Statistics for Earth and Environmental Scientists

John H. Schuenemeyer, Lawrence J. Drew

• Publisher: Wiley
• Year: 2011
• ISBN:
  9781118102213
• Edition: 1
• Topic: Mathematics
• Subtopic: Probability & Statistics
• Index: Mathematics

A comprehensive treatment of statistical applications for solving real-world environmental problems

A host of complex problems face today's earth science community, such as evaluating the supply of remaining non-renewable energy resources, assessing the impact of people on the environment, understanding climate change, and managing the use of water. Proper collection and analysis of data using statistical techniques contributes significantly toward the solution of these problems. Statistics for Earth and Environmental Scientists presents important statistical concepts through data analytic tools and shows readers how to apply them to real-world problems.

The authors present several different statistical approaches to the environmental sciences, including Bayesian and nonparametric methodologies. The book begins with an introduction to types of data, evaluation of data, modeling and estimation, random variation, and sampling—all of which are explored through case studies that use real data from earth science applications. Subsequent chapters focus on principles of modeling and the key methods and techniques for analyzing scientific data, including:

• Interval estimation and Methods for analyzinghypothesis testing of means time series data
  
  

• Spatial statistics
  
  

• Multivariate analysis
  
  

• Discrete distributions
  
  

• Experimental design
  
  

Most statistical models are introduced by concept and application, given as equations, and then accompanied by heuristic justification rather than a formal proof. Data analysis, model building, and statistical inference are stressed throughout, and readers are encouraged to collect their own data to incorporate into the exercises at the end of each chapter. Most data sets, graphs, and analyses are computed using R, but can be worked with using any statistical computing software. A related website features additional data sets, answers to selected exercises, and R code for the book's examples.

Statistics for Earth and Environmental Scientists is an excellent book for courses on quantitative methods in geology, geography, natural resources, and environmental sciences at the upper-undergraduate and graduate levels. It is also a valuable reference for earth scientists, geologists, hydrologists, and environmental statisticians who collect and analyze data in their everyday work.

Chapter 1

Role of Statistics and Data Analysis

1.1 Introduction

The purpose of this chapter is to provide an overview of important concepts in data analysis and statistics. Types of data, data evaluation, and an introduction to modeling and estimation are presented. Random variation, sampling, and different statistical paradigms are also introduced. These concepts are investigated in detail in subsequent chapters. An important distinguishing feature in many earth and environmental science analyses is the need for spatial sampling. Problems are described in the context of case studies, which use real data from earth science applications.

1.2 Case Studies

Wherever possible, case studies are used to illustrate methods. Two studies that are used extensively in this and subsequent chapters are water-well yield data and observations from an ice core.

1.2.1 Water-Well Yield Case Study

A concern in many parts of the world is the availability of an adequate supply of fresh water. Planners and managers want to know how much water is available. Scientists want to gain a greater understanding of transport systems and the relationship of water to other geologic phenomena. Homeowners who do not have access to municipal water want to know where to drill for water on their property. A subset of 754 water-well yield observations (water-well yield case study, Appendix I; see the book's Web site) from the Blue Ridge Geological Province, Loudoun County, Virginia (Sutphin et al., 2001) is used to illustrate graphical procedures. The variables are water-well yield in gallons per minute (gpm) for rock type Yg (Yg is a Middle Proterozoic Leucocratic Metagranite) and corresponding coordinates called easting (x-axis) and northing (y-axis). In Chapter 6 spatial applications are discussed.

1.2.2 Ice Core Case Study

Ice core data help scientists understand how Earth's climate works. The U.S. Geological Survey National Ice Core Laboratory (2004) states that “Over the past decade, research on the climate record frozen in ice cores from the Polar Regions has changed our basic understanding of how the climate system works. Changes in temperature and precipitation, which previously we believed, would require many thousands of years to happen were revealed, through the study of ice cores, to have happened in fewer than twenty years. These discoveries have challenged our beliefs about how the climate system works.”

A record that can extend back many thousands of years may include temperature, precipitation, and chemical composition. An example of ice core data (ice core case study, Appendix II; see the book's Web site) submitted to the National Geophysical Data Center (2004) by Arkhipov et al. (1987) has been chosen. Data submitted by Arkhipov are from 1987 in the Austfonna Ice Cap of the Svalbard Archipelago and go to a depth of 566 m. Melting of ice masses is thought to be contributing to sea-level rise. Only data in the first 50 m are presented. In addition to depth, the variables are pH,

(hydrogen carbonate), and Cl (chlorine), all in milligrams per liter of water.

1.3 Data

Sir Arthur Conan Doyle, physician and writer (1859–1930), noted: “It is a capital mistake to theorize before one has data. Insensibly one begins to twist facts to suit theories, instead of theories to suit facts.” Data are fundamental to statistics. Most data are obtained from measurements. Increasingly, these measurements are obtained from automated processes such as ground weather stations and satellites. However, field studies are still an important way to collect data. Another important source of data is expert judgment. In areas where few hard data (measurements) are available, such as in the Arctic, experts are called upon to express their opinions.

Data may be rock type, wind speed, orientation of a fault, temperature, and a host of other variables. There are several ways to classify data. Two of the most useful classifications are continuous versus discrete and ratio–interval–ordinal–nominal (Table 1.1). A continuous process generates continuous data. Discrete data typically result from counting. Continuous data can be ratio or interval. Discrete data are nominal data. Data classification systems help to select appropriate data analytic techniques and models.

Table 1.1 Data Classification Systems.

	Examples
Continuous vs. Discrete Data
Continuous: measurements can be made as fine as needed	Temperature, depth, sulfur content, well water yield
Discrete: data that can be categorized into a classification where only a finite number of values are possible, typically count data	Number of days above freezing, number of water wells producing among a sample of 50 holes
Ratio, Interval, Ordinal, and Nominal Data
Ratio: continuous data where an interval and ratio are meaningful	Depth, sulfur content
Interval: continuous data with no natural zero	Temperature measured in degrees Celsius
Ordinal: data that are rank ordered	Survey responses such as good, fair, poor; water yields as high, medium, low
Nominal: Data that fit into categories; cannot be rank ordered	Location name, rock type

To distinguish between ratio and interval data, consider the following example. With a ratio scale, zero means an absence of something, such as rainfall. With an interval scale, zero is arbitrary, such as zero degrees Celsius, which is not an absence of temperature and has a different meaning than zero degrees Fahrenheit. The terms quantitative and qualitative are also used. Sometimes qualitative data is considered synonymous with nominal data; and sometimes it just refers to something subjective or not precisely defined. Categorical data are data classified into categories. The terms categorical and nominal are sometimes used interchangeably.

Another way to view data is as primary or secondary. Primary data are collected to answer questions related to a particular study, such as sampling a site to ascertain the level of coal bed methane seepage. Secondary data are collected for some other purpose and may be used as supportive data. Typically, secondary data are historical data. Numerous government agencies routinely collect and publish both types of data on the earth sciences.

In the beginning chapters of this book, properties of a single variable are discussed. This variable may be temperature, water-well yield, or mercury level in fish. A single variable may change over time or space. In later chapters, multivariate data are examined, that is, data where multiple attributes are recorded at each sample point. Most data are multivariate. For example, in a study of climate, the relationships among temperature, atmospheric pressure, and precipitation can be analyzed. Geochemical data often contain dozens of variables.

1.4 Samples Versus the Population: Some Notation

A critical distinction for the analyst to make is sample versus population. A population comprises all the data of interest in a study. In most earth science applications, the population is large to infinite. In air quality studies, it may be the troposphere. A sample is a subset of a population. A statistic is a number derived from a sample. The method used to obtain a sample (the sampling plan) determines the type of inferences that can be made. Generally, in earth science applications, the sample size will be small with respect to the population size. The notations that are used in this book to represent populations and samples are those commonly used in the statistics literature. Statistics involves the use of random variables. A random variable is a function, that maps events into numbers. Each number or range of numbers is assigned a probability. There are two types of random variables, continuous and discrete. For example, a discrete random variab...

Table of contents

• Cover
• Title Page
• Copyright
• Preface
• Chapter 1: Role of Statistics and Data Analysis
• Chapter 2: Modeling Concepts
• Chapter 3: Estimation and Hypothesis Testing on Means and Other Statistics
• Chapter 4: Regression
• Chapter 5: Time Series
• Chapter 6: Spatial Statistics
• Chapter 7: Multivariate Analysis
• Chapter 8: Discrete Data Analysis and Point Processes
• Chapter 9: Design of Experiments
• Chapter 10: Directional Data
• References
• Index