ALBERT

Note: Contents Prologue Acknowledgments List of Symbols PART I Foundations 1 INTRODUCTION: The Basic Challenge 1.1 The Climate System 1.2 Some Basic Observations 1.3 External Forcing 1.3.1 Astronomical Forcing 1.3.2 Tectonic Forcing 1.4 The Ice-Age Problem 2 TECHNIQUES FOR CLIMATE RECONSTRUCTION 2.1 Historical Methods 2.1.1 Direct Quantitative Measurements 2.1.2 Descriptive Accounts of General Environmental Conditions 2.2 Surficial Biogeologic Proxy Evidence 2.2.1 Annually Layered Life Forms 2.2.2 Surface Geomorphic Evidence 2.3 Conventional Nonisotopic Stratigraphic Analyses of Sedimentary Rock and Ice 2.3.1 Physical Indicators 2.3.2 Paleobiological Indicators (Fossil Faunal Types and Abundances) 2.4 Isotopic Methods 2.4.1 Oxygen Isotopes 2.4.2 Deuterium and Beryllium in Ice Cores 2.4.3 Stable Carbon Isotopes 2.4.4 Strontium and Osmium Isotopes 2.5 Nonisotopic Geochemical Methods 2.5.1 Cadmium Analysis 2.5.2 Greenhouse Gas Analysis of Trapped Air in Ice Cores 2.5.3 Chemical and Biological Constituents and Dust Layers in Ice Cores 2.6 Dating the Proxy Evidence (Geochronometry) 3 A SURVEY OF GLOBAL PALEOCLIMATIC VARIATIONS 3.1 The Phanerozoic Eon (Past 600 My) 3.2 The Cenozoic Era (Past 65 My) 3.3 The Plio-Pleistocene (Past 5 My) 3.4 Variations during the Last Ice Age: IRD Events 3.5 The Last Glacial Maximum (20 ka) 3.6 Postglacial Changes: The Past 20 ky 3.7 The Past 100 Years 3.8 The Generalized Spectrum of Climatic Variance 3.9 A Qualitative Discussion of Causes 4 GENERAL THEORETICAL CONSIDERATIONS 4.1 The Fundamental Equations 4.2 Time Averaging and Stochastic Forcing 4.3 Response Times and Equilibrium 4.4 Spatial Averaging 4.5 Climatic-Mean Mass and Energy Balance Equations 4.5.1 The Water Mass Balance 4.5.2 Energy Balance 5 SPECIAL THEORETICAL CONSIDERATIONS FOR PALEOCLIMATE: Structuring a Dynamical Approach 5.1 A Basic Problem: Noncalculable Levels of Energy and Mass Flow 5.2 An Overall Strategy 5.3 Notational Simplifications for Resolving Total Climate Variability 5.4 A Structured Dynamical Approach 5.5 The External Forcing Function, F 5.5.1 Astronomical/Cosmic Forcing 5.5.2 Tectonic Forcing 6 BASIC CONCEPTS OF DYNAMICAL SYSTEMS ANALYSIS: Prototypical Climatic Applications 6.1 Local (or Internal) Stability 6.2 The Generic Cubic Nonlinearity 6.3 Structural (or External) Stability: Elements of Bifurcation Theory 6.4 Multivariable Systems 6.4.1 The Two-Variable Phase Plane 6.5 A Prototype Two-Variable Model 6.5.1 Sensitivity of Equilibria to Changes in Parameters: Prediction of the Second Kind 6.5.2 Structural Stability 6.6 The Prototype Two-Variable System as a Stochastic-Dynamical System: Effects of Random Forcing 6.6.1 The Stochastic Amplitude 6.6.2 Structural Stochastic Stability 6.7 More Than Two-Variable Systems: Deterministic Chaos PART II Physics of the Separate Domains 7 MODELING THE ATMOSPHERE AND SURFACE STATE AS FAST-RESPONSE COMPONENTS 7.1 The General Circulation Model 7.2 Lower Resolution Models: Statistical-Dynamical Models and the Energy Balance Model 7.2.1 A Zonal-Average SDM 7.2.2 Axially Asymmetric SDMs 7.2.3 The Complete Time-Average State 7.3 Thermodynamic Models 7.3.1 Radiative-Convective Models 7.3.2 Vertically Averaged Models (the EBM) 7.4 The Basic Energy Balance Model 7.5 Equilibria and Dynamical Properties of the Zero-Dimensional (Global Average) EBM 7.6 Stochastic Resonance 7.7 The One-Dimensional (Latitude-Dependent) EBM 7.8 Transitivity Properties of the Atmospheric and Surface Climatic State: Inferences from a GCM 7.9 Closure Relationships Based on GCM Sensitivity Experiments 7.9.1 Surface Temperature Sensitivity 7.10 Formal Feedback Analysis of the Fast-Response Equilibrium State 7.11 Paleoclimatic Simulations 8 THE SLOW-RESPONSE "CONTROL" VARIABLES: An Overview 8.1 The Ice Sheets 8.1.1 Key Variables 8.1.2 Observations 8.2 Greenhouse Gases: Carbon Dioxide 8.3 The Thermohaline Ocean State 8.4 A Three-Dimensional Phase-Space Trajectory 9 GLOBAL DYNAMICS OF THE ICE SHEETS 9.1 Basic Equations and Boundary Conditions 9.2 A Scale Analysis 9.3 The Vertically Integrated Ice-Sheet Model 9.4 The Surface Mass Balance 9.5 Basal Temperature and Melting 9.6 Deformable Basal Regolith 9.7 Ice Streams and Ice Shelves 9.8 Bedrock Depression 9.9 Sea Level Change and the Ice Sheets: The Depression-Calving Hypothesis 9.10 Paleoclimatic Applications of the Vertically Integrated Model 9.11 A Global Dynamical Equation for Ice Mass 10 DYNAMICS OF ATMOSPHERIC CO2 10.1 The Air-Sea Flux, Q↑ 10.1.1 Qualitative Analysis of the Factors Affecting Q↑ 10.1.2 Mathematical Formulation of the Ocean Carbon Balance 10.1.3 A Parameterization for Q↑ 10.2 Terrestrial Organic Carbon Exchange, W↑G 10.2.1 Sea Level Change Effects 10.2.2 Thermal Effects 10.2.3 Ice Cover Effects 10.2.4 Long-Term Terrestrial Organic Burial, W↓G 10.2.5 The Global Mass Balance of Organic Carbon 10.3 Outgassing Processes, V↑ 10.4 Rock Weathering Downdraw, W↓ 10.5 A Global Dynamical Equation for Atmospheric CO2 10.6 Modeling the Tectonically Forced CO2 Variations, µˆ : Long-Term Rock Processes 10.6.1 The Long-Term Oceanic Carbon Balance 10.6.2 The GEOCARB Model 10.7 Overview of the Full Global Carbon Cycle 11 SIMPLIFIED DYNAMICS OF THE THERMOHALINE OCEAN STATE 11.1 General Equations 11.1.1 Boundary Conditions 11.2 A Prototype Four-Box Ocean Model 11.3 The Wind-Driven, Local-Convective, and Baroclinic Eddy Circulations 11.3.1 The Wind-Driven Circulation: Gyres and Upwelling 11.3.2 Local Convective Overturnings and Baroclinic Eddy Circulations 11.4 The Two-Box Thermohaline Circulation Model: Possible Bimodality of the Ocean State 11.4.1 The Two-Box System 11.4.2 A Simple Model of the TH Circulation 11.4.3 Meridional Fluxes 11.4.4 Dynamical Analysis of the Two-Box Model 11.5 Integral Equations for the Deep Ocean State 11.5.1 The Deep Ocean Temperature 11.5.2 The Deep Ocean Salinity 11.6 Global Dynamical Equations for the Thermohaline State: θ and Sφ PART III Unified Dynamical Theory 12 THE COUPLED FAST- AND SLOW-RESPONSE VARIABLES AS A GLOBAL DYNAMICAL SYSTEM: Outline of a Theory of Paleoclimatic Variation 12.1 The Unified Model: A Paleoclimate Dynamics Model 12.2 Feedback-Loop Representation 12.3 Elimination of the Fast-Response Variables: The Center Manifold 12.4 Sources of Instability: The Dissipative Rate Constants 12.5 Formal Separation into Tectonic Equilibrium and Departure Equations 13 FORCED EVOLUTION OF THE TECTONIC-MEAN CLIMATIC STATE 13.1 Effects of Changing Solar Luminosity and Rotation Rate 13.1.1 Solar Luminosity (S) 13.1.2 Rotation Rate (Ω) 13.2 General Effects of Changing Land-Ocean Distribution and Topography (h) 13.3 Effects of Long-Term Variations of Volcanic and Cosmic Dust and Bolides 13.4 Multimillion-Year Evolution of CO2 13.4.1 The GEOCARB Solution 13.4.2 First-Order Response of Global Ice Mass and Deep Ocean Temperature to Tectonic CO2 Variations 13.5 Possible Role of Salinity-Driven Instability of the Tectonic-Mean State 13.6 Snapshot Atmospheric and Surficial Equilibrium Responses to Prescribed y-Fields Using GCMs 14 THE LATE CENOZOIC ICE-AGE DEPARTURES: An Overview of Previous Ideas and Models 14.1 General Review: Forced vs. Free Models 14.1.1 Models in Which Earth-Orbital Forcing Is Necessary 14.1.2 Instability-Driven (Auto-oscillatory) Models 14.1.3 Hierarchical Classification in Terms of Increasing Physical Complexity 14.2 Forced Ice-Line Models (Box 1, Fig. 14-1) 14.3 Ice-Sheet Inertia Models 14.3.1 The Simplest Forms (Box 2) 14.3.2 More Physically Based Ice-Sheet Models: First Applications 14.3.3 Direct Bedrock Effects (Box 3) 14.3.4 Bedrock-Calving Effects (Box 4) 14.3.5 Basal Meltwater and Sliding (Box 5) 14.3.6 Ice Streams and Ice Shelf Effects 14.3.7 Continental Ice-Sheet Movement (Box 6) 14.3.8 Three-Dimensional (λ, φ, hI) Ice-Sheet Models 14.4 The Need for Enhancement of the Coupled Ice-Sheet/Atmospheric Climate Models 14.5 Ice-Sheet Variables Coupled with Additional Slow-Response Variables 14.5.1 Regolith Mass, mr (Box 7) 14.5.2 The Deep Ocean Te