Note: Front Cover -- Big Data Mining for Climate Change -- Copyright -- Contents -- Preface -- 1 Big climate data -- 1.1 Big data sources -- 1.1.1 Earth observation big data -- 1.1.2 Climate simulation big data -- 1.2 Statistical and dynamical downscaling -- 1.3 Data assimilation -- 1.3.1 Cressman analysis -- 1.3.2 Optimal interpolation analysis -- 1.3.3 Three-dimensional variational analysis -- 1.3.4 Four-dimensional variational analysis -- 1.4 Cloud platforms -- 1.4.1 Cloud storage -- 1.4.2 Cloud computing -- Further reading -- 2 Feature extraction of big climate data -- 2.1 Clustering -- 2.1.1 K-means clustering -- 2.1.2 Hierarchical clustering -- 2.2 Hidden Markov model -- 2.3 Expectation maximization -- 2.4 Decision trees and random forests -- 2.5 Ridge and lasso regressions -- 2.6 Linear and quadratic discriminant analysis -- 2.6.1 Bayes classi er -- 2.6.2 Linear discriminant analysis -- 2.6.3 Quadratic discriminant analysis -- 2.7 Support vector machines -- 2.7.1 Maximal margin classi er -- 2.7.2 Support vector classi ers -- 2.7.3 Support vector machines -- 2.8 Rainfall estimation -- 2.9 Flood susceptibility -- 2.10 Crop recognition -- Further reading -- 3 Deep learning for climate patterns -- 3.1 Structure of neural networks -- 3.2 Back propagation neural networks -- 3.2.1 Activation functions -- 3.2.2 Back propagation algorithms -- 3.3 Feedforward multilayer perceptrons -- 3.4 Convolutional neural networks -- 3.5 Recurrent neural networks -- 3.5.1 Input-output recurrent model -- 3.5.2 State-space model -- 3.5.3 Recurrent multilayer perceptrons -- 3.5.4 Second-order network -- 3.6 Long short-term memory neural networks -- 3.7 Deep networks -- 3.7.1 Deep learning -- 3.7.2 Boltzmann machine -- 3.7.3 Directed logistic belief networks -- 3.7.4 Deep belief nets -- 3.8 Reinforcement learning -- 3.9 Dendroclimatic reconstructions. , 3.10 Downscaling climate variability -- 3.11 Rainfall-runoff modeling -- Further reading -- 4 Climate networks -- 4.1 Understanding climate systems as networks -- 4.2 Degree and path -- 4.3 Matrix representation of networks -- 4.4 Clustering and betweenness -- 4.5 Cut sets -- 4.6 Trees and planar networks -- 4.7 Bipartite networks -- 4.8 Centrality -- 4.8.1 Degree centrality -- 4.8.2 Closeness centrality -- 4.8.3 Betweenness centrality -- 4.9 Similarity -- 4.9.1 Cosine similarity -- 4.9.2 Pearson similarity -- 4.10 Directed networks -- 4.11 Acyclic directed networks -- 4.12 Weighted networks -- 4.12.1 Vertex strength -- 4.12.2 Weight-degree/weight-weight correlation -- 4.12.3 Weighted clustering -- 4.12.4 Shortest path -- 4.13 Random walks -- 4.14 El Niño southern oscillation -- 4.15 North Atlantic oscillation -- Further reading -- 5 Random climate networks and entropy -- 5.1 Regular networks -- 5.1.1 Fully connected networks -- 5.1.2 Regular ring-shaped networks -- 5.1.3 Star-shaped networks -- 5.2 Random networks -- 5.2.1 Giant component -- 5.2.2 Small component -- 5.3 Con guration networks -- 5.3.1 Edge probability and common neighbor -- 5.3.2 Degree distribution -- 5.3.3 Giant components -- 5.3.4 Small components -- 5.3.5 Directed random network -- 5.4 Small-world networks -- 5.4.1 Main models -- 5.4.2 Degree distribution -- 5.4.3 Clustering -- 5.4.4 Mean distance -- 5.5 Power-law degree distribution -- 5.5.1 Price's models -- 5.5.2 Barabasi-Albert models -- 5.6 Dynamics of random networks -- 5.7 Entropy and joint entropy -- 5.8 Conditional entropy and mutual information -- 5.9 Entropy rate -- 5.10 Entropy-based climate network -- 5.11 Entropy-based decision tree -- Further reading -- 6 Spectra of climate networks -- 6.1 Understanding atmospheric motions via network spectra -- 6.2 Adjacency spectra -- 6.2.1 Maximum degree -- 6.2.2 Diameter. , 6.2.3 Paths of length k -- 6.3 Laplacian spectra -- 6.3.1 Maximum degree -- 6.3.2 Connectivity -- 6.3.3 Spanning tree -- 6.3.4 Degree sequence -- 6.3.5 Diameter -- 6.4 Spectrum centrality -- 6.4.1 Eigenvector centrality -- 6.4.2 Katz centrality -- 6.4.3 Pagerank centrality -- 6.4.4 Authority and hub centralities -- 6.5 Network eigenmodes -- 6.6 Spectra of complete networks -- 6.7 Spectra of small-world networks -- 6.8 Spectra of circuit and wheel network -- 6.9 Spectral density -- 6.10 Spectrum-based partition of networks -- Further reading -- 7 Monte Carlo simulation of climate systems -- 7.1 Random sampling -- 7.1.1 Uniform distribution -- 7.1.2 Nonuniform distribution -- 7.1.3 Normal distribution -- 7.2 Variance reduction technique -- 7.2.1 Control variable method -- 7.2.2 Control vector method -- 7.3 Strati ed sampling -- 7.4 Sample paths for Brownian motion -- 7.4.1 Cholesky and Karhounen-Loève expansions -- 7.4.2 Brownian bridge -- 7.5 Quasi-Monte Carlo method -- 7.5.1 Discrepancy -- 7.5.2 Koksma-Hlawka inequality -- 7.5.3 Van der Corput sequence -- 7.5.4 Halton sequence -- 7.5.5 Faure sequence -- 7.6 Markov chain Monte Carlo -- 7.7 Gibbs sampling -- Further reading -- 8 Sparse representation of big climate data -- 8.1 Global positioning -- 8.1.1 Multidimensional scaling -- 8.1.2 Local rigid embedding -- 8.2 Embedding rules -- 8.2.1 Attractors and fractal dimension -- 8.2.2 Delay embedding -- 8.2.3 Multichannel singular spectrum analysis -- 8.2.4 Recurrence networks -- 8.3 Sparse recovery -- 8.3.1 Sparse interpolation -- 8.3.2 Sparse approximation -- 8.3.3 Greedy algorithms -- 8.4 Sparse representation of climate modeling big data -- 8.5 Compressive sampling of remote sensing big data -- 8.5.1 s-Sparse approximation -- 8.5.2 Minimal samples -- 8.5.3 Orthogonal matching pursuit -- 8.5.4 Compressive sampling matching pursuit. , 8.5.5 Iterative hard thresholding -- 8.6 Optimality -- 8.6.1 Optimization algorithm for compressive sampling -- 8.6.2 Chambolle and Pock's primal-dual algorithm -- Further reading -- 9 Big-data-driven carbon emissions reduction -- 9.1 Precision agriculture -- 9.2 Oil exploitation -- 9.3 Smart buildings -- 9.4 Smart grids -- 9.5 Smart cities -- Further reading -- 10 Big-data-driven low-carbon management -- 10.1 Large-scale data envelopment analysis -- 10.2 Natural resource management -- 10.3 Roadway network management -- 10.4 Supply chain management -- 10.5 Smart energy management -- Further reading -- 11 Big-data-driven Arctic maritime transportation -- 11.1 Trans-Arctic routes -- 11.2 Sea-ice remote-sensing big data -- 11.2.1 Arctic sea-ice concentration -- 11.2.2 Melt ponds -- 11.2.3 Arctic sea-ice extent -- 11.2.4 Arctic sea-ice thickness -- 11.2.5 Arctic sea-ice motion -- 11.2.6 Comprehensive integrated observation system -- 11.3 Sea-ice modeling big data -- 11.4 Arctic transport accessibility model -- 11.5 Economic and risk assessments of Arctic routes -- 11.6 Big-data-driven dynamic optimal trans-Arctic route system -- 11.7 Future prospects -- Further reading -- Index -- Back Cover.

Note: Front Cover -- Mathematical and Physical Fundamentals of Climate Change -- Copyright -- Contents -- Preface: Interdisciplinary Approaches to Climate Change Research -- Chapter 1: Fourier Analysis -- 1.1 Fourier Series and Fourier Transform -- 1.2 Bessel's 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 -- Bibliography -- Chapter 2: Time-Frequency Analysis -- 2.1 Windowed Fourier Transform -- 2.2 Wavelet Transform -- 2.3 Multiresolution Analyses and Wavelet Bases -- 2.3.1 Multiresolution Analyses -- 2.3.2 Discrete Wavelet Transform -- 2.3.3 Biorthogonal Wavelets, Bivariate Wavelets,and Wavelet Packet -- 2.4 Hilbert Transform, Analytical Signal, and Instantaneous Frequency -- 2.5 Wigner-Ville Distribution and Cohen's Class -- 2.6 Empirical Mode Decompositions -- Problems -- Bibliography -- Chapter 3: Filter Design -- 3.1 Continuous Linear Time-Invariant Systems -- 3.2 Analog Filters -- 3.3 Discrete Linear Time-Invariant Systems -- 3.3.1 Discrete Signals -- 3.3.2 Discrete Convolution -- 3.3.3 Discrete System -- 3.3.4 Ideal Digital Filters -- 3.3.5 Z-Transforms -- 3.3.6 Linear Difference Equations -- 3.4 Linear-Phase Filters -- 3.4.1 Four Types of Linear-Phase Filters -- 3.4.2 Structure of Linear-Phase Filters -- 3.5 Designs of FIR Filters -- 3.5.1 Fourier Expansions -- 3.5.2 Window Design Method -- 3.5.3 Sampling in the Frequency Domain -- 3.6 IIR Filters -- 3.6.1 Impulse Invariance Method -- 3.6.2 Matched Z-Transform Method -- 3.6.3 Bilinear Transform Method -- 3.7 Conjugate Mirror Filters -- Problems -- Bibliography -- Chapter 4: Remote Sensing -- 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 -- Bibliography -- Chapter 5: Basic Probability and Statistics -- 5.1 Probability Space, Random Variables, and Their Distributions -- 5.1.1 Discrete Random Variables -- 5.1.2 Continuous Random Variables -- 5.1.3 Properties of Expectations and Variances -- 5.1.4 Distributions of Functions of Random Variables -- 5.1.5 Characteristic Functions -- 5.2 Jointly Distributed Random Variables -- 5.3 Central Limit Theorem and Law of Large Numbers -- 5.4 Minimum Mean Square Error -- 5.5 2-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 -- Bibliography -- Chapter 6: Empirical Orthogonal Functions -- 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 -- 6.9.1 Normal Modes -- 6.9.2 Estimates of Principal Oscillation Patterns -- Problems -- Bibliography -- Chapter 7: Random Processes and Power Spectra -- 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 -- 7.4.1 Linear Time-Invariant System for WSS Processes -- 7.4.2 Power Spectral Density -- 7.4.3 Shannon Sampling Theorem for Random Processes -- 7.5 Wiener Filtering. , 7.6 Spectrum Estimation -- 7.7 Significance Tests of Climatic Time Series -- 7.7.1 Fourier Power Spectra -- 7.7.2 Wavelet Power Spectra -- Problems -- Bibliography -- Chapter 8: Autoregressive Moving Average Models -- 8.1 ARMA Processes -- 8.1.1 AR(p) Processes -- 8.1.2 MA(q) Processes -- 8.1.3 Shift Operator -- 8.1.4 ARMA(p,q) Processes -- 8.2 Yule-Walker Equation andSpectral Density -- 8.3 Prediction Algorithms -- 8.3.1 Innovation Algorithm -- 8.3.2 Durbin-Lovinson Algorithm -- 8.3.3 Kolmogorov's Formula -- 8.4 Asymptotic Theory -- 8.4.1 Gramer-Wold Device -- 8.4.2 Asymptotic Normality -- 8.5 Estimates of Means and CovarianceFunctions -- 8.6 Estimation for ARMA Models -- 8.6.1 General Linear Model -- 8.6.2 Estimation for AR(p) Processes -- 8.6.3 Estimation for ARMA(p,q) Processes -- 8.7 ARIMA Models -- 8.8 Multivariate ARMA Processes -- 8.9 Application in Climatic and Hydrological Research -- Problems -- Bibliography -- Chapter 9: Data Assimilation -- 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 -- Bibliography -- Chapter 10: Fluid Dynamics -- 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 -- 10.4.1 Continuity Equation -- 10.4.2 Euler's Equation -- 10.4.3 Bernoulli's Equation -- 10.5 Energy Flux and Momentum Flux -- 10.6 Kelvin Law -- 10.7 Potential Function and Potential Flow -- 10.8 Incompressible Fluids -- Problems -- Bibliography -- Chapter 11: Atmospheric Dynamics -- 11.1 Two Simple Atmospheric Models -- 11.1.1 The Single-Layer Model -- 11.1.2 The Two-Layer Model -- 11.2 Atmospheric Composition. , 11.3 Hydrostatic Balance Equation -- 11.4 Potential Temperature -- 11.5 Lapse Rate -- 11.5.1 Adiabatic Lapse Rate -- 11.5.2 Buoyancy Frequency -- 11.6 Clausius-Clapeyron Equation -- 11.6.1 Saturation Mass Mixing Radio -- 11.6.2 Saturation Adiabatic Lapse Rate -- 11.6.3 Equivalent Potential Temperature -- 11.7 Material Derivatives -- 11.8 Vorticity and Potential Vorticity -- 11.9 Navier-Stokes Equation -- 11.9.1 Navier-Stokes Equation in an Inertial Frame -- 11.9.2 Navier-Stokes Equation in a Rotating Frame -- 11.9.3 Component Form of the 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 -- 11.13.1 Internal Gravity Waves -- 11.13.2 Inertia Gravity Waves -- 11.14 Rossby Waves -- 11.15 Atmospheric Boundary Layer -- Problems -- Bibliography -- Chapter 12: Oceanic Dynamics -- 12.1 Salinity and Mass -- 12.2 Inertial Motion -- 12.3 Oceanic Ekman Layer -- 12.3.1 Ekman Currents -- 12.3.2 Ekman Mass Transport -- 12.3.3 Ekman Pumping -- 12.4 Geostrophic Currents -- 12.4.1 Surface Geostrophic Currents -- 12.4.2 Geostrophic Currents from Hydrography -- 12.5 Sverdrup's Theorem -- 12.6 Munk's Theorem -- 12.7 Taylor-Proudman Theorem -- 12.8 Ocean-Wave Spectrum -- 12.8.1 Spectrum -- 12.8.2 Digital Spectrum -- 12.8.3 Pierson-Moskowitz Spectrum -- 12.9 Oceanic Tidal Forces -- Problems -- Bibliography -- Chapter 13: Glaciers and Sea Level Rise -- 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 -- Bibliography. , Chapter 14: Climate and Earth System Models -- 14.1 Energy Balance Models -- 14.1.1 Zero-Dimensional EBM -- 14.1.2 One-Dimensional EBM -- 14.2 Radiative Convective Models -- 14.3 Statistical Dynamical Models -- 14.4 Earth System Models -- 14.4.1 Atmospheric Models -- 14.4.2 Oceanic Models -- 14.4.3 Land Surface Models -- 14.4.4 Sea Ice Models -- 14.5 Coupled Model Intercomparison Project -- 14.6 Geoengineering Model Intercomparison Project -- Problems -- Bibliography -- Index.