Proceedings of MatricesFor IITTEP – ICoMaNSEd 2015
ISBN: 978-602-74204-0-3
Physics Page 244
change of microclimate variable magnitude. Without synchronization, time based spatial function modeling will be bias due to the change of variable magnitude during that time
difference. Data synchronization is done by entering time difference data to the temporal function or Fourier function and then we got the corrected time based data. This procedure
included in our software.
2.3. Determination of Spatial Function
Mathematical model of spatial function is:
F x = k + k e
k − k x
………………………………………………….…3
x is the distance from the edge to the center of mangrove. The constants k
1
, k
2
, k
3
and k
4
obtained by iteration techniques. Usually it takes four pairs of data x,T, but if it select the reference point data x = 0, then the constants and coefficients can be determined using three
pairs of data, e.g. : 0, T0, x1, T1, and x2, T2 Medellu, 2012, 2013. Procedure of iteration by computer was:
T0-T1T0-T2=[expk4.x2.expk4.x1-1][expk4.x1.expk4.x2-1] k3 = T0
– T11-1expk4.x1 k2 = T0
– T1expk3 – expk3 – k4.x1 k1 = y0
– k2.expk3 Spatial function graphics for air temperature and humidity presents in Figure-3 and Figure-4
Spatial function of air temperature at 12.00, for transect no-2 – Talengen bay is:
Tx = 32.99674 + 0.18068.
�
. − .
.x
C and the spatial function of humidity at 12.00 for transect no.2 is:
Hx = 65.22828 - 775.01073.
�
− . − .
.x
2.4. Determination of Edge Gradient
Figure-3 and Figure-4 shows that the spatial function changes over time as a result of the irradiation and thermal energy transfer processes in forest ecosystems and the environment.
Figure-3. Spatial function of air tempera- ture at 07.00 , 12.00 and
21.00 . Data: transect-2, Talengen Bay. Source: Medellu, 2012
Distance from forest edge m Te
m per
a tu
re C
5 10
15 20
25 30
24 26
28 30
32 34
36 38
posisijarak meter m S
u h
u C
F igure-4. Spatial function of humidity at
07.00 , 12.00 and 21.00 . Data: transect-2, Talengen Bay.
Source: Medellu, 2012
Distance from forest edge m Hu
m idi
ty
5 10
15 20
25 30
60 65
70 75
80 85
posisijarak meter k
e le
m b
a b
a n
Proceedings of MatricesFor IITTEP – ICoMaNSEd 2015
ISBN: 978-602-74204-0-3
Physics Page 245
Mathematically, this spatial function change means the changes of the spatial gradient at the edge of forest. Gradient of spatial function at the edge of forest determined using formula:
G = dFxdx for x = 0 Medellu, 2012, 2013, or
G = - k
2
.k
3
.exp k
3
................................................................................................4 The constants k
2
and k
3
change over time, so that G is time dependent or daily dynamic. Figure-3 and Figure-4 shows the change of slope and gradient direction, that represents the
direction and intensity of thermal diffusion across the forest edge Medellu, 2012.
2.5. Determination of Edge Gradient Diurnal Dynamic Area
Diurnal dynamics of microclimate gradient function at the forest edge is the Fourier function. This function determined by the same procedure with procedure of the point-1. Figure 5 and
Figure 6 are the graphics of the daily dynamics of the edge gradient of air temperature and humidity on a transect-2, in Talengen bay.
Fourier functions of edge gradient diurnal dynamic of air temperature and humidity: Tt = - 0.2944 -
0.2822 cos2πt12 - 0.7046 sin2πt12 + 0.0246 cos4πt12 + 0.0455 sin4πt12 - 0.047λ cos6πt12 - 0.0306 sin6πt12 - 0.0440 cos8πt12 +
0.0658 sin8πt12 - 0.0λ37 cos10πt12 + 0.0001 sin10πt12 - 0.0812 cosπt + 0.018λ sinπt……….
and Ht = 0.4875 + 0.8627 cos2πt12 + 1.5645 sin2πt12 + 0.3071 cos4πt12 -
0.1561 sin4πt12 + 0.1218 cos6πt12 + 0.1218 sin6πt12 + 0.1424 cos8πt12 - 0.1072 sin8πt12 + 0.2327 cos10πt12 + 0.0164 sin10πt12 + 0.202λ cosπt -
0.0λ77 sinπt ……….. The accuracy of each function for first six harmonic was 95.9 percent and 96.86 percent.
2.6. Determine the Area and Index of Edge Gradient Diurnal Dynamic
