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Global median empirical model of Total Electron Content (GTEC) is developed driven by re-calibrated sunspot numbers, SSN2, for the quiet geomagnetic conditions (ap

In this chapter, we shall look at the Sun, bearing in mind it is a star on the main sequence. Therefore, we shall not discuss in any depth topics such as sunspots, the sunspot cycle, etc. Instead, we will concentrate on the internal structure, means of energy production, and the manner in which energy is transported from its source to us on Earth. With this approach, it is possible to use the Sun as a benchmark with which to compare stars of differing size.

The recalibration of the sunspot number series, the primary long-term record of the solar cycle, requires the recovery of the entire collection of raw sunspot counts collected by the Zurich Observatory for the production of this index between 1849 and 1980. Here, we report about the major progresses accomplished recently in the construction of this global digital sunspot number database, and we derive global statistics of all the individual observers and professional observatories who provided sunspot data over more than 130 years. First, we can announce the full recovery of long-lost source-data tables covering the last 34 years between 1945 and 1979, and we describe the unique information available in those tables. We then also retrace the evolution of the core observing team in Zurich and of the auxiliary stations. In 1947, we find a major disruption in the composition of both the Zurich team and the international network of auxiliary stations. This sharp transition is unique in the history of the Zurich Observatory and coincides with the main scale-jump found in the original Zurich sunspot number series, the so-called "Waldmeier" jump. This adds key historical evidence explaining why methodological changes introduced progressively in the early $20^{th}$ century could play a role precisely at that time. We conclude on the remaining steps needed to fully complete this new sunspot data resource., Comment: 22 pages, 9 figures

To explain the observed phenomenon of 11-year sunspot cycle with two peaks, we draw attention to the possible role of the turbulent magnetic pumping effects in the solar convection zone (SCZ) at the reconstructing of the toroidal magnetic field that generates the sunspots. Turbulent radial pumping of magnetic field has both kinetic (diamagnetism) and magnetic (vertical advection) contributions. We take into account five physical processes for the combined magnetic reconstructing in deep layers of the SCZ. They are the Ω effect near the tachocline, magnetic buoyancy of the smoothed field, macroscopic diamagnetism, rotational magnetic advection, and deep equatorward meridional circulation. It is the effect of advection with taking into account Sun's rotation that plays a key role in the proposed scenario of magnetic reconstructing. We found that reconstructing of deep toroidal field develops differently in the near-polar and equatorial domains of the SCZ. In the lower half of the near-polar domain, two downward pumping effects (diamagnetism and advection) act against magnetic buoyancy and, as a result, they neutralize magnetic buoyancy and thereby block the toroidal field near the tachocline. At the same time, in the deep layers of the equatorial domain, the rotational advection due to the latitudinal convection anisotropy changes its direction to the opposite (from downward to upward), thereby helping magnetic buoyancy. As a result, this upward magnetic pumping here contributes to the transport of the toroidal field to the solar surface. We call this transport as first upward magnetic advection surge. It ensures a transfer of the deep strong fields to the surface in the latitudes belt of sunspots. Meanwhile, a deep equatorward meridional flow transports the blocked near pole toroidal field in the tachocline from high latitudes to low ones where are favourable conditions for floating up of the magnetic field. Here this belated field is transported upward to the solar surface (the second upward magnetic advection surge). Ultimately, two time-delayed upward magnetic surges may cause on the surface in the “royal zone” the first and second peaks of the sunspots cycle.

In this article, we examine the possible influence of the hemispheric sunspot areas (SSAs) on the interplanetary plasma parameters. For this purpose, the daily data of hemispheric SSAs, interplanetary magnetic field, magnitude (B), plasma density (n), plasma velocity (V), plasma temperature (T), and plasma dynamic pressure (P) during the period, 1967–2017, have been used. A long-term relationship between the SSAs and each interplanetary plasma parameter has been identified, if and only if, both SSAs and the daily averages of each interplanetary plasma parameter have been smoothed by a window of a 3-years running average and a specific time-lag has been applied. The daily data of each interplanetary plasma parameter has been classified into two groups, northern (N) and southern (S), based on the dominance of hemispheric SSAs. The absolute asymmetry index (N–S) for each parameter between the northern and the southern sorted group has been calculated. The asymmetry between the northern and the southern sorted groups for each parameter was detected significantly at random years during the entire period. The asymmetry of B over the solar activity cycles is not detectable; indicating that the solar cycles are magnetically symmetric. During the solar cycles 20, 21, and 24, the solar plasma for the southern sorted group was faster (hotter) by 20.3 km/s (15.7 × 103 K), 13 km/s (8 × 103 K), and 29 km/s (14.5 × 103 K) than that of the northern sorted group, respectively. In contrast, during the solar cycle 23, the solar plasma of the southern sorted group was slower (colder) by 7.4 km/s (7.2 × 103 K) than that of the northern sorted one. In addition, the periodic behavior of the N–S asymmetry of the considered solar plasma parameters has been investigated using Fast Fourier Transformation. Many mid- and long-term periodicities have been detected. We present our results and discuss their possible explanations.

One of the main features of the quality of the Dnieper water is the content of natural organic substances which determine the water oxidizability and color indexes. A special problem is that organic substances are poorly removed by water treatment plants. A significant problem in the operation of water treatment plants is the unpredictability of annual changes in the quality of Dnieper water, which complicates logistics management, for example, the supply of reagents. Many years of experience related to the Dnieper water supply station in Kyiv (DnWS) have led to the hypothesis that these changes are in some way related to the cycles of solar activity. The purpose of this work is to test this hypothesis to substantiate the possibility of predicting the quality of Dnieper water depending on the action of such a global factor as solar activity. The work was performed by statistical methods using 60-year results of Dnieper water analyzes provided by the DnWS laboratory, as well as Wolf numbers (Sunspot Numbers) provided for free use by the Royal Observatory of Belgium. The influence of solar activity on the quality indicators of Dnieper water, especially in its peak and post-peak periods, has been statistically confirmed. The interaction of biological and physicochemical parameters as factors influencing water quality is shown. As a result of the construction of six reservoirs in 1931-1976, the Dnieper from the river actually turned into a network of water bodies. Now these reservoirs are a kind of reactors in which water is treated by electromagnetic solar radiation, which leads to the cyclic transformation of phytoplankton and natural organic matter. Taking into account the cycles of solar activity, the logistical planning of the operation of water treatment facilities receives an independent "base", changes in which can be predicted with some reliability for years to come. Однією з характеристик якості дніпровської води є вміст природних органічних речовин, які визначають показники її окиснюваності та кольоровості. Особливість полягає в тому, що ці органічні речовини погано видаляються водоочисними спорудами. Істотною проблемою в роботі водоочисних споруд є непередбачуваність щорічних змін якості води Дніпра, що ускладнює логістику, наприклад, постачання реагентів. Багаторічний досвід робіт, пов’язаних з Дніпровською водопровідною станцією м. Києва (ДнВС), привів до гіпотези, що ці зміни певним чином пов’язані з циклами сонячної активності. Метою даної роботи є перевірка цієї гіпотези для обґрунтування можливості прогнозування якості дніпровської води залежно від дії такого глобального чинника, як сонячна активність. Робота виконана статистичними методами з використанням 60-річних результатів аналізів води з Дніпра, наданих лабораторією ДнВС, а також чисел Вольфа (кількості сонячних плям), наданих у вільне використання Королівською обсерваторією Бельгії. Статистично підтверджено вплив сонячної активності на показники якості дніпровської води, особливо в її піковий та післяпіковий періоди. Показано взаємодію біологічних та фізико-хімічних параметрів як чинників, що впливають на якість води. Внаслідок будівництва шести водосховищ у 1931-1976 рр. Дніпро з річки фактично перетворився на мережу водойм. Зараз ці резервуари є своєрідними реакторами, в яких вода обробляється електромагнітним сонячним опромінюванням, що призводить до циклічного перетворення фітопланктону та природної органічної речовини. З урахуванням циклів сонячної активності логістичне планування роботи водоочисних споруд отримує незалежну "базу", зміни в якій можна з певною достовірністю прогнозувати на довгі роки.

Effects on galactic cosmic rays (GCRs) of several heliospheric factors during the minimum phases of the sunspot cycles are studied. Times of maximum GCR intensity are determined for the last five sunspot minima, including the present one, together with the corresponding main heliospheric factors important for the modulation of GCRs in the heliosphere. The quantitative relation between these factors and the solar magnetic field is studied with the poloidal magnetic field of the Sun considered as a governing factor for many heliospheric characteristics during sunspot minima. The dependence of GCR proton spectra on these heliospheric factors for the last five sunspot minima 21/22–24/25 is calculated and discussed. Special attention is paid to the energy at which spectral cross-overs occur for consecutive minima, related to the changing polarity of the heliospheric magnetic field. The long-term observational series on GCR proton modulation at the Earth are considered with respect to the energy of these cross-overs.

A study is performed of phases of solar cycle minima in sunspots, the heliosphere, and the intensity of Galactic cosmic rays (GCRs). Times of maximum GCR intensity in the minima of the last five cycles (including the current one), corresponding main heliospheric factors, and relationships between them are determined. The dependence of the near-Earth GCR proton spectrum on heliospheric factors of their linear trend in the minima of solar cycles 21/22, 22/23, and 23/24 (1987, 1997, 2009) is calculated and analyzed with emphasis on the behavior of crossover energy for successive minima.

Evaluating the coincidence accuracy and time-varying characteristics of global total electron content (TEC) grid data can contribute to the improvement of the performance of global ionosphere maps (GIMs) and provide effective data support and theoretical verification for GIMs model update. This paper applies the global TEC grid data and GPS single-station ionospheric TEC data published by IGS from 1999 to 2020, as well as the F10.7 and SSN data series provided by the World Sunspot Index Data Center in Belgium. Using correlation, time series, and contour chart analyses, the correlation between TEC RMS and F10.7, SSN, and the accuracy-compliant space–time variation characteristics in the global TEC grid data are studied and analyzed. The results show the accuracy of the global TEC grid data is highly correlated with the solar activity intensity. The mean values of the correlation coefficients R between TEC RMS and F10.7, SSN are 0.755 and 0.707, respectively. The internal coincidence accuracy of single station GPS-TEC and global grid TEC is better than 3 TECU and is closely related to the solar activity. Globally, TEC RMS in land and ocean areas have significant differences. In general, the accuracy of the northern hemisphere is significantly higher than that of the southern hemisphere, and the accuracy of land is higher than that of the ocean. Among them, the accuracy of Europe and North America is the highest, the precision of the Pacific region is obviously on the low side, and “double hump” phenomenon can be observed. The accuracy of the global TEC grid data is closely related to the number of stations and satellites. The accuracy of the TEC grid data is higher in areas where the number of stations is dense, or when there are more satellites.

K index is the oldest measure of geomagnetic activity estimation in a unified scale over the globe, maintained until today. Recently, Russian and Japanese scientific teams have managed to digitize a huge collection of K index analog records from the observatories located in the northwestern Pacific region. This has made it possible to study long-term evolution of geomagnetic activity in this area over 1954–2020. Using these unique data, we reveal their most appropriate distribution laws. We also analyze the correlation between their time-varying distribution features and sunspot numbers over the 19–24 solar cycles. The distribution features are considered in terms of (a) quasi-linear regression coefficients derived from logarithmic scale cumulative frequency distributions, and (b) occurrences of different K index values binned by year as a function of time. We establish that the probability of K ≥ 8 event detected simultaneously at all observatories in the region over the period of simultaneous data availability is less than one hundredth of a percent; the same for the clusters of neighboring observatories is an order of magnitude larger.

In this study, using various statistical methods such as trend analysis, Mann–Kendall (MK) test and Morlet Wavelet Analysis (MWA), the Frequency of Thunderstorm Days (FTD) and its relationship with Sunspots Frequency (SF) and Global Atmospheric Carbon Dioxide Concentration (GACDC) in the 68-year statistical period of 1951–2018 in Tabriz Synoptic Station has been studied. In terms of distribution and temporal concentration, the highest incidence of Thunderstorm Days (TD) is concentrated in the months of May and June and the lowest in the cold months of the year, i.e. January, February and December, with spring having the highest and winter having the lowest FTD. The analysis of the trend of FTD in the study area showed that except for the trends of January, February, June and December, which have no clear and significant trend, other months, especially April, have an upward and significant trend and the seasonal trend of FTD in Tabriz increase significantly in all seasons, especially in the peak of spring; Also, in the annual time scale, a significant upward trend was observed. Decadal changes in the FTD show a sharp increase in the occurrence of TD in Tabriz, especially in the second decade of the twenty-first century. The results of MWA showed that the FTD, like sunspots, has a periodic cycle in its emergence and occurrence. Based on the results of cross-wavelet analysis, there is a strong negative and anti-phased relationship between SF and the FTD in Tabriz. Also, according to the results of MWA, no significant relationship between the GACDC and the FTD in Tabriz has been found.

The ionosphere layer (F2) is known as the most important layer for High frequency (Hf) radio communication because it is a permanent layer and excited during the day and night so it is able to reflect the frequencies at night and day due to its high critical frequency, and this layer is affected by daily and monthly solar activity. In this study the characteristics and behavior of F2 layer during Solar cycle 24 were studied, the effect of Sunspots number (Ri) on the critical frequency (foF2), were investigated for the years (2015, 2016, 2017, 2018, 2019, 2020) which represents the down phase of the solar cycle 24 over Erbil station (36° N, 44° E) by finding the critical frequency (foF2) values, the layer’ s impression times are determined for the days of solstice as well as equinox, where the solar activity was examined for the days of the winter and summer solstice and the days of the spring and autumn equinoxes for a period of 24 hours by applied the International Reference Ionosphere model IRI (2016). The output data for foF2 were verified by using the IRI-Ne- Quick option by specifying the time, date and Sunspot number parameters. Statistical analysis was caried out through the application of the Minitab (version 2018) in order to find the correlation between the critical frequency (foF2) of Ionospheric layer F2 and Sunspot number. It was concluded that the correlation is strong and positive, this indicate that critical frequency (foF2) increase with increasing Sunspots number (Ri) for solar cycle 24.

Variations of maximum height of F2 ionospheric layer are analysed over ionospheric stations of Pakistan located at Islamabad (geog. coord. 33.75°N, 72.87°E), Multan (30.18°N, 71.48°E) and Karachi (24.95°N, 67.14°E) during the years, 1987 (LSA), 1990 (HSA) and 1993 (MSA) representing low, high and moderate solar activity years, respectively. Results showed that hmF2 in summer is higher than in winter during LSA and MSA at all stations. However, diurnal pattern is not consistently followed during winters of LSA and MSA. The lowest hmF2 values are observed around sunrise and sunset; whereas, higher values are observed around noon and midnight which may be due to upward and downward plasma drift velocity as diurnal behaviour of hmF2 is similar to diurnal behaviour of E × B drift. No specific latitudinal trend is observed in hmF2 during the period of this study over Pakistan which may be due to the combined effect of E × B drift and energy transferred to ionosphere by atmospheric planetary waves. Solar quiet current seems responsible for the variation of hmF2 over Multan and Islamabad. For Karachi equatorial electrojet seems controlling the daytime hmF2 during LSA. The hmF2 is found to have linear correlation with solar activity and this correlation is stronger with solar index F10.7 as compared to the sunspot numbers. The correlation coefficients for both solar indices are above 80%; whereas, geomagnetic indices Ap and Kp are weakly correlated having correlation coefficients less than 30%. Ionosonde-derived hmF2 are compared with regional model based on expansion of Empirical Orthogonal Function (EOF) with linear and spline interpolation of coefficients of time, seasons, magnetic dip & sunspot numbers and, global model, International Reference Ionosphere (IRI), with International Union of Radio Science (URSI) and Consultative Committee for International Radio (CCIR) options of IRI-2012 and AMTB-2013, SHU-2015 and BSE-1979 sub-models in combination with URSI and CCIR of IRI-2016 versions. The daytime hmF2 values over Pakistan modelled by AMTB of IRI-2016 (with URSI and CCIR) are found to be the most converging of all IRI options during all solar periods. AMTB-2013 also predicted nighttime values with least errors in most cases except during LSA. In addition, IRI showed better equinoctial and annual correlations with ionosonde-derived hmF2 as compared to EOF model. EOF based model showed higher nighttime Mean Absolute Errors (MAE) as compared to IRI. The lowest daytime and nighttime errors in hmF2 are observed over Multan during LSA shown by IRI-2016-AMTB-2013 (using URSI and CCIR) with MAE being 7.8 km and IRI-2016-SHU-2015 (using URSI and CCIR) with MAE being 4.7 km.

The objective of this work is to model the variable number of cold fronts that affect the Cuban territory in a winter season for a long series of data, to establish if the trend is significant and to see which are the main statistics of the model, to observe the impact of prediction using the number of sunspots with the help of Objective Regressive ROR modeling. In this work, the series of cold fronts per season that affect the Cuban territory was modeled in the years from the 1916-1917 seasons to the 2006-2007 seasons. There are more moderate cold fronts than any other front, on average there are more classic fronts than any other type, on average 19 fronts can be presented per season with a standard deviation of 4.8 Sunspots and they only have a significant linear correlation with sunspots. In moderate fronts, as the stains increase, the number of fronts decreases. The ROR model explains 98% of the variance with an error of 4.2 cases and depends on the fronts returned in 5 seasons, which could coincide with the ENSO event, and also depends on the number of sunspots returned in 12 years. From 1916-1917 approximately the 1952-1953 season, moderate fronts predominated, later from 1953-1954 to the end of the data, weak fronts predominate over the rest with some exceptions throughout history. No significant trend was observed in the model. It is concluded that forecasts of the number of cold fronts can be made with the variable number of sunspots.

The first solar radio line attributed to atomic hydrogen was theoretically grounded by J.P. Wild in 1952. Its Zeeman profile was calculated and reliably established in the radiation from quiet Sun regions and activity features over sunspots in 2018 using observations with the RATAN-600 radio telescope, leading to the determination of several parameters of the line emitting regions and the estimation of magnetic fields in the solar atmosphere. In this paper, we calculate the Zeeman profile for two more hydrogen radio lines and show that they can be observed in activity features over sunspots.

The retrodiction and prediction of solar activity are two closely-related problems in dynamo theory. We applied Machine Learning (ML) algorithms and analyses to the World Data Center’s newly constructed annual sunspot time series (1700–2019; Version 2.0). This provides a unique model that gives insights into the various patterns of the Sun’s magnetic dynamo that drives solar activity maxima and minima. We found that the variability in the ~ 11 -year Sunspot Cycle is closely connected with 120-year oscillatory magnetic activity variations. We also identified a previously under-reported 5.5 year periodicity in the sunspot record. This 5.5-year pattern is co-modulated by the 120-year oscillation and appears to influence the shape and energy/power content of individual 11-year cycles. Our ML algorithm was trained to recognize such underlying patterns and provides a convincing hindcast of the full sunspot record from 1700 to 2019. It also suggests the possibility of missing sunspots during Sunspot Cycles −1, 0, and 1 (ca. 1730s-1760s). In addition, our ML model forecasts a new phase of extended solar minima that began prior to Sunspot Cycle 24 (ca. 2008–2019) and will persist until Sunspot Cycle 27 (ca. 2050 or so). Our ML Bayesian model forecasts a peak annual sunspot number (SSN) of 95 with a probable range of 80–115 for Cycle 25 between 2023 and 2025.

Solar activity indices differ over the solar disk, and different activity parameters are not considered to be symmetric between the northern and southern solar hemispheres. In the present paper, the daily data of a set of solar parameters (solar radio flux F10.7, total solar irradiance TSI, plage area PA, coronal index CI, solar flare index SFI, and solar mean magnetic field ǀBǀ) as well as the daily hemispheric sunspot areas (SSAs) and sunspot numbers (SSNs) during a timeframe 1945–2017 (covering almost the last seven solar cycles, 18 24) have been employed to investigate the north-south (N-S) asymmetry of the considered solar parameters based on the dominance of hemispheric distributions of SSAs and SSNs. The N-S asymmetry for each solar parameter has been investigated and the results revealed that it is a significant aspect through different years in the entire period. The grand average of each solar parameter for the northern and southern groups over each solar activity cycle has been calculated to investigate the statistical significance of N-S asymmetry of each solar parameter in each solar activity cycle. The solar cycles 19 and 24 displayed the dominance of the southern F10.7 and PA over the northern one. However, the solar cycle 23 showed the reverse. The grand average of CI displayed the southern preference in the solar cycle 19 while, the northern dominance of CI is revealed for the solar cycle 23. The grand averages of CI demonstrated nearly symmetric distribution in solar cycles 18, and 20–22. The N-S asymmetry of the grand averages of SFI exhibited a southern dominance during solar cycles 21 and 24. On the other hand, the northern preference is observed for the grand average of SFI through the solar cycle 23. The asymmetry of the grand averages of ǀBǀ obviously has the same dominance (sign) of hemispheric sunspot activity indices for the solar cycles 21–24. The periodic behavior of the N-S asymmetry of SSAs, SSNs, F10.7, and ǀBǀ has been investigated using Fast Fourier Transformation. Many mid- and long term periodicities have been detected. We present our results and discuss their possible explanations.

In manuscript considered human factor in traffic control. It was showed, that we cannot highlight one factor, which most influence to traffic controller or pilot. We need to consider a group of factors. We performed analysis of the influence of human factor in aviation shows that the latter should comprise several external factors, namely: intensity of traffic, weather conditions and magnetic storms, which are related with solar activity and unpredictability of magnetic storms caused by arising sunspots, as well as with putting into operation the new models of airplanes, to avionics of which pilots are forced to adapt for a definite period and acquire their own experience in operation with this model of aircraft.

Recent observations reveal the surprising breakdown of stellar gyrochronology relations at about the Sun's age hinting that middle-aged, solar-like stars transition to a magnetically inactive future. We provide a theoretical basis for these intriguing observations inspired by simulations with a mathematical dynamo model that can explore long-term solar cycle fluctuations. We reproduce the observed bimodal distribution of sunspot numbers, but only for subcritical dynamos. Based on a bifurcation analysis, we argue that ageing of solar-like stars makes the magnetically-weak dynamo regime readily accessible. Weak magnetic field production in this regime compromises wind-driven angular momentum losses thus disrupting the hegemony of magnetic braking on stellar rotational spin-down. This hypothesis of {\emph{subcritical magnetic dynamos}} of solar-like stars provides a self-consistent, unifying physical basis for a diversity of solar-stellar phenomena such as why stars beyond their mid-life do not spin-down as fast as in their youth, the break-down of stellar gyrochronology relations, the observed bimodal distribution of long-term sunspot observations and recent findings suggesting that the Sun may be transitioning to a magnetically inactive future., Comment: Press release by the Royal Astronomical Society, UK, at https://ras.ac.uk/news-and-press/research-highlights/magnetic-fields-implicated-mysterious-midlife-crisis-stars

Although the source active regions of some coronal mass ejections (CMEs) were identified in CME catalogues, vast majority of CMEs do not have an identified source active region. We propose a method that uses a filtration process and machine learning to identify the sunspot groups associated with a large fraction of CMEs and compare the physical parameters of these identified sunspot groups with properties of their corresponding CMEs to find mechanisms behind the initiation of CMEs. These CMEs were taken from the Coordinated Data Analysis Workshops (CDAW) data base hosted at NASA’s website. The Helioseismic and Magnetic Imager (HMI) Active Region Patches (HARPs) were taken from the Stanford University’s Joint Science Operations Center (JSOC) data base. The source active regions of the CMEs were identified by the help of a custom filtration procedure and then by training a long short-term memory network (LSTM) to identify the patterns in the physical magnetic parameters derived from vector and line-of-sight magnetograms. The neural network simultaneously considers the time series data of these magnetic parameters at once and learns the patterns at the onset of CMEs. This neural network was then used to identify the source HARPs for the CMEs recorded from 2011 till 2020. The neural network was able to reliably identify source HARPs for 4895 CMEs out of 14 604 listed in the CDAW data base during the aforementioned period.

The paper provides a short historical overview of sunspot observations from their discovery until the present. The review goes beyond collecting all known historical information about the study of sunspots but highlights the research of five scientists of different epochs over five centuries since the 16th. Not as much attention is deliberately given to some well-known studies and discoveries. The focus is on the utmost long-term observations of sunspots, which provide information that expands the boundaries of classical Wolf numbers or the number of sunspots groups. Sunspots have been observed since ancient times and they were documented in ancient chronicles. Active observation of sunspots began after the invention of the telescope, probably by Hans Lippershey in the early 17th century. It is documented that Thomas Harriot was the first to observe sunspots with a telescope on December 8, 1610. It is probable that Galileo Galilei and Johann Fabricius observed sunspots almost simultaneously with him in December 1610 using a telescope, independently of each other and of Harriot. The first publication about sunspots was issued by Fabricius in June 1611. We dwell on the observations of Christoph Scheiner, Christian Horrebow, Heinrich Schwabe, and Hisako Koyama. Christoph Scheiner described his long-term observations and studies of sunspots from 1611 to 1630 in his book Rosa Ursina sive Sol, which became a model for the Sun observers for many years afterwards. Christian Horrebow was the first to speculate on the regularity of sunspots, and Heinrich Schwabe was the first in 1843 to discover the periodicity (with a period of approximately 10 years) of the number of groups of sunspots. In 1852 Rudolf Wolf, analyzing all available sources, clarified that solar activity has an 11-year periodicity. He introduced the concept of the relative sunspot number and organized regular observations and publication of their results. Hisako Koyama’s 40-year observations have helped reconcile current sunspot counts with earlier ones. Wolf’s system lasted until the beginning of the 21st century. In July 2015, a new version of the relative sunspot numbers was adopted (Version 2.0). In this paper, the ratio of “new” and “old” Wolf numbers is calculated and a table of characteristics of 11‑year cycles according to Version 2.0 is proposed. Two forecasts of the maximum of solar cycle 25 are also calculated. In the case when the precursor of the maximum is the value of the relative sunspot number in the cycle minimum (correlation coefficient r = 0.557 and P

The main goal of this research project is to explore the properties, drawbacks and the robustness of the BX and KW methods to elicit NE and assess potential variations and improvements.

Sun is the primary source of energy in space. It generates a magnetic field which released in solar flares or coronal mass ejections for 11-year solar cycle that causes the occurrence of space weather. Different researchers in different parts of the world indicated that space weather highly affects agriculture production. However, in Ethiopia context especially Chokie mountain basin the influence of space weather on agriculture was not documented. Hence, this paper was aimed at investigating the impact of space weather on agriculture products over Chokie mountain basin. Assessment of space weather impacts on agriculture product is quite useful to balance energy and food security over developing countries like Ethiopia. Space weather (sunspot number), precipitation, temperature, and agriculture data were used for this study. Descriptive quantitative design method was applied on the data of agriculture products and climate variables. Furthermore, regression models with the help of MATLAB software were applied for data analysis. The relation between crop yield (teff, wheat, and maize) with sunspot number, temperature, and precipitation were analyzed in each agro-ecological zones using 31 years (1990–2019) data over Chokie mountain basin. The results showed that correlation coefficients between sunspot number with annual average value of temperature, precipitation, maize, teff, and wheat were found 0.11, − 0.32, − 0.47, − 0.52, and − 0.59, respectively. Sunspot had highly negatively correlated with annual spatial average value of teff and wheat. Generally, the occurrence of space weather (sunspot) leads to reduction of wheat and teff over the study area. Hence, shifting cultivation strategy is needed for local community during the occurrence of 11-year solar cycles frequency.

Study of sunspots cycles is a significant tool to understand space weather and its influence on the earth’s climate. This communication aims to study the sunspots individual cycles ranging from cycle 1st–23rd (1755–2008). Cycle 24th is still in continuation, so it is not included. The oscillatory behavior of sunspots in consecutive cycles in all these 23rd cycles is separately investigated. The study of sunspots cycles is focused on the relevance of numerous generalized autoregressive conditional heteroskedasticity (GARCH) models fitted to analyze and study their performance for delivering volatility forecasts for sunspot cycles. The GARCH (1, 1) model is used for detecting the aptness of autoregressive conditional heteroscedastic (ARCH) effect on sunspot cycles data, and Lagrange multiplier test is also applied. Most of the sunspot cycles follow auto-regressive (AR (2))-GARCH except cycles 7th, 15th, and 17th which follow AR (3)-GARCH model. AR (2)-GARCH model is the finest model which forecasts better as compared to other models. However, AR (2)-GARCH model is the adequate model for estimation and forecasting most of the sunspot cycles.

The active regions (ARs) on the Sun, which are distinguished by high values of the flare index and simultaneously developed outside activity complexes (ACs), have been analyzed. Thirteen such objects were identified in cycle 24. We showed that these ARs belong to the category of relatively long-lived large groups of sunspots, characterized by an increased rate of area growth. These ARs are part of the AR complexes, connect with other AR systems of high coronal systems, including trans-equatorial ones. We associated some of these ARs with short-lived (less than 3 Carrington rotations) ACs and some ARs are components of complexes of ARs. All 13 considered ARs were located near coronal holes.

We have located a forgotten record of sunspot observations made by Jean Charles Gallet in the year 1677, in the middle of the Maunder Minimum (the period between 1645 and 1715 characterized by very low solar activity). Gallet observed one sunspot group from April 9 to 15 and another from October 1 to 6. While the group observed in April was also recorded by other astronomers of that time, no observer recorded the group observed by Gallet in 1677 October. Moreover, Gallet indicated the latter group was composed by four different spots and provided astrometric measurements of the main spot. We have calculated the latitudes corresponding to the main sunspot recorded in the October. The mean latitude is around 10º south. Therefore, this sunspot was observed in the southern hemisphere, as were most of the spots observed during the Maunder Minimum.

The variable electromagnetic environment in geospace plays a crucial role in influencing the occurrence probability of satellite anomalies. FORMOSAT-3 (FS3) is a Low-Earth-Orbit (LEO) mission, which consists of six identical microsatellites that orbit in the altitude of 700–800 km and with an inclination of 72°. The dependences of the FS3 satellite anomalies on space weather conditions have not been investigated in the past. With an exception of a small number of extremely high geomagnetic events, we find that the occurrence rate of the FS3 anomalies is negatively correlated with the level of geomagnetic activity. Moreover, the relationship between numbers of anomalies and sunspots is also anti-correlated. A superposed epoch analysis demonstrates that the intensity of galactic cosmic rays (GCR) is relatively high at the times of the anomalies. All these results infer that the FS3 anomalies predominantly occurred under the conditions associated with low solar activity. The possible main cause for the FS3 anomalies is high-energy trapped protons or GCR. In summary, this paper presents a statistical result that a satellite can be prone to suffer an anomaly under low solar or geomagnetic activity.

We examined cycles of solar activity reconstructed based on the number of auroras observed at the middle and low latitudes in 1000–1700. We used a wavelet analysis method. Variations in the Earth’s magnetic moment influence the propagation of cosmic particles that cause auroras. We took this influence into account when reconstructing solar activity based on variations in the number of auroras. The analysis was carried out for a combined series: the reconstructed series of sunspots SN (1000–1700) and the modern SN series (1700–2000). Two dominant components were found in the SN spectrum: the near-centennial Gleissberg cycle, which consists of two modes with periods of 60–80 and 90–140 years, and a nearly two-century Suess cycle. When the the contribution of the magnetic moment is taken into account, the amplitudes of the periods of the Gleissberg group in the SN spectrum increase as compared to the initial spectrum of the aurora number, and their intensity approaches the intensity of the Suess variation. Analysis of changes in the amplitudes and periods of all cycles showed the presence of long-wave modulation with a possible period ranging from 1300 to 1700 years. As for the Gleissberg cycles, a frequency modulation with a period of 216 years by the Suess cycle was also revealed. We believe that the ~200-year component has an extrasolar nature and may reflect the result of the duplication of the fundamental frequency (11 and 22-year cycles) on multiple modulator modes.

The Maunder Minimum (MM) was a period of prolonged solar activity minimum between 1645 and 1715. Several works have identified a significant number of problematic spotless days in the MM included in existing data bases. We have found a list of exact spotless (in the second half of 1709) and spot days (January and August 1709) provided by Johann Heinrich Müller. We computed the most probable value and upper/lower limits of the active day fraction (ADF) from Müller's data using the hypergeometrical probability distribution. Our sample is not strictly random because Müller recorded observations in consecutive days when he observed sunspots. Therefore, our result represents an upper threshold of solar activity for 1709. We compared this result with annual values of the ADF calculated for the Dalton Minimum and the most recent solar cycles. We concluded that, although 1709 is one of the most active years in the MM, it was less active than most years both in the Dalton Minimum and in the most recent solar cycles. Therefore, the solar activity level estimated in this work for 1709 represents robust evidence of low solar activity levels in the MM.

We prove that positive recursive general quitting games, which are quitting games in which (a) each player has a single quitting action and possibly several continue actions, (b) the stage payoff as long as quitting does not occur is 0, and (c) the payoff when quitting occurs is non-negative, admit a sunspot $$\varepsilon $$ -equilibrium, for every $$\varepsilon > 0$$ .

We compare spectra of the zonal harmonics of the large-scale magnetic field of the Sun using observation results and solar dynamo models. The main solar activity cycle as recorded in these tracers is a much more complicated phenomenon than the eigen solution of solar dynamo equations with the growth saturated by a back reaction of the dynamo-driven magnetic field on solar hydrodynamics. The nominal 11(22)-year cycle as recorded in each mode has a specific phase shift varying from cycle to cycle; the actual length of the cycle varies from one cycle to another and from tracer to tracer. Both the observation and the dynamo model show an exceptional role of the axisymmetric $\ell_{5}$ mode. Its origin seems to be readily connected with the formation and evolution of sunspots on the solar surface. The results of observations and dynamo models show a good agreement for the low $\ell_{1}$ and $\ell_{3}$ modes. The results for these modes do not differ significantly for the axisymmetric and nonaxisymmetric models. Our findings support the idea that the sources of the solar dynamo arise as a result of both the distributed dynamo processes in the bulk of the convection zone and the surface magnetic activity., 12 pages, 12 Figures, accepted in MNRAS

The number of sunspots shows the solar activity level. During the high solar activity, emissions of matter and electromagnetic fields from the Sun make it difficult for cosmic rays to penetrate the Earth. When solar energy is high, cosmic ray intensity is lower, so that the solar magnetic field and solar winds affect the Earth externally and originate new viruses. In this paper, we assess the possible effects of sunspot numbers on the world virus appearance. The literature has no sufficient results about these phenomena. Therefore, we try to relate solar ray extremum to virus generation and the history of pandemics. First, wavelet decomposition is used for smoothing the sunspot cycle to predict past pandemics and forecast the future time of possible virus generation. Finally, we investigate the geographical appearance of the virus in the world to show vulnerable places in the world. The result of the analysis of pandemics that occurred from 1750 to 2020 shows that world's great viral pandemics like COVID-19 coincide with the relative extrema of sunspot number. Based on our result, 27 pandemic (from 36) incidences are on sunspot extrema. Then, we forecast future pandemics in the world for about 110 years or 10 cycles using presented multi-step autoregression (MSAR). To confirm these phenomena and the generation of new viruses because of solar activity, researchers should carry out experimental studies.

The relation between sunspots and rainfall patterns is still obscure in Africa, especially for Sudan and South Sudan. This research explores the response of rainfall to solar activity in eastern regions of Africa, with a case study in Sudan and South Sudan. Rainfall varies with time; therefore, skillful monitoring, predicting, and early warning of rainfall events is indispensable. Severe climatic events, such as droughts and floods, are critical factors in planning and managing all socioeconomic activities. Similar trends for the sunspot activity (sunspot number and sunspot groups) changes and rainfall variations for different stations in East Africa during the years 1910–2018 were not found. Correlation analysis carried out for the above period indicated a weak negative correlation between the total rainfall and the average number of sunspots over the long-term scale for selected stations in Sudan and South Sudan. The overall result of the paper indicated no significant relationship between sunspot numbers and rainfall in temporal and spatial scales in Sudan and South Sudan. HIGHLIGHTS This paper analyzed the rainfall variability of Sudan and South Sudan.; Many statistical measures were employed to evaluate the rainfall trend.; The paper specified the link between sunspot numbers and groups with rainfall variability.; The paper assessed the impact of climate change on rainfall annually and seasonally.

This work is a continuation of the author's studies,1,2,3 related to the elucidation of the physical nature of dark sunspots. They showed that the appearance of cold sunspots, the temperature of which is below the temperature of the photosphere, is incompatible with the second law of thermodynamics. Sunspots in the Sun's photosphere can only be hot. This article provides a thermodynamic analysis of the work of the Sun as a heat engine. It is shown that sunspots are dissipative structures that spontaneously appear in the photosphere of the Sun and ensure its viability as a source of optical radiation. Sunspots play the role of a cooler for the sun's global heat engine, and without them its radiant glow would be impossible, just like the operation of any heat engine without a cold heat sink. In addition, it is shown that all the phenomena of solar activity are caused by the operation of the photospheric heat engine of the Sun, in which sunspots are the source of heat.

The total solar irradiance fluctuates on the scale of 11 year cycle and is associated to sunspots, solar activity and climate. The sunspot number is an essential parameter for presenting the intens...