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2 Planetary and Space Science 96 (2014) Contents lists available at ScienceDirect Planetary and Space Science journal homepage: Prominent short-, mid-, and long-term periodicities in solar and geomagnetic activity: Wavelet analysis Y.P. Singh a,n, Badruddin b a IET, Mangalayatan University, Aligarh , India b Department of Physics, Aligarh Muslim University, Aligarh , India article info Article history: Received 27 October 2013 Received in revised form 19 February 2014 Accepted 28 March 2014 Available online 12 April 2014 Keywords: Wavelet analysis Solar activity Sunspot number Geomagnetic activity abstract Study of periodicities in solar and geomagnetic parameters has been useful in relating solar variability to variations in other phenomena in order to search for the solar cause of, and effects in, the variability observed in near earth space environment. Implementing wavelet analysis on daily, monthly and yearly time resolution data of sunspot number and geomagnetic aa-index, we observed periodicities of 27.8-, 157-, 370-days, and 2.2-, 5.5-, 11-, 22.7-, 38.6-years in the sunspot spot number and 13.8-, 26.6-, 185-days, and 5.3-, 11-, 30-, 46-years in the geomagnetic aa-index. We discuss these periodicities, relation between solar and geomagnetic periodicities and their implications for near-earth space environmental effects. & 2014 Elsevier Ltd. All rights reserved. 1. Introduction The variability in the solar output is responsible for the changes in the solar environment and these variations affect the Earth's environment as well as the environment around other planets. This variability disturbs the geomagnetic activity and produces geomagnetic storms of various amplitudes. Long range of periodic and non-periodic variations in the solar activity data have been reported in previous studies. On the basis of all the observed variations, they are grouped into three broad categories, short-, mid- and long-term periods. Variations of different periods in solar, interplanetary plasma, geomagnetic activity and cosmic ray intensity data have been reported in the past (e.g. Svalgaard and Wilcox, 1975; Bolton, 1990; Alicia et al., 1993; Richardson et al., 1994; Mursula and Zieger, 1996, 2000; Nayar et al., 2001, 2002; Kudela et al., 1993, 2010; Valdes-Galicia et al., 1996; Mavromichalaki et al., 2003a, 2003b; Alania et al., 2008; Sabbah and Kudela, 2009, 2011; Laurenza and Storini, 2009; Chowdhury et al., 2010; Ahluwalia, 2012; Katsavrias et al., 2012; Perez-Peraza et al., 2012; Singh et al., 2012). The geomagnetic activity depends strongly on the solar wind velocity and interplanetary magnetic field at the Earth's orbit (e.g., see Badruddin, 1998; Badruddin and Singh, 2009; Singh and Badruddin, 2012 and references there in). The 1 2 years of periodicities have been reported in solar wind velocity, geomagnetic activity and cosmic ray intensity (Bolton, 1990). Solar wind and geomagnetic activity index Ap were found to exhibit around 1.3- years during even cycles and around years during odd cycles (Valdes-Galicia et al., 1996; Mursula and Zieger, 2000). The 154-day periodicity in solar flare activity, 10.7 cm radio flux, sunspot number and global magnetic field were reported by many authors (e.g. Rieger et al., 1984; Bai and Sturrock, 1993 and others). Although a long range of periodicities have been reported in various solar, cosmic and geomagnetic parameters starting from short- to long-term, but the exact cause of many of the periodicities are still unknown. However, few well known periodicities like days from minimum to maximum epochs relate to helio-latitudinal distribution of active region. Few periodicities are sub harmonics of a fundamental period reported in many papers (e.g. Bai and Sturrock, 1991; Krivova and Solanki, 2002; Sabbah and Kudela, 2011). There are quasi-biennial variations in solar activity like years(hathaway, 2010) and associated with double peaks of the solar cycle. Besides these, regular and quasi-biennial variations, there are many ephemeral periodicities in the solar, geomagnetic activity and cosmic ray data (e.g. Polygiannakis et al., 2002; Rouillard and Lockwood, 2004; Mavromichalaki et al., 2003a; Alania et al., 2008; Laurenza and Storini, 2009; Sabbah and Kudela, 2011; Singh et al., 2012). However, the study of periodicities of different periods using data of different time resolutions is still required. 2. Data and analysis technique n Corresponding author. Tel.: þ addresses: yatendrapalsingh@gmail.com (Y.P. Singh), badr.physamu@gmail.com (Badruddin). In this work, we have utilized the three different time resolution data of solar activity parameter sunspot number (SSN) and /& 2014 Elsevier Ltd. All rights reserved.

3 Y.P. Singh, Badruddin / Planetary and Space Science 96 (2014) geomagnetic parameter (aa-index) averaged over three time resolutions, daily, monthly and yearly. About 160-years ( ) daily SSN data, 260-years ( ) of monthly SSN data and 310-years ( ) of yearly SSN data, in addition to about 140-years ( ) of daily, monthly and yearly aa-index data have been utilized in this work. These data were subjected to wavelet analysis. Utilizing the wavelet software developed by C. Torrence and G. Compo ( sunspot numbers and geomagnetic aa-index data with three time resolutions have been analyzed using Morlet wavelet, and both the global spectra and scalogram were obtained to study the presence and evolution of various periodicities. The results have been obtained using a single selected mother function and selected scaling parameters. In the wavelet power spectrum (WPS), the contours provide information about the levels of spectral power corresponding to each variation at different time periods. The yellow and green areas correspond to lower power regions and red color areas correspond to the regions of larger power. The colored regions, however in all the figures indicate the region of the spectrum below the 95% confidence level and thick (black line) contours are the regions of the spectrum at the 95% confidence level. In global power spectrum (right panel) of the each wavelet figure the variation of power is shown with period, the thick dashed line in the panel is the line at 95% confidence level. The Cone of Influence (COI) is also shown in all the wavelet power spectra that describe the region influenced by the zero padding or shows edge effect. 3. Results and discussion Fig. 1 shows the wavelet power spectrum and corresponding global wavelet spectrum (GWS) of yearly sunspot number. In the wavelet power spectrum of the figure, three long-term variations can be seen. The well-known Schwabe ( 11 year) variation is dominating and significant variation seen in both the spectra (WPS and GWS). This variation was first demonstrated by Schwabe (1843). The whole time length of the 11-year variation in the wavelet power spectrum is divided in to two significant contours. The first significant contour is observed around the years 1725 to 1790, while the other starts around 1830 and lasts till In between these two contours, feeble signature of Schwabe period is observed. This period may be of interest from the point of view of solar physicists. Since there are more temporal variations (WPS of Fig. 1) in this periodicity, therefore power distribution around the variation is broad at the base. Periodicities 5-year and 52- years are the other observed long-term variations in the yearly SSN data. These variations are observed in the GWS spectrum of the figure with low-peak power values. The 5-year variation shows random behavior in the GWS, but 52-year variation is more prominent during Le and Wang (2003) found that 53-year variation is dominant during and has much higher power than that of 11-year variation. Signature of a period 36-year (38.6-year) seen in WPS of the figure is worth mentioning. This is one of the controversial variations the Bruckner cycle (Bruckner, 1890) mainly observed in the climate data (e.g. Henry, 1927; Raspopov et al., 2004). Since the power of this variation is not high enough, it appears only in the WPS, during Fig. 2 shows the WPS and GWS of monthly average SSN. In the spectrum three well known, and one controversial variation, are observed with different power values. 11-year variation is the dominating and highly significant variation, which is found throughout the time length of the SSN. From the wavelet power spectrum it is also clear that there is about 1 2 years of temporal variation in the upper and lower boundaries of the 11-year variation contour, but the lower (high periodicity) side boundary is smoother than upper one. The power density of this variation is more pronounced during followed by during , and then around The study of wavelet power spectrum of this figure is important in view of the clear signature of the controversial Bruckner cycle (36-year) and can be easily seen during However, this cycle is apparently less pronounced with week signatures in the spectrum obtained using yearly average SSN data. This periodicity was observed in climate data. Fig. 4 shows the WPS and corresponding GWS of yearly averages geomagnetic aa-index data. The well-known 11-year periodicity variation is dominant variation in both the spectra. Although seen throughout the spectrum, this variation is more pronounced around 1920 and during In the GWS, there are two signatures of smaller amplitudes, one corresponds to 22-year and other 32-years. The former is more pronounced in the early phase, while the later during the end phase of the spectrum. The distribution of the powers of these two variations in the WPS is not good, as both the power peaks corresponding to these variations lie below the 95% confidence level, but their signatures are reeled in the power spectrum. The digital values of power give six periodic variations in the wavelet analysis of monthly aa-data. These variations are of 6-month, 5.2-year, 11.0-year, 23.5-year, 31.4-year and 45-year period. The 11-year variation is the most dominating variation of the data and more pronounced during and from 1980 Fig. 1. Wavelet power (a) and global wavelet (b) spectrum for yearly sunspot number (SSN) during The cone of influence is also shown in WPS. The dashed line in GWS represents the 95% significant level. (a) SSN WPS and (b) GWS. (For interpretation of the references to color in this figure, the reader is referred to the web version of this article.) Fig. 2. Same as Fig. 1, but for monthly sunspot number (SSN) during (For interpretation of the references to color in this figure, the reader is referred to the web version of this article.)

4 122 Y.P. Singh, Badruddin / Planetary and Space Science 96 (2014) Table 1 Observed periodicities and corresponding power determined from wavelet analysis of daily SSN and aa-index data. S. no. Sunspot number aa-index Periodicity time Power ( 10 5 ) Periodicity time Power ( 10 3 ) Fig. 3. Same as Fig. 1, but for daily sunspot number (SSN) during The horizontal axis shows number of days starting from January 01, (For interpretation of the references to color in this figure, the reader is referred to the web version of this article.) days days days days days days years years years years years years years years years 1.78 Fig. 4. Same as Fig. 1, but for yearly geomagnetic aa data during (For interpretation of the references to color in this figure, the reader is referred to the web version of this article.) to 2010, as shown in Fig. 5. This variation is smoother in the wavelet spectrum of aa-index as compared to that in monthly SSN wavelet spectrum. The 22-year variation is observed in the early phase of the spectrum and lasts till A feeble signature of period 31 year is found after 1960 in the spectrum. One more variation of period 45-year is observed after 1960 in this spectrum. The close-up view of the wavelet spectrum shows that there is coupling at some level between the 22-, 31- and 45-years of variations. The digital values of all the observed periodic variations along with the power using daily time resolution data and monthly and yearly data of SSN and aa-data are given in Tables 1 and 2 respectively. In addition to monthly and yearly data, we have obtained the WPS and GPS of daily average sunspot number (see Fig. 3). In the daily resolution data, we have observed regular periodicities of 27.8-day, 157-day, 1-, 2.2-, 5.5-, 11-, and 38.6-year. In Tables 1 and 2, we have tabulated each observed periodicity along with its peak power value, for both the parameters SSN and aa, and for all three time resolutions. From these tables it is clear that maximum power is distributed around 11-year variation and minimum around the Rieger period. The well known 11-year variation has maximum peak power value followed by 38.6-year and then 22.7 year variations. Black contours of 27.8-day variation is prominently observed after 1920, however, 1.0-year variation show normal behavior, 2.2- and 5.5-year variations show random behavior, while the 11-year variation shows continuous behavior throughout the time span in the wavelet power spectrum. Study of WPS shows a feeble signature of 38.6-year variation in the spectrum after This is one of the controversial periodicity that has been observed in climate data. The 154-day periodicity was first detected by Rieger et al. (1984) in gamma-ray flare activity and later recognized in the solar flare rate, the 10.7-cm radio flux, sunspot number and the global magnetic field of the sun (Lean, 1990; Cane et al., 1998). The interpretation of this periodicity was given by Bai and Sturrock (1993). Katsavrias et al. (2012) reported that the quasi-biennial (1.3 2 years) variations were associated with double peak solar cycle (see review by Hathaway (2010)). Kudela (2012) reported periodicities of 156- day and 1.7-, 2.3-, 5.5-, 6.4-, 8.2-, and 11-year in cosmic ray data during The wavelet study of daily average geomagnetic aa-index gives periodicities at 13.8-, 26.6-, 185-day, 5.3-, 11-, 30- and 46-years of variations. These periodicities are listed along with power in Tables 1 and 2. Significant 11-year variation is observed with maximum peak power followed by 5.3-year, 30.0-year, 46.0 year, 185-day and then 26.6-day. The second harmonics of 27-day variation are also observed with lesser power value. Short- and mid-term variations of aa-index are tabulated in Tables 1 and 2, while long-term variations are shown in Fig. 6. The well known 27-day periodicity has been reported in solar data (SSN, solar irradiance) by Bower (1992), Nayar et al. (2002), and Chowdhury and Dwivedi (2011), interplanetary data (solar wind velocity, IMF) and terrestrial magnetism (Ap, kp) by Nayar et al. (2002) and Singh et al. (2012) and ground-based cosmic ray data by Singh et al. (2012), Sabbah and Kudela (2011) and others. The periodicities closer to 154-day observed in SSN data in this study has been reported in solar flare activity (155-day) by Ichimoto et al. (1985), ( day) by Oliver et al. (1998), sunspot area ( day) by Verma et al. (1992), interplanetary plasma velocity IMF (153-day) by Cane et al. (1998), coronal index (155- day) by Chowdhury and Dwivedi (2011), geomagnetic parameter Ap (154-day) by Nayar et al. (2002) and cosmic ray intensity (150-day) by Kudela et al. (2002). However in geomagnetic aa-index data, we detected semi-annual periodicity (185-day). A periodicity close to 30-year is detected using geomagnetic aa-index data of daily (30- year), monthly (31.4-year) and yearly (31-year) time resolutions. It is interesting to note that a periodicity of around 30 year (the socalled three cycle quasi-periodicity) in cosmic ray data has been reported earlier by Ahluwalia (1997, 2012) and Perez-Peraza et al. (2012). As aa-index has been reported closely following the global surface temperature data (Cliver et al., 1998), it will be interesting to see if the 30-year periodicity observed in aa-indices data is also related to 30-year periodicity reported in all India summer monsoon rainfall data (Agnihotri et al., 2002; Agnihotri and Dutta, 2003); it will be further evidence of sun-climate relationship.

5 Y.P. Singh, Badruddin / Planetary and Space Science 96 (2014) Table 2 Periodicities and peak power found from wavelet analysis of monthly and yearly averaged SSN and aa-index. S. no. Monthly Yearly Sunspot number aa-index Sunspot number aa-index Periodicity time Power ( 10 5 ) Periodicity time Power ( 10 3 ) Periodicity time Power 10 4 ) Periodicity time Power ( 10 3 ) 1. 6 months years years years years years years years years years years years years years years years years years We have observed periodicity of 38.6 years in SSN data and 30 years in geomagnetic data, closer to Bruckner climate cycle ( 35 years) reported in climate data. Acknowledgments We gratefully acknowledge the use of NOAA, National Geophysical Data Centre, USA based sunspot number data, and World Data Center, Kyoto based geomagnetic aa-index data. Wavelet software provided by C. Torrence and G. Compo is also acknowledged with thanks. We also thank the reviewer for helpful comments and suggestions. Fig. 5. Same as Fig. 1, but for monthly geomagnetic aa data during (For interpretation of the references to color in this figure, the reader is referred to the web version of this article.) Fig. 6. Same as Fig. 1, but for daily geomagnetic aa data during The horizontal axis shows number of days starting from January 01, (For interpretation of the references to color in this figure, the reader is referred to the web version of this article.) 4. Conclusions 1. Wavelet analysis of yearly sunspot number and geomagnetic aa-index reveal periodicities, in order of decreasing power as 11-years, 38.6-years, 22.7-years. In addition, many more periodicities have also been observed. In geomagnetic data, the periodicities in order of decreasing power are 11-years, 5.3- years, 30-years and 46-years and 6-months and some others. 2. The 11 years periodicity is found to be the most significant periodicity in SSN as well as in aa-index data using daily, monthly and yearly data, in agreement with earlier studies. 3. Periodicities of 27 days, 5.3 years, and 11 years in both SSN and aa-index data suggest that at least these periodicities in geomagnetism have solar origin. References Agnihotri, R., Dutta, K., Centennial scale variation in monsoon rainfall (Indian, east equatorial and Chinese monsoon): manifestations of solar activity. Curr. Sci. 85, 459. Agnihotri, R., Dutta, K., Bhushan, R., Somayajulu, B.L.K., Evidence for solar forcing on the Indian monsoon during the last millennium. Earth Planet. Sci. Lett. 198, 521. Ahluwalia, H.S., Three activity cycle periodicity in galactic cosmic rays? In: Proceedings of the 25th International Cosmic Ray Conference, vol. 2, Durban, p Ahluwalia, H.S., Three-cycle quasi-periodicity in solar, geophysical, cosmicray data and global climate change. Indian J. Radio Space Phys. 41, 509. Alicia, L.C.G., Gonzalez, W.D., Dutra, S.L.G., Tsurutani, B.T., Periodic variation in the geomagnetic activity: a study based on the Ap index. J. Geophys. Res. 98, Alania, M.V., Gil, A., Modzelewska, R., Study of the 27-day variations of the galactic cosmic ray intensity and anisotropy. Adv. Space Res. 41, 280. Badruddin, Interplanetary shocks, magnetic clouds, stream interfaces and resulting geomagnetic disturbances. Planet. Space Sci. 46, Badruddin, Singh, Y.P., Geoeffectiveness of magnetic cloud, shock/sheath, interaction region, high-speed stream and their combined occurrence. Planet. Space Sci. 57, 318. Bai, T., Sturrock, P.A., The 154-day and related periodicities as subharmonics of a fundamental period. Nature 350, 141. Bai, T., Sturrock, P.A., Evidence for the fundamental period of the Sun: Its relation to the 154-day complex of periodicities. Astrophys. J. 409, 476. Bolton, S.J., One year variations in the near earth solar wind ion density and bulk flow speed. Geophys. Res. Lett. 17, 37. Bower, S.D., Periodicities of solar irradiance and solar activity indices, II. Sol. Phys. 142, 365. Bruckner, E., Klimaschwankungen seit 1700 nebenst Bemerkungen uber die Klimaschwankungen der Diluvialzeit. Geogr. Abh. IV (2), 153. Cane, H.V., Richardson, I.G., von Rosenvinge, T.T., Interplanetary magnetic field periodicity of 153 days. Geophys. Res. Lett. 25, Chowdhury, P., Khan, M., Ray, P.C., Evaluation of the intermediate-term periodicities in solar and cosmic ray activities during cycle 23. Astrophys. Space Sci. 326, 191. Chowdhury., P., Dwivedi, B.N., Periodicities of sunspot number and coronal index time series during solar cycle 23. Sol. Phys. 270, 365. Cliver, E.W., Borikoff, V., Feynman, J., Solar variability and climate change: geomagnetic aa index and global surface temperature. Geophys. Res. Lett. 25, Hathaway, D.H., The solar cycle. Living Rev. Sol. Phys. 7, 1. Henry, A.J., The Bruckner cycle of climatic oscillations in the United States. Ann. Assoc. Am. Geogr. 17 (2), 60. Ichimoto, K., Kubota, J., Suzuki, M., Tohmura, I., Kurokawa, H., Periodic behavior of solar flare activity. Nature 316, 422.

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