111111 7 7 6 7 7 9 9 7 8 8 0 1 6 6 7 7 7 6 7 711111111 -15--- 1111111111111111 6 10 8 a a 8 4 10 7 0 6 9 13 7 11 11 911111111 611111111 -20--- 111111111111 7 71111 11 7 5 s1111 9 9 6 8 5 9 7 111111111111111111111111111111 -25--- 111111111111 6 12 11 9 s111111111111111111111111 7 a a 10 151111111111111111111111111111 -30--- 11111111 6 7 7 7 10 111111111111111111111111111111 7 8 S 91111111111111111111111111111 -35--- 9 9 6 13 10 10 13111111111111111111111111111111111111 12 12 9 9111111111111111111111111 -40--- It 12 13111111111111111111111111111111111111111111111111111111111111 12 S 7 a 9 11 10 15 -45--- 11 1 1 1 1 1 1 1 1 1 1 1 11 1 1 1 1 1 1 1 1 1 1 1 1 11 1 1 1 1 1 1 1 1 1 1 1 11 1 1 1 1 1 1 1 1 1 1 1 1 .50 --- I

20 25 30 35 40 45 50 55 60 65 70 75 80 35 90 95 100 105 110 115 120 125 130 135 140 145 150

Indian 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 95 100 105 110 115 120 125 130 135 140 145 150

35--- 5 S 1011111111111111111111111111111111111111111111111111111111111111111111111111111111111111111 30--- 6 6 711111111111111111111111111111111111111111111111111111111111111111111 19 151111111111111111 75--- 11111111 10 911111111 6 9111111111111111111111111111111111111111111111111 6 61111111111111111 20--- 111111111111 6111111111111 3 6 511111111111111111111111111111111 6 6 S 51111111111111111 Is--- 1111111111111111 61111 S 8 7 4 41111 8 7 611111111 8 4 5 6 51111111111111111 10--- . 1111111111111111 13 8 6 5 5 5 5 6 4 4 5 10 7 5 4 4 8 51111111111111111 5-- 11111111111111111111 15 6 7 4 4 4 5 3 3 3 3 6 3 4 5 7 41111111111111111 0--- 1111111111111111 12 - 8 6 I 5 6 6 5 6 5 7 4 3 3 6 5 5 111111111111111111 -5--- 111111111111111 6 7 10 I 7 7 6 7 6 5111111111111 6 7 7111111111111111111111111 -10--- 1111111111111111 7 6 6 6 6 8 7 5 8 5 8 5 7 10 10 5 7 5 6 911111111 -15-- 111111111111111 5 9 8 12 7 5 6 7 7 11 9 9 12 4 10 10 711111111 711111111 -20--- 111111111111 6 61111 S 7 6 51111 8 a 9 16 1 8 7 1511111111111111111111111111 -25--- 111111111111 6 9 20 9 111I11111111111111111111 3 3 9 9 71111111111111111111111111111 -30--- 11111111 7 10 9 25 15 71111111111111111111111111111 S 11 7 *111111111111111111111111111 -35--- 8 11 10 22 9 10 13111111111111111111111111111111111111 12 10 7 10111111111111111111111111 -40--- 10 10 11111111111111111111111111111111111111111111111111111111111111 15 1 10 11 10 12 12 12

20 25 30 35 40 45 50 55 60 65 70 75 30 IS 90 95 100 105 110 115 120 12A 130 135 140 145 150

Figure 3.9 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. If we have a normally distributed variable, ',I~f puu

Xiefunuu JOJ UO1IP1AUP pJVpuVS I(TIUOW wUOl 2UO'1 :ISS Uva3J DTJT~ud OTtC aIl2rd

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tili111i111111l1ittilitittit111!ttii111t11110ol It 0 6 11 If El C 1 1 I L 6 6 IT 6 Il11111111il09- til111111111l1l1111111111111tll!l El El of St 8 L N 6 TV 11 9 9 S 01 IT 6 L tIITIMIT1 ist- ET 11I111I1111111111111Il1ll ' 6 9 L 6 L 01 S S 9 01 6 8 6 C C a S lllII11IIl*0E- II S TttittlttilitIItIIT6 3 9 L 9 3 1 6 L 01 6 6 01 6 6 L 9 9 9 L S 1111T11111CE*St- Sf II It llllllllllllll 9 I L 6 S 6 9 1 R 6 9 9 L 1 9 L 6 9 L Fl 9 111litiillU*0E- t11191 LI 11111TIL 9 C L S 01 01 L 9 L 9 L L 9 5 9 4 It 9 I1i1titlif1iti11111111lasI- 11l111161 LI A L 9 0 L L 9 9 111111111111111111111111111111111111111111111111111111:;111101-

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Aft-3TIl30d 101 1 u943UOW J0T *30 93111.1 X&M bulIo (6.6.661) uOIIST~aeG P30pully AT44YOW U*83o DTI139d 41

Atlantic Ocean Monthly Standard Deviation (1949-1979) Using New Filled Data for Months i for Atlantic.$&T

*100 -95 -90 -85 -10 o75 -70 -65 -60 -55 -50 -45 -40 -35 -30 -25 e20 -15 -10 -5 0 5 10 15 20 65--. 7 1511111111 1 10 711111111 80--. 111111111111111111111111111111111111 9 10 15 16 6 10 7 7 12 11 1 5 811111111 55--- 111111111111111111111111111111111111 9 11 8 9 10 10 S 7 5 7 7 9 1011111111 SO0--- 111111111111111111111111111111111111 10 14 13 9 9 10 7 6 5 7 9 13 1911111111 45--. 111111111111111111111111 20 17 9 7 12 12 7 7 G 4 4 3 3 101111111111111111 40--- 11111111111111111111 14 16 19 17 19 13 S 1 7 5 4 4 5 51111 6 7 6 13 35--- 1111111111111111 18 16 12 6 6 5 6 5 5 5 5 5 S 5 S 5 3 411111111 30--- 1111111111111111 11 6 6 6 5 6 6 4 5 5 5 4 3 4 811111111111111111111 25--- 15 10 1 7 6 5 5 5 4 5 5 5 5 6 6 9 5 8111111111111111111111111 20--- 12 7 4 6 5 5 4 5 5 6 6 S 5 6 12 10 15--- 11111111 7 3 4 4 5 5 4 4 6 4 6 6 8 7 10 111111111111 5 5 5 3 3 3 4 6 8 6 6 7 1 --- 11111111111111111111111111111111 6 5 4 5 5 2 5 8 9 0--- 1111111111111111111111111111111111111111 5 3 4 5 5 4 10 5 5 8 711111111 05- 111111111111111111111111111111111111111111111111 4 5 8 7 6 8 5 8 10 911111111 -10--- 111111111111111111111111111111111111111111111111 7 5 5 8 8 5 5 8 11 911111111 15-- 111111111111111111111111111111111111111111111111 3 7 S 8 8 5 8 7 6 &1 111111 -20--- 111111111111111111111111111111111111111111111111 1 10 68 10 7 7 5 8 7 141111 -25-0- 1111111111111111111111111111111111111111 12 11 9 14 9 11 17 12 9 9 7 4 81111 -30--- 1111111111111111111111111111111111111111 8 U 12 13 17 10 13 10 11 12 9 7 81111 -35--- 1 17 12 14111111111111 14 14 13 10 11 12 U 7 -40---7 71 2 11 111 11111111

-100 -95 -90 -35 -30 -75 -70 -85 -80 -5S -50 -45 -40 -35 -30 -25 -20 -15 -10 -5 0 5 10 15 20

Atlantic Ocean Monthly Standard Deviation (1949-1979) Using New filled Data lot Months 7 tor £tlantlc-6ST

-100 -95 -90 -35 -30 -75 .70 -65 *60 -55 -50 -45 .40 -35 -30 -25 -20 -15 -10 a$ 0 5 10 15 20

5-. 11 12 1611111111 9 107 911111111 80--.. 10 17 20 t 9 107 1 9 7 9 17 911111111 55-- 1..1511 94311111111111111117 9 9 7 9 12 1 S.00 11 9 10 9 7 9 9 9 7 9 7 10 1211111111 45-- 11 5 12 i 11 13 15 11 9 7 8 8 6 8 71111111111111111 40-1 11 17 20 19 19 15 14 12 9 7 6 81111 13 12 10 13 35- 1 7 5 5 5 7 7 7 8 8 17 5 1 7 1 911111111 30--- 111 4 5 7 5 8 5 6 8 5 8 7 8 8 11111111111111111111 25- 4 4 3 4 3 3 4 5 5 5 8 6 8 1 10 9 9 7111111111111111111111111 20- 9 7 4 3 5 4 3 3 4 4 11 1011111111 15-. 11111111 7 4 4 4 4 4 3 b 8 7 5 7 8 5 111111111111111 10 111111111111 4 4 5 4 3 4 4 5 6 511111111 5-- 111111111111111111 3 4 5 6 13 5 4 5 4 SIIIIIII1I1II 0-- 16 5 4 6 4 5 9 106 10 10 9 10 1011111111 5--- 115 5 7 7 7 11 7 8 11 1111111111 -10-- 111111111111111111111111 7 4 6 1 a 4 5 4 I111111 -15 --- 15 6 10 7 8 8 5 6 7 10 121111 -20--- 5 10 4 15 13 0 7 8 9 131111 -25--- 111111111111111111111111111111111111 1 1111 4 1710 9 19 17 9 8 7 4 S 91111 -30--- 1111111111111111111111111111111111111111101 1 11 12 13 10 13 13 12 8 5 111 1 -35--- 111111111111111111111111111111111111 13 12111111111111 11 12 11 9 3 7 7 8 8 -40--- 1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111

-100 -95 -90 -35 -80 -75 -70 -65 -60 -55 -50 -45 -40 -35 -30 -25 -20 -15 -10 -5 0 S 10 15 20

Figure 3.11 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. For example, anomalies more than two times its standard deviation should not occur more than 4.5% of the time and anomalies three times its standard deviation should not occur more than .2% of the time if a given variable is normally distributed. We have calculated histograms for every grid point of the ocean and applied the normality test (p.121 Bendat and Piersol) to check whether SST's are normally distributed. The result is overwhelmingly negative. 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 -lotitude b) Subtropics 90 50N, 175W 30N, 150w

80-

70-

60- 50-

40-

30- Z20- I- >10

o 2 4 6 8 10 12 14 16 18 20 22 24 26 28 90- c) Tropics d) Eastern tropics - 5N/170W IOS, 95W I 80-

:70 -

60-

50-

40-

30-

20-

10 -

262830824 32 20 22 24 26 28 30 32

Figure 3.12 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. It is clearly a bimodal distribution. 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. This led us to conclude that the bimodal structure is 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. C-3 PACIFIC (b) E INDIAN EEM ATLANTIC

0 x0 a - x

2.

0 5 10 15 20 25 30 0 5 s0 15 20. . 25 SST IN DEGREES C AIR TEMPERATURE IN DEGREES C

Figure 3.13 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). CHAPTER IV. ENERGY BUDGET

1V.1l Theory

IV.la Energy Balance of the Surface Layer

The equation governing the change of sea surface temperature can be derived from the second law of thermodynamics (conservation of enthalpy) as:

DT = q (4.1) 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:

3T I -- V VT + q (4.2) at

Here aT/at is the local time derivative operator. 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, the integral form of the above equation can be written as

t 0 aT t 0 t 0 f f (pC ...) dz dt f f (Qv + Q) dz dt + f f Qd dt 0 -D at 0 -D 0 -D (4.3) where p = water density

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. However, we do have data available to perform 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 = K -- - (4.7) a z

Here Kx 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 01111bJ11161111M I 11111,111 , AM1 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 q = (4.8) 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 is missing, none of the heat fluxes are calculated. 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 in watt/m2 *T-4

C = cloud cover in tenths 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.

2 Qin = Qo (- ainC - .38 C ) (1 - A) (4.10)

He used values from Berliand's (1960) 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. For example, in 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 the Atlantic Ocean

(personal communication). 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. Transport results from Georgi and Toole (1982) at 40*S were used. 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. With the above three considerations, 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"] PACIFIC E INDIAN EZ ATLANTIC

1 6 8 o e 14 a W 2D ZZ 24 26 Os-0o IN G/KG DEW POINT TEMPERATURE IN DEGREES C

MERIDIONAL WIND (v) IN m/sec ZONAL IN m/sec

0 x

WIND SPEED IN M/S

Figure 4.1 Frequency distribution histogram of the wind speed, zonal and meridional wind components, dew point temDerature, cloud cover, and drag coefficients. Table IV.2 Oceanic Albedo

Latitude Jan Fcb Mlar Apr 'May Jun Jul Aug Sep Oct Nov Dcc SON 0.33 0.14 0.10 0.09 0.08 0.08 0.12 70N 0.41 0.15 0.10 0.08 0.07 0.07 0.09 0.11 0.25 6ON 0.28 0.12 0.09 0.07 0.07 0.07 0.06 0.07 0.07 0.10 0.16 0.44 5ON 0.11 0.10 0.08 0.07 0.06 0.06 0.06 0.07 0.07 0.08 0.11 0.12 40N 0.10 0.09 0.07 0.07 0.06 0.06 0.06 0.06 0.07 0.08 0.10 0.11 30N 0.09 0.07 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.07 0.08 0.09 20N 0.07 z0.06 -0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.07 0.07 10N 0.07 .0.06 -0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.07 0 0.06 9. 0.06 -0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 10S 0.06 ;, 0.06 '0.06 0.06 0.07 0.07 0.06 0.06 0.06 0.06 0.06 0.06 20S 0.06 2 0.06 10.06 0.06 0.07 0.07 0.07 0.07 0.06 0.06 0.06 0.06 30S 0.06 0.06 - 0.06 0.07 0.08 0.09 0.08 0.07 0.07 0.06 0.06 0.06 40S 0.06 0.06 0.07 0.08 0.09 0.11 0.10 0.08 0.07 0.07 0.06 0.06 5s 0.06 0.07 0.07 0.08 0.10 0.13 0.11 0.08 0.08 0.07 0.06 0.06 605. 0.06 0.07 0.08 0.11 0.13 0.27 0.07 0.08 0.07 0.06 0.06 surface. Payne (1972) expressed the albedo as a function of atmospheric

transmittance and sun altitudes and found that the uncertainty in the

measurement of albedo is greater at low sun altitudes (< 20%). The

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 Range Most Frequent

Ta *C 10 to 31 27 Ts 'C 10 to 31 28 Ta-Ts 'C -2 to 2 -.5 Td 'C 4 to 26 23 Qs~Qa g/kg 0 to 8 5 v m/sec 0 to 10 6 u m/sec -8 to 8 -4 v m/sec -3 to 7 4 C octal 0 to 8 5,6 Month: 1 2 3 4 5 6 7 8 9 10 11 12 Lat. 0.00 0.00 14.22 218.61 423.29 515.71 479.38 324.56 87.75 0.00 0.00 0.00 89.50 0.00 0.00 17.14 218.41 422.90 515.24 478.94 324.26 90.60 0.00 0.00 0.00 87.50 0.00 0.00 39.22 219.18 419.68 511.31 475.29 321.80 109.45 5.20 0.00 0.00 82.50 0.00 2.71 72.76 229.84 413.27 503.50 468.03 318.28 139.27 23.18. 0.00 0.00 77.50 17.22 108.46 251.80 404.89 491.86 457.21 322.71 172.01 53.01 2.37 0.00 72.50 0.003.52 44.7-1- 144. 12 277. 75 404. 50 476. 53 445. 91 J38. 00 204. 49 96.80 17.63 0. 19 67. SOM 23.69 77.26 179.03 303.72 413.96 470.90 447.05 356.50 235.88 121.60 44.98 14.98 62.50 52.51 111.70 212.76 328.50 425.45 473.29 453.09 374.87 265.74 156.35 76.83 41.66 57.50 85.08 146.75 245.00 351.45 436.50 476.91 459.60 391.92 190.46 110.74 73.07 52.50 119.57 181.65 275.46 372.17 446.00 479.78 406.97 293.73 223.48 145.52 106.96 47.50 154.92 215.84 303.88 390.39 453.34 480.99 465.02468.57 419.64 319.60343.11 255.06 180.39 142.12 42.50 190.40 248.92 405.89 458.17 479.99 469.80 429.65 364.07 284.90 214.77 177.72 37.50 225.45 280. 51 330.03 418.50 460.24 476.46 468.41 436.82 382.31 312.73 248.23 213.17 32.50 259.63 310.31 353.71374.72 428.08 459.40 470.24 464.24 441.01 338.31 280.38 247.96 27.50 338. 03' 392.91 455.58 457.22 442.15 397.68410.05 361.43 310.88 281.69 22.50 292.55 363.44 408.13 437.83434.55 448.75 449.461.22 38' 419.34 381.89 339.46 314.00 17.50 323.86 386.31 420.27 438.90 434.74 447.30 440.18 399.55 365.84 12.50 437.90 435.11 425.46 344.57 353.28 406.46 429.22 434.73 426.09 417.36 434.52418.91 426.94 414.24 389.61 373.12 7.50 405.38380.53 434.93 428.36 410440 397.36 428.37428.04 425.86 411.15 399.41 2.50 427.63 423.72437.96 437.35 418.82 391.94 374.86 379.68400.59 415.74 424.48 434.32 429.71 423.22 -2.50 447.12 384.401.59 58 439.56 445.34 444.'37 -7.50 463.70 456.96449.06 436.46 406.20 370.84 323.12350.05 330.76356.34 364.86 417.71 441.53 457.92 462.72 -12.50 477.27 461.59 432.26424.79 372.09390.58 321.46347.28 294.30 303.15 342.58 407.79 440.22 467.38 478.15 -17.50 462.94 414.11 350.89 293.59 273.76 317.94 394.79 435.65 473.68 490.59 -22.50 495.20487.78 461.02 400.30 327.14 263.94 232.10263.86 242.88 291.14 427.87 476.81 500.02 378.81 -27.50 499.57 455.88 383.47 301.03 232.80 199.36 210.83 262.42 338.45 416.94 476.81 506.46 -32.50 500.97 363.76 272.80 200.48 166.03 177.96 232.06 314.38359.96 402.97 473.75 510.03 -37.50 499. 58 436.35447.61 341.31 242.70 167.36 132.57 144.70 200.36 287.96 386.09 467.80 510.91 -42.50 495.70 422.29 316.31 210.99 133.91 99.55 111.58 167.67 259.41 366.48 459.17 509.43 -47.50 405.69 288. 96 178.01 79.27 134.41 228.97 344.33 448.25 506.14 -52.50 482.78489.82 386.97 259.49 144.12 100.6768.45 67.75 48.77 101.13 196.89 319.93 435.62 502.04 -57.50 476.21 366.77 228.17 109.81 38.48 13.4538.34 21.82 68.60 16b. 47 293.64 422.33 499.18 -62.50 474.85 195.30 75.78 13.42 0.06 3.01 38.14 129.07 265.99 410.67 504.51 -67.50 486.55 346.26 43.30 1.18 0.00 13.16 94.15 237.98 408.10 520.61 -72.50 498.07 321.36 161.30 16.41 0.00 0.00 1.40 59.56 212.54 415.34 532.94 -77.50 328.50 126.85 0.00 505.80 323.60 94.15 2.44 0.00 0.00 0.00 28.51 197.50 421.78 541.21 -82.50 509.68 72.49 0.00 0.00 0.00 9.04 193.77 425.02 545.36 -87.50 510.15 326.08 69.62 0.00 0.00 0.00 0.00 0.00 6.12 193.95 425.40 545.85 -89.50 326.38 0.00

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 three oceans. Since these are the two main parameters that make up the 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. The difference is not very large. 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 not present in our calculations. 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. Stability is defined as the surface air-sea temperature difference. 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

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 2.5- 7 2.0- unstable

1.5 - 5

1.0 -

.5 2

3 6 9 12 15 20 25 30 35 ws

3.C

2.5

2.0

- NOT -T 1.5 CC 4 3 2 o I 1.0 '.2 - 3 4 -2to 5 -1.Oto -. 2 .5 2 6 '.5 to -I.O 7 <5

p I I I I I . 5 10 15 20 25 30 35 40 45

Figure 4.2 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

F igure 4.3 LATENT HEAT IN WA TT/M*2 1 2 3 4 5 6 7 8 9 10

IL ~1

5

- 7 / ~ I 7

/1. 9

F/I 'I too 50 200 250 300 350 400 450 is~o I ~ 1 1 1 1 ii r 2.3243 S 6 7 a 9 to QS-QR IN G/KG Figure 4.4 OUTGOING RADIATION

L -%_ I ,_T

7-

9-

11

13 / 15-

17' 84 19 -

21-

23 76

25 68 27-~

29-6

I 52 4 £ 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. Its two biggest contributors are cloud cover and air temperature. 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:

Q, = A -f(V)-V-6q (4.12)

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:

DQl 8Ql 3Qi = - dv + - d(6q) av 36q

The magnitude of 3Q1 can be estimated by:

3Qi 1/2 aiQ 2 2 = [( AV) + ( A6q) ] (4.13) 3V 36q

From (4.12),

301 1 f'(V) = Qi -(- + - ) (4.14) 3V V f(V)

and

DQ1 Ql = - (4.15) 36q 6q

Substituting (4.14) and (4.15) into (4.13), we have

AQi AV A(6q) AV-f'(V) f'(V)-AV 2 1/2 = ()2_ + ( )2 + ( )2 + 2 ] Ql V 6q 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) This would give us an expression for as: 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

V=5 m/s and 6q 5 g/kg, we have

AQ1 1 1 04 2-0.4 1 1/2 =[(..)2,+ (_)2, (____] Ql 5 5 1.46 1.46 5 .30

If we assume AV to be 2 m/s (a typical standard deviation in the mid-latitudes), then

AQ1 2 2 0.8 2-0.4 4 1/2 = [(-)2 + (_)2 + (______.2 Q1 5 5 1.46 1.46 5

.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 considerably. In the Northern Hemisphere, the only significant energy

loss region is confined to the Gulf Stream in the Atlantic. There is 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 the Northern Hemisphere and a net loss in the Southern

Hemisphere. 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

LONGI TUDE Figure 4.6 Long term monthly mean of net heat flux for April 64a NET HEAT FLUX MON=7

I- i - i i.2 i f i.2' i i I 30 60 90 120 ISOE 180 NiSO 120 90 60 30 N 0E LONGITUDE Figure 4.7 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

LC!GIT IPF Figure 4.10 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 T TITUDE Figure 4.12 Long term monthly mean of incoming solar radiation for October 66

LATENT HEAT MON=1

C- -4j

LrC'GiT'JDE Figure 4.13 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,

LONGITUDE Figure 4.15 Long term monthly mean of latent heat for July LATENT HEAT MON=10

3

m < rn3

I_OK IT U 0F Figure 4.16 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

CM

LONGITUDE Figure 4.19 Long term monthly mean of outgoing radiation for July OUTGOING RADIATION MON=10

C i-n

LCNG!T'0JE Figure 4.20 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 90 120 1SOE 180 Hi50 120 90 60 de N L LONGITUDE Figure 4.23 Long term monthly mean of sensible heat for July SENSIBLE HEAT MON=10

LCT'I TU'' Figure 4.24 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. In July, the maximum shifts north to the

20*-30'N latiude belt. In October, the maximum is centered around

10*S. 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 season (Figures 4.17 to 4.20). Most of the values range from 40 to 50 watt/m2 . 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. There is substantially more energy loss in the north Atlantic than in the north

Pacific in the same latitudes. 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 -22- C)i22

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 14 16 18 20 22 2426283 TS ("C) TS (C)

Figure 4.29 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 for these two regions.

Newell et al (1981) 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. This is in accord with our result that the latent heat loss is much greater in the

North Atlantic than in the North Pacific at the same latitude. The denser water with higher salinity in 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, and e, central ocean regions at 20'N from three oceans are compared. 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 0 W1 udklllilondomilg|Ig|MillI a

76

45N/2SN CENTAAL NORTH ATLANTIC 2AN/70E NORTH CENTAAL INOIAN 29N/165N CENTRAL N. PAC. 2N/2SN CENTRAL NORTH ATLANTIC

cca a;

so6 3iof 6 I." L." 11.9611 8 i 16." .6 ttsi UN 1."4L ii. i an IN I . I."i MONTH .NORTH d) MONTH e MONTH 4SN/16S NOAT: CENTRAL PACIFIC 8/?65N CENTRALECUATORIAL PACIFIC 1/70E CENTRAL EQUATORIAL INDIAN 1/25N CENTRAL EQUATOAIAL ATLANTIC 1 4

i Z2a

a . 14I .6 I."4 MIN I U PM NE U .4 L . . I N i .4 PM NE 5.3t. j MONTH f MNONTH g MONTH h) MO--H

-Net Flux (On.,) olf -t-A-fr-m QL Qout ...... Ti -M----A Q ...... T

Figure 4.25 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 July and January, a decrease

in incoming radiation is observed due to enhanced cloudiness. Net Flux (Clout '''''''' T

Q~Q -S4-- -.L......

)SS/7E CENTRAL SOUTH INDIAN 0j/t65NSOUTH CENTRAL PACIFIC ISS/2SW CENTRALSOUTH ATLANTIC

3W3

aMONTH :ONTH -MONTH 353S/73E CENTRAL SOUTU INDIAN IIS6SWSOUTH CENTRAL PACIFIC 3SZNCNRLSUHALNI

Fiue42 Saoa yceo nrg lxcmpnnsa 1 11

NMn LN lN a Ca INN0 M .40 La '**INP. IN N. I. MONTH MNTH M__ONTH

Figure 4.26 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 monsoon cycle is still present in the Indian Ocean at this latitude. 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. It is greatest in January with a secondary peak in July. 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 winds. Coupled with less solar radiation, this results in a energy

deficit in 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 greater than it is 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 the summer and.a deficit in

winter. In the Pacific, latent heat loss stays high throughout the

year, eliminating any significant energy surplus in the Southern

Hemisphere summer months. Thus, for most of the central southern

hemisphere in 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. These are

regions where maximum energy loss are observed. In the Northern

Hemisphere winter months, the warm current from the south sets up a

tremendous sea-air temperature difference and therefore large amounts of Net Flux ;x

0* U

-- -- -

)OUT. b) MONT

ISS/tiRE SOUTH WESTERN PACIFIC IIS/1256 CENTRAL EQUATORIAL PAC. SS/SIN EASTERN EQUATORIAL PACIFIC

a

MONTH MONTH MONTH C) d) P

Figure 4.27 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 I EllEN,.

80

To contrast the different characteristics in the energy balance profile between eastern and western coast in the tropical Pacific,

Figure 4.27c, d,and e are presented. The eastern coast Pacific is a 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. In the

out *"----- Ta -Net Flux (One,) -

ISN/ISNEASTERN ATLANTIC SIN/55E NESTERN INOIAN 483/125E SOUTHEASTERN INDIAN 4 a

It01 *N . N 9.849.0. ~ . ~ ~ .9. 111 a) MONTH b) MONTH -- c N-

3IN/IISN NORTHEASTERN PACIFIC 305/15i SOUTHEASTERN ATLANTIC 31S/4SN SOUTHWESTERN ATLANTIC

3 3

d) d)MONTH 0)MONTH M)f MONTH

Figure 4.28 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. One is from the western Indian ocean at 10'N

and the other is south of western Australia at 40*S. The point at 10*N

is north of the Somali Republic. Here the effect of the summer monsoon

is clearly evident. 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 therefore smaller than in

the central region. This is 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 . One is off the

Sahara desert in the Cape Verde Island region, the other is off the Baja

California coast. The eastern subtropical Atlantic is a major heat gain area. Maximum annual heat gain is observed there. This is a region where major upwelling is observed. 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 so5 ~2 L7~ 40-f ~ ~ -~ ~ 14

20- /~. \2

S10" 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

4.30. In general, there is a net surplus of energy in the equatorial

Pacific region, most of the Indian Ocean, and in the eastern tropical

Atlantic Ocean. 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

LONGITUDE Figure 4.32 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 solar radiation. Figure 4.35 illustrates the annual mean pattern of cloudiness. One can clearly see the similarity of annual mean cloud cover to that of the incoming solar radiation. The absorption is high where the mean cloud cover is low and vice versa.

Another radiative flux is outgoing radiative flux from long wave radiation (Figure 4.32). 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. One feature worth noting is that the mean value of outgoing radiative flux is less in the North Pacific than it is in the North Atlantic at the same latitude. 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), latent heat is overwhelmingly the dominant flux (Figure 4.33). One might say that the net energy is 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

LONGITUDE - Figure 4.34 Long term annual mean of sensible heat flux loss are also areas of large net heating. These are mostly regions

where there is cooler surface water. Three factors contribute to the

calculation of latent heat flux: wind speed, specific humidity difference and the bulk transfer coefficient(Ce). The annual mean value of Ce is shown in Figure 4.36 . The values vary from 1.1 to

1.6. Spatially, Ce does not vary much. 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. The latent heat flux is essentially a product of these two fields. Their annual mean patterns are shown in

Figures 4.37 and 4.38 . The humidity difference roughly follows the pattern of temperature: it is high where the oceans are warm and low where they are cold. The wind speeds are greater in high latitudes than in low latitudes. 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 ITU D E 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

LONGITUDE Figure 4.37 Long term annual mean of air-sea temperature diff. ANNUAL MEAN OF QS - QA

04 C

LC'G ITUDE Figure 4.38 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

160 0 I 140 -% 120 /O 100

80 I % 0 OUT -60 %J~~% 40 ode

420 Iii

0- ONET

0- 0O

60 50 40 30 20 10 EO 10 20 30 40 50

Figure 4.40 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. Qout exhibits little or no latitudinal variation. The latitudinal profile of Qnet has a local maximum at 45'N and a local minimum at 35'N. This is mostly from the variation in Ql. The minimum in 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

.. 4 s IR-.

S80--6- 0.1 -4 01

Ta-Ts,wind speedT C* lodcoe, n

The ~ ~ ~ ~ ~ ~ ~ T prflTfQe a aiu t5S and lack thI ymti

Figumreidi onalflso ara ofnergyir bdew oithe three

oceanssepartely wrenprstessnFgr .2 Teeeg upu

teudesfile onrthaof a0'Simumh atndiandOceacks soth 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, MERIDIONAL PROFILE OF ANNUAL HEAT BUDGET FOR 3 OCEANS

NET HEAT (Onet ) LATENT HEAT ( L) SENSIBLE HEAT (OH, INDIAN PACIFIC - - -- OUTGOING RADIATION (O0UT) ATLANTIC INCOMING RADIATION (QIN)

2 2 0 220, s r

20 N EQ S 20 40 60 40 20 N EQ S 20 40 60 40 20 N EQ 5 20 LATITUDE LATITUDE LATITUDE Figure 4.42 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: First of all the data processing criterion are usually different. 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 tropical Atlantic and the eastern Pacific oceans. Bunker (1976) has results for the North

Atlantic and Clark (1965) has estimates for the North Pacific. Weare et

300, a) North Pacific b) North Atlantic

, 160W

I 2 3 4 5 6 7 8 9 10 11 12 MONTH

Figure 4.43 Comparison of seasonal cycle of net energy flux estimates for a) North Pacific, and b) North Atlantic al (1980) has also published values for the tropical Pacific. We will compare results region by region.

In the North Atlantic, our net energy term agrees fairly well with

Bunker's estimate. 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, especially in the Northern Hemisphere winter seasons. Bunker's estimate in regions of maximum energy loss in the Gulf Stream are approximately

10% higher than ours. The same discrrepancy is found (not shown) in upwelling regions where there is a maximum energy gain. 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 much better at subtropical region than that at higher latitudes. In general, our estimate of net heat loss is higher

than his. This is a direct consequence of the fact that our estimates - l~M1IM111l11 ih~ HIl o= lM i ln lI llll~lmill l 4llN, 1111''

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

and stability. With higher wind speed in the winter at higher

latitudes,

0) INDIAN OCEAN O - ION- 45-55E 100

clE 50 S0 -50

X

10S-20S, IIOE-120E

0 10 z -5 UJ A

z -54 10O

I4 2 3 4 5 6 7 8 9 10 lI 12

b) TROPICAL PACIFIC c) TROPICAL ATLANTIC

O0S , 85W 0- 5N1,10W

00 % O,95W 0-5S 30-35W

This study astenrato and Lanb (1978 ,1979) -- - - Wooe it al. (1980) 8 9 10 1I 12 i 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7

Figure 4.44 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 the estimate of latent heat flux. Our incoming radiation estimates are also different due to different formulae used. Clark used Budyko's formulation while in this study we used Reed's formulation. Estimates of sensible heat and 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, 1979). In the Pacific Ocean (Figure 4.44b), our net energy term agree well with

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. In the tropical Atlantic

(Figure 4.44c), our net heat flux is again in between Weare's estimate and Hasterath and Lamb'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 11111111111WWI

can be. Basically all of the estimates are made from the same set of

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.

IV.4 Error Analysis

IV.4a On monthly fluxes

No energy budget calculations are complete without an analysis of

errors. In addition to errors associated with meteorological

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. Their values vary from one study to another, 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 important components in the total energy budget. Radiative fluxes, 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

2 the range of 10%. This translates to be about 10 watt/m at high

latitudes and about 20 watt/m 2 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, it will dominate errors

associated with long term mean calculations. 100

The second source from which error may arise is from sampling errors associated with observation, reporting and archiving method. For example, take latent heat flux and radiative flux. 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. This type of error varies greatly both in time and in space. 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 from these averaged values.

He found a difference in 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 MIN11bill11,161

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. The accuracy of Qout is hard to estimate in the absence of published observations. Although the magnitude of Qout is small compared to

Qin and Q1 , it is comparable to the magnitude of Qnet- Qh is small and any error associated with it 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 2 respectively if one assumes these fluxes are normally distributed. 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 inRout

SA Div (Fa)

Qin

S t - Div (F 0 )

Figure 5.1 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. This can be accomplished by either the atmosphere or by the oceans. The role that the ocean plays in maintaining the temperature field relative to that of the atmosphere is one of the critical problems in understanding the present climate and its potential changes. 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 the

Atlantic ocean in both hemispheres. 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 value of transport from one or two years data for a given season. Without a knowledge of seasonal variability and the interannual variability of the transport, it is ,i Nilil llil Wli 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 = net energy flux at the ocean surface

Qin = 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. An appropriate boundary condition has

to be assumed. The most common assumption (and perhaps the safest) is

to 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. The error associated with

this may be large. 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. If we

assume a flux of zero at 70'N and if 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 transported from the

north). So a northward transport of .54 x 1014 watts is obtained for

65*N. At 60'N, to take care of the total deficit 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 the Pacific. The integration is performed from north to south. The presence of continents in northern boundaries makes it relatively safe to assume a zero flux for the northern boundary conditions. Of course, one could also integrate from south to north. 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. The transport values are calculated 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. The results for this computation are presented in Table V.2. To help ease the digestion of the data, the net flux divergence (weighted by the area) for each 5* latitude belt and for each ocean is presented schematically in 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 II

112

TABLE V.1 Annual Mean Heat Flux and Heat Transport *Error bars on the flux estimates are approximately 35% to 70%

Lat. Indian Ocean Pacific Ocean Atlantic Ocean Flux Area F*A Trsprt Flux Area F*A Trsprt Flux Area F*A ITrsprt watt m2 watt watt watt m2 watt watt watt m2 watt watt /m2* 1012 1012 1014 /m2* 1012 1012 1014 /m2* 1012 1012 1014 72.5 0.0- 67.5 -50.2 1.07 -54 54 62.5 -59.4 1.72 -102 A Al 56 57.5 -11.2 2.37 -27 -54.5 2.2 -120 27 2. 76 52.5 -0.4 3.54 -1 -39.1 1.98 -86 28. 3. 62 47.5 5.8 4.31 25 -25.1 2.3 -58 03 -4. 20 42.5 -17.0 5.10 -87 -32.2 3.18 -102

90 _5. 22 37.5 -54.2 5.24 -284 -51.0 3.58 -183

______3 . 74 -_-- - - - 7. 05 32.5 -46.5 5.83 -271 -32.7 3.51 -167 0A .-0 6 45- - 8. 72 27.5 13.1 .93 12 -22.8 6.29 -143. -8.1 4.53 -37 .12.7 ,88- 9.09 22.5 22.4 1.76 39 -12.9 7.08 -91 5.4 4.51 24 .51- -8 .79- -8. 85 17.5 45.5 3.10 141 -9.1 7.80 -71 5.5 4.23 23

______-1 .92. 9 50L 8. 62 12.5 43.8 3.94 173 -3.4 8.71 -30 14.9 3.9 58 -3.65. -9.80 8. 04 7.5 42.3 4.68 198 -1.6 9.15 -15 29.2 2.8 82

_-5 .63 9.95------_- - 7. 22 N2.5 60.6 4.41 267 36.5 9.22 337 43.3 3.75 152

______-8 .30 -6 .58-- 5.70 S2.5 53.9 5.38 290 63.2 7.95 502 66.7 3.37 225 -11.20.-1 .5--3. 45 7.5 40.6 6.1 248 26.5 7.93 210 24.0 2.86 69 -13 .68- .54 2. 76 12.5 19.7 6.08 120 5.3 8.11 43 8.4 3.02 25 -14 .88 .97. - ..------.-. - 2. 51 17.5 1.1 4.98 5 -7.4 8.22 -61 13.7 2.94 40 -14.93 - . -. ..-. .-. - . - - .36 2. 11 22.5 -12.5 4.21 -53 -18.3 7.97 -146 20.1 3.25 65 _ _ :-14 .40 -- 1 .10 1. 46 27.5 -27.1 4.23 -115 -27.5 7.66 -211 15.9 3.55 56

_-13 .25.-3 .21- 90 32.5 -23.6 5.0 -118 -27.8 7.19 -200 0.3 3.61 1

___-12 07. -- _------5 .21 _ 89 . 37.5 -32.8 6.0 -197 -25.1 6.66 -167 -21.5 3.82 -82 I-10 . 101 1 6 8818 1 1 ' l.- 113

TABLE V.2 Total Oceanic Heat Transport ErrorLat. bars are approximately 34% to 70% Flux Area F*A TrsFrt watt M2 watt wat t 4 /m2* 1012 1012 101n 0.0- 67.5 -50.2 1.07 -54 54 62.5 -44.4 2.3 -102 5& 57.5 -32.1 4.57 -147

______3. 01 52.5 -17.4 5.52 -96

__ -3. 99. 47.5 -6.9 6.61 -46 -.45. 42.5 -23.9 8.28 -198 6.4 37.5 -46.5 10.03 -466 _11. 09- 32.5 -35.5 10.71 -380

______-14. .89 27.5 -11.3 11.74 -133 -16. .22- 22.5 -0.6 13.40 -8 16. 17.5 9.4 15.13 142 -14. 88- 12.5 14.8 16.55 242 12..46- 7.5 17.5 16.63 291 .55- N2.5 45.0 17.38 782 1..73- S2.5 60.3 16.73 1009

______-8. .36- 7.5 31.4 16.89 530

_ _ _-13. 66. 12.5 11.2 17.21 193 -15..59- 17.5 -0.6 16.14 -10 -15. 49- 22.5 -8.1 15.45 -125 -14,.24 27.5 -15.9 15.44 -245 ____ '11. .79- 32.5 -18.9 15.83 -299 .-8..80. 37.5 -27.5 16.48 -453 -4 27-

142.5 1 _ I I I IIIWI - 11.,

114

0 6 90 20 10 E 180 Wjs0 120 9a 60 30 W o E

707

60 10 Watt 6 -. 5-.-86 5- +.25 AZ-~ 585 -. 87 -1.0 2 - 2-84 - 1.83 - 2.71 - 1-67/ .37 9 - - 1.43.I.s .24 7D 3 - .0 1 - .30 - .58 1.98,1- .15 *.92 -:0 2.67 +3.37 - 105 1.52 2.90u +5.02 - n2.25 rM 2.48 A- +2.10 - .69 I 1.20 1 - -+ .43 .25 1.0 5 115 e' -. 6-1 .40 21 -.53 - 1.46 - .65 -1.15 - 2.1li 90- 1.18 . - 2.00 -01 U -l.97 -1.67 - .82 40 - 50415

60 61

'/0 30 60 990 120 150 E 180 Wise 120 90 60 .30 W 0 E /I

Figure 5.2 The net energy flux divergenece for each 5' latitude belt and the direction of the purposed meridional transport of energy

25*S. 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

latitudes with a maximum of 15 X 101 4 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 150S. 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 Hastenrath Fu Bunker Bennett Bryan Wunsch Roemmich Study* 1980,1982 1982 1976 1978 1962 1980 1981

60N 1.56 2.6,2.6 1.8

50N 3.62 4.1

40N 5.22 6.3 0.

36N 7. 7.5 8.

30N 8.72 15.5,10.7 9.7

25N 9.09 12. 12.

15N 8.62 15.8,11.1 13,6

1ON 8.04 4.2, 1.8 8.2

0 5.70 14.4, 9.8 6.6

10S 2.76 3.9

15S 2.51 8.6,7.3

20S 2.11 5.4 3.9

25S 1.46 3,6.5 3.

30S .90 11.5, 6.9 8.3,5.4 4.1

32S 7.7 1.6,1.8 4.

40S 1.71 1.7,.67(Georgi & Toole, 1982)

*Errors on these estimates are from 34% to 70% 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, particularly at latitudes under the

influence of the Gulf Stream. Although the energy surplus area in the

tropical region has one of the largest values per square meter, the

total area with this surplus is small. Therefore, the total available

energy for the tropical region is 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) made transport estimates using the same

data set as Hastenrath's. 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, opposite to that for the rest of the year. The

Roemmich (1981), Wunsch (1980) and Fu (1981) data are direct estimates

obtained using inverse methods. Results from Bryan (1962), Bryden and

Hall (1980) and Bennett (1978) are also direct estimates using hydrographic data . 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. Most

estimates fall within this range. In the Southern Hemisphere, the magnitudes of various estimates are quite variable although the

directions are the same. Our estimates are uniformly lower than

others. 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) used a 1 x

1014 watts at 66.5'N as his boundary condition. With a correction of

the northern boundary value at 70'N , our values would be in better

agreements with others. Note, however, our final flux across 40'S of

1.7 x 1014 watts is 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. The

TABLE V.3a. Comparison of Various Estimates for Indian Ocean

Meridional Heat Transport in 1014 Watts

Latitude This Hastenrath Georgi & Bennett Study* 1982 Toole 1982 1978

0 -8.30 -4.8

15S -14.88 -7.7

30S -13.25 -4.9

32S 4.6-6.4, 15.5-17.6

40S -10.10 -8.77,-6.35 119

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). He obtained a significant northward transport at 32*S. 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 This Hastenrath Bennett Bryan Georgi & Wunsch Roemmich Study* 1982 1978 1962 Toole 1982 1983 1980

60N 0 .1

32N -12.

30N 6.45 11.4

0 6.58 -2.3

20S -.36 -20.7

28S -11.6,-1.7 -1.8+2.2 -2.5

30S 3.21 -19.2

40S 6.88 -18.0 0.4, -8.9

43S -1.5, 4.2 -.3+3.5 -2.

*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. Georgi

and Toole (1982) also found a small northward flux at 40*S. 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 Hastenrath Oort & Von Vonder Haar Emig Newell Atmo. Study* 1982 der Haar 1976 & Oort 1973 1967 et al. Newell

70N 0.0 -1.±4 +1. 0. -.48 14.5

60N 1.56 2.5 -2.±5 1. 1.84 0. 27.1

50N 3.99 10.±7 11. 4.38 6.29 32.4

40N 6.43 18.±12 21. 6.98 15.5 30.

30N 14.89 22.5 20.±15 25. 9.74 20.8 23.2

20N 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 1.0 -7.±21 3. -13.59 -1.45 -1.4

10S -13.66 -25.0 -9.69 -12.6

20S -15.49 -20.0 -27.87 -16.9 -21.3

30S -11.79 -17.5 -25.43 -23.2 -24.7

40S -4.27 -17.29

*Errors on these estimates are from 34% to 70% hiilllIl l l l iH .

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. Our estimate of approximately 7 x

1014 watts across 40'S seems large. 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. Again, her values

are higher than ours in the Southern Hemisphere. 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 much greater than those by the oceans in the mid-latitudes, especially in the North Hemisphere where it is 123

about twice to five times the oceanic energy transport. In regions between 30*N and 30*S, the transport values much more comparable.

In summary, our results indicate a northward transport at all latitudes in the Atlantic with a maximum of about 9 x 1014 watts at

25*N. The Atlantic Ocean as a whole experiences a net energy deficit.

It would require transport from other ocean areas to maintain its temperature field. The Indian Ocean transports energy southward in all latitudes with a maximum of 15 x 1014 watts at 20'S and it has a energy 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 change in the transport estimates with the possible errors. If we consider a more or less systematic change in all latitudes, the answer to that question is that in the Indian Ocean, 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. We should perhaps be reminded of a point Wunsch (1980) stressed. 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. We would like to know whether there is any significant difference among the means for these two periods. 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

55 -26( 8) -5(16) -21 -53(15) -53(15) 0

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) 6 -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

25 29( 6) 2( 9) 27 -30(24) -17(24) -13 -5(18 -11(18) 6

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 7(13) -23(16) 30 Ii

127

TABLE V.5b Difference in Latent 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 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

5N 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 -5 128

TABLE V.5c Difference in Incoming Radiation

Units in watt/m 2

Latitude Indian Ocean Pacific Ocean Atlantic Ocean

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 IN11", ,,1'11 INI,

130

TABLE V.5e Difference in Outgoing Radiation

Units in watt/n 2

Latitude Indian Ocean Pacific Ocean Atlantic Ocean

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

Having found the regions with the largest difference, one might want to check and see if the difference observed in latent heat flux is truly significant. 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 testing the difference of the means for these two periods. One would 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 no real difference between the means is tested. The results imply that there

is 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 - 1979 1949 - 1964 Xi + X2

Location X1 S1 N 1 X 2 S2 N2 Sl/Ni+S2/Nz

40E/20S 135 49 180 112 63 175 3.8

45E/20S 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

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

of 40*S. Due to the larger latent heat loss, the energy surplus in the

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. The northern part of the ocean therefore cools in response

to a deficit 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 matrix of the original data field. 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. The calculation of the single value decomposition is different from that of the conventional

EOF. 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. 372 monthly anomalies at 876 grid square were used. 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

z 6

.J

0

z 0: < 4

IA-3

z

C-

0 5 10 15 NUMBER OF MODES

Figure 6.1 The eigenvalues and the associated sampling errors for the first twenty modes of the nonseasonal SST EOF analysis...... OWSONSONOM 19111

138

In the second method, we use one of the testing procedures suggested by

Preisendorfer and Barnett (1977) to separate the noise from the signal in the data. 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 (6.2) 9=1 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 almost identical to

the first eignevector found by Weare el al (1976) 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 WO i~d Vo543m *0 135 1Zo lO 90 75 60 45 30' Figure 6.2 First nonseasonal SST eigenvector pattern for 1949-1979 (7.67% of total variance explained)

Pacific. 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 .3- 5- 6.8-

7. 8- W -1.

3- -

I I I I * I . I . I a I . I . I . I . I a I a I a I a I a 949 51 53 55 57 59 61 63 65 67 69 71 73 75 77 1979 1949-1964 EOF #1 TIME SERIES AND 1965-1979 EOF *1 TIME 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 111,11HIM 19111, , '111111111 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 time series show

the same characteristics 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 61 65 69 73 77 WINTER EOF # I SPRING EOF *1 22'

174 - f 124 12 8 74 7 4-- W 24 2 4-- -1 nc-26 -26 2 -76 -76 ~-126 -126 -176 (w- 49 53 5 7 6I 65 69 73 77 AtUTUMN EOF #1

Figure 6.3c 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). This is mostly due to the addition of the rest of the global ocean. 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 41 o0iiiW11114 11'.

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

each 5* by 5' grid region was calculated. The global pattern of this

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.

75 60 45 30 a W 0 EI 0 E 45 60 75 90 105 120 15 150 65 E 10 W 165 150 135 120 105 90 ORRELATION COEFFICIENT WITH EOF *1 TIME SERIES _.2 50

25 00-50AO 5 .. - 0

a ___44

1 4

9C 75 60 45 30 065W i OE 45 60 75 90 120 135 IS0 5E60W165 I50 10535 120 05 Figure 6.5 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

Figure 6.6 Cross correlation between time series of EOF #1 and selected grid squares 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, 1972 and more recently, in

1982. 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 ,,II'd1, 11,11 MidINN 1111',,,

148

120 150 E 180 W 150 1 90 60 30 W 0 E of- SST ANOMALY (C) N NOVEMBER 1982 0

-I 00-I

0

0 0 0 0

3D- 0 0 0 0 2 -0t

0

120 150 E 1I0 W 150 120 90 60 30 W 0 E

Figure 6.8 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

suggesting that more cloud cover lowers the SST. The solar flux at the

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) at 30'N and 165*W and

the association between the curves is evident. For the eastern

equatorial Pacific, the association is not so clear (the correlation

coefficient is -0.02). Changes in the parameters are clearly related

in some periods. 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 - INCOMING RADIRTION

-I I I 5 .55 .56 .57171 .55 '59 '61 4IS11~1 6 .67 .64 61 .7 .71 '7Z 73 '74 576 77

16lH/3IN NORTH CENTRAL PACIFIC - INCOMING RADIATION

4V II I 7 1 I I S T1zui.MfII 11 16 677 65I 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 71 7 ' 7 4 3 74 '75 '76 77

168/3IN NORTH CENTRAL PACIFIC

* I 11 1 1 4 '55 '6 'byl 'as 'Go 6S3 ' I 9la" . 6 .1 61 75 .7 1 79 71 74 '76 '76 77 '1

Figure 6.9 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

(Figure 6.12). A substantial negative region appearing in the the west

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. The time series of this mode is shown in Figure

6.11b. It is apparent that the cooling trend occurred mostly in the

second half of the 31-year period. The pattern from the eigenvectors

shows that the north Atlantic and the north Pacific dominated the

cooling. This cooling trend was also evident in a previous ____ 1,

152

TIME SERIES OF EOF #2 20

wL' 15 0 -10 U) w i5 WC0 U) w-5

1949 51 53 55 57 59 61 ~ 63 65 67 69 71 73 75 77 1979 1949- 1964 EOF #2 TIME SERIES AND- 1965 -1979 EOF #2 TIME SERIES

-2010- --5-

-15-

1949 51 53 55 57 59 61 63 5 6"{ 69 71 73 75 77 1979

Figure 6.11 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* 901 105 120 135 50 165 E 80 W 15 50 15 120 105 90 75 60 45 30 15W Figure 6.12 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. Most of the conversion from bucket to

engine intake took place in the mid-1940's. At any rate, the switch to

engine intake method would have given us a warming trend, rather than

the cooling trend observed. 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 by Namias. In a previous paper on global SST (Newell and Hsiung, 1979), a cooling trend was also found to be present in the north Atlantic (as found by others; see for example Kukla et al, 1977). Boer and Higuchi

(1980) also showed that the zonal mean 1000-700 mb thickness

(geopotential difference) of the polar cap showed a cooling trend after

1964. Douglas et al ascribe the cooling to stronger winds, and greater 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

30 E 45 60 75 90 105 120 35 50 65 00 W 165 -40 0 05 90 75 60 45 30 15

60 0 45SST 20EOF *3.1949-I979I3, . 1949-1979.60T 45 20040 0

3

15 - 20 0- -- 080 1-

0 0 3 0 -00 - -26 s. -0 0 -40

40 - \_40 20 .'-o

7 " o / o0 -r < 60 40- ~

30 E 45 60 75 90 105 120 135 150 165 E 180 W 165 150 135 120059 75 604 30 5W

TIME SERIES OF EOF #3

U' 10 to5 0 C,5

--5

-t0

77 1979 1949 51 53 55 57 59 61 63 65 67 69 71 73 75

pattern for Figure 6.13 a)Third nonseasonal SST eigenvector

1949-1979 (3.44% of the total variance explained)

and b) time series of the eigenvector 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 the patterns

(Figure 6.14). 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

1949-1979 1949 -1964 1965-1979 WU: I. ,...... ,,....,..,.. 1.0 0 0 0.8 - 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- 0.1 0- -0.1 -0.1 -0.I 0 -0.3 -0.3 -0.3 -0.5 1 0C 6 I 16 21 26 31 36 I 6 11 16 21 26 31 36 0 6 -1 16 2 26 31 36 LAG IN MONTHS OF EOF *1 1.0 . . , . . . , . . . , , , . .... I.U ,,,,, ... .. ,,,.. t.0. S0 z 0.6 0.48' 0.6 -- 04 OA 0.4 0.2- 0.2 02 C 0.1 0.1 0.1 o -0.1 -0.1 -0.I 0 -0. -0.3 .0.3 -0.51...... 1 6 il 16 21 26 31 36 1 6 11 16 21 26 31 36 I 6 11 16 21 26 31 36 LAG IN MONTHS OF EOF *2 If-.

0.8 0.6- 0.4- Q2

-0.1- -0.3. -0.3

I 6 I1 6 21 26 31 36 I 6 II 16 21 26 31 36 LAG IN MONTHS OF EOF *3 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 '62 "r i 6 ~6 1 67 6 I 73 71 72 73 71, 71 76 77 7

SST RNOMALY AT CR10 0117 30N 165*W

49 53 St bZ '53 54 155 56 *57 '5 '5 69I '61 'i f i 61I 6 1 7 'G. .69 75 71 '7? 73 7 1 7 7 W 7 7

Figure 6.15 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 and ETP are presented in Figure 6.15. In ETP, the grid point at 5*S and

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. The amplitude of the fluctuations is larger than that in the NCP. 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. As expected, the observed thermocline during El Nino is 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) = at, t=p+l,p+2,... (6.3) 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. Of course, more complicated process can also be considered. 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

rk= (6.4) bo where

1 N-k (6.5) bk = - (xt ~ (t+k - ~) N t=1

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.) This is the opposite of the autocorrelation function of the air temperature anomalies at higher levels. Newell et al (1983) have found that for air temperature

AUTOCORRELATION OF SST AT LAG=1

5060

33

20 20

to'1 N CDC-: 0 I *0

LONGITUDE

Figure 6.17 Autocorrelation coefficient at lag=l 162

fluctuations the areas with highest persistence (as measured by the

autocorrelation at lag=l) are in tropical regions and decreasing towards

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 1 N 2 2 0 ( P) _ - [Xt - At(P)] (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 a penalty function for the p+l parameters that needs to be

estimated. 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

information criterion (AIC). However, the BIC procedure is more

parsimonious and would select as low order a model as possible. As we

can see, for the north central Pacific, a first order autoregressive

model gives the best fit. 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) Eastern Tropical Pacific(5*S/80*W)

Model Parameter BIC Model Parameter BIC Order Estimates Order Estimates

1 .67 1339.0* 1 .64 1725.7

2 .644,.038 1342.0 2 .52,.187 1699.9*

3 .641,0.010,.075 1341.6 3 .517,.178,.017 1700.9

4 .639,-O.Ol, 1343.7 4 .517,.178, 1702.3 .055,.031 .017,-.001

5 .637,-.014,.056 1343.8 5 .517,.177,.008 1703.2 -.010,.064 .028,.052

*Minimum 164

As an additional check, the order of autoregressive models can be obtained from looking at the residuals from the selected order. The residuals are plotted in Figure 6.18. 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. For ETP, the residual from a

Figure 6.18 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 order

9 - - Eastern tropical Pacific North centrol Pacific .8-

.6-

.5- Ist order

.3-

.2 -

-.2 - 2nd order

3L 23 5 10 15 20 25 30 Log in months

Figure 6.19 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 - + BY = Z (6.10) dt

substituting (6.7) into (6.8), we have

d2 X dX - + (A+B)-- + AB-X = Z (6.11) dt 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 is a second order model rather than a simple first 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 for

the forcing functions Y and Z. Figure 6.20 gives a plot of the zonal wind 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 Q is approximately distributed as a X2 variate with k degree of freedom. 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. The same

Figure 6.20 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 true for the heat flux anomaly in NCP. The heat flux anomaly at ETP

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. While the latter

can be explained 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

fluctuations may be in the form of equation 6.11. Since the net heat

flux anomaly in ETP has more structure to it than a simple random noise

--.---- o stelrn tropical Pacific North central Pacific

2 -Z

Autocorelation function of zonal onoaoamaswind

Aotocorrelton function of not heet (out anomnalies

'L 450 t 1 5 20O 25 ' 32~ Log in months Figure 6.21 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. Unfortunately, there was so much missing data in 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 Ql

1 5.0857 3.3115 5.6787 2 2.8830 2.2456 2.7949 3 2.8131 1.9636 2.5008 4 2.2607 1.8550 2.2634 5 2.1624 1.7881 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 method used is the same as those described in Chapter VI.la. The 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 Qnet-

The 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. The pattern itself is not shown here because it is identical to that of the net heat flux. Again, 172

EOF #1 NET HEAT BUDGET

LONGITUDE

#A.-. TiME SEIE OF NET HEAT FLUX U) E-v r r - - EOF1 \~v~ 0 -SC

______' ' IV I ' - 7w2 7 7- 7 63 64 65 66 67 6 69N IV0 TIME IN YERR

- 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 ''.I i 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. The time

series associated with the first eigenvector (Figure 6.23) exhibits a

behavior that is 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. Here we found the principal mode of nonseasonal variation in incoming radiation is also associated with El Nino, supporting the theory proposed in Chapter VI.lc that cloud cover change is a major factor that ties the variations in tropical oceans together. 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.

AIR-SEA CORRELATION 90 20 o E teo Wiso 12 ~0~ 60 3

0 \7

(.5 ZI

~ 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. The seasonal variation of this

Figure 6.25 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 the

Atlantic they decrease from west to east. 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 above argument cannot be invoked to explain the difference. The 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,1lul~ lol lll alMMIIMmloMMMMh ili in n,"AN Ig I1ilil0 , , i ,u II Wm111, 1,

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 Qins Qout, and are Qh are presented in Figures 6.26 to 6.30. These coefficients 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. This suggests that the nonseasonal fluctuation in the net heat flux is dominated by the fluctuation in 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. This reveals that changes in 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. The maximum

relationship is 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. In

general, his results agree with ours. 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. Illlitill1.ilolllelu.. acoins., ilulleillInlliitiinimi, i.1lu.i. I1.iliWll .. WIllN....

186

SEA-NET HEAT BALANCE CORRELATION

bj 9k it3 1b3L 1dl W150 120 90 60 36 W I 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

C-

c 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-

LONGITUDE Figure 6.32 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. The purpose of this thesis is two fold: 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. 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 2 in the southern oceans. The sensible heat flux is 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 western boundary currents (up to 140 watt/m 2 in the Gulf Stream). The upwelling regions in both the Atlantic and the Pacific have the maximum heat gain with approximately 100 watt/m 2 found at eastern tropical

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. The North Atlantic seems to be completely detached from this mode. 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. However, it is hard to verify this theory from one incident. 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 illllIl hu i a m llllll, MI il Mil 26iu klllk all

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 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 a(ASST)/at. Again,

this effect is most pronounced in the tropics. 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 other is the calculation of oceanic meridional-heat transport 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. The complete coverage both

in 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 FNWC MARINE CONSOLIDATED DATA SUBSET PARAMETER SJM4ARY

PARAM PARAM NAME CODE BITStWO) TOTAL BITS REHAIKS , SOURCE 59 () 0=TOF-118 i=FNWZ SPOT 2 LATITUDE LAT 58-48 (1) 11' +/- .90 TO NEAREST TE4THl SOUTH IS COMIP 3 LONGITUOE LOqG 47-36 (1) 12 +/-'180 TO NEAREST TENTIf WEST IS COMD 4. CLASSIFICATION C 35-34 (i. 2 5 SHIP DIR KDSD 33-30 (1) 4 REF CtL),P.s' 6 SHIP VFLDCITY KV3 29-26 (1) 4 KNOTS/S 7 PRESSURE KPPD 25-15 (1) 1± TOF-11. P'±0-q000: SPOT 0OULO t00 8 AIR TEMP KDlY 14-4. (1) 11 RANGEI -60 TO 55 OEG C*Lo 9 SEA TEMP KSEA 59-54 (t) 4 RANGEt -8 TO 50 DEG O1 9 SEA TEMIP KSEA 3-0 (2) '6 SAHE AS ABOVE 10 .DE4 POINT TEMP KOEW 53-47 (2) 7 RfjNGEI -60 TO 40 DEG C 11 PRESSURE CH.ANGE HASP 46-37 (2) 10 RcEF (1), P. 12 12 INDICATOR IN) 36-35 (2) 2 *10, ADO TO PP 3NLY' 13 WAVE PERIOD LPA 34-30 (2) 5 REF CL), P. 10, WHOLE SEC 14 WAVE HEIGHT LH4 29-24 (2) .6 RANGE: 0 TO 63, HALF m1ErERS 15 SWELL PERIOD KP4 23-20 (2) ,4 RE-F (1), P. 10e WHOLE SEc 16 SWELL HEIGHT KH4 19-14 (2) 6 RANGE: 0 TO 631 HALF METERS 17 SWELL DIqECTIO K04 13-7 (2) 7 RANGE: 0 TO 73 ZIT CO01PA3%S,01G/5 18 WINO DIRECTION 6-0 (2) 7 RANGE: 0 TO 73 3T C04IPASS, OEr'G/5. . -19 WINO SPEEU LFir 59-53 (3) 7 M*ETERS/SECONO 20 CLOUD AHT 52-49 (3) 4 REF (Lis Ps..7 0 21 PAST W.EATHER mW. 48-45- (3) 4 RE:'SANE W1tAS ABOVEPs 6 22 TOTAL AMT LO NL. 44-41 (3) 4 REF (t.)lPs 7 23 LO CLOUD TYPE LC 40-37 (3) 4 REF (i)v Ps 7 - 24 HID CLOUD TYPE MC 36-33 (3) -4 OREF (t)., P. a 25 HI CLOUQ TYPE .32-29 (3) 4 REF (1.),P. 9 26 CLOUD HEIGHT LH 28-25 (3) 4 *REFRc01 1),P.1(1) g.P (I 27 PRESENT 4EATHER LWd 24-18 (3) 7 REF (L ).0P v 2 28 VISIBILITY KVV 17-14 (3) - 4 REFR W-,. P. 2 29 ERR3R INDICATOR 13 (3) * FLAGS ERROR IN IEPORT- 30 DSV 12 (3) 31 ICE TYPE ICETr 1.1-9 (3) 3. 0-5 32 ICE THICKNESS ICE 8-0 (3) 9 REF (i), P. 11 32 ICE THICKNESS ICE 59 (4) 33 ICE ACCRETION KRAL 58-56 (4) 3 34 SIG CLOUD AHT KS IG C 55-50 (4) 6 35 SIG 'CLOUD TYPE. KSIGT 49-42 (4) 8 36 SIG CLOUD HEIGJT KSE3CI 41-30 (4) 12 37 AIR-SEA TEMP 0IF LT3S 29-24 (4) .6' WHELE DEG C 38 YEAR NYrAR 23-14 (4) . 10 39 MONTH 13-10 (4) 4 40 DAY 9-5 (4) 5 01-31 41 HOUR JH3JR 4-0 (4) 00-2f 42 SHIP 10 SHIP .59-24 (5) 36 REF (I, P. 13 43 WET BULR 23- 0 (5) .24 REF (t), P. W REF (1) TOF-1t SURIFA" %IARI9e OBSERVATION--(REVi.E SEPT A196T) +--PARAMETER CROSSES WOR BOUDOARIES. 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, one can clearly see the drift of the ship's movement within this 5' by 5* square in time. 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 the ocean during the latter period, ships were able to take advantage of the shorter northern route. 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. This particular location, however, is 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 averaging methods.

Figure B.2c is the anomaly calculated using long term monthly means from

5* by 5' square monthly values. There is a marked trend in this time series, corresponding closely to the time series in Figure B.1b. What we are interested in knowing is how much of this trend is real and how much of it is an artificial result of the ship's northward movement?

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 by 1* long term monthly means. This can be considered the 'true' anomaly time series for the 5' by 5* square. Figure B.2b is the anomaly obtained by taking the 5* by 5* 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 400N, 600W 1715.a

1501.5

zo1288.0

z asa

40

434.0 = 220.5

-651.8

S-62.1

-- 63.0 z -63.3-63.5

1949 1951 1953 1955 1957 1959 1961 1963 1965 1967 1969 1971 1973 1975 1977 1979 c Figure B.lc) MONTHLY MEAN LONGITUDE POSITION FOR GRID AT 40N/60W4 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 1957 1959 1961 1963 1965 1967 1969 1971 1973 1975 1977 1979 - -- AVERAGE SST ANOMALY FOR 25 1 BY 1 DEG. SQUARES-

4.9

3.7 SM cc

-22.4 ii

b. . SS AN.L SE IE F. BY ..5 DEG...... S AR .T .. .Y. .EAN

0-1.4

-3.9. -1. 1949 1951 1953 1955 1957 1959 1961 1963 1965 1967 1969 1971 1973 1975 1977 1972 C 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. .z o-1.15 94 95 15 15 91 16 95 97 16 91'193 17 97 Ii SSzNML O Y5SUAEWRT Y5MAS cn -. '',fl II j911 111lik,,,Ill i. .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 1111kil - |- | |,

208

MONTHLY MEAN CLOUD COVER MON=7

2i

M1m <

LONGITUDE Figure C.7 Long term July means of cloud cover

MONTHLY MEAN CLOUD COVER MON=10

2: M4

LONGITUDE Fimure C.8 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

LONGITUDE Figure C.12 Long term October means of specific humidity difference 211

MEAN WIND FIELD MON=1

\\\, - Jii \\\\\\\\\-% .su s. ae rN/o ry2 20

40 1 i ~t' % i ' A i 140

30 60 90 120 150 E 180 NISO 120 90 60 30 N 0 t LONGITUDE - Figure C.13 Long term January aeaus of surface wind

MEAN WIND FIELD MON=4 30 40 2o 2 SOE soWio12o go 60 3o W o E & TV "AXI I2PI/ V

23.~~ I lilu W .1\ \\\\\\%n '% % 4 , -1\ ~ 4

-9.'~~ %...-

T\A\\\ r\\ \ 1 \ \ fl\ n

,*-rI n~~%.an i%%A litik-11ezi:- MIs

I I 'I I I I I 30 60 90 120 150 180 N150 120 90 60 30 W 0E LONGITUDE Figure C.14 Long term April neans of surface wind I'll, M =Nlk,, 1 IV

212

MEAN WIND FIELD MON=7

I~~~ I/ / / / / .. // //////i-%

30 , {

20-

10 / n

4 20 I // JV\,N u \S

3 0

Sol' 30 60 90 120 50 180 WiSO 120 90 60 30 0 LONGITUDE Figure C.15 Long term July means of surface wind

MEAN WIND FIELD MON=10

607 fill 60 INk, ZI

50-

40 1 // ///////// 9 / I// ////// J ellj \\\jl%%%///////li ll l -L

30 V'1 j

40 .----- / / I/ !! !, , --

30 60 90 120 ISOE 180 WiSO 120 90 60 30 W 0 E LONGITUDE Figure C.16 Long term October means of surface wind 213

MONTHLY MEAN AIR MON=1

-1

LONGITUDE Figure C.17 Long term Junary means of air temperature

MONTHLY MEAN AIR MON=4

30-

20 - 126-

i it

1 28

20

3 0 24- -

- 1 8 2-0- 16 16181

9 12 150E 10180 isO 120 90 60 33 W 0 E LONGITUDE Figure C.18 Long term April means of air temperature wwnn flh ww - wwwN w11UW1i1w1k11w1

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 I fNGITilDE Figure C.20 Long term October means of air temperature 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, ' -' .- 1016 1020

30 60 90 120 150 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-

LONGITUDE Figure C.24 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. Empirical orthogonal function analysis 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 we denote by xij the deviation of the ith observed value of the jth variable from its mean xj where 218

I n xj -- I kj n k=1

Store our deviations into a nxp matrix X:

x1l ...... xlp X21- --. X2p

Xnl----- Xnp

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:

X = Z*Y (D.1) 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' (D.4)

Using (D.4) and (D.1) we obtain the following: 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 It turns out that the rows of Y (or equivalently, the columns of Y') are the eigenvectors of the matrix (X'X) 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 diagonal elements). In other words, the sum of the eigenvalues di, 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 =9 i=1,2,..,p p Idj j=1 Alol WIilll , i , I I il li lld ileElil1liiili ib i1ilil MI lllil1ellulI k " " o '111a1W11l la iM Ml 1.ll1ll'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' by the ith vector that is associated with the ith

eigenvalue. 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 K = ri 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). For

example, 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

U'u = I (D.9)

V'V = I (D.10)

From (D.8) we have

X' = V-S'-U' (D.1l)

and 221

X'X = VS'U'-USV' = VS2V' (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' = US2U' (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. MMnIMM nlimillllilliwillleli. 111 1 1

222

In summary, to find the eigenvector Y in EOF analysis, one can form

XX' first. Calculate its eigenvector U' and from (D.8) find the matrix V

(which is equivalent to Y.). This approach can be a considerable saving in both computing space and time, especially if p is much larger than n. 223

APPENDIX E. WIND STRESS CALCULATIONS

E.1 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, lv is the wind speed, Pa is the air density, and Cd is the drag coefficient.

The development of these formulas are from the same equation of vertical flux as the heat fluxes(see Eq.4.7). The specification of Cd is controversial - 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. This dependence on wind speed is illustrated in Figure 4.1b for various stability conditions. 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. At low wind speed (say less than 10 m/s), 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, July and

October) are presented in Figures E.1 to E.4. 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. For reference, 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. His maximum values are typically 10% larger than ours. 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

C-

C) 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 60 90 120 150E 180 WISO 120 90 60 30 W OE LONGITUDE Figure E.9 Long term monthly means of wind stress vector for January WIND STRESS MON=4 E W N E

tE9 NEUTON/NMu.2 -. c, ILk -

{ 7 //P 1H f /J

.I////// I

.V / - -A //SH

30 60 90 120 150 E 180 WiSO 120 90 60 30 W 0 E LONGITUDE Figure E.10 Long term monthly means of wind stress vector for April 232

W[ND STRESS MON=7

1o6L 90 12 0 io E 180 Wiso 120 90 60 30 HoE

-E e 1 0- I 1 ti

16-o 11% 14 I kv S," -P 60 3

ff V -/i

\\\ Y

90 60 90 120 \50 E 180 His0 120 90 60 30 H 0 LONGITUDE Figure E.11 Long term montn.Ly means of wind stress vector for July 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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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. All the non-computer generated graphs in the thesis were done by the steady hands of Isabelle

Kole. 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. I went to work at Meteorology Research, Inc. for a year as a meteorologist and came to Massachusetts Institute of Technology in 1976 for my graduate work in Meteorology. 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. I married Michael A.

Wojcik in July, 1980.