JOUR. OF NAT. RESOUR. & ENVIRON. STU. , 2. 2, 42-49, (6) 2014 ISSN 1683-6456 (Print): ISSN 2332-0109 (Online)
42
Modelling the Relationship between
Crown width and Diameter at Breast
Height for Naturally grown Terminalia
tree species
1
2
3
ELMUGHEIRA M. IBRAHIM (1), ELMAMOUN H. OSMAN (2) and ELZEIN A. IDRIS (3)
College of Natural Resources and Environmental Studies-Department of Forestry, University of Bahri.
Khartoum- Sudan
E mail: [email protected]
Telephone: +249911986534
College of Natural Resources and Environmental Studies-Department of Forestry, University of Bahri.
Khartoum- Sudan
E mail: [email protected]
Telephone: +249911347139
College of Natural Resources and Environmental Studies-Department of Forestry, University of Bahri.
Khartoum- Sudan
E mail: [email protected]
Telephone: +249911270310
(Received: May 06, 2014; Accepted: June 03, 2014)
Abstract: The present study was carried out at ElNour Natural Forest Reserve, Roseries district, Blue
Nile State with objective of Modelling the
Relationship between Crown width and Diameter at
Breast Height for Naturally grown Terminalia tree
species. Five models for predicting crown width were
tested for two selected species, namely, Terminalia
brownii Fresen, and Terminalia laxiflora Engl. &
Diels. Depending on the species dominancy and the
species abundance, seven compartments were
selected for further study where selective sampling
was used. For each species, dbh, total height and
crown width were recorded. DataFit-9 statistical
package of the Oakadale Engineering was used to fit
the selected models. Akaike’s information criterion
(AIC), adjusted coefficient of determination (Ra 2),
root mean squared error (RMSE), numerical and
graphical analyses of the residuals were used for
evaluating the models.
The results of the study showed that, all fitted models
were found to give satisfactory results with Ra2 range
of 0.56 to 0.66 and RMSE of 2.00 to 2.05. The AIC
values range from 284.292 for Terminalia laxiflora
and to 292.373 for Terminalia brownii. The study
concluded that, the crown width could be estimated
by the mean of diameter at breast height as it is easy
to measure for ground-based inventory and stand
structure determination. The crown width-diameter
models examined in this study produced reasonably
precise estimates for crown width and could be used
to predict the crown width of the species under
consideration.
The study recommended that, it is necessary to
introduce new additional parameters such as basal
area, tree age, site-index and density in the equations
in order to improve the performance of the models for
more précised results.
Index Terms: Forest canopy, tree crown, crown
width-diameter relationship, modelling, non-linear
regression, models evaluation.
I.INTRODUCTION
A tree's crown is defined as that part of a tree
bearing live branches and foliage [1].
Photosynthesis occurs in leaves and the products
from photosynthesis (photosynthates) are
translocated through the crown's branches from
the leaves to the remainder of the tree.
Concurrently, water and mineral nutrients
absorbed by the roots are translocated through
the trunk to branches and leaves. A tree's crown
therefore represents the aboveground spatial
requirements needed for a tree to survive, grow,
and reproduce [2]. The shape of a tree's crown is
influenced by two broad factors: genetics and
physical environment [3].
Forest canopy cover, also known as canopy
coverage or crown cover, is defined as the
proportion of the forest floor covered by the
vertical projection of the trees crowns [4].
Estimation of forest canopy cover has recently
become an important part of forest inventories.
First, canopy cover has been shown to be a
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multi-purpose ecological indicator, which is
useful for distinguishing different plant and
animal habitats, assessing forest floor microclimate and light conditions, and estimating
functional variables like the leaf area index
(LAI) that quantifies the photosynthesizing leaf
area per unit ground area [4] and [5]. Secondly,
many remote sensing applications involve
estimation of either canopy cover [6] or
individual tree canopy area [7] as an
intermediate stage in distinguishing the signals
reflected from forest canopy and forest floor,
after which, for instance, estimation of timber
volume becomes possible [8] and [9].
The United Nations Food and Agricultural
Organization (FAO) have defined forest as land
of at least 0.5 ha with potential canopy cover
over 10% and potential tree height of at least
five meters [10]. To ensure compatibility of
international forestry statistics, forest canopy
cover needs to be included in national forest
inventories.
All activities and processes that take place inside
forest areas, such as forest protection,
silvicultural operations, and harvesting process
are related to forest management. For good
forest management, there is a need for up-todate information about the forest to initiate a
comprehensive plan based on available
information that collected from the forests and
its historical records.
Modern forest management requires precise,
accurate,
timely and complete forest
information. Forest information can be acquired
by forest inventory, which includes collection of
individual tree parameters such as location,
Diameter at Breast Height (dbh), tree height,
tree crown size and tree species within a
sampled forest plot, and also includes the
derivation of forest stand measurements such as
forest density, age, mean height, and crown
closure, etc using statistical extrapolation of plot
measurements [11].
The main problems facing forests management
particularly inventory operations in Sudan
natural forests is that, usually the cost of
inventory operations are more than the value of
harvested timber due to under-stocked and poor
quality. The main causes of under-stocking and
poor quality timber in this forest are illicit
felling, over grazing, shifting cultivation and
wild fires. The absence of proper forest
management activities due to the poor control
and lack of enforcing forest laws, paved the way
for the local people to take forest products,
especially fire wood and charcoal as their main
source of income [12].
Natural forests in Sudan are generally known to
be under the public ownership supervised by the
local government authorities. The control over
such types of forests and protective measures
offered to them are generally poor due to the
absence of up-to-date growth information. Any
effort to ease and reduce the cost of forest
inventories in such cases would be highly
appreciated and could save the existence of a
number of very valuable indigenous tree species
in these forests [13].
The objective of this study is to test the
performance of five predicting models for crown
width-diameter at breast height (Cw-dbh)
relationship for Terminalia brownii Fresen and
Terminalia laxiflora Engl. & Diels in Blue Nile
Area, Sudan.
II. STUDY AREA AND METHDOLOGY
The study was done in El-Nour Natural
Reserved Forest which is located in Blue Nile
State, Sudan, between longitudes 110 48/19// N
and 110 53/30// N and latitudes 340 28/ 47// E and
340 32/ 35// E with total area of about 11,100
feddan. The forest encompass more than 55
species dominated by Sterculia setigera,
Combretum hartmannianum, Acacia seyal,
Terminalia brownii, Terminalia laxiflora,
Anogeissus leiocarpus, Balanites aegyptiaca,
Combretum micranthum and Lannea fruticosa
[14]. The topography of El-Nour Forest is
generally flat or semi-flat with cracky clay soil
in northern-part and sandy soil in southern-part
of the forest.
The species selection for this study was mainly
based on the economic value and trees uses by
local communities around the forest. Terminalia
brownii is used locally for fire wood, charcoal,
local buildings, beams and rafters [14]. Its bark
is also used for cough, rheumatism and
bronchitis [15]. While Terminalia laxiflora is
used for fire wood, charcoal, railway sleepers,
general constructions, local furniture, joinery
and turnery [14]. Its leaves used for stomach
pains and wounds [15].The wide uses of these
two species in the area in the absence of proper
natural regeneration, due to overgrazing, wild
fires and draught, has resulted in gradual
depletion of these species especially in areas
close to villages. Estimation of the present
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growing stock in such large area using the
traditional inventory system is expected to be
both uneconomic and time consuming. The idea
therefore is to establish a relationship between
the dbh and the crown dimensions so as to
facilitate the use of remote sensing/GIS
techniques as cheaper alternatives.
Selective sampling was used for data collection
where each individual open grown tree was
considered as a sample and dbh, total tree height
Species
Terminalia brownii
Terminalia laxiflora
Terminalia brownii
Terminalia laxiflora
Terminalia brownii
Terminalia laxiflora
and crown width (Cw) were recorded for all
sampled trees. The dbh (cm) was measured over
bark at 1.3m to the nearest millimetre using tree
calliper and diameter tape for larger trees (Table
1). Total tree height (m) was measured using
Suunto Clinometer (Tables 1), while crown
width (m) was measured in eight directions from
the main bole (every 450 beginning with
magnetic north) to the vertically projected edge
of the crown (Table 1).
Table 1:
Diameter, height and crown width characteristic
N
Max
Min
Mean
Diameter at breast height characteristics (cm)
204
72
18
41.73
206
68
21
36.7
Total tree height characteristics (m)
204
21
4.5
14.15
206
19.5
8.5
13.1
Crown width characteristics (m)
204
20.25
3.5
10.53
206
19
4.5
10.4
Five equations for predicting crown diameter
(Cw) using dbh were selected as candidate
functions to model the dbh-Cw relationship
(Table 2). DataFit-9 was used to fit the selected
models [16].
Akaike’s Information Criterion (AIC), adjusted
coefficient of determination (Ra2), root mean
squared error (RMSE), numerical and graphical
analyses of the residuals were used for
S.dev
CV%
8.9
8.47
%
21.33
23.08
1.97
2.34
13.92
17.86
2.56
2.77
24.31
26.63
evaluating the models. Model resulting in the
largest Ra2, least RMSE, and smallest values of
AIC and average bias was selected as the best
model for the selected tree species [17].
The formula of AIC used as criterion for
selection of best model can be calculated as
indicated in equation 1while RMSE is calculated
as
indicated
in
equation
2
[18].
AIC = n*ln (RSS/n) + 2*K ------------------------------------------------------------------------------------------------------ (1)
RMSE = √ (RSS/n-P) ------------------------------------------------------------------------------------------------------------ (2)
Where:
n = Number of observations
ln = Natural logarithm
RSS = Residual sums of squares
K= Number of parameters in the model
P = Number of regression coefficients
Table 2: Regression models
Code
Function form
Reference
M1
Cw = b0+ b1*dbh
[19]
Code
M2
Cw= (dbh) / (b0+b1dbh)
[20]
dbh
M
Cw = b0*b1
[21]
Md3
b1
M
4
Cw
=
b
*dbh
[21]
0
Me
M5
Cw = b0 + b1*dbh+ b2*dbh2
[20]
Cw:Mh
Crown width, dbh: diameter at breast height, b0,b1,b2 and b3are equation parameters.
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III. RESULTS AND DESCUSSIONS
For data analysis, the dbh was taken as the
independent variable, while the crown width
was taken as the dependent variable. Tables 3
and 4 show the regression parameter estimates
and fit statistics for the five tested models.
Figures 1, 2, 4and 5 describe the crown width
curves predicted by the same models while,
figures 3 and 6 represented the residual plots of
one top model for Terminalia brownii and
Terminalia laxiflora respectively.
Code
M3
M1
M4
M2
M5
Code
M3
M4
M1
M2
M5
Generally, all fitted models gave acceptable
results with Ra2 range from 0.5620 to 0.5741
and RMSE of 2.0278 to 2.0540 for Terminalia
brownii, and 0.6501 to 0.6653 and 2.0005 to
2.0323 for Terminalia laxiflora. The AIC values
range from 288.432 to 292.373 for Terminalia
brownii and 284.292 to 290.757 Terminalia
laxiflora.
Table 3: Parameter estimates and fit statistics for Terminalia brownii
Models Statistics (n = 204)
Coefficient Estimates
2
2
R
Ra
RMSE
AIC
P
Value
S
t-ratio
Prob(t)
b
0.7717
0.1856
4.1588
0.0001
0
0.5772 0.5741 2.0278 288.432
b1 0.7016 0.0637
11.021 0.0000
4.621
0.0000
0.5757 0.5726 2.0303 289.934 b0 3.1583 0.6835
b1 0.1766 0.0160
11.025 0.0000
10.601 0.0000
0.5751 0.5720 2.0313 290.127 b0 4.5385 0.4281
b1 0.1972 0.0010
19.755 0.0000
b
5.4514
0.3473
15.698 0.0000
0
0.5660 0.5629 2.0459 292.062
b1 1.0157 0.0014
712.80 0.0000
b0 1.4470 2.3999
0.6029 0.5472
0.5640 0.5620 2.0540 292.373 b1 0.2576 0.1100
2.3413 0.0202
b2 -0.001 0.0012
-0.744
0.4577
Table 4: Parameter estimates and fit statistics for Terminalia laxiflora
Models Statistics (n = 205)
Coefficient Estimates
R2
Ra2
RMSE
AIC
P
Value
S
t-ratio
Prob(t)
b
0.5685
0.1226
4.6357
0.0000
0
0.6679 0.6653 2.0005 284.292
b1 0.8082 0.0589 13.7179 0.0000
0.6670 0.6644 2.0021 284.618 b0 4.7668 0.3557 13.4004 0.0000
b1 0.1777 0.0093 19.1455 0.0000
0.6667 0.6641 2.0028 286.748 b0 2.0562 0.6408 3.2088 0.0016
b1 0.2278 0.0171 13.3283 0.0000
0.6508 0.6481 2.0032 287.829 b0 5.0541 0.2921 17.3055 0.0000
b1 1.0195 0.0014 704.856 0.0000
b0 -0.032 2.2834 -0.0142 0.9887
0.6501 0.6431 2.0323 290.757 b1 0.3365 0.1154 2.9158 0.0040
b2 -0.001 0.0014 -0.9530 0.3417
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Fig. 1: Predicted for Terminalia brownii (All tested models)
Fig. 2: Predicted for Terminalia brownii (Top models)
Fig 3: Residual plot for Terminalia brownii
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Fig. 4: Predicted for Terminalia laxiflora (All tested models)
Fig. 5: Predicted for Terminalia laxiflora (Top models)
Fig, 6: Residual plot for Terminalia laxiflora
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There are many studies investigated the relationships between crown diameter and dbh e.g. [22]
and [23], the crown radius-dbh [24] and the
crown width-bole diameter relationships [25].
These studies, which were carried out on various
tree species, indicated a strong relationship
between crown width and tree diameter.
In this study non-linear and linear models were
tested, among all models, generally model
3(M3) show higher performance for both two
species (Tables 3 and 4), (Figures 1 and 4).The
highest Ra2 value was obtained in model 5 (M3)
in case of Terminalia laxiflora (Ra2 = 0.6653),
(Table 4), and the lowest Ra2 was obtained in
model 5 (M5) in case of Terminalia brownii
(Ra2 = 0.5620), (Table 3).
Models M3, M1 and M4 were present in both
two species among the best three models for two
species but in different ranking order, while
M5was appear as lowest Ra2 model for the two
species. All the three best models for the two
species consist of two parameters (b0and b1)
which mean that, the two parameter equations
were more efficient than their counterparts. All
parameters were statistically significant (p
<0.0001).
These results imply that simple regression
models are to be preferred for modelling the
dbh-Cw relationship. [26] concluded that the
dbh-Cw relationship is close to linear and it
provided the best fit model [19]. However, [25]
settled on the power model to describe Cw-dbh
relationships. While the dbh- Cw relationship
would be sigmoid for forest grown trees [27] it
is expected to be linear for open grown tree
species.
Figures 2 and 5 represent the crown width
predicted curves produced by the top three
models for Terminalia brownie and Terminalia
laxiflora respectively. These crown curves
indicated that, all top three models performed
well within the data range. The Terminalia
brownie curves produced almost the same curve
where they appeared as one curve, such trend
could be referred to the general form of
Terminalia brownii in El-Nour forest where it
characterized by rounded crown shape for opengrown trees.
IV. CONCLUSIONS
From the results of this study, it was concluded
that crown width could be estimated by the
mean of diameter at breast height as it is easy to
measure for ground-based inventory and stand
structure determination. The crown widthdiameter models examined in this study
produced reasonably precise estimates for crown
width and could be used to predict the crown
width of the species under consideration. The
best predictor model for both two species was
model3 (M3).
V. RECOMMENDATIONS
It should be noted that, the models developed by
this study were based on data collected from ElNour Natural Forest Reserve in Blue Nile State;
therefore, it should be used with caution outside
this area.
It necessary to introduce additional parameters
such as basal area, tree age, site index and
density incoming equations in order to improve
the performance of the models and executed
more précised results.
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