Environmental Data Analysis With Matlab

Environmental Data Analysis with MatLab is for students and researchers working to analyze real data sets in the environmental sciences. One only has to consider the global warming debate to realize how critically important is the skill to derive clear conclusions from often-noisy data drawn from a broad range of sources. The book teaches the basics of the underlying theory of data analysis, and then reinforces that knowledge by its immediate use in carefully chosen, realistic data analysis scenarios. MatLab, a commercial data processing environment, is used in these scenarios; significant content is devoted to teaching how it can be effectively used in an environmental data analysis setting. The book, though written in a self-contained way, is supplemented with a set of data sets and MatLab scripts that can be used as a data analysis tutorial. Well written and outlines a clear learning path for researchers and students Uses real world environmental examples and case studies MatLab software for application in a readily-available software environment Homework problems help user follow up upon case studies with homework that expands them

Data analysis with MatLab
Why MatLab?	p. 1
Getting started with MatLab	p. 3
Getting organized	p. 3
Navigating folders	p. 4
Simple arithmetic and algebra	p. 5
Vectors and matrices	p. 7
Multiplication of vectors of matrices	p. 7
Element access	p. 8
To loop or not to loop	p. 9
The matrix inverse	p. 11
Loading data from a file	p. 11
Plotting data	p. 12
Saving data to a file	p. 13
Some advice on writing scripts	p. 13
Problems	p. 15
A first look at data
Look at your data!	p. 17
More on MatLab graphics	p. 24
Rate information	p. 28
Scatter plots and their limitations	p. 30
Problems	p. 33
Probability and what it has to do with data analysis
Random variables	p. 35
Mean, median, and mode	p. 37
Variance	p. 41
Two important probability density functions	p. 42
Functions of a random variable	p. 44
Joint probabilities	p. 46
Bayesian inference48
Joint probability density functions	p. 49
Covariance52
Multivariate distributions	p. 54
The multivariate Normal distributions	p. 54
Linear functions of multivariate data
Problems	p. 60
The power of linear models
Quantitative models, data, and model parameters	p. 61
The simplest of quantitative models	p. 63
Curve fitting	p. 64
Mixtures	p. 67
Weighted averages	p. 68
Examining error	p. 71
Least squares	p. 74
Examples	p. 76
Covariance and the behavior of error	p. 79
Problems	p. 81
Quantifying preconceptions
When least square fails	p. 83
Prior information	p. 84
Bayesian inference	p. 86
The product of Normal probability density distributions	p. 88
Generalized least squares	p. 90
The role of the covariance of the data	p. 92
Smoothness as prior information	p. 93
Sparse matrices	p. 95
Reorganizing grids of model parameters	p. 98
Problems	p. 101
Detecting periodicities
Describing sinusoidal oscillations	p. 103
Models composed only of sinusoidal functions	p. 105
Going complex	p. 112
Lessons learned from the integral transform	p. 114
Normal curve	p. 115
Spikes	p. 116
Area under a function	p. 118
Time-delayed function	p. 118
Derivative of a function	p. 120
Integral of a function	p. 120
Convolution	p. 121
Nontransient signals	p. 122
Problems	p. 124
The past influences the present
Behavior sensitive to past conditions	p. 127
Filtering as convolution	p. 131
Solving problems with filters	p. 132
Predicting the future	p. 139
A parallel between filters and polynomials	p. 140
Filter cascades and inverse filters	p. 142
Making use of what you know	p. 145
Problems	p. 147
Patterns Suggested by data
Samples as mixtures	p. 149
Determining the minimum number of factors	p. 151
Application to the Atlantic Rocks dataset	p. 155
Spiky factors	p. 156
Time-Variable functions	p. 160
Problems	p. 163
Detecting correlations among data
Correlation is covariance	p. 167
Computing autocorrelation by hand	p. 173
Relationship to convolution and power spectral density	p. 173
Cross-correlation	p. 174
Using the cross-correlation to align time serie	p. 176
Least squares estimation of filters	p. 178
The effect of smoothing on time series	p. 180
Band-pass filters	p. 184
Frequency-dependent coherence	p. 188
Windowing before computing Fourier transforms	p. 195
Optimal window functions	p. 196
Problems	p. 201
Filling in missing data
Interpolation requires prior information	p. 203
Linear interpolation	p. 205
Cubic interpolation	p. 206
Kriging	p. 208
Interpolation in two-dimensions	p. 210
Fourier transforms in two dimensions	p. 213
Problems	p. 215
Are my results significant?
The difference is due to random variation!	p. 217
The distribution of the total error	p. 218
Four important probability density functions	p. 220
A hypothesis testing scenario	p. 222
Testing improvement in fit	p. 228
Testing the significance of a spectral peak	p. 229
Bootstrap confidence intervals	p. 234
Problems	p. 238
Notes
On the persistence of MatLab variables	p. 239
On time	p. 240
On reading complicated text files	p. 241
On the rule for error propagation	p. 242
On the eda_draw( )function	p. 242
On complex least squares	p. 243
On the derivation of generalized least squares	p. 245
On MatLab functions	p. 245
On reorganizing matrices	p. 246
On the MatLab atan2() function	p. 246
On the orthonormality of the discrete Fourier data kernel	p. 246
On singular value decomposition	p. 247
On coherence	p. 248
On Lagrange multipliers	p. 249
Index	p. 251
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Environmental Data Analysis With Matlab

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