Joint International Conference on Long-term Experiments ...

With proper replacement the element of parameter vectors d0 and d1, independent
variable i=1, 2,…N, dependent variable Y1, Y2,… YN and errors y1, y2,…yN can be
obtained the series without trend.
d
2(
N − 2)
− 3
∗Y
− i ∗Yi
= 3
2(
N + 2)
− 3 N 1
−
3 2
0 +
where d0 = constant of trend function
d1 = coefficient of trend function
N = number of element
i = i th element
Y = mean of original time series
P i
= a
0
2π
2π
+ acos
∗i
+ bsin
∗i
r r
d
1
N + 1
− ∗Y
+ i ∗Yi
=
2
2
N −1
12
(eqv. 3.)
Calculated result of Equation 2. is the following: Ti=0.5113+0.0007i.
The Pi periodic component of time steps of annual biomass intensity is exists in
temperate climate. As next step the periodic component was detached by using the
model. In that case when the periodic time of periodic component is known, the
determination of the period amplitude has to be done only. We suppose there is a 12
months periodic in biomass change. The calculation of one time period is the following:
where:
(eqv. 4.)
a0 = constant of period
a és b = coefficient of function
The relevant period time is r = 12 months. The value of i can be counted in month. The
a0, a and b parameters were determined. In this case y1 time step without trend with Pi
periodic component was converged (Eqv. 5.):
yi = Pi + p (eqv.5.)
The value of pi is: pi = yi - Pi
The determination “a” and “b” (Eqv. 6.) is needed to count Pi.
N 2 2π
a = yi
cos i
N 12
∑
i=
1
N 2 2π
b = yi
sin i
N 12
48
∑
i=
1
(eqv. 6.)