S-Plus for Windows Version 6 Release 2 was used to analyse the data. A program
code based on S-language was written to summarize the data by each forest
stratum classified using the FDC Model.
The study site was divided into four strata: (1) > 70 percent; (2) 50-70 percent;
(3) 30-50 percent; and (4) < 30 percent of canopy density cover. Tree species
were grouped into dipterocarps, non-dipterocarps and all species combined.
Four data analysis program codes (FAO 1 to 4) were written:
FAO-1
A data summary of trees greater than 15 cm dbh for each stratum and species group.
The stand parameters analysed were:
Stand and stock tables were generated for each sampling point. A calculation
of the stand and stock tables is given below:
Analysis steps:
Calculate basal area per tree (bat) and volume per trees (volt).
batj =
π * dbhi2 / 40000
[1]
voltj = batj * FQ * Log * 5
[2]
where FQ: form quotient of 0.65
Log: number of 5 m logs
j is the individual tree record
The number of 5 m logs differs by size class (Table
7).
Table 7. Tree dbh and its equivalent 5 m logs
|
Tree dbh |
Number of 5 m logs |
|
15< 30 cm |
1 |
|
30< 60 cm |
2 |
|
60< 75 cm |
3 |
|
> 75 cm |
4 |
For example, for tree no. 4 (see Table 6) with a dbh of 30.8 cm, the basal area
and volume are:
bat4 =
π * 30.82 / 40000 = 0.07 m2
volt4 = 0.07 * 0.65 * 2 * 5 = 0.48 m3
Calculate the number of trees per hectare (tph), basal area per hectare (bah)
and volume per hectare (volh) for individual tree data
tphj = BAF/batj [4a]
bahj = batj * tphj [4b]
volhj = voltj * tphj
[4c]
where BAF is 4.
For example, for sample tree no. 1 (Table 8) with a dbh of 20 cm, the number
of trees, basal area and volume per hectare,
tph1
= 4/0.03 = 130 trees
bah1 = 0.03 * 130 = 4 m2/ha
volh1= 0.10 * 130 = 13 m3/ha
Table 8. Example of stand and stock table for point sample 1
|
(1) Sample tree |
(2) dbh |
(3) bat (m2/tree) |
(4) volt (m3/tree) |
(5) tph BAF/(3) (trees/ha) |
(6) bah (m2/ha) (3) x (5) |
(7) volh (m3/ha) (4) x (5) |
|
1 |
19.80 |
0.03 |
0.10 |
130 |
4.00 |
13.00 |
|
2 |
130.60 |
1.34 |
17.41 |
3 |
4.00 |
52.00 |
|
3 |
59.90 |
0.28 |
1.83 |
14 |
4.00 |
26.00 |
|
4 |
30.80 |
0.07 |
0.48 |
54 |
4.00 |
26.00 |
|
5 |
56.60 |
0.25 |
1.64 |
16 |
4.00 |
26.00 |
|
6 |
66.30 |
0.35 |
3.37 |
12 |
4.00 |
39.00 |
|
7 |
41.50 |
0.14 |
0.88 |
30 |
4.00 |
26.00 |
Summarize data by sampling points
The summary of sampling point data for each parameter
is constructed by summation of the individual tree data (Table 7).
tphi = Σ tphj [5a]
bahi = Σ bahj [5b]
volhi= Σ volhj [5c]
where i is the sampling point
tph, bah, volh and j as explained
above
For example, for point sample 1 (Table 2), the number of trees, basal area and
volume per hectare are:
tph1
= 130 +3 +…..+ 30 = 258 trees/ha
bah1 = 4 + 4 +……. + 4 = 28 m2/ha
volh1= 13 + 52 + … +26 = 208 m3/ha
Summarize the data by forest density class and
calculate the CV
The calculation of tph, bah and volh is done by dividing the sum of parameters
of a sampling point within each forest canopy density class by the number
of sampling points.
tphh = Σ tphi/n
[6a]
bahh = Σ bahi/n [6b]
volhh = Σ volhi/n [6c]
where k is the forest canopy density class.
tph, bah volh and j as explained above
n is
the number of sampling points in each forest density class
For example, for Forest Canopy Density Class 1 (Table 9) for trees of 15 cm dbh
and above, the number of trees, basal area and volume is:
tph1
= (258 + 469 +…..+ 161)/5 =
195.8 trees/ha
bah1 = (28 + 40 +……. + 20)/5 = 22.4
m2/ha
volh1= (208 + 325 +……+ 130)/5 = 174.2 m3/ha
Table 9. Example of stand and stock table summary for Forest Canopy Density
Class 1
|
Sampling point |
tph (trees/ha) |
bah (m2/ha) |
volh (m3/ha) |
|
1 |
258 |
28 |
208 |
|
2 |
469 |
40 |
325 |
|
3 |
28 |
12 |
130 |
|
4 |
63 |
12 |
78 |
|
5 |
161 |
20 |
130 |
The CV was calculated as the ratio of the standard
deviation (Sy) of the sampling units to the mean within each forest
canopy density class:
CV = Sy/Ybar
where CV is the coefficient
of variation
Sy
is the standard deviation of the sampling unit to the mean
Ybar is the mean of Y, and Y can be the number
of trees, basal area or volume per hectare
For example, if the mean of stratum A is 25.5 and
the standard deviation is 10, the CV is:
(10/25) * 100 = 40%.
Point sampling estimators
Besides average values, other important point sample estimators are variances
and standard errors, which can be used to determine the tract total of variables
of interest. In general, the following equation is used to calculate the average
value, variances and standard error of a variable (e.g. basal area or volume
per hectare):
Yi = ΣBAF * Yij / batij
[7]
where: Yi is
the per hectare estimate of Y (or characteristic of interest) at point i
(i=1,2….,n)
BAF is the Basal Area Factor
batij is the basal area of tree j on point i
mi the
number of sample trees in point i
Yij
the volume or basal area for tree j on point i
The variance of Y among points is
S2y = (ΣYi
2 - (ΣYi)2/n)/(n-1) [8]
The variance of Ybar is
S2ybar =
S2y/n [9]
The standard error of Ybar is
Sybar = Sy/Ön [10]
Estimates of the stand parameters of the tract total
can be obtained simply by:
Thaty = Ybar * A
[11]
SThat = A * Sybar
[12]
Where A is the tract area
in hectares
Thaty
is the tract total value of Y
Ybar is the
per hectare average value of Y
SThat is
the tract total standard error
Sybar
is the per hectare standard error of Ybar
For example, for Forest Canopy Density Class 1, >15 cm dbh and above (Table
9),
If Yi = volume per hectare at point i (i.e., Y1 = 208, Y2 =325, and so on), therefore
ΣYi = 871 and ΣYi2=188 773
Using the previous equation, the average volume per hectare is calculated as
Ybar =(1/n) * ΣYi = 871/5 = 174.2 m3
The variance among points is calculated as
S2y = (ΣYi 2 - (ΣYi)2/n)/(n-1)
= (188 773 - (871)2/5)/(5-1) = 9 261.2 m3
The variance of the mean is calculated as
S2ybar = S2y/n = 9 261.2/5
= 1 852.2 m3
The standard error of the mean (Sybar ) per hectare is Ö1852.2 m3 = 43.04 m3
An approximate 95 percent confidence interval for the mean volume per hectare
is calculated as
174.2 ± 2(43.04) or LCL = 88.1 m3 UCL = 260.3
m3
Given a tract area of 50 ha, the total tract stand parameters can be calculated,
Thaty = Ybar * A
Thaty = 174.2 * 50 = 8 710 m3
The standard error of the tract total is calculated
as
SThat = A * Sy
= 50 * 43.0 =2151.9 m3
An approximate 95 percent confidence interval for
the mean volume per hectare is calculated as
8 710 ± 2(2 151.9) or LCL = 13 013.8 m3 and UCL = 4 406.2 m3
FAO-2
A data summary of trees between 5 to 15 cm dbh. The
stand parameters analysed were:
The method of calculation for the number of trees, basal area and the CV is similar
to FAO-1.
FAO-3
A data summary of trees between 1.5 m height to 5
cm dbh. The stand parameter analysed was:
Number of trees per hectare
FAO-4
A data summary of NTFPs. The stand parameter analysed
was:
Percentage of area occupied by the vegetation
The analysis of the plots placed in the different strata revealed the distribution of trees (Table 10). It must be stressed that this is not a
complete ground truthing exercise and thus the number of plots for each stratum
is not sufficient. A more complete ground truthing exercise requires about
10 plots per stratum. At this stage, the results are only of an indicative
nature. Consequently, the results did not yield a consistent trend for the
different FCD classes. However, some patterns emerged.
FCD class 1 (blue stratum) for trees 15
cm dbh and above, although the total number of trees (360 trees/ha) is much
higher compared to the other classes (class 4 with lowest average trees per
hectare), the volume per hectare (174 m3/ha) is lower than that of class 4 (green stratum),
which had 224 m3/ha with only 253 trees/ha (Table 10). This could
be attributed to class 1 having more small trees compared to class 4, which
had larger trees. It could also mean that the logging intensity in classes
1 and 2 could have been higher. The FCD class maps indicate that most
of classes 1 and 2 are located closer to the roads compared to class 4. At
the same time, it could also mean that classes 1 and 2 have a much lower number
of large trees. If records on the number of trees and logging intensity were available the actual situation
could be verified based on the number of trees removed. However, based on
experience and field inspection, this assumption is probably correct. Logging
records that were provided contained
information of logging year, total volume removed and cutting regime. Information
on the stocking of the original stand conditions and logging intensity was
not available. However, the trend is less clear in a comparison of classes 2 and 3.
Table 10. Summary of point sample estimators by minimum
dbh class and FCD class
|
Dbh class (cm) |
FCD class |
No pt |
avg tph |
avg bah |
avg volh |
Variance |
Standard error |
QD |
||
|
bah |
volh |
bah |
volh |
|||||||
|
15++ |
1 |
5 |
360.8 |
28.0 |
174.2 |
17.6 |
635.4 |
4.2 |
25.2 |
31.4 |
|
15++ |
2 |
6 |
228.5 |
23.3 |
160.3 |
1.5 |
289.2 |
1.2 |
17.0 |
36.1 |
|
15++ |
3 |
7 |
341.9 |
26.9 |
163.4 |
8.2 |
835.8 |
2.9 |
28.9 |
31.6 |
|
15++ |
4 |
8 |
253.1 |
28.5 |
224.3 |
27.1 |
1 785.1 |
5.2 |
42.3 |
37.9 |
|
|
||||||||||
|
30++ |
1 |
5 |
110.8 |
18.4 |
143.0 |
4.2 |
422.5 |
2.0 |
20.6 |
46.0 |
|
30++ |
2 |
6 |
113.5 |
18.7 |
145.2 |
2.8 |
320.2 |
1.7 |
17.9 |
45.8 |
|
30++ |
3 |
7 |
104.9 |
17.7 |
133.7 |
20.5 |
1 204.8 |
4.5 |
34.7 |
46.4 |
|
30++ |
4 |
8 |
128.0 |
24.0 |
209.6 |
17.7 |
1 553.8 |
4.2 |
39.4 |
48.9 |
|
45++ |
1 |
5 |
46.6 |
12.8 |
106.6 |
7.0 |
463.1 |
2.7 |
21.5 |
59.2 |
|
45++ |
2 |
6 |
45.0 |
12.0 |
101.8 |
6.4 |
523.0 |
2.5 |
22.9 |
58.3 |
|
45++ |
3 |
5 |
73.5 |
17.6 |
140.4 |
20.2 |
1 122.2 |
4.5 |
33.5 |
55.2 |
|
45++ |
4 |
8 |
47.2 |
16.0 |
157.6 |
11.4 |
1 131.3 |
3.4 |
33.6 |
65.7 |
|
60++ |
1 |
4 |
16.1 |
7.0 |
74.8 |
1.0 |
151.4 |
1.0 |
12.3 |
74.5 |
|
60++ |
2 |
5 |
14.6 |
6.4 |
70.2 |
2.6 |
432.6 |
1.6 |
20.8 |
74.8 |
|
60++ |
3 |
5 |
17.1 |
6.4 |
67.6 |
1.0 |
142.0 |
1.0 |
11.9 |
68.9 |
|
60++ |
4 |
7 |
22.2 |
11.4 |
135.6 |
7.2 |
892.1 |
2.7 |
29.9 |
81.0 |
Note:
No. pt: Number of point samples
in each FCD class
avg: average
tph: average trees per hectare (trees/ha)
bah: average basal
area per hectare (m2/ha)
volh: average volume
per hectare (m3/ha)
QD: Quadratic mean
dbh (cm)
Class 1: blue stratum on the FCD
map
Class 2: brown stratum on the FCD
map
Class 3: yellow stratum on the
FCD map
Class 4: green stratum on the FCD
map
Class 3 had a significantly higher concentration of trees greater than 45 cm
dbh compared to the other classes. However, it did not contain as many large
trees. This could be seen from the quadratic mean. Class 4 had more trees
of larger sizes (>60 cm), where the quadratic mean was higher
and the basal area and volume of trees was also proportionally higher. Class
3 was comparatively more uniform than class 4, which was considered least
disturbed or best regenerated. The most uniform was class 2. This is reflected
by the low variance and standard error for this class, which is considerable compared to the other three classes. Figures 11, 12 and 13 provide a graphical
presentation of tree distribution by FCD classes expressed in trees/ha, basal
area/ha and volume/ha respectively.
Figure 11. Distribution of number of trees per hectare by dbh class and Forest Canopy
Density (FCD) class
Figure 12. Distribution of basal area per hectare by dbh class and Forest Canopy Density (FCD) class
Figure 13. Distribution of volume per hectare
by dbh class and Forest Canopy Density FCD) class
