CHAPTER IV: Volume tables and equations

The main objective of a TOF inventory is to estimate the growing stock, which is essential for sound management, planning and policy formulation. For management purposes, the user is often concerned with determining the volume of a large number of trees of distinct dimensions. To do this requires volume tables. Volume tables are based on diameter and/or height and/or tree form. They are often derived via volume equations that are statistically sound and based of regression analysis.

1. Local volume equation: Local volume equations are applicable for a small forest or land area and are based on only one variable, i.e. DBH.
   The basic assumption is that trees of a given species, at a given location, with the same DBH, will have the same height and form. This assumption is only valid as long as site conditions are homogenous.

2. Regional volume equation: This type of equation is normally based on two variables (e.g. DBH and height) and covers a larger geographical area. Regional volume equations are standard volume equations with limited application. Care needs to be taken that the trees measured, for the formulation of this equation, are truly representative of the variation encountered in the region.

3. General or standard volume equation: This is an even broader equation and covers the full distribution of the species. It is normally based on two variables such as DBH and height.

A local volume equation can be easily prepared from a standard or regional volume equation by analysing the DBH/height relationship of the species for the given location.

Destructive method

In this method, 40-50 individuals of a particular species, representing all diameter classes of interest are selected randomly and felled. Each tree is cut into appropriate lengths of logs, generally between 2-3 m. The volume of each log is calculated individually, using suitable formulae, generally Huber’s formula for parabolides, cylindrical, conical or Newton’s formula for neiloidic form. The volume of each individual log is added to obtain the total volume of the tree.

Non-destructive method

This is similar to the destructive method but the trees are not felled. Diameters are measured at different heights by climbing the trees. Tree height is estimated with the help of e.g. an altimeter, a clinometer, a cruiser stick or a relaskop. The volume is then calculated using the same formulae as above. Volume tables can be prepared for particular species, on the basis of these calculations.

V = s_m x l

V = volume (m³)

s_m = the sectional area at the middle (m²)

l = the length of the log or height of the log (m)

Earlier methods of developing volume tables involved large-scale data collection for different diameter and height classes. However, the present trend is to use multiple regression methods in which basal area, girth or DBH along with height or a form factor is taken into consideration. Although these methods have certain inherent limitations, they provide a high degree of correlation and statistically acceptable relationships.

General volume equations

General volume equations (GVEs), i.e. regression functions in volume, diameter and height are selected for each species. The GVEs are obtained from randomly selected tree data by applying multiple regression methods. The following regression equations are generally used:

1. V = a + bD²H

2. V = a + bD + cD²H

3. V = a + bD² + c(D²H) 2

4. V = a + bD + cD²H + d(D²H) 2

5. V = a + bD + cH + dD²H

6. V = a + bD + cD²+ dD²H

7. log_e V = a + b log_e D + c log_e H

8. V/D²H = a + bD²H

9. V/D²H = a + bD²H + c/D²H

Where,		V = volume under bark (m3)
		D = diameter at breast height (1.37 m) over bark (m)
		(Unless otherwise specified)
		H = height of tree (m)
		a is the intercept and b, c & d are regression coefficients

The best fit regression equation is used to estimate the volume of trees.

Local volume equations

Local volume equations (LVEs) are developed with only one independent variable, i.e. diameter (D). The following types of regression equations are used to obtain LVEs:

1. V = a + bD2

2. V = a + bD + cD2

3. V = a + bD + cD² + dD3

4. V = a + bÖ D + c D2

5. V = a + bD

6. Ö V = a + bD + cÖ D

7. V/D² = a + b/D2

8. V/D² = a + b/D + c/D2

9. V/D² = a + b/D² + c/D + dD

10. log_e V = a + log_e D

Where,		V = volume under bark (m3)
		D = diameter at breast height (1.37 m) over bark (m)
		(Unless otherwise specified)
		a is the intercept and b, c & d are regression coefficients

The best fit regression equation is used to estimate the volume of trees.

On the basis of developed volume equations volume tables can be prepared. An example of a volume table for some species is given below:

Local volume table for Jalgaon district