Python Recipes for Earth Sciences, Second Edition

Python is used in a wide range of geoscientific applications, such as in processing images for remote sensing, in generating and processing digital elevation models, and in analyzing time series. This book introduces methods of data analysis in the geosciences using Python that include basic statistics for univariate, bivariate, and multivariate data sets, time series analysis, and signal processing; the analysis of spatial and directional data; and image analysis. The text includes numerous examples that demonstrate how Python can be used on data sets from the earth sciences. Codes are available online through GitHub. Preface Contents 1 Data Analysis in the Earth Sciences 1.1 Introduction 1.2 Data Collection 1.3 Data Types 1.4 Methods of Data Analysis Anchor 6 References 2 Introduction to Python 2.1 Introduction 2.2 Getting Started 2.3 Python Syntax 2.4 Array Manipulation 2.5 Data Types in Python 2.6 Data Storage and Handling 2.7 Control Flow 2.8 Scripts and Functions 2.9 Basic Visualization Tools Anchor 11 References 3 Univariate Statistics 3.1 Introduction 3.2 Empirical Distributions 3.2.1 Measures of Central Tendency 3.2.2 Measures of Dispersion 3.3 Examples of Empirical Distributions 3.4 Theoretical Distributions 3.4.1 Uniform Distribution 3.4.2 Binomial Distribution 3.4.3 Poisson Distribution 3.4.4 Normal or Gaussian Distribution 3.4.5 Logarithmic Normal (or Log-Normal) Distribution 3.4.6 Student's t-Distribution 3.4.7 Fisher's F-Distribution 3.4.8 χ2- (or Chi-Squared-) Distribution 3.5 Examples of Theoretical Distributions 3.6 Hypothesis Testing 3.7 The t-Test 3.8 The F-Test 3.9 The χ2-Test 3.10 The Kolmogorov–Smirnov Test 3.11 The Mann–Whitney Test 3.12 The Ansari–Bradley Test 3.13 Distribution Fitting 3.14 Error Analysis Anchor 26 References 4 Bivariate Statistics 4.1 Introduction 4.2 Correlation Coefficients 4.3 Classical Linear Regression Analysis 4.4 Analyzing Residuals 4.5 Bootstrap Estimates of Regression Coefficients 4.6 Jackknife Estimates of Regression Coefficients 4.7 Cross-Validation 4.8 Reduced Major Axis Regression 4.9 Curvilinear Regression 4.9.1 Nonlinear and Weighted Regression Anchor 12 References 5 Time Series Analysis 5.1 Introduction 5.2 Generating Signals 5.3 Fourier Transforms FT, DFT and FFT 5.4 Schuster’s Periodogram Method 5.5 The Blackman–Tukey Method and Welch’s Method 5.6 Interpolating and Analyzing Unevenly Spaced Data 5.7 The Spectrogram (Sonogram, Sonograph) Method 5.8 Thomson’s Multitaper Method 5.9 The Lomb–Scargle Power Spectrum 5.10 The Wavelet Power Spectrum 5.11 Nonlinear Time Series Analysis (by N. Marwan) 5.11.1 Phase Space Portrait 5.11.2 Recurrence Plots 5.11.3 Recurrence Quantification 5.12 Detecting Abrupt Transitions in Time Series 5.13 Describing Gradual Transitions in Time Series References 6 Signal Processing 6.1 Introduction 6.2 Generating Signals 6.3 Linear Time Invariant Systems 6.4 Convolution, Deconvolution, and Filtering 6.5 Comparing Functions for Filtering Data Series 6.6 Recursive and Nonrecursive Filters 6.7 Impulse Response 6.8 Frequency Response 6.9 Filter Design 6.10 Adaptive Filtering Anchor 12 References 7 Spatial Data 7.1 Introduction 7.2 The Global Geography Database GSHHG 7.3 The 15 Arc-Second Global Relief Model ETOPO 2022 7.4 The 30 Arc-Second Elevation Model GTOPO30 7.5 The Shuttle Radar Topography Mission SRTM 7.6 Gridding and Contouring 7.7 Comparison of Methods and Potential Artifacts 7.8 Statistics of Point Distributions 7.9 Analysis of Digital Elevation Models (by R. Gebbers) 7.10 Geostatistics and Kriging (by R. Gebbers) Anchor 12 References 8 Image Processing 8.1 Introduction 8.2 Data Storage 8.3 Importing, Processing, and Exporting Images 8.4 Importing, Processing, and Exporting Landsat Images 8.5 Importing and Georeferencing Terra ASTER Images 8.6 Processing and Exporting EO-1 Hyperion Images 8.7 The Normalized Difference Vegetation Index NDVI 8.8 Image Enhancement, Correction, and Rectification 8.9 Removing Periodic Noise from Images 8.10 Grain Size Analysis from Microscopic Images 8.11 Quantifying Charcoal in Microscopic Images 8.12 Shape-Based Object Detection in Images 8.13 Digitizing from the Screen Anchor 15 References 9 Multivariate Statistics 9.1 Introduction 9.2 Principal Component Analysis 9.3 Independent Component Analysis (by N. Marwan) 9.4 Discriminant Analysis 9.5 Cluster Analysis 9.6 Multiple Linear Regression 9.7 Aitchison’s Log-Ratio Transformation Anchor 9 References 10 Directional Data 10.1 Introduction 10.2 The Graphical Representation of Circular Data 10.3 Empirical Distributions of Circular Data 10.4 Theoretical Distributions of Circular Data 10.5 Testing for the Randomness of Circular Data 10.6 Testing for the Significance of a Mean Direction 10.7 Testing for the Difference Between Two Sets of Directions 10.8 The Graphical Representation of Spherical Data 10.9 The Statistics of Spherical Data Anchor 11 References