Data Analysis for the Geosciences - Essentials of Uncertainty, Comparison, and Visualization

An initial course in scientific data analysis and hypothesis testing designed for students in all science, technology, engineering, and mathematics disciplines
 
Data Analysis for the Geosciences: Essentials of Uncertainty, Comparison, and Visualization is a textbook for upper-level undergraduate STEM students, designed to be their statistics course in a degree program.
 
This volume provides a comprehensive introduction to data analysis, visualization, and data-model comparisons and metrics, within the framework of the uncertainty around the values. It offers a learning experience based on real data from the Earth, ocean, atmospheric, space, and planetary sciences.
 
About this volume:
* Serves as an initial course in scientific data analysis and hypothesis testing
* Focuses on the methods of data processing
* Introduces a wide range of analysis techniques
* Describes the many ways to compare data with models
* Centers on applications rather than derivations
* Explains how to select appropriate statistics for meaningful decisions
* Explores the importance of the concept of uncertainty
* Uses examples from real geoscience observations
* Homework problems at the end of chapters
 
The American Geophysical Union promotes discovery in Earth and space science for the benefit of humanity. Its publications disseminate scientific knowledge and provide resources for researchers, students, and professionals.

List of contents

Preface xv
 
Acknowledgments xxi
 
About the Companion Website xxiii
 
1 Assessment and Uncertainty: Examples and Introductory Concepts 1
 
1.1 Chicken Little, Amateur Meteorologist 2
 
1.2 Uncertainty Ascribes Meaning to Values 3
 
1.3 Significant Figures 3
 
1.4 Types of Uncertainty 7
 
1.5 Example: Finding Saturn's Moons 9
 
1.6 Comparing Two Numbers: Are They Measuring the Same Value? 11
 
1.6.1 Distributions of Number Sets 12
 
1.6.2 The Gaussian Distribution 13
 
1.6.3 Testing a Specific Value within a Data Set: The z Test 14
 
1.6.4 Comparing Two Values Revisited 18
 
1.7 Use and Misuse of Statistics 19
 
1.8 Example: Solar Wind Density and Space Weather 20
 
1.9 Uncertainty and the Scientific Method 22
 
1.10 Further Reading 24
 
1.11 Exercises in the Geosciences 26
 
2 Plotting Data: Visualizing Sets of Numbers 27
 
2.1 Plotting One- Dimensional Data 27
 
2.1.1 What Makes a Good Plot? 29
 
2.1.2 Exploratory Versus Explanatory Plot Styles 31
 
2.2 Example: Earth's Magnetic Field Strength 33
 
2.3 Probability Distributions-- The Histogram 35
 
2.4 Plotting Two Data Sets Against Each Other 39
 
2.4.1 Overlaid Histograms 39
 
2.4.2 The Scatterplot 40
 
2.4.3 The Box Plot 42
 
2.4.4 The Box- and- Whisker Scatterplot 43
 
2.4.5 The Running Average Plot 44
 
2.5 Example: Temperature and Carbon Dioxide 48
 
2.6 Scientific Visualization: A Sampling from the Literature 50
 
2.6.1 A Very Brief History of Visualization 51
 
2.6.2 Good Modern- Day Example Visualizations 53
 
2.7 Visualization Best Practices 58
 
2.7.1 Levels of Abstraction 58
 
2.7.2 A Process for a Good Graphic 61
 
2.7.3 Types of Colorblindness 63
 
2.7.4 Color Scales 63
 
2.8 Further Reading 65
 
2.9 Exercises in the Geosciences 67
 
3 Uncertainty Analysis: Techniques for Propagating Uncertainty 69
 
3.1 Propagating Uncertainty 69
 
3.1.1 Calculating Uncertainty with One Independent Variable 69
 
3.1.2 Calculating Uncertainty with Two Independent Variables 70
 
3.1.3 Calculating Uncertainty with Many Independent Variables 72
 
3.2 Example: Atmospheric Density 72
 
3.2.1 The Hydrostatic Equilibrium Approximation 72
 
3.2.2 One Independent Variable 73
 
3.2.3 Two Independent Variables 74
 
3.2.4 Many Independent Variables 74
 
3.3 Fractional and Percentage Uncertainties 75
 
3.4 Special Cases of Uncertainty Propagation 77
 
3.4.1 Addition and Subtraction 77
 
3.4.2 Multiplication and Division 78
 
3.4.2.1 Multiplication of Two Parameters 78
 
3.4.2.2 Uncertainty of Air Pressure 79
 
3.4.2.3 Division with Correlated Variables 80
 
3.4.2.4 Multiplication and Division with Independent Variables 81
 
3.4.3 Power Laws 82
 
3.4.4 Exponentials and Logarithms 82
 
3.4.4.1 Exponential Functions 83
 
3.4.4.2 Logarithmic Functions 84
 
3.4.5 Trigonometric Functions 84
 
3.5 Stepwise Uncertainty Propagation 85
 
3.6 Example: Planetary Equilibrium Temperature 87
 
3.7 Multistep Processing 90
 
3.8 Final Advice on Uncertainty Propagation 91
 
3.9 Further Reading 93
 
3.10 Exercises in the Geosciences 93
 
4 Centroids and Spreads: Analyzing a Set of Numbers 95
 
4.1 Quantitatively Describing a Data Set: The Centroid 95
 
4.1.1 Three Versions of Mean 96
 
4.1.2 More Centroids: Med

About the author

Michael W. Liemohn, University of Michigan, USA

Summary

An initial course in scientific data analysis and hypothesis testing designed for students in all science, technology, engineering, and mathematics disciplines

Data Analysis for the Geosciences: Essentials of Uncertainty, Comparison, and Visualization is a textbook for upper-level undergraduate STEM students, designed to be their statistics course in a degree program.

This volume provides a comprehensive introduction to data analysis, visualization, and data-model comparisons and metrics, within the framework of the uncertainty around the values. It offers a learning experience based on real data from the Earth, ocean, atmospheric, space, and planetary sciences.

About this volume:
* Serves as an initial course in scientific data analysis and hypothesis testing
* Focuses on the methods of data processing
* Introduces a wide range of analysis techniques
* Describes the many ways to compare data with models
* Centers on applications rather than derivations
* Explains how to select appropriate statistics for meaningful decisions
* Explores the importance of the concept of uncertainty
* Uses examples from real geoscience observations
* Homework problems at the end of chapters

The American Geophysical Union promotes discovery in Earth and space science for the benefit of humanity. Its publications disseminate scientific knowledge and provide resources for researchers, students, and professionals.

Product details

• Authors: Michael W Liemohn, Michael W. Liemohn, Michael W. (University of Michigan Liemohn
• Publisher: Wiley, John and Sons Ltd
• Languages: English
• Product format: Paperback / Softback
• Released: 02.11.2023
• EAN: 9781119747871
• ISBN: 978-1-119-74787-1
• No. of pages: 448
• Series: AGU Advanced Textbooks
• Subjects: Natural sciences, medicine, IT, technology > Geosciences; Statistik, Geologie, Datenanalyse, Geowissenschaften, Statistics, Earth Sciences, Statistik in den Ingenieurwissenschaften, Engineering Statistics, Rechnergestützte u. graphische Statistik, Computational & Graphical Statistics, Geology & Geophysics, Geologie u. Geophysik