Environmental Data Analysis with MatLab

Environmental Data Analysis with MatLab is a reference work designed to teach students and researchers the basics of data analysis in the environmental sciences using MatLab, and more specifically how to analyze data sets in carefully chosen, realistic scenarios. Although written in a self-contained way, the text is supplemented with data sets and MatLab scripts that can be used as a data analysis tutorial, available at the author's website: http://www.ldeo.columbia.edu/users/menke/edawm/index.htm.

This book is organized into 12 chapters. After introducing the reader to the basics of data analysis with MatLab, the discussion turns to the power of linear models; quantifying preconceptions; detecting periodicities; patterns suggested by data; detecting correlations among the data; filling in missing data; and determining whether your results are significant. Homework problems help users follow up upon case studies.

This text will appeal to environmental scientists, specialists, researchers, analysts, and undergraduate and graduate students in Environmental Engineering, Environmental Biology and Earth Science courses, who are working to analyze data and communicate results.

• 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

Environmental scientists, specialists, researchers, analysts, undergraduate and graduate students in Environmental Engineering, Environmental Biology and Earth Science, who are working to analyze data and communicate results

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