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Mathematical and Physical Fundamentals of Climate Change
1st Edition - November 25, 2014
Authors: Zhihua Zhang, John C. Moore
Language: English
Hardback ISBN:9780128000663
9 7 8 - 0 - 1 2 - 8 0 0 0 6 6 - 3
eBook ISBN:9780128005835
9 7 8 - 0 - 1 2 - 8 0 0 5 8 3 - 5
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 atmosp…Read more
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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
Upper-level UG/Grad Students, post-docs, researchers in meteorology, climatology, oceanography, earth science and environmental science
Preface: Interdisciplinary Approaches to Climate Change Research
Chapter 1: Fourier Analysis
Abstract
1.1 Fourier series and fourier transform
1.2 Bessel'a inequality and parseval's identity
1.3 Gibbs phenomenon
1.4 Poisson summation formulas and shannon sampling theorem
1.5 Discrete fourier transform
1.6 Fast fourier transform
1.7 Heisenberg uncertainty principle
1.8 Case study: arctic oscillation indices
Problems
Chapter 2: Time-Frequency Analysis
Abstract
2.1 Windowed Fourier Transform
2.2 Wavelet Transform
2.3 Multiresolution Analyses and Wavelet Bases
2.4 Hilbert Transform, Analytical Signal, and Instantaneous Frequency
2.5 Wigner-Ville Distribution and Cohen's Class
2.6 Empirical Mode Decompositions
Problems
Chapter 3: Filter Design
Abstract
3.1 Continuous linear time-invariant systems
3.2 Analog filters
3.3 Discrete linear time-invariant systems
3.4 Linear-phase filters
3.5 Designs of FIR filters
3.6 IIR filters
3.7 Conjugate mirror filters
Problems
Chapter 4: Remote Sensing
Abstract
4.1 Solar and thermal radiation
4.2 Spectral regions and optical sensors
4.3 Spatial filtering
4.4 Spatial blurring
4.5 Distortion correction
4.6 Image fusion
4.7 Supervised and unsupervised classification
4.8 Remote sensing of atmospheric carbon dioxide
4.9 Moderate resolution imaging spectroradiometer data products and climate change
Problems
Chapter 5: Basic Probability and Statistics
Abstract
5.1 Probability space, random variables, and their distributions
5.2 Jointly distributed random variables
5.3 Central limit theorem and law of large numbers
5.4 Minimum mean square error
5.5 χ2-distribution, t-distribution, and F-distribution
5.6 Parameter estimation
5.7 Confidence interval
5.8 Tests of statistical hypotheses
5.9 Analysis of variance
5.10 Linear regression
5.11 Mann-Kendall trend test
Problems
Chapter 6: Empirical Orthogonal Functions
Abstract
6.1 Random vector fields
6.2 Classical EOFs
6.3 Estimation of EOFs
6.4 Rotation of EOFs
6.5 Complex EOFs and hilbert EOFs
6.6 Singular value decomposition
6.7 Canonical correlation analysis
6.8 Singular spectrum analysis
6.9 Principal oscillation patterns
Problems
Chapter 7: Random Processes and Power Spectra
Abstract
7.1 Stationary and non-stationary random processes
7.2 Markov process and brownian motion
7.3 Calculus of random processes
7.4 Spectral analysis
7.5 Wiener filtering
7.6 Spectrum estimation
7.7 Significance tests of climatic time series
Problems
Chapter 8: Autoregressive Moving Average Models
Abstract
8.1 Arma processes
8.2 Yule-Walker equation and spectral density
8.3 Prediction algorithms
8.4 Asymptotic theory
8.5 Estimates of means and covariance functions
8.6 Estimation for ARMA models
8.7 Arima models
8.8 Multivariate ARMA processes
8.9 Application in climatic and hydrological research
Problems
Chapter 9: Data Assimilation
Abstract
9.1 Concept of data assimilation
9.2 Cressman method
9.3 Optimal interpolation analysis
9.4 Cost function and three-dimensional variational analysis
9.5 Dual of the optimal interpolation
9.6 Four-dimensional variational analysis
9.7 Kalman filter
Problems
Chapter 10: Fluid Dynamics
Abstract
10.1 Gradient, divergence, and curl
10.2 Circulation and flux
10.3 Green's theorem, divergence theorem, and stokes's theorem
10.4 Equations of motion
10.5 Energy flux and momentum flux
10.6 Kelvin law
10.7 Potential function and potential flow
10.8 Incompressible fluids
Problems
Chapter 11: Atmospheric Dynamics
Abstract
11.1 Two simple atmospheric models
11.2 Atmospheric composition
11.3 Hydrostatic balance equation
11.4 Potential temperature
11.5 Lapse rate
11.6 Clausius-clapeyron equation
11.7 Material derivatives
11.8 Vorticity and potential vorticity
11.9 Navier-stokes equation
11.10 Geostrophic balance equations
11.11 Boussinesq approximation and energy equation
11.12 Quasi-geostrophic potential vorticity
11.13 Gravity waves
11.14 Rossby waves
11.15 Atmospheric boundary layer
Problems
Chapter 12: Oceanic Dynamics
Abstract
12.1 Salinity and mass
12.2 Inertial motion
12.3 Oceanic ekman layer
12.4 Geostrophic currents
12.5 Sverdrup's theorem
12.6 Munk's theorem
12.7 Taylor-proudman theorem
12.8 Ocean-wave spectrum
12.9 Oceanic tidal forces
Problems
Chapter 13: Glaciers and Sea Level Rise
Abstract
13.1 Stress and strain
13.2 Glen's law and generalized glen's law
13.3 Density of glacier ice
13.4 Glacier mass balance
13.5 Glacier momentum balance
13.6 Glacier energy balance
13.7 Shallow-ice and shallow-shelf approximations
13.8 Dynamic ice sheet models
13.9 Sea level rise
13.10 Semiempirical sea level models
Problems
Chapter 14: Climate and Earth System Models
Abstract
14.1 Energy balance models
14.2 Radiative convective models
14.3 Statistical dynamical models
14.4 Earth system models
14.5 Coupled model intercomparison project
14.6 Geoengineering model intercomparison project
Problems
Index
No. of pages: 494
Language: English
Edition: 1
Published: November 25, 2014
Imprint: Elsevier
Hardback ISBN: 9780128000663
eBook ISBN: 9780128005835
ZZ
Zhihua Zhang
Zhihua Zhang is a Taishan distinguished professor and director of climate modeling laboratory in Shandong University, China. His research interests are Mechanisms of Climate Change, Big Data Mining, Carbon Emissions, Climate Policy and Sustainability. Prof. Zhang has published 4 first-authored books and about 50 first-authored papers. He is a Chief Editor, Associate Editor, or Editorial Board Member in several global and regional known journals on Climate Change, Meteorology and Environmental Data.
Affiliations and expertise
Taishan Distinguished Professor, Shandong University, China
JM
John C. Moore
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. Moore’s 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. Moore’s research is supported by European Science Foundation, EU Northern Periphery Program, National Key Science Program for Global Change Research (China), Finnish Academy, and NSFC
Affiliations and expertise
Research Professor, University of Lapland, Finland; Chief Scientist & Research Professor, Beijing Normal University, China
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