This chapter introduces the concept of data mining, some basic notations, and three important types of the data mining algorithms.
Supervised; Unsupervised; Semi-Supervised; Regression; Classification; Clustering; Dimensionality Reduction
This chapter introduces the concept of data, data types, and operators that can be applied on certain data types. It continues on the topic of data quality. Three types of quality issues, i.e., noise and outliers, missing values, and sample distortion, need to be addressed before feeding the data into the models. To get a sense of the new data set, we need to use some summary statistics, as well as some visualization techniques, to know the structure of the data and find some interesting features.
Categorical; Ordinal; Continuous; Noise; Outliers; Missing Value; Sample Distortion; Summary Statistics; Frequency; Location; Spread; Distribution; Histogram; Boxplot; Scatter Plot
Linear regression is the simplest and the most important supervised learning, parametric model. Aside from some very basic concepts of what the model is, how to fit it based on Ordinary Least Squares (OLS), what the solution is, this chapter digs deeper into many important properties of the projection matrix, coefficients, residuals, and so on.
Supervised Learning; Regression; Parametric; Intercept; Slope; Ordinary Least Squares (OLS); Projection Matrix; Residual; Residual Sum of Squares (RSS); R Squared; Interaction; Significance Test; Collinearity; ANOVA;
As a representative of the non-parametric models, KNN is a very simple but very powerful tool. Its idea is simple: Find K closest training points to the new data point, and average the response. It can serve for both regression and classification problems. The choice of hyperparameter K relates to a critical issue that all models suffer from: bias-variance tradeoff.
Non-Parametric; Euclidean Distance; Overfitting; Underfitting; Training Set; Test Set; Mean Squared Error (MSE); Curse of Dimensionality;
This chapter details the bias-variance tradeoff problem.
Bias; Variance; Training MSE; Test MSE; Model Complexity; Irreducible Error; Overfitting; Underfitting
This chapter introduces the LDA and QDA, two examples of parametric generative classification methods. They make use of Bayes rule to estimate the posterior probability and try to maximize it.
Bayes Classifier; Bayes Rule; Posterior Probability; Generative Classification Methods; Gaussian Predictor; Discriminant Function; Decision Boundary; Naive Bayes Classifier; Diagonal LDA; Diagonal QDA
As one of the discriminative classification methods, logistic regression directly estimates the logit of the posterior probability by a linear expression, similar with the linear regression.
Discriminative Classification Methods; Logistic Function (logit); Sigmoid Function; Odds; Maximum Likelihood Estimator(MLE); Linear Decision Boundary
To increase the number of samples and make the model and the error estimation robust, resampling methods are invented to repeatedly draw samples from a training set and refit a model of interest.
Cross-Validation (CV); Validation Set; Leave-One-Out Cross-Validation (LOOCV); K-fold Cross-Validation; Bootstrap
In addition to increasing the sample size by resampling, reducing the dimensions by feature selection is another way to build a robust model. Subset selection is introduced in this chapter.
Feature Selection; Subset Selection; Shrinkage; Dimension Reduction; Adjusted R Squared; Mallow Cp; Akaike Information Criterion (AIC); Bayesian Information Criterion (BIC); Forward Selection; Backward Elimination; Best Subset Selection
Two important shrinkage methods are introduced in this chapter: Ridge Regression and Lasso Regression.
Ridge Regression; Lasso Regression; Penalty; Optimization; Loss Function; Tuning Parameter Lambda
The basic idea of dimension reduction is to project predictors into a small-dimensional space and fit a linear regression model. Principal Component Analysis (PCA), as well as Partial Least Squares (PLS), are introduced.
Orthogonality; Variance; Eigenvectors; Eigenvalues; Loadings; Scores; Principle Component Regression (PCR)
Single classification / regression tree is introduced in this chapter.
Node; Split; Gini Index; Entropy; Pruning; Misclassification Error; Linear Decision Boundary
Single model is far from enough to make a robust prediction. To combine the advantages of different models, ensemble methods are invented. Bagging, random forests, and boosting are three representatives. Note that they can also be used in general models other than trees.
Bagging; Bootstrap Aggregating; Flexible Decision Boundary; Random Forests; AdaBoost; Gradient Boost
Support Vector Machines (SVM), which are popular in Machine Learning community, are introduced in this chapter. The main goal is to give the best separation between the correctly classified points, and to keep the points on the wrong side not too far from the separating hyperplane.
Separating Hyperplane; Margin; Support Vectors; Slack Variables; Fitted Lagrange Multipliers; Basis Functions; Kernels (dth Degree Polynomial & Radial)
Here the basic concepts of clustering are explained. It is a very important unsupervised learning method, which aims to put similar samples in the same group, and put very different samples in different groups.
Partition Methods; K-Means; Model-based Clustering; Hierarchical Clustering; Dissimilarity; Similarity; Minikowski Distance; Euclidean; Manhattan; Cohesion; Separations; Within Cluster Sum of Squared Errors (WSS); Between Cluster Sum of Squared Errors (BSS); Monte-Carlo; Significance Test; Silhouette Coefficient
This chapter details some popular algorithms in partitional clustering, such as K-means clustering. Please read Chapter 15 before if you have no idea about some basic concepts of clustering.
K-Means; Centroid; Partitioning Around Medoids (PAM); Spectral Clustering; Model-based Clustering; Gaussian Mixture Models (GMM);
This chapter details the algorithm in hierarchical clustering. Two types of hierarchical clustering and five options of dissimilarity measures are introduced. Please read Chapter 15 before if you have no idea about some basic concepts of clustering.
Dendrogram; Agglomerative; Divisive; Dissimilarity Measures; Single Linkage; Complete Linkage; Average Linkage; Centroids; Greedy Algorithm; Private Algorithm
This document summarizes some basic concepts and how to use all basic models covered in this course in R.
R Programming; Linear Regression; ANOVA; K Nearest Neighbors (KNN); Linear Discriminant Analysis (LDA); Quadratic Discriminant Analysis (QDA); Logistic Regression; Subset Selection; Exhaustive Search; Forward Selection; Backward Elimination; Significance Regression; Resampling Methods; k-fold Cross-Validation; Bootstrap; Shrinkage Methods; Ridge Regression; Lasso Regression; Dimension Reduction; Principal Component Analysis; Principal Component Regression; Decision Trees; Ensemble Methods; Bagging; Random Forests; Gradient Boosting; AdaBoost; Support Vector Machines (SVM); Hierarchical Clustering; K-Means Clustering
What is radiative transfer? Why is it very difficult to study? Why is it so important?
Remote Sensing; Radiative Heating; Atmospheric Chemistry; Quantum Mechanics; Sun; Earth; Solar Radiation; Thermal Infrared Radiation
This is the most fundamental part of the electromagnetic radiation. In the former half of the chapter, some maths are reviewed, and Maxwell equations are heavily discussed. Followed are some concepts of the spectrum and the polarization.
Scalars; Vectors; Operators; Field; Complex Numbers; Maxwell Equations; Electric Field (E); Electric Displacement Field (D); Magnetic Field (H); Magnetic Induction Field (B); Permittivity; Permeability; Gauss Law; Ampere Law; Faraday Law; Lorentz Force; Poynting Vector; Gauge Transformation; Lorentz Gauge; Transverse Wave; Refraction Index; Fourier Series; Parseval Theorem; Phase Speed; Group Velocity; Polarization; Spectrum; Stokes Parameters; Muller Matrix
In the latter half of this chapter, some very important concepts (e.g. intensity and flux) are introduced. This chapter ends with some discussion of wave-particle duality.
Solid Angle; Zenith Angle; Azimuth Angle; Flux (Irradiance); Intensity (Spectral Radiance); Isotropic; Interference; Diffraction; Huygens-Fresnel Principle; Diffraction Grating; Photoelectric Effect; Ultraviolet Catastrophe; Photons;
Reflection, refraction, and absorption are the main focus of this section, based on the classical picture.
Snell's Law; Total Internal Reflection; Fresnel Relationships; Brewster Angle; Oscillator; Damped Oscillator; Dipole; Electric Susceptibility; Electric Displacement Vector; Index of Refraction; Penetration Depth; Transmittance; Beer-Bouguer-Lambert Law (Beer Law); Absorption Coefficient
Some additional discussion on reflection and absorption.
Reflectivity (Albedo); Absorptivity; Transmissivity; Graybody Approximation; Bidirectional Reflection Function (BDRF); Specular Reflection; Lambertian Surface
The Earth is warmed by the Sun. This chapter introduces the solar radiation. Basic concepts of insolation and spectrum are introduced. Most discussion is about the variability of the solar radiation, including 11-year solar cycle, location, and orbital variability.
Angstrom; Total Solar Irradiance (TSI); Solar Constant; Solar Luminosity (L); Solar Spectral Irradiance (SSI); Albedo; Stefan-Boltzmann; 11-year Solar Cycle; Spectrum; UV-C; UV-B; UV-A; Kepler's Law; Seasons; Angular Momentum; Diurnal Cycle; Eccentricity; Apsidal Precession; Moon Tidal Effect; Obliquity; Precession; Milankovich Cycles
The Earth can also emit back to space. In this chapter, important theories about thermal radiation are explained.
Thermodynamic Equilibrium; Blackbody; First Law of Thermodynamics; Entropy; Schwarz Theorem; Ultraviolet Catastrophe; Quantum Mechanics; Planck Function; Stefan Boltzmann Law; Rayleigh-Jeans Law; Wien's Limit; Wien's Displacement Law; Emissivity; Kirchhoff Law; Graybody; Brightness Temperature; Atmospheric Window; Plane Parallel Atmosphere; Single Layer RT Model; Greenhouse Effect; Nighttime Radiative Cooling
After introducing two main players the Sun and the Earth, this chapter continues to investigate the atmospheric transmission: how the radiation transmits through the atmosphere.
Index of Refraction; Extinction Coefficient; Single Scatter Albedo; Absorption; Scattering; Beer Law; Optical Path; Transmittance; Absorptance; Penetration Depth; Mass Extinction; Extinction Cross Section; Extinction Efficiency; Line-of-Sight Approach; Plane Parallel Approximation; Optical Depth; Transmission Spectra; Liquid Water Path;
Like the surface of the Earth, atmosphere can also emit radiation. This chapter studies the atmospheric emission and reveals the Schwarzschild Equation, with an additional emission term to the Beer Law.
Schwarzschild Equation; Optical Depth; Transmittance; Emission Weighting Function; Plane-Parallel Atmosphere; Flux Weighting Function; Atmospheric Spectra; Atmospheric Temperature Profile; Inversion Methods; Water Vapor Imaging; Cloud Shortwave Cooling and Longwave Heating
Now comes the longest chapter and the most difficult one. In order to accurately quantify the absorption properties, we need to know some quantum mechanics. This chapter introduces some quantum mechanics, studies the one-electron atom / ion and the multielectron atom / ion, and then studies the interaction between radiation and atom.
Damped Oscillator; Heisenberg Uncertainty Principle; Wave Functions; Schrodinger Equation; Hamiltonian Operator; Complete Set of Commuting Operators (CSCO); Legendre Polynomials; Spherical Harmonics; Laguerre Polynomials; Degeneracy; Parity; Bosons; Fermions; Anti-symmetrization; Slater Determinant; Pauli Exclusion Principle; Quantum Numbers; Russell-Saunders Coupling; Configurations; Terms; Level; Spin-Orbit; Relativistic Correction; Absorption; Stimulated Emission; Spontaneous Emission; Einstein Coefficients; Selection Rules
This section continues the discussion of atmospheric absorption, which mainly focuses on the line broadening mechanisms, and the interaction between radiation and molecules.
Instrumental Broadening; Natural Broadening; Line Profile; Lorentz Profile; Full Width Half Maximum; Doppler Broadening; Voigt Profile; Gaussian Profile; Pressure Broadening; Dipole Moment; Hamiltonian; Born-Oppenheimer Approximation; Selection Rules; Rotational Transition; Vibrational Transition; Electronical Transition; Asymmetrical Stretch; Scissoring; Symmetrical Stretch
This small section finalizes this long long chapter. It discusses some extra topics, for example, continuum absorption and main absorbers in the Earth's atmosphere.
Broadening; Line Overcrowding; Photoionization; Photodissociation; Water Vapor Continuum Absorption; Carbon Dioxide; Ozone; Methane
To make a step from monochromatic intensity to broadband flux, it takes a lot. This chapter provides some methods to calculate the broadband fluxes.
HITRAN; Spectroscopy; Line Strength; Line Profile; Schwarzschild Equation; Emission Weighting Function; Optical Depth; Transmissivity; Flux Weighting Function; Effective Zenith Angle; Monochromatic Flux Transmittance; Average Flux Transmittance; Line-by-Line Approach; Band Models; Equivalent Width; Lorentzian Line; Elsasser Model; Malkmus Model; Hulst/Curtis/Godson Approximation; k-Distribution Method
The remaining of this chapter consists of some applications of the broadband fluxes. For example, radiative heating & cooling rate can be calculated, and model atmopsheres can be built for convenience.
Radiative Heating Rate; Model Atmospheres
While the wavelength dependence is much important to the longwave absorption, the angular dependence is of great importance to the shortwave scattering. This chapter gives a basic introduction of atmospheric scattering.
Extinction Coefficient; Single Scatter Albedo; Scattering Phase Function; General Radiative Transfer Equation; Sink Function; Source Function; Plane Parallel Atmopshere; Asymmetry Parameter; Henvey-Greenstein SPF
Based on the previous chapter, this section digs deeper to study the physical mechanisms of the scattering. Three types of scattering are introduced: Thomson Scattering, Rayleigh Scattering, and Mie Scattering.
Size Parameter; Geometric Optics; Thomson Scattering; Cross Section; Rayleigh Scattering; Scattering Efficiency; Scattering Phase Function; Mie Scattering; Extinction Efficiency; Absorption Efficiency; Scattering Asymmetry Parameter; Single Scattering Albedo; Corona; Fogbow; Glory; Rainbow
Size Distribution; Radar Meteorology; Backscatter Cross-section; Reflectivity Factor; Z-R Relationship; Marshall-Palmer Distribution
As the final topic in radiative transfer, multiple scattering is a rather annoying issue that needs to be addressed.
Two-Stream Approximation; Backscatter Fraction; Semi-Infinite Cloud; Beer Law; Heating Rate; Monte Carlo Approach
Very basic review of probability and statistics.
Random Number and Pseudo Random Number; Cumulative Distribution Function (CDF); Probability Density Function (PDF); Conditional Probability; Bayes Theorem; Normal Distribution (Gaussian Distribution); Central Limit Theorem; Joint PDF; Marginal PDF; Statistically Independent; Gamma Function; Sample Mean; Expectation; Sample Variance; Skewness; Kurtosis; Leptokurtic; Platykurtic; Mesokurtic; Covariance; Linear Correlation Coefficient; Rank Correlation Coefficient; Z Statistics; Student's T Distribution; Chi Squared Distribution; F Distribution; Confidence Intervals; Significance Level; Parametric Hypothesis Tests; Null Hypothesis; Alternative Hypothesis; p-value; Non-Parametric Hypothesis Tests; Sign Test; Rank Sum Test
Resampling methods including monte-carlo and bootstrap.
Monte-Carlo; Bootstrap; Resampling
In-depth discussion about the basic Fourier Transform, the most classical spectral analysis approach.
Orthogonality; Conjugate; Convolution; Convolution Theorem; Parseval's Theorem; Wiener-Khinchin Theorem; Periodogram; Cross-correlation; Autocorrelation; Nyquist Frequency; Aliasing; White Noise; Power Spectrum; Window Function; Boxcar Function; Hanning Function; Hamming Function; Fast Fourier Transform (FFT); Spectral Leakage; Autoregressive Process; Red Noise; Degree of Freedom; Welch's Method (WOSA); A-priori; Posteriori
This section introduces some advanced techniques to perform spectral analysis.
Multiple Taper Method (MTM); Spectral Leakage; Discrete Prolate Slepian Tapers; Maximum Entropy Method (MEM); Wavelet Analysis; Morlet; Meyer; Mexican Hat; Non-stationary Waves; Empirical Mode Decomposition (EMD); Hilbert-Huang Transform; Cauchy Principal Value; Instantaneous Frequency (IF); Intrinsic Mode Function (IMF); Sifting
This section introduces some filters for the time series.
Low-Pass; High-Pass; Band-Pass; Moving Average; Running Mean; Lanczos Filter; Kolmogorov-Zurbenko (KZ) Filter; Spectral Leakage; Convolution; Gibbs Oscillation; Sinc Function; Boxcar Function; Spectral Response Function; Deseasonalization
This section introduces the concept of composite analysis.
Composite Analysis; K-Nearest Neighbors (KNN)
This section introduces the basics of linear regression.
Scatter Plots; Jittering; Scatterplot Matrices; Ordinary Least Square (OLS); Residual Plots; Cost Function; R Squared; Root Mean Squared Error (RMS); Analysis of Variance (ANOVA); Standard Error; Prediction Error; Confidence Interval; Prediction Interval
This section extends the scope and introduces some advanced techniques to make the linear regression robust.
Feature Selection; Forward Selection; Backward Elimination; Stepwise Regression; All Subset Regression; Maximum Likelihood Estimation (MLE); Weighted Regression; Robust Fit; Collinearity; Chi Squared Fit
This chapter introduces dimension reduction techniques, and this section introduces the most popular one called principal component analysis (PCA).
Unsupervised Learning; Eigenvector; Eigenvalue; Variance; Covariance Matrix; Correlation Matrix; Singular Value Decomposition (SVD); Orthogonality; Data Compression; Principal Components; Loading; Score; Expansion Coefficient; Empirical Orthogonal Functions (EOF)
Principal Component Analysis can serve as a spectral analysis approach, which is termed as singular spectrum analysis. The magic is enabled by the lagged time series matrix.
Harmonic Oscillation; Quadrature; Multi-Channel SSA
Some improvements based on PCA.
Orthogonal Rotations; Oblique Rotations; Varimax; Quartimax; Equamax; Parsimax
Very brief introduction about cluster analysis.
Unsupervised Learning; Euclidean Distance; Karl Pearson Distance; Simple Linkage; Complete Linkage; Average Linkage; Centroid Linkage; Hierarchical Clustering; K-Means Method
This chapter introduces the concept of weather and climate and the main players in the Earth's climate system.
The Butterfly Effect; Billiard Ball; Lorenz Attractor; Transitive System; Intransitive System; Internal Variability; External Forcing; Pressure; Hydrostatic Balance; Scale Height; Clausius-Clapeyron Relationship; Dry Adiabatic Lapse Rate; Moist Adiabatic Lapse Rate; Temperature Inversion; Thermocline
Some basic concepts of the Earth's energy balance, detailed discussion about the greenhosue effect, and some discussion about the insolation variability.
Radiation; Conduction; Convection; Solar Constant; Blackbody; Stephan-Boltzmann Theory; Shortwave; Longwave; Terrestrial; Planetary Albedo; Greenhouse Effect; Atmospheric Window; Faint Young Sun Paradox; 11-year Solar Cycle; Eccentricity; Precession; Obliquity; Zenith Angle; Elevation Angle; Azimuth Angle; Declination Angle; Hour Angle; Equinox; Solstice; Insolation
This section presents some satellite observations on the global energy budget.
Outgoing Longwave Radiation; Meridional Energy Transport; Cloud Radiative Effect; Radiative Forcing
The very basic concepts of the radiation transfer and its relationship with the climate system is well included in this chapter.
Transmission; Scattering; Absorption; Solar; Terrestrial; Planck's Law; Stefan-Boltzmann Law; Emissivity; Translational (Kinetic); Rotational; Vibrational; Electronic; Symmetric; Bending; Antisymmetric; Dipole Moment; Atmospheric Window; Pressure Broadening; Doppler Broadening; Emission Height; Radiative-Convetive Equilibrium; Convective Adjustment; Heating Rate; Greenhouse Effect; Condensed Water Path (CWP)
Main processes of the surface energy budget, including heat transfer in soils, sensible heat, and latent heat.
Penetration Depth; Borehole Data; Sensible Heat; Latent Heat; Bulk Aerodynamic Method; Aerodynamic Transfer Coefficient; Bulk Richardson Number; Bowen Ratio
This chapter introduces the hydrologic cycle, including the surface water balance equation, precipitation and evaporation, and sea level change due to the climate change.
Precipitation; Condensation; Evaporation; Gulf Stream; Intertropical Convergence Zone (ITCZ); Isostasy
This chapter introduces the most important topic in the field of climate physics - climate sensitivity and feedbacks. Definitions of many important terms are explained. Mathematical formation of the radiative forcing is studied. Main feedbacks in the climate system are well described.
Climate Sensitivity; Radiative Forcing; Positive Feedback; Negative Feedback; Equilibrium Climate; Fast Response; Stefan-Boltzmann Feedback; Ice-Albedo Feedback; Budyko's Model; Water Vapor Feedback; Lapse Rate Feedback; Polar Amplification; Cloud Feedback; Tropical Sea Surface Feedback (TSS); IPCC AR5
This chapter continues the discussion of climate sensitivity, and extends the discussion to non-equilibrium response.
Climate Sensitivity; Equilibrium; Response Time; Absolute Global Warming Potential (AGWP); Global Warming Potential (GWP); Absolute Global Temperature Potential (AGTP); Global Temperature Response (GTP)
This chapter gives a brief introduction of a very important subdecadal oscillation in climate system - ENSO.
El Nino; La Nina; Southern Oscillation; Teleconnections; Madden-Julian Oscillation (MJO); Kelvin Waves; Rossby Waves; Southern Oscillation Index (SOI); Nino Index
This chapter gives a brief introduction of the ocean circulation, and its relationship with the climate system.
Salinity; Thermocline; Deep Water; Thermohaline Circulation; Wind-Driven Circulation; Ekman Spiral; Ocean Gyres; Ekman Pumping; Sverdrup Balance
This mindmap series introduces parts of radiative transfer that are most relavant to the atmospheric sciences.
Classical Mechanics; Classical Electromagnetic; Thermodynamics; Special Relativity; Statistical Physics; Quantum Mechanics; Phenomenology; Wave-Particle Duality; Photon; Spectrum; Zenith Angle; Azimuthal Angle; Solid Angle; Steradian (sr); Intensity; Flux; Monochromatic; Actinic Flux; Emission; Extinction; Attenuation; Absorption; Scattering; Blackbody; Emissivity; Absorptivity; Graybody; Planck's Law; Kirchhoff's Law; (Local) Thermodynamic Equilibrium; Beer-Bouguer-Lambert Law (Beer's Law); Optical Path; Optical Thickness; Optical Depth; Transmissivity; Single Scattering Albedo; Phase Function; Schwarzschild's Equation; Intrinsic Optical Parameters (IOP); Weighting Function; Integro-Differential Equation; Limb Brightening / Darkening; Radiative Cooling / Heating
This mindmap series introduces parts of radiative transfer that are most relavant to the atmospheric sciences.
Spectroscopy; Line Intensity; Line Profile; Quantum Mechanics; Electronic Transition; Vibration Transition; Rotational Transition; Dipole Moment; Harmonic Oscillator; Symmetric; Bending; Asymmetric; Selection Rule; Overtone Band; Hot Band; Fundamental Band; R-Branch; Q-Branch; P-Branch; Nature Broadening; Briet-Wigner Form; Lorentzian Line; Half-Width; Uncertainty Principle; Pressure Broadening; AR-1; Doppler Broadening; Voigt Lineshape; Convolution; HITRAN
This mindmap series introduces parts of radiative transfer that are most relavant to the atmospheric sciences.
Continuum Absorption; Water Dimer; Far-Wing Absorption; Line-by-Line Approach; Band Model; Band Transmittance; Band Absorptance; Equivalent Width; Curve of Growth; Weak-Line Limit; Strong-Line Limit; Lorentz-Elsasser Band Model; Grayness Parameter; Gray Limit; Line Intensity Probability Distribution; Godson; Malkmus; Random Lorentz-Malkmus Band Model; K-Distribution; Correlated-K; Broadband Emittance Model
Definition and tracks of fluid dynamics.
Continuous; Irreversible; Hydraulics
Review of Newtonian Mechanics, which consists of vectorial mechanics and Lagrangian mechanics.
Cartesian Coordinates; Velocity; Acceleration; Conservative Force; Angular Momentum; Torque; Variational Approach; Functional; Kinetic Energy; Potential Energy; Lagrangian Functional; Hamilton's Principle; Euler-Lagrange Equation
This chapter introduces the basic equation set for perfect fluids.
Label Space; Open Sets; Eulerian Description; Lagrangian Description; Material / Substantial Derivative; Equation of Continuum; Equation of Motion; Conservation of Entropy; Incompressible Approximation
This chapter introduces other ways to derive the equation set, and add some additional terms into the basic equation set.
Kinetic Theory; Deviatoric Stress; Stress Rate Tensor; Viscosity; Newtonian Fluid; Distribution Function; Sampling Function; Number Density; Expectation; Tensor; Thermodynamic Pressure; Chapman-Enskog Expansion
This chapter gives some examples of fluids.
Bernoulli's Principle; Steady Flow; Dynamics Pressure Drop; Hydrostatic Approximation; Magnetic Pressure
This chapter introduces the general equation of motion, and discuss the Cauchy stress tensor in detail.
Incompressible Fluids; Navier-Stokes Equation; Strain Rate (Rate of Deformation); Dynamic Viscosity; Kinematic Viscosity; Cauchy Stress Tensor; Deviatoric Stress; Rheology; Principle Axes Theorem
This chapter introduces a very important technique in atmospheric science - dimensional analysis.
Drag Force; Geometric Similarity; Dynamic Similarity; Reynold Number; Quadratic Drag Law; Linear Drag Law; Boussinesq Approximation; Incompressibility; Anelastic Approximation; Mach Number; Froude Number; Argand Number; Peclet Number
This chapter discusses the geophysical fluid dynamics, where Coriolis force and centrifugal force are introduced.
Coriolis Force; Centrifugal Force; Euler Force; Conservation of Angular Momentum; Coriolis Parameter; Beta Plane Approximation; Rossby Number; Geostrophic Balance; Taylor Proudman Theorem; Shallow Water Equations
Vorticity describes the rotation of the fluids. This chapter explains some important concepts of vorticity.
Circulation; Kelvin's Circulation Theorem; Barotropic; Potential Vorticity; Absolute Vorticity; Relative Vorticity; Planetary Vorticity
Wave theory is applied on the fluid dynamics in this chapter. Some popular waves in the atmosphere are studied here.
Perturbation Theory; Phase Speed; Group Velocity; Dispersive Wave; Fourier Supposition; Wave Packet; Acoustic Waves; Linearization; Shallow Water Gravity Waves; Poincare Waves; Kelvin Waves; Radius of Deformation; Rossby Waves; Stream Function
This chapter introduces instability, which is the imaginary part of the wave function, describing the growth of waves.
Kelvin-Helmholtz Instability; Rayleigh-Taylor Instability
This chapter introduces turbulence.
Reynold Numbers; Energy Cascade; Kolmogorov; Energy Transmission Rate; 5/3 Dependence; Reynolds Averaging; Eddy Viscosity; Hyper-Viscosity; Reynolds Stress
This chapter introduces many basic concepts in the field of machine learning. Instead of being explicitly programmed, it gives computers the ability to learn the data. It becomes widespread and popular in more and more applications. All the algorithms can be divided in to several categories, given different criteria.
Image Classification; Semantic Segmentation; Natural Language Processing; Regression; Speech Recognition; Anomaly Detection; Clustering; Recommender; Game Bot; Supervised; Unsupervised; Semisupervised; Reinforcement Learning; Classification; Visualization; Dimension Reduction; Association Rule Learning; Batch Learning; Online Learning; Learning Rate; Out-of-Core Learning; Incremental Learning; Instance-Based Learning; Model-Based Learning
This chapter introduces many basic concepts in the field of machine learning. Challenges in the field of machine learning include bad data and inappropriate algorithms for certain data set. Testing and validating thus become critical.
Outliers; Feature Engineering; Feature Selection; Feature Extraction; Feature Creation; Overfitting; Underfitting; Regularization; Hyperparameters; Generalization Error (Out-of-Sample Error); Holdout Validation (Validation Set); No Free Lunch (NFL) Theorem
This chapter takes the housing price data in California as an example, and walks through the overall processes of data preprocessing, model application, fine-tuning, test & validation, and deployment & maintanence.
Data Pipeline; Root Mean Square Error (RMSE); Mean Absolute Error (MAE); Hash Sampling; Stratified Sampling; Transformers; Estimators; Predictors; Min-Max Scaling (Normalization); Standardization; K-Fold Cross-Validation; Grid Search; Randomized Search; Ensemble Methods