Energy Balance Climate Models (eBook)

Gerald R. North is University Distinguished Professor of Atmospheric Sciences Emeritus at Texas A&M University, having obtained his BS degree in physics from the University of Tennessee, PhD (1966) in theoretical physics from the University of Wisconsin, Madison. Among other positions he served eight years as research scientist at Goddard Space Flight Center before joining Texas A&M in 1986, where he served as department head 1995-2003. He is a fellow of AAAS, AGU, AMS, and recipient of several awards including the Jule G. Charney Award of the American Meteorology Society. He has served as Editor in Chief of the Reviews of Geophysics and Editor in Chief of the Encyclopedia of the Atmospheric Sciences, 2nd Edition. He has coauthored books on Paleoclimatology and Atmospheric Thermodynamics. Kwang-Yul Kim is a professor in climatology and physical oceanography at Seoul National University. Upon graduation from Texas A&M with his Ph.D. degree in physical oceanography he was inducted into the Phi Kappa Phi Honor Society. He authored two books: Fundamentals of Fluid Dynamics and Cyclostationary EOF Analysis. He programmed several new energy balance models.

Preface

CLIMATE AND CLIMATE MODELS
Defining Climate
Elementary Climate System Anatomy
Radiation and Climate
Hiercharchy of Climate Models
Greenhouse Effect and Modern Climate Change
Reading 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 Instability
Snow 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