Contents lists available at ScienceDirect

Planetary and Space Science

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

Short- and mid-term oscillations of solar, geomagnetic activity and cosmic-ray intensity during the last two solar magnetic cycles

Y.P. Singha,⁎, Badruddinb

a IAS, Mangalayatan University, Aligarh 202145, Indiab Astronomy Department, Faculty of Science, King Abdulaziz University, Jeddah, Saudi Arabia

A R T I C L E I N F O

Keywords:Solar periodicitySolar activityGeomagnetic activityCosmic raysWavelet analysis

A B S T R A C T

Short-and mid-term oscillations of the solar activity (sunspot number and 10.7 cm solar flux), geomagneticactivity (Ap index) and cosmic-ray intensity (neutron monitor count rate) are analysed during the past two solar-magnetic cycles (1968–1989 and 1989–2014). We have implemented the wavelet analysis on the daily timeresolution data of sunspot number (SSN), 10.7 cm solar flux, geomagnetic Ap index and Oulu neutron monitorcount rate. Results suggest that few quasi and intermittent oscillations are observed with remarkable powerdensity in addition to fundamental periods, like 27 day (synodic period), 154 day (Rieger period), semi-annual,annual, 1.3 year, and 1.7 year. We have consistently observed first (27 day), second (13.5 day) and third(9.0 day) solar-rotation harmonics in the geomagnetic Ap-index during both the magnetic cycles. Rieger periodis more pronounced in SSN and solar flux during 1980-82 and 1990-92. Semi-annual variation of Ap-index isconsistently observed during both the magnetic cycles. The annual and ~1.85 year variation are also observed inall the considered parameters with good signatures in CRI.

1. Introduction

The Sun has been a composite object that reflects abnormalbehavior because of its complex features. The fundamental ingredientbehind this complex system is its magnetic field. The solar magneticfield directly or indirectly disturbs the interplanetary space, ionosphere,and magnetosphere and even in lower atmosphere. The study of solarvariability and its influence on the Earth and Earth's environment hasalways been a challenging problem to researchers. When solar activitytriggers geomagnetic activity, the geomagnetic storms of variousmagnitudes occur. Investigations of time series of solar and solar windplasma, geomagnetic activity indices and galactic cosmic ray intensityhave unveiled a large range of periodic and aperiodic behaviours (e.g.Bazilevskaya et al., 2014; Kudela and Sabbah, 2016 and referencestherein). Study of the periodicities in the solar and geomagnetic activityparameters have been useful in relating solar variability to variationsobserved in various interplanetary phenomena in order to search for thesolar cause and effects in the near-earth space environment.

The observation of sunspots, a useful indicator of solar activity, hasstarted long back and variability in sunspot number has been studiedsince long. However, the variations of cosmic-ray intensity, solar windand geomagnetic activity have started since their systematic ground-based and/or space-based observations started. The observed variations

periodic or non-periodic have been related directly or indirectly tochanges in the magnetic activity of the sun (e.g. McIntosh et al., 2014).The variations of cosmic ray particles are reported e.g. by Maeda(1967), Akioka et al. (1987), Hill et al. (2001), Rybak et al. (2001),Kudela et al. (2002), Mavromichalaki et al. (2003), Singh et al. (2012),Modzelewska and Alania (2013), Potgieter (2014), Singh andBadruddin (2015a, 2015b), Aslam and Badruddin (2015), Badruddinand Kumar (2016), Chowdhury et al. (2016), Kudela and Sabbah(2016), and Rieger et al. (1984) reported periodicities in solar flaresand Mclntosh et al. (1992) examined periodicities in coronal observa-tions. Periodic and quasi-periodic variations of solar wind parameterswas reported by many researchers e.g. Mursula and Zieger (2000),Nayar et al. (2002), Valdes-Galicia and Velasco (2008), Chowdhury andDwivedi (2011), Katsavrias et al. (2012), Singh et al. (2012), Singh andBadruddin (2014), and Chowdhury et al. (2015), while the oscillationsof geomagnetic indices by Gonzalez et al. (1993), Paularena et al.(1995), Nayar et al. (2002), Mursula et al. (2003), Singh and Badruddin(2014), and Chowdhury et al. (2015) and many others. These oscilla-tions may be classified in three categories, short-term, mid-term andlong-term oscillations. The mid-term periodicities are referred to asintermediate quasi-periodicities (Lou et al., 2003; Valdes-Galicia andVelasco, 2008; Kudela et al., 2010) or quasi-biennial oscillations(QBOs) as reported by Bazilevskaya et al. (2014).

http://dx.doi.org/10.1016/j.pss.2017.02.011Received 31 December 2016; Received in revised form 2 February 2017; Accepted 16 February 2017

⁎ Corresponding author.E-mail address: yatendrapalsingh@gmail.com (Y.P. Singh).

Planetary and Space Science 138 (2017) 1–6

Available online 22 February 20170032-0633/ © 2017 Elsevier Ltd. All rights reserved.

MARK

http://www.sciencedirect.com/science/journal/00320633http://www.elsevier.com/locate/psshttp://dx.doi.org/10.1038/ncomms7491http://dx.doi.org/10.1038/ncomms7491mailto:yatendrapalsingh@gmail.comhttp://dx.doi.org/10.1016/j.pss.2017.02.011http://crossmark.crossref.org/dialog/?doi=10.1016/j.pss.2017.02.011&domain=pdf

It has been reported that the geomagnetic activity depends stronglyon the solar wind velocity and interplanetary magnetic field at theEarth's orbit (Burton et al., 1975; Echer et al., 2008; Gopalswamy et al.,2008; Alves et al., 2011; Constantin, 1989; Bothmer and Schwenn,1995; Badruddin, 1998; Badruddin and Singh, 2009; Badruddin andAslam, 2013 and references therein). The mechanism of reconnectionbetween the interplanetary magnetic field (IMF) and Earth's magneticfield due to interaction between the solar wind plasma and themagnetosphere was established by Dungey (1961). Garrett et al.(1974) reported the influence of solar wind variability on geomagneticactivity, while an empirical relationship between interplanetary condi-tions and geomagnetic disturbance parameter was given by Burton(1975).

The fluctuations in the solar wind plasma parameters includingtemporal shift in these variations play a vital role in the solar-magnetosphere coupling efficiency (Garrett et al., 1974; Kane andEcher, 2007; Singh and Badruddin, 2012; Katsavrias et al., 2016 andreferences therein). The periodicities and fluctuations in the cosmic rayintensity are intimately related to behavior/variations in solar andinterplanetary magnetic activity (e.g. Mavromichalaki et al., 2003;Modzelewska and Alania, 2013; Aslam and Badruddin, 2015; Singh andBadruddin, 2015a; Bazilevskaya, 2014 and references therein). Themagnetic field that appears at the solar surface is generated by the solardynamo located at the base of the convection zone and the differentialrotation of the sun is one of the fundamental constituent of the dynamo.The ~1.7 year periodicity is also an important phenomenon that mightbe closely linked to the solar dynamo. All the variations originate fromwithin the Sun and hence directly or indirectly reflect the internalfeatures of the Sun (Howe et al., 2000). Hence, study of the variabilityof the solar, interplanetary and geomagnetic parameters as well as thecosmic ray intensity has become an area of intense research.

2. Data and analysis technique

We have used the sunspot number, solar radio flux (10.7 cm),cosmic ray data (Oulu neutron monitor, location: 65.05°N, 25.47°E, cut-off rigidity: 0.81 GV), geomagnetic activity index Ap for the period1968–2014. The sunspot number come from http://www.sidc.be/silso/,10.7 cm solar flux from http://www.ngdc.noaa.gov/stp/solar/, geo-magnetic Ap index from http://www.ngdc.noaa.gov/stp/GEOMAG/and cosmic ray data from http://www.cosmicrays.oulu.fi/. The selecteddata was then divided into two solar magnetic cycles, one from 1968 to1989 and other from 1989 to 2014. As the solar magnetic polarityreverses around each solar maximum and the polarity repeats atalternate or subsequent maximum, therefore, we selected periods fromone maximum to an alternate maximum, which is essentially a solarmagnetic cycle (Hale cycle). Daily average data were then subjected towavelet analysis.

We used Morlet wavelet for wavelet analysis (Torrence and Compo,1998) to study the short- and mid-term periodicities of solar, geomag-netic and cosmic ray intensity. The results are obtained using a singleselected mother function and scaling parameters.

3. Results and discussion

Fig. 1 depicts the wavelet power spectrum (WPS), global waveletanalysis (GWS) and daily averaged time series of sunspot number (SSN)during the period of 1968–2014 (upper panel), 1968–1989 (middlepanel) and 1989–2014 (lower panel). The complete period covers twocomplete magnetic cycles (maximum to maximum). The contours in thewavelet power spectrum (WPS), provide information about the levels ofspectral power corresponding to each variation at different timeperiods. In each wavelet figure, yellow and green (light) areascorrespond to lower power regions and red color (light dark) areascorrespond to the regions of larger power. The colored (moderatelydark) regions, however, in all of the figures indicate the region of the

spectrum below the 95% confidence level and thick black contours arethe regions of the spectrum at the 95% confidence level. In the waveletspectrum of each wavelet figure, the variation of power is shown; thethick dashed line in the panel is the line at 95% confidence level. In allthe wavelet power spectra the Cone of Influence (COI) is also shown asit describes the region influenced by the zero padding or shows edgeeffect.

Three fluctuations (local peaks in the power spectrum) appearduring the period as seen in GWS of the figure (upper panel). In thestudy of wavelet analysis during the two magnetic cycles (middle andlower panels), we observe that 1.85 year (675 day) period is prominentvariation appears during the solar maximum and during the decreasingphases of the solar cycles; also the period is significant during the latermagnetic cycle (1989–2014). The synodic period, Rieger period, semi-annual and annual fluctuations are also observed in the time series ofsunspot number. The observed periodicities along with the peak powervalues of all the considered parameters during both the magnetic cyclesare tabulated in Table 1 and Table 2.

Fig. 1. Wavelet power (WPS), global wavelet (GWS) spectrum and variation of daily timeseries of sunspot number during 1968–2014 (upper panel), during 1968–1989 (middlepanel) and during 1989–2014 (lower panel). The cone of influence is also shown in eachWPS. The dashed line in the GWS represents the 95% significant level. The color bar ofthe figure is also shown. (For interpretation of the references to color in this figure legend,the reader is referred to the web version of this article.)

Y.P. Singh, Badruddin Planetary and Space Science 138 (2017) 1–6

2

http://www.sidc.be/silso/http://www.ngdc.noaa.gov/stp/solar/http://www.ngdc.noaa.gov/stp/GEOMAG/http://www.cosmicrays.oulu.fi/

Wavelet analysis and variation of daily average time series of solarflux (10.7 cm) is shown in Fig. 2. This band of emission originates highin the chromospheres and low in the corona of the solar atmosphere.Solar radio flux at 10.7 cm (2800 MHz) is an excellent indicator of solaractivity and the importance to study the 10.7 flux parameter forpredicting the characteristics of solar cycles (Lampropoulos et al.,2016); hence its variability is important from the earth perspective.Three local maxima in the power spectrum are appearing in the globalwavelet spectrum (GWS) of the solar flux time series of the figure(upper panel). The wavelet power spectrum of the figure appear as thestacking of the power columns around the solar maximum, indicatingthat all the variations are more pronounced during increasing, max-imum and decreasing phase of the solar cycle. The 27 days variation ismore pronounced during the solar maximum, when the solar activity ishigh. Rieger period is more pronounced during the maximum and thedecreasing phases of solar cycles 21 and 22, while ~300 day period isactive during the solar cycles 21, 22 and during the decreasing phase ofsolar cycle 23 (middle and lower panels of the figure). A quasi-variation~1.91 year (697 day) period is also appeared during the solar cycle 22and decreasing phases of the cycles 20 and 23.

Fig. 3 depicts the wavelet analysis of geomagnetic storm measuringparameter Ap index. It shows a number of fluctuations during theexamined magnetic cycles. Four periods (27 day and its secondharmonic, semi-annual and 1.61 (in former)/1.45 (in latter magneticcycle) year) are appeared as prominent fluctuation during the examinedperiod (Fig. 3, upper panel). In WPS, the signatures of second harmonicand one solar rotation variations are found throughout the periodhowever signatures of these variations are become faint during theincreasing phase of the solar cycle 24. Figure shows that the semi-annual variation is more pronounced during the 1972–2006 period. The1.61 year (586.9 day) period is one of the prominent mid-termvariations of Ap index in the former magnetic cycle (middle panel),while 1.45 year (528.9 day) period during the later magnetic cycle(lower panel). These variations are more active during the solarmaximum and decreasing phases of the solar cycles. A broad and anextended region appear around 1990, which is focused around 1.3 year

(474.5 day) period and seems to be significant as seen in the GWS ofupper panel of the figure.

Energetic charged particles travelling through the interstellar spacenearly at the speed of light are known as galactic cosmic ray particles.The wavelet analysis of cosmic ray particles during the examined periodis shown in Fig. 4. The signature of synodic period is continuouslyobserved throughout the period. The second and third harmonics ofsynodic period are observed in later magnetic cycle with weeksignatures. The good signature of Rieger period is found in formermagnetic cycle while a variation of 325.6 day is observed in latermagnetic cycle. Extended significant regions corresponding to mid-termperiods are continuously observed during the examined period in theWPS of the upper panel of the figure and more this region ispronounced during the maximum and decreasing phases of the solarcycles 20, 21 and 23 (upper panel). The power in these contours variesfrom ~1.3 year period to more than 1.9 year period, a significantvariation of 1.72 year (629 day) period is observed in all the panels ofthe figure.

Quasi-periodic variability due to solar magnetic activity bandinteraction and instabilities was discussed by Mclntosh et al. (2014).Recently, Singh and Badruddin (2015b) reported the third (9.0 days),fourth (7.0 days), fifth (5.5 days) and sixth (4.5 days) harmonics ofsynodic period of various solar wind plasma and geomagnetic para-meters. Sabbah and Kudela (2011) observed the third harmonics ofsynodic period in CR intensity. Earlier, Bai and Sturrock (1991, 1993)reported the period of 25.5 days as the fundamental period of solar flareoccurrence time and 51.0, 76.5, 102.0, 127.5 and 153.0 days oscilla-tions are the sub harmonics of the fundamental period. Valdes-Galiciaet al. (1996) gave a clue to understand the nature of solar cycle by the1.68 year period of cosmic ray. Krivova and Solanki (2002) suggested acommon origin of Rieger (154 days) and 1.3 year fluctuation and Riegerperiod is third harmonic of the 1.3 year period. The 1.7 year period isan integral multiple of Rieger period and these two variations mayappear at the same time Howe et al. (2000) hence Rieger period may bethe fourth harmonics of fundamental 1.7 year period.

In this work, we report the signature of the harmonics both lower

Table 1Observed short- and mid-term periodicities of sunspot number, 10.7 cm solar flux, ap index and cosmic ray intensity (Oulu NM) and corresponding power during the 1968–89 period.

S. No. SSN Solar flux Ap index Oulu NM

Periodicity Time Power [104] Periodicity Time Power [104] Periodicity Time Power [103] Periodicity Time Power [106]

1 9.2 d 0.342 13.6 d 0.53 27.8 d 0.10 27.8 d 0.67 26.9 d 0.72 28.8 d 0.544 45.2 d 0.415 73.4 d 0.416 157.2 d 0.13 157.2 d 1.11 180.6 d 1.27 151.9 d 0.957 337.1 d 0.19 314.5 d 1.48 1.14 yr 2.008 1.61 yr 1.88 1.72 yr 4.12

Table 2Observed short- and mid-term periodicities of sunspot number, 10.7 cm solar flux, ap index and cosmic ray intensity (Oulu NM) and corresponding power during the 1989–2014 period.

S. No. SSN Solar flux Ap index Oulu NM

Periodicity Time Power [104] Periodicity Time Power [104] Periodicity Time Power [104] Periodicity Time Power [104]

1 9.5 d 0.30 7.7 d 0.062 13.6 d 0.38 11.3 d 0.083 25.1 d 0.77 26.9 d 0.74 26.9 d 0.56 25.9 d 0.154 63.9 d 0.315 100.2 d 0.486 180.6 d 0.87 162.8 d 0.66 187.0 d 1.207 374.0 d 1.74 303.8 d 1.78 325.6 d 1.068 1.45 yr 2.329 1.85 yr 3.68 1.91 yr 4.02 1.72 yr 3.56

Y.P. Singh, Badruddin Planetary and Space Science 138 (2017) 1–6

3

and higher side of synodic period in geomagnetic index Ap during boththe magnetic cycles. The Rieger period is consistently observed in solardata (SSN, 10.7 cm solar flux) and cosmic ray data during the firstmagnetic cycle. Results show that a ~337 day quasi periodicity isobserved in SSN in addition to annual variation and near annual(~326 day) and 1.14 year periods are observed in Oulu NM time series.A quasi period of ~300 day is found in solar flux series in both themagnetic cycles besides the synodic period. The ~1.45 and ~1.72 yearperiod are observed in Ap index and Oulu NM time series respectivelyduring both the magnetic cycle and significant ~1.85 and ~1.91 yearperiods are found in SSN and solar flux in the latter magnetic cycle.Results also suggest that the observed periodicities of considered timeseries are more active during the time of solar maximum and decreasingphases of the solar cycles.

Although all the reported periodicities are not significant at 95%confidence level, however, the possibilities of their existence in otherrelated solar/interplanetary parameters needs to be explored.

4. Conclusions

In this work, we have examined short- and mid-term oscillations inthe time series of sunspot number, solar flux (10.7 cm), geomagneticindex Ap and cosmic ray intensity. For this purpose, the waveletanalysis of all the considered parameters has been performed duringthe period 1968–2014 consisting two solar magnetic cycles. Thefollowing conclusions have been drawn:

i) The sub harmonics of 27 days period both on the lower (13.5 daysand 9.0 days) and higher (51 days, 76 days and 101 days) side arepresent in the Ap index.

ii) All the short- and mid-term variations of Ap index are smoother andclear during the examined period.

iii) Solar maximum period and decreasing phases of the solar cycles aremore appropriate to study short- and mid-terms variations.

iv) Mid-term variations 1.85 year of sunspot number, 1.91 year of solar

Fig. 2. Wavelet power (WPS), global wavelet (GWS) spectrum and variation of daily timeseries of 10.7 cm solar flux during 1968 – 2014 (upper panel), during 1968–1989 (middlepanel) and during 1989–2014 (lower panel). The cone of influence is also shown in eachWPS. The dashed line in the GWS represents the 95% significant level. The color bar ofthe figure is also shown. (For interpretation of the references to color in this figure legend,the reader is referred to the web version of this article.)

Fig. 3. Wavelet power (WPS), global wavelet (GWS) spectrum and variation of daily timeseries of geomagnetic index Ap during 1968–2014 (upper panel), during 1968–1989(middle panel) and during 1989–2014 (lower panel). The cone of influence is also shownin each WPS. The dashed line in the GWS represents the 95% significant level. The colorbar of the figure is also shown. (For interpretation of the references to color in this figurelegend, the reader is referred to the web version of this article.)

Y.P. Singh, Badruddin Planetary and Space Science 138 (2017) 1–6

4

flux, 1.45 year of Ap index and 1.72 year of cosmic ray intensity aresignificant variations.

v) The observed mid-term variations ~1.3 year and ~1.7 year areintegral multiples of Rieger period. Hence, 1.3 year variation is firstand Rieger period be fourth harmonics of fundamental period ~1.7year. Moreover, there is mixing of these observed mid-termsoscillations of the time series.

Acknowledgements

We gratefully acknowledge the use of OMNI data from the NationalSpace Science Data Centre (http://www.omniweb.gsfc.nasa.gov). Wealso gratefully acknowledge the use of Oulu neutron monitor data. Wethank the Station Manager of Oulu NM (Ilya Usoskin) for making thedata available. Wavelet software provided by C. Torrence and G.Compo is acknowledged with thanks. We also thank anonymousreviewers for their helpful and constructive comments.

References

Alves, M.V., Echer, E., Gonzalez, W.D., 2011. Geoeffectiveness of solar windinterplanetary magnetic structures. J. Atmos. Sol. Terr. Phys. 73, 1380–1384.

Akioka, M., Kubota, J., Ichimoto, K., Tohmura, I., Suzuki, M., 1987. The 17-monthperiodicity of sunspot activity. Sol. Phys. 112, 313.

Aslam, O.P.M., Badruddin, 2015. Study of cosmic-ray modulation during the recentunusual minimum and mini-maximum of solar cycle 24. Sol. Phys. 290, 2333.

Badruddin, 1998. Interplanetary shocks, magnetic clouds, stream interfaces and resultinggeomagnetic disturbances. Planet. Space Sci. 46, 1015.

Badruddin, Singh, Y.P., 2009. Geoeffectiveness of magnetic cloud, shock/sheath,interaction region, high-speed stream and their combined occurrence. Planet. SpaceSci. 57, 318.

Badruddin, Aslam, O.P.M., 2013. Study of solar wind-magnetosphere coupling ondifferent time scales. Planet. Space Sci. 85, 123.

Badruddin, Kumar, A., 2016. Study of cosmic-ray modulation during the passage of ICMEsand CIRs. Sol. Phys. 291, 559.

Bothmer, V., Schwenn, R., 1995. The interplanetary and solar causes of majorgeomagnetic storms. J. Geomagn. Geoelectr. 47, 1127.

Burton, R.K., McPherron, R.L., Russell, C.T., 1975. An empirical relationship betweeninterplanetary conditions and Dst. J. Geophys. Res. 80, 4204.

Bai, T., Sturrock, P.A., 1991. The 154-day and related periodicities as sub-harmonics of afundamental period. Nature 350, 141.

Bai, T., Sturrock, P.A., 1993. Evidence for the fundamental period of the Sun: its relationto the 154-day complex of periodicities. Astrophys. J. 409, 476.

Bazilevskaya, G., Broomhall, A.-M., Elsworth, Y., Nakariakov, V.M., 2014. A combinedanalysis of the observational aspects of the quasi-biennial oscillation in the solarmagnetic activity. Space Sci. Rev. 186, 359.

Constantin, J., 1989. Analysis of geomagnetic activity with regard to different solarcauses. Ann. Geophys 7, 311.

Chowdhury, P., Dwivedi, B.N., 2011. Periodicities of sunspot number and coronal indextime series during solar cycle 23. Sol. Phys. 270, 365–383.

Chowdhury, P., Choudhary, D.P., Gosain, S., Moon, J., 2015. Short-term periodicities ininterplanetary, geomagnetic and solar phenomena during solar cycle 24. Astrophys.Space Sci. 356, 7–18.

Chowdhury, P., Kudela, K., Moon, J., 2016. A study of heliospheric modulation andperiodicities of galactic cosmic rays during cycle 24. Sol. Phys. 291 (2), 581–602.

Dungey, I.W., 1961. Interplanetary magnetic field and the auroral zones. Phys. Rev. Lett.6, 47–48.

Echer, E., Gonzalez, W.D., Tsurutani, B.T., Gonzalez, A.L.C., 2008. Interplanetaryconditions causing intense geomagnetic storms (Dstr_100 nT) during solar cycle 23(1996–2006). J. Geophys. Res. 113, A05221. http://dx.doi.org/10.1029/2007JA012744.

Garrett, H.B., Dessler, A.J., Hill, T.W., 1974. Influence of solar wind variability ongeomagnetic activity. J. Geophys. Res. 79, 4603.

Gonzalez, A.L.C., Gonzalez, W.D., Dutra, S.L.G., Tsurutani, B.T., 1993. Periodic variationin the geomagnetic activity: a study based on the Ap index. J. Geophys. Res. 98,9215–9231.

Gopalswamy, N., Akiyama, S., Yashiro, S., Michalek, G., Lepping, R.P., 2008. Solarsources and geospace consequences of interplanetary magnetic clouds observedduring solar cycle 23. J. Atmos. Sol. Terr. Phys. 70, 245–253.

Hill, M.E., Hamilton, D.C., Krimigis, S.M., 2001. Periodicity of 151 days in outerheliosphere anomalous cosmic ray fluxes. J. Geophys. Res. 106, 8315.

Howe, R., Christensen-Dalsgaard, J., Hill, F., et al., 2000. Dynamic variations at the baseof the solar convection zone. Science 287, 2456.

Kane, R.P., Echer, E., 2007. Phase shift (time) between storm-time maximum negativeexcursions of geomagnetic disturbance index Dst and interplanetary Bz. J. Atmos. Sol.Terr. Phys. 69, 1009.

Katsavrias, C., Preka-Papadema, P., Moussas, X., 2012. Wavelet analysis on solar-windparameters and geomagnetic indices. Sol. Phys. 280, 623.

Katsavrias, C., Hillaris, A., Preka–Papadema, P., 2016. A wavelet based approach to solar–terrestrial coupling. Adv. Space Res. 57 (10), 2234–2244.

Krivova, N.A., Solanki, S.K., 2002. The 1.3-year and 156-day periodicities in sunspot data:wavelet analysis suggests a common origin. Astron. Astrophys. 394, 701.

Kudela, K., Rybak, J., Antalova, A., Storini, M., 2002. Time evolution of the low-frequency periodicities in cosmic ray intensity. Sol. Phys. 205, 165–175.

Kudela, K., Mavromichalaki, H., Papaioannou, A., Gerontidou, M., 2010. On mid- termperiodicities in cosmic rays. Sol. Phys 266, 173.

Kudela, K., Sabbah, I., 2016. Quasi-periodic variations of low energy cosmic rays. Science59, 547.

Lampropoulos, G., Mavromichalaki, H., Tritakis, V., 2016. Possible estimation of the solarcycle characteristic parameters by the 10.7 cm solar radio flux. Sol. Phys. 291, 989.

Lou, Y.-Q., Wang, Y.-M., Fan, Z., Wang, S., Wang, J.X., 2003. Periodicities in solar coronalmass ejections. Mon. Not. R. Astron. Soc. 345, 809–818.

Maeda, K., 1967. Quasi-biennial cycles in cosmic-ray intensity. J. Atmos. Sci. 24, 320.Mavromichalaki, H., Preka-Papadema, P., Liritzis, I., Petropoulos, B., Kurt, V., 2003.

Short-term variations of cosmic-ray intensity and flare related data in 1981–1983.New Astron. 8, 777.

Mclntosh, P.S., Thompson, R.J., Willock, E.C., 1992. A 600-day periodicity in solarcoronal holes. Nature 360, 322–324.

Mclntosh, S.W., Leamon, R.J., Krista, L.D., Title, A.M., Hudson, H.S., Riley, P., Harder,J.W., Kopp, G., Snow, M., Woods, T.N., Kasper, J.C., Stevens, M.L., Ulrich, R.K., 2014.The solar magnetic activity band interaction and instabilities that shape quasi-periodic variability. Nat. Commun. 6, 6491. http://dx.doi.org/10.1038/ncomms7491.

Fig. 4. Wavelet power (WPS), global wavelet (GWS) spectrum and variation of daily timeseries of cosmic ray intensity (Oulu NM) during 1968–2014 (upper panel), during 1968–1989 (middle panel) and during 1989–2014 (lower panel). The cone of influence is alsoshown in each WPS. The dashed line in the GWS represents the 95% significant level. Thecolor bar of the figure is also shown. (For interpretation of the references to color in thisfigure legend, the reader is referred to the web version of this article.)

Y.P. Singh, Badruddin Planetary and Space Science 138 (2017) 1–6

5

http://www.omniweb.gsfc.nasa.govhttp://refhub.elsevier.com/S0032-0633(16)30497-4/sbref1http://refhub.elsevier.com/S0032-0633(16)30497-4/sbref1http://refhub.elsevier.com/S0032-0633(16)30497-4/sbref2http://refhub.elsevier.com/S0032-0633(16)30497-4/sbref2http://refhub.elsevier.com/S0032-0633(16)30497-4/sbref3http://refhub.elsevier.com/S0032-0633(16)30497-4/sbref3http://refhub.elsevier.com/S0032-0633(16)30497-4/sbref4http://refhub.elsevier.com/S0032-0633(16)30497-4/sbref4http://refhub.elsevier.com/S0032-0633(16)30497-4/sbref5http://refhub.elsevier.com/S0032-0633(16)30497-4/sbref5http://refhub.elsevier.com/S0032-0633(16)30497-4/sbref5http://refhub.elsevier.com/S0032-0633(16)30497-4/sbref6http://refhub.elsevier.com/S0032-0633(16)30497-4/sbref6http://refhub.elsevier.com/S0032-0633(16)30497-4/sbref7http://refhub.elsevier.com/S0032-0633(16)30497-4/sbref7http://refhub.elsevier.com/S0032-0633(16)30497-4/sbref8http://refhub.elsevier.com/S0032-0633(16)30497-4/sbref8http://refhub.elsevier.com/S0032-0633(16)30497-4/sbref9http://refhub.elsevier.com/S0032-0633(16)30497-4/sbref9http://refhub.elsevier.com/S0032-0633(16)30497-4/sbref10http://refhub.elsevier.com/S0032-0633(16)30497-4/sbref10http://refhub.elsevier.com/S0032-0633(16)30497-4/sbref11http://refhub.elsevier.com/S0032-0633(16)30497-4/sbref11http://refhub.elsevier.com/S0032-0633(16)30497-4/sbref12http://refhub.elsevier.com/S0032-0633(16)30497-4/sbref12http://refhub.elsevier.com/S0032-0633(16)30497-4/sbref12http://refhub.elsevier.com/S0032-0633(16)30497-4/sbref13http://refhub.elsevier.com/S0032-0633(16)30497-4/sbref13http://refhub.elsevier.com/S0032-0633(16)30497-4/sbref14http://refhub.elsevier.com/S0032-0633(16)30497-4/sbref14http://refhub.elsevier.com/S0032-0633(16)30497-4/sbref15http://refhub.elsevier.com/S0032-0633(16)30497-4/sbref15http://refhub.elsevier.com/S0032-0633(16)30497-4/sbref15http://refhub.elsevier.com/S0032-0633(16)30497-4/sbref16http://refhub.elsevier.com/S0032-0633(16)30497-4/sbref16http://refhub.elsevier.com/S0032-0633(16)30497-4/sbref17http://refhub.elsevier.com/S0032-0633(16)30497-4/sbref17http://dx.doi.org/10.1029/2007JA012744http://dx.doi.org/10.1029/2007JA012744http://refhub.elsevier.com/S0032-0633(16)30497-4/sbref19http://refhub.elsevier.com/S0032-0633(16)30497-4/sbref19http://refhub.elsevier.com/S0032-0633(16)30497-4/sbref20http://refhub.elsevier.com/S0032-0633(16)30497-4/sbref20http://refhub.elsevier.com/S0032-0633(16)30497-4/sbref20http://refhub.elsevier.com/S0032-0633(16)30497-4/sbref21http://refhub.elsevier.com/S0032-0633(16)30497-4/sbref21http://refhub.elsevier.com/S0032-0633(16)30497-4/sbref21http://refhub.elsevier.com/S0032-0633(16)30497-4/sbref22http://refhub.elsevier.com/S0032-0633(16)30497-4/sbref22http://refhub.elsevier.com/S0032-0633(16)30497-4/sbref23http://refhub.elsevier.com/S0032-0633(16)30497-4/sbref23http://refhub.elsevier.com/S0032-0633(16)30497-4/sbref24http://refhub.elsevier.com/S0032-0633(16)30497-4/sbref24http://refhub.elsevier.com/S0032-0633(16)30497-4/sbref24http://refhub.elsevier.com/S0032-0633(16)30497-4/sbref25http://refhub.elsevier.com/S0032-0633(16)30497-4/sbref25http://refhub.elsevier.com/S0032-0633(16)30497-4/sbref26http://refhub.elsevier.com/S0032-0633(16)30497-4/sbref26http://refhub.elsevier.com/S0032-0633(16)30497-4/sbref27http://refhub.elsevier.com/S0032-0633(16)30497-4/sbref27http://refhub.elsevier.com/S0032-0633(16)30497-4/sbref28http://refhub.elsevier.com/S0032-0633(16)30497-4/sbref28http://refhub.elsevier.com/S0032-0633(16)30497-4/sbref29http://refhub.elsevier.com/S0032-0633(16)30497-4/sbref29http://refhub.elsevier.com/S0032-0633(16)30497-4/sbref30http://refhub.elsevier.com/S0032-0633(16)30497-4/sbref30http://refhub.elsevier.com/S0032-0633(16)30497-4/sbref31http://refhub.elsevier.com/S0032-0633(16)30497-4/sbref31http://refhub.elsevier.com/S0032-0633(16)30497-4/sbref32http://refhub.elsevier.com/S0032-0633(16)30497-4/sbref32http://refhub.elsevier.com/S0032-0633(16)30497-4/sbref33http://refhub.elsevier.com/S0032-0633(16)30497-4/sbref34http://refhub.elsevier.com/S0032-0633(16)30497-4/sbref34http://refhub.elsevier.com/S0032-0633(16)30497-4/sbref34http://refhub.elsevier.com/S0032-0633(16)30497-4/sbref35http://refhub.elsevier.com/S0032-0633(16)30497-4/sbref35http://dx.doi.org/10.1038/ncomms7491http://dx.doi.org/10.1038/ncomms7491

Modzelewska, R., Alania, M.V., 2013. The 27-day cosmic ray intensity variations duringsolar minimum 23/24. Sol. Phys. 286, 593–607.

Mursula, K., Zieger, B., 2000. The 1.3 year variation in solar wind speed and geomagneticactivity. Adv. Space Res. 25, 1939.

Mursula, K., Zieger, B., Vilppola, J.H., 2003. Mid-term quasi-periodicities in geomagneticactivity during the last 15 solar cycles: connection to solar dynamo strength. Sol.Phys. 212, 201–207.

Nayar, S.R.P., Radhika, V.N., Revathy, K., Ramadas, V., 2002. Wavelet analysis of solarwind and geomagnetic parameter. Sol. Phys. 208, 359.

Paularena, K.I., Szabo, A., Richardson, J.D., 1995. Coincident 1.3-year periodicities in theap geomagnetic index and the solar wind.Geophys. Res. Lett. 22, 3001–3004.

Potgieter, M.S., 2014. Modulation of galactic protons in the heliosphere during theunusual solar minimum of 2006 to 2009. Sol. Phys. 289, 391–406.

Rybak, J., Antalova, A., Storini, M., 2001. The wavelet analysis of the solar and cosmicray data. Space Sci. Rev. 97, 359–362.

Rieger, E., Kanbach, G., Reppin, C., Share, G.H., Forrest, D.J., Chupp, E.L., 1984. A 154-day periodicity in the occurrence of hard solar flares. Nature 312, 623.

Sabbah, I., Kudela, K., 2011. Third harmonic of the 27-day periodicity of galactic cosmicray: coupling with interplanetary parameters. J. Gophys. Res. 116, A04103.

Singh, Y.P., Badruddin, 2012. Study of the influence of magnetic fluctuations and solar

plasma density on the solar wind-magnetosphere coupling. J. Atmos. Sol. Terr. Phys.75–76, 15.

Singh, Y.P., Gautam, S., Badruddin, 2012. Temporal variations of short- and mid-termperiodicities in solar wind parameters and cosmic ray intensity. J. Atmos. Sol. Terr.Phys. 89, 48.

Singh, Y.P., Badruddin, 2014. Prominent short-, mid-, and long-term periodicities in solarand geomagnetic activity: wavelet analysis. Planet. Space Sci. 96, 120.

Singh, Y.P., Badruddin, 2015a. Short-term variations of cosmic ray particles during therecent deep solar minimum and the previous four solar minima: a wavelet analysis.Sol. Phys. 290, 3071.

Singh, Y.P., Badruddin, 2015b. Solar-rotational oscillation and its harmonics in the solar-wind, geomagnetic and cosmic ray particles during the last two solar minima.Astrophys. Space Sci. 359, 60.

Torrence, C., Compo, G.P., 1998. A practical guide to wavelet analysis. Bull. Am.Meteorol. Soc. 79 (1), 61–78.

Valdes-Galicia, J.F., Perez-Enriquez, R., Otaola, J.A., 1996. The cosmic ray 1.68-yearvariation: a clue to understand the nature of the solar cycle. Sol. Phys. 167, 409.

Valdes-Galicia, J.F., Velasco, V.M., 2008. Variations of mid-term periodicities in solaractivity physical phenomena. Adv. Space Res. 41, 297–305.

Y.P. Singh, Badruddin Planetary and Space Science 138 (2017) 1–6

6

http://refhub.elsevier.com/S0032-0633(16)30497-4/sbref37http://refhub.elsevier.com/S0032-0633(16)30497-4/sbref37http://refhub.elsevier.com/S0032-0633(16)30497-4/sbref38http://refhub.elsevier.com/S0032-0633(16)30497-4/sbref38http://refhub.elsevier.com/S0032-0633(16)30497-4/sbref39http://refhub.elsevier.com/S0032-0633(16)30497-4/sbref39http://refhub.elsevier.com/S0032-0633(16)30497-4/sbref39http://refhub.elsevier.com/S0032-0633(16)30497-4/sbref40http://refhub.elsevier.com/S0032-0633(16)30497-4/sbref40http://refhub.elsevier.com/S0032-0633(16)30497-4/sbref41http://refhub.elsevier.com/S0032-0633(16)30497-4/sbref41http://refhub.elsevier.com/S0032-0633(16)30497-4/sbref42http://refhub.elsevier.com/S0032-0633(16)30497-4/sbref42http://refhub.elsevier.com/S0032-0633(16)30497-4/sbref43http://refhub.elsevier.com/S0032-0633(16)30497-4/sbref43http://refhub.elsevier.com/S0032-0633(16)30497-4/sbref44http://refhub.elsevier.com/S0032-0633(16)30497-4/sbref44http://refhub.elsevier.com/S0032-0633(16)30497-4/sbref45http://refhub.elsevier.com/S0032-0633(16)30497-4/sbref45http://refhub.elsevier.com/S0032-0633(16)30497-4/sbref46http://refhub.elsevier.com/S0032-0633(16)30497-4/sbref46http://refhub.elsevier.com/S0032-0633(16)30497-4/sbref46http://refhub.elsevier.com/S0032-0633(16)30497-4/sbref47http://refhub.elsevier.com/S0032-0633(16)30497-4/sbref47http://refhub.elsevier.com/S0032-0633(16)30497-4/sbref47http://refhub.elsevier.com/S0032-0633(16)30497-4/sbref48http://refhub.elsevier.com/S0032-0633(16)30497-4/sbref48http://refhub.elsevier.com/S0032-0633(16)30497-4/sbref49http://refhub.elsevier.com/S0032-0633(16)30497-4/sbref49http://refhub.elsevier.com/S0032-0633(16)30497-4/sbref49http://refhub.elsevier.com/S0032-0633(16)30497-4/sbref50http://refhub.elsevier.com/S0032-0633(16)30497-4/sbref50http://refhub.elsevier.com/S0032-0633(16)30497-4/sbref50http://refhub.elsevier.com/S0032-0633(16)30497-4/sbref51http://refhub.elsevier.com/S0032-0633(16)30497-4/sbref51http://refhub.elsevier.com/S0032-0633(16)30497-4/sbref52http://refhub.elsevier.com/S0032-0633(16)30497-4/sbref52http://refhub.elsevier.com/S0032-0633(16)30497-4/sbref53http://refhub.elsevier.com/S0032-0633(16)30497-4/sbref53

Short- and mid-term oscillations of solar, geomagnetic activity and cosmic-ray intensity during the last two solar magnetic cyclesIntroductionData and analysis techniqueResults and discussionConclusionsAcknowledgementsReferences