ALBERT

Anmerkung: Contents: Contributors. - Preface. - Introduction and Scientific Background / J.C.R. Hunt, J. Norbury and I. Roulstone. - 1. A view of the equations of meteorological dynamics and various approximations / A. A. White. - 2. Extended-geostrophic Euler-Poincare models for mesoscale oceanographic flow / J. S. Allen, D. D. Holm and P. A. Newberger. - 3. Fast singular oscillating limits of stably-stratified 3D Euler and Navier-Stokes equations and ageostrophic wave fronts / A. Babin, A. Mahalov and B. Nicolaenko. - 4. New mathematical developments in atmosphere and ocean dynamics, and their application to computer simulations / M. J. P. Cullen. - 5. Rearrangements of functions with applications to meteorology and ideal fluid flow / R. J. Douglas. - 6. Statistical methods in atmospheric dynamics: probability metrics and discrepancy measures as a means of defining balance / S. Baigent and J. Norbury.

Anmerkung: Contents Introduction 1 Climatic System: Data, Processes, Scales, and Deterministic Models 1.1 Main Components of the Climate System 1.1.1 "Thick" Subsystems 1.1.2 "Thin" Subsystems 1.1.3 Local and Discrete Objects 1.2 Climate Processes 1.2.1 Overview of Climate Processes 1.2.2 External Climate Mechanisms 1.2.3 Internal Mechanisms of Climatie Variations 1.2.4 Transfer-Accumulation Processes 1.3 Scales of Climatic Variability 1.3.1 Spatial Scales 1.3.2 Temporal Scales 1.4 Deterministic Climate Models 1.4.1 General Circulation Models and Coupled Models 1.4.2 Other Types of Climate Models 1.5 Observational Basis for Stochastic Climate Theory 1.5.1 Data on Variability of "Thick" Climatic Subsystems 1.5.1.1 Near-Surface Air Temperature 1.5.1.2 Other Atmospheric Variables 1.5.1.3 Sea Surface Temperature 1.5.1.4 Sea Level 1.5.1.5 lce Sheets 1.5.2 Data on Variables of Thin Earth Covers 1.5.2.1 Snow Cover 1.5.2.2 Sea lce 1.5.2.3 Vegetation Cover 1.5.3 Data on Discrete and Local Climatic Objects 1.5.3.1 River Runoff 1.5.3.2 Lakes 1.5.3.3 Mountain Glaciers 1.5.4 Conclusions on Observational Data 2 Theoretical Foundations of the Stochastic Approach to Climate Variability Studies 2.1 Basic Ideas and Principles of the Stochastic Climate Theory 2.1.1 Mathematical Models and Natural Processes 2.1.2 A Climatic Variable as a Random Variable 2.1.3 Evolution of a Climatic Variable as a Random Function 2.1.4 Stationarity of Climatic Processes 2.2 Introduction to the Theory of Random Functions with Emphasis on Climate Variability 2.2.1 Moments, Mean Value, Correlation Function 2.2.2 The Ergodicity of Climate Variability 2.2.3 Examples of Stationary Random Sequences 2.2.3.1 Uncorrelated Random Variables 2.2.3.2 Moving Averages 2.2.4 Spectral Representation of the Random Process 2.2.5 Climatic Meanings of the Spectral Distribution Function 2.2.6 Spectral Representation of Stationary Sequences 2.2.7 The Markov Sequence 2.2.8 The Discrete Wiener Process 2.2.9 Other Types of Random Functions 2.2.9.1 Autoregressive Models 2.2.9.2 Seasonal Models 2.2.9.3 Threshold Models 2.3 Estimation of Model Parameters 2.3.1 Theoretical Models and the Practice of Model Identification 2.3.2 Informational Approach to the Identification of Stochastic Models 2.3.3 Maximum Entropy Method and Autoregressive Models 2.3.4 Model Identification and Estimation of Model Parameters 2.3.5 An Example ofModel Identification and Parameter Estimation 2.3.6 Frequency Truncation Method of Normalized Spectral Estimates 2.3.7 Other Methods of Time Series Processing 2.3.7.1 Conventional Methods. Moving Average and ARMA models 2.3.7.2 "Deterministic Chaos". Other Methods of Nonlinear Analysis 2.4 Physical Basis of the Stochastic Climate Theory 2.4.1 Atmospheric Forcing ofthe Climate System 2.4.1.1 Observational Evidence 2.4.1.2 Atmospheric Model Results 2.4.1.3 Simple Nonlinear Model as Analog of Atmospheric Forcing 2.4.2 Hasselmann's Stochastic Climate Models 2.4.2.1 Hypothesis on Weather-Climate Two-Scale Separation 2.4.2.2 Classification of Climate Models 2.4.2.3 Analogies with Turbulent Fluid, Brownian Motion, and Other Physical Processes. The Central Limit Theorem 2.4.2.4 Spectra and Correlation Functions of the Stochastic Climate Models. Models Without Feedback 2.4.2.5 Models with Feedback 3 Stochastic Models of Recent Climatic Changes 3.1 Changes in Thick Climatic Subsystems 3.1.1 Local Changes 3.1.1.1 Analysis of Observational Data 3.1.1.2 Local Stochastic Dynamical Models 3.1.2 Regional, Spatially Averaged, and Two-Dimensional Patterns 3.1.2.1 20 Stochastic Patterns of Observational Data 3.1.2.2 Stochastic Dynamical Regional Models 3.1.2.3 Stochastic Models of ENSO Events 3.1.3 Globally Averaged Climate Variables 3.1.3.1 Global Water Mass Exchange. Global Mean Sea Level 3.1.3.2 Global Temperatures 3.1.3.3 "Minus Two" Law of Climatic Variability 3.1.3.4 Stochastic Dynamical Models of Global Temperatures 3.1.3.5 Local-Global Polarization Phenomenon 3.2 Variabilities of Thin Climatic Subsystems 3.2.1 Analyzed Oata 3.2.1.1 37 GHz Polarization Oifference and Related Data 3.2.1.2 Snow and Sea lce Remotely Sensed Data 3.2.1.3 Related Satellite-Based and Conventional Data on Global Air and Sea Temperatures 3.2.2 Comparison of Results for Remotely Sensed and Conventional Data 3.2.2.1 Comparison of Results on Local Scales 3.2.2.2 Globally Averaged 37 GHz Polarization Difference Data. Concentration of Carbon Dioxide in the Atmosphere 3.2.3 Results of Stochastic Analysis of Local and Regional Hydrological Changes 3.2.3.1 Results of 37 GHz PD Data Analysis for Floodable Areas 3.2.3.2 Results for 37 GHz PD Data on Vegetation Cover in Different Natural Zones 3.2.4 Results of Analysis of Global Changes in Hydrological and Related Parameters 3.2.5 Modeling the Dynamics of Thin Subsystems 3.2.6 Local-Global Polarization Phenomenon and Thin Climatic Subsystems 3.2.7 Discussion on the Global Climatic Subsystems 3.3 Changes in Local and Discrete Climatic Objects 3.3.1 Rivers and River Runoff 3.3.2 Mountain Glaciers 4 Stochastic Models for Glacial Cycles 4.1 Stochastic Analysis of Reconstructed Data on Glacial Cycles 4.1.1 Existing Paleoreconstructed Time Series 4.1.2 Results of Stochastic Analysis of the Last Deglaciation Period, 0 - 18 ka B.P. 4.1.3 Analysis of 200 - 300 ka Time Series 4.1.4 Longer Time Series. Features of Cyclicity 4.1.5 High Resolution Paleorecords 4.2 Zero-Dimensional Model of Glacial Cycles 4.2.1 Hypotheses, Assumptions, and Equations 4.2.2 Results of Numerical Experiments 4.3 Two-Dimensional Stochastic Dynamical Model of Glacial Cycles 4.3.1 Mathematical Model, Parameters, and Experiments 4.3.1.1 Computational Area 4.3.1.2 Equations and Parameters of the Model 4.3.1.3 Numerical Experiments 4.3.2 Results 4.3.2.1 Experiments Without External Forcing 4.3.2.2 Experiments With External Forcing. Globally Averaged Results 4.3.2.3 Zonally Averaged Results 4.3.2.4 Regional Results Conclusion References Index

Anmerkung: Contents List of Contributors Preface Acknowledgements 1. Determining Timescales for Groundwater Flow and Solute Transport / Peter G. Cook and John-Karl Bohlke 2. Inorganic Ions as Tracers / Andrew L. Herczeg and W. Mike Edmunds 3. Isotope Engineering - Using Stable Isotopes of the Water Molecule to Solve Practical Problems / Tyler B. Coplen, Andrew L. Herczeg and Chris Barnes 4. Radiocarbon Dating of Groundwater Systems / Robert M. Kalin 5. U-Series Nuclides as Tracers in Groundwater Hydrology / J. Kenneth Osmond and James B. Cowart 6. Radon-222 / L. DeWayne Cecil and Jaromy R. Green 7. Sulphur and Oxygen Isotopes in Sulphate / H. Roy Krouse and Bernhard Mayer 8. Strontium Isotopes / Robert H. McNutt 9. Nitrate Isotopes in Groundwater Systems / Carol Kendall and Ramon Aravena 10. Chlorine-36 / Fred M. Phillips 11. Atmospheric Noble Gases / Martin Stute and Peter Schlosser 12. Noble Gas Radioisotopes: 37Ar, 85 Kr, 39Ar, 81 Kr / Heinz H. Loosli, Bernhard E. Lehmann and William M. Smethie, Jr. 13. 3H and 3He / D. Kip Solomon and Peter G. Cook 14. 4He in Groundwater / D. Kip Solomon 15. Chlorofluorocarbons / L. Niel Plummer and Eurybiades Busenberg 16. δ11 B, Rare Earth Elements, δ 37Cl, 32 Si, 35S, 129I / Avner Vengosh, Arthur J. Spivack, Kevin J. Johannesson, W. Berry Lyons, Tamie R. Weaver, Uwe Morgenstern, Robert L. Michel, June Fabryka-Martin Appendix 1: Stable Isotope Notation and Fractionation Appendix 2: Decay Constants and Half-Lives of Radioactive Isotopes Appendix 3: Solubilities of Environmental Gas Tracers Appendix 4: Liquid and Gas-Phase Diffusion Coefficients Index

Anmerkung: Contents List of Acronyms List of Symbols Foreword Preface Prologue Chapter 1 Introduction to Ocean Dynamics 1.1 Types, Advantages, and Limitations of Ocean Models 1.2 Recent Examples 1.3 Governing Equations 1.4 Vorticity Conservation 1.5 Nondimensional Numbers and Scales of Motion 1.6 Geostrophic Flow and Thermal Wind 1.7 Inertial Motions 1.8 Ekman Layers 1.9 Sverdrup Transport 1.10 Western Boundary Intensification (Stommel Solution) 1.11 Gyre Scale Circulation (Munk Solution) 1.12 Barotropic Currents over Topography 1.13 Baroclinic Transport over Topography 1.14 Coastal Upwelling and Fronts 1.15 Mesoscale Eddies and Variability 1.16 Thermohaline Circulation and Box (Reservoir) Models 1.17 Numerical Models Chapter 2 Introduction to Numerical Solutions 2.1 Introduction 2.1.1 Architecture 2.1.2 Computational Errors 2.2 Ordinary Differential Equations 2.2.1 Runge-Kutta Method 2.3 Partial.Differential Equations 2.3.1 Consistency, Convergence, and Stability 2.3.2 Elliptic, Hyperbolic, and Parabolic Systems 2.4 Elliptic Equations and Steady-State Problems 2.4.1 Direct Solvers 2.4.2 Iterative Solvers and Relaxation Methods 2.4.3 Preconditioned Conjugate Gradient Method 2.4.4 Multigrid Methods 2.4.5 Pseudo-transient Method 2.5 Time Dependent Problems 2.5.1 Advection Equation and Hyperbolic Systems 2.5.2 Diffusion Equation and Parabolic Systems 2.6 Finite-Difference (Grid Point) Methods 2.6.1 Staggered Grids 2.6.2 Time Differencing and Filtering 2.6.3 Computational Grids 2.7 Spectral (Spectral Transform) Methods 2.8 Finite-Element Methods 2.8.1 Spectral Element Approach 2.9 Parameterization of Subgrid Scale Processes 2.10 Lateral Open Boundary Conditions 2.11 Computational Issues 2.12 Examples 2.12.1 Inertial Oscillations 2.12.2 Thermohaline Circulation 2.12.3 Normal Modes 2.12.4 Gyre Scale Circulation 2.12.5 Advection Problems 2.12.6 M.I.T. Nonhydrostatic Global Model Chapter 3 Equatorial Dynamics and Reduced Gravity Models Solutions 3.1 Oceanic Dynamical Response to Forcing 3.2 Governing Equations 3.3 Equatorial Waves 3.3.1 Kelvin Waves 3.3.2 Yanai Waves 3.3.3 Rossby Waves 3.3.4 Inertia-Gravity (Poincare) Waves 3.4 Equatorial Currents 3.5 Reduced Gravity Model of Equatorial Processes Chapter 4 Midlatitude Dynamics and Quasi-Geostrophic Models 4.1 Linear Motions 4.1.1 Inertia-Gravity (Sverdrup/Poincare) Waves 4.1.2 Kelvin Waves 298 4.1.3 Planetary Ross by Waves 4.1.4 Topographic Rossby Waves 4.2 Continuous Stratification 4.3 Geostrophic Adjustment and Instabilities 4.3.1 Geostrophic Adjustment 4.3.2 Instabilities 4.4 Spinup 4.5 Quasi-Geostrophic Models 4.5.1 Governing Equations 4.5.2 Applications Chapter 5 High-Latitude Dynamics and Sea-Ice Models 5.1 Salient Features of Ice Cover 5.2 Momentum Equations for Sea Ice 5.3 Constitutive Law for Sea Ice (Ice Rheology) 5.3.1 Viscous-Plastic Ice Rheology 5.3.2 Elastic-Viscous-Plastic Ice Rheology 5.4 Continuity Equations for Sea Ice 5.5 Response of Sea Ice to Storm Passage 5.6 Numerics 5.6.1 Governing Equations in Orthogonal Curvilinear Coordinates 5.6.2 Solution Technique Chapter 6 Tides and Tidal Modeling 6.1 Description of Tides 6.2 Formulation: Tidal Potential 6.3 Body, Load, Atmospheric, and Radiational Tides 6.3.1 Body (Solid Earth) Tides 6.3.2 Load Tides 6.3.3 Atmospheric Tides 6.3.4 Radiational Tides 6.4 Dynamical Theory of Tides: Laplace Tidal Equations 6.5 Equilibrium Theory of Tides 6.6 Tidal Analysis: Orthotides 6.7 Tidal Currents 6.8 Global Tidal Models 6.9 Regional Tidal Models 6.10 Geophysical Implications 6.10.1 Tidal Dissipation and LOD 6.10.2 Tidal Energetics 6.11 Changes in Earth's Rotation 6.12 Baroclinic (Internal) Tides 6.13 Long-Period Tides 6.14 Shallow Water Tides and Residual Currents 6.15 Summary Chapter 7 Coastal Dynamics and Barotropic Models 7.1 Wind- and Buoyancy-Driven Currents 7.2 Tidal Motions 7.3 Continental Shelf Waves 7.4 Modeling Shelf Circulation 7.5 Barotropic Models 7.5.1 Coastal Ocean Response to Wind Forcing 7.5.2 Storm Surges and Storm Surge Modeling 7.5.3 Response to Pressure Forcing Chapter 8 Data and Data Processing 8.1 In Situ Observational Data 8.1.1 XBT, CTD, CM, ADCP, and Drifter Data 8.1.2 Historical Hydrographic Data 8.1.3 Historical Marine Surface Data 8.2 Remotely Sensed Data 8.2.1 Sea Surface Temperature from IR Sensors 8.2.2 Sea Surface Winds from Microwave Sensors 8.2.3 Chlorophyll and Optical Clarity from Color Sensors 8.2.4 Sea Surface Height from Satellite Altimetry 8.3 NWP Products 8.4 Preprocessing of Observational Data and Postprocessing of Model Output 8.4.1 Graphics and Visualization of Model Output 8.4.2 Analyses Chapter 9 Sigma-Coordinate Regional and Coastal Models 9.1 Introduction 9.2 Governing Equations 9.3 Vertical Mixing 9.4 Boundary Conditions 9.5 Mode Splitting 9.6 Numerics 9.6.1 Vertical Direction 9.6.2 Horizontal Direction 9.7 Numerical Problems 9.8 Applications 9.9 Code Structure Chapter 10 Multilevel Basin Scale and Global Models 10.1 Introduction 10.2 Governing Equations 10.3 Isopycnal Diffusion 10.4 Architecture and Other Model Features 10.5 Applications 10.6 Hybrid s-Coordinate Models 10.7 Regional z-Level Models Chapter 11 Layered and Isopycnal Models 11.1 Layered Models 11.2 Isopycnal Models Chapter 12 Ice-Ocean Coupled Models 12.1 Sea-Ice Models 12.2 Coupled Ice-Ocean Models Chapter 13 Ocean-Atmosphere Coupled Models 13.1 Coupling between the Ocean and the Atmosphere 13.2 Coupled Ocean-Atmosphere General Circulation Models 13.3 Regional Coupled Ocean-Atmosphere Models Chapter 14 Data Assimilation and Nowcasts/ Forecasts 14.1 Introduction 14.2 Direct Insertion 14.3 Nudging 14.4 Statistical Assimilation Schemes 14.4.1 Kalman Filter 14.4.2 Reduced State Space Kalman Filters 14.4.3 Optimal Interpolation (OI) Scheme 14.5 Variational Methods 14.5.1 Adjoint Models 14.6 Predictability of Nonlinear Systems-Low Order Paradigms 14.7 Nowcasts/Forecasts in the Gulf of Mexico Appendix A Equations of State A.1 Equation of State for the Ocean A.2 Equation of State for the Atmosphere Appendix B Wavelet Transforms B.1 Introduction B.1.1 Theory B.1.2 Continuous Wavelet Transforms (CWT) B.1.3 Discrete Wavelet Transforms (DWT) B.2 Examples B.3 Wavelet Transforms and Stochastic Processes B.4 Two-Dimensional Wavelet Transforms B.5 Cross Wavelet Transforms (CrWT) B.6 Error Analysis Appendix C Empirical Orthogonal Functions and Empirical Normal Modes C.1 Empirical Orthogonal Functions C.1.1 Complex EOFs C.1.2 Singular Spectrum Analysis C.1.3 Extended EOFs C.1.4 Coupled Pattern Analysis C.2 Empirical Normal Modes Appendix D Units and Constants D.1 Useful Quantities D.1.1 SI (International System of Units) Units and Conventions D.1.2 Useful Conversion Factors D.1.3 Useful Universal Constants D.1.4 Useful Geodetic Constants D.1.5 Useful Physical Constants D.1.6 Useful Dynamical Quantities D.2 Important Scales and Quantities D.2.1 Length Scales D.2.2 Timescales D.2.3 Velocity Scales D.2.4 Nondimensional Quantities D.3 Useful Websites References Biographies Index