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E-grāmata: Mathematical and Physical Fundamentals of Climate Change

(Taishan Distinguished Professor, Shandong University, China), (Research Professor, University of Lapland, Finland; Chief Scientist & Research Professor, Beijing Normal University, China)
  • Formāts: EPUB+DRM
  • Izdošanas datums: 06-Dec-2014
  • Izdevniecība: Elsevier Science Publishing Co Inc
  • Valoda: eng
  • ISBN-13: 9780128005835
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Mathematical and Physical Fundamentals of Climate ChangePalielināt
  • Formāts: EPUB+DRM
  • Izdošanas datums: 06-Dec-2014
  • Izdevniecība: Elsevier Science Publishing Co Inc
  • Valoda: eng
  • ISBN-13: 9780128005835
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Mathematical and Physical Fundamentals of Climate Change is the first book to provide an overview of the math and physics necessary for scientists to understand and apply atmospheric and oceanic models to climate research. The book begins with basic mathematics then leads on to specific applications in atmospheric and ocean dynamics, such as fluid dynamics, atmospheric dynamics, oceanic dynamics, and glaciers and sea level rise.Mathematical and Physical Fundamentals of Climate Change provides a solid foundation in math and physics with which to understand global warming, natural climate variations, and climate models. This book informs the future users of climate models and the decision-makers of tomorrow by providing the depth they need. Developed from a course that the authors teach at Beijing Normal University, the material has been extensively class-tested and contains online resources, such as presentation files, lecture notes, solutions to problems and MATLab codes.
  • Includes MatLab and Fortran programs that allow readers to create their own models
  • Provides case studies to show how the math is applied to climate research
  • Online resources include presentation files, lecture notes, and solutions to problems in book for use in classroom or self-study

Papildus informācija

Mathematical and Physical Fundamentals of Climate Change is the first book to provide an overview of the math and physics necessary for scientists to understand and apply atmospheric and oceanic models to climate research.
Preface: Interdisciplinary Approaches to Climate Change Research xi
1 Fourier Analysis
1.1 Fourier Series and Fourier Transform
1(17)
1.2 Bessel's Inequality and Parseval's Identity
18(4)
1.3 Gibbs Phenomenon
22(4)
1.4 Poisson Summation Formulas and Shannon Sampling Theorem
26(9)
1.5 Discrete Fourier Transform
35(3)
1.6 Fast Fourier Transform
38(4)
1.7 Heisenberg Uncertainty Principle
42(3)
1.8 Case Study: Arctic Oscillation Indices
45(4)
Problems
46(1)
Bibliography
47(2)
2 Time-Frequency Analysis
2.1 Windowed Fourier Transform
49(2)
2.2 Wavelet Transform
51(4)
2.3 Multiresolution Analyses and Wavelet Bases
55(10)
2.3.1 Multiresolution Analyses
55(5)
2.3.2 Discrete Wavelet Transform
60(2)
2.3.3 Biorthogonal Wavelets, Bivariate Wavelets, and Wavelet Packet
62(3)
2.4 Hilbert Transform, Analytical Signal, and Instantaneous Frequency
65(6)
2.5 Wigner-Ville Distribution and Cohen's Class
71(4)
2.6 Empirical Mode Decompositions
75(4)
Problems
76(1)
Bibliography
77(2)
3 Filter Design
3.1 Continuous Linear Time-Invariant Systems
79(3)
3.2 Analog Filters
82(3)
3.3 Discrete Linear Time-Invariant Systems
85(8)
3.3.1 Discrete Signals
85(1)
3.3.2 Discrete Convolution
86(1)
3.3.3 Discrete System
87(3)
3.3.4 Ideal Digital Filters
90(1)
3.3.5 Z-Transforms
90(2)
3.3.6 Linear Difference Equations
92(1)
3.4 Linear-Phase Filters
93(4)
3.4.1 Four Types of Linear-Phase Filters
95(1)
3.4.2 Structure of Linear-Phase Filters
96(1)
3.5 Designs of FIR Filters
97(4)
3.5.1 Fourier Expansions
98(1)
3.5.2 Window Design Method
99(1)
3.5.3 Sampling in the Frequency Domain
100(1)
3.6 MR Filters
101(3)
3.6.1 Impulse Invariance Method
101(2)
3.6.2 Matched Z-Transform Method
103(1)
3.6.3 Bilinear Transform Method
103(1)
3.7 Conjugate Mirror Filters
104(7)
Problems
108(1)
Bibliography
108(3)
4 Remote Sensing
4.1 Solar and Thermal Radiation
111(2)
4.2 Spectral Regions and Optical Sensors
113(2)
4.3 Spatial Filtering
115(1)
4.4 Spatial Blurring
116(1)
4.5 Distortion Correction
117(2)
4.6 Image Fusion
119(1)
4.7 Supervised and Unsupervised Classification
120(1)
4.8 Remote Sensing of Atmospheric Carbon Dioxide
121(1)
4.9 Moderate Resolution Imaging Spectroradiometer Data Products and Climate Change
122(3)
Problems
123(1)
Bibliography
123(2)
5 Basic Probability and Statistics
5.1 Probability Space, Random Variables, and Their Distributions
125(7)
5.1.1 Discrete Random Variables
126(1)
5.1.2 Continuous Random Variables
127(1)
5.1.3 Properties of Expectations and Variances
128(1)
5.1.4 Distributions of Functions of Random Variables
129(1)
5.1.5 Characteristic Functions
130(2)
5.2 Jointly Distributed Random Variables
132(3)
5.3 Central Limit Theorem and Law of Large Numbers
135(3)
5.4 Minimum Mean Square Error
138(2)
5.5 x2-Distribution, t-Distribution, and F-Distribution
140(3)
5.6 Parameter Estimation
143(5)
5.7 Confidence Interval
148(1)
5.8 Tests of Statistical Hypotheses
149(1)
5.9 Analysis of Variance
150(4)
5.10 Linear Regression
154(1)
5.11 Mann-Kendall Trend Test
155(6)
Problems
158(1)
Bibliography
159(2)
6 Empirical Orthogonal Functions
6.1 Random Vector Fields
161(2)
6.2 Classical EOFs
163(8)
6.3 Estimation of EOFs
171(2)
6.4 Rotation of EOFs
173(5)
6.5 Complex EOFs and Hilbert EOFs
178(4)
6.6 Singular Value Decomposition
182(3)
6.7 Canonical Correlation Analysis
185(4)
6.8 Singular Spectrum Analysis
189(2)
6.9 Principal Oscillation Patterns
191(8)
6.9.1 Normal Modes
191(3)
6.9.2 Estimates of Principal Oscillation Patterns
194(1)
Problems
195(1)
Bibliography
196(3)
7 Random Processes and Power Spectra
7.1 Stationary and Non-stationary Random Processes
199(4)
7.2 Markov Process and Brownian Motion
203(4)
7.3 Calculus of Random Processes
207(7)
7.4 Spectral Analysis
214(7)
7.4.1 Linear Time-Invariant System for WSS Processes
214(2)
7.4.2 Power Spectral Density
216(3)
7.4.3 Shannon Sampling Theorem for Random Processes
219(2)
7.5 Wiener Filtering
221(3)
7.6 Spectrum Estimation
224(5)
7.7 Significance Tests of Climatic Time Series
229(10)
7.7.1 Fourier Power Spectra
229(3)
7.7.2 Wavelet Power Spectra
232(4)
Problems
236(1)
Bibliography
236(3)
8 Autoregressive Moving Average Models
8.1 ARMA Processes
239(9)
8.1.1 AR(p) Processes
240(1)
8.1.2 MA(q) Processes
241(3)
8.1.3 Shift Operator
244(1)
8.1.4 ARMA(p, q) Processes
245(3)
8.2 Yule-Walker Equation and Spectral Density
248(3)
8.3 Prediction Algorithms
251(10)
8.3.1 Innovation Algorithm
252(5)
8.3.2 Durbin-Lovinson Algorithm
257(3)
8.3.3 Kolmogorov's Formula
260(1)
8.4 Asymptotic Theory
261(6)
8.4.1 Gramer-Wold Device
261(4)
8.4.2 Asymptotic Normality
265(2)
8.5 Estimates of Means and Covariance Functions
267(6)
8.6 Estimation for ARMA Models
273(10)
8.6.1 General Linear Model
273(2)
8.6.2 Estimation for AR(p) Processes
275(7)
8.6.3 Estimation for ARMA(p, q) Processes
282(1)
8.7 ARIMA Models
283(2)
8.8 Multivariate ARMA Processes
285(2)
8.9 Application in Climatic and Hydrological Research
287(4)
Problems
288(1)
Bibliography
289(2)
9 Data Assimilation
9.1 Concept of Data Assimilation
291(3)
9.2 Cressman Method
294(1)
9.3 Optimal Interpolation Analysis
295(4)
9.4 Cost Function and Three-Dimensional Variational Analysis
299(5)
9.5 Dual of the Optimal Interpolation
304(1)
9.6 Four-Dimensional Variational Analysis
305(3)
9.7 Kalman Filter
308(5)
Problems
309(1)
Bibliography
310(3)
10 Fluid Dynamics
10.1 Gradient, Divergence, and Curl
313(6)
10.2 Circulation and Flux
319(2)
10.3 Green's Theorem, Divergence Theorem, and Stokes's Theorem
321(1)
10.4 Equations of Motion
322(9)
10.4.1 Continuity Equation
322(2)
10.4.2 Euler's Equation
324(4)
10.4.3 Bernoulli's Equation
328(3)
10.5 Energy Flux and Momentum Flux
331(6)
10.6 Kelvin Law
337(2)
10.7 Potential Function and Potential Flow
339(2)
10.8 Incompressible Fluids
341(6)
Problems
345(1)
Bibliography
345(2)
11 Atmospheric Dynamics
11.1 Two Simple Atmospheric Models
347(5)
11.1.1 The Single-Layer Model
349(1)
11.1.2 The Two-Layer Model
350(2)
11.2 Atmospheric Composition
352(2)
11.3 Hydrostatic Balance Equation
354(2)
11.4 Potential Temperature
356(2)
11.5 Lapse Rate
358(4)
11.5.1 Adiabatic Lapse Rate
359(1)
11.5.2 Buoyancy Frequency
360(2)
11.6 Clausius-Clapeyron Equation
362(4)
11.6.1 Saturation Mass Mixing Radio
363(1)
11.6.2 Saturation Adiabatic Lapse Rate
363(2)
11.6.3 Equivalent Potential Temperature
365(1)
11.7 Material Derivatives
366(4)
11.8 Vorticity and Potential Vorticity
370(2)
11.9 Navier-Stokes Equation
372(6)
11.9.1 Navier-Stokes Equation in an Inertial Frame
372(2)
11.9.2 Navier-Stokes Equation in a Rotating Frame
374(2)
11.9.3 Component Form of the Navier-Stokes Equation
376(2)
11.10 Geostrophic Balance Equations
378(2)
11.11 Boussinesq Approximation and Energy Equation
380(3)
11.12 Quasi-Geostrophic Potential Vorticity
383(3)
11.13 Gravity Waves
386(7)
11.13.1 Internal Gravity Waves
387(4)
11.13.2 Inertia Gravity Waves
391(2)
11.14 Rossby Waves
393(5)
11.15 Atmospheric Boundary Layer
398(9)
Problems
404(1)
Bibliography
405(2)
12 Oceanic Dynamics
12.1 Salinity and Mass
407(1)
12.2 Inertial Motion
408(1)
12.3 Oceanic Ekman Layer
409(6)
12.3.1 Ekman Currents
410(2)
12.3.2 Ekman Mass Transport
412(2)
12.3.3 Ekman Pumping
414(1)
12.4 Geostrophic Currents
415(5)
12.4.1 Surface Geostrophic Currents
415(3)
12.4.2 Geostrophic Currents from Hydrography
418(2)
12.5 Sverdrup's Theorem
420(4)
12.6 Munk's Theorem
424(4)
12.7 Taylor-Proudman Theorem
428(3)
12.8 Ocean-Wave Spectrum
431(4)
12.8.1 Spectrum
431(1)
12.8.2 Digital Spectrum
432(1)
12.8.3 Pierson-Moskowitz Spectrum
433(2)
12.9 Oceanic Tidal Forces
435(6)
Problems
437(1)
Bibliography
438(3)
13 Glaciers and Sea Level Rise
13.1 Stress and Strain
441(2)
13.2 Glen's Law and Generalized Glen's Law
443(1)
13.3 Density of Glacier Ice
444(1)
13.4 Glacier Mass Balance
445(1)
13.5 Glacier Momentum Balance
446(3)
13.6 Glacier Energy Balance
449(1)
13.7 Shallow-Ice and Shallow-Shelf Approximations
450(2)
13.8 Dynamic Ice Sheet Models
452(1)
13.9 Sea Level Rise
452(1)
13.10 Semiempirical Sea Level Models
453(4)
Problems
454(1)
Bibliography
454(3)
14 Climate and Earth System Models
14.1 Energy Balance Models
457(3)
14.1.1 Zero-Dimensional EBM
457(1)
14.1.2 One-Dimensional EBM
458(2)
14.2 Radiative Convective Models
460(1)
14.3 Statistical Dynamical Models
460(2)
14.4 Earth System Models
462(4)
14.4.1 Atmospheric Models
462(1)
14.4.2 Oceanic Models
463(2)
14.4.3 Land Surface Models
465(1)
14.4.4 Sea Ice Models
465(1)
14.5 Coupled Model Intercomparison Project
466(1)
14.6 Geoengineering Model Intercomparison Project
467(6)
Problems
470(1)
Bibliography
470(3)
Index 473
Prof. Zhangs long-standing researches focus on big earth data, climate change mechanisms, ocean dynamics, environmental evolution and sustainability. Prof Zhang has published six books as first author:

Ų Frame Theory in Data Science (Springer, 2024),

Ų Environmental Data Analysis (DeGruyter, 2nd Edition, 2023),

Ų Big Data Mining for Climate Change (Elsevier, 2020),

Ų Patterns and Mechanisms of Climate, Paleoclimate and Paleoenvironmental Change from Low-Latitude Regions (Springer, 2019),

Ų Multivariate Time Series Analysis in Climate & Environmental Research (Springer, 2018),

Ų Mathematical and Physical Fundamentals of Climate Change (Elsevier, 2015)

Prof. Zhang has published more than 80 articles, highlighting many times by New Scientist (UK), China Science Daily, and China Social Science Daily. Currently, Prof. Zhang is serving as an Editor-in-Chief of Int J Big Data Mining for Global Warming (World Scientific); an Associate Editor of Environ Dev Sustain (Springer), EURASIP J Adv Signal Process (Springer), and Int J Climate Change Strat & Manag (Emerald); and an Editorial Board Member of Earth Sci Informatics (Springer), PLoS ONE, Open Geosci (DeGruyter), Int J Global Warming (Indersci). Prof. Zhang is serving as the first track chair of Mediterranean Geosciences Union Annual Meeting (2021-now), and was invited as a plenary/keynote speaker at 2023 Mediterranean Geosciences Union Annual Meeting (Turkey) and 2024 International Conference on Intelligent Information Processing (Romania)

John C. Moore is a Research Professor at Universities of Lapland (Finland) and Uppsala (Sweden), a Chief Scientist & Research Professor, Beijing Normal University (China), Guest professor at Polar Research Institute of China, as well as the Director of Polar Climate and Environment Key Laboratory. John C. Moore has published over 100 papers, where six papers have been published in Proceedings of the National Academy of Sciences (PNAS). John C. Moores research includes climate change; past sea level change and prediction, natural and anthropogenic climate forcing, impacts of extreme climate events, and computer modelling of glacier flow and evolution. John C. Moore was Finnish representative on the International Arctic Science Committee, Glaciology Group. John Moore is the Editor-in-Chief of American Journal of Climate Change” and an Editorial Board Member of The Cryosphere”. John C. Moores research is supported by European Science Foundation, EU Northern Periphery Program, National Key Science Program for Global Change Research (China), Finnish Academy, and NSFC
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