Forest SamplingSimulation

Loukas G. Arvanitis

University of Florida

Robin M. Reich

Colorado State University

Valentina S. Boycheva

Post-doctoral Associate, Univ. of Florida

“It is the mark of an educated mind to rest satisfied with the degree of precision, which the nature of the subject admits, and not to seek exactness where only an approximation is possible.”

Aristotle (384-322 B.C.)

Main Objective

Assist students of all ages in:

• Designing

• Implementing

• Interpreting

COST-EFFECTIVE forest inventories

(Maximize information per unit cost)

Prerequisites

a) An introductory course in statistics.

b) Basic knowledge of computer simulation

c) Critical thinking

d) Perseverance

Basic Components of FOSS

• Spatial distribution of trees• Cost and precision constraints• Sampling units• Allocation of samples (sampling designs).

FOSS

• Spatial pattern of trees

Random Aggregated Uniform (plantation type)

• Distribution of tree DBH Normal Weibull

Random Pattern

Aggregated Pattern

Uniform Pattern

Tree Gradients

• East - West

• North - South

• Combination of E-W and N-S

Sequence of Tasks

• Assess spatial pattern of the population• Decide on cost and precision constraints• Determine number, size, and shape of the

elementary sampling unit• Select sampling method• Decide on single or repeated sampling• Implement selected sampling method• Evaluate results

Elementary Sampling Units

– Square

– Rectangle

– Circle

– Strip

– Line

– Point

Available Sampling Designs

• Simple random• Systematic • Stratified (Proportional, Neyman, Optimal)• 3-P• Vertical Point• Vertical Line• Horizontal Line • Multi-phase• Multi-stage• List Sampling• Double sampling with regression

Vertical Point Sampling

Vertical Line Sampling

Horizontal Line Sampling

(Hush, Beers, & Kershaw, Jr. 2003)

Density Estimation

• Quadrat sampling is used in forestry, range, wildlife, and ecology to sample frequency, density, abundance, and presence.

• Distance sampling was developed primarily to study the spatial relationships that exist in biological populations.

Forest Variables of Interest in FOSS

• Mean/total basal area

• Mean/total volume

• Mean DBH

• Total tree height

1

Selection of Sampling Units

• Most efficient: one that samples proportional to the variance of the stand parameter of interest.

– Density: fixed area plots– Basal Area and Volume: horizontal point sample

• Unbiased estimates of forest parameters can be obtained from any plot type and size.

• The precision and cost may vary significantly.

Selection of Sampling Units

• For a given sampling intensity, the smaller the sampling unit, the greater will be the precision because there will be more samples.

• However, large (n) will increase the cost of sampling.

• In general, the cost of sampling will be greater for a large number of sample units than for fewer samples of larger size.

Selection of Sampling Units

Cos

t $yS

Sample Size (n)

Selection of Sampling Units

• If sampling units are too small, the probability that they may be representative of the population decreases.

• Ultimately, the size of the sampling unit should be large enough to include a representative number of trees but small enough that the time required for measurements is not excessive.

Concluding Remarks

• FOSS: interactive program to enhance students’ comprehension of basic concepts on sampling forests in a cost effective manner.

• Main idea: assist students in advancing from dependent memorization to independent thinking and problem solving ability.

Concluding Remarks

• Allows students to explore a wide variety of alternative solutions through computer simulation, linking theory and practice.

• Gradients of different densities: East-West, N-S, and E-W /N-S, valuable for foresters,

ecologies, range specialists, and wildlife professionals.

Concluding Remarks

• Aims at student’s awareness of fundamental concepts related to sampling efficiency and the thinking process of maximizing the amount of information per unit effort or cost.

Concluding Remarks

• Assists students in becoming actively involved in the decision-making process (rewards and penalties) attributed to their actions.

• Although FOSS does not process field data, it is a powerful scientific tool for understanding, implementing, and properly interpreting forest sampling.

Concluding Remarks

FOSS works in the following operating systems:

• MS Windows NT

• MS Windows 2000

• MS Windows XP

Words of Wisdom

Jonathan Swift, an Irish-born satirist of the 17th century said that:

“A man should never be ashamed to own he had

been in the wrong, which is but saying, in other words, that he is wiser today than he was yesterday”.

THANK YOU FOR YOUR ATTENTION