Volume Equation for Cedrus deodara in Kullu District of Himachal Pradesh

Abstract

The aim of the study was to construct a simple volume equation for Cedrus deodara to raise two way volume table on the basis of diameter at breast height (dbh) and total height from 100 trees in different three locations viz. Naggar (L-1), Manali (L-2) and Kasol (L-3) of Kullu district in Himachal Pradesh. The data were subjected to variability analysis in order to test the variability among different locations. Bartlett's chi-square calculated values were 4.87, 3.46 and 3.91 which was less than Bartlett's chi-square tabulated value (5.99) for testing the homogeneity of variances with respect to diameter, height and volume respectively. Various probability distributions were fitted to find out the expected number of trees in each diameter class and its significance was tested by using Kolmogorov-Smirnov test statistic. Gamma distribution (0.0618) was observed best fitted for Cedrus deodara. Linear regression analysis was best to estimate the volume for the _ 2 2 construction and prediction of two way volume table on the basis of maximum value of R (0.885) and R (0.884), minimum RMSE (0.791) and Theil's U-statistic (0.036), whereas validation was tested by half-split method and Chow test.

Full text

Volume Equation for Cedrus deodara in Kullu District of
Himachal Pradesh
Abstract: The aim of the study was to construct a simple volume equation for Cedrus deodara to raise two way volume table on the basis of
diameter at breast height (dbh) and total height from 100 trees in different three locations viz. Naggar (L-1), Manali (L-2) and Kasol (L-3) of Kullu
district in Himachal Pradesh. The data were subjected to variability analysis in order to test the variability among different locations. Bartlett's
chi-square calculated values were 4.87, 3.46 and 3.91 which was less than Bartlett's chi-square tabulated value (5.99) for testing the
homogeneity of variances with respect to diameter, height and volume respectively. Various probability distributions were fitted to find out the
expected number of trees in each diameter class and its significance was tested by using Kolmogorov-Smirnov test statistic. Gamma
distribution (0.0618) was observed best fitted for Cedrus deodara. Linear regression analysis was best to estimate the volume for the
_
2 2
construction and prediction of two way volume table on the basis of maximum value of R (0.885) and R (0.884), minimum RMSE (0.791) and
Theil's U-statistic (0.036), whereas validation was tested by half-split method and Chow test.
Keywords: Volume equation, Cedrus deodara, Linear model, Variability and regression
Manuscript Number:
NAAS Rating: 4.96
163
Ajit Sharma, R.K. Gupta, P.K. Mahajan and Shilpa
Dr Yashwant Singh Parmar University of Horticulture and Forestry, Nauni-173 230, India
E-mail: ajitstats5152@gmail.com
Cedrus deodara (Devdar) belongs to family Pinaceae is
one of the most important naturally durable commercial
timber species of western Himalayas. Detailed information of
forest stand is crucial for forest research and planning and
this information can be used as an input for ecosystem
modeling, forest growth and yield models. Volume tables
showing the contents of trees of given size according to some
unit of measure are essential to most of the forestry work.
They are used to estimate standing timber for timber sales,
forest management plans and forest surveys, appraisal of
damage and forest valuation in general. Even though volume
equations have been studied for many years, they continue
to attract forest research. One reason is that there is no single
theory in volume equations that can be used satisfactorily for
all tree species and no single model is best for all purposes.
Another reason is that volume equations are required to be
increasingly accurate and flexible in their predictions. Forest
measurement needs to be improved because market
requirements for timber have become more specific in recent
years. Volume tables are used to estimate standing timber for
timber sales, forest management plans and forest surveys,
appraisal of damage and forest valuation in general. The
variables used for volume table preparation are diameter at
breast height (dbh) and height. Volume tables have a long
history in forest science and are still a commonly used
operational tool (Vanclay and Baynes, 2005). Various volume
tables may list expected height of the stands (dominant
height, some form of mean height or both), mean diameters,
stand basal area, standing volume, gross volume production
and a range of other variables that can be derived from these.
The intent of the study was to measure variability analysis
among three different locations of Kullu for diameter, height
and volume of devdar and to study the trend of devdar in Kullu
with regression analysis and probability distributions. It could
also be useful in the programming of forests and can
guarantee an optimal and economical production and
stability of the forest stand. Using appropriate statistical
distributions in forest planning is very beneficial and has a lot
of importance in predicting the expected number of trees in
various diameter classes of different conifer forest stands.
The provided equations are considered as a valuable
contribution in the development of tools to assist the forest
planners in providing a more accurate prediction of forest
resources in terms of volume as well as to support the proper
management strategies for temperate zones.
MATERIAL AND METHODS
The present study was conducted on high density
plantation of Cedrus deodara in three different forest
locations of Kullu. The data on diameter at breast height
(dbh) and height of 100 trees were recorded from each forest
location on an average elevation of 1,478 m to 2100 m and
volume was collected from the State Forest Department,
Kullu. December and January during winter observe lowest
temperatures ranged from - 4 to 20 °C (25 to 68 °F), with
some snowfall. Evenings and mornings are very cold during
Indian Journal of Ecology (2017) 44 Special Issue (6): 781-784

winters. Annual maximum temperature in summer ranged
from 24 to 34 °C (75 to 93 °F) during May to August. Months of
July and August are rainy because of monsoon, having
around 150 mm monthly rainfall. Breast height was marked
by measuring stick on standing trees at 1.37 m (4 ft 6 in)
above the ground level. With the help of vernier caliper data
measured at two sides, right angle to each other and an
average of these was considered as diameter over bark (dob)
and girth over bark was recorded. Height of each selected
tree was measured with the help of Ravi multimeter and as an
ocular estimate. Two sides of tree were selected from where
the top and base of the tree were visible and observations
were recorded. The average of these readings was taken as
the height of the tree in meters. In order to compare the
consistency and variability of various parameters such as
diameter, height and volume, the coefficient of variation has
been worked out. Bartlett's chi-square test was used to
compare the homogeneity of variances among three
locations whether two or more independent samples are
drawn from same population or from different population.
Normal, lo g- no rm al , gamma, laplace a nd uniform
distributions were fitted to find out the expected number of
trees in different diameter classes. Kolmogorov-Smirnov
test-statistic measures the compatibility of a random sample
with a theoretical probability distribution function. In present
investigation, volume estimation of devdar was done by
taking volume as explained variable and diameter at breast
height (dbh) and height of trees as explanatory variables.
Equations used for volume estimation were Linear (straight
line), logarithmic, quadratic, inverse, cubic, compound,
power, S, growth and exponential. Testing the significance of
the regression coefficient by F-test and goodness of fit
2 2 2
statistic was measure R , Adjusted R (R ) Root mean square
error (RMSE) and Theil's inequality coefficient. Validation of
models assessed in some sense the degree of agreement
between the model and real system being modeled. Once a
model which gives an adequate fit to the data has been
found, the next step in the process is to use the model for
prediction purposes. Before a model is to be used or
recommended, it is advised to check its validity. In the
present study, half split method and Chow test was used to
test the validation purpose.
RESULTS AND DISCUSSION
The mean value for diameter of Cedrus deodara were
maximum in L-3 followed by L-1 and L-2 i.e., 61.78 cm, 56.72
cm and 54.53 cm, with standard error 2.38, 1.95 and 2.37,
respectively. So, there is presence of homogeneity with
respect to diameter in three locations. Fudicial limits are
similar to confidence limit for the situation when the true value
of parameter lies between the calculated upper and lower
limits. The respective fudicial limits for three locations were
57.12-66.44 cm, 52.90-60.54 cm, and 49.89-59.17 cm i.e.
the difference between the upper and lower limit was less so
that sample statistic approaches to population parameter.
Coefficient of variation (CV) was computed for diameter,
height and volume. The classes of diameter at breast height,
height and volume were homogeneous for all the three
locations. The CV ranged between 34.34% to 41.43% for
diameter which showed higher consistency and lesser
Locations amsl (m) Mean Range SE Fudicial limits CV (%)
Diameter (cm)
Naggar (L-1) 2047 56.72 21-118 1.95 52.90-60.54 34.34
Manali (L-2) 1912 54.53 16-99 2.37 49.89-59.17 43.41
Kasol (L-3) 1580 61.78 15-118 2.38 57.12-66.44 38.48
Bartlett's chi-square calculated values for diameter variance was 4.87
Height (m)
Naggar (L-1) 2047 14.64 7-24 0.45 13.75-15.52 30.74
Manali (L-2) 1912 15.68 8-26 0.45 14.79-16.57 28.85
Kasol (L-3) 1580 13.48 6-21 0.34 12.82-14.14 25.10
Bartlett's chi-square calculated values for height variance was 3.46
3
Volume (m )
Naggar (L-1) 2047 3.24 0.28-9.11 0.21 2.83-3.64 63.46
Manali (L-2) 1912 3.24 0.11-8.99 0.25 2.75-3.73 76.87
Kasol (L-3) 1580 3.79 0.11-8.75 0.24 3.33-4.62 62.75
Bartlett's chi-square calculated values for volume variance was 3.46
3
Table1. Statistical parameters for diameter (cm), height (m) and volume (m ) of Cedrus deodara trees at three different
locations
782 Ajit Sharma, R.K. Gupta, P.K. Mahajan and Shilpa

variability. Bartlett's chi-square calculated values for
characters diameter, height and volume were 4.87, 3.46 and
3.91, respectively, which were compared with chi-square
table value (5.99) at 5% level of significance at 2 degree of
freedom, it indicated that diameter, height and volume had
homogeneous variance. Hence, results were non significant
among three locations. This showed that there is no
significant variation among three locations with respect to
diameter and volume. Due to high data homogeneity, all the
three locations i.e. Naggar, Manali and Kasol were found to
me more consistent and we prepare combined two way
volume table for devdar.
The parameter estimated for Cedrus deodara with
respect to all fitted distributions viz. gamma distribution were
á and â with values being 6.55 and 8.79, normal distribution
with estimated parameters = 57.67 and ó= 22.52, lognormal
distribution with and ó (3.96 and 0.45), respectively, uniform
with a = 18.65, b = 96.69 and laplace distribution has two
parameters i.e. ë and with values 0.06 and 57.67
respectively. The
Kolmogorov-
Smirnov test statistic
hypothesis regarding the fitting of gamma
distribution to diameter class on the basis of
was accepted at the chosen
Distributions Parameters
estimated
Parameters
values
KS-Statistic
Gamma á
â
6.55
8.79
0.061
Normal µ
ó
57.67
22.52
0.063
Lognormal µ
ó
3.96
0.45
0.069
Uniform a
b
18.65
96.69
0.086
Laplace ë
µ
0.06
57.67
0.125
››››››››››
Table 2. Parameters of various probability distributions for
Cedrus deodara
Models Equations 2
R
_2
RRMSE Theil's U -
statistic
Chow Test
FCal.
Linear -5
V = 1.054 + 3.641×10 I 0.885 0.884 0.791 0.036 0.917
Logarithmic _
V = 15.858 + 1.825 ln I 0.839 0.838 0.935 0.050 1.325
Inverse V = 4.154 – 12636.092/I 0.314 0.311 1.928 0.215 6.347
Quadratic -5 -10 2
V = 0.378 + 6.001×10 I – 1.099×10 I 0.844 0.842 0.810 0.057 1.652
Cubic -5 -10 2 -16 3
V = 0.241 + 6.806×10 I – 1.939×10 I + 2.110×10 I 0.846 0.845 0.843 0.057 2.455
Compound I
V = 1.046 × 1.000 0.570 0.569 0.665 1.357 4.642
Power 0.850
V = 0.000 I 0.755 0.753 0.814 0.058 3.927
S V = exp (1.356 – 8329.866/ I) 0.716 0.715 0.740 0.178 3.136
Growth -5
V = exp ( 0.045 + 1.275×10 I) 0.570 0.569 0.665 1.357 5.764
Exponential 0.0000127 I
V = 1.046 e 0.570 0.569 0.665 1.357 5.862
2
Table 3. Linear and non-linear functions for volume estimation using D H (I)* for Cedrus deodara
2
*D H (I): two times diameter was taken and one time height (combination of two variables) denoted by (I)
significance level (5%) because the test statistic, D ( )
was less than the critical value (0.070) and had minimum
statistic value among all the fitted distributions. So, we follow
the gamma distribution to find out the expected number of
trees in each class for devdar in Kullu.
0.061
The parameter estimates and goodness of fit statistic of
different linear and non-linear functions for estimating volume
2
of Cedrus deodara on the basis of D H (I) in Kullu. High value
2 2
of R and R (0.885 and 0.884), respectively, minimum RMSE
(0.791) and Theil's U-statistic (0.036) of linear model gave
good results for the volume estimation and prediction.
Validation of best fitted linear model is tested by Chow test, the
F value being 0.917 followed by logarithmic and quadratic
cal.
1.325 and 1.652, respectively. These calculated values were
less than F (3.026) at 5% level of significance. Hence, for
tab.
volume prediction fitted models were valid and on the basis of
goodness of fit and test statistic we predict the volume of
-5
devdar with the help of Linear model (V = 1.054 + 3.641×10 I).
Presents the volume overbark of devdar trees for different
diameters ranges from 10 to 100 cm and height ranges from 5
to 25 m, which was calculated by using projected equations V
-5
= 1.054 + 3.641×10 I.
CONCLUSION
The study constitutes the first attempt of the development
of volume equations for native commercial devdar species in
Kullu district of Himachal Pradesh. The provided equations
are considered as a valuable contribution in the development
of tools to assist the forest planners in providing a more
accurate prediction of forest resources in terms of volume as
well as to support the proper management strategies for this
region. Because of the increased interest in the use of devdar
the ability to predict its yields using stem volume data will be
greatly valued. Suitable equations can be used for estimating
the volume of a devdar tree and forest stand. Using
783
Volume Equation for Cedrus deodara

Height (m) Diameter (cm)
10 20 30 40 50 60 70 80 90 100
5 1.07 1.13 1.22 1.35 1.51 1.71 1.95 2.22 2.53 2.87
6 1.08 1.14 1.25 1.40 1.60 1.84 2.12 2.45 2.82 3.24
7 1.08 1.16 1.28 1.46 1.69 1.97 2.30 2.69 3.12 3.60
8 1.08 1.17 1.32 1.52 1.78 2.10 2.48 2.92 3.41 3.97
9 1.09 1.19 1.35 1.58 1.87 2.23 2.66 3.15 3.71 4.33
10 1.09 1.20 1.38 1.64 1.96 2.36 2.84 3.38 4.00 4.70
11 1.09 1.21 1.41 1.69 2.06 2.50 3.02 3.62 4.30 5.06
12 1.10 1.23 1.45 1.75 2.15 2.63 3.19 3.85 4.59 5.42
13 1.10 1.24 1.48 1.81 2.24 2.76 3.37 4.08 4.89 5.79
14 1.11 1.26 1.51 1.87 2.33 2.89 3.55 4.32 5.18 6.15
15 1.11 1.27 1.55 1.93 2.42 3.02 3.73 4.55 5.48 6.52
16 1.11 1.29 1.58 1.99 2.51 3.15 3.91 4.78 5.77 6.88
17 1.12 1.30 1.61 2.04 2.60 3.28 4.09 5.02 6.07 7.24
18 1.12 1.32 1.64 2.10 2.69 3.41 4.27 5.25 6.36 7.61
19 1.12 1.33 1.68 2.16 2.78 3.54 4.44 5.48 6.66 7.97
20 1.13 1.35 1.71 2.22 2.87 3.68 4.62 5.71 6.95 8.34
21 1.13 1.36 1.74 2.28 2.97 3.81 4.80 5.95 7.25 8.70
22 1.13 1.37 1.77 2.34 3.06 3.94 4.98 6.18 7.54 9.06
23 1.14 1.39 1.81 2.39 3.15 4.07 5.16 6.41 7.84 9.43
24 1.14 1.40 1.84 2.45 3.24 4.20 5.34 6.65 8.13 9.79
25 1.15 1.42 1.87 2.51 3.33 4.33 5.51 6.88 8.43 10.16
Table 4. Two way volume table (overbark) for Cedrus deodara
-5
*V = 1.054 + 3.641×10 I
appropriate statistical distributions in forest planning is very
beneficial and has a lot of importance in predicting the
expected number of trees in various diameter classes of
different conifer forest stands.
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Received 12 September, 2017; Accepted 10 November, 2017
784 Ajit Sharma, R.K. Gupta, P.K. Mahajan and Shilpa