Mathematical and physical fundamentals of climate change:
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Amsterdam [u.a.]
Elsevier
2015
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis Klappentext |
| Physical Description: | XII, 481 S. graph. Darst. |
| ISBN: | 9780128000663 012800066X |
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Record in the Search Index
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| adam_text | Titel: Mathematical and physical fundamentals of climate change
Autor: Zhang, Zhihua
Jahr: 2015
Contents
Preface: Interdisciplinary Approaches to Climate Change Research xi
1. Fourier Analysis
1.1 Fourier Series and Fourier Transform 1
1.2 Bessel s Inequality and Parseval s Identity 18
1.3 Gibbs Phenomenon 22
1.4 Poisson Summation Formulas and Shannon Sampling Theorem 26
1.5 Discrete Fourier Transform 35
1.6 Fast Fourier Transform 38
1.7 Heisenberg Uncertainty Principle 42
1.8 Case Study: Arctic Oscillation Indices 45
Problems 46
Bibliography 47
2. Time-Frequency Analysis
2.1 Windowed Fourier Transform 49
2.2 Wavelet Transform 51
2.3 Multiresolution Analyses and Wavelet Bases 55
2.3.1 Multiresolution Analyses 55
2.3.2 Discrete Wavelet Transform 60
2.3.3 Biorthogonal Wavelets, Bivariate Wavelets,
and Wavelet Packet 62
2.4 Hilbert Transform, Analytical Signal, and Instantaneous
Frequency 65
2.5 Wigner-Ville Distribution and Cohen s Class 71
2.6 Empirical Mode Decompositions 75
Problems 76
Bibliography 77
3. Filter Design
3.1 Continuous Linear Time-Invariant Systems 79
3.2 Analog Filters 82
3.3 Discrete Linear Time-Invariant Systems 85
3.3.1 Discrete Signals 85
3.3.2 Discrete Convolution 86
3.3.3 Discrete System 87
3.3.4 Ideal Digital Filters 90
3.3.5 Z-Transforms 90
3.3.6 Linear Difference Equations 92
3.4 Linear-Phase Filters 93
3.4.1 Four Types of Linear-Phase Filters 95
3.4.2 Structure of Linear-Phase Filters 96
3.5 Designs of FIR Filters 97
3.5.1 Fourier Expansions 98
3.5.2 Window Design Method 99
3.5.3 Sampling in the Frequency Domain 100
3.6 MR Filters 101
3.6.1 Impulse Invariance Method 101
3.6.2 Matched Z-Transform Method 103
3.6.3 Bilinear Transform Method 103
3.7 Conjugate Mirror Filters 104
Problems 108
Bibliography 108
4. Remote Sensing
4.1 Solar and Thermal Radiation 111
4.2 Spectral Regions and Optical Sensors 113
4.3 Spatial Filtering 115
4.4 Spatial Blurring 116
4.5 Distortion Correction 117
4.6 Image Fusion 119
4.7 Supervised and Unsupervised Classification 120
4.8 Remote Sensing of Atmospheric Carbon Dioxide 121
4.9 Moderate Resolution Imaging Spectroradiometer Data
Products and Climate Change 122
Problems 123
Bibliography 123
5. Basic Probability and Statistics
5.1 Probability Space, Random Variables, and Their Distributions 125
5.1.1 Discrete Random Variables 126
5.1.2 Continuous Random Variables 127
5.1.3 Properties of Expectations and Variances 128
5.1.4 Distributions of Functions of Random Variables 129
5.1.5 Characteristic Functions 130
5.2 Jointly Distributed Random Variables 132
5.3 Central Limit Theorem and Law of Large Numbers 135
5.4 Minimum Mean Square Error 135
8-8 X2-Distribution, f-Distribution, and F-Distribution 140
5.6 Parameter Estimation 143
5.7 Confidence Interval 148
5.8 Tests of Statistical Hypotheses 149
5.9 Analysis of Variance 150
5.10 Linear Regression 154
5.11 Mann-Kendall Trend Test 155
Problems 158
Bibliography 159
6. Empirical Orthogonal Functions
6.1 Random Vector Fields 161
6.2 Classical EOFs 163
6.3 Estimation of EOFs 171
6.4 Rotation of EOFs 173
6.5 Complex EOFs and Hilbert EOFs 178
6.6 Singular Value Decomposition 182
6.7 Canonical Correlation Analysis 185
6.8 Singular Spectrum Analysis 189
6.9 Principal Oscillation Patterns 191
6.9.1 Normal Modes 191
6.9.2 Estimates of Principal Oscillation Ffetterns 194
Problems 195
Bibliography 196
7. Random Processes and Power Spectra
7.1 Stationary and Non-stationary Random Processes 199
7.2 Markov Process and Brownian Motion 203
7.3 Calculus of Random Processes 207
7.4 Spectral Analysis 214
7.4.1 Linear Time-Invariant System for WSS Processes 214
7.4.2 Power Spectral Density 216
7.4.3 Shannon Sampling Theorem for Random Processes 219
7.5 Wiener Filtering 221
7.6 Spectrum Estimation 224
7.7 Significance Tests of Climatic Time Series 229
7.7.1 Fourier Power Spectra 229
7.7.2 Wavelet Power Spectra 232
Problems 236
Bibliography 236
8. Autoregressive Moving Average Models
8.1 ARMA Processes 239
8.1.1 AR(p) Processes 240
8.1.2 MA(q) Processes 241
8.1.3 Shift Operator 244
8.1.4 ARMA(p, q) Processes 245
8.2 Yule-Walker Equation and
Spectral Density 248
8.3 Prediction Algorithms 251
8.3.1 Innovation Algorithm 252
8.3.2 Durbin-Lovinson Algorithm 257
8.3.3 Kolmogorov s Formula 260
8.4 Asymptotic Theory 261
8.4.1 Cramer-Wold Device 261
8.4.2 Asymptotic Normality 265
8.5 Estimates of Means and Covariance
Functions 267
8.6 Estimation for ARMA Models 273
8.6.1 General Linear Model 273
8.6.2 Estimation for AR(p) Processes 275
8.6.3 Estimation for ARMA(p,q) Processes 282
8.7 ARIMA Models 283
8.8 Multivariate ARMA Processes 285
8.9 Application in Climatic and Flydrological Research 287
Problems 288
Bibliography 289
9. Data Assimilation
9.1 Concept of Data Assimilation 291
9.2 Cressman Method 294
9.3 Optimal Interpolation Analysis 295
9.4 Cost Function and Three-Dimensional Variational Analysis 299
9.5 Dual of the Optimal Interpolation 304
9.6 Four-Dimensional Variational Analysis 305
9.7 Kalman Filter 308
Problems 309
Bibliography 310
10. Fluid Dynamics
10.1 Gradient, Divergence, and Curl 313
10.2 Circulation and Flux 319
10.3 Green s Theorem, Divergence Theorem, and Stokes s Theorem 321
10.4 Equations of Motion 322
10.4.1 Continuity Equation 322
10.4.2 Euler s Equation 324
10.4.3 Bernoulli s Equation 328
10.5 Energy Flux and Momentum Flux 33I
10.6 Kelvin Law 337
10.7 Potential Function and Potential Flow 339
10.8 Incompressible Fluids 341
Problems 343
Bibliography 345
11. Atmospheric Dynamics
11.1 Two Simple Atmospheric Models 347
11.1.1 The Single-Layer Model 349
11.1.2 The Two-Layer Model 350
11.2 Atmospheric Composition 352
11.3 Hydrostatic Balance Equation 354
11.4 Potential Temperature 356
11.5 Lapse Rate 358
11.5.1 Adiabatic Lapse Rate 359
11.5.2 Buoyancy Frequency 360
11.6 Clausius-Clapeyron Equation 362
11.6.1 Saturation Mass Mixing Radio 363
11.6.2 Saturation Adiabatic Lapse Rate 363
11.6.3 Equivalent Potential Temperature 365
11.7 Material Derivatives 366
11.8 Vorticity and Potential Vorticity 370
11.9 Navier-Stokes Equation 372
11.9.1 Navier-Stokes Equation in an Inertial Frame 372
11.9.2 Navier-Stokes Equation in a Rotating Frame 374
11.9.3 Component Form of the Navier-Stokes Equation 376
11.10 Geostrophic Balance Equations 378
11.11 Boussinesq Approximation and Energy Equation 380
11.12 Quasi-Geostrophic Potential Vorticity 383
11.13 Gravity Waves 386
11.13.1 Internal Gravity Waves 387
11.13.2 Inertia Gravity Waves 391
11.14 Rossby Waves 393
11.15 Atmospheric Boundary Layer 398
Problems 404
Bibliography 405
12. Oceanic Dynamics
12.1 Salinity and Mass 407
12.2 Inertial Motion 408
12.3 Oceanic Ekman Layer 409
12.3.1 Ekman Currents 410
12.3.2 Ekman Mass Transport 412
12.3.3 Ekman Pumping 414
12.4 Geostrophic Currents 415
12.4.1 Surface Geostrophic Currents 415
12.4.2 Geostrophic Currents from Hydrography 418
12.5 Sverdrup s Theorem 420
12.6 Munk s Theorem 424
12.7 Taylor-Proudman Theorem 428
12.8 Ocean-Wave Spectrum 431
12.8.1 Spectrum 431
12.8.2 Digital Spectrum 432
12.8.3 Pierson-Moskowitz Spectrum 433
12.9 Oceanic Tidal Forces 435
Problems 437
Bibliography 438
13. Glaciers and Sea Level Rise
13.1 Stress and Strain 441
13.2 Glen s Law and Generalized Glen s Law 443
13.3 Density of Glacier Ice 444
13.4 Glacier Mass Balance 445
13.5 Glacier Momentum Balance 446
13.6 Glacier Energy Balance 449
13.7 Shallow-Ice and Shallow-Shelf Approximations 450
13.8 Dynamic Ice Sheet Models 452
13.9 Sea Level Rise 452
13.10 Semiempirical Sea Level Models 453
Problems 454
Bibliography 454
14. Climate and Earth System Models
14.1 Energy Balance Models 457
14.1.1 Zero-Dimensional EBM 457
14.1.2 One-Dimensional EBM 458
14.2 Radiative Convective Models 460
14.3 Statistical Dynamical Models 460
14.4 Earth System Models 462
14.4.1 Atmospheric Models 462
14.4.2 Oceanic Models 463
14.4.3 Land Surface Models 465
14.4.4 Sea Ice Models 465
14.5 Coupled Model Intercomparison Project 466
14.6 Geoengineering Model Intercomparison Project 467
Problems 470
Bibliography 470
Index 473
Zhihua Zhang, Tenured Research Professor and Senior Scientist,
University China
John
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in mathematics and physics with which to understand global warming, natural
climate variations, and climate models. This book informs the future users
of climate
medels
and the decision-makers of tomorrow by providing the
depth they need. Developed from several courses 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
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|
| any_adam_object | 1 |
| author | Zhang, Zhihua 1979- Moore, John C. |
| author_GND | (DE-588)1127791818 (DE-588)1067878564 |
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| ctrlnum | (OCoLC)900410032 (DE-599)BVBBV042227984 |
| discipline | Mathematik Geographie |
| format | Book |
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| id | DE-604.BV042227984 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T01:15:50Z |
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| isbn | 9780128000663 012800066X |
| language | English |
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| spelling | Zhang, Zhihua 1979- Verfasser (DE-588)1127791818 aut Mathematical and physical fundamentals of climate change Zhihua Zhang ; John C. Moore Amsterdam [u.a.] Elsevier 2015 XII, 481 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Mathematisches Modell (DE-588)4114528-8 gnd rswk-swf Mathematik (DE-588)4037944-9 gnd rswk-swf Klimaänderung (DE-588)4164199-1 gnd rswk-swf Physik (DE-588)4045956-1 gnd rswk-swf Klimaänderung (DE-588)4164199-1 s Physik (DE-588)4045956-1 s Mathematik (DE-588)4037944-9 s DE-604 Mathematisches Modell (DE-588)4114528-8 s 1\p DE-604 Moore, John C. Verfasser (DE-588)1067878564 aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027666344&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Augsburg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027666344&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Zhang, Zhihua 1979- Moore, John C. Mathematical and physical fundamentals of climate change Mathematisches Modell (DE-588)4114528-8 gnd Mathematik (DE-588)4037944-9 gnd Klimaänderung (DE-588)4164199-1 gnd Physik (DE-588)4045956-1 gnd |
| subject_GND | (DE-588)4114528-8 (DE-588)4037944-9 (DE-588)4164199-1 (DE-588)4045956-1 |
| title | Mathematical and physical fundamentals of climate change |
| title_auth | Mathematical and physical fundamentals of climate change |
| title_exact_search | Mathematical and physical fundamentals of climate change |
| title_full | Mathematical and physical fundamentals of climate change Zhihua Zhang ; John C. Moore |
| title_fullStr | Mathematical and physical fundamentals of climate change Zhihua Zhang ; John C. Moore |
| title_full_unstemmed | Mathematical and physical fundamentals of climate change Zhihua Zhang ; John C. Moore |
| title_short | Mathematical and physical fundamentals of climate change |
| title_sort | mathematical and physical fundamentals of climate change |
| topic | Mathematisches Modell (DE-588)4114528-8 gnd Mathematik (DE-588)4037944-9 gnd Klimaänderung (DE-588)4164199-1 gnd Physik (DE-588)4045956-1 gnd |
| topic_facet | Mathematisches Modell Mathematik Klimaänderung Physik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027666344&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027666344&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT zhangzhihua mathematicalandphysicalfundamentalsofclimatechange AT moorejohnc mathematicalandphysicalfundamentalsofclimatechange |