As a subject of greater importance, the formation of cubing tables takes the timber volume as its function, so that the main group is formed by shafts.
Introduction
In the expression of the individual volume, the following parameters are considered as tabular arguments: the normal diameter with bark, the height of the stem up to the diameter of 7 cm, and the morphic coefficient, all contained in the dimension formula.
Depending on which parameters are included, the tables can be of three types.
- Local tables: V = f (DAP) Normal tables: V = f (DAP, h) General tables: V = f (DAP, h, di)
In the first case, the table has only one entry. The DAP, which assumes a homogeneity of the population in terms of its height for each metric day class. For this reason its application is restricted to certain defined areas, with commercial plantations with similar silvicultural treatment; that is, they are for local use.
In the second case, the stem lengths vary to such a degree that their representation by an average for each class or value is not supported. Therefore, the volume must be represented by two parameters: the DBH and the height. It is understood that these tables are applicable to a variety of situations and extensions, that is, they are normal use.
The general tables are used in European national inventories, with a huge variety of silvicultural sites and treatments. They have as input the DBH, the total height and a second diameter higher, generally at 5 or 7 m high.
When tables are used and there are parameter values that are not listed (for example, measurements in millimeters), it should be interpolated between the two closest. If DBH or height is greater than the table limit, it is extrapolated.
In both local and normal tables the morphic coefficient is implicit in the input arguments.
For example, if we have the height and the volume and the DBH is missing, using the table we can determine the DBH by multiplying by f.
Similarly, with the height we will obtain the reduced height fh. The cubing tables are used not only to calculate the individual volumes but also to determine the volume of the stands according to different methods.
Volume functions
Tree volumes can be easily determined by volume functions or morphic coefficient functions.
There are a variety of functions that describe volume, and its shape varies as precisely as desired. Some examples for tables of 1, 2, 3 entries, respectively.
Equation of one variable
Represents a function that produces estimates of volume as a function of D, like one-entry tables, they are suitable for localities where the quality of the site is homogeneous and the differences in height within the same ages are small.
One-input volume table
1) V = a * Db
2) V = a + b * D2
3) V = a + bD + c * D2
Equation of two variables
Double entry volume tables
1) V = a + b (D * H)
2) V = a + b (D2 * H)
3) V = a * D * H
Equation of three variables
Triple input volume tables
V = f (b * H * D)
V = f (D1: 30 * D1 / 2 * H)
Steps required for volume table construction
1: calculate the volume in tons using different methods for calculating volumes, such as Huber, Smalian, Newton ……..etc.
2: Organize the data and make the corresponding calculations using the following table.
3: calculate correction terms (TC)
a) TC for ∑ (D2 * H) 2 = ∑ (D2 * H) 2 / n
b) TC for ∑ V2 = (∑V) 2 / n
c) TC for ∑ (D2 * H) * V = ∑ (D2 * H) * (∑V) / n
4: calculate the sum of corrected squares (SCC)
a) SCC of (D2 * H) = ∑ (D2 * H) 2 - (∑ D2 * H) 2 / n
b) SCC of V = ∑ (V) 2 - (∑V) 2 / n
c) SCC of (D2 * H) * V = ∑ (D2 * H) * V - ∑ (D2 * H) * ∑ V / n
5: calculate the regression coefficient (b)
V = a + b (D2 * H) double entry.
b = SCC (D2 * H) * V / SCC of (D2 * H)
6: calculate constant (a)
a = ∑V / n - b (∑D2 * H) / n
7: Substitute the values of (a), (b) into the equation
V = a + b (D2 * H) double entry.
8: build the table
V = a + b (D2 * H) double entry.
D / H
D: diameter
H: height
To build the table, each diameter corresponding to each height must be used.
And substitute in the volume equation.
9: determination of the precision for this calculation.
When:
r = 0.96 - 1 within this interval the table is accepted.
r = SCC of (D2 * H) * V / √ SCC of (D2 * H) * SCC of V
The volume table must be accompanied by a series of information such as:
- The title of the table. Where the table was made. Input Ecological description of the species where the table was made. Dendrological characteristics of the species and the stem. Procedure followed. The formula used to calculate the volume.
Example
Volume table construction
The two-input model:
V = a + b (D2 * H) double entry.
Formula used to calculate Newton volume.
V = a + b (D2 * H) double-entry student
Volume table
