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Energy Balance Climate Models

Book Description

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.


Table of Contents

  1. Wiley Series in Atmospheric Physics and Remote Sensing
  2. Title Page
  3. Copyright
  4. Dedication
  5. Preface
  6. Chapter 1: Climate and Climate Models
    1. 1.1 Defining Climate
    2. 1.2 Elementary Climate System Anatomy
    3. 1.3 Radiation and Climate
    4. 1.4 Hierarchy of Climate Models
    5. 1.5 Greenhouse Effect and Modern Climate Change
    6. 1.6 Reading This Book
    7. 1.7 Cautionary Note and Disclaimer
    8. Notes on Further Reading
  7. Chapter 2: Global Average Models
    1. 2.1 Temperature and Heat Balance
    2. 2.2 Time Dependence
    3. 2.3 Spectral Analysis
    4. 2.4 Nonlinear Global Model
    5. 2.5 Summary
    6. Suggestions for Further Reading
  8. Chapter 3: Radiation and Vertical Structure
    1. 3.1 Radiance and Radiation Flux Density
    2. 3.2 Equation of Transfer
    3. 3.3 Gray Atmosphere
    4. 3.4 Plane-Parallel Atmosphere
    5. 3.5 Radiative Equilibrium
    6. 3.6 Simplified Model for Water Vapor Absorber
    7. 3.7 Cooling Rates
    8. 3.8 Solutions for Uniform-Slab Absorbers
    9. 3.9 Vertical Heat Conduction
    10. 3.10 Convective Adjustment Models
    11. 3.11 Lessons from Simple Radiation Models
    12. 3.12 Criticism of the Gray Spectrum
    13. 3.13 Aerosol Particles
    14. Notes for Further Reading
  9. Chapter 4: Greenhouse Effect and Climate Feedbacks
    1. 4.1 Greenhouse Effect without Feedbacks
    2. 4.2 Infrared Spectra of Outgoing Radiation
    3. 4.3 Summary of Assumptions and Simplifications
    4. 4.4 Log Dependence of the Forcing
    5. 4.5 Runaway Greenhouse Effect
    6. 4.6 Climate Feedbacks and Climate Sensitivity
    7. 4.7 Water Vapor Feedback
    8. 4.8 Ice Feedback for the Global Model
    9. 4.9 Probability Density of Climate Sensitivity
    10. 4.10 Middle Atmosphere Temperature Profile
    11. 4.11 Conclusion
    12. Notes for Further Reading
    13. Exercises
  10. Chapter 5: Latitude Dependence
    1. 5.1 Spherical Coordinates
    2. 5.2 Incoming Solar Radiation
    3. 5.3 Extreme Heat Transport Cases
    4. 5.4 Heat Transport Across Latitude Circles
    5. 5.5 Diffusive Heat Transport
    6. 5.6 Deriving the Legendre Polynomials
    7. 5.7 Solution of the Linear Model with Constant Coefficients
    8. 5.8 The Two-Mode Approximation
    9. 5.9 Poleward Transport of Heat
    10. 5.10 Budyko's Transport Model
    11. 5.11 Ring Heat Source
    12. 5.12 Advanced Topic: Formal Solution for More General Transports
    13. 5.13 Ice Feedback in the Two-Mode Model
    14. 5.14 Polar Amplification through Ice Cap Feedback
    15. 5.15 Chapter Summary
    16. Notes for Further Reading
  11. Chapter 6: Time Dependence in the 1-D Models
    1. 6.1 Differential Equation for Time Dependence
    2. 6.2 Decay of Anomalies
    3. 6.3 Seasonal Cycle on a Homogeneous Planet
    4. 6.4 Spread of Diffused Heat
    5. 6.5 Random Winds and Diffusion
    6. 6.6 Numerical Methods
    7. 6.7 Spectral Methods
    8. 6.8 Summary
    9. Notes for Further Reading
    10. Exercises
    11. 6.9 Appendix to Chapter 6: Solar Heating Distribution
  12. Chapter 7: Nonlinear Phenomena in EBMs
    1. 7.1 Formulation of the Nonlinear Feedback Model
    2. 7.2 Stürm–Liouville Modes
    3. 7.3 Linear Stability Analysis
    4. 7.4 Finite Perturbation Analysis and Potential Function
    5. 7.5 Small Ice Cap Instability
    6. 7.6 Snow Caps and the Seasonal Cycle
    7. 7.7 Mengel's Land-Cap Model
    8. 7.8 Chapter Summary
    9. Notes for Further Reading
    10. Exercises
  13. Chapter 8: Two Horizontal Dimensions and Seasonality
    1. 8.1 Beach Ball Seasonal Cycle
    2. 8.2 Eigenfunctions in the Bounded Plane
    3. 8.3 Eigenfunctions on the Sphere
    4. 8.4 Spherical Harmonics
    5. 8.5 Solution of the EBM with Constant Coefficients
    6. 8.6 Introducing Geography
    7. 8.7 Global Sinusoidal Forcing
    8. 8.8 Two-Dimensional Linear Seasonal Model
    9. 8.9 Present Seasonal Cycle Comparison
    10. 8.10 Chapter Summary
    11. Notes for Further Reading
    12. Exercises
  14. Chapter 9: Perturbation by Noise
    1. 9.1 Time-Independent Case for a Uniform Planet
    2. 9.2 Time-Dependent Noise Forcing for a Uniform Planet
    3. 9.3 Green's Function on the Sphere:
    4. 9.4 Apportionment of Variance at a Point
    5. 9.5 Stochastic Model with Realistic Geography
    6. 9.6 Thermal Decay Modes with Geography
    7. Notes for Further Reading
    8. Exercises
  15. Chapter 10: Time-Dependent Response and the Ocean
    1. 10.1 Single-Slab Ocean
    2. 10.2 Penetration of a Periodic Heating at the Surface
    3. 10.3 Two-Slab Ocean
    4. 10.4 Box-Diffusion Ocean Model
    5. 10.5 Steady State of Upwelling-Diffusion Ocean
    6. 10.6 Upwelling Diffusion with (and without) Geography
    7. 10.7 Influence of Initial Conditions
    8. 10.8 Response to Periodic Forcing with Upwelling Diffusion Ocean
    9. 10.9 Summary and Conclusions
    10. Exercises
  16. Chapter 11: Applications of EBMs: Optimal Estimation
    1. 11.1 Introduction
    2. 11.2 Independent Estimators
    3. 11.3 Estimating Global Average Temperature
    4. 11.4 Deterministic Signals in the Climate System
    5. Notes for Further Reading
    6. Exercises
  17. Chapter 12: Applications of EBMs: Paleoclimate
    1. 12.1 Paleoclimatology
    2. 12.2 Precambrian Earth
    3. 12.3 Glaciations in the Permian
    4. 12.4 Glacial Inception on Antarctica
    5. 12.5 Glacial Inception on Greenland
    6. 12.6 Pleistocene Glaciations and Milankovitch
    7. Notes for Further Reading
    8. Exercises
  18. References
  19. Index
  20. End User License Agreement