Energy Balance Climate Models

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.

Auteur

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 19952003. 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 PhD 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.

Contenu

Preface xiii

1 Climate and Climate Models 1

1.1 Defining Climate 3

1.2 Elementary Climate System Anatomy 7

1.3 Radiation and Climate 9

1.3.1 Solar Radiation 9

1.3.2 Albedo of the EarthAtmosphere System 13

1.3.3 Terrestrial Infrared Radiation into Space (The IR or Longwave Radiation) 14

1.4 Hierarchy of Climate Models 15

1.4.1 General Circulation Models (GCMs) 16

1.4.2 Energy Balance Climate Models 17

1.4.3 Adjustable Parameters in Phenomenological Models 19

1.5 Greenhouse Effect and Modern Climate Change 20

1.6 Reading This Book 20

1.7 Cautionary Note and Disclaimer 22

Notes on Further Reading 23

Exercises 23

2 Global Average Models 27

2.1 Temperature and Heat Balance 27

2.1.1 Blackbody Earth 28

2.1.2 Budyko's Empirical IR Formula 29

2.1.3 Climate Sensitivity 30

2.1.4 Climate Sensitivity and Carbon Dioxide 31

2.2 Time Dependence 31

2.2.1 Frequency Response of Global Climate 32

2.2.2 Forcing with Noise 35

2.2.3 Predictability from Initial Conditions 37

2.2.4 Probability Density of the Temperature 39

2.3 Spectral Analysis 40

2.3.1 White Noise Spectral Density 41

2.3.2 Spectral Density and Lagged Correlation 41

2.3.3 AR1 Climate Model Spectral Density 42

2.3.4 Continuous Time Case 42

2.4 Nonlinear Global Model 44

2.4.1 Ice-Albedo Feedback 44

2.4.2 Linear Stability Analysis: A Slope/Stability Theorem 46

2.4.3 Relaxation Time and Sensitivity 47

2.4.4 Finite Amplitude Stability Analysis 48

2.4.5 Potential Function and Noise Forcing 49

2.4.6 Relation to Critical Opalescence 52

2.5 Summary 52

Suggestions for Further Reading 53

Exercises 53

3 Radiation and Vertical Structure 57

3.1 Radiance and Radiation Flux Density 58

3.2 Equation of Transfer 61

3.2.1 Extinction and Emission 61

3.2.2 Terrestrial Radiation 62

3.3 Gray Atmosphere 63

3.4 Plane-Parallel Atmosphere 64

3.5 Radiative Equilibrium 65

3.6 Simplified Model for Water Vapor Absorber 68

3.7 Cooling Rates 72

3.8 Solutions for Uniform-Slab Absorbers 73

3.9 Vertical Heat Conduction 75

3.9.1 K > 0 77

3.10 Convective Adjustment Models 77

3.11 Lessons from Simple Radiation Models 79

3.12 Criticism of the Gray Spectrum 80

3.13 Aerosol Particles 82

Notes for Further Reading 83

Exercises 83

4 Greenhouse Effect and Climate Feedbacks 85

4.1 Greenhouse Effect without Feedbacks 85

4.2 Infrared Spectra of Outgoing Radiation 85

4.2.1 Greenhouse Gases and the Record 92

4.2.2 Greenhouse Gas Computer Experiments 92

4.3 Summary of Assumptions and Simplifications 99

4.4 Log Dependence of the CO 2 Forcing 101

4.5 Runaway Greenhouse Effect 102

4.6 Climate Feedbacks and Climate Sensitivity 105

4.6.1 Equilibrium Feedback Formalism 107

4.7 Water Vapor Feedback 108

4.8 Ice Feedback for the Global Model 109

4.9 Probability Density of Climate Sensitivity 110

4.10 Middle Atmosphere Temperature Profile 112

4.10.1 Middle Atmosphere Responses to Forcings 113

4.11 Conclusion 115

Notes for Further Reading 116

Exercises 116

5 Latitude Dependence 119

5.1 Spherical Coordinates 120

5.2 Incoming Solar Radiation 121

5.3 Extreme Heat Transport Cases 122

5.4 Heat Transport Across Latitude Circles 122

5.5 Diffusive Heat Transport 123

5.6 Deriving the Legendre Polynomials 125

5.6.1 Properties of Legendre Polynomials 127 5.6.2 FourierLegendre Series 128&lt...