Books-23_Introduction to Physical Oceanography

8/2/2019 Books-23_Introduction to Physical Oceanography

1/351

Introduction To

Physical Oceanography

Robert H. StewartDepartment of Oceanography

Texas A & M University

Copyright 2006September 2006 Edition


2/351

ii


3/351

Contents

Preface vii

1 A Voyage of Discovery 1

1.1 Physics of the ocean . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Goals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.3 Organization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31.4 The Big Picture . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31.5 Further Reading . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

2 The Historical Setting 72.1 Definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82.2 Eras of Oceanographic Exploration . . . . . . . . . . . . . . . . . 82.3 Milestones in the Understanding of the Ocean . . . . . . . . . . . 122.4 Evolution of some Theoretical Ideas . . . . . . . . . . . . . . . . 152.5 The Role of Observations in Oceanography . . . . . . . . . . . . 162.6 Important Concepts . . . . . . . . . . . . . . . . . . . . . . . . . 20

3 The Physical Setting 213.1 Ocean and Seas . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223.2 Dimensions of the ocean . . . . . . . . . . . . . . . . . . . . . . . 233.3 Sea-Floor Features . . . . . . . . . . . . . . . . . . . . . . . . . . 253.4 Measuring the Depth of the Ocean . . . . . . . . . . . . . . . . . 293.5 Sea Floor Charts and Data Sets . . . . . . . . . . . . . . . . . . . 333.6 Sound in the Ocean . . . . . . . . . . . . . . . . . . . . . . . . . 343.7 Important Concepts . . . . . . . . . . . . . . . . . . . . . . . . . 37

4 Atmospheric Influences 394.1 The Earth in Space . . . . . . . . . . . . . . . . . . . . . . . . . . 39

4.2 Atmospheric Wind Systems . . . . . . . . . . . . . . . . . . . . . 414.3 The Planetary Boundary Layer . . . . . . . . . . . . . . . . . . . 434.4 Measurement of Wind . . . . . . . . . . . . . . . . . . . . . . . . 434.5 Calculations of Wind . . . . . . . . . . . . . . . . . . . . . . . . . 464.6 Wind Stress . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 484.7 Important Concepts . . . . . . . . . . . . . . . . . . . . . . . . . 49

iii


4/351

iv CONTENTS

5 The Oceanic Heat Budget 51

5.1 The Oceanic Heat Budget . . . . . . . . . . . . . . . . . . . . . . 51

5.2 Heat-Budget Terms . . . . . . . . . . . . . . . . . . . . . . . . . . 53

5.3 Direct Calculation of Fluxes . . . . . . . . . . . . . . . . . . . . . 57

5.4 Indirect Calculation of Fluxes: Bulk Formulas . . . . . . . . . . . 58

5.5 Global Data Sets for Fluxes . . . . . . . . . . . . . . . . . . . . . 61

5.6 Geographic Distribution of Terms . . . . . . . . . . . . . . . . . . 65

5.7 Meridional Heat Transport . . . . . . . . . . . . . . . . . . . . . 68

5.8 Variations in Solar Constant . . . . . . . . . . . . . . . . . . . . . 70

5.9 Important Concepts . . . . . . . . . . . . . . . . . . . . . . . . . 72

6 Temperature, Salinity, and Density 73

6.1 Definition of Salinity . . . . . . . . . . . . . . . . . . . . . . . . . 73

6.2 Definition of Temperature . . . . . . . . . . . . . . . . . . . . . . 766.3 Geographical Distribution . . . . . . . . . . . . . . . . . . . . . . 79

6.4 The Oceanic Mixed Layer and Thermocline . . . . . . . . . . . . 79

6.5 Density . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83

6.6 Measurement of Temperature . . . . . . . . . . . . . . . . . . . . 88

6.7 Measurement of Conductivity or Salinity . . . . . . . . . . . . . . 92

6.8 Measurement of Pressure . . . . . . . . . . . . . . . . . . . . . . 94

6.9 Temperature and Salinity With Depth . . . . . . . . . . . . . . . 95

6.10 Light in the Ocean and Absorption of Light . . . . . . . . . . . . 97


7 The Equations of Motion 103

7.1 Dominant Forces for Ocean Dynamics . . . . . . . . . . . . . . . 1037.2 Coordinate System . . . . . . . . . . . . . . . . . . . . . . . . . . 104

7.3 Types of Flow in the ocean . . . . . . . . . . . . . . . . . . . . . 105

7.4 Conservation of Mass and Salt . . . . . . . . . . . . . . . . . . . 106

7.5 The Total Derivative (D/Dt) . . . . . . . . . . . . . . . . . . . . 107

7.6 Momentum Equation . . . . . . . . . . . . . . . . . . . . . . . . . 108

7.7 Conservation of Mass: The Continuity Equation . . . . . . . . . 111

7.8 Solutions to the Equations of Motion . . . . . . . . . . . . . . . . 113


8 Equations of Motion With Viscosity 115

8.1 The Influence of Viscosity . . . . . . . . . . . . . . . . . . . . . . 115

8.2 Turbulence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116

8.3 Calculation of Reynolds Stress: . . . . . . . . . . . . . . . . . . . 119

8.4 Mixing in the Ocean . . . . . . . . . . . . . . . . . . . . . . . . . 123

8.5 Stability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127



5/351

CONTENTS v

9 Response of the Upper Ocean to Winds 1339.1 Inertial Motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133

9.2 Ekman Layer at the Sea Surface . . . . . . . . . . . . . . . . . . 1359.3 Ekman Mass Transport . . . . . . . . . . . . . . . . . . . . . . . 1439.4 Application of Ekman Theory . . . . . . . . . . . . . . . . . . . . 1459.5 Langmuir Circulation . . . . . . . . . . . . . . . . . . . . . . . . 1479.6 Important Concepts . . . . . . . . . . . . . . . . . . . . . . . . . 147

10 Geostrophic Currents 15110.1 Hydrostatic Equilibrium . . . . . . . . . . . . . . . . . . . . . . . 15110.2 Geostrophic Equations . . . . . . . . . . . . . . . . . . . . . . . . 15310.3 Surface Geostrophic Currents From Altimetry . . . . . . . . . . . 15510.4 Geostrophic Currents From Hydrography . . . . . . . . . . . . . 15810.5 An Example Using Hydrographic Data . . . . . . . . . . . . . . . 16410.6 Comments on Geostrophic Currents . . . . . . . . . . . . . . . . 16410.7 Currents From Hydrographic Sections . . . . . . . . . . . . . . . 17110.8 Lagrangian Measurements of Currents . . . . . . . . . . . . . . . 17210.9 Eulerian Measurements . . . . . . . . . . . . . . . . . . . . . . . 17910.10Important Concepts . . . . . . . . . . . . . . . . . . . . . . . . . 181

11 Wind Driven Ocean Circulation 18311.1 Sverdrups Theory of the Oceanic Circulation . . . . . . . . . . . 18311.2 Western Boundary Currents . . . . . . . . . . . . . . . . . . . . . 18911.3 Munks Solution . . . . . . . . . . . . . . . . . . . . . . . . . . . 19011.4 Observed Circulation in the Atlantic . . . . . . . . . . . . . . . . 19211.5 Important Concepts . . . . . . . . . . . . . . . . . . . . . . . . . 197

12 Vorticity in the Ocean 19912.1 Definitions of Vorticity . . . . . . . . . . . . . . . . . . . . . . . . 19912.2 Conservation of Vorticity . . . . . . . . . . . . . . . . . . . . . . 20212.3 Influence of Vorticity . . . . . . . . . . . . . . . . . . . . . . . . . 20412.4 Vorticity and Ekman Pumping . . . . . . . . . . . . . . . . . . . 20512.5 Important Concepts . . . . . . . . . . . . . . . . . . . . . . . . . 210

13 Deep Circulation in the Ocean 21113.1 Defining the Deep Circulation . . . . . . . . . . . . . . . . . . . . 21113.2 Importance of the Deep Circulation . . . . . . . . . . . . . . . . . 21213.3 Theory for the Deep Circulation . . . . . . . . . . . . . . . . . . 21813.4 Observations of the Deep Circulation . . . . . . . . . . . . . . . . 22213.5 Antarctic Circumpolar Current . . . . . . . . . . . . . . . . . . . 229


14 Equatorial Processes 23314.1 Equatorial Processes . . . . . . . . . . . . . . . . . . . . . . . . . 23414.2 El Nino . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23814.3 El Nino Teleconnections . . . . . . . . . . . . . . . . . . . . . . . 246


6/351

vi CONTENTS

14.4 Observing El Nino . . . . . . . . . . . . . . . . . . . . . . . . . . 24814.5 Forecasting El Nino . . . . . . . . . . . . . . . . . . . . . . . . . 249


15 Numerical Models 25315.1 IntroductionSome Words of Caution . . . . . . . . . . . . . . . . 25315.2 Numerical Models in Oceanography . . . . . . . . . . . . . . . . 25515.3 Global Ocean Models . . . . . . . . . . . . . . . . . . . . . . . . . 25615. 4 Coastal Model s . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26015.5 Assimilation Models . . . . . . . . . . . . . . . . . . . . . . . . . 26415.6 Coupled Ocean and Atmosphere Models . . . . . . . . . . . . . . 26615.7 Important Concepts . . . . . . . . . . . . . . . . . . . . . . . . . 269

16 Ocean Waves 27116.1 Linear Theory of Ocean Surface Waves . . . . . . . . . . . . . . . 271

16.2 N onlinear waves . . . . . . . . . . . . . . . . . . . . . . . . . . . 27616.3 Waves and the Concept of a Wave Spectrum . . . . . . . . . . . 27716.4 Ocean-Wave Spectra . . . . . . . . . . . . . . . . . . . . . . . . . 28316.5 Wave Forecasting . . . . . . . . . . . . . . . . . . . . . . . . . . . 28716.6 Measurement of Waves . . . . . . . . . . . . . . . . . . . . . . . . 28916.7 Important Concepts . . . . . . . . . . . . . . . . . . . . . . . . . 291

17 Coastal Processes and Tides 29317.1 Shoaling Waves and Coastal Processes . . . . . . . . . . . . . . . 29317.2 T sunamis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29717.3 Storm Surges . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29817.4 Theory of Ocean Tides . . . . . . . . . . . . . . . . . . . . . . . . 30017.5 Tidal Prediction . . . . . . . . . . . . . . . . . . . . . . . . . . . 308


References 313


7/351

Preface

This book is written for upper-division undergraduates and new graduate stu-dents in meteorology, ocean engineering, and oceanography. Because these stu-dents have a diverse background, I have emphasized ideas and concepts more

than mathematical derivations.Unlike most books, I am distributing this book for free in digital format viathe world-wide web. I am doing this for two reasons:

1. Textbooks are usually out of date by the time they are published, usuallya year or two after the author finishes writing the book. Randol Larson,writing in Syllabus, states: In my opinion, technology textbooks are awaste of natural resources. Theyre out of date the moment they arepublished. Because of their short shelf life, students dont even want tohold on to them(Larson, 2002). By publishing in electronic form, I canmake revisions every year, keeping the book current.

2. Many students, especially in less-developed countries cannot afford thehigh cost of textbooks from the developed world. This then is a gift

from the US National Aeronautics and Space Administration nasa to thestudents of the world.

Acknowledgements

I have taught from the book for several years, and I thank the many studentsin my classes and throughout the world who have pointed out poorly writtensections, ambiguous text, conflicting notation, and other errors. I also thankProfessor Fred Schlemmer at Texas A&M Galveston who, after using the bookfor his classes, has provided extensive comments about the material.

I also wish to thank many colleagues for providing figures, comments, andhelpful information. I especially wish to thank Aanderaa Instruments, KevinBartlett, Don Chambers, Gerben de Boer, Daniel Bourgault, Richard Eanes,

Gregg Foti, Nevin S. Fuckar, Luiz Alexandre de Araujo Guerra, Hazel Jenkins,Judith Lean, Christian LeProvost, Brooks Martner, Nikolai Maximenko, KevinMcKone, Mike McPhaden, Pim van Meurs, Gary Mitchum, Peter Niiler, Is-mael Nunez-Riboni, Alex Orsi, Mark Powell, Richard Ray, Joachim Ribbe, WillSager, David Sandwell, Sea-Bird Electronics, Achim Stoessel, David Stooksbury,Tom Whitworth, Carl Wunsch and many others.

vii


8/351

viii PREFACE

Of course, I accept responsibility for all mistakes in the book. Please sendme your comments and suggestions for improvement.

Figures in the book came from many sources. I particularly wish to thankLink Ji for many global maps, and colleagues at the University of Texas Centerfor Space Research. Don Johnson redrew many figures and turned sketches intofigures. Trey Morris tagged the words used in the index.

I especially thank nasas Jet Propulsion Laboratory and the Topex/Poseidonand Jason Projects for their support of the book through contracts 960887 and1205046.

Cover photograph of an island in the Maldives was taken by Jagdish Agara(copyright Corbis). Cover design is by Don Johnson.

The book was produced in LATEX 2 using TeXShop 2.03 on a dual-processorMacintosh G4 computer running OS-X 10.4. I especially wish to thank GerbenWierda for his very useful i-Installer package that made it all possible, andRichard Koch, Dirk Olmes and many others for writing the TeXShop softwarepackage. Their software is a pleasure to use. All figures were drawn in AdobeIllustrator.


9/351

Chapter 1

A Voyage of Discovery

The role of the ocean on weather and climate is often discussed in the news.Who has not heard of El Nino and changing weather patterns, the Atlantichurricane season and storm surges? Yet, what exactly is the role of the ocean?And, why do we care?

1.1 Why study the Physics of the ocean?

The answer depends on our interests, which devolve from our use of theocean. Three broad themes are important:

1. We get food from the ocean. Hence we may be interested in processeswhich influence the sea just as farmers are interested in the weather andclimate. The ocean not only has weather such as temperature changesand currents, but the oceanic weather fertilizes the sea. The atmospheric

weather seldom fertilizes fields except for the small amount of nitrogenfixed by lightning.

2. We use the ocean. We build structures on the shore or just offshore. Weuse the ocean for transport. We obtain oil and gas below the ocean. And,we use the ocean for recreation, swimming, boating, fishing, surfing, anddiving. Hence we are interested in processes that influence these activities,especially waves, winds, currents, and temperature.

3. The ocean influence the atmospheric weather and climate. The oceaninfluence the distribution of rainfall, droughts, floods, regional climate,and the development of storms, hurricanes, and typhoons. Hence we areinterested in air-sea interactions, especially the fluxes of heat and wateracross the sea surface, the transport of heat by the ocean, and the influence

of the ocean on climate and weather patterns.

These themes influence our selection of topics to study. The topics then deter-mine what we measure, how the measurements are made, and the geographicareas of interest. Some processes are local, such as the breaking of waves on abeach, some are regional, such as the influence of the North Pacific on Alaskan

1


10/351

2 CHAPTER 1. A VOYAGE OF DISCOVERY

weather, and some are global, such as the influence of the ocean on changingclimate and global warming.

If indeed, these reasons for the study of the ocean are important, lets begina voyage of discovery. Any voyage needs a destination. What is ours?

1.2 GoalsAt the most basic level, I hope you, the students who are reading this text,

will become aware of some of the major conceptual schemes (or theories) thatform the foundation of physical oceanography, how they were arrived at, andwhy they are widely accepted, how oceanographers achieve order out of a ran-dom ocean, and the role of experiment in oceanography (to paraphrase Shamos,1995: p. 89).

More particularly, I expect you will be able to describe physical processesinfluencing the ocean and coastal regions: the interaction of the ocean with theatmosphere, and the distribution of oceanic winds, currents, heat fluxes, andwater masses. The text emphasizes ideas rather than mathematical techniques.We will try to answer such questions as:

1. What is the basis of our understanding of physics of the ocean?

(a) What are the physical properties of sea water?

(b) What are the important thermodynamic and dynamic processes in-fluencing the ocean?

(c) What equations describe the processes and how were they derived?

(d) What approximations were used in the derivation?

(e) Do the equations have useful solutions?

(f) How well do the solutions describe the process? That is, what is the

experimental basis for the theories?(g) Which processes are poorly understood? Which are well understood?

2. What are the sources of information about physical variables?

(a) What instruments are used for measuring each variable?

(b) What are their accuracy and limitations?

(c) What historic data exist?

(d) What platforms are used? Satellites, ships, drifters, moorings?

3. What processes are important? Some important process we will studyinclude:

(a) Heat storage and transport in the ocean.

(b) The exchange of heat with the atmosphere and the role of the oceanin climate.

(c) Wind and thermal forcing of the surface mixed layer.

(d) The wind-driven circulation including the Ekman circulation, Ekmanpumping of the deeper circulation, and upwelling.


11/351

1.3. ORGANIZATION 3

(e) The dynamics of ocean currents, including geostrophic currents andthe role of vorticity.

(f) The formation of water types and masses.

(g) The deep circulation of the ocean.

(h) Equatorial dynamics, El Nino, and the role of the ocean in weather.

(i) Numerical models of the circulation.

(j) Waves in the ocean including surface waves, inertial oscillations,tides, and tsunamis.

(k) Waves in shallow water, coastal processes, and tide predictions.

4. What are a few of the major currents and water masses in the ocean, andwhat governs their distribution?

1.3 Organization

Before beginning a voyage, we usually try to learn about the places we willvisit. We look at maps and we consult travel guides. In this book, our guide willbe the papers and books published by oceanographers. We begin with a briefoverview of what is known about the ocean. We then proceed to a descriptionof the ocean basins, for the shape of the seas influences the physical processesin the water. Next, we study the external forces, wind and heat, acting onthe ocean, and the oceans response. As we proceed, I bring in theory andobservations as necessary.

By the time we reach chapter 7, we will need to understand the equationsdescribing dynamic response of the ocean. So we consider the equations ofmotion, the influence of Earths rotation, and viscosity. This leads to a study ofwind-driven ocean currents, the geostrophic approximation, and the usefulness

of conservation of vorticity.Toward the end, we consider some particular examples: the deep circulation,the equatorial ocean and El Nino, and the circulation of particular areas of theocean. Next we look at the role of numerical models in describing the ocean.At the end, we study coastal processes, waves, tides, wave and tidal forecasting,tsunamis, and storm surges.

1.4 The Big PictureThe ocean is one part of the earth system. It mediates processes in the

atmosphere by the transfers of mass, momentum, and energy through the seasurface. It receives water and dissolved substances from the land. And, it laysdown sediments that eventually become rocks on land. Hence an understandingof the ocean is important for understanding the earth as a system, especially for

understanding important problems such as global change or global warming. Ata lower level, physical oceanography and meteorology are merging. The oceanprovides the feedback leading to slow changes in the atmosphere.

As we study the ocean, I hope you will notice that we use theory, observa-tions, and numerical models to describe ocean dynamics. Neither is sufficientby itself.


12/351


1. Ocean processes are nonlinear and turbulent. Yet we dont really under-stand the theory of non-linear, turbulent flow in complex basins. Theories

used to describe the ocean are much simplified approximations to reality.

2. Observations are sparse in time and space. They provide a rough descrip-tion of the time-averaged flow, but many processes in many regions arepoorly observed.

3. Numerical models include much-more-realistic theoretical ideas, they canhelp interpolate oceanic observations in time and space, and they are usedto forecast climate change, currents, and waves. Nonetheless, the numer-ical equations are approximations to the continuous analytic equationsthat describe fluid flow, they contain no information about flow betweengrid points, and they cannot yet be used to describe fully the turbulentflow seen in the ocean.

By combining theory and observations in numerical models we avoid some ofthe difficulties associated with each approach used separately (figure 1.1). Con-tinued refinements of the combined approach are leading to ever-more-precisedescriptions of the ocean. The ultimate goal is to know the ocean well enoughto predict the future changes in the environment, including climate change orthe response of fisheries to over fishing.

NumericalModels

Data

Understanding Prediction

Theory

Figure 1.1 Data, numerical models, and theory are all necessary to understand the ocean.Eventually, an understanding of the o cean-atmosphere-land system will lead to predictionsof future states of the system.

The combination of theory, observations, and computer models is relativelynew. Four decades of exponential growth in computing power has made avail-able desktop computers capable of simulating important physical processes andoceanic dynamics.

All of us who are involved in the sciences know that the computer has be-come an essential tool for research . . . scientific computation has reachedthe point where it is on a par with laboratory experiment and mathe-matical theory as a tool for research in science and engineeringLanger(1999).

The combination of theory, observations, and computer models also impliesa new way of doing oceanography. In the past, an oceanographer would devise


13/351

1.5. FURTHER READING 5

a theory, collect data to test the theory, and publish the results. Now, the taskshave become so specialized that few can do it all. Few excel in theory, collecting

data, and numerical simulations. Instead, the work is done more and more byteams of scientists and engineers.

1.5 Further ReadingIf you know little about the ocean and oceanography, I suggest you begin

by reading MacLeishs (1989) book The Gulf Stream: Encounters With theBlue God, especially his Chapter 4 on Reading the ocean. In my opinion, itis the best overall, non-technical, description of how oceanographers came tounderstand the ocean.

You may also benefit from reading pertinent chapters from any introductoryoceanographic textbook. Those by Gross, Pinet, or Thurman are especiallyuseful. The three texts produced by the Open University provide a slightlymore advanced treatment.

Gross, M. Grant and Elizabeth Gross (1996) oceanographyA View of Earth.7th Edition. Upper Saddle River, New Jersey: Prentice Hall.

MacLeish, William (1989) The Gulf Stream: Encounters With the Blue God.Boston: Houghton Mifflin Company.

Pinet, Paul R. (2000) Invitation to oceanography. 2nd Edition. Sudbury, Mas-sachusetts: Jones and Bartlett Publishers.

Open University (1989a) Ocean Circulation. Oxford: Pergamon Press.

Open University (1989b) Seawater: Its Composition, Properties and Behav-ior. Oxford: Pergamon Press.

Open University (1989c) Waves, Tides and Shallow-Water Processes. Ox-ford: Pergamon Press.

Thurman, Harold V. and Elizabeth A. Burton (2001) Introductory oceanogra-phy. 9th Edition. Upper Saddle River, New Jersey: Prentice Hall.


14/351



15/351

Chapter 2

The Historical Setting

Our knowledge of oceanic currents, winds, waves, and tides goes back thousandsof years. Polynesian navigators traded over long distances in the Pacific as earlyas 4000 bc (Service, 1996). Pytheas explored the Atlantic from Italy to Norwayin 325 bc. Arabic traders used their knowledge of the reversing winds andcurrents in the Indian Ocean to establish trade routes to China in the MiddleAges and later to Zanzibar on the African coast. And, the connection betweentides and the sun and moon was described in the Samaveda of the Indian Vedicperiod extending from 2000 to 1400 bc (Pugh, 1987). Those oceanographerswho tend to accept as true only that which has been measured by instruments,have much to learn from those who earned their living on the ocean.

Modern European knowledge of the ocean began with voyages of discovery byBartholomew Dias (14871488), Christopher Columbus (14921494), Vasco daGama (14971499), Ferdinand Magellan (15191522), and many others. Theylaid the foundation for global trade routes stretching from Spain to the Philip-pines in the early 16th century. The routes were based on a good workingknowledge of trade winds, the westerlies, and western boundary currents in theAtlantic and Pacific (Couper, 1983: 192193).

The early European explorers were soon followed by scientific voyages ofdiscovery led by (among many others) James Cook (17281779) on the Endeav-our, Resolution, and Adventure, Charles Darwin (18091882) on the Beagle,Sir James Clark Ross and Sir John Ross who surveyed the Arctic and Antarc-tic regions from the Victory, the Isabella, and the Erebus, and Edward Forbes(18151854) who studied the vertical distribution of life in the ocean. Otherscollected oceanic observations and produced useful charts, including EdmondHalley who charted the trade winds and monsoons and Benjamin Franklin who

charted the Gulf Stream.Slow ships of the 19th and 20th centuries gave way to satellites, drifters,

and autonomous instruments toward the end of the 20th century. Satellitesnow observe the ocean, air, and land. Thousands of drifters observe the uppertwo kilometers of the ocean. Data from these systems, when fed into numer-ical models allows the study of earth as a system. For the first time, we can

7


16/351

8 CHAPTER 2. THE HISTORICAL SETTING

-60o

-40o

-20o

0o

20o

40o

60o

180o60o-60o 0o 120o -120o

Figure 2.1 Example from the era of deep-sea exploration: Track of H.M.S. Challenger

during the British Challenger Expedition 18721876. After Wust (1964).

study how biological, chemical, and physical systems interact to influence ourenvironment.

2.1 Definitions

The long history of the study of the ocean has led to the development ofvarious, specialized disciplines each with its own interests and vocabulary. Themore important disciplines include:

Oceanography is the study of the ocean, with emphasis on its character asan environment. The goal is to obtain a description sufficiently quantitative tobe used for predicting the future with some certainty.

Geophysics is the study of the physics of the Earth.

Physical Oceanography is the study of physical properties and dynamics ofthe ocean. The primary interests are the interaction of the ocean with the at-mosphere, the oceanic heat budget, water mass formation, currents, and coastaldynamics. Physical Oceanography is considered by many to be a subdisciplineof geophysics.

Geophysical Fluid Dynamics is the study of the dynamics of fluid motion onscales influenced by the rotation of the Earth. Meteorology and oceanographyuse geophysical fluid dynamics to calculate planetary flow fields.

Hydrography is the preparation of nautical charts, including charts of oceandepths, currents, internal density field of the ocean, and tides.

Earth-system Science is the study of earth as a single system comprisingmany interacting subsystems including the ocean, atmosphere, cryosphere, and

biosphere, and changes in these systems due to human activity.

2.2 Eras of Oceanographic Exploration

The exploration of the sea can be divided, somewhat arbitrarily, into variouseras (Wust, 1964). I have extended his divisions through the end of the 20thcentury.


17/351

2.2. ERAS OF OCEANOGRAPHIC EXPLORATION 9

-40o -20o-60o-80o 0o 20o 40o

0o

20o

40o

60o

-20o

-40o

-60o

Stations

AnchoredStations

Meteor19251927

XII

XIV

XII IX X

XI

VII

VI

VII

IV

II

I

III

V

Figure 2.2 Example of a survey from the era of national systematic surveys. Track of theR/V Meteor during the German Meteor Expedition. Redrawn from Wust (1964).

1. Era of Surface Oceanography: Earliest times to 1873. The era is character-ized by systematic collection of mariners observations of winds, currents,waves, temperature, and other phenomena observable from the deck ofsailing ships. Notable examples include Halleys charts of the trade winds,Franklins map of the Gulf Stream, and Matthew Fontaine Maurys Phys-ical Geography of the Sea.

2. Era of Deep-Sea Exploration: 18731914. Characterized by a few, wide-ranging oceanographic expeditions to survey surface and subsurface condi-


18/351


60o

40o

20o

0o

-20o

-40o

20o0o-20o-40o-60o-80o-100o

Figure 2.3 Example from the era of new methods. The cruises of the R/V Atlantis out ofWoods Hole Oceanographic Institution. After Wust (1964).

tions, especially near colonial claims. The major example is the ChallengerExpedition (figure 2.1), but also the Gazelle and Fram Expeditions.

3. Era of National Systematic Surveys: 19251940. Characterized by detailedsurveys of colonial areas. Examples include Meteor surveys of the Atlantic(figure 2.2), and the Discovery Expeditions.

4. Era of New Methods: 19471956. Characterized by long surveys usingnew instruments (figure 2.3). Examples include seismic surveys of theAtlantic by Vema leading to Heezens maps of the sea floor.

5. Era of International Cooperation: 19571978. Characterized by multina-tional surveys of ocean and studies of oceanic processes. Examples includethe Atlantic Polar Front Program, the norpac cruises, the InternationalGeophysical Year cruises, and the International Decade of Ocean Explo-ration (figure 2.4). Multiship studies of oceanic processes include mode,polymode, norpax, and jasin experiments.


19/351

2.2. ERAS OF OCEANOGRAPHIC EXPLORATION 11

Crawford

Crawford

Crawford

Crawford

Crawford

Crawford

Crawford

Crawford

Chain

Discovery II

DiscoveryII

DiscoveryII

DiscoveryII

Atlantis

Atlan

tis

Discovery II

Atlantis

Capt. Canepa

Capt. Canepa

20o 40o-0o-20o-40o-60o-80o

-60o

-40o

-20o

0o

20o

40o

60o

AtlanticI.G.Y.

Program

19571959

Figure 2.4 Example from the era of international cooperation . Sections measured by theInternational Geophysical Year Atlantic Program 1957-1959. After Wust (1964).

6. Era of Satellites: 19781995. Characterized by global surveys of oceanicprocesses from space. Examples include Seasat, noaa 610, nimbus7,Geosat, Topex/Poseidon, and ers1 & 2.

7. Era of Earth System Science: 1995 Characterized by global studies ofthe interaction of biological, chemical, and physical processes in the oceanand atmosphere and on land using in situ (which means from measure-ments made in the water) and space data in numerical models. Oceanicexamples include the World Ocean Circulation Experiment (woce) (fig-


20/351


60o

80o

40o

0o

-20o

-40o

-60o

-80o0o 60

o 100o

180o-140o

Committed/completed

S4

15

Atlantic Indian Pacific

S423

16

1

3

5

7

9

10

11

1221

1

18

2

20

422

8 13

1415

17

1

3

4

19171614

13

S4

10

5

6

4

1

2

3

7S 8S 9S

9N8N

7N

10

2

5

21

712

14S 17

3120

18

1189

30

25

28

2627

29

6

-100o140o20o-80o -40o

620o

11S

Figure 2.5 World Ocean Circulation Experiment: Tracks of research ships making a one-timeglobal survey of the ocean of the world. From World Ocean Circulation Experiment.

ure 2.5) and Topex/Poseidon (figure 2.6), the Joint Global Ocean FluxStudy (jgofs), the Global Ocean Data Assimilation Experiment (godae,and the SeaWiFS, Aqua, and Terra satellites.

2.3 Milestones in the Understanding of the OceanWhat have all these programs and expeditions taught us about the ocean?

Lets look at some milestones in our ever increasing understanding of the ocean

-60o

-40o

-20o

0o

20o

40o

60o

120o 160o -160o -120o -80o -40o180o

Figure 2.6 Example from the era of satellites. Topex/Poseidon tracks in the PacificOcean during a 10-day repeat of the orbit. From Topex/Poseidon Project.


21/351

2.3. MILESTONES IN THE UNDERSTANDING OF THE OCEAN 13

Figure 2.7 The 1786 version of Franklin-Folger map of the Gulf Stream.

beginning with the first scientific investigations of the 17th century. Initiallyprogress was slow. First came very simple observations of far reaching impor-

tance by scientists who probably did not consider themselves oceanographers, ifthe term even existed. Later came more detailed descriptions and oceanographicexperiments by scientists who specialized in the study of the ocean.

1685 Edmond Halley, investigating the oceanic wind systems and currents,published An Historical Account of the Trade Winds, and Monsoons,observable in the Seas between and near the Tropicks, with an attempt toassign the Physical cause of the said Winds Philosophical Transactions.

1735 George Hadley published his theory for the trade winds based on con-servation of angular momentum in Concerning the Cause of the GeneralTrade-Winds Philosophical Transactions, 39: 58-62.

1751 Henri Ellis made the first deep soundings of temperature in the tropics,finding cold water below a warm surface layer, indicating the water camefrom the polar regions.

1769 Benjamin Franklin, as postmaster, made the first map of the Gulf Streamusing information from mail ships sailing between New England and Eng-land collected by his cousin Timothy Folger (figure 2.7).

1775 Laplaces published his theory of tides.


22/351


1800 Count Rumford proposed a meridional circulation of the ocean with watersinking near the poles and rising near the Equator.

1847 Matthew Fontaine Maury published his first chart of winds and currentsbased on ships logs. Maury established the practice of international ex-change of environmental data, trading logbooks for maps and charts de-rived from the data.

18721876 Challenger Expedition marks the beginning of the systematic studyof the biology, chemistry, and physics of the ocean of the world.

1885 Pillsbury made direct measurements of the Florida Current using currentmeters deployed from a ship moored in the stream.

1903 Founding of the Marine Biological Laboratory of the University of Cali-fornia. It later became the Scripps Institution of Oceanography.

19101913 Vilhelm Bjerknes published Dynamic Meteorology and Hydrogra-

phy which laid the foundation of geophysical fluid dynamics. In it hedeveloped the idea of fronts, the dynamic meter, geostrophic flow, air-seainteraction, and cyclones.

1930 Founding of the Woods Hole Oceanographic Institution.

1942 Publication ofThe ocean by Sverdrup, Johnson, and Fleming, a compre-hensive survey of oceanographic knowledge up to that time.

Post WW 2 The need to detect submarines led the navies of the world togreatly expand their studies of the sea. This led to the founding ofoceanography departments at state universities, including Oregon State,Texas A&M University, University of Miami, and University of Rhode Is-land, and the founding of national ocean laboratories such as the variousInstitutes of Oceanographic Science.

19471950 Sverdrup, Stommel, and Munk publish their theories of the wind-driven circulation of the ocean. Together the three papers lay the foun-dation for our understanding of the oceans circulation.

1949 Start of California Cooperative Fisheries Investigation of the CaliforniaCurrent. The most complete study ever undertaken of a coastal current.

1952 Cromwell and Montgomery rediscover the Equatorial Undercurrent in thePacific.

1955 Bruce Hamon and Neil Brown develop the CTD for measuring conduc-tivity and temperature as a function of depth in the ocean.

1958 Stommel publishes his theory for the deep circulation of the ocean.

1963 Sippican Corporation (Tim Francis, William Van Allen Clark, GrahamCampbell, and Sam Francis) invents the Expendable BathyThermographxbt now perhaps the most widely used oceanographic instrument deployedfrom ships.

1969 Kirk Bryan and Michael Cox develop the first numerical model of theoceanic circulation.


23/351

2.4. EVOLUTION OF SOME THEORETICAL IDEAS 15

1978 nasa launches the first oceanographic satellite, Seasat. The project de-veloped techniques used by generations of remotes sensing satellites.

19791981 Terry Joyce, Rob Pinkel, Lloyd Regier, F. Rowe and J. W. Youngdevelop techniques leading to the acoustic-doppler current profiler for mea-suring ocean-surface currents from moving ships, an instrument widelyused in oceanography.

1988 nasa Earth System Science Committee headed by Francis Brethertonoutlines how all earth systems are interconnected, thus breaking down thebarriers separating traditional sciences of astrophysics, ecology, geology,meteorology, and oceanography.

1991 Wally Broecker proposes that changes in the deep circulation of the oceanmodulate the ice ages, and that the deep circulation in the Atlantic couldcollapse, plunging the northern hemisphere into a new ice age.

1992 Russ Davis and Doug Webb invent the autonomous, pop-up drifter thatcontinuously measures currents at depths to 2 km.

1992 nasa and cnes develop and launch Topex/Poseidon, a satellite that mapsocean surface currents, waves, and tides every ten days, revolutionizing ourunderstanding of ocean dynamics and tides.

1993 Topex/Poseidon science-team members publish first accurate global mapsof the tides.

More information on the history of physical oceanography can be found in Ap-pendix A of W.S. von Arx (1962): An Introduction to Physical Oceanography.

Data collected from the centuries of oceanic expeditions have been used

to describe the ocean. Most of the work went toward describing the steadystate of the ocean, its currents from top to bottom, and its interaction withthe atmosphere. The basic description was mostly complete by the early 1970s.Figure 2.8 shows an example from that time, the surface circulation of the ocean.More recent work has sought to document the variability of oceanic processes,to provide a description of the ocean sufficient to predict annual and interannualvariability, and to understand the role of the ocean in global processes.

2.4 Evolution of some Theoretical Ideas

A theoretical understanding of oceanic processes is based on classical physicscoupled with an evolving understanding of chaotic systems in mathematics andthe application to the theory of turbulence. The dates given below are approx-imate.

19th Century Development of analytic hydrodynamics. Lambs Hydrodynam-ics is the pinnacle of this work. Bjerknes develops geostrophic methodwidely used in meteorology and oceanography.

192540 Development of theories for turbulence based on aerodynamics andmixing-length ideas. Work of Prandtl and von Karman.


24/351


Arctic Circle

East

Australia

Alaska

CaliforniaGulf

Stream

Labrador

Florida

Equator

Brazil

Peruor

Humboldt

Greenland

Guinea

Somali

Benguala

Agulhas

Canaries

Norway

Oyeshio

North Pacific

Kuroshio

North Equatorial

Equatorial Countercurrent

South Equatorial

West wind driftor

Antarctic Circumpolar

West wind driftor

Antarctic Circumpolar

Falkland

S. Eq. C. Eq.C.C.

N. Eq. C.

S. Eq. C.

West Australia

Murman

Irminger

NorthAtlanticdrift

N. Eq. C.

60o

45o

30o

15o

-15o

-30o

-45o

-60o

0oC.C.

warm currents N. north S. south Eq. equatorialcool currents C. current C.C. counter current

Figure 2.8 The time-averaged, surface circulation of the ocean during northern hemispherewinter deduced from a century of oceanographic expeditions. After Tolmazin (1985: 16).

19401970 Refinement of theories for turbulence based on statistical correla-tions and the idea of isotropic homogeneous turbulence. Books by Batch-elor (1967), Hinze (1975), and others.

1970 Numerical investigations of turbulent geophysical fluid dynamics basedon high-speed digital computers.

1985 Mechanics of chaotic processes. The application to hydrodynamics isjust beginning. Most motion in the atmosphere and ocean may be inher-ently unpredictable.

2.5 The Role of Observations in Oceanography

The brief tour of theoretical ideas suggests that observations are essentialfor understanding the ocean. The theory describing a convecting, wind-forced,turbulent fluid in a rotating coordinate system has never been sufficiently wellknown that important features of the oceanic circulation could be predictedbefore they were observed. In almost all cases, oceanographers resort to obser-vations to understand oceanic processes.

At first glance, we might think that the numerous expeditions mountedsince 1873 would give a good description of the ocean. The results are indeedimpressive. Hundreds of expeditions have extended into all ocean. Yet, much

of the ocean is poorly explored.By the year 2000, most areas of the ocean will have been sampled from top

to bottom only once. Some areas, such as the Atlantic, will have been sampledthree times: during the International Geophysical Year in 1959, during theGeochemical Sections cruises in the early 1970s, and during the World OceanCirculation Experiment from 1991 to 1996. All areas will be under sampled.


25/351

2.5. THE ROLE OF OBSERVATIONS IN OCEANOGRAPHY 17

This is the sampling problem (See box on next page). Our samples of the oceanare insufficient to describe the ocean well enough to predict its variability and

its response to changing forcing. Lack of sufficient samples is the largest sourceof error in our understanding of the ocean.

The lack of observations has led to a very important and widespread con-ceptual error:

The absence of evidence was taken as evidence of absence. The greatdifficulty of observing the ocean meant that when a phenomenon was notobserved, it was assumed it was not present. The more one is able toobserve the ocean, the more the complexity and subtlety that appearsWunsch (2002a).

As a result, our understanding of the ocean is often too simple to be right.

Selecting Oceanic Data Sets Much of the existing oceanic data have been

organized into large data sets. For example, satellite data are processed anddistributed by groups working with nasa. Data from ships have been collectedand organized by other groups. Oceanographers now rely more and more onsuch collections of data produced by others.

The use of data produced by others introduces problems: i) How accurateare the data in the set? ii) What are the limitations of the data set? And, iii)How does the set compare with other similar sets? Anyone who uses public orprivate data sets is wise to obtain answers to such questions.

If you plan to use data from others, here are some guidelines.

1. Use well documented data sets. Does the documentation completely de-scribe the sources of the original measurements, all steps used to processthe data, and all criteria used to exclude data? Does the data set include

version numbers to identify changes to the set?2. Use validated data. Has accuracy of data been well documented? Was

accuracy determined by comparing with different measurements of thesame variable? Was validation global or regional?

3. Use sets that have been used by others and referenced in scientific papers.Some data sets are widely used for good reason. Those who produced thesets used them in their own published work and others trust the data.

4. Conversely, dont use a data set just because it is handy. Can you doc-ument the source of the set? For example, many versions of the digital,5-minute maps of the sea floor are widely available. Some date back tothe first sets produced by the U.S. Defense Mapping Agency, others arefrom the etopo-5 set. Dont rely on a colleagues statement about the

source. Find the documentation. If it is missing, find another data set.

Designing Oceanic Experiments Observations are exceedingly importantfor oceanography, yet observations are expensive because ship time and satel-lites are expensive. As a result, oceanographic experiments must be carefullyplanned. While the design of experiments may not fit well within an historical


26/351


Sampling Error

Sampling error is the largest source of error in the geosciences. It is causedby a set of samples not representing the population of the variable beingmeasured. A population is the set of all possible measurements, and a sam-ple is the sampled subset of the population. We assume each measurementis perfectly accurate.

To determine if your measurement has a sampling error, you must firstcompletely specify the problem you wish to study. This defines the popu-lation. Then, you must determine if the samples represent the population.Both steps are necessary.

Suppose your problem is to measure the annual-mean sea-surface tem-perature of the ocean to determine if global warming is occurring. For thisproblem, the population is the set of all possible measurements of surfacetemperature, in all regions in all months. If the sample mean is to equal

the true mean, the samples must be uniformly distributed throughout theyear and over all the area of the ocean, and sufficiently dense to include allimportant variability in time and space. This is impossible. Ships avoidstormy regions such as high latitudes in winter, so ship samples tend not torepresent the population of surface temperatures. Satellites may not sampleuniformly throughout the daily cycle, and they may not observe tempera-ture at high latitudes in winter because of persistent clouds, although theytend to sample uniformly in space and throughout the year in most regions.If daily variability is small, the satellite samples will be more representativeof the population than the ship samples.

From the above, it should be clear that oceanic samples rarely representthe population we wish to study. We always have sampling errors.

In defining sampling error, we must clearly distinguish between instru-ment errors and sampling errors. Instrument errors are due to the inac-curacy of the instrument. Sampling errors are due to a failure to makea measurement. Consider the example above: the determination of meansea-surface temperature. If the measurements are made by thermometerson ships, each measurement has a small error because thermometers are notperfect. This is an instrument error. If the ships avoids high latitudes inwinter, the absence of measurements at high latitude in winter is a samplingerror.

Meteorologists designing the Tropical Rainfall Mapping Mission havebeen investigating the sampling error in measurements of rain. Their resultsare general and may be applied to other variables. For a general descriptionof the problem see North & Nakamoto (1989).

chapter, perhaps the topic merits a few brief comments because it is seldommentioned in oceanographic textbooks, although it is prominently described intexts for other scientific fields. The design of experiments is particularly impor-tant because poorly planned experiments lead to ambiguous results, they maymeasure the wrong variables, or they may produce completely useless data.


27/351

2.5. THE ROLE OF OBSERVATIONS IN OCEANOGRAPHY 19

The first and most important aspect of the design of any experiment is todetermine why you wish to make a measurement before deciding how you will

make the measurement or what you will measure.

1. What is the purpose of the observations? Do you wish to test hypothesesor describe processes?

2. What accuracy is required of the observation?

3. What resolution in time and space is required? What is the duration ofmeasurements?

Consider, for example, how the purpose of the measurement changes how youmight measure salinity or temperature as a function of depth:

1. If the purpose is to describe water masses in an ocean basin, then measure-ments with 2050 m vertical spacing and 50300 km horizontal spacing,repeated once per 2050 years in deep water are required.

2. If the purpose is to describe vertical mixing in the ocean, then 0.51.0 mmvertical spacing and 501000 km spacing between locations repeated onceper hour for many days may be required.

Accuracy, Precision, and Linearity While we are on the topic of experi-ments, now is a good time to introduce three concepts needed throughout thebook when we discuss experiments: precision, accuracy, and linearity of a mea-surement.

Accuracy is the difference between the measured value and the true value.Precision is the difference among repeated measurements.The distinction between accuracy and precision is usually illustrated by the

simple example of firing a rifle at a target. Accuracy is the average distancefrom the center of the target to the hits on the target. Precision is the average

distance between the hits. Thus, ten rifle shots could be clustered within a circle10 cm in diameter with the center of the cluster located 20 cm from the centerof the target. The accuracy is then 20 cm, and the precision is roughly 5 cm.

Linearity requires that the output of an instrument be a linear function ofthe input. Nonlinear devices rectify variability to a constant value. So a non-linear response leads to wrong mean values. Non-linearity can be as importantas accuracy. For example, let

Output = Input + 0.1(Input)2

Input = a sin t

then

Output = a sin t + 0.1 (a sin t)2

Output = Input +0.1

2a2 0.1

2a2 cos2t

Note that the mean value of the input is zero, yet the output of this non-linear instrument has a mean value of 0.05a2 plus an equally large term at


28/351


twice the input frequency. In general, if input has frequencies 1 and 2, thenoutput of a non-linear instrument has frequencies 1

2. Linearity of an

instrument is especially important when the instrument must measure the meanvalue of a turbulent variable. For example, we require linear current meters whenmeasuring currents near the sea surface where wind and waves produce a largevariability in the current.

Sensitivity to other variables of interest. Errors may be correlated withother variables of the problem. For example, measurements of conductivityare sensitive to temperature. So, errors in the measurement of temperature insalinometers leads to errors in the measured values of conductivity or salinity.

2.6 Important ConceptsFrom the above, I hope you have learned:

1. The ocean is not well known. What we know is based on data collected

from only a little more than a century of oceanographic expeditions sup-plemented with satellite data collected since 1978.

2. The basic description of the ocean is sufficient for describing the time-averaged mean circulation of the ocean, and recent work is beginning todescribe the variability.

3. Observations are essential for understanding the ocean. Few processeshave been predicted from theory before they were observed.

4. Lack of observations has led to conceptual pictures of oceanic processesthat are often too simplified and often misleading.

5. Oceanographers rely more and more on large data sets produced by others.The sets have errors and limitations which you must understand before

using them.6. The planning of experiments is at least as important as conducting the

experiment.

7. Sampling errors arise when the observations, the samples, are not repre-sentative of the process being studied. Sampling errors are the largestsource of error in oceanography.

8. Almost all our observations of the ocean now come from satellites, drifters,and autonomous instruments. Fewer and fewer observations come fromships at sea.


29/351

Chapter 3

The Physical Setting

Earth is an oblate ellipsoid, an ellipse rotated about its minor axis, with anequatorial radius of Re = 6, 378.1349 km (West, 1982) slightly greater thanthe polar radius of Rp = 6, 356.7497 km. The small equatorial bulge is due toEarths rotation.

Distances on Earth are measured in many different units, the most commonare degrees of latitude or longitude, meters, miles, and nautical miles. Latitudeis the angle between the local vertical and the equatorial plane. A meridian is theintersection at Earths surface of a plane perpendicular to the equatorial planeand passing through Earths axis of rotation. Longitude is the angle betweenthe standard meridian and any other meridian, where the standard meridian isthe one that passes through a point at the Royal Observatory at Greenwich,England. Thus longitude is measured east or west of Greenwich.

A degree of latitude is not the same length as a degree of longitude exceptat the equator. Latitude is measured along great circles with radius R, whereR is the mean radius of Earth. Longitude is measured along circles with radiusR cos , where is latitude. Thus 1 latitude = 111 km, and 1 longitude= 111 cos km.

Because distance in degrees of longitude is not constant, oceanographersmeasure distance on maps using degrees of latitude.

Nautical miles and meters are connected historically to the size of Earth.Gabriel Mouton proposed in 1670 a decimal system of measurement based onthe length of an arc that is one minute of a great circle of Earth. This eventuallybecame the nautical mile. Moutons decimal system eventually became themetric system based on a different unit of length, the meter, which was originallyintended to be one ten-millionth the distance from the Equator to the pole along

the Paris meridian. Although the tie between nautical miles, meters, and Earthsradius was soon abandoned because it was not practical, the approximations arevery good. For example, Earths polar circumference is approximately 40,008km. Therefore one ten-millionth of a quadrant is 1.0002 m. Similarly, a nauticalmile should be 1.8522 km, which is very close to the official definition of theinternational nautical mile: 1 nm 1.8520 km.

21


30/351

22 CHAPTER 3. THE PHYSICAL SETTING

-80o -40o 0o 40o-90o

-60o

-300

00

30o

60o

90o

-4000 -3000 -1000 -200 0

Figure 3.1 The Atlantic Ocean viewed with an Eckert VI equal-area projection. Depths, inmeters, are from the etopo 30 data set. The 200 m contour outlines continental shelves.

3.1 Ocean and SeasThere is only one ocean. It is divided into three named parts by international

agreement: the Atlantic, Pacific, and Indian ocean (International HydrographicBureau, 1953). Seas, which are part of the ocean, are defined in several ways.We consider two.

The Atlantic Ocean extends northward from Antarctica and includes all ofthe Arctic Sea, the European Mediterranean, and the American Mediterraneanmore commonly known as the Caribbean sea (figure 3.1). The boundary betweenthe Atlantic and Indian ocean is the meridian of Cape Agulhas (20E). The

boundary between the Atlantic and Pacific ocean is the line forming the shortestdistance from Cape Horn to the South Shetland Islands. In the north, the ArcticSea is part of the Atlantic Ocean, and the Bering Strait is the boundary betweenthe Atlantic and Pacific.

The Pacific Ocean extends northward from Antarctica to the Bering Strait(figure 3.2). The boundary between the Pacific and Indian ocean follows the


31/351

3.2. DIMENSIONS OF THE OCEAN 23

12 0o 160o -160o -120o -80o-90o

-60o

-30o

0o

30o

60o

90o

-4000 -3000 -1000 -200 0

Figure 3.2 The Pacific Ocean viewed with an Eckert VI equal-area projection. Depths, inmeters, are from the etopo 30 data set. The 200 m contour outlines continental shelves.

line from the Malay Peninsula through Sumatra, Java, Timor, Australia at CapeLondonderry, and Tasmania. From Tasmania to Antarctica it is the meridianof South East Cape on Tasmania 147E.

The Indian Ocean extends from Antarctica to the continent of Asia in-cluding the Red Sea and Persian Gulf (figure 3.3). Some authors use the nameSouthern Ocean to describe the ocean surrounding Antarctica.

Mediterranean Seas are mostly surrounded by land. By this definition,the Arctic and Caribbean Seas are both Mediterranean Seas, the Arctic Mediter-ranean and the Caribbean Mediterranean.

Marginal Seas are defined by only an indentation in the coast. The ArabianSea and South China Sea are marginal seas.

3.2 Dimensions of the oceanThe ocean and seas cover 70.8% of the surface of earth, which amounts to

361,254,000 km2. The areas of the named parts vary considerably (table 3.1).


32/351


40o 80o 120o-90o

-60o

-30o

0o

30o

-4000 -3000 -1000 -200 0

Figure 3.3 The Indian Ocean viewed with an Eckert VI equal-area projection. Depths, inmeters, are from the etopo 30 data set. The 200 m contour outlines continental shelves.

Oceanic dimensions range from around 1500 km for the minimum width ofthe Atlantic to more than 13,000 km for the north-south extent of the Atlanticand the width of the Pacific. Typical depths are only 34 km. So horizontal

dimensions of ocean basins are 1,000 times greater than the vertical dimension.A scale model of the Pacific, the size of an 8 .5 11 in sheet of paper, wouldhave dimensions similar to the paper: a width of 10,000 km scales to 10 in, anda depth of 3 km scales to 0.003 in, the typical thickness of a piece of paper.

Because the ocean are so thin, cross-sectional plots of ocean basins musthave a greatly exaggerated vertical scale to be useful. Typical plots have a ver-tical scale that is 200 times the horizontal scale (figure 3.4). This exaggerationdistorts our view of the ocean. The edges of the ocean basins, the continentalslopes, are not steep cliffs as shown in the figure at 41W and 12E. Rather, theyare gentle slopes dropping down 1 meter for every 20 meters in the horizontal.

The small ratio of depth to width of ocean basins is very important forunderstanding ocean currents. Vertical velocities must be much smaller than

Table 3.1 Surface Area of the ocean

Pacific Ocean 181.34 106 km2

Atlantic Ocean 106.57 106 km2

Indian Ocean 74.12 106 km2

From Menard and Smith (1966)


33/351

3.3. SEA-FLOOR FEATURES 25

Depth(km)

-45o -30o -15o 0o 15o-6

-4

-2

0

Longitude

6km

6km

-45o -30o -15o 0o 15o

Figure 3.4 Cross-section of the south Atlantic along 25S showing the continental shelfoffshore of South America, a seamount near 35W, the mid-Atlantic Ridge near 14W, theWalvis Ridge near 6E, and the narrow continental shelf off South Africa. Upper Verticalexaggeration of 180:1. Lower Vertical exaggeration of 30:1. If shown with true aspect ratio,the plot would be the thickness of the line at the sea surface in the lower plot.

horizontal velocities. Even over distances of a few hundred kilometers, thevertical velocity must be less than 1% of the horizontal velocity. We will usethis information later to simplify the equations of motion.

The relatively small vertical velocities have great influence on turbulence.Three dimensional turbulence is fundamentally different than two-dimensionalturbulence. In two dimensions, vortex lines must always be vertical, and there

can be little vortex stretching. In three dimensions, vortex stretching plays afundamental role in turbulence.

3.3 Sea-Floor FeaturesEarths rocky surface is divided into two types: oceanic, with a thin dense

crust about 10 km thick, and continental, with a thick light crust about 40 kmthick. The deep, lighter continental crust floats higher on the denser mantlethan does the oceanic crust, and the mean height of the crust relative to sealevel has two distinct values: continents have a mean elevation of 1100 m, oceanhave a mean depth of -3400 m (figure 3.5).

The volume of the water in the ocean exceeds the volume of the ocean basins,and some water spills over on to the low lying areas of the continents. Theseshallow seas are the continental shelves. Some, such as the South China Sea,

are more than 1100 km wide. Most are relatively shallow, with typical depthsof 50100 m. A few of the more important shelves are: the East China Sea, theBering Sea, the North Sea, the Grand Banks, the Patagonian Shelf, the ArafuraSea and Gulf of Carpentaria, and the Siberian Shelf. The shallow seas helpdissipate tides, they are often areas of high biological productivity, and they areusually included in the exclusive economic zone of adjacent countries.


34/351


0.0 0.5 1.0 1.5 2.0 2.5 3.0

-8

-6

-4

-2

0

2

4

Depth(km)

0 20 40 60 80 100

-8

-6

-4

-2

0

2

4

Histogram

Cumulative

Frequency Curve

Height(km)

Figure 3.5 Left Histogram of elevations of land and depth of the sea floor as percentage ofarea of Earth, in 50 m intervals showing the clear distinction between continents and seafloor. Right Cumulative frequency curve of height, the hypsographic curve. The curves arecalculated from the etopo 30 data set.

The crust is broken into large plates that move relative to each other. Newcrust is created at the mid-ocean ridges, and old crust is lost at trenches. The

Shore

High Water

Low Water

Sea Level

OCEANSHELF

(Gravel,Sand

Av slope1 in 500)

SLOPE

(Mud

av slope1 in 20)

CONTINENT

RISE

BASIN

MID-OCEAN

RIDGE

DEEP SEA

(Clay & Oozes)

Mineral OrganicSEAM

OUNT

TRENCH

ISLAND

ARC

Figure 3.6 Schematic section through the ocean showing principal features of the sea floor.Note that the slope of the sea floor is greatly exaggerated in the figure.


35/351

3.3. SEA-FLOOR FEATURES 27

relative motion of crust, due to plate tectonics, produces the distinctive featuresof the sea floor sketched in figure 3.6, including mid-ocean ridges, trenches,

island arcs, and basins. The names of the subsea features have been definedby the International Hydrographic Bureau (1953), and the following definitionsare taken from Sverdrup, Johnson, and Fleming (1942), Shepard (1963), andDietrich et al. (1980).

Basins are deep depressions of the sea floor of more or less circular or ovalform.

Canyons are relatively narrow, deep furrows with steep slopes, cutting acrossthe continental shelf and slope, with bottoms sloping continuously downward.

Continental shelves are zones adjacent to a continent (or around an island)and extending from the low-water line to the depth, usually about 120 m, wherethere is a marked or rather steep descent toward great depths. (figure 3.7)

Continental slopes are the declivities seaward from the shelf edge into greater

depth.Plains are very flat surfaces found in many deep ocean basins.

Figure 3.7 An example of a continental shelf, the shelf offshore of Monterey Californiashowing the Monterey and other canyons. Canyons are common on shelves, often extendingacross the shelf and down the continental slope to deep water. Figure copyright MontereyBay Aquarium Research Institute (mbari).


36/351


21.4o

21.3o

21.2o

21.1o

21.0o

20.9o

20.8o

163.0o 163.1o 163.2o 163.3o 163.4o 163.5o 163.6o

40

20

14

40

40

2040

48

30

30

Figure 3.8 An example of a seamount, the Wilde Guyot. A guyot is a seamount with a flattop created by wave action when the seamount extended above sea level. As the seamount is

carried by plate motion, it gradually sinks deeper b elow sea level. The depth was contouredfrom echo sounder data collected along the ship track (thin straight lines) supplementedwith side-scan sonar data. Depths are in units of 100 m. From William Sager, Texas A&MUniversity.

Ridges are long, narrow elevations of the sea floor with steep sides and roughtopography.

Seamounts are isolated or comparatively isolated elevations rising 1000 m ormore from the sea floor and with small summit area (figure 3.8).

Sills are the low parts of the ridges separating ocean basins from one anotheror from the adjacent sea floor.

Trenches are long, narrow, and deep depressions of the sea floor, with rela-tively steep sides (figure 3.9).

Subsea features strongly influences the ocean circulation. Ridges separatedeep waters of the ocean into distinct basins. Water deeper than the sill betweentwo basins cannot move from one to the other. Tens of thousands of seamountsare scattered throughout the ocean basins. They interrupt ocean currents, andproduce turbulence leading to vertical mixing in the ocean.


37/351

3.4. MEASURING THE DEPTH OF THE OCEAN 29

Longitude (West)

Latitude(North)

-5000

-5000

-5000

-5000

-4000

-4000

-3000

-3000

-2000

-2000

-1000

-1000

-500

-500

-200

-200

-50

-50

-200

0

0

-50

-200

-500

0

-6000

167o 165o 163o 161o 159o 157o 155o51o

52o

53o

54o

55o

56o

57o

51o 52o 53 o 54 o 55o 56o 57o

Latitude (North)

-6000

-4000

-2000

0

Depth(m)

Section A:B

A

B

Alaska

nPeninsula

Bering Sea

Aleutia

nTrench

Pacific Ocean

Figure 3.9 An example of a trench, the Aleutian Trench; an island arc, the Alaskan Peninsula;and a continental shelf, the Bering Sea. The island arc is composed of volcanos producedwhen oceanic crust carried deep into a trench melts and rises to the surface. Top: Map ofthe Aleutian region of the North Pacific. Bottom: Cross-section through the region.

3.4 Measuring the Depth of the Ocean

The depth of the ocean is usually measured two ways: 1) using acousticecho-sounders on ships, or 2) using data from satellite altimeters.

Echo Sounders Most maps of the ocean are based on measurements madeby echo sounders. The instrument transmits a burst of 1030 kHz sound and

listens for the echo from the sea floor. The time interval between transmissionof the pulse and reception of the echo, when multiplied by the velocity of sound,gives twice the depth of the ocean (figure 3.10).

The first transatlantic echo soundings were made by the U.S. Navy DestroyerStewart in 1922. This was quickly followed by the first systematic survey of anocean basin, made by the German research and survey ship Meteor during its


38/351


Transmitter

transducer

Receiver

transducer

Oscillator

Electromechanical

drive

Electronics

Bottom

Transmittertransducer

Receivertransducer

Amplifier Oscillator

Time-intervalMeasurment,

Display, Recording

Strip chart

Surface

Contact bank

Zero-contactswitch

Slidingcontact

Endlessribbon

33 kHz

sound pulse

Figure 3.10 Left: Echo sounders measure depth of the ocean by transmitting pulses of soundand observing the time required to receive the echo from the bottom. Right: The time isrecorded by a spark burning a mark on a slowly moving roll of paper. After Dietrich et al.(1980: 124).

expedition to the south Atlantic from 1925 to 1927. Since then, oceanographicand naval ships have operated echo sounders almost continuously while at sea.Millions of miles of ship-track data recorded on paper have been digitized toproduce data bases used to make maps. The tracks are not well distributed.

Tracks tend to be far apart in the southern hemisphere, even near Australia(figure 3.11) and closer together in well mapped areas such as the North Atlantic.

Echo sounders make the most accurate measurements of ocean depth. Theiraccuracy is 1%.Satellite Altimetry Gaps in our knowledge of ocean depths between shiptracks have now been filled by satellite-altimeter data. Altimeters profile theshape of the sea surface, and its shape is very similar to the shape of the seafloor (Tapley and Kim, 2001; Cazenave and Royer, 2001; Sandwell and Smith,2001). To see this, we must first consider how gravity influences sea level.

The Relationship Between Sea Level and the Oceans Depth Excess mass atthe sea floor, for example the mass of a seamount, increases local gravity becausethe mass of the seamount is larger than the mass of water it displaces. Rocks

are more than three times denser than water. The excess mass increases localgravity, which attracts water toward the seamount. This changes the shape ofthe sea surface (figure 3.12).

Lets make the concept more exact. To a very good approximation, the seasurface is a particular level surface called the geoid (see box). By definition alevel surface is a surface of constant gravitational potential, and it is everywhere


39/351

3.4. MEASURING THE DEPTH OF THE OCEAN 31

90o 100o 110o 120o 130o 140o 150o 160o 170o 180o

-40o

-30o

-20o

-10o

0o

Walter H. F. Smith and David T. Sandwell, Ship Tracks, Version 4.0, SIO, September 26, 1996 Copyright 1996, Walter H. F. Smith and David T. Sandwell

Figure 3.11 Locations of echo-sounder data used for mapping the ocean floor near Australia.Note the large areas where depths have not been measured from ships. From David Sandwell,Scripps Institution of Oceanography.

perpendicular to gravity. In particular, it must be perpendicular to the localvertical determined by a plumb line, which is a line or cord having at one enda metal weight for determining vertical direction (Oxford English Dictionary).

The excess mass of the seamount attracts the plumb lines weight, causingthe plumb line to point a little toward the seamount instead of toward Earths

center of mass. Because the sea surface must be perpendicular to gravity, it musthave a slight bulge above a seamount as shown in figure 3.12. If there were nobulge, the sea surface would not be perpendicular to gravity. Typical seamountsproduce a bulge that is 120 m high over distances of 100200 kilometers. Thisbulge is far too small to be seen from a ship, but it is easily measured bysatellite altimeters. Oceanic trenches have a deficit of mass, and they producea depression of the sea surface.

The correspondence between the shape of the sea surface and the depth ofthe water is not exact. It depends on the strength of the sea floor, the age ofthe sea-floor feature, and the thickness of sediments. If a seamount floats on thesea floor like ice on water, the gravitational signal is much weaker than it wouldbe if the seamount rested on the sea floor like ice resting on a table top. As

a result, the relationship between gravity and sea-floor topography varies fromregion to region.

Depths measured by acoustic echo sounders are used to determine the re-gional relationships. Hence, altimetry is used to interpolate between acousticecho sounder measurements (Smith and Sandwell, 1994).

Satellite-altimeter systems Now lets see how altimeters measure the shape


40/351


The Geoid

The level surface that corresponds to the surface of an ocean at restis a special surface, the geoid. To a first approximation, the geoid is anellipsoid that corresponds to the surface of a rotating, homogeneous fluidin solid-body rotation, which means that the fluid has no internal flow.To a second approximation, the geoid differs from the ellipsoid becauseof local variations in gravity. The deviations are called geoid undulations.The maximum amplitude of the undulations is roughly 60 m. To a thirdapproximation, the geoid deviates from the sea surface because the oceanis not at rest. The deviation of sea level from the geoid is defined to be thetopography. The definition is identical to the definition for land topography,for example the heights given on a topographic map.

The oceans topography is caused by tides, heat content of the water, andocean surface currents. We will return to their influence in chapters 10 and

17. The maximum amplitude of the topography is roughly 1 m, so it issmall compared to the geoid undulations.

Geoid undulations are caused by local variations in gravity due to theuneven distribution of mass at the sea floor. Seamounts have an excess ofmass because they are more dense than water. They produce an upwardbulge in the geoid (see below). Trenches have a deficiency of mass. Theyproduce a downward deflection of the geoid. Thus the geoid is closely re-lated to sea-floor topography. Maps of the oceanic geoid have a remarkableresemblance to the sea-floor topography.

sea surface

sea floor

10 m

2 km

200 km

Figure 3.12 Seamounts are more dense than sea water. They increase local gravity,causing a plumb line at the sea surface (arrows) to be deflected toward the seamount.Because the surface of an ocean at rest must be perpendicular to gravity, the sea surfaceand the local geoid must have a slight bulge as shown. Such bulges are easily measuredby satellite altimeters. As a result, satellite altimeter data can be used to map the sea

floor. Note, the bulge at the sea surface is greatly exaggerated, a two-kilometer highseamount would produce a bulge of approximately 10 m.

of the sea surface. Satellite altimeter systems include a radar to measure theheight of the satellite above the sea surface and a tracking system to determinethe height of the satellite in geocentric coordinates. The system measures the


41/351


42/351


60o

0o

30o

-30o

-60o

180o120o60o -120o -60o 0oWalter H. F. Smith and David T. Sandwell Seafloor Topography Version 4.0 SIO September 26, 1996 1996 Walter H. F. Smith and David T. Sandwell

0o

Figure 3.14 The sea-floor topography of the ocean with 3 km resolution produced fromsatellite altimeter observations of the shape of the sea surface. From Smith and Sandwell.

reau. The atlas consists primarily of the location of depth contours, coastlines,and tracklines from the gebco 5th Edition published at a scale of 1:10 million.The original contours were drawn by hand based on digitized echo-sounder dataplotted on base maps.

The U.S. National Geophysical Data Center publishes the etopo-2 cd-romcontaining digital values of oceanic depths from echo sounders and altimetryand land heights from surveys. Data are interpolated to a 2-minute (2 nautical

mile) grid. Ocean data between 64

N and 72

S are from the work of Smithand Sandwell (1997), who combined echo-sounder data with altimeter data fromgeosat and ers1. Seafloor data northward of 64N are from the InternationalBathymetric Chart of the Arctic Ocean. Seafloor data southward of 72S arefrom are from the US Naval Oceanographic Offices Digital Bathymetric DataBase Variable Resolution. Land data are from the globe Project, that produceda digital elevation model with 0.5-minute (0.5 nautical mile) grid spacing usingdata from many nations.

National governments publish coastal and harbor maps. In the USA, thenoaa National Ocean Service publishes nautical charts useful for navigation ofships in harbors and offshore waters.

3.6 Sound in the OceanSound provides the only convenient means for transmitting information over

great distances in the ocean. Sound is used to measure the properties of thesea floor, the depth of the ocean, temperature, and currents. Whales and otherocean animals use sound to navigate, communicate over great distances, andfind food.


43/351

3.6. SOUND IN THE OCEAN 35

Salinity

0o

5o

10o

15o

20o

-6

-5

-4

-3

-2

-1

0

Depth(km)

33.0 33.5 34.0 34.5 35.0

Speed Corrections (m/ s)

0 20 40 60 80 100

0 20 40 60 80 100

Sound Speed (m/s)

1500 1520 1540 1560

1500 1520 1540 1560

-6

-5

-4

-3

-2

-1

-0

t S

C

ToC

Ct CPCS

Figure 3.15 Processes producing the sound channel in the ocean. Left: Temperature T andsalinity S measured as a function of depth during the R.V. Hakuho Maru cruise KH-87-1,station JT, on 28 January 1987 at Latitude 3352.90 N, Long 14155.80 E in the NorthPacific. Center: Variations in sound speed due to variations in temperature, salinity, anddepth. Right: Sound speed as a function of depth showing the velocity minimum near 1km depth which defines the sound channel in the ocean. (Data from jpots Editorial Panel,1991).

Sound Speed The sound speed in the ocean varies with temperature, salinity,and pressure (MacKenzie, 1981; Munk et al. 1995: 33):

C = 1448.96+ 4.591 t 0.05304 t2 + 0.0002374 t3 + 0.0160 Z (3.1)+ (1.340 0.01025 t)(S 35) + 1.675 107 Z2 7.139 1013 t Z3

where C is speed in m/s, t is temperature in Celsius, S is salinity (see Chapter6 for a definition of salinity), and Z is depth in meters. The equation has anaccuracy of about 0.1 m/s (Dushaw et al. 1993). Other sound-speed equationshave been widely used, especially an equation proposed by Wilson (1960) whichhas been widely used by the U.S. Navy.

For typical oceanic conditions, C is usually between 1450 m/s and 1550 m/s(figure 3.15). Using (3.1), we can calculate the sensitivity of C to changes of

temperature, depth, and salinity typical of the ocean. The approximate valuesare: 40 m/s per 10C rise of temperature, 16 m/s per 1000 m increase in depth,and 1.5 m/s per 1 increase in salinity. Thus the primary causes of variability ofsound speed is temperature and depth (pressure). Variations of salinity are toosmall to have much influence.

If we plot sound speed as a function of depth, we find that the speed usually


44/351


+9

+10

-9

ray +8

Range (km )

0 100 200 1.50 1.55

-0

-1

-2

-3

-4

Depth(km)

C (km/s)

axis

Figure 3.16 Ray paths of sound in the ocean for a source nearthe axis of the sound channel. After Munk et al. (1995).

has a minimum at a depth around 1000 m (figure 3.16). The depth of minimumspeed is called the sound channel. It occurs in all ocean, and it usually reachesthe surface at very high latitudes.

The sound channel is important because sound in the channel can travelvery far, sometimes half way around the earth. Here is how the channel works:Sound rays that begin to travel out of the channel are refracted back towardthe center of the channel. Rays propagating upward at small angles to thehorizontal are bent downward, and rays propagating downward at small anglesto the horizontal are bent upward (figure 3.16). Typical depths of the channelvary from 10 m to 1200 m depending on geographical area.

Absorption of Sound Absorption of sound per unit distance depends on theintensity I of the sound:

dI = kI0 dx (3.2)where I0 is the intensity before absorption and k is an absorption coefficientwhich depends on frequency of the sound. The equation has the solution:

I = I0 exp(kx) (3.3)

Typical values ofk (in decibels dB per kilometer) are: 0.08 dB/km at 1000 Hz,and 50 dB/km at 100,000 Hz. Decibels are calculated from: dB = 10 log(I/I0),where I0 is the original acoustic power, I is the acoustic power after absorption.

For example, at a range of 1 km a 1000 Hz signal is attenuated by only 1.8%:

I = 0.982I0. At a range of 1 km a 100,000 Hz signal is reduced to I = 105

I0.The 30,000 Hz signal used by typical echo sounders to map the oceans depthsare little attenuated going from the surface to the bottom and back.

Very low frequency sounds in the sound channel, those with frequenciesbelow 500 Hz have been detected at distances of megameters. In 1960 15-Hzsounds from explosions set off in the sound channel off Perth Australia were


45/351

3.7. IMPORTANT CONCEPTS 37

heard in the sound channel near Bermuda, nearly halfway around the world.Later experiment showed that 57-Hz signals transmitted in the sound channel

near Heard Island (75E, 53S) could be heard at Bermuda in the Atlantic andat Monterey, California in the Pacific (Munk et al. 1994).

Use of Sound Because low frequency sound can be heard at great distances,the US Navy, in the 1950s, placed arrays of microphones on the sea floor indeep and shallow water and connected them to shore stations. The SoundSurveillance System sosus, although designed to track submarines, has foundmany other uses. It has been used to listen to and track whales up to 1,700 kmaway, and to find the location of subsea volcanic eruptions.

3.7 Important Concepts1. If the ocean were scaled down to a width of 8 inches they would have

depths about the same as the thickness of a piece of paper. A

Documents

Books-23_Introduction to Physical Oceanography