Level: Technical Certificate Level (TCL) first year

Subject: Forest Mensuration

Date: July 30, 2005

Presented by: Gandhiv Kafle [gkafle@yahoo.com]

Aims: The aims of this session is to help students in analysing the following aspects of Forest Mensuration:

1. Introduction

2. Basic concept and definition of Forest Mensuration

3. Objectives of Forest Mensuration

4. Scope of Forest Mensuration

Introduction

Mensuration is an essential part of mathematics. Mensuration is derived from the Latin Word 'Mensura' meaning 'measure'. It is, thus, concerned with the determination of length, area and volume. In ancient times also, there was a system of standard relating to weights and measures with the use of standardized measuring rods and scales. Some examples are presented below:

Standards Meaning

Mana measure of capacity or volume

Anjuli two hands joined together as a cup, used as a measure of capacity

Hat measure of length by hand

Definition of Forest Mensuration

Forest Mensuration is that branch of forestry that deals with the determination of dimensions (e, g; diameter, height, volume etc.), form, age, and increment of single trees, stands or whole woods, either standing or after felling.

Basic concept of Forest Mensuration

Mensuration means measurement of length, mass and time.

Forest Mensuration includes measurements of

§ Felled and standing trees,

§ Sawn wood and round logs and

§ Minor forest products such as bamboos, bark, fruits, etc

Forest Mensuration, therefore, concerns with linear, area, volume and weight measurements.

In forest Mensuration, the following parameters can be described quantitatively:

Age

Diameter- over and under bark

Length or height

Form or shape

Taper or the rate of change of diameter with length

Volume over or under bark

Crown width

Wood density

In addition to describing the current status of tree or crop, Mensuration also deals with measuring and predicting the growth of trees and crops that is the change in the parameter with time.

Objectives of Forest Mensuration

Forest Mensuration serves the following objects:

1. Basis for sale

2. Basis of management

3. Measurement for research

4. Measurement for planning

Basis for sale

Before any sale and purchase, the quantity of timber or other produce and their prices are estimated. Forest Mensuration serves such measurements.

Basis of management

For proper management, knowledge of the quantity of timber standing in forest and its increment on every year or in a period of years is necessary. This leads to the development of methods of preparing forest inventories using satellite imageries, aerial photographs and various optical and electronic techniques so that forests could be harvested without depleting the capital.

Measurement for research

In order to find out which treatment and method of management would maximize production, it is necessary to layout experiments to compare the results of different treatments. This requires the layout of sample plots and their periodic measurements.

Measurement for planning

With the steeply increasing population and rising standards of living every year, the gap between the demands and supplies of timber and other forest products is widening fast and therefore, the forest manager has to plan to reduce this gap.

For this purpose, fast-growing species have to be introduced. This requires not only reasonably accurate estimates of future yields but also the cost of production so that such projects may be financially sound. Thus, Forest Mensuration supplies basic statistical data to plan for the future and serves to check the viability of projects.

Scope of forest mensuration

Forest mensuration has a very wide scope.

It comes into play every time the wood is sold, converted or used.

With the widening scope of horizon of forestry, the scope of forest mensuration has also widened. The present day forest mensurationist has to concern himself/herself with the measurement problems of wild life management, watershed management, insect and disease incidence, recreation, tourism and, in fact, many of the mensurational aspects of multiple-use forestry.

The application of statistical theory and the use of electronic computer for data processing have brought about revolutionary changes in forest measurement problems.

Forest mensuration concerns not only the foresters, contractors, sawyers and transport labour working in the forest but also the sawn millers and wood-using public in the cities, towns and villages.

Forest mensuration deals with the measurement of cubical contents of trees and crops at present and also it helps in the forecast or predict of yields at any time in their future life. It applies not only to standing trees and crops but also to felled timber and its subsequent conversion till it is used in some work.

Subject: Forest Mensuration

Date: Aug. 2, 2005

Presented by: Gandhiv Kafle [gkafle@yahoo.com]

Aims: The aim of this session is to help students in analysing the following aspects of Forest Mensuration:

1. Definitions

2. Height measurement principles

3. Instruments of height measurement

Definitions

Total height: is the straight-line distance from the highest point of the crown to the ground level.

Bole height: is the distance from the ground level to the position of the first crown forming living or dead branch.

Height of standard timber bole: is the height of the bole from the ground level up to the point where average diameter over bark is 20cm.

Stump height: is the height of the top of the stump above ground.

Crown length: is the vertical measurement of the crown of a tree from the tip to the point half way between the lowest green branches forming green crown all round and the lowest green branch on the bole.

Crown height: is height from the ground level to the point half way between the lowest green branches forming green crown all round and the lowest green branch on the bole.

Height measurement principles

Instruments used for measuring tree heights are collectively referred to as hypsometers.

Trigonometric principle

Trigonometry is a branch of mathematics dealing with measurements of the angles and sides of triangles, and functions based on these measurements. The three basic trigonometric functions that we are concerned with here (sine, cosine, and tangent) are ratios of the lengths of two sides of a triangle. These ratios are the trigonometric functions of an angle, theta, such that

Here, opposite side (y) refers to tree height.

Principle of similar triangles

Two triangles are said to be similar when the corresponding angles are equal and the corresponding sides are proportional.

A'B':AB:: B'C:BC

Therefore, tree height (A'B') = AB*B'C/BC

Instruments based on properties of similar triangle

Christen's hypsometer

Smythies' hypsometer

Improved callipers

Instruments based on trigonometric principles

Brandis hypsometer

Abney's level

Haga altimeter

Blume-leiss hypsometer

Relaskop

Height measurement methods:

Ocular estimate: estimating heights of trees bye eye, accuracy based on experience of the observer

Non-instrumental methods:

Shadow Method: based on similar triangle principle

Single pole method: based on similar triangle principle

Instrumental methods:

Tangent method (on level ground, on sloping ground): based on trigonometric principles

Sine method: based on trigonometric principles

Important questions:

1. What do you mean by crown height? Describe the height measurement principles.

2. Describe the height measurement of a tree by using tangent method.

3. List the instruments of height measurement. Describe the Abney's Level, its advantages and disadvantages.

Notes:

*[For details, please refer to page 53-59 of book Forest Mensuration by A. N. Chaturvedi and L. S. Khanna] *[The details about height measuring instruments and methods will be discussed in tomorrow session and observed in the laboratory on Friday].

Abney’s level

Description of instrument

· Consists of a hollow tube with and eye-piece fitted at one end and a short sighting tube fitted at the other

· The eyepiece consists of 2 or 3 telescopic hollow tubes with a pine hole at the extreme end.

· The sighting tube is a small detachable tube fitted with a horizontal wire across the centre at the inner end, and a mirror behind the horizontal wire but covering only half of the tube so fitted that it makes angle of 45 degree to the longitudinal axis of the main tube.

· The spirit level is fitted to the main tube in such a way that it can be rotated by one screw or a wheel and screw.

· The arc is graduated to read whole degrees.

How to use?

· The observer stands away from the tree at a place from where the top of the tree and the base are visible.

· Then the top of the tree is sighted through the pine hole of the eyepiece after pulling it out. This makes the instrument inclined and the bubble is not seen in the mirror. Therefore, while sighting the top, the screw is rotated to bring the spirit level in a horizontal position.

· The spirit level is continued to be moved slowly to the position when the bubble image is bisected by the line of horizontal wire on the mirror and in the other half the tree top is seen touching the horizontal wire.

· At this position, angle of elevation to the top of the tree is read.

· Similarly, the angle of depression to the base can also be read and the height of the tree determined by using suitable formulae.

Advantages

· Gives accurate angles of elevation or depression with the vernier

· Small and light and can be used even in hills without difficulty.

Disadvantages

· Shaking of the hand makes the sighting of the top or bottom of the tree a little difficult and time-consuming.

· The spirit level has to be adjusted by moving the head of the screw while simultaneously looking to the top or bottom of the tree. This is quite tiresome.

Sunto clinometer

Description of the instrument

Has a double-refracting prism and a separable calibrated target board for establishing the measuring distance
Used to measure tree height directly, usually at 15m and 20m ground distance from the tree

How to use

Should be placed to the eye and move backwards or forwards until the horizontal index line, viewed through the lens, is aligned with the desired object
The reading gives directly the height above the eye level
For 15 horizontal distance, reading on left side of clinometer should be taken, but for 20m, reading on right side should be taken.

Level: Technical Certificate Level (TCL) first year

Subject: Forest Mensuration

Date: Aug 7, 2005

Presented by: Gandhiv Kafle [gkafle@yahoo.com]

Aims: The aim of this session is to help students in analysing the following aspects of Forest Mensuration:

1. Errors in height measurement and their control

2. Form factor: definition, classification, types and uses

3. Introduction to form quotient

Errors in height measurement

instrumental errors:

Instrumental errors are those errors which occur as a result of some deficiency in instrument apart from its incorrectness and drawback.

It is difficult to assess the magnitude of such errors because such errors vary with the instrument, the user and the weather conditions.

personal errors

The shaking hand of the observer can give very inaccurate results even with a fairly accurate instrument like the Abney’s level. The more the observer is steady at the time of measuring the heights of trees, the lesser will be the errors in the calculated height.

errors due to measurement

Errors can take place in

· Distance measurement (in the forest full of shrubs and undergrowth)

· Angles of elevation and depression

To reduce the percentage error in height due to error in the angle, it is generally recommend that the observer should stand at such a distance from the tree that the angle θ is equal to 45 degree or the horizontal distance from the tree may be roughly equal to the height of the tree.

errors due to observation

-If the tree base has not been observed, the height will be incorrect.

-often difficult to see the tip of the tree and a side branch may be mistaken for the tip in the case of broad leaved trees.

errors due to lean of trees

Forest trees are seldom vertical. Therefore, by assuming a leaning tree to be vertical serous error is introduced in the calculation of its height.

Chaturvedi concluded that large error may be introduced in height measurement of a tree by even a deviation of 5 degree from the vertical.

The greater the angle of deviation, the larger the error.

Again, for the same angle of deviation, larger errors are obtained if the tree is leaning away from the observer than towards him.

How to avoid errors due to lean:

take measurement from such a position that the lean is to the side rather than towards or away from the observer
measure the horizontal distance from the point of observation to the point vertically below the tip of the tree
The observer should stand at such a distance from the tree that the angle θ is equal to 45 degree or the horizontal distance from the tree may be roughly equal to the height of the tree.
Measure the height of the tree from two opposite sides, once with the tree leaning towards the observer and the other with the tree leaning away. The average of the two will give the height with minimum error.

Form factor

Definition: Form factor is defined as the ratio of the volume of a tree or its part to the volume of a cylinder having the same length and cross section as the tree. In other words, form factor is the ratio between the volume of a tree to the product of basal area and height.

Form factor classification

a. Artificial form factor: also known as breast-height form factor. The basal area is measured at breast height and the volume refers to the whole tree both above and below the point of measurement. It is universally used because its computation involves handy measurement and because with the standardization of diameter measurement at breast-height.

b. Absolute form factor: basal area is measured at any convenient hiehgt and the volume refers only to that part of the tree above the point of measurement.

c. Normal (or true) form factor: basal area is measured at a constant proportion of the total height of the tree, e.g., 1/10^th, 1/20^th etc., of the total height and the volume refers to the whole tree above ground level.

Disadvantages of normal form factor

The height of the tree has to be determined before the point of measurement can be fixed.
The point of measurement may be very inconvenient in case of very tall as well as short trees.

Absolute form factor and normal form factor are no longer used.

Expression of artificial form factor

F=V/Sh

Where F=form factor, V=tree volume, S=basal area at breast-height and h=height of the tree

Use of form factors

To estimate volume of standing trees
To study laws of growth (particularly stem form)

Types of form factor

Depending on the volume:

Tree form factor
Stem timber form factor and
stem small wood form factor

Form quotient

Normal form quotient: the ratio of mid-diameter or mid-girth of a tree to its diameter or girth at breast-height (Austrian forester A. Schiffel)

Absolute form quotient: the ratio of diameter or girth of a stem at one half its height above the breast height to the diameter or girth at breast height (Swedish forester Tor Jonson)

Important questions

What is form factor? Classify with its application in forestry.
What are the main errors in height measurement?
Write short notes:
1. Disadvantages of normal form factor
2. Kinds of form factors
3. Form quotients

Forest Sampling

Sampling: is a process in which inventory is carried out only in a representative portion of the whole. For example, a forest may be of 1000 ha out of which only 100 ha has been selected for inventory and estimate of the whole population of 1000 ha is made, it is called sampling.

What is sample?

Sample is defined as a part of population consisting of one or more sampling units, selected and examined as a representative of the whole.

Advantages of sampling over total inventory

Reduced cost and saving of time
Relative accuracy
Knowledge of error
Greater scope

Type of sampling

Simple random sampling
Stratified random sampling
Systematic sampling

Simple random sampling

It is a selection process in which every possible combination of sample units has an equal and independent chance of being selected. Sampling units are chosen completely at random.

Samples are either chosen with replacement or without replacement, the latter means that once a sampling unit is chosen it may not be chosen again.

Stratified random sampling

A population is divided into sub-population of known size and a simple random sample of at least two units is selected in each subpopulation.

In forestry stratification can be done on the basis of stand type, stand age, site quality, climate region or ecosystem.

There are two common procedures for distributing the field plots in the strata. They are: 1. proportional allocation method and 2. Optimum allocation method.

proportional allocation of field plots

This approach calls for distribution of field plots in proportion to the areas of each stratum (A). The general formula is:

n_h = (N_h/N)n

Where n_h is the number of plots in each strata, N is total area of forestland, N_h is stratum area in ha and

Optimum allocation of field plots

With this approach, the sample plots are allocated to various strata according to standard statistical procedure resulting in smallest standard error possible with a fixed number of observations. The general formula is:

N_h = [N_hs_h/åN_hs_h]ⁿ

Where, s_h is standard deviation for each stratum type which is used from any previous study or a pilot sample inventory.

Systematic sampling

The initial sample unit (i.e. first plot) is randomly selected. All other units (plots) are spaced at uniform intervals throughout the forest.

Advantages and disadvantages of systematic sampling

Advantages

Sampling units are easy to locate.
Sampling units appear to be representative.
Generally acceptable estimates for the population mean are obtained.

Disadvantages

Impossible to estimate the variance of one sample
Accuracy can be poor (i.e., bias) if a periodic or cyclic variation inherent in the population.

Systematic sampling is generally satisfactory for estimating means in typical forest conditions. When an objective numerical statement of precision need not be appended to inventory estimates systematic sampling may provide more information for the time expended than simple random sampling. In cases in which estimates of variance are important or little is known about the basic characteristics of the population being sampled, it is good to use simple random sampling than systematic sampling.