2 Observing the Ocean Ships Navigation The Electronics Era 16

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1 Contents Preface xiii 1 Introduction 1 2 Observing the Ocean Ships Navigation The Preelectronics Era The Electronics Era The Rise of Satellites Intermediate- and Long-Duration Measurements Experiments and Expeditions The Frontier: Duration Other Generic Observation Issues 47 An Interlude 50 3 What Does the Ocean Look Like? Some Physical Descriptions Gravity and the Shape of the Earth Topography Water Movement Gross Thermal and Salinity Properties A Global View of the Surface Ocean The Atmospheric Forcing Structure The Surface Layer Abyssal Boundary Layers Equations of Motion The Sphere Vorticity How Big Are Terms? Geostrophy Boundary Conditions Cartesian Approximation The β-plane 101

2 viii Contents Copyright, Princeton University Press. No part of this book may be Conservation Laws Instability Models Linear Wave Dynamics Background Surface Gravity Waves Cartesian Approximations of the Rotating System Effects of Topography A Stratified Ocean Separation of Variables The Sphere Inertial Waves Vertical Propagation Infinitely Deep Ocean Nonlinearities Low Frequency Limits Initial Value-Adjustment Problems Observations of Internal and Inertial Waves Introduction The Surprising Garrett and Munk Result Subelements of the Spectrum Inertial Waves Internal Tides Vortical Modes Deviations from the GM Spectrum and the Energy-Source Problem Instabilities and Breaking of Internal Waves The Tide Disturbing Potential and the Milankovitch Forcing Origin Solar Gravitational Tides Solar Motion Lunar Tides Combined Tides Pole Tide Thermal Tides Solid-Earth Tides, Self-Attraction and Load, and Atmospheric Tides The Atmosphere Tidal Analysis Frequency Domain Analysis Hydrodynamic Nonlinearities Time Domain Analysis The Milankovitch Problem Observations of Tides and Related Phenomena Tidal Dynamics Tides of a Flat-Bottom Ocean on a Sphere Cartesian Approximations 198

3 Contents ix Atmospheric Tides Tides of a Flat-Bottom Ocean on a Sphere Basic Tidal Observations Distribution The Many Tidal Constituents Internal Tides Changing Tidal Constituents Dissipation: Tidal Friction Paleotides and the History of Earth Rotation Balanced Motions The Nature of the Variability The Forcing In Situ Observations Moorings Shipborne Instruments Float Observations Altimetric Data: Global Characteristics What Does the Altimeter See? Time-Domain Representations Frequencies and Wave Numbers Vertical Structure Spectral Interpretation Wavenumber Power Laws Frequency Spectra Wave-Like Features Balanced Barotropic Basin Modes Other Contributions: Vortical Modes Generation of Balanced Variability Dissipation of Balanced Variability The Time-Mean Ocean Circulation Geostrophy and the Dynamic Method Resolving the Paradox: The Box Inverse Method The β-spiral Needler s Formula Qualitative Circulation Estimates Circulation Estimates: Inverse Methods Global Property-Weighted Transports Global Heat, Freshwater, Nutrient and Oxygen Transports Regional Estimates Convective Regions Ocean State Estimates Global-Scale Solutions Large-Scale Results Long-Duration Estimates Short-Duration Estimates Global High-Resolution Solutions Regional Solutions 293

4 x Contents Copyright, Princeton University Press. No part of this book may be 10 Large-Scale Circulation Physics Theories of thewind-driven Ocean Stommel and Arons Abyssal Flows Thermocline Theories Nonlinear Theories Western Boundary Currents The Role of Eddies Testing Mean Dynamics The Annual Cycle A Summary Interpreting and Using the Circulation Energetics and Mixing Mean Energy Sources Energy Sinks Mixing Rates The Meridional Overturning Circulation Integrals and Choke-Points Time Scales Time Scales Based on Volume Time Scales Based on Propagation and Advection Time Scales from Diffusion and Viscosity Time Scales Based on Energetics Time Scales Based on Tracers Dynamical Time Scales Consequences of Memory Other Physical Aspects and Regimes Sea Level, the Geoid, and Related Problems Low-Frequency, Time-Varying, Global-Scale Flow Background Forcing Fields Atmospheric Spectra Decadal-Scale Ocean Variability: The Recent Past Hydrographic Results In Situ Measures of Circulation Global Sea Level Change and Heat Uptake The Tide-Gauge Era and Multidecadal Sea Level Changes Sea-Surface Temperature 376 A Brief Afterword 377 A A Primer of Analysis Methods 379 A.1 Expectation and Probability 379 A.2 Time Series Analysis: Fourier Methods 381 A.2.1 Process Types 382 A.3 Basic Fourier Representations 382 A.3.1 Splitting 385

5 Contents xi A.3.2 Discrete Forms 385 A.3.3 Convolution 389 A.3.4 Miscellaneous Notes on Fourier Methods 390 A.3.5 Randomness and Spectral Estimation 391 A.4 Autocorrelations and Autocovariances 403 A.5 Coherence and Multiple Time Series 407 A.6 Power and Coherence in a Wave Field 410 A.7 A Note on Confidence Limits 412 A.8 Spherical Harmonics 414 A.9 Making Maps 416 B Inverse and State Estimation Methods 420 B.1 Inverse Methods and Inverse Models 420 B.2 Least-Squares 421 B.3 State Estimation 428 B.4 The Observations 430 B.5 Data Assimilation and Reanalyses 431 C Problematic Terms and Concepts 435 D Useful Numerical Values 441 E Notation, Abbreviations, and Acronyms 444 References 447 Index 477