Forest Measurements

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Forest Measurements
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1 Introduction

1-1 Purpose of Book

1-2 Need for Measurements

1-3 Measurement Cost Considerations

1-4 Abbreviations and Symbols

Numerical Considerations

1-5 Scales of Measurement

1-6 Significant Digits and Rounding Off

1-7 English Versus Metric Systems

Presenting Information

1-8 Preparation of Graphs

1-9 Preparation of Technical Reports

1-10 Reviews of Technical Literature


2 Statistical Methods

2-1 Introduction

2-2 Bias, Accuracy, and Precision

2-3 Calculating Probabilities

2-4 Factorial Notation, Permutations, and Combinations

Statistical Concepts

2-5 Analysis of Data

2-6 Populations, Parameters, and Variables

2-7 Frequency Distributions

Statistical Computations

2-8 Mode, Median, and Mean

2-9 The Range and Average Deviation

2-10 Variance and Standard Deviation

2-11 Coefficient of Variation

2-12 Standard Error of the Mean

2-13 Confidence Limits

2-14 Covariance

2-15 Simple Correlation Coefficient

2-16 Expansion of Means and Standard Errors

2-17 Mean and Variance of Linear Functions

Simple Linear Regression

2-18 Definitions

2-19 A Linear Equation

2-20 A Sample Problem

2-21 Indicators of Fit

2-22 Regression Through the Origin

2-23 Hazards of Interpretation

2-24 Multiple Regression



3 Sampling Designs

3-1 Introduction

3-2 Sampling Versus Complete Enumeration

3-3 The Sampling Frame

Simple Random and Systematic Sampling

3-4 Simple Random Sampling

3-5 Sampling Intensity

3-6 Effect of Plot Size on Variability

3-7 Systematic Sampling

Stratified Random Sampling

3-8 Stratifying the Population

3-9 Proportional Allocation of Field Plots

3-10 Optimum Allocation of Field Plots

3-11 Sample Size for Stratified Sampling

Regression and Ratio Estimation

3-12 Regression Estimation

3-13 Comparison of Regression Estimation to Simple Random Sampling

3-14 Ratio Estimation

Double Sampling

3-15 Double Sampling with Regression and Ratio Estimators

3-16 Double Sampling for Stratification

Cluster and Two-Stage Sampling

3-17 Cluster Sampling

3-18 Two-Stage Sampling

Sampling for Discrete Variables

3-19 Simple Random Sampling for Attributes

3-20 Cluster Sampling for Attributes

3-21 Relative Efficiencies of Sampling Plans



4 Land Measurements

4-1 Applications of Surveying

Measuring Distances

4-2 Pacing Horizontal Distances

4-3 Chaining Horizontal Distances

4-4 Methods of Tape Graduation

4-5 Electronic Distance Measurement

Using Magnetic Compasses

4-6 Nomenclature of the Compass

4-7 Magnetic Declination

4-8 Allowance for Declination

4-9 Use of the Compass

Area Determination

4-10 Simple Closed Traverse

4-11 Graphical Area Determination

4-12 DOT Grids

4-13 Planimeters

4-14 Transects

4-15 Topographic Maps

Colonial Land Subdivision

4-16 Metes and Bounds Surveys

The U.S. Public Land Survey

4-17 History

4-18 The Method of Subdivision

4-19 The 24-Mile Tracts

4-20 Townships

4-21 Establishment of Sections and Lots

4-22 Survey Field Notes

4-23 Marking Land Survey Lines

Global Positioning Systems

4-24 Purpose of GPS

4-25 How GPS Works

4-26 GPS Accuracy

4-27 Differential Correction

4-28 GPS Data

4-29 GPS Receivers



5 Cubic Volume, Cord Measure, and Weight Scaling

5-1 Logs, Bolts, and Scaling Units

5-2 Computing Cross-Sectional Areas

5-3 Log Volumes and Geometric Solids

5-4 Scaling by the Cubic Foot

5-5 Inscribed Square Timbers

Measuring Stacked Wood

5-6 The Cord

5-7 Solid Contents of Stacked Wood

5-8 An Ideal Measure

Weight Scaling of Pulpwood

5-9 The Appeal of Weight Scaling

5-10 Variations in Weight

5-11 Wood Density and Weight Ratios

5-12 Advantages of Weight Scaling



6 Log Rules, Scaling Practices, and Specialty Wood Products

6-1 Log Rules

6-2 General Features of Board-Foot Log Rules

Derivation of Log Rules

6-3 Mill-Tally Log Rules

6-4 Board Foot-Cubic Root Ratios

6-5 Scribner Log Rule

6-6 Doyle Log Rule

6-7 International Log Rule

6-8 Overrun and Underrun

6-9 Board-Foot Volume Conversions

Board-Foot Log Scaling

6-10 Scaling Straight, Sound Logs

6-11 Log Defects

6-12 Board-Foot Deduction Methods

6-13 Cull Percent Deduction Methods

6-14 Merchantable Versus Cull Logs

6-15 Scaling Records

6-16 Log Scanning

Log Grading

6-17 Need for Log Grading

6-18 Hardwood Log Grading

6-19 Softwood Log Grading

Weight Scaling of Sawlogs

6-20 Advantages and Limitations

6-21 Volume-Weight Relationships for Sawlogs

Specialty Wood Products

6-22 Specialty Products Defined

6-23 Veneer Logs

6-24 Poles and Piling

6-25 Fence Posts

6-26 Railroad Ties

6-27 Mine Timbers

6-28 Stumps for the Wood Naval-Stores Industry

6-29 Bolts and Billets

6-30 Fuel Wood



7 Measuring Standing Trees

7-1 Tree Diameters

7-2 Diameter at Breast Height for Irregular Trees

7-3 Measuring Bark Thickness

7-4 Tree Diameter Classes

7-5 Basal Area and Mean Diameter

7-6 Upper-Stem Diameters

Tree Heights

7-7 Height Poles

7-8 Height Measurement Principles

7-9 Merritt Hypsometer

7-10 Total Versus Merchantable Heights

7-11 Sawlog Merchantability for Irregular Stems

Tree Form Expressions

7-12 Form Factors and Quotients

7-13 Girard Form Class

7-14 Form Measurements

Tree Crowns

7-15 Importance of Crown Measures

7-16 Crown Width

7-17 Crown Length

7-18 Crown Surface Area and Volume

Tree Age

7-19 Definitions

7-20 Age From Annual Rings

7-21 Age Without Annual Rings



8 Volumes and Weights of Standing Trees

8-1 Purpose of Volume and Weight Equations

8-2 Types of Tree Volume and Weight Equations

Multiple-Entry Volume Tables

8-3 Form-Class Versus Non-Form-Class Equations

8-4 Compilation of MEsavage-Girard Form-Class Tables

8-5 Constructing Multiple-Entry Volume Equations

8-6 Selecting a Multiple-Entry Volume Equation

8-7 Making Allowances for Various Utilization Standards

8-8 Tree Volumes From Taper Equations

8-9 Integrating Taper Functions

Single-Entry Volume Equations

8-10 Advantages and Limitations

8-11 Constructing a Single-Entry Equation from Measurements of Felled Trees

8-12 Derivation from a Multiple-Entry Equation

8-13 Tarif Tables

Tree Weight Equations

8-14 Field Tallies by Weight

8-15 Weight Equations for Tree Boles

8-16 Biomass Equations



9 Forest Inventory

9-1 Introduction

9-2 Classes of Timber Surveys

9-3 Inventory Planning

9-4 Forest Inventory and Analysis

Special Inventory Considerations

9-5 Tree Tallies

9-6 Electronic Data Recorders

9-7 Tree-Defect Estimation

9-8 The Complete Tree Tally

9-9 Organizing the Complete Tree Tally

9-10 Timber Inventory as a Sampling Process

Summaries of Cruise Data

9-11 Stand and Stock Tables

9-12 Timber Volumes From Stump Diameters

Sales of Standing Timber

9-13 Stumpage Value

9-14 Methods of Selling Standing Timber

9-15 Timber-Sale Contracts



10 Inventories with Sample Strips or Plots

10-1 Fixed-Area Sampling Units

Strip System of Cruising

10-2 Strip-Cruise Layout

10-3 Computing Tract Acreage From Sample Strips

10-4 Field Procedure for Strip Cruising

10-5 Pros and Cons of Strip Cruising

Line-Plot System of Cruising

10-6 The Traditional Approach

10-7 Plot Cruise Example

10-8 Sampling Intensity and Design

10-9 Cruising Techniques

10-10 Boundary Overlap

10-11 Merits of the Plot System

Use of Permanent Sample Plots

10-12 Criteria for Inventory Plots

10-13 Sample Units: Size, Shape, and Number

10-14 Field-Plot Establishment

10-15 Field-Plot Measurements

10-16 Periodic Reinventories

Regeneration Surveys with Sample Plots

10-17 Need for Regeneration Surveys

10-18 Stocked-Quadrat Method

10-19 Plot-Count Method

10-20 Staked-Point Method



11 Inventories with Point Samples

11-1 The Concept of Point Sampling

11-2 Nomenclature and Variants

11-3 Selecting a Sighting Angle

11-4 Plot Radius Factor

How Point Sampling Works

11-5 Imaginary Tree Zones

11-6 Equality of Tree Basal Area on a Per-Acre Basis

Implementing Point Sampling

11-7 The Stick-Type Angle Gauge

11-8 The Spiegel Relascope

11-9 The Wedge Prism

11-10 Calibration of Prisms or Angle Gauges

11-11 Corrections for Slope

11-12 Doubtful Trees, Limiting Distances, and Bias

11-13 Boundary Overlap

11-14 Choice of Instruments

Volume Calculations

11-15 Example of Computational Procedures

11-16 Basal Area Per Acre

11-17 Trees Per Acre

11-18 Volume Per Acre by the Volume-Factor Approach

11-19 Volume Per Acre by the Volume/Basal-Area Ratios Approach

11-20 Estimating Precision

11-21 Field Tally by Height Class

11-22 Point Sampling in a Double-Sampling Context

11-23 Estimating Growth from Permanent Points

Point-Sample Cruising Intensity

11-24 Comparisons with Conventional Plots

11-25 Number of Sampling Points Needed

11-26 Point Samples Versus Plots

11-27 Attributes and Limitations



12 Inventories with 3P Sampling

12-1 Introduction

12-2 Components of 3P Inventory

How 3P is Applied

12-3 Timber-Sale Example

12-4 Preliminary Steps

12-5 Field Procedure

12-6 Sample-Tree Measurement

12-7 3P Computations

12-8 Numerical Example

Extensions, Attributes, and Limitations of Basic 3P Sampling

12-9 Extensions of Basic 3P Sampling

12-10 Attributes and Limitations of 3P Sampling



13 Using Aerial Photographs

13-1 Purpose of Chapter

13-2 Types of Aerial Photographs

13-3 Black-and-White Aerial Films

13-4 Color Aerial Films

13-5 Seasons for Aerial Photography

13-6 Determining Photographic Scales

13-7 Photogeometry

13-8 Aligning Prints for Stereoscopic Study

Cover-Type Identificaion and Mapping

13-9 Forest Type Recognition

13-10 Identifying Individual Species

13-11 Timber Type Maps

13-12 Using Photos for Field Travel

Basic Forest Measurements

13-13 Measuring Area and Distance

13-14 Measuring Heights by Parallax

13-15 Parallax-Measuring Devices

13-16 Tree-Crown Diameters

13-17 Tree Counts

13-18 Individual-Tree Volumes

13-19 Aerial Stand-Volume Tables

13-20 Crown Closure

13-21 Stand-Volume Estimates

13-22 Adjusting Photo Volumes by Field Checks

Obtaining Aerial Photographs

13-23 The Options

13-24 Photography from Commercial Firms

13-25 Photography from the U.S. Government

13-26 Photography from the Canadian Government

13-27 Taking Your Own Pictures

13-28 Contracting For New Photography

13-29 Other Remote-Sensing Tools



14 Geographic Information Systems

14-1 What is a GIS?

GIS Data Structures

14-2 Data Formats

14-3 Raster Data

14-4 Vector Data

14-5 Raster Versus Vector Systems

Geographic Coordinate Systems

14-6 Types of Coordinate Systems

14-7 The Latitude and Longitude System

14-8 The Universal Transverse Mercator Coordinate System

14-9 The State Plane Coordinate System

GIS Data Sources, Entry, and Quality

14-10 Deriving Digital Maps

14-11 Existing Map Data

14-12 Digitizing and Scanning

14-13 Field and Image Data

14-14 Errors and Accuracy

GIS Analysis Functions

14-15 Analysis-The Power of GIS

14-16 Spatial Analysis Functions

14-17 Cartographic Modeling



15 Site, Stocking, and Stand Density

15-1 The Concepts of Site

15-2 Direct Measurement of Forest Productivity

15-3 Tree Height as a Measure of Site Quality

15-4 Field Measurement of Site Index

15-5 Construction of Site-Index Curves

15-6 Interspecies Site-Index Relationships

15-7 Periodic Height Growth

15-8 Physical-Factors Approach

15-9 Indicator-Plant Approach

15-10 Limitations of Site Index

Stocking and Stand Density

15-11 Definitions

15-12 Measures of Stocking

15-13 Basal Area Per Acre

15-14 Trees Per Acre

15-15 Stand-Density Index

15-16 3/2 Law of Self-Thinning

15-17 Relative Spacing

15-18 Crown Competition Factor

15-19 Stocking Guides

15-20 Measures of Point Density



16 Tree-Growth and Stand-Table Projection

16-1 Increases in Tree Diameter

16-2 Increases in Tree Height

16-3 Periodic and Mean Annual Growth

16-4 Past Growth From Complete Stem Analysis

16-5 Tree Growth as a Percentage Value

16-6 Predictions of Tree Growth

16-7 Future Yields from Growth Percentage

16-8 Growth Prediction from Diameter and Height Increases

Stand-Table Projection

16-9 Components of Stand Growth

16-10 Characteristics of Stand-Table Projection

16-11 Diameter Growth

16-12 Stand Mortality and Ingrowth

16-13 A Sample Stand Projection



17 Growth and Yield Models

17-1 Introduction

17-2 Growth and Yield Relationships

17-3 Mathematical Relationships Between Growth and Yield

Growth and Yield Models for Even-Aged Stands

17-4 Normal Yield Tables

17-5 Empirical Yield Tables

17-6 Variable-Density Growth and Yield Equations

17-7 Size-Class Distribution Models

17-8 Example of Computatins for Size-Class Distribution Model

17-9 Individual-Tree Models for Even-Aged Stands

Growth and Yield Models for Uneven-Aged Stands

17-10 Special Considerations in Modeling Uneven-Aged Stands

17-11 Growth and Yield Equations Based on Elasped Time

17-12 Size-Class Distribution Models Using Stand-Table Projection

17-13 Individual-Tree Models that Include Uneven-Aged Stands

Applying Growth and Yield Models

17-14 Enhancing Output from Growth and Yield Models

17-15 Choosing an Appropriate Growth and Yield Model

17-16 A Word of Caution



18 Assessing Rangeland, Wildlife, Water,and Recreational Resources

18-1 Purpose of Chapter

Measuring Rangeland Resources

18-2 Forage Resources

18-3 Planning Range Measurements

18-4 Sampling Considerations

18-5 Determining Grazing Capacity

18-6 Clipped-Plot Technique

18-7 Range-Utilization Estimates

18-8 Range Condition and Trend

Measuring Wildlife Resources

18-9 Animal Populations and Habitat

18-10 Population Estimates

18-11 Habitat Measurement

Measuring Water Resources

18-12 Importance of Water

18-13 Factors Affecting Runoff

18-14 Physical Characteristics of a Watershed

18-15 Measurement of Water Quantity

18-16 Measurement of Water Quality

Measuring Recreational Resources

18-17 The Problem

18-18 Visitor Use of Recreational Facilities

18-19 Assessing Potential Recreational Sites



Answers to Selected Problems