Proceedings of MatricesFor IITTEP – ICoMaNSEd 2015
ISBN: 978-602-74204-0-3
Physics Page 242
temperature in characterizing the ecosystem of dalugha Cyrtosperma merkusii Hassk. Schott
Besides to vary in variables, the characterization of the ecosystem also varies in the using of parameters. The area was widely studied to characterize forest ecosystems is edge of forest.
Microclimate variables in the edge or in the forest boundaries, fluctuates more than in the central of forest Heithecker and Halpern, 2007, Davies-Colley et al., 2000; Zheng et al.,
2000. Forest edge is an area around the limits of forest ecosystems or the limit of forest fragmentation and patches Medellu, 2012. Parameters are widely used by researchers to
describe the daily changes of microclimate around the edge of the forest were the edge gradient Rambo and North, 2008; Chen et al. 1995; Williams-Linera et al. 1998; Gehlhausen
et al. 2000; Newmark 2001; Cienciala et al. 2002, and the depth of edge effects Gehlhausen et al. 2000; Stewart and Mallik, 2006; Medellu et al., 2012; Ibanez et al., 2012. Edge
gradient and depth of edge effect change throughout the day as a result of the irradiation and thermal energy transfer between the environment and forest ecosystems Medellu, 2012;
Ibanez, 2012.
In 2012, the authors formulate a new parameter that was the edge gradient diurnal dynamic area, for characterization of mangrove forests. The edge gradient diurnal dynamic area is the
area between the curves of diurnal edge gradient with a line of thermal equilibrium between forest and environment. Thermal equilibrium line is a horizontal line in coordinate system of
the time versus gradient. Thermal equilibrium line has a value of zero edge gradient, and demonstrates the condition that no flow of energy between the forest and environment
Medellu, 2012. This paper discus the method and application of parameter: edge gradient diurnal dynamic area in characterizing the mangrove ecosystems. Microclimate variables
discussed here are the air temperature and humidity.
2. Determination of Diurnal Dynamic Area of Microclimate Gradient
Mathematical model of the edge gradient diurnal dynamic area Medellu, 2012; 2013 is: A =
∑ �
� �
�=�
. �……………………..………………………………………1
Δt is the sampling interval of time as the dependent variable and G
i
is the value of edge gradient of sample i in the time interval of t
1
– t
2
. T
1
and t
2
indicates the time of the first and second thermal equilibrium between forest ecosystems and the environment. The procedure
for determine the edge gradient diurnal dynamic area was as follow:
2.1. Determination of Fourier Function of Microclimate Variables
T t = T + ∑ a
m
cos ω
m
t + b
m
sin ω
m
t
� �=
…………………………..…2 where
ω
m
= 2πmN
………………….………………………………………..3
……………………………....……………4a
……….…………….……………………..4b
Proceedings of MatricesFor IITTEP – ICoMaNSEd 2015
ISBN: 978-602-74204-0-3
Physics Page 243
Tt is the Fourier function, m is the harmonic number of Fourier series, N is the number of data pairs of independent t and dependent ft variables. Daily measurement of
microclimate variable with one hour internal, produce data pairs N = 24. T is the average of
dependent variable values. Mathematical procedure for Fourier function formulation of each point of measurement along the transect Medellu, 2012, 2013 is:
a. Determination of Fourier coefficient a
m
and b
m
, using equation 4b and 4c. b.
Determination of coefficient c
m
using the relation c
m 2
= a
m 2
+ b
m 2
. c.
Determination of diversity coefficient : s
m
= c
m 2
2.σ100 σ is the standard deviation of microclimate data. Through these steps we found a
m
, b
m
, c
m
and s
m
data, for m = 1, 2, …..12. Diversity coefficient s
m
, determine the number of harmonic to construct the Fourier function model with define degree of accuracy. Higher number of
harmonic means higher number of Fourier series, guaranties the high precision of function. Figure 1 presents the Fourier function graphics of air temperature at the position of 1 m
outside the forest, at the edge and at position 16 m to the central of mangrove forest in Talengen bay. Figure 2 presents Fourier function graphics of humidity for the same transect
and positions.
Fourier function of air temperature at the edge of mangrove x=0, transect no.2 – Talengen
bay is: Tt = 29.3720 -
1.3072.cosπt12 + 5.5511.sinπt12 - 1.015λ.cosπt6 - 0.3812.sinπt6 + 0.0λλ.cosπt4 - 0.137.sinπt4 + 0.225.cosπt3 - 0.040.sinπt3
C and the Fourier function of humidity at the edge of mangrove, transect -2, Talengen Bay is
Ht = 74.608 + 3.280.cosπt12 - 13.703.sinπt12 + 1.323.cosπt6 + 0.352.sinπt6 - 0.076.cosπt4 - 0.086.sinπt4 - 0.640.cosπt3 - 0.081.sinπt3
The degree of accuracy of each functions are 99.3 percent and 99.185 percent Medellu, 2012, 2013
.
2.2. Data Synchronization
