Math for Soil Scientists

Transcription

1 Math for Soil Scientists Mark S. Coyne University of Kentucky and James A. Thompson West Virginia University THOMSON * ^ : D E L I V I A R L E A R N I N G A u s t r a l i a C a n a d a M e x i c o S i n g a p o r e S p a i n U n i t e d K i n g d o m U n i t e d S t a t e s

2 Contents Preface xiii SECTION I THE BASICS 1 Chapter 1 Basic Math: Scientific Notation, Exponents,,and Logarithms 3 Scientific Notation 5 Exponential Notation 7 Logarithms 14 Chapter 2 Significant Figures 19 Counting Significant Figures 20 Multiplication and Division 20 Addition and Subtraction 21 Rounding Off 21 Chapter 3 Metric and International Scientific (SI) Units 24 Measures of Length 26 Measures of Area 26 Measures of Volume 27 Measures of Mass 28 Measures of Concentration 28 Other Important SI Units of Measure v 29 Chapter 4 Unit Conversions 31 The Conversion Factor Method 32 Converting between SI and Non-SI Units 33 SECTION II QUANTIFYING PHYSICAL AND CHEMICAL PROPERTIES OF SOILS 39 Chapter 5 Soil Texture and Surface Area 41 Soil Texture Particle Size and Surface Area 42 Soil Texture Using the Textural Triangle 43 Chapter 6 Bulk Density, Particle Density, and Porosity 48 Soil Density Bulk Density and Particle Density 48 vn

3 viii CONTENTS Chapter 7 Measurements of Soil Water 53 Measuring Soil Water Content 53 Measurements of Soil Water Availability 58 Chapter 8 Water and Gas Transport 63 Water Flow in Soil 63 Gas Transport in Soil 67 Chapter 9 Soil Temperature, Heat Capacity, and Conductivity 71 Describing Temperature in Soil 71 Heat Capacity 73 Thermal Conductivity 74 SECTION III PROBLEM SOLVING IN SOIL BIOCHEMISTRY 79 Chapter 10 ph, Buffers, and Buffering 81 Acids, Bases, and Water 81 ph 82 Molarity and Normality 83 Neutralizing Strong Acids and Bases 84 Titrating Weak Acids The Henderson-Hasselbach Equation 85 Buffers and Buffering 86 Chapter 11 Oxidation, Reduction, and Energetics 94 Oxidation State or Number 94 Fermentation Balances 96 Free Energy Changes 97 Chapter 12 Kinetics 101 Michaelis-Menten Kinetics 102 First-Order Processes 104 Zero-Order Processes 106 Chapter 13 Stable and Radioactive Isotopes 110 Radioactive Isotopes Ill Stable Isotopes 114 SECTION IV PROBLEM SOLVING IN SOIL BIOLOGY 117 Chapter 14 Microbial Growth, Yield, and Mortality 119 Ideal Bacterial Growth 120 Maximum Growth Rate 122 Yield Coefficients 124 Mortality Rates 125

4 CONTENTS > ix Chapter 15 Microbial Enumeration 129 Serial Dilution 129 Selective Plating 132 Most Probable Number Direct Count Calculations 135 Chapter 16 Microbial Biomass 140 Chloroform Fumigation Incubation 140 Chloroform Fumigation Extraction 142 Chapter 17 Mineralization and Immobilization Rates 145 Mineralization 145 Immobilization 148 Chapter 18 Respiration and Gas Fluxes 152 Respiration by Titration 153 Gas Fluxes Soil Cores 154 Gas Fluxes Soil Covers 156 SECTION V PROBLEM SOLVING IN SOIL CHEMISTRY, FERTILITY, AND MANAGEMENT 159 Chapter 19 ph, Liming, and Lime Requirements 161 ph 162 Liming 163 Lime Requirements 165 Chapter 20 Cation and Anion Exchange 168 Cation Exchange 169 Anion Exchange 172 Salinity and Sodicity \ 172 Chapter 21 Calculating Fertilizer Application Rates and Nutrient Availability 176 Fertilizer Conversions 177 Calculating Fertilizer Applications 179 Mixing Fertilizers 180 Available Nutrients in Manures 182 Liquid Manures 184 Chapter 22 Potential Erosion Working with the Universal Soil Loss Equation 191 Components of the USLE 192 Erodibility Index 195 Predicting Soil Loss 197

5 x < CONTENTS Chapter 23 Waste Management and Bioremediation 199 C:N Ratios and Composting 200 Biochemical Oxygen Demand 202 Bioremediation Calculating Waste Loading Rates for Gasoline Spills 206 SECTION VI DATA ANALYSIS AND SAMPLING 211 Chapter 24 Descriptive Statistics 213 Types of Data 214 Descriptive Statistics 214 Measures of Dispersion 220 Chapter 25 Error Analysis 225 Normally Distributed Data 225 Detecting Outliers with the Z-Score 226 Tests of Normality 227 The Box Plot Test 228 Chapter 26 Hypothesis Testing and Inferential Statistics 230 Hypothesis Testing and Levels of Significance 231 Inferential Statistics the f-test 232 Linear Regression 236 Correlation Coefficients 238 Using t Statistics to Test the Probability of Linearity 239 Confidence Limits 240 Variance Analysis 240 Chapter 27 Sampling 245 Sampling Schemes (. 245 Compositing Samples 247 Estimating the Number of Samples to Take 248 APPENDICES.250 Appendix 1 pk a Values of Common Environmentally Important Buffering Systems 251 Appendix 2 Formulas for Stock Solutions and Buffers of Various ph (The Buffer Cheat Sheet) 252 Appendix 3 Standard Oxidation-Reduction Potentials ( 0 ) at ph Appendix 4 Decay Constants of Radioactive Isotopes 262 Appendix 5 Most Probable Number Tables 264 Appendix 6 Sample Microsoft Excel Program for Determining MPN 266

6 CONTENTS xi Appendix 7 First-order Mineralization Rate Constants for Various Organic Materials 269 Appendix 8 Bunsen Absorption Coefficients for Various Gases in Water 272 Appendix 9 Significant Elements in Soil 273 Appendix 10 Properties of Concentrated Reagent Acids and NH 3 with Dilution Directions to Make One Normal Solution 277 Appendix 11 Microsoft Excel Tips and Pointers 279 INDEX 281