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Energy Balance Climate Models [Hardback]

(Texas A&M University, Texas, USA), (Seoul National University, Seoul, Korea)
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Energy Balance Climate ModelsPalielināt
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Permanent link: https://www.kriso.lv/db/9783527411320.html
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.
Preface xiii
1 Climate and Climate Models 1(26)
1.1 Defining Climate
3(4)
1.2 Elementary Climate System Anatomy
7(2)
1.3 Radiation and Climate
9(6)
1.3.1 Solar Radiation
9(4)
1.3.2 Albedo of the Earth-Atmosphere System
13(1)
1.3.3 Terrestrial Infrared Radiation into Space (The IR or Longwave Radiation)
14(1)
1.4 Hierarchy of Climate Models
15(5)
1.4.1 General Circulation Models (GCMs)
16(1)
1.4.2 Energy Balance Climate Models
17(2)
1.4.3 Adjustable Parameters in Phenomenological Models
19(1)
1.5 Greenhouse Effect and Modern Climate Change
20(1)
1.6 Reading This Book
20(2)
1.7 Cautionary Note and Disclaimer
22(1)
Notes on Further Reading
23(1)
Exercises
23(4)
2 Global Average Models 27(30)
2.1 Temperature and Heat Balance
27(4)
2.1.1 Blackbody Earth
28(1)
2.1.2 Budyko's Empirical IR Formula
29(1)
2.1.3 Climate Sensitivity
30(1)
2.1.4 Climate Sensitivity and Carbon Dioxide
31(1)
2.2 Time Dependence
31(9)
2.2.1 Frequency Response of Global Climate
32(3)
2.2.2 Forcing with Noise
35(2)
2.2.3 Predictability from Initial Conditions
37(2)
2.2.4 Probability Density of the Temperature
39(1)
2.3 Spectral Analysis
40(4)
2.3.1 White Noise Spectral Density
41(1)
2.3.2 Spectral Density and Lagged Correlation
41(1)
2.3.3 AR1 Climate Model Spectral Density
42(1)
2.3.4 Continuous Time Case
42(2)
2.4 Nonlinear Global Model
44(8)
2.4.1 Ice-Albedo Feedback
44(2)
2.4.2 Linear Stability Analysis: A Slope/Stability Theorem
46(1)
2.4.3 Relaxation Time and Sensitivity
47(1)
2.4.4 Finite Amplitude Stability Analysis
48(1)
2.4.5 Potential Function and Noise Forcing
49(3)
2.4.6 Relation to Critical Opalescence
52(1)
2.5 Summary
52(1)
Suggestions for Further Reading
53(1)
Exercises
53(4)
3 Radiation and Vertical Structure 57(28)
3.1 Radiance and Radiation Flux Density
58(3)
3.2 Equation of Transfer
61(2)
3.2.1 Extinction and Emission
61(1)
3.2.2 Terrestrial Radiation
62(1)
3.3 Gray Atmosphere
63(1)
3.4 Plane-Parallel Atmosphere
64(1)
3.5 Radiative Equilibrium
65(3)
3.6 Simplified Model for Water Vapor Absorber
68(4)
3.7 Cooling Rates
72(1)
3.8 Solutions for Uniform-Slab Absorbers
73(2)
3.9 Vertical Heat Conduction
75(2)
3.9.1 K > 0
77(1)
3.10 Convective Adjustment Models
77(2)
3.11 Lessons from Simple Radiation Models
79(1)
3.12 Criticism of the Gray Spectrum
80(2)
3.13 Aerosol Particles
82(1)
Notes for Further Reading
83(1)
Exercises
83(2)
4 Greenhouse Effect and Climate Feedbacks 85(34)
4.1 Greenhouse Effect without Feedbacks
85(1)
4.2 Infrared Spectra of Outgoing Radiation
85(14)
4.2.1 Greenhouse Gases and the Record
92(1)
4.2.2 Greenhouse Gas Computer Experiments
92(7)
4.3 Summary of Assumptions and Simplifications
99(2)
4.4 Log Dependence of the CO2 Forcing
101(1)
4.5 Runaway Greenhouse Effect
102(3)
4.6 Climate Feedbacks and Climate Sensitivity
105(3)
4.6.1 Equilibrium Feedback Formalism
107(1)
4.7 Water Vapor Feedback
108(1)
4.8 Ice Feedback for the Global Model
109(1)
4.9 Probability Density of Climate Sensitivity
110(2)
4.10 Middle Atmosphere Temperature Profile
112(3)
4.10.1 Middle Atmosphere Responses to Forcings
113(2)
4.11 Conclusion
115(1)
Notes for Further Reading
116(1)
Exercises
116(3)
5 Latitude Dependence 119(26)
5.1 Spherical Coordinates
120(1)
5.2 Incoming Solar Radiation
121(1)
5.3 Extreme Heat Transport Cases
122(1)
5.4 Heat Transport Across Latitude Circles
122(1)
5.5 Diffusive Heat Transport
123(2)
5.6 Deriving the Legendre Polynomials
125(4)
5.6.1 Properties of Legendre Polynomials
127(1)
5.6.2 Fourier-Legendre Series
128(1)
5.6.3 Irregular Solutions
128(1)
5.7 Solution of the Linear Model with Constant Coefficients
129(1)
5.8 The Two-Mode Approximation
129(4)
5.9 Poleward Transport of Heat
133(1)
5.10 Budyko's Transport Model
134(2)
5.11 Ring Heat Source
136(1)
5.12 Advanced Topic: Formal Solution for More General Transports
137(1)
5.13 Ice Feedback in the Two-Mode Model
138(2)
5.14 Polar Amplification through Ice Cap Feedback
140(1)
5.15
Chapter Summary
141(1)
5.15.1 Parameter Count
142(1)
Notes for Further Reading
142(1)
Exercises
142(3)
6 Time Dependence in the 1-D Models 145(30)
6.1 Differential Equation for Time Dependence
146(1)
6.2 Decay of Anomalies
146(2)
6.2.1 Decay of an Arbitrary Anomaly
147(1)
6.3 Seasonal Cycle on a Homogeneous Planet
148(5)
6.4 Spread of Diffused Heat
153(4)
6.4.1 Evolution on a Plane
155(2)
6.5 Random Winds and Diffusion
157(2)
6.6 Numerical Methods
159(4)
6.6.1 Explicit Finite Difference Method
159(3)
6.6.2 Semi-Implicit Method
162(1)
6.7 Spectral Methods
163(3)
6.7.1 Galerkin or Spectral Method
163(1)
6.7.2 Pseudospectral Method
164(2)
6.8 Summary
166(1)
6.8.1 Parameter Count
166(1)
Notes for Further Reading
167(1)
Exercises
167(2)
6.9 Appendix to
Chapter 6: Solar Heating Distribution
169(6)
6.9.1 The Elliptical Orbit of the Earth
171(1)
6.9.2 Relation Between Declination and Obliquity
172(1)
6.9.3 Expansion of S(mu, tau)
172(3)
7 Nonlinear Phenomena in EBMs 175(28)
7.1 Formulation of the Nonlinear Feedback Model
176(2)
7.2 Sturm-Liouville Modes
178(2)
7.2.1 Orthogonality of SL Modes
179(1)
7.3 Linear Stability Analysis
180(4)
7.4 Finite Perturbation Analysis and Potential Function
184(3)
7.4.1 Neighborhood of an Extremum
185(2)
7.4.2 Relation to Gibbs Energy or Entropy
187(1)
7.4.3 Attractor Basins-Numerical Example
187(1)
7.5 Small Ice Cap Instability
187(6)
7.5.1 Perturbation of an Exact Ice-Free Solution
190(1)
7.5.2 Frequency Dependence of the Length Scale
191(2)
7.6 Snow Caps and the Seasonal Cycle
193(1)
7.7 Mengel's Land-Cap Model
193(3)
7.8
Chapter Summary
196(3)
Notes for Further Reading
199(1)
Exercises
199(4)
8 Two Horizontal Dimensions and Seasonality 203(26)
8.1 Beach Ball Seasonal Cycle
203(2)
8.2 Eigenfunctions in the Bounded Plane
205(3)
8.3 Eigenfunctions on the Sphere
208(3)
8.3.1 Laplacian Operator on the Sphere
208(1)
8.3.2 Longitude Functions
209(1)
8.3.3 Latitude Functions
209(2)
8.4 Spherical Harmonics
211(1)
8.4.1 Orthogonality
211(1)
8.4.2 Truncation
212(1)
8.5 Solution of the EBM with Constant Coefficients
212(2)
8.6 Introducing Geography
214(2)
8.7 Global Sinusoidal Forcing
216(1)
8.8 Two-Dimensional Linear Seasonal Model
217(3)
8.8.1 Adjustment of Free Parameters
219(1)
8.9 Present Seasonal Cycle Comparison
220(1)
8.9.1 Annual Cycle
220(1)
8.9.2 Semiannual Cycle
220(1)
8.10
Chapter Summary
220(4)
Notes for Further Reading
224(1)
Exercises
224(5)
9 Perturbation by Noise 229(24)
9.1 Time-Independent Case for a Uniform Planet
230(4)
9.2 Time-Dependent Noise Forcing for a Uniform Planet
234(1)
9.3 Green's Function on the Sphere: f = 0
235(2)
9.4 Apportionment of Variance at a Point
237(1)
9.5 Stochastic Model with Realistic Geography
238(5)
9.6 Thermal Decay Modes with Geography
243(5)
9.6.1 Statistical Properties of TDMs
246(2)
Notes for Further Reading
248(1)
Exercises
249(4)
10 Time-Dependent Response and the Ocean 253(34)
10.1 Single-Slab Ocean
254(5)
10.1.1 Examples with a Single Slab
255(3)
10.1.2 Eventual Leveling of the Forcing
258(1)
10.2 Penetration of a Periodic Heating at the Surface
259(3)
10.3 Two-Slab Ocean
262(7)
10.3.1 Decay of an Anomaly with Two Slabs
266(2)
10.3.2 Response to Ramp Forcing with Two Slabs
268(1)
10.4 Box-Diffusion Ocean Model
269(2)
10.5 Steady State of Upwelling-Diffusion Ocean
271(3)
10.5.1 All-Ocean Planetary Responses
273(1)
10.5.2 Ramp Forcing
274(1)
10.6 Upwelling Diffusion with (and without) Geography
274(2)
10.7 Influence of Initial Conditions
276(1)
10.8 Response to Periodic Forcing with Upwelling Diffusion Ocean
277(3)
10.9 Summary and Conclusions
280(2)
Exercises
282(5)
11 Applications of EBMs: Optimal Estimation 287(34)
11.1 Introduction
287(1)
11.2 Independent Estimators
288(2)
11.3 Estimating Global Average Temperature
290(8)
11.3.1 Karhunen-Loeve Functions and Empirical Orthogonal Functions
292(4)
11.3.2 Relationship with EBMs
296(2)
11.4 Deterministic Signals in the Climate System
298(19)
11.4.1 Signal and Noise
299(1)
11.4.2 Fingerprint Estimator of Signal Amplitude
299(1)
11.4.3 Optimal Weighting
299(3)
11.4.4 Interfering Signals
302(1)
11.4.5 All Four Signals Simultaneously
303(3)
11.4.6 EBM-Generated Signals
306(4)
11.4.7 Characterizing Natural Variability
310(1)
11.4.8 Detection Results
311(3)
11.4.9 Discussion of the Detection Results
314(3)
Notes for Further Reading
317(1)
Exercises
317(4)
12 Applications of EBMs: Paleoclimate 321(32)
12.1 Paleoclimatology
321(4)
12.1.1 Interesting Problems for EBMs
322(3)
12.2 Precambrian Earth
325(2)
12.3 Glaciations in the Permian
327(4)
12.3.1 Modeling Permian Glacials
327(4)
12.4 Glacial Inception on Antarctica
331(2)
12.5 Glacial Inception on Greenland
333(2)
12.6 Pleistocene Glaciations and Milankovitch
335(15)
12.6.1 EBMs in the Pleistocene: Short's Filter
338(8)
12.6.2 Last Interglacial
346(2)
12.6.3 EBMs and Ice Volume
348(2)
12.6.4 What Can Be Done without Ice Volume
350(1)
Notes for Further Reading
350(1)
Exercises
351(2)
References 353(12)
Index 365
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.