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

P003

The Predict Of Ionosphere Fof2 Using Multivariat Analyse

Slamet Syamsudin

Space Science Center National Institut e of Aeronautics and Space ( LAPAN )

Jl. Dr. Junjunan 133, Bandung 40173

Abstract

Ionosphere of F2 parameter is not only predicted by sunspot numbers ( R ) but also the other parameter they are season ( Y ) which is defined by cosinus effective sun zenith angle and time ( T ), so that empirical of F2 can defined as the fuction from three parametres above on the shape of harmonic spherical model function. By using ionosphere data from space observatory station Sumedang or another location which we name as local parameter, so there will be obtained coefficient harmonic spherical function which is solved by regression multi variable method, then for predicating regional of F2 is made by entered latitude parameter and longitudinal and local latitude along with sunspot numbers and experimental result with pamengpeuk data is obtained 13% deviation.

1 Introduction

No like as E and F1 layer, that these layer frequency can be modelled as cosinus function sun zenith angle ( cos ) and equivalent with sun activity intension. The physic from F2 layer is generally looked as photochemical interaction and complex ions transportation process, which is caused diurnal, season, and geography of F2 variation which can be simply accommodated as cos function. Although of F2 cannot be modelled as cos function , But empirically observatory data pattern of F2 can be approached by dynamic system which is driven by cos factor which is defined on the form of the first linier deferential equation.

=+ coscos)(cosdtd

effeffD

( 1 ) Analyse the form of diurnal observatory profile

of F2 show an indolence function of su intension of time, It can be used as the first aproaching at empiric model of F2 then a simpy model is developed based on analyse the lag single function of linier system which is driven by proportional temporary cos function. constanta lag along day time is chosen as simply monotonic funtion from noon senith angle , then indolence (lag) night time is constant, free form season or geographyc location. The point from model of F2 forming is that season and geographic variation at prediction value of F2 has a close connection by zenith angle variation at noon, by using math procedure by maping

of F2 and suits by math functions which was available and obtained that of F2 as the function of noon zenith angle , sunspot number, dawn time, twilight time is approaching function at

of F2 as harmonic spherical function.

2 Harmonic Spherical Function.

Approaching function which is used to determine of F2 value at a certain points is harmonic spherical function. Generally harmonic spherical function for a spot or local ionosonde is formulizes as follows:

Slamet Syamsudin, The Predict Of Ionosphere Fof2 Using Multivariat Analyse

P003

)T,R,Y(f2foF = by Y ( 0,2 ) 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

=

++=rN

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

=

++=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 angle which is empirically transformation from the first differential equation like bellow.

cos cos 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

P003

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

arc24T

= )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

= dan )24(mod

2TTT TengahhariSenja

+= ( 7 )

T 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 Eff 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

( ) ( ) ( )

= siangeffD

senjaeffsiangeff cos,24Texpcosmax)(cos (8)

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

=1.0

)(cosmax tengahhari

Peff0

D

2

( 9)

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

+

+

= cos

)TT(expsin

1)(cos

)(cosD

senja2

Tengahharisiangeff (10)

Factor , is determined as follows : T

)TT( Fajar

= ( 11 )

T

D

= ( 12 )

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

+

= 2hariTengaheff y90L

2cos)(cos ( 13 )

3.4 Factor Cos Eff Night

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

)}TT

(exp{.)(cos)(cosN

SenjaSenjaeffhariMalameff

= ( 14)

and )}]Texp(1{[1

cos)(cos

D2

SiangSenjaeff

+

+

= ( 15 )

4 The Finishing Regresion Equation

The form of failure matrix is :

=

+=jN

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,jT ,,,,,, = ( 17 )

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

r,k,j , r,k,j and r,k,j 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

+

=

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

+

=

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

+

=

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

+

=

The equation of minimize failure becomes : TTT bYaXZ +=

by k,j

j

j Aa

.a

a

= , K,j

j

j Bb

.b

b

= and

=

r,k,j

k,j

r,k,j

k,j

r,k,j

k,j

r,k,j

k,j A,A

,A

,A

X ,

=

r,k,j

k,j

r,k,j

k,j

r,k,j

k,j

r,k,j

k,j B,B

,B

,B

Y ,

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

,,,Z

+=

=

data

t

N

1j

kjj0

r,k,j

j

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

+=

=

data

t

N

1j

kjj0o

r,k,j

j

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

+=

=

data

t

N

1j

kjj0o

r,k,j

j

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

+=

=

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,j = 0 ,

r,k,j = 0, 0

r,k,j

= , 0

r,k,j

=

Then is formed the matrix equation as follows: T T oX 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

=

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

Slamet Syamsudin, The Predict Of Ionosphere Fof2 Using Multivariat Analyse

P003

by j = 1 . . . Nj ; k = 1 . . . Nk ; r = 1 . . . Nr as variable value illustration xij matrix X on the form of physics parameter for index value Nj = 6 , Nk = 1 and Nr = 1 is as follow:

column

Variable value

The connection between variable and solution

vector b

0 1..4 5..8

9 10..13 14..17 18..29 30..77

78..125 126..137 138..185 186..233

1

cos ( r Yt ) sin ( r Yt )

Rt Rt cos( r Yt ) Rt sin( r Yt ) Rkt cos( j Tt )

Rkt cos( r Yt ) cos( j Tt ) Rkt sin( r Yt ) cos( j Tt )

Rkt sin( j Tt ) Rkt cos( rYt ) sin( j Tt ) Rkt sin( r Yt ) sin( j Tt )

ooo oor oor o1o o1r o1r jko jkr jkR jko jkr jkr

r

T0,0,r 0,0,1 0,0,2 0,0,3 0,0,N( , , , , ) = L , r

T0,0,r 0,0,1 0,0,2 0,0,3 0,0,N( , , , , ) = L dan

r

T0,0,r 0,0,1 0,0,2 0,0,3 0,0,N( , , , , ) = L

5 Result

Data which is used to make an experiment of this model is of F2 data Space observatory stations Sumedang, Kototabang and Biak by sunspot number Watukosek in 2000 and 2001 the result is on figure 1 and 2 by failure level 13% After we try with ionosphere data in Indonesia its result is not significant because the lack of data is just 3 years and there still incomplete data (no order), but the pattern of data tendencies which is resulted by harmonic spherical model is same with observatory data for Pamengpeuk and Sumedang so to increase this program besides to increase accurate data but also need to make this model validity. These function can be used as an example to make frequency of F2 map and as an example to make (Maximum Usable Frequency ) and FOT (Frequency Optimum Traffic ).

6 The Learning

The connection between of F2 and sunspot number which is usually made is on linear function but on this model is used as the expansion from harmonic spherical coefisient series which is defined on equation ( 2 ). Efective sun zenith angle at F2 layer is the contribution factor of sunspot number at formed of of F2 , at equation ( 2 ) is expansed as harmonic spherical rows from sunspot number coefisient. Generally the influence of sunspot number at this model is not on linear function form but on polynom form. To get the optimal result of predict value of F2 by using equation ( 2 ) so the limit at this equation, included to polynom degree the influence sunspot number at formed of of F2 is simulated by trying some of complete number. The choosing of limit at these equation, is made by taking minimal failure value which is defined on equation 17 ) and is

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

P003

obtained the limit at each equation are Nj = 6 , Nk = 1 , Nr = 4 and its number coeficient are 234. By making the simulation of equation ( 2 ) need to be known that sunspot number is one of physis essential parameter on the form of F2 layer, the characteristic of sunspot number is periodic so that the harmonic spherical coeficient predicts is not refracted statistically so it is nedded physis parameter data form of harmonic spherical equation in many observatory data

of F2 from local station along half of sun cycle so coefficient predict value of equation ( 2 ) above describe the real of F2 population. Harmonic spherical function which is formed from data of local observatory station which is looked as of F2 generator surrounding that station which is a function of longitude and latitude on concentric square at that station. These concentric squares can be used flexibility as control point of HF communication and also can be used as the base of making foF2 contour. This method is efficient because from one observatory station ionosphere ( of F2 local ) determine spatially for of F2 regional, is tried by several east European countries, and Pakistan by using a half solar cylce data.

7 Conclusions

Empirically it can be concluded that of F2 is not only depend on sunspot number, but depend on another parameter they are the location which is determined solar zenith angle and day, dawn, noon, and twilight period time. To get optimal result value predict of F2 is nedded of F2 data in order minimum time along half of solar cycle. Harmonic spherical function can be used as

of F2 generator, as latitude and longitude functions or approaching value of F2 spatially.

figure 2. Frequency of F2 ( Predicts and Data ) 5 February 2000, Kototabang

figure 3. Frequency of F2 ( Predicts, Data ) 15 March 2000, Biak

References

[1] Stanislaswska, I. , Klos, Z. , Stasiewiccz,

K. , 1991, Local Model of the ionosphere based upon Data from Miedzsyn Station, Working Book, III Workshop PRIME, Instintuto Nazionale di Geofisica. 161-164.

[2] Ostrow, S. M. , 1992, Ionospheric Predictions, National Bureau of Standars, U.S Government Printing Office, Washington D.C , pp 1-6.

[3] Rishbeth, H. and Garriot , 1989, Introduction to ionospheric Physics, Academic Press, New York, pp 173-186.