Basic Environmental Data Analysis for Scientists and Engineers

Ralph R.B. Von Frese

• Publisher: CRC Press
• Year: 2019
• Print ISBN: 9781032475066
• eBook ISBN: 9781000725759
• Edition: 1
• Topic: Mathematics
• Subtopic: Probability & Statistics
• Index: Mathematics

Classroom tested and the result of over 30 years of teaching and research, this textbook is an invaluable tool for undergraduate and graduate data analysis courses in environmental sciences and engineering. It is also a useful reference on modern digital data analysis for the extensive and growing community of Earth scientists and engineers.

Basic Environmental Data Analysis for Scientists and Engineers introduces practical concepts of modern digital data analysis and graphics, including numerical/graphical calculus, measurement units and dimensional analysis, error propagation and statistics, and least squares data modeling. It emphasizes array-based or matrix inversion and spectral analysis using the fast Fourier transform (FFT) that dominates modern data analysis. Divided into two parts, this comprehensive hands-on textbook is excellent for exploring data analysis principles and practice using MATLAB®, Mathematica, Mathcad, and other modern equation solving software.

Part I, for beginning undergraduate students, introduces the basic approaches for quantifying data variations in terms of environmental parameters. These approaches emphasize uses of the data array or matrix, which is the fundamental data and mathematical processing format of modern electronic computing. Part II, for advanced undergraduate and beginning graduate students, extends the inverse problem to least squares solutions involving more than two unknowns.

Features:

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• Offers a uniquely practical guide for making students proficient in modern electronic data analysis and graphics

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• Includes topics that are not explained in any existing textbook on environmental data analysis

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• Data analysis topics are very well organized into a two-semester course that meets general education curriculum requirements in science and engineering

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• Facilitates learning by beginning each chapter with an ' Overview ' section highlighting the topics covered, and ending it with a ' Key Concepts ' section summarizing the main technical details that the reader should have acquired

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• Indexes many numerical examples for ready access in the classroom or other venues serviced by electronic equation solvers like MATLAB®, Mathematica, Mathcad, etc.

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• Offers supplemental exercises and materials to enhance understanding the principles and practice of modern data analysis

Part I

Digital Data Calculus, Units, Errors, Statistics, and Linear Regression

1

Computing Trends

1.1 Overview

Modern data analysis incorporates the internationally recognized Arabric numerals 1,2,…,9 supplemented by the symbol 0 for the Hindu invention of zero. These 10 numerals are used to represent any number no matter how large or small.

The plural of ‘datum’ is ‘data,’ which are discrete numbers with or without attached units of measurement. Analog data are measured against continuous quantities [e.g., lengths of a ruler, heights of mercury in a tube, slide rule calculations, etc.], whereas digital data are referenced against discrete quantities [e.g., clock ticks, fingers, abacus beads, open and closed electronic circuits, etc.]. Digital data, as well as digital mathematics and graphics dominate modern data analysis.

Numerical derivatives and integrals of successive 3- and 2-data point sequences, respectively, form a closed system that completely defines the data’s analytical attributes. Thus, numerically evaluating and graphing the inverse derivative and integral properties of data fully describe their analytical attributes. The rise-to-run ratios of successive 3-data point sequences define [n − 2] of the derivatives of the n-point signal. The defined derivative estimates involve minimal assumptions in application because they are constrained by the observed datum at the center of each sequence. The two undefined derivatives at each end of the signal can be determined using the First Fundamental Theorem of Calculus, which states that the signal is the integral to within a constant of its derivative. Here, the integral values are just the cumulative areas under the derivative curve established from the equivalent areas of simple rectangles with vertically extending triangles [i.e., trapezoids]. The integral values are defined everywhere except at the first data point where the...

Table of contents

• Cover
• Half Title
• Title Page
• Copyright Page
• Dedication
• Contents
• Preface
• Part I: Digital Data Calculus, Units, Errors, Statistics, and Linear Regression
• Part II: Digital Data Inversion, Spectral Analysis, Interrogation, and Graphics
• References
• Index