A summary of the applications of a weighted average method determining times of solar cycle extrema

This paper is a summary of our recent researches on the applications of a weighted average method determining times of solar cycle extrema in the prediction of solar activity. Some correlation coefficients among the parameters in solar cycle according to this definition are higher than those according to the conventional definition. The descending time is found to be correlated (r = −0.77) with the ascending time 3 cycles earlier. The amplitude of solar cycle is found to be correlated (r = −0.77) with the max–max solar cycle length 2 cycles earlier. The ascending time is found to be correlated (r = −0.72) with the amplitude. A newly defined parameter called effective duration is found to be well correlated (r = 0.86) with the amplitude 5 cycles later. These correlations suggest that earlier cycles should influence later ones. The next (24th) solar cycle is estimated to start in March 2007 ± 7 months, reach its maximum in January 2011 ± 14 months, with a size of 150 ± 22, larger than those from some correlations according to the conventional definition.     

Synoptic magnetic field in cycle 23 and in the beginning of the cycle 24

The SOHO/MDI data provide the uniform time series of the synoptic magnetic maps which cover the period of the cycle 23 and the beginning of the cycle 24. It is very interesting period because of the long and deep solar minimum between the cycles 23 and 24. Synoptic structure of the solar magnetic field shows variability during solar cycles. It is known that the magnetic activity contributes to the solar irradiance. The axisymmetrical distribution of the magnetic flux (Fig. 3c) is closely associated with the ‘butterfly’ diagram in the EUV emission (Benevolenskaya et al., 2001). And, also, the magnetic field (B_∥) shows the non-uniform distributions of the solar activity with longitude, so-called ‘active zones’, and ‘coronal holes’ in the mid-latitude. Polar coronal holes are forming after the solar maxima and they persist during the solar minima. SOHO/EIT data in the emission of Fe XII (195 Å) could be a proxy for the coronal holes tracking. The active longitudinal zones or active longitude exist due to the reappearance of the activity and it is clearly seen in the synoptic structure of the solar cycle. On the descending branch of the solar cycle 23 active zones are less pronounced comparing with previous cycles 20, 21 and 22. Moreover, the weak polar magnetic field precedes the long and deep solar minimum. In this paper we have discussed the development of solar cycles 23 and 24 in details.     

Decadal variability of tropical Pacific temperature in relation to solar cycles

We use the 8-year long satellite temperature data (2002–2010) from Atmospheric InfraRed Sounder (AIRS) and Atmospheric Microwave Sounding Unit (AMSU) on the Aqua satellite to identify temperature trends in the troposphere and low stratosphere over the Niño 3.4 region of the Tropical Pacific Ocean in the most recent 11-year solar cycle. Employing more extended sea surface temperature (SST) data for five solar cycles (1950–2009) in this region we show that the satellite trends reflect a typical decrease of the sea surface temperature (SST) in the Niño 3.4 region in the declining phase of the solar cycle. The magnitude of the SST decrease depends on the solar cycle and ranges between 0.07 K/yr and 0.27 K/yr for the last five solar cycles.     

Even–odd cycle parity in complexity of hemispheric sunspot activity

We have used the Lempel–Ziv measure to describe the complexity in sunspot activity during the solar cycles 18–23. In particular, we examined the time series of daily sunspot numbers in the northern and southern hemispheres in each of the six cycles and calculated the Lempel–Ziv complexity (LZC) value for each time series. Our results indicate that in the even cycles, the LZC values of the sunspot numbers in the two hemispheres are very close to each other, whereas in the odd cycles they differ significantly between the two hemispheres. We also find that within each hemisphere the LZC varies from cycle to cycle. This even–odd cycle parity reflects the variations in inter-hemispheric strengths of the solar magnetic field leading to different temporal distributions of sunspots in the two hemispheres. The degree of complexity may influence the predictability of sunspot activity in the two hemispheres during the various cycles. Although the physical implication of the results is not clear, these results may stimulate new ideas into modeling the complex dynamics of the solar dynamo.     

Preliminary forecast for the peak of solar activity cycle 24

Our forecast for the development phase of solar cycle 23 came out to be true; one of the very few to have attained this status out of several forecasts made. We review the details of the forecast and how it fared as the events unfolded in time. We note the present status of IMF intensity B and the planetary index Ap. We draw inferences as to what to expect for the development phase of cycle 24; several forecasts have already been made, they cover all possible scenarios, ranging from a very active to the quietest cycle in a century. Our preliminary forecast for the smoothed sunspot number at cycle 24 maximum is 101 ± 5, indicating that cycle 24 will be about 20% less active than cycle 23; the possibility that next three solar cycles may be progressively less active cannot be ruled out.     

Perspective on space radiation for space flights in 2020–2040

The Sun undergoes several well known periodicities in activity, such as the Schwabe 11 year cycle, the Gleissberg 80–90 year cycle, the Suess 200–210 year cycle and the Halstatt 2200–2300 year cycle. In addition, there is evidence that the 20th century levels of solar activity are unusually high. The years 2020–2040 are expected to coincide with increased activity in human space flight beyond low Earth orbit. The solar cycles and the present level of solar activity are reviewed and their activities during the years 2020–2040 are discussed with a perspective on space radiation and the future program of space flight. It is prudent to prepare for continuing levels of high solar activity as well as for the low levels of the current deep minimum, which has corresponded to high galactic cosmic ray flux.     

An empirical approach to predicting the key parameters for a sunspot number cycle

The common methodologies used to predict the smooth sunspot number (SSN) at peak (Rmax) and the rise time (Tr) for a cycle are noted. The estimates based on geomagnetic precursors give the best prediction of Rmax for five SSN cycles (20–24). In particular, an empirical technique invoking three-cycle quasi-periodicity (TCQP) in Ap index has made accurate predictions of Rmax and Tr for two consecutive SSN cycles (23 and 24). The dynamo theories are unable to account for TCQP. If it endures in the 21st century the Sun shall enter a Dalton-like grand minimum. It was a period of global cooling. The current status of the ascending phase of cycle 24 is described and the delayed reversal of the solar polar field reversal in the southern hemisphere in September 2013 is noted.     

Galactic cosmic ray modulation for sunspot cycle 23

We present a study of the galactic cosmic ray modulation for sunspot cycle 23. We use the monthly and the annual mean hourly, pressure corrected, data from neutron monitors of the global network (monthly rate is calculated as the average of the hourly pressure corrected values). We draw attention to an asymmetry in the galactic cosmic ray (GCR) recovery during odd and even cycles for the monthly mean hourly rate data. For over half a century of observations, we find that the recovery for the odd cycles is to a higher level than for the even cycles. Qualitatively the effect is ascribed to charged particle drifts in inhomogeneous interplanetary magnetic field. Even so it has not been possible to arrive at a quantitative, self-consistent, explanation in terms of drifts at higher and lower GCR rigidities. We also study the rigidity dependence of the amplitude of 11-year modulation over a wide range (1–200 GV) of GCR spectrum; it is a power law in rigidity with an exponent −1.22. We discuss the implication of these findings on quasi-linear diffusion theories of modulation. We reflect on GCR recovery pattern for 2006–2009.     

On the time lag between solar wind dynamic parameters and solar activity UV proxies

The solar activity displays variability and periodic behaviours over a wide range of timescales, with the presence of a most prominent cycle with a mean length of 11 years. Such variability is transported within the heliosphere by solar wind, radiation and other processes, affecting the properties of the interplanetary medium. The presence of solar activity–related periodicities is well visible in different solar wind and geomagnetic indices, although their time lags with respect to the solar cycle lead to hysteresis cycles. Here, we investigate the time lag behaviour between a physical proxy of the solar activity, the Ca II K index, and two solar wind parameters (speed and dynamic pressure), studying how their pairwise relative lags vary over almost five solar cycles. We find that the lag between Ca II K index and solar wind speed is not constant over the whole time interval investigated, with values ranging from 6 years to $～$1 year (average 3.2 years). A similar behaviour is found also for the solar wind dynamic pressure. Then, by using a Lomb-Scargle periodogram analysis we obtain a 10.21-year mean periodicity for the speed and 10.30-year for the dynamic pressure. We speculate that the different periodicities of the solar wind parameters with respect to the solar 11-year cycle may be related to the overall observed temporal evolution of the time lags. Finally, by accounting for them, we obtain empirical relations that link the amplitude of the Ca II K index to the two solar wind parameters.     

Modelling of galactic Carbon in an asymmetrical heliosphere: Effects of asymmetrical modulation conditions

Observations of galactic cosmic rays (GCRs) from the two Voyager spacecraft inside the heliosheath indicate significant differences between them, suggesting that in addition to a possible global asymmetry in the north–south dimensions (meridional plane) of the heliosphere, it is also possible that different modulation (turbulence) conditions could exist between the two hemispheres of the heliosphere. We focus on illustrating the effects on GCR Carbon of asymmetrical modulation conditions combined with a heliosheath thickness that has a significant dependence on heliolatitude. To reflect different modulation conditions between the two heliospheric hemispheres in our numerical model, the enhancement of both polar and radial perpendicular diffusion off the ecliptic plane is assumed to differ from heliographic pole to pole. The computed radial GCR intensities at polar angles of 55° (approximating the Voyager 1 direction) and 125° (approximating the Voyager 2 direction) are compared at different energies and for both particle drift cycles. This is done in the context of illustrating how different values of the enhancement of both polar and radial perpendicular diffusion between the two hemispheres contribute to causing differences in radial intensities during solar minimum and moderate maximum conditions. We find that in the A > 0 cycle these differences between 55° and 125° change both quantitatively and qualitatively for the assumed asymmetrical modulation condition as reflected by polar diffusion, while in the A < 0 cycle, minute quantitative differences are obtained. However, when both polar and radial perpendicular diffusion have significant latitude dependences, major differences in radial intensities between the two polar angles are obtained in both polarity cycles. Furthermore, significant differences in radial intensity gradients obtained in the heliosheath at lower energies may suggest that the solar wind turbulence at and beyond the solar wind termination shock must have a larger latitudinal dependence.     

Statistical analysis of the occurrence rate of geomagnetic storms during solar cycles 20–24

This study examines the occurrences rate of geomagnetic storms during the solar cycles (SCs) 20–24. It also investigates the solar sources at SCs 23 and 24. The Disturbed storm time (Dst) and Sunspot Number (SSN) data were used in the study. The study establishes that the magnitude of the rate of occurrences of geomagnetic storms is higher (lower) at the descending phases (minimum phases) of solar cycle. It as well reveals that severe and extreme geomagnetic storms (Dst < -250 nT) seldom occur at low solar activity but at very high solar activity and are mostly associated with coronal mass ejections (CMEs) when occurred. Storms caused by CME + CH-HSSW are more prominent during the descending phase than any other phase of the solar cycle. Solar minimum features more CH-HSSW- associated storms than any other phase. It was also revealed that all high intensity geomagnetic storms (strong, severe and extreme) are mostly associated with CMEs. However, CH-HSSW can occasionally generate strong storms during solar minimum. The results have proven that CMEs are the leading cause of geomagnetic storms at the ascending, maximum and the descending phases of the cycles 23 and 24 followed by CME + CH-HSSW. The results from this study indicate that the rate of occurrence of geomagnetic storms could be predicted in SC phases.     

Specific features of the high-speed plasma stream cycles

The high-speed plasma streams in the solar wind are investigated during the solar cycles nos. 20–22 (1964–1996), separately on the two types of streams according to their solar origin: the HSPS produced by coronal holes (co-rotating) and the flare-generated, in keeping with the classification made in different catalogues. The analysis is performed taking into account the following high-speed stream parameters: the durations (in days), the maximum velocities, the velocity gradients and, the importance of the streams. The time variation of these parameters and the high-speed plasma streams occurrence rate show an 11-year periodicity with some differences between the solar cycles considered. A detailed analysis of the high-speed stream 11-year cycles is made by comparison with the “standard” cycles of the sunspot relative number (Wolf number). The different behaviour of the high-speed stream parameters between even and odd solar cycles could be due to the 22-year solar magnetic cycle. The increased activity of the high-speed plasma streams on the descendant phases of the cycles, regardless of their solar sources, proves the existence of some special local conditions of the solar plasma and the magnetic field on a large scale that allow the ejection of the high energy plasma streams. This fact has led us to the analysis the stream parameters during the different phases of the solar cycles (minimum, ascendant, maximum and, descendant) as well as during the polar magnetic field reversal intervals. The differences between the phases considered are pointed out. The solar cycles 20 and 22 reveal very similar dynamics of the flare-generated and also co-rotating stream parameters during the maximum, descendant and reversal intervals. This fact could be due to their position in a Hale Cycle (the first component of the 22-year solar magnetic cycle). The 21st solar cycle dominance of all co-rotating stream parameters against the 20th and 22nd solar cycle ones, during almost all phases, could be due to the same structure of a Hale Cycle – solar cycle 21 is the second component in a 22-year SC. During the reversal intervals, all high-speed stream parameters have comparable values with the ones of the maximum phases of the cycles even if this interval contains a small part of the descendant branch (solar cycles 20 and 22).     

Essential features of long-term changes of areas and diameters of sunspot groups in solar activity cycles 12–24

We analyze the Greenwich catalog data on areas of sunspot groups of last thirteen solar cycles. Various parameters of sunspots are considered, namely: average monthly smoothed areas, maximum area for each year and equivalent diameters of groups of sunspots. The first parameter shows an exceptional power of the 19th cycle of solar activity, which appears here more contrastively than in the numbers of spots (that is, in Wolf’s numbers). It was found that in the maximum areas of sunspot groups for a year there is a unique phenomenon: a short and high jump in the 18th cycle (in 1946–1947) that has no analogues in other cycles. We also studied the integral distributions for equivalent diameters and found the following: (a) the average value of the index of power-law approximation is 5.4 for the last 13 cycles and (b) there is reliable evidence of Hale's double cycle (about 44?years). Since this indicator reflects the dispersion of sunspot group diameters, the results obtained show that the convective zone of the Sun generates embryos of active regions in different statistical regimes which change with a cycle of about 44?years.     

Solar proton events recorded in the stratosphere during cosmic ray balloon observations in 1957–2008

Long-term balloon observations have been performed by the Lebedev Physical Institute since 1957 up to the present time. The observations are taken several times a week at the polar and mid latitudes and allow us to study dynamics of galactic and solar cosmic ray as well as secondary particle fluxes in the atmosphere and in the near-Earth space. Solar energetic particles (120) – mostly protons – (SEP) events with >100 MeV proton intensity above 1 cm⁻² s⁻¹ s⁻¹ were recorded during 1958–2006. Before the advent of the SEP monitoring on spacecraft these results constituted the only homogeneous series of >100 MeV SEP events. The SEP intensities and energy spectra inferred from the Lebedev Physical Institute observations are consistent with the results taken in the adjacent energy intervals by the spacecraft and neutron monitors. Joint consideration of the SEP events series recorded by balloons and by neutron monitors during solar cycles 20–23 makes it possible to restore the probable number of events in solar cycle 19, which was not properly covered by observations. Some correlation was found between duration of SEP event production in a solar cycle and sunspot cycle characteristics.     

Investigation of N–S asymmetry of solar differential rotation by various patterns for solar cycles 20 and 21

For solar cycles 20 and 21 the latitudinal variations of the solar rotation rates are found using data of the H_α filaments and the long-lived magnetic features of negative and positive polarities. Analysis of the data showed that: (a) there is N–S asymmetry in the equatorial rotation of the H_α filaments and the long-lived magnetic features; (b) for both solar cycles the long-lived magnetic features of both polarities have similar behavior; (c) in the solar cycle 20 the long-lived magnetic features of both polarities vary in phase to each other but show some difference during cycle 21. For the long-lived magnetic features of positive polarity the confidence level is lower than for those of negative one.     

Sunspot activity and cosmic ray modulation at 1 a.u. for 1900–2013

The descent of sunspot cycle 23 to an unprecedented minimum of long duration in 2006–2009 led to a prolonged galactic cosmic ray (GCR) recovery to the highest level observed in the instrumental era for a variety of energetic charged particle species on Earth, over a wide range of rigidities. The remarkable GCR increase measured by several ground-based, balloon-borne, and detectors on a satellite is described and discussed. It is accompanied by a decrease in solar wind velocity and interplanetary magnetic field at 1 a.u., reaching the lowest values since measurements of the solar wind began in October 1963; the solar polar field strength (μT) measured at the Wilcox Solar Observatory (WSO) is also significantly reduced compared to prior cycles since the start of the program in 1976, the polar field in the northern hemisphere reversed in June 2012 and again in February 2014, that in the southern hemisphere reversed in July 2013. If updates of WSO data confirm the second reversal in northern solar hemisphere, it would pose a serious challenge to the Dynamo Theory. The long-term change in solar behavior may have begun in 1992, perhaps earlier. The physical underpinnings of these solar changes need to be understood and their effect on GCR modulation processes clarified. The study discusses the recent phenomena in the context of GCR modulation since 1900. These happenings affected our empirical predictions for the key parameters for the next two sunspot cycles (they may be progressively less active than sunspot cycle 24) but it enhanced support for our prediction that solar activity is descending into a Dalton-like grand minimum in the middle of the twentyfirst century, reducing the frequency of the coronal mass ejections; they determine the space weather affecting the quality of life on Earth, radiation dose for hardware and human activities in space as well as the frequency of large Forbush decreases at 1 a.u.     

Sunspot cycle prediction using Warped Gaussian process regression

Solar cycle prediction is a key activity in space weather research. Several techniques have been employed in recent decades in order to try to forecast the next sunspot-cycle maxima and time. In this work, the Gaussian process, a machine-learning technique, is used to make a prediction for the solar cycle 25 based on the annual sunspot number 2.0 data from 1700 to 2018. A variation known as Warped Gaussian process is employed in order to deal with the non-negativity constraint and asymmetrical data distribution. Tests using holdout data yielded a root mean square error of 10.0 within 5 years and 25.0–35.0 within 10 years. Simulations using the predictive distribution were performed to account for the uncertainty in the prediction. Cycle 25 is expected to last from 2019 to 2029, with a peak sunspot number about 117 (110 by the median) occurring most likely in 2024. Thus our method predicts that solar Cycle 25 will be weaker than previous ones, implying a continuing trend of declining solar activity as observed in the past two cycles.     

Prediction of clear-sky biologically effective erythematic radiation (EER) From global solar radiation (250–2800 nm) at Cairo,Egypt

The hourly and daily measured clear-sky global solar radiation (G) and biologically important effective erythematic radiation (EER) incident on a horizontal surface at Cairo, Egypt (latitude 30° 05′ N & Longitude 31° 15′ E), during the period from January 1995 to December 2005 are used in this paper. The relationship between daily integrated totals of EER and the daily totals of broadband global solar radiation (250–2800 nm) is established. The temporal variability of the percentage ratio of the total daily erythema to total daily broadband solar global irradiation (EER/G) is determined. The monthly and the seasonal averages of the extraterrestrial UVB solar radiation, Mesurad and estímated UVB solar radiation and clearness index K_tUVB of UVB radiation are discussed. The average monthly mean variation of slant ozone (Z) and UVB transmission (K_tUVB) at the present work are found. The two variables show an opposite seasonal behavior, and the average monthly of slant ozone column and UVB transmission values shows the relationship between them in a clearer way than those of daily values. The estimated values of UVB solar radiation a good agreement with the measured values of the UVB solar radiation, the difference between the estimated and measured values of UVB solar radiation varies from 1.2% to 2.8%. The effect of the annual cycles of solar zenith angle (SZA) and total column ozone (TCO) on the ratios (EER/G) are presented and the correction factors are determined for removal of the ozone cycle. The seasonal variability of EER/G is also discussed. The effect of the annual cycles of solar zenith angle (SZA) and total column ozone (TCO) on the ratios (EER/G) is presented and the correction factors are determined for removal of the ozone cycle.     

Geomagnetic activity and solar cycles

Multiple linear regression method is used to estimate the total number of geomagnetic storms per solar cycle and to predict cycle 23’s maximum amplitude. A recurrence trend of 7 and 12 cycles are used as lagged values to estimate the amplitude of the current cycle, which resulted to be equal to 137 (±65) smoothed monthly mean sunspots.     

太阳周的模糊分类和对22周的预报

本文根据模糊集合理论, 讨论了太阳周的分类和预报.利用模糊聚类分析方法对22周作出的预报如下:21周降段长。Δt_降(21周)=8或9年;22周开始于1987或1988年;22周初始谷值R_M头(22周)=4.3;22周上升段长。Δt_升(22周)=4年;22周极大年均值R_M(22周)=118.9;22周降段长。Δt_降(22周)=(6.5)或8年.