Energy Balance Climate Models (Wiley Series in Atmospheric Physics and Remote Sensing)

Energy Balance Climate Models Written by renowned experts in the field, this first book to focus exclusively on energy balance climate models provides a concise overview of the topic. It covers all major aspects, from the simplest zero-dimensional models, proceeding to horizontally and vertically resolved models. The text begins with global average models, which are explored in terms of their elementary forms yielding the global average temperature, right up to the incorporation of feedback mechanisms and some analytical properties of interest. The eff ect of stochastic forcing is then used to introduce natural variability in the models before turning to the concept of stability theory. Other one dimensional or zonally averaged models are subsequently presented, along with various applications, including chapters on paleoclimatology, the inception of continental glaciations, detection of signals in the climate system, and optimal estimation of large scale quantities from point scale data. Throughout the book, the authors work on two mathematical levels: qualitative physical expositions of the subject material plus optional mathematical sections that include derivations and treatments of the equations along with some proofs of stability theorems. A must-have introduction for policy makers, environmental agencies, and NGOs, as well as climatologists, molecular physicists, and meteorologists. 3.5 Radiative Equilibrium -- 3.6 Simplified Model for Water Vapor Absorber -- 3.7 Cooling Rates -- 3.8 Solutions for Uniform-Slab Absorbers -- 3.9 Vertical Heat Conduction -- 3.9.1 K>0 -- 3.10 Convective Adjustment Models -- 3.11 Lessons from Simple Radiation Models -- 3.12 Criticism of the Gray Spectrum -- 3.13 Aerosol Particles -- Notes for Further Reading -- Exercises -- Chapter 4 Greenhouse Effect and Climate Feedbacks -- 4.1 Greenhouse Effect without Feedbacks -- 4.2 Infrared Spectra of Outgoing Radiation -- 4.2.1 Greenhouse Gases and the Record -- 4.2.2 Greenhouse Gas Computer Experiments -- 4.3 Summary of Assumptions and Simplifications -- 4.4 Log Dependence of the CO2 Forcing -- 4.5 Runaway Greenhouse Effect -- 4.6 Climate Feedbacks and Climate Sensitivity -- 4.6.1 Equilibrium Feedback Formalism -- 4.7 Water Vapor Feedback -- 4.8 Ice Feedback for the Global Model -- 4.9 Probability Density of Climate Sensitivity -- 4.10 Middle Atmosphere Temperature Profile -- 4.10.1 Middle Atmosphere Responses to Forcings -- 4.11 Conclusion -- Notes for Further Reading -- Exercises -- Chapter 5 Latitude Dependence -- 5.1 Spherical Coordinates -- 5.2 Incoming Solar Radiation -- 5.3 Extreme Heat Transport Cases -- 5.4 Heat Transport Across Latitude Circles -- 5.5 Diffusive Heat Transport -- 5.6 Deriving the Legendre Polynomials -- 5.6.1 Properties of Legendre Polynomials -- 5.6.2 Fourier-Legendre Series -- 5.6.3 Irregular Solutions -- 5.7 Solution of the Linear Model with Constant Coefficients -- 5.8 The Two-Mode Approximation -- 5.9 Poleward Transport of Heat -- 5.10 Budyko's Transport Model -- 5.11 Ring Heat Source -- 5.12 Advanced Topic: Formal Solution for More General Transports -- 5.13 Ice Feedback in the Two-Mode Model -- 5.14 Polar Amplification through Ice Cap Feedback -- 5.15 Chapter Summary -- 5.15.1 Parameter Count -- Notes for Further Reading Cover -- Title Page -- Copyright -- Dedication -- Contents -- Preface -- Chapter 1 Climate and Climate Models -- 1.1 Defining Climate -- 1.2 Elementary Climate System Anatomy -- 1.3 Radiation and Climate -- 1.3.1 Solar Radiation -- 1.3.2 Albedo of the Earth-Atmosphere System -- 1.3.3 Terrestrial Infrared Radiation into Space (The IR or Longwave Radiation) -- 1.4 Hierarchy of Climate Models -- 1.4.1 General Circulation Models (GCMs) -- 1.4.2 Energy Balance Climate Models -- 1.4.3 Adjustable Parameters in Phenomenological Models -- 1.5 Greenhouse Effect and Modern Climate Change -- 1.6 Reading This Book -- 1.7 Cautionary Note and Disclaimer -- Notes on Further Reading -- Exercises -- Chapter 2 Global Average Models -- 2.1 Temperature and Heat Balance -- 2.1.1 Blackbody Earth -- 2.1.2 Budyko's Empirical IR Formula -- 2.1.3 Climate Sensitivity -- 2.1.4 Climate Sensitivity and Carbon Dioxide -- 2.2 Time Dependence -- 2.2.1 Frequency Response of Global Climate -- 2.2.2 Forcing with Noise -- 2.2.3 Predictability from Initial Conditions -- 2.2.4 Probability Density of the Temperature -- 2.3 Spectral Analysis -- 2.3.1 White Noise Spectral Density -- 2.3.2 Spectral Density and Lagged Correlation -- 2.3.3 AR1 Climate Model Spectral Density -- 2.3.4 Continuous Time Case -- 2.4 Nonlinear Global Model -- 2.4.1 Ice-Albedo Feedback -- 2.4.2 Linear Stability Analysis: A Slope/Stability Theorem -- 2.4.3 Relaxation Time and Sensitivity -- 2.4.4 Finite Amplitude Stability Analysis -- 2.4.5 Potential Function and Noise Forcing -- 2.4.6 Relation to Critical Opalescence -- 2.5 Summary -- Suggestions for Further Reading -- Exercises -- Chapter 3 Radiation and Vertical Structure -- 3.1 Radiance and Radiation Flux Density -- 3.2 Equation of Transfer -- 3.2.1 Extinction and Emission -- 3.2.2 Terrestrial Radiation -- 3.3 Gray Atmosphere -- 3.4 Plane-Parallel Atmosphere Exercises -- Chapter 6 Time Dependence in the 1-D Models -- 6.1 Differential Equation for Time Dependence -- 6.2 Decay of Anomalies -- 6.2.1 Decay of an Arbitrary Anomaly -- 6.3 Seasonal Cycle on a Homogeneous Planet -- 6.4 Spread of Diffused Heat -- 6.4.1 Evolution on a Plane -- 6.5 Random Winds and Diffusion -- 6.6 Numerical Methods -- 6.6.1 Explicit Finite Difference Method -- 6.6.2 Semi-Implicit Method -- 6.7 Spectral Methods -- 6.7.1 Galerkin or Spectral Method -- 6.7.2 Pseudospectral Method -- 6.8 Summary -- 6.8.1 Parameter Count -- Notes for Further Reading -- Exercises -- 6.9 Appendix to Chapter 6: Solar Heating Distribution -- 6.9.1 The Elliptical Orbit of the Earth -- 6.9.2 Relation Between Declination and Obliquity -- 6.9.3 Expansion of S( , t) -- Chapter 7 Nonlinear Phenomena in EBMs -- 7.1 Formulation of the Nonlinear Feedback Model -- 7.2 Stürm-Liouville Modes -- 7.2.1 Orthogonality of SL Modes -- 7.3 Linear Stability Analysis -- 7.4 Finite Perturbation Analysis and Potential Function -- 7.4.1 Neighborhood of an Extremum -- 7.4.2 Relation to Gibbs Energy or Entropy -- 7.4.3 Attractor Basins-Numerical Example -- 7.5 Small Ice Cap Instability -- 7.5.1 Perturbation of an Exact Ice-Free Solution -- 7.5.2 Frequency Dependence of the Length Scale -- 7.6 Snow Caps and the Seasonal Cycle -- 7.7 Mengel's Land-Cap Model -- 7.8 Chapter Summary -- Notes for Further Reading -- Exercises -- Chapter 8 Two Horizontal Dimensions and Seasonality -- 8.1 Beach Ball Seasonal Cycle -- 8.2 Eigenfunctions in the Bounded Plane -- 8.3 Eigenfunctions on the Sphere -- 8.3.1 Laplacian Operator on the Sphere -- 8.3.2 Longitude Functions -- 8.3.3 Latitude Functions -- 8.4 Spherical Harmonics -- 8.4.1 Orthogonality -- 8.4.2 Truncation -- 8.5 Solution of the EBM with Constant Coefficients -- 8.6 Introducing Geography -- 8.7 Global Sinusoidal Forcing 8.8 Two-Dimensional Linear Seasonal Model -- 8.8.1 Adjustment of Free Parameters -- 8.9 Present Seasonal Cycle Comparison -- 8.9.1 Annual Cycle -- 8.9.2 Semiannual Cycle -- 8.10 Chapter Summary -- Notes for Further Reading -- Exercises -- Chapter 9 Perturbation by Noise -- 9.1 Time-Independent Case for a Uniform Planet -- 9.2 Time-Dependent Noise Forcing for a Uniform Planet -- 9.3 Green's Function on the Sphere: f=0 -- 9.4 Apportionment of Variance at a Point -- 9.5 Stochastic Model with Realistic Geography -- 9.6 Thermal Decay Modes with Geography -- 9.6.1 Statistical Properties of TDMs -- Notes for Further Reading -- Exercises -- Chapter 10 Time-Dependent Response and the Ocean -- 10.1 Single-Slab Ocean -- 10.1.1 Examples with a Single Slab -- 10.1.2 Eventual Leveling of the Forcing -- 10.2 Penetration of a Periodic Heating at the Surface -- 10.3 Two-Slab Ocean -- 10.3.1 Decay of an Anomaly with Two Slabs -- 10.3.2 Response to Ramp Forcing with Two Slabs -- 10.4 Box-Diffusion Ocean Model -- 10.5 Steady State of Upwelling-Diffusion Ocean -- 10.5.1 All-Ocean Planetary Responses -- 10.5.2 Ramp Forcing -- 10.6 Upwelling Diffusion with (and without) Geography -- 10.7 Influence of Initial Conditions -- 10.8 Response to Periodic Forcing with Upwelling Diffusion Ocean -- 10.9 Summary and Conclusions -- Exercises -- Chapter 11 Applications of EBMs: Optimal Estimation -- 11.1 Introduction -- 11.2 Independent Estimators -- 11.3 Estimating Global Average Temperature -- 11.3.1 Karhunen-Loève Functions and Empirical Orthogonal Functions -- 11.3.2 Relationship with EBMs -- 11.4 Deterministic Signals in the Climate System -- 11.4.1 Signal and Noise -- 11.4.2 Fingerprint Estimator of Signal Amplitude -- 11.4.3 Optimal Weighting -- 11.4.4 Interfering Signals -- 11.4.5 All Four Signals Simultaneously -- 11.4.6 EBM-Generated Signals

Written by renowned experts in the field, this first book to focus exclusively on energy balance climate models provides a concise overview of the topic. It covers all major aspects, from the simplest zero-dimensional models, proceeding to horizontally and vertically resolved models.
The text begins with global average models, which are explored in terms of their elementary forms yielding the global average temperature, right up to the incorporation of feedback mechanisms and some analytical properties of interest. The effect of stochastic forcing is then used to introduce natural variability in the models before turning to the concept of stability theory. Other one dimensional or zonally averaged models are subsequently presented, along with various applications, including chapters on paleoclimatology, the inception of continental glaciations, detection of signals in the climate system, and optimal estimation of large scale quantities from point scale data. Throughout the book, the authors work on two mathematical levels: qualitative physical expositions of the subject material plus optional mathematical sections that include derivations and treatments of the equations along with some proofs of stability theorems.
A must-have introduction for policy makers, environmental agencies, and NGOs, as well as climatologists, molecular physicists, and meteorologists.

Annotation Written by renowned experts in the field, this first book to focus exclusively on energy balance climate models provides a concise overview of the topic. It covers all major aspects, from the simplest zero-dimensional models, proceeding to horizontally and vertically resolved models. The text begins with global average models, which are explored in terms of their elementary forms yielding the global average temperature, right up to the incorporation of feedback mechanisms and some analytical properties of interest. The effect of stochastic forcing is then used to introduce natural variability in the models before turning to the concept of stability theory. Other one dimensional or zonally averaged models are subsequently presented, along with various applications, including chapters on paleoclimatology, the inception of continental glaciations, detection of signals in the climate system, and optimal estimation of large scale quantities from point scale data. Throughout the book, the authors work on two mathematical levels: qualitative physical expositions of the subject material plus optional mathematical sections that include derivations and treatments of the equations along with some proofs of stability theorems. A must-have introduction for policy makers, environmental agencies, and NGOs, as well as climatologists, molecular physicists, and meteorologists 11.4.7 Characterizing Natural Variability -- 11.4.8 Detection Results -- 11.4.8.1 Convergence -- 11.4.9 Discussion of the Detection Results -- Notes for Further Reading -- Exercises -- Chapter 12 Applications of EBMs: Paleoclimate -- 12.1 Paleoclimatology -- 12.1.1 Interesting Problems for EBMs -- 12.2 Precambrian Earth -- 12.3 Glaciations in the Permian -- 12.3.1 Modeling Permian Glacials -- 12.4 Glacial Inception on Antarctica -- 12.5 Glacial Inception on Greenland -- 12.6 Pleistocene Glaciations and Milankovitch -- 12.6.1 EBMs in the Pleistocene: Short's Filter -- 12.6.2 Last Interglacial -- 12.6.3 EBMs and Ice Volume -- 12.6.4 What Can Be Done without Ice Volume -- Notes for Further Reading -- Exercises -- References -- Index -- EULA