frequency over Wakkanai

RESEARCH ARTICLE

J.Natn.Sci.Foundation Sri Lanka 2018 46 (4): 527 - 538 DOI: http://dx.doi.org/10.4038/jnsfsr.v46i4.8628

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FULWLFDO

frequency over Wakkanai

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1 Institute of Space and Planetary Astrophysics (ISPA), University of Karachi, Karachi, Pakistan.

2 Department of Electronics and Power Engineering, Pakistan Navy Engineering College, NUST Karachi, Pakistan.

Revised: 20 March 2018; Accepted: 25 May 2018

*&RUUHVSRQGLQJDXWKRUPX]DPPLOPXVKWDTXH#RXWORRNFRP https://orcid.org/0000-0002-3545-1886)

This article is published under the Creative Commons CC-BY-ND License (http://creativecommons.org/licenses/by-nd/4.0/).

$EVWUDFW For many decades ionospheric researchers investigated the variations in the ionosphere due to solar activity. The suggested relevant models are based on single- VWDWLRQ GDWD FRQVLGHULQJ UHJLRQDO DQG JOREDO JHRJUDSKLF

conditions. The present study investigated the impact of the solar cycles 21^st (1976 to 1986) and 23^rd (1996 to 2008) on the ionospheric F₂ layer’s critical frequency (f₀F₂) at mid-latitude RYHUWKH:DNNDQDLUHJLRQž1ž(-DSDQ7KH

statistical analyses showed that monthly median f₀F₂ has a VLJQL¿FDQW QRQOLQHDU DVVRFLDWLRQ ZLWK KLJK VXQVSRW QXPEHUV

661 RYHU :DNNDQDL ZKLFK UHSUHVHQWV D VDWXUDWLRQ HIIHFW

depending on the time of the day in different months and on the magnitude of the solar cycle. Polynomial empirical models of f₀F₂ based on parameters such as SSN and geomagnetic index A_p were examined. Considering the rate of change in solar activity factor much improved the accuracy of our empirical model and also reduces the hysteresis effect. The most appropriate empirical model for single-station diurnal models of f₀F₂ was developed using Fourier series. Diurnal models LQFRUSRUDWH -DSDQHVH VWDQGDUG WLPH PRQWKV DQG VXQVSRW

numbers. The computed f₀F₂ models were compared with the IRI-2012 model’s predicted f₀F₂ YDOXHV ZKLFK GHPRQVWUDWHG

the better accuracy of the Fourier model compared to the global IRI model. The models obtained in this study are useful for UHVHDUFKHUVDQGRUJDQLVDWLRQVZRUNLQJLQWKH¿HOGRIVXQVSRW

performance relating to the dynamics of the ionosphere.

.H\ZRUGV f0F₂ geomagnetic A_p LQGH[ LRQRVSKHUH PLG

ODWLWXGHVXQVSRW

INTRODUCTION

The atmosphere of the earth consists of the layers of gases surrounding the earth. Each layer differs in the FRPSRVLWLRQRIJDVVSHFLHVDOWLWXGHVWHPSHUDWXUHVDQG

pressures. The Earth’s atmosphere extends from 50 km WRNPZKHUHWKHVRODUUDGLDWLRQVHVSHFLDOO\(89

DQG;UD\VKLJKO\LQÀXHQFHLWDQGFUHDWHWKHUHJLRQRI

charged particles (positive and electrons). The region where the concentration of charged particles is high HQRXJK WR UHÀHFW WKH WUDMHFWRU\ RI UDGLR ZDYHV VHQW

from the ground is called the ionospheric layer. The ionosphere lies between 140 km to 600 km in altitude and under certain solar-terrestrial conditions; ionosphere LVVXEGLYLGHGLQWR'()₁)₂ layers. F₂ layer is the most important region of the ionosphere from the point of view RI UDGLR FRPPXQLFDWLRQ DQG QDYLJDWLRQ +RZHYHU WKH

ionosphere is not a stable ionised medium. The variation of electron density in the F₂ layer possibly enhances or reduces the transmission of a signal propagating at a high frequency between the transmitter and the receiver or it may suddenly interrupt the communication. This disturbance highly depends on the level of solar activity 6L]XQ-L[LDQJ

528 Muzammil Mushtaq et al.

December 2018 Journal of the National Science Foundation of Sri Lanka 46(4)

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Much effort has been made to study the variations in Earth’s ionosphere with respect to different locations on (DUWKDQGDWGLIIHUHQWWLPHV7KXVE\XVLQJLRQRVSKHULF

FKDUDFWHULVWLF GDWD D ODUJH QXPEHU RI VWDWLRQV KDYH

developed regional and global models of the ionosphere.

These empirical models are established by conducting statistical studies of ionospheric data over a prolonged SHULRG%LOLW]DKDVSUHVHQWHGDUHYLHZRIWKHPDQ\

DYDLODEOH HPSLULFDO PRGHOV $PRQJ WKRVH PRGHOV WKH

international reference ionosphere (IRI) model is broadly XVHG)URPGLIIHUHQWLRQRVSKHULFSDUDPHWHUVWKHFULWLFDO

frequency of the F₂ layer (f₀F₂) is one of the most vital parameters that represents the concentration of electron density in the F₂OD\HU&ULWLFDOIUHTXHQF\LVGH¿QHGDV

WKHPD[LPXPIUHTXHQF\ZKLFKLVWUDQVPLWWHGYHUWLFDOO\

to the sky and is refracted back to the ground. The f₀F₂ describes the F₂ region of the ionosphere and at night WLPHI₀F₂ completely explores the F region.

 $W PLGGOH DQG ORZ ODWLWXGHV WKH VRODU H[WUHPH

XOWUDYLROHW UDGLDWLRQ (89 LV WKH SULPDU\ VRXUFH RI

ionisation in the F region (Lakshmi et al7KXV

ionospheric empirical models depend on the high energy UDGLDWLRQFRPLQJIURPWKH6XQ+RZHYHUWKHLQWHQVLW\

RI(89DQGRWKHUKLJKHQHUJ\UDGLDWLRQGHSHQGVRQWKH

magnitude of the solar cycle. As a result of the lack of ORQJWHUPGLUHFWPHDVXUHPHQWVRIVRODU(89DQGRWKHU

KLJKHQHUJ\UDGLDWLRQUHVHDUFKHUVKDYHWRUHO\RQRWKHU

VRODU DFWLYLW\ SUR[LHV ;UD\V (89 DQG 89 FDQ EH

precisely estimated by different solar indices such as VXQVSRWQXPEHUVVRODUUDGLRÀX[DWFPZDYHOHQJWK

)0J,,FRUHWRZLQJLQGH[DQG+H0DOWE\

$OEUHJWVHQ6DPV,,,et al$FWRQ

Floyd et al5DPHVK 5RKLQL/XNLDQRYD

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most interesting solar photospheric feature that can be simply observed through a solar telescope in white light DUHWKHVXQVSRWVZKLFKDUHWKHVHDWRIVRODUDFWLYLW\

 6XQVSRWV LQLWLDWH DV VPDOOHU GDUNHU UHJLRQV RQ WKH

solar disk which may develop into larger and much GDUNHUVSRWVVXUURXQGHGE\OLJKWGDUNUHJLRQVFDOOHG

penumbrae (Antia et al.7KHVXQVSRWQXPEHULV

one of the most commonly used solar proxies because the sunspot number is well correlated to high energy radiation and with other solar proxies. It is convenient to use it because of its long series of observations and its characteristics of reliability and predictability. The solar activity reliance of ionospheric characteristics has been found in early regular ionospheric observations 5LFKDUGV  6HWKL et al $WDF et al 

0DUX\DPD$GHQL\L ,NXEDQQL0LHOLFK 

%UHPHU  (OLDV et al  ,NXEDQQL $GHQL\L

2017). Earlier researchers suggested the idea about the linear relationship between sunspot numbers and f₀F₂ for HYHU\KRXUDQGPRQWKZKLFKKDVEHHQIUHTXHQWO\XVHG

IRUJOREDOUHJLRQDODVZHOODVVLQJOHVWDWLRQLRQRVSKHULF

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Holt et al  ZKLOH DIWHU IXUWKHU VWXG\LQJ SURYHG

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2]JXFet al'DEDVet al

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International reference ionosphere is a purely empirical VWDQGDUG PRGHO RI WKH LRQRVSKHUH EDVHG RQ WKH ODUJH

collection of ground-based and space observations.

It provides monthly average values of ionospheric SDUDPHWHUV VXFK DV HOHFWURQ GHQVLW\ LRQ DQG HOHFWURQ

WHPSHUDWXUHV FRPSRVLWLRQ RI JDV VSHFLHV HWF XQGHU

the quiet geomagnetic condition (Rawer et al,Q

WKHVWXGLHVWKHI₀F₂ data of IRI-2012 (https://omniweb.

gsfc.nasa.gov/vitmo/iri2012_vitmo.html) model was considered for comparison with the spectral model.

The critical frequency F₂ layer directly represented the electron density of the F₂. The highest electron density (N_mF₂) reaches the F₂ peak height (h_mF₂) from where it divides into lower and upper parts. In IRI both parts are normalised to the F₂ peak density and height. Electron density below the F₂ peak is normalised to the E and F₂ peaks. The region between F₁ and F₂ height is of special interest because of its effect on HF radio wave propagation. Electron density (N_e) in that region is GHVFULEHGE\WKH,5,IXQFWLRQDVVKRZQLQHTXDWLRQ

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determined by the lower thickness parameter (B₀) and the shape parameter (B₁). The B₀ LV GH¿QHG DV

is defined as ሺܤ_଴ൌ ݄_௠ܨ_ଶെ ݄ݔሻ in which the ͲǤʹͶ ൈ ܰ_௠ܨ_ଶ). The parameters B

in which the hx is the height where WKH GHQVLW\ SUR¿OH GURSSHG GRZQ WR

ሺܤ_଴ൌ ݄_௠ܨ_ଶെ ݄ݔሻ density profile dropped down to (ͲǤʹͶ ൈ ܰ_௠ܨ_ଶ). The parameters B

by IRI for the better description of the global and temporal variation of ionosphere (Bilitza .

The parameters B₀ and B₁ are upgraded every few years by IRI for better description of the global and temporal variation of theLRQRVSKHUH%LOLW]Det al

 ,Q WKLV VWXG\ ZH KDYH LOOXVWUDWHG WKH HIIHFWV RI

sunspots on f₀F₂ RYHU:DNNDQDL6LPLODUWRRWKHUPRGHOV

we have constructed a local-station model of f₀F₂ that usually gives an average value of f₀F₂ incorporating the HIIHFW RI WHPSRUDO VHDVRQDO HIIHFW VRODU F\FOH DQG WKH

ODWLWXGHRIWKHVWDWLRQ,WKDVEHHQREVHUYHGWKDWVSHFL¿F

Modelling the ionospheric f₀F₂LQÀXHQFHGE\VRODUDFWLYLW\ 

models of a particular region are very useful and widely UHIHUUHGWRLRQRVSKHULFVHUYLFHV3DQFKHYD 0XNKWDURY

1998). The diurnal f₀F₂ models for each month for solar maximum and solar minimum years are successfully presented in this study.

METHODOLOGY

From 1948 onwards the ionosonde/digisonde station in Wakkanai has consistently measured ionospheric parameters. These measurements are recorded by the World Data Center (WDC) for Ionosphere and Space :HDWKHU LQ WKH -DSDQHVH FLW\ RI 7RN\R 7KH FHQWHU LV

under the management of the National Institute of ,QIRUPDWLRQ DQG &RPPXQLFDWLRQV 7HFKQRORJ\ 1,&7

-DSDQ7KHJHRJUDSKLFORFDWLRQRI:DNNDQDLLVƒ1

DQG  ƒ( LQ WKH PLGODWLWXGH UHJLRQ RI -DSDQ ,Q

WKLVUHVHDUFKWKHKRXUO\GDWDRII₀F₂LQ-DSDQHVHVWDQGDUG

WLPH-67DQGVXQVSRWQXPEHUZHUHXVHGIRUWKH\HDUV

of 21^st and 23^rd VRODU F\FOHV LQVWHDG WKH \HDUV RI ^nd  ௅  VRODU F\FOH GXH WR WKH KXJH GH¿FLHQF\

in observational data of f₀F₂. To study the average behaviour of the ionosphere the monthly median hourly values of f₀F₂ were extracted IURPWKHHQWLUHGDWDEDVH

while the missing f₀F₂YDOXHVZHUH¿OOHGZLWK,5,

model values obtained from the Virtual Ionosphere Thermosphere Mesosphere Observatory (VITMO) (http://omniweb.gsfc.nasa.gov/vitmo/). Considering only WKHHIIHFWRIVHDVRQVI₀F₂LVLQGHSHQGHQWRIVRODU]HQLWK

DQJOH*HQHUDOO\I₀F₂ peaks in winter and decreases in VXPPHUDQGWKLVHIIHFWLVNQRZQDVZLQWHUDQRPDO\,Q

WKHVXPPHUVHDVRQWKHHQKDQFHPHQWLQQLJKWWLPHI₀F₂ called midlatitude summer nighttime anomaly (MSNA) KDVDOVREHHQREVHUYHGRYHU:DNNDQDLž10XVKWDT

et al7KHSUHIHUHQFHRIPRQWKO\PHGLDQYDOXHV

over monthly mean values is because of the 27 days solar rotation. The solar rotation has conspicuous variation in (89UDGLDWLRQZKLFKFRQWULEXWHV±LQHOHFWURQ

density in the ionosphere (Ruiping et al

Regression method was used to investigate the dependence of sunspot numbers on the ionospheric F₂OD\HULHI₀F₂) over Wakkanai. Regression analysis PDNHVLWSRVVLEOHWR¿QGWKHOLQHZKLFKEHVWGHVFULEHVWKH

association between two variables. This line is usually UHIHUUHG WR DV WKH µOLQH RI EHVW ¿W¶ -DLVLQJK 

Spectral models explain the complex data as a hypothesis;

it predicts the dynamics of f₀F₂ in the frequency domain by observing long-term data records. The diurnal cycles KDYH D VLJQL¿FDQW LPSDFW RQ PDQ\ SKHQRPHQD LQ WKH

(DUWK¶V DWPRVSKHUH PDLQO\ RQ WKH LRQRVSKHUH 7R

model the complex nature of the ionosphere the spectral approach has been implemented.

)RU VRODU SUR[\ WKH PRQWKO\ PHDQ VXQVSRW QXPEHUV

are used for the said solar cycles given by the Royal 2EVHUYDWRU\ RI %HOJLXP ORFDWHG LQ 8FFOH %HOJLXP

ZKLFK KDV WKH JHRJUDSKLF SRVLWLRQ  ƒ1 DQG

ƒ(7KHUHODWLYHVXQVSRWQXPEHULVFDOFXODWHGRQ

the basis of all observations available from different REVHUYDWRULHV +RZHYHU IRU UHSUHVHQWLQJ JOREDO

JHRPDJQHWLF DFWLYLW\ WKH PRQWKO\ PHDQ JHRPDJQHWLF

index A_p is utilised for 1976 – 1986 and 1996 – 2008.

3ULRUWR-DQXDU\GDWDZHUHWDNHQIURPWKH,QVWLWXWH

IXU *HRSK\VLN *RWWLQJHQ *HUPDQ\ 6LQFH  XS WR

QRZ GRFXPHQWDWLRQ FDOFXODWLRQ DQG GLVWULEXWLRQ RI

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RESULTS AND DISCUSSION

(PSLULFDOPRGHOVRII0)2DQGVXQVSRWQXPEHU

,W LV VLJQL¿FDQW WR ¿QG WKH HPSLULFDO PRGHOV EHWZHHQ

monthly median hourly f₀F₂ ZLWK DQ\ EHVW ¿WWHG VRODU

proxies. The key parameter used is the sunspot number for ionospheric long-term predictions. Sunspots are one of the best ways to indicate the emission of high energy radiation from the solar surface and its atmosphere LH(89DQG;UD\VZKLFKDUHWKHPDLQVRXUFHVRI

LRQLVDWLRQ LQ WKH LRQRVSKHUH :H ¿WWHG IRXU UHJUHVVLRQ

models and to authenticate the correlation of solar activity on f₀F₂)WHVWKDVEHHQSHUIRUPHGDWFRQ¿GHQFH

LQWHUYDOZKLFKYHUL¿HGWKDWUHJUHVVLRQDQDO\VHVEHWZHHQ

SSN and f₀F₂DUHVWDWLVWLFDOO\VLJQL¿FDQWIRUDOOPRQWKV

7KH¿UVWUHJUHVVLRQPRGHOLVWKHOLQHDUOLQHRIEHVW¿W

The linear relationships between f₀F₂ and solar proxies have been used in many previous models which are in JRRGDJUHHPHQWZLWKRXUUHVXOWV*XO\DHYD+ROW

et al<DQKRQJet al<DGDYet al$

good linear relation depends on the following situations:

i) It has been found that at moderate sunspot numbers   661   WKH OLQHDU UHODWLRQ EHWWHU H[SODLQHG

the behaviour of f₀F₂+RZHYHUQROLQHDUFRUUHODWLRQLV

found at low and high SSN (Ikubanni et al ii) ,Q GLIIHUHQW ORFDWLRQV RQ WKH (DUWK WKH QDWXUH RI

ionosphere is varying. At equator and low-latitudes the effect of saturation is so strong that no linear relation is suitable for explaining f₀F₂. Mid-latitudes show less variability in f₀F₂DWKLJK661WKHUHIRUHWKHOLQHDUUHODWLRQ

can also be considered (Liu et al(TXDWLRQ describes the linear correlation between the sunspot number and f₀F₂DV

530 Muzammil Mushtaq et al.

݂݋ܨʹሺݐሻ௠ൌ ܽ଴௠ሺݐሻ ൅ ܽଵ௠ሺݐሻǤ ܵܵܰ௠ ---- (2)

ܽ଴ ܽଵ

݂݋ܨʹሺݐሻ_௠ ൌ  ܾ_଴௠ሺݐሻ ൅ ܾଵ௠ሺݐሻǤ ܵܵܰ௠൅ ܾ_ଶ௠ሺݐሻǤ ܵܵܰ௠ଶ

ܾ଴ǡ ܾଵ ܾଶ

„ଶ

...(2) where Į₀ and Į₁ DUH WKH FRHI¿FLHQWV ZKLOH t and m VKRZWKH-DSDQHVHVWDQGDUGWLPHLQKRXUVDQGGLIIHUHQW

PRQWKV UHVSHFWLYHO\ DQG 661 LV WKH PRQWKO\ PHDQ

sunspot number for the current month. We analysed the relationship at midnight (t = 00 h) and noontime (t = 12 h) LQ-67ZKLOVWmVKRZVWKHZKROHPRQWKVRID\HDUDQG

WKHOLQHDUOLQHRIEHVW¿WLVUHSUHVHQWHGDVGRWWHGOLQHVDV

shown in Figures 1 and 2.

 $WPLGQLJKWWKHOLQHDUUHJUHVVLRQ¿WVHHPVJRRGLQ

PDQ\PRQWKVHVSHFLDOO\DURXQGWKHHTXLQRFWLDOWLPHDQG

WKHKLJKHVWDGMXVWHGFRHI¿FLHQWRIGHWHUPLQDWLRQDGMB5²) occurred in April (adj_R²    ZKLOH WKH ORZHVW

adj_R² ZDV IRXQG LQ 'HFHPEHU LH   +LJKHU

values of adj_R² illustrate that the regression model explains the majority of the variations in f₀F₂ while low values of adj_R² show the opposite.

$WQRRQWLPHOLQHDU¿WVDUHVWLOODJRRGLQGLFDWLRQRIWKH

relationship between sunspot numbers and f₀F₂DQGWKH

maximum and minimum adj_R²DUHDQG

LQWKHPRQWKVRI0DUFKDQG-XO\UHVSHFWLYHO\,WKDVEHHQ

observed that f₀F₂ shows a good linear relationship for low and moderate numbers of sunspots while it shows almost constant or decreasing values at extremely high VRODU HSRFKV ZKLFK LV NQRZQ DV WKH VDWXUDWLRQ HIIHFW

6DWXUDWLRQ GHSHQGV RQ ORFDO KRXUV PRQWKV DQG RQ WKH

magnitude of the solar cycle. In Figures 1 and 2 it is REVHUYHGWKDWLQZLQWHULQFOXGLQJWKHPRQWKV'HFHPEHU

DQG -DQXDU\ WKH I₀F₂ values show generally constant YDOXHVRIKLJKVXQVSRWQXPEHUVZKLFKRXU¿UVWUHJUHVVLRQ

PRGHOGRHVQRWGHPRQVWUDWH7KHUHIRUHDEHWWHUPRGHO

LVH[SHFWHGE\XVLQJWKHVHFRQGUHJUHVVLRQPRGHOLH

quadratic relationship between sunspot numbers and f₀F₂ DV

݂݋ܨʹሺݐሻ_௠ൌ ܽ_଴௠ሺݐሻ ൅ ܽ_ଵ௠ሺݐሻǤ ܵܵܰ_௠

ܽ_଴ ܽ_ଵ

݂݋ܨʹሺݐሻ_௠ ൌ  ܾ_଴௠ሺݐሻ ൅ ܾଵ௠ሺݐሻǤ ܵܵܰ௠൅ ܾ_ଶ௠ሺݐሻǤ ܵܵܰ௠ଶ ---- (3)

ܾ_଴ǡ ܾ_ଵ ܾ_ଶ

„_ଶ ...(3)

)LJXUH The relationship between monthly median f0F₂ DQGPRQWKO\PHDQ661DW-67KIRUWKHZKROHLQWHUYDORI±DQG±

RYHU:DNNDQDL2EVHUYHGYDOXHVDUHSORWWHGDVGRWVGRWWHGOLQHVUHSUHVHQWWKHOLQHDUUHJUHVVLRQ¿WZKLOHVROLGOLQHVVKRZWKHTXDGUDWLF

UHJUHVVLRQ¿W

Modelling the ionospheric f₀F₂LQÀXHQFHGE\VRODUDFWLYLW\ 

b₀ b₁ and b₂ DUH WKH FRHI¿FLHQWV RI WKH TXDGUDWLF

UHJUHVVLRQHTXDWLRQDWVSHFL¿HG-67WLPHt) and month (m) represented by a solid line in Figures 1 and 2. In this FDVHWKHVLJQL¿FDQFHRIFRHI¿FLHQWb₂ is;

i) b₂   LQGLFDWHV WKDW I₀F₂ declines with increasing VRODUDFWLYLW\ZKLFKUHSUHVHQWVWKHVDWXUDWLRQHIIHFW

ii) b₂ !LPSOLHVWKDWI₀F₂ rises at excessively high solar epochs.

The saturation at noon and midnight in different months is clearly shown by the second regression model in Figures 1 and 2. The maximum difference in adj_R² LHDQGLVIRXQGLQ'HFHPEHUDWQRRQ

DQG PLGQLJKW UHVSHFWLYHO\ 7KH FOHDU VDWXUDWLRQ LQ WKH

noontime monthly median values of f₀F₂ during the winter VHDVRQLQFOXGLQJPRQWKVRI'HFHPEHUDQG-DQXDU\DW

:DNNDQDLž1LVGXHWRWKHHQKDQFHPHQWRIWKH

recombination process. Molecular nitrogen (N₂) plays a

NH\UROHLQWKHUHFRPELQDWLRQSURFHVV5LVKEHWK

Hedin et al. (1979) demonstrated that the density ratio of atomic oxygen and molecular nitrogen (O/N₂) decreases VLJQL¿FDQWO\ ZLWK WKH LQFUHDVH LQ VRODU DFWLYLW\ IRU

ZLQWHUDWžODWLWXGH7KLVLVGXHWRWKHLQFUHDVHLQWKH

VFDOHKHLJKWRIPROHFXODUVSHFLHVHVSHFLDOO\1₂UDWKHU

than the scale height of atomic oxygen at high solar HSRFKV6FKXQN :DONHU7KLVDQRPDORXVUROH

of N₂ UDLVHV WKH UHFRPELQDWLRQ SURFHVV HPHUJLQJ DV D

saturation effect.

Polynomial regression models of higher orders KDYHEHHQWHVWHGDQGDJRRGUHODWLRQEHWZHHQI₀F₂ and SSN at low and moderate sunspot numbers was found.

+RZHYHU UDQGRPO\ VWHHS GRZQZDUG RU XSZDUG WUHQGV

at larger sunspot numbers contradicts the actual physical SKHQRPHQDRIWKHVDWXUDWLRQHIIHFW$ORQJZLWKWKLVWKH

adjusted R² also showed no improvement with higher orders.

Figure 2: Same as Figure 1 but for JST 12 h.

)LJXUH The relationship between monthly median f0F₂ DQGPRQWKO\PHDQ661DW-67KIRUWKHZKROHLQWHUYDORI±DQG

±RYHU:DNNDQDL2EVHUYHGYDOXHVDUHSORWWHGDVGRWVGRWWHGOLQHVUHSUHVHQWWKHOLQHDUUHJUHVVLRQ¿WZKLOHVROLGOLQHVVKRZWKH

TXDGUDWLFUHJUHVVLRQ¿W

532 Muzammil Mushtaq et al.

,WKDVEHHQVKRZQWKDWIRUORZHUOHYHOVRIVRODUDFWLYLW\

f₀F₂ may vary during ascending and descending parts of the 11-year solar cycles; an effect which is known as the hysteresis effect. This effect is attributed to the activities of geomagnetic storms throughout the VRODU F\FOH 5DR  5DR $SRVWRORY $OEHUFD

 0LNKDLORY  0LNKDLORY  7KH HQKDQFHG

geomagnetic activity during the declining period of the solar cycle can produce stronger storm effects on the F₂ layer than during the increasing period of the solar F\FOH.DQHDUJXHGWKDWWZRNH\SDUDPHWHUVLH

VRODU DQG WKH JHRPDJQHWLF LQGH[ VKRXOG EH WDNHQ LQWR

DFFRXQWIRUORQJWHUPSUHGLFWLRQPRGHOV7KHUHIRUH;X

et al. (2008) used a multiple regression model by taking WZRSDUDPHWHUVLHWKHVXQVSRWQXPEHUDVVRODUDFWLYLW\

index and geomagnetic index A_p for geomagnetic perturbations of the dependence on the monthly median f₀F₂RYHU&KRQJTLQJ&KLQD

Our analysis of f₀F₂ RYHU :DNNDQDL  ž1 supports the model by Kane (1992) that uses both solar and geomagnetic index parameters which improved the regression model. Our third regression model is represented as dashed-square lines in Figure 3 and H[SUHVVHGDV

݂݋ܨʹሺݐሻ_௠ ൌ ܿ_଴௠ሺݐሻ ൅ ܿ_ଵ௠ሺݐሻǤ ܵܵܰ_௠൅ ܿ_ଶ௠ሺݐሻǤ ܵܵܰ_௠^ଶ ൅ ܿ_ଷ௠ሺݐሻǤ ܣ݌_௠Ǥ ܵܵܰ_௠൅ ܿ_ସ௠ሺݐሻǤ ܣ݌_௠൅

ܿ_ହ௠ሺݐሻǤ ܣ݌^ଶ ---- (4)

݂݋ܨʹሺݐሻ௠ൌ ܿ଴௠ሺݐሻ ൅ ܿଵ௠ሺݐሻǤ ܵܵܰ௠൅ ܿଶ௠ሺݐሻǤ ܵܵܰ௠ଶ ൅ ܿଷ௠ሺݐሻǤ ܣ݌௠Ǥ ܵܵܰ௠൅ ܿସ௠ሺݐሻǤ ܣ݌௠൅

ܿହ௠ሺݐሻǤ ܣ݌^ଶ ---- (4)

݂݋ܨʹሺݐሻ௠ ൌ ܿ଴௠ሺݐሻ ൅ ܿଵ௠ሺݐሻǤ ܵܵܰ௠൅ ܿଶ௠ሺݐሻǤ ܵܵܰ௠ଶ ൅ ܿଷ௠ሺݐሻǤ ܣ݌௠Ǥ ܵܵܰ௠൅ ܿସ௠ሺݐሻǤ ܣ݌௠൅

ܿହ௠ሺݐሻǤ ܣ݌^ଶ ---- (4)

݂݋ܨʹሺݐሻ_௠ ൌ ܿ_଴௠ሺݐሻ ൅ ܿଵ௠ሺݐሻǤ ܵܵܰ௠൅ ܿ_ଶ௠ሺݐሻǤ ܵܵܰ௠ଶ ൅ ܿ_ଷ௠ሺݐሻǤ ܣ݌௠Ǥ ܵܵܰ_௠൅ ܿ_ସ௠ሺݐሻǤ ܣ݌௠൅

ܿହ௠ሺݐሻǤ ܣ݌^ଶ ---- (4)

...(4) where c₀ to c₅ DUHWKHFRHI¿FLHQWVRIWKHWKLUGUHJUHVVLRQ

PRGHOLQDGLIIHUHQW-67WLPHt) and month (m) while A_p and SSN are the monthly mean geomagnetic index DQGVXQVSRWQXPEHUDWWKHSUHVHQWPRQWKUHVSHFWLYHO\

7KHFRHI¿FLHQWVc₁ and c₂ are the quantitative expressions of the current month's sunspot number whilst c₄ and c₅ represent the current month’s A_pLQGH[YDOXHV+RZHYHU

c₃ depicts the combination of solar and geomagnetic disturbances.

The standard deviations of the change in f₀F₂ calculated from regression models and observed values for the years 1976 – 1986 and 1996 – 2008 are illustrated in Figure 3. The diurnal variations of these standard deviations are determined for all months. It is VHHQWKDWWKHWUHQGLVVOLJKWO\QHDUHUWR]HURZKHQXVLQJ

ERWKIDFWRUVLHVRODUDQGJHRPDJQHWLFLQGH[IRUWKH

empirical model represented as dashed-square lines. It concludes that the third regression model better explains the observed values rather than the second regression

model. The root mean square deviation (RMSD) is often used to measure the difference between two time series trends; RMSD is calculated from the trend of the standard deviations measured from equations (3) and  ,Q WKLV VFHQDULR WKH KLJKHU YDOXHV RI 506' LQ D

VSHFL¿F PRQWK LQGLFDWH WKDW WKH FDOFXODWHG I₀F₂ values from equation (4) are much closer to the observed values than the f₀F₂ calculated from equation (3) for that particular month. The maximum RMSD was reported in WKHPRQWKVRI-DQXDU\DQG-XO\LHDQG and the maximum differences appear at 11:00 and 09:00 KRXUV-67UHVSHFWLYHO\7KHUHIRUHWKHWKLUGUHJUHVVLRQ

model is preferable over the second regression model.

+RZHYHULWLVLQVLJQL¿FDQWWKDWLQWKHPRQWKVRI$SULO

0D\ DQG 6HSWHPEHU ZKHUH WKH 506' YDOXHV DUH WKH

OHDVWLHDQGUHVSHFWLYHO\

The hysteresis effect has a great impact on the mid- ODWLWXGHFRPSDUHGWRWKHORZDQGKLJKODWLWXGHVZKLFK

cannot be neglected for empirical and spectral models of f₀F₂ HVSHFLDOO\ DW :DNNDQDL ž 1 5DR DQG 5DR

(1969) observed that noontime f₀F₂ values are higher in the decreasing part of the solar cycle while it is low in the rising phase of the solar cycle. This is the consequence of some weak solar activities which can occur with or without sunspot formation because the required magnetic

¿HOGWKUHVKROGWRIRUPVXQVSRWLV*DXVV3HQQ  /LYLQJVWRQ  +RZHYHU WKH ZHDN PDJQHWLF ¿HOG

FDQ SURGXFH HYHQWV VXFK DV VRODU ÀDUHV FRURQDO PDVV

HMHFWLRQVRODUZLQGVDQGHQHUJHWLFSURWRQV7KRVHHYHQWV

occur near or close to the time of formation of sunspots /HJUDQG 6LPRQ+LJKVSHHGVRODUZLQGVWUHDPV

from low solar-latitude coronal holes enhanced much later than sunspots maxima in the falling part of a solar cycle whose effect on ionosphere is even more non-linear 6LPRQ /HJUDQG7KHUHIRUHLQDV\VWHPDWLFZD\

one can consider the rate of change in sunspot numbers for a few-month’s time interval from a given month. This approach can potentially cover all the solar activities that occur before and after the formation of sunspots as shown previously by Pancheva and Mukhtarov (1998).

Pancheva and Mukhtarov (1998) found that the rate of change in solar activity is low in the descending part of WKHVRODUF\FOHWKDQLQWKHDVFHQGLQJSDUW7KHLQÀXHQFH

of the tendency for a change of solar activity is essential for the years when solar activity varies very rapidly (i.e.;

ascending part of the solar cycle). The study (Pancheva  0XNKWDURY  XVHG WKH .U SDUDPHWHU DQG WULHG

WR JHW PRUH DFFXUDF\ LQ HPSLULFDO PRGHOV DOWKRXJK LW

is inconvenient because the Kr parameter includes the IDFWRURIVRODUDFWLYLW\DIWHU¿YHPRQWKVIURPWKHJLYHQ

PRQWKZKLFKPD\EHXQNQRZQ7KHQDQHZ¿QGLQJZDV

published by Liu et al. (2004) in which they only replaced

Modelling the ionospheric f₀F₂LQÀXHQFHGE\VRODUDFWLYLW\ 

.UZLWK)SLHWKHSULRUPRQWK¶V)YDOXHVDVD

solar activity parameter over the Wuhan region (30.6 ž1

ž(WKDWJDYHDQHYHQEHWWHUUHVXOW,QWKHSUHVHQW

VWXG\661Swas used LHWKHPRQWKO\PHDQVXQVSRW

QXPEHU RI WKH SUHYLRXV PRQWK 7KHUHIRUH WKH IRXUWK

UHJUHVVLRQPRGHOFDQEHJLYHQDV

݂݋ܨʹሺݐሻ_௠ൌ ݀_଴௠ሺݐሻ ൅ ݀ଵ௠ሺݐሻǤ ܵܵܰ௠൅ ݀_ଶ௠ሺݐሻǤ ܵܵܰ௠ଶ ൅ ݀_ଷ௠ሺݐሻǤ ܵܵܰ݌௠൅ ݀_ସ௠ሺݐሻǤ ܵܵܰ݌௠ଶ

–ǡ ǡ ƒ†’ǡ

–

݂݋ܨʹሺݐሻ_௠ൌ ݀_଴௠ሺݐሻ ൅ ݀ଵ௠ሺݐሻǤ ܵܵܰ௠൅ ݀_ଶ௠ሺݐሻǤ ܵܵܰ௠ଶ ൅ ݀_ଷ௠ሺݐሻǤ ܵܵܰ݌௠൅ ݀_ସ௠ሺݐሻǤ ܵܵܰ݌௠ଶ ---- (5)

–ǡ ǡ ƒ†’ǡ

–

...(5) The trend of standard deviations by evaluating equation (5) LVUHSUHVHQWHGDVDVROLGOLQHLQ)LJXUH)RUDOOPRQWKV

it is seen that the fourth regression model has a much lower standard deviation that made it easier to explain

the observed f₀F₂ values over Wakkanai. The highest drop in the standard deviation occurs in November from DERXW0+]WR0+]DWKRXU-67)RUDOO

PRQWKV506'LVFRPSXWHGIURPWKHVWDQGDUGGHYLDWLRQ

trends measured from equations (3) and (5). The RMSD KDV KLJK YDOXHV ZKLFK LV DQ LQGLFDWLRQ WKDW WKH EHVW

relationship exists between the calculated f₀F₂ from equation (5) with observed f₀F₂HVSHFLDOO\LQ)HEUXDU\

and September with maximum RMSD value of 0.114 DQG  UHVSHFWLYHO\ ,QWURGXFLQJ 661S LPSURYHV

the depiction of solar cycle dependence of f₀F₂. In other ZRUGV LW LV REVHUYHG WKDW WKH UDWH RI FKDQJH LQ VRODU

DFWLYLW\KDVDVLJQL¿FDQWHIIHFWRQI₀F₂ over Wakkanai and its response depends on the month and partially on the diurnal cycle as seen in Figure 3. The results demonstrate that the fourth regression model accurately explains the complex behaviour of the ionospheric f₀F₂ parameter.

Figure 3: Diurnal variation of the standard deviation of f0F2 computed from equations 3, 4 and 5 from the

)LJXUH Diurnal variation of the standard deviation of f0F₂ FRPSXWHGIURPHTXDWLRQVDQGIURPWKHREVHUYHGI0F₂ for the whole LQWHUYDO±DQG±RYHU:DNNDQDL/LQHGRWVUHSUHVHQWWKHVHFRQGUHJUHVVLRQ¿WGDVKHGVTXDUHOLQHVVKRZWKHWKLUG

UHJUHVVLRQ¿WVROLGOLQHVDUHIRUWKHIRXUWKUHJUHVVLRQ¿W

6SHFWUDODQDO\VLV

We have constructed a diurnal f₀F₂ model for Wakkanai

ž1EDVHGRQ)RXULHUVHULHV)RXUNH\SDUDPHWHUV

ZHUHXVHGIRUWKHPRGHO7KHVHDUHWP661DQG661S

ZKLFK UHSUHVHQW WKH GLXUQDO VHDVRQDO DQG VRODU F\FOH

variations and the effect of prior solar activity on f₀F₂

UHVSHFWLYHO\ZKHUHWLVWKH-DSDQHVHVWDQGDUGWLPHPLV

534 Muzammil Mushtaq et al.

WKHPRQWK661DQG661SDUHWKHPRQWKO\PHDQVXQVSRW

numbers’ YDOXH LQ WKH VSHFL¿HG DQG SUHYLRXV PRQWK

respectively.

)RXULHUPRGHODQGLWVDXWKHQWLFDWLRQ

Fourier series represents periodic functions in terms of cosines and sines. There are diurnal periodicities SUHVHQW LQ WKH LRQRVSKHULF SDUDPHWHUV 7KHUHIRUH WKH

Fourier series is generally preferred when constructing spectral models. The diurnal variations can be expressed by a Fourier series with periods of 24 hours and higher harmonics. A Fourier series for f₀F₂ can be generally H[SUHVVHGDV

  ’

݂݋ܨʹሺݐሻ_௠ൌ ݔ_଴ǡ௠൅ σ^ே_௡ୀଵቀݔ_௡ǡ௠…‘• ቀ^ଶగ௡௧_் ቁ ൅ݕ_௡ǡ௠•‹ ቀ^ଶగ௡௧_் ቁቁ



 š_୬ǡ୫ ›_୬ǡ୫

 ’

  ’

݂݋ܨʹሺݐሻ_௠ൌ ݔ_଴ǡ௠൅ σ^ே_௡ୀଵቀݔ_௡ǡ௠…‘• ቀ^ଶగ௡௧_் ቁ ൅ݕ_௡ǡ௠•‹ ቀ^ଶగ௡௧_் ቁቁ ---- (6)



 š_୬ǡ୫ ›_୬ǡ୫

 ’

...(6) ZKHUHWKHKDUPRQLFQXPEHULVQ «1DQGLQ

RXUPRGHOVZHWDNHKDUPRQLFQXPEHUVWRHQVXUHPRGHO

accuracy and T LV HTXDO WR  KRXUV 7KH FRHI¿FLHQWV

x_n,m and y_n,m are functions of SSN and SSNp. These FRHI¿FLHQWVDUHFRPSXWHGIURPHTXDWLRQE\XVLQJWKH

FXUYH¿WWLQJWRROLQ0$7/$%VRIWZDUHRIWKHVSHFL¿HG

months for solar minimum and solar maximum years LH  DQG  UHVSHFWLYHO\ KRZHYHU WKH I₀F₂ values for every month are evaluated from equation (5).

The predicted f₀F₂ values from the Fourier model

>LHHTXDWLRQ@DQG,5,PRGHODUHUHSUHVHQWHGDVVROLG

OLQHV ZKLOVW WKH REVHUYHG I₀F₂ values are symbolised with dots as shown in Figure 4. Left panels are for the Fourier model while right panels are for the IRI-2012 model; both are compared with the observed f₀F₂ values.

The solar minimum year (1976) and solar maximum year (1979) were chosen for constructing the f₀F₂ models. For YHUL¿FDWLRQRIWKHPRGHOVZHXVHGWKH\HDUVDQG

ZKLFKDUHWKHVRODUPLQLPDDQGVRODUPD[LPD\HDUV

RIVRODUF\FOHUHVSHFWLYHO\$VI₀F₂ data were missing for the years of solar cycle 22 (1986 – 1996) and 24 (2008

±SUHVHQWZHZHUHXQDEOHWRZRUNRQLW7KH\HDUVXVHG

IRUYHUL¿FDWLRQRIRXUPRGHOVZHUHQRWLQFOXGHGLQLWLDOO\

LQ WKH GDWDVHW IRU UHJUHVVLRQ PRGHOV 7KHUHIRUH WKH

regression fit.

Fourier Model IRI (2012) Model

J F M A M J J A S O N D

2 4 6 8

J F M A M J J A S O N D

0 2 4 6 8

J F M A M J J A S O N D

0 5 10 15

J F M A M J J A S O N D

0 5 10 15

J F M A M J J A S O N D

2 4 6 8

J F M A M J J A S O N D

2 4 6 8

J F M A M J J A S O N D

0 5 10 15

J F M A M J J A S O N D

0 5 10 15

foF2 (MHz)

1976

1979

1964

1968 1968 1964 1979 1976

Months Months

)LJXUH The computed and predicted diurnal variation of the monthly median f0F₂ represented as solid lines with observed f₀F₂ shown with dots for solar minimum years (1976 and 1964) and for solar maximum years (1979 and 1968).

Modelling the ionospheric f₀F₂LQÀXHQFHGE\VRODUDFWLYLW\ 

correctness of our work can be demonstrated by showing the results of the model f₀F₂ values that almost do not change in the years which are not included originally in

the dataset for analysis. Hence our Fourier models can be employed for the long-term prediction of the ionospheric f₀F₂SDUDPHWHURYHU:DNNDQDLž1

)LJXUH The deviation of computed and predicted (Fourier and IRI-2012) f0F₂ from observed f₀F₂IRUWKH\HDUVDQG

Green colour bars are for the Fourier model and non-colour bars are for the IRI-2012 model.

)LJXUH The probability density funtion plot of the change in f0F₂ of the solar minimum and maximum years of the cycle 21 and 23. The Dagum

3LQEODFNFRORXUDQGQRUPDOLQUHGFRORXUGLVWULEXWLRQVDUH¿WWHG

536 Muzammil Mushtaq et al.

The deviation of models (Fourier and IRI-2012) from observed f₀F₂ for the solar minimum (1976 and 1996) and maximum (1979 and 2000) years is shown in Figure 5.

The missing data of f₀F₂ of the year 2000 for the months of May and August to December are not included in the graph. Figure 5 demonstrates that:

i) )LUVWO\ WKH GHYLDWLRQ RI )RXULHU PRGHO I₀F₂ mostly OD\VFORVHUWR]HURDVVKRZQLQWKHJUHHQFRORXUEDUV

while divergence is much larger for IRI model f₀F₂ as displayed in none colour bars. This illustrates that Fourier model better explains the real behaviour of F2 layer critical frequency than IRI-2012 model over Wakkanai.

ii) 6HFRQGO\WKHHVWLPDWLRQRII₀F₂ by Fourier model in WKH PRQWKV RI$SULO -XQH DQG 2FWREHU KDYH PRUH

QHJDWLYHYDOXHVWKDWLOOXVWUDWHRXUPRGHOVLJQL¿FDQWO\

and underestimate the observed f₀F₂ values while in -XO\ DQG 6HSWHPEHU PRGHO RYHUHVWLPDWHV WKH I₀F₂ YDOXHV$OWKRXJKIRUDOOPRQWKVWKHVFDWWHULVPXFK

higher in the IRI-2012 model as compared to the observed f₀F₂.

The probability density functions (PDF) of the change in f₀F₂ YDOXHVDUHSORWWHGLQ)LJXUHZKHUHWKH

frequency on the y-axis shows the probability that x-axis can occupy between two maxima. It explained that high IUHTXHQF\ SHDN QHDU ]HUR PHDQV REVHUYHG I₀F₂ values are close to the calculated (or IRI) f₀F₂ values and low frequency shows opposite behaviour. The peak frequency QHDUWR]HURLVDFFXUDWHO\UHSUHVHQWHGE\'DJXPW\SH,,

(4P) distribution that is also compared with the normal distribution. The Dagum 4P distribution is a heavy-tail distribution that contains four parameters; two parameters GHVFULEHWKHVKDSHRQHLVIRUVFDOHDQGODVWLVWKHORFDWLRQ

parameter. The Dagum 4P is frequently used in economic SUREOHPV LQ ZKLFK QXOO DQG QHJDWLYH GDWD KDYH DVVHWV

and it is highly applicable in the cases of extreme data YDOXHVWKDWDUHQRWVXSSRVHGWREHQHJOHFWHG,QRXUFDVH

comparison of models gives high frequencies with long- tail that are fully explained by the Dagum 4P distribution besides normal distribution that partially explained peak frequency with overestimating frequency at the second- VWDQGDUGGHYLDWLRQRIWKHPHDQ.OHLEHU%HQMDPLQ

et al7KHSYDOXHWHVWKDVSUHIHUUHGWKH'DJXP

4P distribution and aborted the normal distribution

¿WWLQJ3')UHYHDOVWKDWWKH,5,PRGHOLVVFDWWHUHGPRUH

and under estimate f₀F₂ values from observed values with respect to the Fourier model.

 $V D ZRUOGZLGH HPSLULFDO PRGHO WKH ,5, PRGHO LV

outstanding at many spatial locations in the Earth’s LRQRVSKHUH+RZHYHUWKHEHKDYLRXURIWKHLRQRVSKHUHLV

extremely complex and it changes in different latitudes.

We worked on single-station empirical models so the effects of solar activity on f₀F₂RYHU:DNNDQDLž1DUH

highly considered that enabled us to precisely measure the saturation and hysteresis effects and include them in models. A similar methodology has been applied by Liu et alRYHU:XKDQž1DQGE\;Xet al. (2008) RYHU&KRQJTLQJž1&KLQD7KHUHIRUHWKH)RXULHU

model provides much higher accuracy as compared to WKH,5,PRGHORYHU:DNNDQDLž1

CONCLUSION

The non-linear relationship between f₀F₂ and SSN GHSHQGV RQ WKH WLPH RI D GD\ VHDVRQPRQWKV DQG WKH

PDJQLWXGH RI VRODU DFWLYLW\ +RZHYHU D TXDGUDWLF

UHJUHVVLRQ¿WLVVWLOOEHWWHUIRUDOOPRQWKVWRH[SODLQWKH

small variations and especially the saturation effects.

7R UHGXFH WKH K\VWHUHVLV HIIHFW LQWHJUDWHG IDFWRUV

of geomagnetic index A_p DQG 661 DUH XVHG ZKLFK

LPSURYHG WKH HPSLULFDO UHODWLRQVKLS +RZHYHU WKH

UHODWLRQLVVWLOOODFNLQJHVSHFLDOO\LQWKHPRQWKVRI$SULO

0D\ DQG 6HSWHPEHU ZKLOH LQWURGXFLQJ SULRU PRQWK

VXQVSRWQXPEHUVLH661SZLWKFXUUHQWPRQWK661

VLJQL¿FDQWO\ LPSURYHG WKH UHODWLRQVKLS EHWZHHQ VRODU

F\FOHYDULDWLRQDQGLWVLQÀXHQFHRQI₀F₂ over Wakkanai.

The tendency of change in solar activity factor makes the empirical model more appropriate than other regression models and it is suitable to use equation (5) for the spectral models of f₀F₂.

Spectral models are constructed using Fourier series for the solar minimum and solar maximum years (1976 and 1979). A good agreement has been found between the computed f₀F₂ from our models and the observed f₀F₂. We applied our models to the years 1964 and 1968 showing the solar minimum and solar maximum years. Comparable predictions of f₀F₂ from the IRI-2012 PRGHOZHUHDOVRDQDO\VHG)URP)LJXUHVDQGLWFDQ

be seen that the accuracy of our Fourier model is better WKDQ WKH ,5, PRGHO ZKLOH WKH ,5, PRGHO ODUJHO\

underestimated the f₀F₂ values from observed values.

The implementation of the Dagum 4P distribution is appropriate to model high frequencies and extreme values. The Dagum distribution is an appealing choice for modelling extreme values when using maximum likelihood estimators.

The Fourier models can be used as a relevant tool to study the effect of sunspot numbers on the F layer of ionosphere during solar minimum and solar maximum periods and it can be also used as a reference for predictions of the f₀F₂ parameter.

Modelling the ionospheric f₀F₂LQÀXHQFHGE\VRODUDFWLYLW\ 

$FNQRZOHGJHPHQW

All researchers of this paper are thankful for Virtual Ionosphere Thermosphere Mesosphere Observatory (VITMO) for providing the IRI 2007 and 2012 model values of f₀F₂. The sunspot number data are downloaded IURP WKH 6RODU ,QÀXHQFH 'DWD &HQWHU http://sidc.

oma.be/). The source of the geomagnetic index is

*HR)RUVFKXQJV=HQWUXP +HOPKROW] &HQWHU 3RVWGDP

Germany. The f₀F₂ data over Wakkanai station is made available from the World Data Center for Ionosphere DQG6SDFH:HDWKHU7RN\R-DSDQ1DWLRQDO,QVWLWXWHRI

Information and Communications Technology http://

wdc.nict.go.jp/IONO/wdc/index.html.

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other solar activity parameters for November 1991 to 1RYHPEHU,Q&RRO6WDUV6WHOODU6\VWHPVDQGWKH

Sun. Proceedings of the 9^th Cambridge Workshop (eds. R.

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௅2FWREHU$VWURQRPLFDO6RFLHW\RIWKH3DFL¿F$63

p. 45.

$GHQL\L -2  ,NXEDQQL 62  'HWHUPLQDWLRQ RI WKH

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%HQMDPLQ60+XPEHUWR9+ %DUU\&$8VHRI

WKH 'DJXP GLVWULEXWLRQ IRU PRGHOLQJ WURSRVSKHULF R]RQH

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%LOLW]D '  ,QWHUQDWLRQDO UHIHUHQFH LRQRVSKHUH 

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%LOLW]D '  ,RQRVSKHULF PRGHOV IRU UDGLR SURSDJDWLRQ

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pp. 625 – 679. IEEE and Wiley Press.

%LOLW]D ' $OWDGLOO ' =KDQJ < 0HUWHQV & 7UXKOLN 9

5LFKDUGV 3 0F.LQQHOO /$  5HLQLVFK % 7KH

international reference ionosphere 2012 - a model of international collaboration I. Journal of Space Weather and Space Climate 4(2014): Article number A07.

DOI: http://doi.org/10.1051/swsc/2014004

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)OR\G / 1HZPDUN - &RRN - +HUULQJ /  0F0XOOLQ '

6RODU(89DQG89VSHFWUDOLUUDGLDQFHVDQGVRODU

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DOI: http://doi.org/10.1029/1999RS900080

+HGLQ$(5HEHU&$6SHQFHU1:%ULQWRQ+& .D\VHU

'&*OREDOPRGHORIORQJLWXGH87YDULDWLRQVLQ

thermospheric composition and temperature based on mass spectrometer data. Journal of Geophysical Research: Space Physics 84(A1): 1 – 9.

DOI: KWWSGRLRUJ-$L$S

+ROW -0 =KDQJ 6  %XRQVDQWR 0-  5HJLRQDO

and local ionospheric models based on Millstone Hill incoherent scatter radar data. Geophysical Research Letters 29(8): 2 – 4.

,NXEDQQL 62 $GHEHVLQ %2$GHEL\L 6- $GHQL\L -2

(2013). Relationship between F2 layer critical frequency and solar activity indices during different solar epochs.

Indian Journal of Radio and Space Physics 42(April):

73 – 81.

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