Slamet Syamsudin, The Predict Of Ionosphere Fof2 Using Multivariat Analyse

P003

)T,R,Y(f2foF = by Y ( 0,2 )∈ π and T ( 180 ,180 )∈ − ° ° , then Y is effective cosinus sun zenith angle, T is local observatory time

])jTsin()R,Y(b)jTcos()R,Y(a[)R,Y(a)T,R,Y(fJN

1jjj0 ∑

=

++= ( 2 )

by ∑=

=kN

0k

kk,jj R)Y(A)R,Y(a and ∑

=

=kN

0k

kk,jj R)Y(B)R,Y(b

∑=

β+α+α=rN

1rr,k,jr,k,j0,k,jk,j )]rYsin()rYcos([)Y(A and

∑=

ω+γ+γ=rN

1rr,k,jr,k,j0,k,jk,j )rYsin()rYcos([)Y(B

3 Methodology

Physic Parameter of F2 at this observatory case is the function of effective cosinus function sun zenith angle and observatory time of F2 . For F2

layer sun zenith angle factor indirectly influences frequency of F2 but effective cosinus zenith χ angle which is empirically transformation from the first differential equation like bellow.

cos χ cos χ effektif So it is needed three input data to determine harmonic spherical regression function they are : 1. Observatory data of F2 from observatory station for a certain time period. 2. Effective cosinus sun zenith angle for every observatory data of F2 3. Observatory time of F2

By using of F2 data local station the coefficient value of harmonic spherical function can be determined by making regression at of F2 data. Then by using this function so dots in surrounding that station can be approximated like at figure 1

Transformation function

3rd International Conferences and Workshops on Basic and Applied Sciences 2010 ISBN: 978-979-19096-1-7

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latitude longitude

Gambar 1: Lokasi yang bisa ditentukan harga of F2 secara spasial.

Approximation of of F2 value is used harmonic spherical function for area 2 dimension they are latitude and longitude are counted from local observatory station. Carefulness’ radius harmonic spherical function must be done experiment in the area. 3.1 Effective Zrnith Cosinus Angle One of parameter from regresion function above is effective cosinus solar zenith angle, As we known that solar activity at noon and night time is diferent besides that it is needed the equation to differ night and day interval. The limit of day and night is determined as follows, if T is universal time so day interval is determined as follows: TFAJAR < T < TSENJA (3) and night is TSENJA < T < TFAJAR ( 4 ) To determine TFAJAR dan TSENJA is needed duration or long period sun sycle for interval day and middday. Solar cycle time for day is used the equation as follows,

3.2 Midday Equation

arc24Tπ

=Δ )Lcosycos

Lsinysin26.0cos(2

2+− ...(5)

Beside midday duration, To determine the limit of midday is needed midday time parameter universally is defined by equation as follows: TTENGAH HARI =

)}Y2sin(2.1Y{sin13.01215W

21 +++°

. . .(6)

With 12 Ycos49.0y = )10D(172.0Y1 +=

D = 30.4 ( M1 – 1) + D1 D1 = Day [ 1, 31 ] M1 = month [ 1, 12 ]

W = latitude location , West Green Wich [ 0 , 360° ] L = Longitude [ -90° , 90° ]

So Dawn and twilight time can be determined as follows:

)24(mod2TTT TengahhariFajar

Δ−= dan )24(mod

2TTT TengahhariSenja

Δ+= ( 7 )

ΔT is midday duration. By getting the equation of difference day or night, then the calculation is to determine efective cosinus factor solar zenith angle for day and night. 3. 3 Factor Cos χEff Day

The angle of effective co sinus solar zenith factor for F2 layer is obtained empirically is the solution from the first orde differential equation by input is cosinus solar zenith it is:

Slamet Syamsudin, The Predict Of Ionosphere Fof2 Using Multivariat Analyse

P003

( ) ( ) ( )⎪⎭

⎪⎬⎫

⎪⎩

⎪⎨⎧

χ⎥⎦

⎤⎢⎣

⎡τ−Δ

⋅χ=χ siangeffD

senjaeffsiangeff cos,24Texpcosmax)(cos (8)

factor τD is relaxation factor in mid day which is obtained from equation

⎩⎨⎧ χτ

=τ1.0

)(cosmax tengahhari

Peff0

D

2

( 9)

0τ , 2P : is constantan, free to geographic location and time Function value siangeff )(cosχ at equation ( 8 ) above is counted as follows :

⎪⎭

⎪⎬⎫

⎪⎩

⎪⎨⎧

⎟⎟⎠

⎞⎜⎜⎝

⎛α⎥

⎦

⎤⎢⎣

⎡τ

−−β+α

β+

χ=χ cos

)TT(expsin

1)(cos

)(cosD

senja2

Tengahharisiangeff (10)

Factor α , β is determined as follows : T

)TT( Fajar

Δ

−π=α ( 11 )

T

D

Δτπ

=β ( 12 )

factor ( cosχ ) hariTengah is sun angle midday at equation ( 9 ) is counted as follows:

⎥⎦

⎤⎢⎣

⎡+⎟

⎠⎞

⎜⎝⎛

°π

=χ 2hariTengaheff y90L

2cos)(cos ( 13 )

3.4 Factor Cos χEff Night

The angle of co sinus effective zenith factor for night is used the equation as follow

)}TT

(exp{.)(cos)(cosN

SenjaSenjaeffhariMalameff τ

−−χ=χ ( 14)

and )}]Texp(1{[1

cos)(cos

D2

SiangSenjaeff τ

Δ−+β

β+

χ=χ ( 15 )

4 The Finishing Regresion Equation

The form of failure matrix is :

∑=

+−−=ωγβαεjN

1jjj0or,k,jr,k,jr,k,jr,k,j )]jTsin()R,Y(b)jTcos()R,Y(a[)R,Y(a2Ff(),,,( ( 16 )

By using failure matrix, the equation of regression degree failure is obtained as follows: ( ) ( )r,k,jr,k,jr,k,jr,k,jr,k,jr,k,jr,k,jr,k,j

T ,,,,,, ωγβαεωγβαε=ξ ( 17 )

By using the characteristic of chain rule, so the minimal failure is obtained by differ function ξ at r,k,jα ,

r,k,jβ , r,k,jγ and r,k,jω they are :

3rd International Conferences and Workshops on Basic and Applied Sciences 2010 ISBN: 978-979-19096-1-7

P003

r,k,j

k,j

k,j

j

jr,k,j

k,j

k,j

j

jr,k,j

B.

Bb

.b

A.

Aa

.a α∂

∂

∂

∂

∂ξ∂

+α∂

∂

∂

∂

∂ξ∂

=α∂ξ∂

r,k,j

k,j

k,j

j

jr,k,j

k,j

k,j

j

jr,k,j

B.

Bb

.b

A.

Aa

.a β∂

∂

∂

∂

∂ξ∂

+β∂

∂

∂

∂

∂ξ∂

=β∂ξ∂

r,k,j

k,J

k,j

j

jr,k,j

k,j

k,j

j

jr,k,j

B.

Bb

.b

A.

Aa

.a γ∂

∂∂

∂

∂ξ∂

+γ∂

∂

∂

∂

∂ξ∂

=γ∂ξ∂

r,k,j

k,j

k,j

j

jr,k,j

k,j

k,j

j

jr,k,j

B.

Bb

.b

A.

Aa

.a ω∂

∂

∂

∂

∂ξ∂

+ω∂

∂

∂

∂

∂ξ∂

=ω∂ξ∂

The equation of minimize failure becomes : TTT bYaXZ +=

by k,j

j

j Aa

.a

a∂

∂

∂ξ∂

= , K,j

j

j Bb

.b

b∂

∂

∂ξ∂

= and ⎟⎟⎠

⎞⎜⎜⎝

⎛

ω∂

∂

γ∂

∂

β∂

∂

α∂

∂=

r,k,j

k,j

r,k,j

k,j

r,k,j

k,j

r,k,j

k,j A,

A,

A,

AX ,

⎟⎟⎠

⎞⎜⎜⎝

⎛

ω∂

∂

γ∂

∂

β∂

∂

α∂

∂=

r,k,j

k,j

r,k,j

k,j

r,k,j

k,j

r,k,j

k,j B,

B,

B,

BY , ⎟

⎟⎠

⎞⎜⎜⎝

⎛

ω∂ξ∂

γ∂ξ∂

β∂ξ∂

α∂ξ∂

=r,k,jr,k,jr,k,jr,k,j

,,,Z

∑ ∑⎪⎭

⎪⎬⎫

⎪⎩

⎪⎨⎧

+−−=α∂ξ∂

=

data

t

N

1j

kjj0

r,k,j

j

R)jTcos()rYcos()])jTsin()R,Y(b)jTcos()R,Y(a[)R,Y(a2foF(

∑ ∑⎪⎭

⎪⎬⎫

⎪⎩

⎪⎨⎧

+−−=β∂ξ∂

=

data

t

N

1j

kjj0o

r,k,j

j

R)jTcos()rYsin()])jTsin()R,Y(b)jTcos()R,Y(a[)R,Y(a2Ff(

∑ ∑⎪⎭

⎪⎬⎫

⎪⎩

⎪⎨⎧

+−−=γ∂ξ∂

=

data

t

N

1j

kjj0o

r,k,j

j

R)jTsin()rYcos()])jTsin()R,Y(b)jTcos()R,Y(a[)R,Y(a2Ff(

∑ ∑⎪⎭

⎪⎬⎫

⎪⎩

⎪⎨⎧

+−−=ω∂ξ∂

=

data

t

N

1j

kjj0o

r,k,j

j

R)jTsin()rYsin()])jTsin()R,Y(b)jTcos()R,Y(a[)R,Y(a2Ff(

Failure minimal is obtained by taking zero value from differential equation above, is:

r,k,jα∂ξ∂ = 0 ,

r,k,jβ∂ξ∂ = 0, 0

r,k,j

=γ∂ξ∂ , 0

r,k,j

=ω∂ξ∂

Then is formed the matrix equation as follows: T ToX X b X f F2=

1

2

o 3

t

yy

f F2 y

y

⎛ ⎞⎜ ⎟⎜ ⎟⎜ ⎟=⎜ ⎟⎜ ⎟⎜ ⎟⎝ ⎠

M

,

11 21 n1

12 22 n2

13 23 n3

1t 2t nt

1 x x ... x1 x x ... x

X 1 x x ... x

1x x ... x

⎛ ⎞⎜ ⎟⎜ ⎟⎜ ⎟=⎜ ⎟⎜ ⎟⎜ ⎟⎝ ⎠

M

,

0,0,0

0,0,r

0,0,r

0,1,0

0.0,r

0,1.r

j,k,r

j,k,r

b

α⎛ ⎞⎜ ⎟α⎜ ⎟⎜ ⎟β⎜ ⎟⎜ ⎟α⎜ ⎟

= α⎜ ⎟⎜ ⎟β⎜ ⎟⎜ ⎟⎜ ⎟γ⎜ ⎟⎜ ⎟ω⎝ ⎠

M

,

11 12. 1t

21 22 2tT

31 32 3t

n1 n2 nt

1 1 1x x xx x x

Xx x x

x x x

⎛ ⎞⎜ ⎟⎜ ⎟⎜ ⎟

= ⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟⎝ ⎠

L

L

L

L

M

L