Basic Environmental Data Analysis for Scientists and Engineers

Description

Classroom tested and the result of over 30 years of teaching and research, this textbook is an invaluable tool for undergraduate and graduate data analysis courses in environmental sciences and engineering. It is also a useful reference on modern digital data analysis for the extensive and growing community of Earth scientists and engineers. Basic Environmental Data Analysis for Scientists and Engineers introduces practical concepts of modern digital data analysis and graphics, including numerical/graphical calculus, measurement units and dimensional analysis, error propagation and statistics, and least squares data modeling. It emphasizes array-based or matrix inversion and spectral analysis using the fast Fourier transform (FFT) that dominates modern data analysis. Divided into two parts, this comprehensive hands-on textbook is excellent for exploring data analysis principles and practice using MATLAB®, Mathematica, Mathcad, and other modern equation solving software. Part I, for beginning undergraduate students, introduces the basic approaches for quantifying data variations in terms of environmental parameters. These approaches emphasize uses of the data array or matrix, which is the fundamental data and mathematical processing format of modern electronic computing. Part II, for advanced undergraduate and beginning graduate students, extends the inverse problem to least squares solutions involving more than two unknowns. Features: Offers a uniquely practical guide for making students proficient in modern electronic data analysis and graphics Includes topics that are not explained in any existing textbook on environmental data analysis Data analysis topics are very well organized into a two-semester course that meets general education curriculum requirements in science and engineering Facilitates learning by beginning each chapter with an ‘Overview’ section highlighting the topics covered, and ending it with a ‘Key Concepts’ section summarizing the main technical details that the reader should have acquired Indexes many numerical examples for ready access in the classroom or other venues serviced by electronic equation solvers like MATLAB®, Mathematica, Mathcad, etc. Offers supplemental exercises and materials to enhance understanding the principles and practice of modern data analysis Cover Half Title Title Page Copyright Page Dedication Contents Preface 0.1 Book Objectives and Organization 0.2 Related Books 0.3 Acknowledgments 0.4 Author Biography Part I: Digital Data Calculus, Units, Errors, Statistics, and Linear Regression Chapter 1: Computing Trends 1.1 Overview 1.2 Numeration 1.3 Numerical Calculus 1.4 Computing Devices 1.5 Key Concepts Chapter 2: Data Attributes 2.1 Overview 2.2 Types 2.3 Formats 2.3.1 Elementary Matrix Algebra 2.4 Units 2.4.1 Dimensional Analysis 2.4.2 Similitude 2.4.3 Summary 2.5 Key Concepts Chapter 3: Error Analysis 3.1 Overview 3.2 Error Types 3.3 Accuracy and Precision 3.4 Absolute and Relative Errors 3.5 Significant Figures 3.6 Error Propagation 3.7 Key Concepts Chapter 4: Statistics 4.1 Overview 4.2 Basic Parameters 4.2.1 Population Mean, Variance, and Standard Deviation 4.2.2 Sample Mean, Variance, and Standard Deviation 4.2.3 Variance/Covariance Propagation 4.2.4 Probability and Distributions 4.3 Binomial Distribution 4.3.1 Permutations and Combinations 4.3.2 Probability Interpretation 4.4 Gaussian or Normal Distribution 4.4.1 Probability Interpretation 4.4.2 Curve Fitting a Histogram 4.4.3 Central Limits Theorem 4.5 Statistical Inference 4.5.1 Confidence Intervals on the Mean 4.5.2 Hypothesis Tests of the Mean 4.5.3 Confidence Intervals on the Variance 4.5.4 Hypothesis Tests of the Variance 4.5.5 Analysis of Variance 4.5.5.1 One-way ANOVA 4.5.5.2 Two-way ANOVA 4.5.6 Distribution Testing 4.5.7 Non-Parametric Testing 4.6 Key Concepts Chapter 5: Data Sampling 5.1 Overview 5.2 Introduction 5.3 Sampling Considerations 5.3.1 Sufficiency 5.3.2 Biasing 5.3.3 Distribution 5.3.4 Errors 5.4 Sampling Methods 5.4.1 Systematic 5.4.2 Random 5.4.3 Cluster 5.4.4 Selecting a Method 5.5 Key Concepts Chapter 6: Algebraic Linear Regression 6.1 Overview 6.2 Concept of Least Squares 6.3 Straight Line Modeling 6.4 Measures of the Fit 6.4.1 Variances of the Intercept and Slope 6.4.1.1 Uniform Error Observations 6.4.1.2 Variable Error Observations 6.4.2 Confidence Intervals on the Intercept and Slope 6.4.3 Confidence Intervals on the Predictions 6.4.4 Correlation Coefficient 6.4.4.1 Interpretation 6.4.4.2 Significance 6.4.5 Significance of the Fit 6.5 Additional Linear Regression Strategies 6.5.1 Weighted Linear Regression 6.5.2 Reversed Variables 6.5.3 Least Squares Cubic Line 6.5.4 Reduced Major Axis Line 6.6 Key Concepts Chapter 7: Matrix Linear Regression 7.1 Overview 7.2 Introduction 7.3 Solving for the Unknowns 7.3.1 Cramer’s Rule 7.3.2 Inverse Determination 7.3.3 Elimination Methods 7.4 Sensitivity Analysis 7.4.1 Intercept and Slope Variances 7.4.2 Intercept and Slope Error Bars 7.4.3 Prediction Variance and Error Bars 7.4.4 Correlation Coefficient 7.4.5 ANOVA Significance 7.5 Additional Linear Regression Strategies 7.6 Summary 7.7 Key Concepts Part II: Digital Data Inversion, Spectral Analysis, Interrogation, and Graphics Chapter 8: Basic Digital Data Analysis 8.1 Overview 8.2 Introduction 8.3 Data Inversion or Modeling 8.4 Trial and Error Methods 8.5 Key Concepts Chapter 9: Array Methods 9.1 Overview 9.2 Introduction 9.3 Matrix Inversion 9.3.1 Error Statistics 9.3.2 Sensitivity Analysis 9.4 Generalized Linear Inversion 9.4.1 Eigenvalues and Eigenvectors 9.4.2 Singular Value Decomposition 9.4.3 Generalized Linear Inverse 9.4.3.1 Information Density 9.4.3.2 Model Resolution 9.4.3.3 Model Variance 9.4.4 Sensitivity Analysis 9.5 Summary 9.6 Key Concepts Chapter 10: Spectral Analysis 10.1 Overview 10.2 Introduction 10.3 Analytical Fourier Transform 10.4 Numerical Fourier Transform 10.4.1 Numerical Errors 10.4.1.1 Gibbs’ Error 10.4.1.2 Wavenumber Leakage 10.4.1.3 Wavenumber Aliasing 10.4.1.4 Wavenumber Resolution 10.5 Key Concepts Chapter 11: Data Interrogation 11.1 Overview 11.2 Introduction 11.3 Convolution 11.3.1 Analytical Convolution 11.3.2 Numerical Convolution and Deconvolution 11.3.3 Convolution and Correlation Theorems 11.3.4 Summary 11.4 Isolation and Enhancement 11.4.1 Spatial Filtering 11.4.1.1 Geological Methods 11.4.1.2 Graphical Methods 11.4.1.3 Trend Surface Analysis 11.4.1.4 Analytical Grid Methods 11.4.2 Spectral Filtering 11.4.2.1 Wavelength Filters 11.4.2.2 Directional Filters 11.4.2.3 Correlation Filters 11.4.2.4 Derivative and Integral Filters 11.4.2.5 Interpolation and Continuation Filters 11.5 Key Concepts Chapter 12: Data Graphics 12.1 Overview 12.2 Introduction 12.3 Map Projections and Transformations 12.4 Gridding 12.4.1 Linear Interpolation 12.4.2 Cubic Spline Interpolation 12.4.3 Equivalent Source Interpolation 12.4.4 Polynomial Interpolation 12.4.5 Statistical Interpolation 12.5 Graphical Parameters and Practice 12.5.1 Standardized and Normalized Data 12.5.2 Local Favorability Indices 12.6 Presentation Modes 12.7 Key Concepts References Index