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
The area of edge gradient diurnal dynamic is the area surrounded by the diurnal dynamic gradient curve above and below the thermal equilibrium line red line, Figure 5 and 6. For
air temperature, the area above the equilibrium line represents the area of edge gradient at night, while the area below the equilibrium line represents the day edge gradient. For
humidity variable, the area above the equilibrium represents the day and below represents the
Figure-5. Graphic of diurnal dynamic of air temperature at the edge of mangrove, transect-
2, Talengen Bay. Source: Medellu, 2012
07.00 11.00 16.00 21.00 02.00 07.00
Time
5 10
15 20
25 -1.5
-1 -0.5
0.5 1
time g
ra d
ie n
t o
C m
Figure-6. Graphic of diurnal dynamic of humidity at the edge of mangrove, transect-
2, Talengen Bay. Source: Medellu, 2012
07.00 11.00 16.00 21.00 02.00 07.00
Time
5 10
15 20
25 -2
-1 1
2 3
time
g ra
d ie
n t
m
Proceedings of MatricesFor IITTEP – ICoMaNSEd 2015
ISBN: 978-602-74204-0-3
Physics Page 246
night. The area of edge gradient diurnal dynamic determined using the numeric integral method, with sampling interval of time Δt about 0.1 minute. The number of data obtained by
dividing the area above and below the equilibrium line by Δt. Using equation 1 we get the day and night area of edge gradient diurnal dynamic. The unit of edge gradient diurnal
dynamics area is the multiplication of gradient unit with time unit. The unit of edge gradient diurnal dynamics area for temperature is
o
C.hourmeter, while the unit for humidity variable is: .hourmeter. Microclimate edge gradient diurnal dynamics index is a quantity of night
divided by day area. This index is no unit. The procedure of determining the edge gradient diurnal dynamic area, include other parameters, such as the maximum difference of
microclimate variable inside and outside the forest, the maximum edge gradient, and the depth of edge effects. The excess of parameter: edge gradient diurnal dynamic area, is able to
demonstrate the energy accumulated in forest ecosystems as well as the transfer of energy between forests and the environment during one day. This parameter can be used to
characterize forest ecosystems and to monitor changes in ecosystems and ecosystem- environment interactions Medellu, 2012.
3. Application of Parameter: Edge Gradient Diurnal Dynamic Area
