Data Synchronization Determination of Spatial Function

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

Data synchronization needed for not simultaneous measuring between positions along transect. The difference in time of measuring for subsequent positions, are followed by the Figure-1. Diurnal changes of air tempera- ture at: 1 m out of mangrove , the edge , and 16 m in mangrove , transect-2 Talengen Bay Source: Medellu, 2012 07.00 11.00 16.00 21.00 02.00 07.00 Time of measurement Te m per a tu re C 5 10 15 20 25 25 30 35 waktu jam te m p e ra tu r o C Figure-2. Diurnal changes of humidity at: 1 m out of mangrove , the edge , and 16 m in mangrove , transect-2 Talengen Bay Source: Medellu, 2012 07.00 11.00 16.00 21.00 02.00 07.00 Time of measurement Hu m idi ty 5 10 15 20 25 55 60 65 70 75 80 85 90 waktu ke le m ba ba n 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