Two-phase storm profile of global electron content in the ionosphere and plasmasphere of the Earth

Transcription

1 JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 117,, doi:1.129/212ja1817, 212 Two-phase storm profile of global electron content in the ionosphere and plasmasphere of the Earth T. L. Gulyaeva 1,2 and I. S. Veselovsky 3,4 Received 9 June 212; revised 22 August 212; accepted 22 August 212; published 29 September 212. [1] The global electron content (GEC) derivation is initiated by summing up the total electron content of each cell of Global Positioning System GPS-TEC global map multiplied by the cell area. Algorithm of GEC calculation is improved in the present paper using the electron density varying with height through the total volume of a spherical layer in near-earth space up to 2,2 km (GPS orbit) reconstructed from TEC with the International Reference Ionosphere model extended to the Plasmasphere (IRI-Plas). An analytical model is first derived for two-phase typical GEC storm profile by a common epoch analysis of 1 storms during with the starting time put at the origin of the negative phase of GEC departure from the quiet reference (5 day median). It is found that GEC depletion occurs synchronously with decrease of the solar wind velocity and the outset of recovery of the magnetospheric ring current (the equatorial Dst index) and the auroral electrojet (AE index). Thus, the GEC is an indicator of the plasma injection in the ionosphere and plasmasphere with the solar wind energy inducing the positive phase of GEC storm during 24 h with electron number increased by 1 2% followed by a negative phase with GEC decrease by 1 2% during 4 h of a plasma release (ejection) into the magnetosphere tail beyond the three Earth radii (GPS orbit). Citation: Gulyaeva, T. L., and I. S. Veselovsky (212), Two-phase storm profile of global electron content in the ionosphere and plasmasphere of the Earth, J. Geophys. Res., 117,, doi:1.129/212ja Introduction [2] The parameter of global electron content (GEC) has been introduced by Afraimovich et al. [26a]. By definition, GEC is equal to the total number of electrons in the near-earth space (NES), limited by the orbit height of the navigation satellites of Global Positioning System (GPS), 2,2 km. The advantage of GEC parameter is the possibility to analyze the state and variability of the ionosphere and the plasmasphere as a whole similar to planetary averaged the F2 layer ionization [Lal, 1997] and the planetary derived the ionosphere storm index [Gulyaeva and Stanislawska, 28], while most other parameters are bound to local or regional features of the near-earth plasma. [3] The calculations of GEC advanced due to advent of the Global Ionospheric Maps (GIM) of the total electron content produced by the International Geodetic Service, IGS, Data Analysis Centers [Afraimovich and Perevalova, 26]. The calculations are based on measurements of the integral total electron content (TEC) by the satellite navigation GPS 1 IZMIRAN, Moscow, Russia. 2 Space Research Center, PAS, Warsaw, Poland. 3 Skobeltsyn Institute of Nuclear Physics, Moscow State University, Moscow, Russia. 4 Space Research Institute, RAS, Moscow, Russia. Corresponding author: T. L. Gulyaeva, IZMIRAN, Troitsk, Moscow, Russia. (gulyaeva@izmiran.ru) 212. American Geophysical Union. All Rights Reserved /12/212JA1817 system, permanently recorded in the worldwide observation network, and processed for global spatial interpolation in several Data Analysis Centers in the form of global ionospheric maps, GIM. GPS receivers record the information on the signal group and phase delay in a special files system in RINEX format. The RINEX files are processed with satellite ephemerides files to obtain the line integral of electron density along a raypath, Slant TEC (STEC), under the Single Layer Ionospheric Model (SLIM). The STEC are converted to Vertical TEC (VTEC) using a mapping function for each receiver, satellite and epoch. VTEC or TEC is generally used to indicate the value along the local zenith direction of the GPS receiver. The total electron content in a vertical column of unit cross section, TEC, is measured in TEC units, TECU = 1 16 el/m 2, each value indicates the number of free electrons in a column of unit cross section from the lower boundary of the ionosphere above the Earth (65 8 km) to the GPS navigation satellite orbit, 2,2 km. Similar to unit of TEC measure, a measure of GEC is introduced, GECU = 1 32 el. [4] GIM-TEC database is available since July 1998 with the 2 h resolution and since October 21 with 1 h resolution up to date on the Internet in IONEX format at ftp://cddis.gsfc. nasa.gov/pub/gps/products/ionex/. Each GIM map contains 5184 TEC values in cells of size of 2.5 in latitude [ 9 < 8 <9 ], and 5 in longitude [ 18 < l < 18 ]. [5] In the initial papers [Afraimovich et al., 26a, 26b, 28a, 28b] the GEC is determined by summing of the total electron content, TEC, in each map cell, multiplied 1of6

2 [Obayashi, 1964; Prölls, 1995; Mendillo, 26; Mannucci et al., 28; Gulyaeva and Stanislawska, 21], the formulation of this problem with GEC parameter is performed for the first time. Evidence is obtained that GEC storms effects are manifestations of processes within the context of Sun solar wind magnetosphere ionosphere coupling scenarios rather than a result from redistribution of electron density within the ionosphere and plasmasphere shells over the Earth. The results of the study are presented below. Figure 1. (a) The nighttime and daytime electron density height profiles fitted to GPS-TEC input by IRI-Plas model at [5 N, 3 E]. (b) The altitude profiles of total electron content for night and day: vertical TEC in the column of 1m 2, TEC(h), and total electron content in the truncated spherical cone over a base of 1 m 2 on the Earth s surface, TEC eff (h). by the area of the unit map cell, over all GIM cells. Afraimovich et al. [28b] provided a general formula for a total number of electrons in a spherical shell up to altitude h max = 2,2 km above the Earth s surface, but the initial GEC calculations have been carried out ignoring the NES sphericity. It is improved in the present study by taking into account the vertical electron density distribution through the total volume of spherical segment in the ionosphere and plasmasphere. The algorithm of GEC calculation accounting for the NES sphericity is improved using GPS-TEC inversion into 3-D electron density profile with the International Reference Ionosphere Plasmasphere model, IRI-Plas [Gulyaeva et al., 211; Gulyaeva, 212; Gulyaeva and Bilitza, 212], and relevant GEC calculations from the GPS-TEC maps are performed for the period of 1999 to 211. [6] The initial GEC calculations have been carried out with 1 day, 1 day and 27 day time window of GIM [Afraimovich et al., 26a, 26b, 28a, 28b; Astafyeva et al., 28]. Under these assumptions the GEC changes have been investigated in the solar cycle, the 27 day variations associated with the rotation of the Sun, and seasonal variation, as well as changes for dayside and nightside of the Earth and their components in different latitudinal zones. With so specified time scales the short-term variations are averaged and smoothed out and some very important effects of the more rapid changes of GEC during the disturbances in the ionosphere and plasmasphere induced by the rapid changes on the Sun and in the interplanetary medium [Veselovsky et al., 24] are leveled out. Our attention is focused on these processes during typical space weather storms in [7] Although the processes of perturbations (irregularities) in the Earth s ionosphere and plasmasphere are the subject of many years of theoretical and experimental studies 2. GEC Calculation in Spherical Segment [8] The global electron content depends on 3-D electron density distribution, N(r, q, 8), integrated over the volume of the ionosphere and plasmasphere from the surface of the Earth to the altitude of GPS satellites h max. In geocentric spherical coordinates the expression for GEC within the spherical layer from height R E to R E + h max is represented by an integral of N(r, q, 8) [Afraimovich et al., 28a, 28b]: GEC ¼ ¼ R 2 E R Eþh max Z p Z 2p Z R E Z h max Z p Z 2p Nr; ð q; 8Þr 2 sin qdrdqd8 Nh; ð q; 8 ð Þ R E þ hþ 2 sin qdhdqd8: [9] The vertical electron density distribution for each cell of TEC map is required for GEC production. Fortunately, there is a tool for the automatic time-effective 3-D decomposition of GPS-derived TEC into the electron density height profile. It is the International Reference Ionosphere model extended to the Plasmasphere (IRI-Plas) operated in GPS-TEC assimilative mode which allows conversion of TEC into Ne(h) profile by the instantaneous peak electron density updating [Gulyaeva et al., 211; Gulyaeva and Bilitza, 212] accompanied by the relevant model for the F2 layer peak height [Gulyaeva, 212]. The outcome of IRI- Plas implementation is illustrated in Figure 1a in which the night and day electron density height profiles fitted to TEC input for selected location of latitude 5 N and longitude 3 E are plotted. Figure 1b presents the altitude profiles of total electron content, TEC(h), within a columnar tube over the GIM cell according to primary assumptions by Afraimovich et al. [28a, 28b], and effective total electron content, TEC eff (h), with the spherical divergence of space over the cell taken into account (equation (1)), produced by integrating the Ne(h) profile from the Earth s surface (h = ) to the varying upper height of the electron density distribution (h). The TEC eff is calculated from the electron density height profile (Figure 1a) for the spherical segments of successive height ranges of the 2 km thickness (up to 2,2 km). Details of numerical integration of equation (1) are given elsewhere. [1] Results of day-to-day GEC changes for 21 near the solar maximum, 27 at solar minimum of the 23rd solar cycle, and 211 at the rising phase of the current 24th solar cycle are shown in Figure 2. Figure 2 (left) refers to GEC produced ignoring the sphericity of space environment [Afraimovich et al., 28a]; Figure 2 (right) presents results R 2 E ð1þ 2of6

3 Figure 2. Day-to-day GEC changes for 21, 27 and 211. (left) GEC results ignoring spherical space segments. (right) GEC calculation through the electron density varying with altitude in the spherical segments through the ionosphere and plasmasphere. performed recently by Mannucci et al. [28] by defining the start time of the epoch with a certain threshold of parameter of the reconnection electric field at magnetopause. At such period the synchronous changes are observed in the transition from positive to negative sign of the direction of the interplanetary magnetic field, By <, Bz <, a significant decrease of magnitude of the magnetospheric ring current (SYM-H), the corresponding changes in the equatorial Dst index, the proton temperature, dynamic pressure, speed and plasma density of the solar wind and other interplanetary parameters. Analysis of measurements of the total electron content (TEC) on the CHAMP satellite and ground-based observations of the GPS navigation satellite signals on the sunlit side of the American continent, revealed the effect of appearance of the daytime positive phase of TEC storm in response to the prompt penetration of the electric field (PPEF) in the Earth s magnetosphere. [13] The positive-to-negative sign change of DGEC (2) is used as the starting point of the superposed epoch method in the present study. An example of DGEC variation for a few days before and during the Halloween superstorm of October November 23 [Veselovsky et al., 24; Gulyaeva and Stanislawska, 212] are shown in Figure 3 for the period from 24 October to 2 November 23. Figure 3a shows hourly GEC (marked by plus) and 5 day median of calculation with equation (1). An increase of GEC with increasing solar activity as compared with reduced GEC at solar minimum is evident from Figure 2. The seasonal variation near the maximum of solar activity shows the amplitude variation of GEC by 2 3 times during a year, it decreases to 25% during the solar cycle minimum. Although the absolute values of GEC with equation (1) are greater than the results of the initial calculations by 1.5 to 2 times, the relative seasonal changes, changes from day to day and 27 day variations confirm the patterns obtained previously by Afraimovich et al. [26a, 26b, 28a, 28b]. 3. Modeling of GEC Storm Changes [11] For assessment of GEC changes during the space weather storms one needs to compare these with the undisturbed quiet reference. We accept 5 day hour-to-hour median centered on a given day as the quiet reference thus excluding the solar cycle, seasonal, 27 days and any variations in excess of the current 5 days. The relative changes of GEC are estimated as percentage deviation of GEC from the quiet reference, GECq, normalized by the quiet reference: DGEC ¼ ðgec GECqÞ=GECq 1 ð2þ Positive sign of DGEC estimate (2) refers to electron number enlargement during the positive phase of the ionospheric storm, the negative sign refers to loss of the electron population in the ionosphere-plasmasphere segment of space environment. [12] To identify general pattern of GEC changes during the space weather storms an analysis of 1 intense ionosphereplasmasphere storms during the period from 21 to 211 is carried out in this study by a common-epoch analysis. A superposed epoch analysis during the TEC storms is Figure 3. GEC storm profile along with other parameters during the Halloween superstorm of October November 23: (a) hour-to-hour GEC data, 5 day median and the planetary Wp index; (b) DGEC variation; (c) solar wind velocity; and (d) equatorial Dst index. 3of6

4 Table 1. GEC Negative Storm Onset Times and Planetary Wp Index Date Time (UT) Wp (i.u.) 2 Mar 21 23: Mar 21 9: May 21 23: 7. 3 May 23 7: Oct 23 4: Nov 23 23: Jul 24 1: 8. 8 Nov 24 12: Nov 24 1: Sep 211 5: 6. (thin curve), and the GIM-TEC-based planetary Wp index [Gulyaeva and Stanislawska, 28, 21]. While the planetary Wp index is a cumulative characteristic of the positiveto-negative span of the local W index at different latitudes of GIM-TEC map, the GEC represents global integrated electron content throughout the ionosphere and plasmasphere. [14] The percentage deviation DGEC which is capable of manifestation of GEC expansion/depletion regarding the quiet level (equation (2)) is presented in Figure 3b. The both Figures 3a and 3b testify on plasma injection into the ionosphere-plasmasphere segment (the positive phase of GEC increment) on 28 and 29 October, followed by the plasma depletion on 3 and 31 October (the negative phase of GEC storm). The solar wind ionosphere coupling for this event cannot be traced straightforward because reliable data about solar wind, SW, density and temperature is unavailable for several days [Dmitriev et al., 25]. To overcome this shortcoming, part-time modeling of SW stream speed for a low cadence of 3 min velocity observations on 29 and 3 October is shown in Figure 3c along with near-continuous SW velocity measurements at the rest of time [Veselovsky et al., 24]. Finally, Figure 3d shows effective ring current characteristics as measured by the equatorial Dst index, with double-peak features of Dst minimum on midnight of 29 to 3 and 3 to 31 October nights. Figure 3 demonstrates the solar wind magnetosphere plasmasphere ionosphere relations during the space weather superstorm period. This event is included into the list of 1 intense storms for the superposed epoch analysis given in Table 1. [15] Table 1 provides the date and the universal time when the storm epoch begins at the positive-to-negative GEC storm phase transition for 1 storms selected for the analysis. Also the planetary Wp index, i.u. (index units), for the starting time of superposed epoch analysis is provided. In particular, for the Halloween superstorm (Figure 3) the zero epoch time is equal to 4: UT on 3 October 23. The results of superposed epoch analysis are provided in Figure 4 reproducing the history of the different space environment parameters during 4 h before zero and 4 h after the zero time selected. [16] The points shown in Figure 4a denote DGEC hourly values for 1 storms given in Table 1. The average dependence of DGEC on time is presented with triangles and standard deviation is provided by vertical bar. The positive and negative two-phase DGEC profile is approximated analytically, and from different approximations the closest one (dashed curve in Figure 4a) is found to be the Epstein Figure 4. Observation and average typical storm profile of the set of space environment parameters obtained by superposed epoch analysis: (a) observations and modeling of two-phase storm profile of global electron content; (b) solar wind velocity profile; (c) auroral electrojet AE index storm profile; and (d) equatorial Dst index profile. 4of6

5 type step function expressed in terms of the peak DGEC values, DGEC max = 1.5%, DGEC min = 9.5%, and time t, hours: varying electron density profile with updated IRI-Plas model [Gulyaeva et al., 211; Gulyaeva and Bilitza, 212; Gulyaeva, 212]. The effective values of TEC eff are produced 8 DGEC max 1= 1 þ e ðtþ5þ=2 :838= 1 þ e ðtþ15þ=2 < t < ; positive phase DGEC ¼ t ¼ ; start time : : DGEC min 1= ð1 þ e tþ2 Þ :863= 1 þ e ð tþ18þ=4 t < ; negative phase ð3þ [17] The solar wind (SW) velocity is plotted in Figure 4b in a similar way as in Figure 4a for the same 1 events and the starting time given in Table 1. The average SW speed (solid diamonds) is accompanied by the vertical bars of standard deviation. The mean SW velocity of about 7 km/s peaks around the starting time (t = ) of a common epoch period, followed by a gradual decrease of SW speed afterward. Appearance of the high-speed SW stream at the origin of a solar storm occurred at time of t = 3 h prior to selected starting time (Figure 4b). For more details of the positive ionosphere storm effects related with high-speed SW streams the interested reader could see Veselovsky et al. [24, 21, and references therein] and Mannucci et al. [28, and references therein]. [18] Interaction of the high-speed solar wind with the magnetosphere reveals in generating global ionospheric electric fields with sharp amplification of the auroral electrojet index (AE), generating strong internal gravitation waves propagating from high to lower latitudes. Evolution of the AE index for the selected family of storms is plotted against time in Figure 4c (points). The mean AE index (squares) is given with the standard deviation (vertical bar). The mean AE peak is about 1 nt at t = 18 h prior the start time of epoch. After the peak, AE index is kept high (from 1 to 8 nt) till zero time, t =, and then gradually restores to lower (quiet) values afterward. [19] The typical profile of the equatorial disturbance storm time, Dst index, is constructed in Figure 4d. Here the source Dst index for 1 selected events is shown by points; average Dst profile (triangles) is plotted together with the standard deviation (vertical bar). Peak of the average Dst = 19 nt is reached at the start of the superposed epoch time. Remarkably good coincidence is obtained for the onset of Dst recovery phase with the negative phase of GEC average storm profile. 4. Conclusions [2] Derivation of global electron content (GEC) in the near-earth space is introduced by Afraimovich et al. [26a, 26b]. The initial GEC has been calculated as a sum of the total electron content of each cell of GPS-TEC map multiplied by the cell area. With this assumption variation of GEC parameter with solar cycle, season, 27 day period of solar rotation and night-day variations are investigated. Algorithm of GEC calculation is improved in the present paper by integrating the electron density distribution N(r, q, 8) through the total volume of a spherical layer in near-earth space up to 2,2 km (GPS orbit). This is achieved by implementing the 3-D decomposition of TEC into height from 3-D electron density distribution with the spherical space divergence taken into account from the Earth s surface to 2,2 km. The GEC results in the spherical segments are increased by times against the former values estimated by Afraimovich et al. [26a, 26b, 28a, 28b]. [21] The two-phase typical GEC storm profile is constructed by a common-epoch analysis of 1 storms during with the starting time put at the origin of the negative phase of GEC departure from the quiet reference (5 day median). An analytical model of two-phase GEC storm profile is developed in terms of the peak DGEC departures from the quiet reference and time of the storm in progress. The negative phase of GEC storm is found to occur synchronously with decrease of the solar wind velocity and the outset of recovery of the magnetospheric ring current (the equatorial Dst index) and the auroral electrojet (AE index). [22] The solar wind is now generally accepted to be the cause of geomagnetic activity, auroral activity and particle intensity variations within the radiation belts. Our results of GEC excess over the quiet reference during 24 h with electron number increased by 1 2% followed by a negative phase with GEC decrease by 1 2% for 4 h during a recovery phase of the solar wind and the magnetosphere storm parameters suggest that the solar wind may be responsible for contributing the energy into the ionosphere plasmasphere system confirmed earlier with the planetary averaged F2 layer ionization [Lal, 1997]. Though the state of the ionosphere and plasmasphere is highly variable with time and geographic location, the GEC plasma density variations stress out the dominant processes in the ionosphere-plasmasphere segment. Thus, GEC enhancement testifies of a dominant plasma injection on the dayside part of the globe as compared with nightside loss of ionization at this period of storm while the GEC depletion during the negative phase of the storm is manifestation of the typical global dominant plasma release (ejection) into the magnetosphere tail beyond the three Earth radii (GPS orbit) detected earlier with TEC observations as the ionosphere expansion into the nighttime tail of the magnetosphere [Gulyaeva and Jayachandran, 24]. [23] Though the history of investigations of the ionospheric storms progressed from the local effects to regional features and then to the global models, the above results suggest that the opposite chain should have priority by a natural succession of storm development and propagation: from the Sun to the solar wind to the magnetosphere to global plasmasphere and ionosphere and then to the regional and/or local ionospheric effects. In this context the global electron content takes the proper place as a proxy of the global parameter for the plasmasphere-ionosphere segment of the Earth s space environment. 5of6

6 [24] Acknowledgments. The support by the joint grant from RFBR CT_a and TUBITAK EEEAG 11E296 project for this work is gratefully acknowledged. GPS-derived hourly global ionospheric maps (GIM) were provided at ftp://cddis.gsfc.nasa.gov/pub/gps/products/ionex/, courtesy of M. Hernandes-Pajares. Catalogue of planetary ionosphereplasmasphere storms is provided online at ( iweather/storm/). The authors are indebted to two unknown referees for the important comments led to the total reevaluation of GEC in this study. [25] Robert Lysak thanks the reviewers for their assistance in evaluating the paper. References Afraimovich, E. L., and N. P. Perevalova (26), GPS Monitoring of the Upper Atmosphere of the Earth, 48 pp., Inst. of Solar-Terr. Phys. SB RAS, Irkutsk, Russia. Afraimovich, E. L., E. I. Astafyeva, and I. V. Zhivetiev (26a), Solar activity and global electron content, Dokl. Akad. Nauk, 49(3), Afraimovich, E. L., E. I. Astafyeva, A. V. Oinats, Y. V. Yasukevich, and I. V. Zhivetiev (26b), Global electron content as a new index of solar activity: Comparison with IRI modeling results, IRI News, 13(1), Afraimovich, E. L., E. I. Astafyeva, I. V. Zhivetiev, A. V. Oinats, and Y. V. Yasukevich (28a), Global electron content during solar cycle 23, Geomagn. Aeron., Engl. Transl., 48(2), 187 2, doi:1.1134/ S Afraimovich, E. L., E. I. Astafyeva, A. V. Oinats, Y. V. Yasukevich, and I. V. Zhivetiev (28b), Global electron content: A new conception to track solar activity, Ann. Geophys., 26(2), , doi:1.5194/angeo Astafyeva, E. I., E. L. Afraimovich, A. V. Oinats, Y. V. Yasukevich, and I. V. Zhivetiev (28), Dynamics of global electron content in derived from global GPS data and IRI modeling, Adv. Space Res., 42(4), , doi:1.116/j.asr Dmitriev, A. V., et al. (25), Indirect estimation of the solar wind conditions in October 23, J. Geophys. Res., 11, A9S2, doi:1.129/24ja186. Gulyaeva, T. (212), Empirical model of ionospheric storm effects on the F 2 layer peak height associated with changes of peak electron density, J. Geophys. Res., 117, A232, doi:1.129/211ja Gulyaeva, T. L., and D. Bilitza (212), Towards ISO standard earth ionosphere and plasmasphere model, in New Developments in the Standard Model, edited by R. J. Larsen, pp. 1 48, NOVA, Hauppauge, New York. [Available at php?products_id=35812.] Gulyaeva, T. L., and B. Jayachandran (24), Expanding ionosphere during geomagnetic storms, Geomagn. Aeron., Engl. Transl., 44(3), Gulyaeva, T. L., and I. Stanislawska (28), Derivation of a planetary ionospheric storm index, Ann. Geophys., 26(9), , doi:1.5194/ angeo Gulyaeva, T. L., and I. Stanislawska (21), Magnetosphere associated storms and autonomous storms in the ionosphere-plasmasphere environment, J. Atmos. Sol. Terr. Phys., 72, 9 96, doi:1.116/j.jastp Gulyaeva, T. L., and I. Stanislawska (212), Deformation of the ionosphere structure during the space weather events on October November 23, Adv. Space Res., doi:1.116/j.asr , in press. Gulyaeva, T. L., F. Arikan, and I. Stanislawska (211), Inter-hemispheric imaging of the ionosphere with the upgraded IRI-Plas model during the space weather storms, Earth Planets Space, 63(8), , doi:1.547/eps Lal, C. (1997), Contribution to F2 layer ionization due to the solar wind, J. Atmos. Sol. Terr. Phys., 59(17), , doi:1.116/s (97) Mannucci, A. J., B. T. Tsurutani, M. A. Abdu, W. D. Gonzales, A. Komjathy, E. Echer, B. A. Ijima, G. Crowley, and D. Anderson (28), Superposed epoch analysis of the dayside ionospheric response to four intense geomagnetic storms, J. Geophys. Res., 113, AA2, doi:1.129/27ja Mendillo, M. (26), Storms in the ionosphere: Patterns and processes for total electron content, Rev. Geophys., 47, RG41, doi:1.129/ 25RG193. Obayashi, T. (1964), Morphology of storms in the ionosphere, in Research in Geophysics, vol. 1, edited by H. Odishaw, pp , MIT Press, Cambridge, Mass. Prölls, G. W. (1995), Ionospheric F region storms, in Handbook of Atmospheric Electrodynamics, vol. 2, edited by H. Volland, pp , CRC Press, Boca Raton, Fla. Veselovsky, I. S., et al. (24), Solar and heliospheric phenomena in October-November 23: Causes and effects, Cosmic Res., Engl. Transl., 42(5), Veselovsky, I. S., A. V. Dmitriev, and A. V. Suvorova (21), Algebra and statistics of the solar wind, Cosmic Res., Engl. Transl., 48(2), , doi:1.1134/s of6