Dynamical Paleoclimatology

Transcription

1 Dynamical Paleoclimatology Generalized Theory of Global Climate Change Barry Saltzman Department of Geology and Geophysics Yale University New Haven, Connecticut ACADEMIC PRESS A Harcourt Science and Technology Company San Diego San Francisco New York Boston London Sydney Tokyo

2 Contents Prologue xv Acknowledgments List of Symbols xxi xix PART I Foundations 1 INTRODUCTION: The Basic Challenge The Climate System Some Basic Observations External Forcing Astronomical Forcing Tectonic Forcing The Ice-Age Problem 14 2 TECHNIQUES FOR CLIMATE RECONSTRUCTION Historical Methods Direct Quantitative Measurements Descriptive Accounts of General Environmental Conditions Surficial Biogeologic Proxy Evidence Annually Layered Life Forms Surface Geomorphic Evidence Conventional Nonisotopic Stratigraphic Analyses of Sedimentary Rock and Ice Physical Indicators Paleobiological Indicators (Fossil Faunal Types and Abundances) Isotopic Methods Oxygen Isotopes Deuterium and Beryllium in Ice Cores Stable Carbon Isotopes 25 Vll

3 viii Contents Strontium and Osmium Isotopes Nonisotopic Geochemical Methods Cadmium Analysis Greenhouse Gas Analysis of Trapped Air in Ice Cores Chemical and Biological Constituents and Dust Layers in Ice Cores Dating the Proxy Evidence (Geochronometry) 27 3 A SURVEY OF GLOBAL PALEOCLIMATIC VARIATIONS The Phanerozoic Eon (Past 600 My) The Cenozoic Era (Past 65 My) The Plio-Pleistocene (Past 5 My) Variations during the Last Ice Age: IRD Events The Last Glacial Maximum (20 ka) Postglacial Changes: The Past 20 ky The Past 100 Years The Generalized Spectrum of Climatic Variance A Qualitative Discussion of Causes 44 4 GENERAL THEORETICAL CONSIDERATIONS The Fundamental Equations Time Averaging and Stochastic Forcing Response Times and Equilibrium Spatial Averaging Climatic-Mean Mass and Energy Balance Equations The Water Mass Balance Energy Balance 65 5 SPECIAL THEORETICAL CONSIDERATIONS FOR PALEOCLIMATE: Structuring a Dynamical Approach A Basic Problem: Noncalculable Levels of Energy and Mass Flow An Overall Strategy Notational Simplifications for Resolving Total Climate Variability A Structured Dynamical Approach The External Forcing Function, F Astronomical/Cosmic Forcing Tectonic Forcing 82

4 Contents ix 6 BASIC CONCEPTS OF DYNAMICAL SYSTEMS ANALYSIS: Prototypical Climatic Applications Local (or Internal) Stability The Generic Cubic Nonlinearity Structural (or External) Stability: Elements of Bifurcation Theory Multivariable Systems The Two-Variable Phase Plane A Prototype Two-Variable Model Sensitivity of Equilibria to Changes in Parameters: Prediction of the Second Kind Structural Stability The Prototype Two-Variable System as a Stochastic-Dynamical System: Effects of Random Forcing The Stochastic Amplitude Structural Stochastic Stability More Than Two-Variable Systems: Deterministic Chaos 108 PART II Physics of the Separate Domains 7 MODELING THE ATMOSPHERE AND SURFACE STATE AS FAST-RESPONSE COMPONENTS The General Circulation Model Lower Resolution Models: Statistical-Dynamical Models and the Energy Balance Model A Zonal-Average SDM Axially Asymmetric SDMs The Complete Time-Average State Thermodynamic Models Radiative-Convective Models Vertically Averaged Models (the EBM) The Basic Energy Balance Model Equilibria and Dynamical Properties of the Zero-Dimensional (Global Average) EBM Stochastic Resonance The One-Dimensional (Latitude-Dependent) EBM Transitivity Properties of the Atmospheric and Surface Climatic State: Inferences from a GCM Closure Relationships Based on GCM Sensitivity Experiments 134

5 x Contents Surface Temperature Sensitivity Formal Feedback Analysis of the Fast-Response Equilibrium State Paleoclimatic Simulations THE SLOW-RESPONSE "CONTROL" VARIABLES: An Overview The Ice Sheets Key Variables Observations Greenhouse Gases: Carbon Dioxide The Thermohaline Ocean State A Three-Dimensional Phase-Space Trajectory GLOBAL DYNAMICS OF THE ICE SHEETS Basic Equations and Boundary Conditions A Scale Analysis The Vertically Integrated Ice-Sheet Model The Surface Mass Balance Basal Temperature and Melting Deformable Basal Regolith Ice Streams and Ice Shelves Bedrock Depression Sea Level Change and the Ice Sheets: The Depression-Calving Hypothesis Paleoclimatic Applications of the Vertically Integrated Model A Global Dynamical Equation for Ice Mass DYNAMICS OF ATMOSPHERIC CO The Air-Sea Flux, Q^ Qualitative Analysis of the Factors Affecting Q^ Mathematical Formulation of the Ocean Carbon Balance A Parameterization for Q^ Terrestrial Organic Carbon Exchange, W^ Sea Level Change Effects Thermal Effects Ice Cover Effects Long-Term Terrestrial Organic Burial, W^ The Global Mass Balance of Organic Carbon 196

6 Contents xi 10.3 Outgassing Processes, V^ Rock Weathering Downdraw, W^ A Global Dynamical Equation for Atmospheric CO Modeling the Tectonically Forced CO2 Variations, jit: Long-Term Rock Processes The Long-Term Oceanic Carbon Balance The GEOCARB Model Overview of the Full Global Carbon Cycle SIMPLIFIED DYNAMICS OF THE THERMOHALINE OCEAN STATE General Equations Boundary Conditions A Prototype Four-Box Ocean Model The Wind-Driven, Local-Convective, and Baroclinic Eddy Circulations The Wind-Driven Circulation: Gyres and Upwelling Local Convective Overturnings and Baroclinic Eddy Circulations The Two-Box Thermohaline Circulation Model: Possible Bimodality of the Ocean State The Two-Box System A Simple Model of the TH Circulation Meridional Fluxes Dynamical Analysis of the Two-Box Model Integral Equations for the Deep Ocean State The Deep Ocean Temperature The Deep Ocean Salinity Global Dynamical Equations for the Thermohaline State: 6 and S^ 229 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 The Unified Model: A Paleoclimate Dynamics Model Feedback-Loop Representation Elimination of the Fast-Response Variables: The Center Manifold 241

7 xii Contents 12.4 Sources of Instability: The Dissipative Rate Constants Formal Separation into Tectonic Equilibrium and Departure Equations FORCED EVOLUTION OF THE TECTONIC-MEAN CLIMATIC STATE Effects of Changing Solar Luminosity and Rotation Rate Solar Luminosity (5) Rotation Rate ($2) General Effects of Changing Land-Ocean Distribution and Topography (h) Effects of Long-Term Variations of Volcanic and Cosmic Dust and Bolides Multimillion-Year Evolution of CO The GEOCARB Solution First-Order Response of Global Ice Mass and Deep Ocean Temperature to Tectonic CO 2 Variations Possible Role of Salinity-Driven Instability of the Tectonic- Mean State Snapshot Atmospheric and Surficial Equilibrium Responses to Prescribed y-fields Using GCMs THE LATE CENOZOIC ICE-AGE DEPARTURES: An Overview of Previous Ideas and Models General Review: Forced vs. Free Models Models in Which Earth-Orbital Forcing Is Necessary Instability-Driven (Auto-oscillatory) Models Hierarchical Classification in Terms of Increasing Physical Complexity Forced Ice-Line Models (Box 1, Fig. 14-1) Ice-Sheet Inertia Models The Simplest Forms (Box 2) More Physically Based Ice-Sheet Models: First Applications Direct Bedrock Effects (Box 3) Bedrock-Calving Effects (Box 4) Basal Meltwater and Sliding (Box 5) Ice Streams and Ice Shelf Effects Continental Ice-Sheet Movement (Box 6) Three-Dimensional (X, ip, h\) Ice-Sheet Models The Need for Enhancement of the Coupled Ice-Sheet/Atmospheric Climate Models 271

8 Contents xiii 14.5 Ice-Sheet Variables Coupled with Additional Slow-Response Variables Regolith Mass, m r (Box 7) The Deep Ocean Temperature 0 (Box 8) The Salinity Gradient S<p (Box 9) Carbon Dioxide, \x (Box 10) Earlier History Quantitative Revival of the Carbon Dioxide Hypothesis Summary A GLOBAL THEORY OF THE LATE CENOZOIC ICE AGES: Glacial Onset and Oscillation Specialization of the Model The 100-ky Oscillation as a Free Response: Determination of the Adjustable Parameters Nondimensional Form Internal Stability Analysis to Locate a Free 100-ky-Period Oscillation in Parameter Space Milankovitch Forcing of the Free Oscillation Structural Stability as a Function of the Tectonic CO2 Level A More Complete Solution Predictions Robustness and Sensitivity Summary: A Revival of the CO2 Theory of the Ice Ages MILLENNIAL-SCALE VARIATIONS Theory of Heinrich Oscillations The "Binge-Purge" Model Scale Analysis of the Factors Influencing 7B Diagnostic Analysis Dynamical Analysis: A Simple Heinrich-Scale Oscillator Dynamics of the D-O Scale Oscillations CLOSING THOUGHTS: EPILOGUE Toward a More Complete Theory Epilogue: The "Ice Ages" and "Physics" 318 Bibliography 321 Index 343 List of Volumes in the Series 351