Mathematical and Physical Fundamentals of Climate Change

1st Edition - November 25, 2014
Authors: Zhihua Zhang, John C. Moore
Language: English
Paperback ISBN:
9 7 8 - 0 - 1 2 - 8 1 0 2 4 2 - 8
Hardback ISBN:
9 7 8 - 0 - 1 2 - 8 0 0 0 6 6 - 3
eBook ISBN:
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

Purchase options

ROBOTICS & AUTOMATION

Empowering Progress

Up to 25% off Essentials Robotics and Automation titles

Explore now

Image with Robotics & Automation book covers

Institutional subscription on ScienceDirect

Request a sales quote

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.

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

Zhihua Zhang

Prof. Zhang’s 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:

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

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

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

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

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

Ø 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)

Affiliations and expertise

Taishan Distinguished Professor, Shandong University, China

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

Life Sciences

Physical Sciences & Engineering

Social Sciences & Humanities

Health