fof2 correlation studies with solar and geomagnetic indices for two equatorial stations

Journal of Atmospheric and Solar-Terrestrial Physics 80 (2012) 312–322

Contents lists available at SciVerse ScienceDirect

Journal of Atmospheric and Solar-Terrestrial Physics

1364-68

doi:10.1

n Corr

Oyo sta

E-m

journal homepage: www.elsevier.com/locate/jastp

foF2 correlation studies with solar and geomagnetic indices fortwo equatorial stations

E.O. Joshua a, N.M. Nzekwe a,b,n

a Department of Physics, University of Ibadan, Ibadan Oyo state, Nigeriab Physical Science Department, Yaba college of Technology Yaba, Lagos state, Nigeria

a r t i c l e i n f o

Article history:

Received 6 December 2011

Received in revised form

15 February 2012

Accepted 22 February 2012Available online 2 March 2012

Keywords:

Ionospheric prediction

Nigerian equatorial ionosphere

Solar indices and geomagnetic indices

26/$ - see front matter & 2012 Elsevier Ltd. A

016/j.jastp.2012.02.015

esponding author at: Department of Physics,

te, Nigeria. Tel.: þ234 8038095307.

ail address: [email protected] (N.M

a b s t r a c t

The analysis of the contributions of solar and geomagnetic indices on the critical frequency of the

ionospheric F2 layer (foF2)-, for different seasons and two Nigerian equatorial stations- Ibadan (Lat. 7.41N,

Long. 3.91N) and Ilorin (Lat. 8.51N, Long. 4.551E)- are presented. The data set was randomly sampled across

three solar cycles of periods of low, moderate and high solar activities. Solar indices used in this work are

Coviten solar flux (F10.7 cm), daily solar radio flux (dF10.7), International Sunspot Number (ISSN), Smoothen

Sunspot Number (SmSSN), and Sun Spot Number (SSN). The geomagnetic indices used are planetary indices

Am, Aa, Ap, C9, Cp, and Kp. foF2 showed a non-linear trend with an average coefficient (R) of 0.70 across the

various seasons. Regression lines for polynomials of degree n¼1 to n¼6 was fitted, for each data set. Am, Ap,

Aa, SSN, ISSN, F10.7 cm, and dF10.7 with R values of 0.71,0.74,0.61,0.59,0.72,0.80, and 0.86, for the various

geomagnetic and solar indices, had the highest contributions. We therefore advocate for SSN, ISSN, F10.7 cm,

dF10.7 and Am, Ap or Aa in modeling foF2 for the African equatorial ionosphere. The results of this work are

in line with the results of other works carried out at different equatorial stations.

& 2012 Elsevier Ltd. All rights reserved.

1. Introduction

The state of the ionosphere at any given time is generally knownto depend on solar and geomagnetic activities as a result of theenergy input from the sun and the self-existing dynamo in the earthcore. Since the early days of examination of ionospheric morphology,it has been recognized that the variations of foF2 are complex andcannot be derived from theoretical consideration which only takesaccount of production by photo-ionization. Many groups haveinvestigated the long-term changes of foF2 as they were seeking toestablish empirical relationships in terms of indices of solar andgeomagnetic activities. However, not all workers have agreed on thebest index to use (Bradley, 1994). This is perhaps not surprisingbecause there are several factors which influence choice. Theseinclude correlation, linearity, non-linearity, index predictability, andavailability (Kouris and Agathonikos, 1992).

The monthly median values of the ionospheric characteristics arefrequently presented with linear dependence on SSN for every hourin the day and every month in the year, e.g. the InternationalReference Ionosphere (IRI) (Bilitza, 2001), ionospheric regionalmodel (Zolesi et al., 1993; De Franceschi and Desantis, 1994) aswell as single-station model (Pancheva and Mukhtarov, 1996;

ll rights reserved.

University of Ibadan, Ibadan

. Nzekwe).

Holt et al., 2002). For low and medium sunspot numbers, therelationship is reasonably linear; nevertheless, at large sunspotnumbers, foF2 seems to show saturation effect (Huang, 1963; Kane,1992). To take into account this behavior, a second-degree relation-ship between foF2 and solar activity indices is frequently resortedto (Sizun, 1992; Xenos et al., 1996; Pancheva and Mukhtarov,1998).This hysteresis effect depends on latitude (Sethi et al., 2002)and historical solar activity (Rao and Rao, 1969). Sethi et al. (2002)claimed that for low-latitudes, a second-degree relationship mademuch improvement, while Kouris and Nissopoulos (1994) havedemonstrated that a second-degree equation is needed for Europeanstations especially during evening and night hours in winter- andsummer-times. Moreover, the variations of foF2 are complex andcannot be described leaving one to consider only sunspot number.The variations are as a result of the influence of the solar andgeomagnetic activities as well as other sources (Forbes et al., 2000;Zhang et al., 2004). For the same SSN, foF2 may show different valuesduring the ascending and descending of the cycle (Rao and Rao,1969) and is attributable to possible geomagnetic storm effect (Kane,1992), a view also shared by Apostolov et al. (1994). Pancheva andMukhtarov (1996), who developed a single-station spectral modelover Sofia with SSN and geomagnetic index K, demonstrated that inmany cases the increase in the monthly standard deviation coincidedwith the increase in the geomagnetic activity index Aa.

Of recent, Liu et al., (2004), used half hourly values of foF2from 1957 to 1991 for Wuhan ionospheric observatory to establish

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E.O. Joshua, N.M. Nzekwe / Journal of Atmospheric and Solar-Terrestrial Physics 80 (2012) 312–322 313

a non-linear dependence on solar activity index (F10.7) beforeformulating the model that compares favorably with IRI. Similarly,Xu et al., (2008), established a significant non-linear relationshipfor the geomagnetic index Ap and solar activity index R (SunspotNumber) on the hourly values of foF2 by obtaining a general multiplenon-linear function at Chongqing station (29.51N, 106.41E) in China,during the interval of 1977–1997. Kane (1992) argued that long termprediction models need to take into account not just SSN but somesolar index and geomagnetic index as two key parameters whichhave not received much attention. It is, therefore, one objective ofthis work to demonstrate which solar and geomagnetic index aremore convenient for ionospheric prediction of foF2 over two Nigerianequatorial stations.

R² = 0.8944

0123456789

foF2

(M

Hz)

UT

Mar'64

0

50

100

Sola

r Ind

ices

R² = 0.8201

02468

101214

foF2

(MH

z)

UT

JUN'68

0

10

20

30

Geo

. Ind

ices

R² = 0.7831

02468

1012

foF2

(MH

z)

UT

SEP 71

0

100

200

Sola

r. In

dice

s

R² = 0.8115

0

2

4

6

8

10

1 3 5 7 9 11 13 15 17 19 21 23

1 3 5 7 9 11131517192123

1 3 5 7 9 11 13 15 17 19 21 23

1 3 5 7 9 11131517192123

foF2

(MH

z)

UT

DEC'2010

0

2

4

Geo

. Ind

ices

Fig. 1. Polynomial fittings with trends for foF2, solar and geomagnetic indices for

respectively, for the various seasons. 2010 is for Ilorin station. The symbols plus line are

fittings.

2. Data and method

foF2 data from Ibadan (7.41N, 3.91E) and Ilorin (8.51N, 4.551E)together with solar (S) and geomagnetic (G) indices data werefitted to polynomial functions of the form

f oF2¼ aoþa1tþa2t2þa3t3þ . . . ð1Þ

G¼ boþb1tþb2t2þb3t3þ . . . ð2Þ

S¼ coþc1tþc2t2þc3t3þ . . . ð3Þ

R² = 0.5695

R² = 0.4483R² = 2E-15

R² = 0.6086R² = 0.5027

DN

MAR'64 F10.7cm

ISSN

SmSSN

SSN

dF10.7

Poly. (F10.7cm)

Poly. (ISSN)

Linear (SmSSN)

R² = 0.6675

R² = 0.7306

R² = 0.6358

UT

JUN'68 Am

Aa

AP

Poly. (Am)

Poly. (Aa)

Poly. (AP)

R² = 0.7367R² = 0.5377

R² = 1E-15R² = 0.5131

R² = 0.7575

DN

SEP 71

F10.7cm

ISSN

SmSSN

SSN

dF10.7

Poly. (F10.7cm)

Poly. (ISSN)

R² = #N/A

R² = 0.6373

1 8 15 22 29

1 5 9 13 17 21

1 7 13 19 25

1 5 9 13 17 21UT

DEC'2010

Cp

Kp

Linear (Cp)

Poly. (Kp)

1964, 1968, and 1971/2010 periods of low, high, and moderate solar activities

the observed data and the dotted and the smooth lines are the various polynomial

0.0

0.2

0.4

0.6

0.8

1.0MAR'64

R

N

0.0

0.2

0.4

0.6

0.8

1.0

MAR'64

R

N

0.0

0.2

0.4

0.6

0.8

1.0

R

N

MAR'68

0.0

0.2

0.4

0.6

0.8

1.0

R

MAR'68

N

0.0

0.2

0.4

0.6

0.8

1.0

FoF2

Am

Aa

Ap

C9

Cp

Kp

MAR'71

R

N

1 2 3 4 5 6 1 2 3 4 5 6

1 2 3 4 5 6 1 2 3 4 5 6

1 2 3 4 5 6 1 2 3 4 5 6

0.0

0.2

0.4

0.6

0.8

1.0

FoF2 F10.7cm ISSN SmSSN SSN dF10.7

MAR'71

R

N

Fig. 2. Non-linear correlation of geomagnetic and solar indices with foF2 for different order polynomial over the years 1964, 1968 and 1971, during low, high and

moderate solar activity periods respectively. MAR. (March) represent March equinox months.

E.O. Joshua, N.M. Nzekwe / Journal of Atmospheric and Solar-Terrestrial Physics 80 (2012) 312–322314

foF2 data for 1964, 1968, and 1971 for periods of low, high andmoderate solar activities were obtained from Ibadan ionosphericcenter, while foF2 data for 2010, solar indices and geomagnetic datawere obtained from the Space Physics Interactive Data Resources(SPIDR) hosted by the World Data Center (WDC) on http://spidr.ngdc.noaa.gov. The significance of applying different order polynomialswas considered and the times were confirmed when the higher orderterms are important. Coefficient of determination (R2) was obtained

for each polynomial fitting. This was used to calculate the non-linearcorrelation coefficient (R).

Seasonal grouping was done in such a way that Springequinox; the months of March and April are represented byMAR., summer solstice comprising of May, June, July and Augustare represented by JUN., while Autumn equinox; September andOctober is represented by SEP., and Winter solstice: November,December, January and February are represented by DEC.

http://spidr.ngdc.noaa.gov

http://spidr.ngdc.noaa.gov

0.0

0.2

0.4

0.6

0.8

1.0 JUN'64R

N

0.0

0.2

0.4

0.6

0.8

1.0 JUN'64

R

N

0.0

0.2

0.4

0.6

0.8

1.0 JUN'68

R

N

0.0

0.2

0.4

0.6

0.8

1.0 JUN'68

R

N

0.0

0.2

0.4

0.6

0.8

1.0 JUN'71

N

R

0.0

0.2

0.4

0.6

0.8

1.0JUN'71

R

N

0.0

0.2

0.4

0.6

0.8

1.0

FoF2 Am Aa Ap C9 Cp Kp

N

JUN'10

R

1 2 3 4 5 6 1 2 3 4 5 6

1 2 3 4 5 6 1 2 3 4 5 6

1 2 3 4 5 6 1 2 3 4 5 6

1 2 3 4 5 6 1 2 3 4 5 6

0.0

0.2

0.4

0.6

0.8

1.0


R

N

JUN'10

Fig. 3. Non-linear correlations of geomagnetic and solar indices with foF2 for the different order polynomials during the years 1964, low solar activity period, 1968, high

solar activity period, 1971, and 2010 moderate solar activity period. 2010 is specific to Ilorin station. JUN. represents June solstices months.


0.0

0.2

0.4

0.6

0.8

1.0 SEP'64

R

N

0.0

0.2

0.4

0.6

0.8

1.0SEP'64

R

N

0.0

0.2

0.4

0.6

0.8

1.0 SEP'68

R

N

0.0

0.2

0.4

0.6

0.8

1.0 SEP'68

R

N

0.0

0.2

0.4

0.6

0.8

1.0 SEP'71

R

N

0.0

0.2

0.4

0.6

0.8

1.0 SEP'71

R

N

0.0

0.2

0.4

0.6

0.8

1.0 SEP'10

FoF2 Am Aa Ap C9 Cp Kp

R

N

1 2 3 4 5 6 1 2 3 4 5

1 2 3 4 5 6 1 2 3 4 5 6

1 2 3 4 5 6 1 2 3 4 5 6

1 2 3 4 5 6 1 2 3 4 5 6

0.0

0.2

0.4

0.6

0.8

1.0


SEP'10

R

N

Fig. 4. Same as Fig. 3, except for SEP. representing September equinox months.



For polynomial order one, the linear correlation coefficient wasobtained from the Spearman relationship

RS,f oF2 ¼nPðS,f oF2Þ�

PS,P

f oF2ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi½nP

S22ðP

SÞ2�½nPðf oF2Þ2�

Pðf oF2Þ2�

q ð4Þ

0.0

0.2

0.4

0.6

0.8

1.0DEC'64

R

N

0.0

0.2

0.4

0.6

0.8

1.0

N

R

DEC'68

0.0

0.2

0.4

0.6

0.8

1.0DEC'71

R

N

0.0

0.2

0.4

0.6

0.8

1.0 DEC'10

R

N

FoF2AmAaApC9CpKp

1 2 3 4 5 6

1 2 3 4 5 6

1 2 3 4 5 6

1 2 3 4 5 6

Fig. 5. Same as Fig. 3, except for December r

RG,f oF2 ¼nPðG,f oF2Þ�

PG,P

f oF2ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi½nP

G22 ðP

GÞ2�½nPðf oF2Þ2�

Pðf oF2Þ2�

q ð5Þ

The symbols S and G in the equations represent the indices ofsolar and geomagnetism respectively. The non-linear correlation

0.0

0.2

0.4

0.6

0.8

1.0

DEC'64

R

N

0.0

0.2

0.4

0.6

0.8

1.0 DEC'68R

N

0.0

0.2

0.4

0.6

0.8

1.0 DEC'71

R

N

1 2 3 4 5 6

1 2 3 4 5 6

1 2 3 4 5 6

1 2 3 4 5 6

0.0

0.2

0.4

0.6

0.8

1.0DEC'10

R

N

FoF2F10.7cmISSNSmSSNSSNdF10.7

epresenting December solstices months.


coefficient was obtained from

R2f oF2 ¼

Pðf oF2est2f oF2Þ2Pðf oF22f oF2Þ2

ð6Þ

R2S ¼

PðSest2SÞ2PðS2SÞ2

ð7Þ

R2G ¼

PðGest2GÞ2PðG2GÞ2

ð8Þ

Eqs. (6)–(8), give the ratio of the explained variation to the totalvariation for each parameter from which we obtained the non-linear correlation coefficient R (Spiegel, 1987). This measures howwell a non-linear regression curve fits the data.

3. Result and discussion

Fig. 1 shows the polynomial fitting with trend for foF2 solar andgeomagnetic indices for 1964, 1968, and 1971/2010 periods oflow, high, and moderate solar activities respectively for the variousseasons. The displayed trends showed a signature of non-lineardependence of the ionospheric data foF2 and; obtained solar and

0

0.2

0.4

0.6

0.8

1

FoF2 Am Aa

AP C9

Cp

Kp

R

MAR'64

R

00.20.40.60.8

1

FoF2 Am Aa

AP C9

Cp

Kp

MAR'68

R

00.20.40.60.8

1

FoF2 Am Aa

AP C9

Cp

Kp

R

MAR'71

0000

Fig. 6. Average geomagnetic and solar contributions to foF2 for March equinox months

measured in MHz., Am, Aa, Ap, C9, Cp and Kp are the geomagnetic indices measured

Wm�2Hz�1 and ISSN, SmSSN and SSN are measured in counts.

geomagnetic indices with respect to time of the day, season of theyear, and solar epochs (low, high, and moderate solar activities).

The non-linear correlation of the geomagnetic and solar indiceswith foF2 for different order polynomials over the different yearsand seasons under consideration is depicted fromFigs. 2–5. For the months of March equinoxes in Fig. 2, the solarindices SSN and F10.7 cm dominates and corresponds more withchanges in foF2, while Am and Kp-geomagnetic indices dominateduring the selected years of different solar activities (1964, 1968and 1971). Fig. 3 is for June solstices. Geomagnetic indices Ap andKp describe the signatures of foF2 for 1964 a period of low solaractivity. Aa has greater control during the year 1968 (high solaractivity year) and during 1971/2010 (period of moderate solaractivity epochs). In the same way, the solar indices parametersdF10.7, (SSN and ISSN), (ISSN and dF10.7), and (F10.7 cm anddF10.7) for months of June 1964, 1968, 1971 and 2010 respec-tively, on the defined solar periods, have greater control over foF2.June 2010, at Ilorin station, showed a likelihood of the smoothedsun spot number (SmSSN) having strong control over foF2. Thesesuggest that the geomagnetic indices Aa or Ap together with thesolar indices dF10.7 or ISSN may produce accurate result if they areused in modeling foF2 analytically or by neural network. This is inline with the following work (Wintoft and Cander, 2000; Xenos,2002; Liu et al 2004; Yue et al., 2006; Oyeyemi et al., 2007).

00.20.40.60.8

1

FoF2

F10.

7cm

ISS

N

Sm

SS

N

SS

N

dF10

.7

MAR'64

00.20.40.60.8

1MAR'64

0.2.4.6.81

MAR'71

during low (1964), moderate (1971) and high (1968) solar activity periods. foF2 is

in nano Tesla (nT), while F10.7 cm. and dF10.7 cm solar indices are measured in


During the months of September equinoxes in Fig. 4, thegeomagnetic indices that produce the signatures of the observedfoF2 are Aa and Ap for 1964. Am, Ap and Aa for 1968, Am and Kpfor 1971, and Aa, Ap and Am for 2010, while for the solar indicesdF10.7 at 1964, SSN during 1968, ISSN and dF10.7 during 1971and ISSN, SSN and F10.7 cm during 2010 produce marked changeswith the observed foF2. These also suggest that the geomagneticindices Aa, Am, Ap together with the solar indices dF10.7, SSN orISSN may be the most suitable for modeling foF2 during Septem-ber equinoxes.

Similarly, December solstices have Ap and Kp for 1964,Am and Ap for 1968, Am, Ap and Aa for 1971, Am and Kpfor 2010, showing marked changes with foF2 at various solar

0

0.5

1

FoF2 Am Aa

AP C9

Cp

Kp

R

JUN'64

0

0.5

1

FoF2 Am Aa

AP C9

Cp

Kp

R

JUN'68

0

0.5

1

FoF2 Am Aa

AP C9

Cp

Kp

R

JUN'71

0

0.5

1

Fo… Am Aa

AP C9

Cp

Kp

R

JUN'10

Fig. 7. Same as Fig. 6 except for months of Jun

activities, while for the solar indices ISSN at 1964, F10.7 cm andISSN at 1968, SSN at 1971, ISSN and SSN at 2010 had muchcontrol over foF2 during the December solstices season. Thisjustifies the use of the geomagnetic index Ap and solar indexSSN by most ionospheric researchers (Xu et al., 2008; Liu et al.,2004; Holt et al., 2002 and Apostolov et al., 1994) and a host ofothers.

Figs. 6–9 show the average geomagnetic and solar contributionto observed foF2 for the various seasons (March equinoxes Fig. 6,June solstices Fig. 7, September equinoxes Fig. 8 and Decembersolstices Fig. 9.) at the respective solar epochs. All the results arein line and agreement with the results of Fig. 2 to Fig. 5. Marchhas Am and SSN, June has Aa/Ap and dF10.7, ISSN and F10.7 cm

0

0.5

1

FoF2

F10.

7cm

ISS

N

Sm

SS

N

SS

N

dF10

.7

R

JUN'64

0

0.5

1

FoF2

F10.

7…

ISS

N

Sm

SS

N

SS

N

dF10

.7

R

JUN'68

00.20.40.60.8

1

FoF2

F10.

…

ISS

N

Sm

SS

N

SS

N

dF10

.7

R

JUN'71

0

0.5

1

FoF2

F10.

7…

ISS

N

Sm

SS

N

SS

N

dF10

.7

R

JUN'10

e solstices, June 2010 is for Ilorin station.

Fig. 8. Same as Fig. 6, but for September, representing the months of September equinoxes. September 2010 a period of moderate solar activity is for Ilorin station.


September has Aa, Am, Ap and F10.7 cm, SSN, ISSN and dF10.7and December has Ap, Am, Aa and Kp and ISSN, F10.7 cm and SSNfor the respective geomagnetic and solar indices . These further goto prove that geomagnetism and solar activities have strongcontrol on the ionospheric parameter foF2.

4. Conclusion

The objective of this work was to arrive at the solar andgeomagnetic indices that will be the most suitable for modelingfoF2, whether analytically or empirically by neural network (sinceit chooses activation function that best approximates linear, near

linear and non-linear relation). We therefore summarize ourfindings for the two Nigerian equatorial stations as follows:

1.
For March equinox months, geomagnetic indices Am and solarindices SSN or F10.7 cm may be most suitable for modeling foF2.
2.
Aa or Ap geomagnetic index and dF10.7 or ISSN solar indexmay be best for foF2 prediction during June solstices.
3.
Months of September equinoxes showed Aa, Am, or Apgeomagnetic indices and dF10.7, ISSN or SSN solar indices asbest indicators of foF2.
4.
December solstices months can allow the geomagnetic indicesAm or Ap and solar indices ISSN, SSN or F10.7 cm for suitablemodeling of foF2.

0

0.5

1

FoF2 Am Aa

AP C9

Cp

Kp

R

DEC'64

0

0.5

1

R

DEC'64

00.20.40.60.8

1

FoF2 Am Aa

AP C9

Cp

Kp

R

DEC'68

00.20.40.60.8

1

R

DEC'68

0

0.5

1

FoF2 Am Aa

AP C9

Cp

Kp

R

DEC'71

0

0.5

1

DEC'71

0

0.5

1

FoF2 Am Aa

AP C9

Cp

Kp

R

DEC'10

0

0.5

1

R

DEC'10

Fig. 9. Same as Fig. 6, except for the months of December solstices and December 2010, for Ilorin station.


5.
For the phenomenon of hysteresis during high SSN, F10.7 cmor dF10.7 may be best suitable for modeling foF2.
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dx.doi.org/10.1029/2003Rs003005

dx.doi.org/10.1029/2005JA011577

dx.doi.org/10.1029/2005JA011577

fof2 correlation studies with solar and geomagnetic indices for two equatorial stations

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