Preface CLIMATE AND CLIMATE MODELS Defining Climate Elementary Climate System Anatomy Radiation and Climate Hiercharchy of Climate Models Greenhouse Effect and Modern Climate ChangeReading this Book Cautionary Note and Disclaimer Notes on Further Reading GLOBAL AVERAGE MODELS Temperature and Heat Balance Time Dependence Spectral Analysis Nonlinear Global Model Summary RADIATION AND VERTICAL STRUCTURE Radiance and Radiation Flux Density Equation of Transfer Gray Atmosphere Plane Parallel Atmosphere Radiative Equilibrium Simplified Model for Water Vapor Absorber Cooling Rates Solutions for Uniform-Slab Absorbers Vertical Heat Conduction Convective Adjustment Models Lessons from Simple Radiation Models Criticism of the Gray Spectrum Aerosol Particles GREENHOUSE EFFECT AND CLIMATE FEEDBACKS Greenhouse Effect without Feedbacks Infrared Spectra of Outgoing Radiation Summary of Assumptions and Simplifications Log Dependence of the CO2 Forcing Runaway Greenhouse Effect Climate Feedbacks and Climate Sensitivity Water Vapor Feedback Ice Feedback for the Global Model Probability Density of Climate Sensitivity Middle Atmosphere Temperature Profile Conclusion Notes for Further Reading LATITUDE DEPENDENCE Spherical Coordinates Incoming Solar Radiation Extreme Heat Transport Cases Heat Transport Across Latitude Circles Diffusive Heat Transport Deriving the Legendre Polynomials Solution of the Linear Model with Constant Coefficients The Two-Mode Approximation Poleward Transport of Heat Budyko's Transport Model Ring Heat Source Advanced Topic: Formal Solution for More General Transports Ice Feedback in the 2-Mode Model Polar Amplification through Icecap Feedback Chapter Summary TIME DEPENDENCE IN THE 1-D MODEL Differential Equation for Time Dependence Decay of Anomalies Seasonal Cycle on a Homogeneous Planet Spread of Diffused Heat Random Winds and Diffusion Numerical Methods Spectral Methods Chapter Summary Appendix: Solar Heating Distribution NONLINEAR PHENOMENA IN EBMS Formulation of the Nonlinear Feedback Model Stürm-Liouville Modes Linear Stability Analysis Finite Perturbation Analysis and Potential Function Small Ice Cap InstabilitySnow Caps and the Seasonal Cycle Mengel's Land Cap Model Chapter Summary TWO HORIZONTAL DIMENSIONS AND SEASONALITY Beach Ball Seasonal Cycle Eigenfunctions in the Bounded Plane Eigenfunctions on the Sphere Spherical Harmonics Solutions of the EBM with Constant Coefficients Introducing Geography Global Sinusoidal Forcing Two Dimensional Linear Seasonal Model Present Seasonal Cycle Comparison Chapter Summary PERTURBATION BY NOISE Time-Independent Case for Uniform Planet Time-Dependent Noise Forcing for Uniform Planet Green's Function on the Sphere: f=0 Apportionment of Variance at a Point Stochastic Model with Realistic Geography Thermal Decay Modes with Geography TIME-DEPENDENT RESPONSE AND THE OCEAN Single-Slab Ocean Penetration of a Periodic Heating at the Surface Two-Slab Ocean Box-Diffusion Ocean Model Steady State of Upwelling-Diffusion Ocean Upwelling Diffusion with (and without) Geography Influence of Initial Conditions Response to Periodic Forcing with Upwelling Diffusion Ocean Summary and Conclusions APPLICATIONS OF EBSM: OPTIMAL ESTIMATION Introduction Independet Estimators Estimating Global Average Temperature Deterministic Signals in the Climate System APPLICATIONS OF EBMS: PALEOCLIMATE Paleoclimatology Precambrian Earth Glaciations in the Permian Glacial Inception on Antarctica Clacial Inception on Greenland Pleistocene Glaciations and Milankovic