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 it is to be able to derive clear conclusions from often-noisy data drawn from a broad range of sources. This book teaches the basics of the underlying theory of data analysis, and then reinforces that knowledge with carefully chosen, realistic 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 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

- Cover image
- Table of Contents
- Front matter
- Copyright
- Dedication
- Preface
- Advice on scripting for beginners
- 1. Data analysis with MatLab
- 1.1. Why MatLab?
- 1.2. Getting started with MatLab
- 1.3. Getting organized
- 1.4. Navigating folders
- 1.5. Simple arithmetic and algebra
- 1.6. Vectors and matrices
- 1.7. Multiplication of vectors of matrices
- 1.8. Element access
- 1.9. To loop or not to loop
- 1.10. The matrix inverse
- 1.11. Loading data from a file
- 1.12. Plotting data
- 1.13. Saving data to a file
- 1.14. Some advice on writing scripts
- 2. A first look at data
- 2.1. Look at your data!
- 2.2. More on MatLab graphics
- 2.3. Rate information
- 2.4. Scatter plots and their limitations
- 3. Probability and what it has to do with data analysis
- 3.1. Random variables
- 3.2. Mean, median, and mode
- 3.3. Variance
- 3.4. Two important probability density functions
- 3.5. Functions of a random variable
- 3.6. Joint probabilities
- 3.7. Bayesian inference
- 3.8. Joint probability density functions
- 3.9. Covariance
- 3.10. Multivariate distributions
- 3.11. The multivariate Normal distributions
- 3.12. Linear functions of multivariate data
- 4. The power of linear models
- 4.1. Quantitative models, data, and model parameters
- 4.2. The simplest of quantitative models
- 4.3. Curve fitting
- 4.4. Mixtures
- 4.5. Weighted averages
- 4.6. Examining error
- 4.7. Least squares
- 4.8. Examples
- 4.9. Covariance and the behavior of error
- 5. Quantifying preconceptions
- 5.1. When least square fails
- 5.2. Prior information
- 5.3. Bayesian inference
- 5.4. The product of Normal probability density distributions
- 5.5. Generalized least squares
- 5.6. The role of the covariance of the data
- 5.7. Smoothness as prior information
- 5.8. Sparse matrices
- 5.9. Reorganizing grids of model parameters
- 6. Detecting periodicities
- 6.1. Describing sinusoidal oscillations
- 6.2. Models composed only of sinusoidal functions
- 6.3. Going complex
- 6.4. Lessons learned from the integral transform
- 6.5. Normal curve
- 6.6. Spikes
- 6.7. Area under a function
- 6.8. Time-delayed function
- 6.9. Derivative of a function
- 6.10. Integral of a function
- 6.11. Convolution
- 6.12. Nontransient signals
- 7. The past influences the present
- 7.1. Behavior sensitive to past conditions
- 7.2. Filtering as convolution
- 7.3. Solving problems with filters
- 7.4. Predicting the future
- 7.5. A parallel between filters and polynomials
- 7.6. Filter cascades and inverse filters
- 7.7. Making use of what you know
- 8. Patterns suggested by data
- 8.1. Samples as mixtures
- 8.2. Determining the minimum number of factors
- 8.3. Application to the Atlantic Rocks dataset
- 8.4. Spiky factors
- 8.5. Time-Variable functions
- 9. Detecting correlations among data
- 9.1. Correlation is covariance
- 9.2. Computing autocorrelation by hand
- 9.3. Relationship to convolution and power spectral density
- 9.4. Cross-correlation
- 9.5. Using the cross-correlation to align time series
- 9.6. Least squares estimation of filters
- 9.7. The effect of smoothing on time series
- 9.8. Band-pass filters
- 9.9. Frequency-dependent coherence
- 9.10. Windowing before computing Fourier transforms
- 9.11. Optimal window functions
- 10. Filling in missing data
- 10.1. Interpolation requires prior information
- 10.2. Linear interpolation
- 10.3. Cubic interpolation
- 10.4. Kriging
- 10.5. Interpolation in two-dimensions
- 10.6. Fourier transforms in two dimensions
- 11. Are my results significant?
- 11.1. The difference is due to random variation!
- 11.2. The distribution of the total error
- 11.3. Four important probability density functions
- 11.4. A hypothesis testing scenario
- 11.5. Testing improvement in fit
- 11.6. Testing the significance of a spectral peak
- 11.7. Bootstrap confidence intervals
- 12. Notes
- Note 1.1. On the persistence of MatLab variables
- Note 2.1. On time
- Note 2.2. On reading complicated text files
- Note 3.1. On the rule for error propagation
- Note 3.2. On the eda_draw() function
- Note 4.1. On complex least squares
- Note 5.1. On the derivation of generalized least squares
- Note 5.2. On MatLab functions
- Note 5.3. On reorganizing matrices
- Note 6.1. On the MatLabatan2() function
- Note 6.2. On the orthonormality of the discrete Fourier data kernel
- Note 8.1. On singular value decomposition
- Note 9.1. On coherence
- Note 9.2. On Lagrange multipliers
- Index