Sunspot Number Research Articles

The influence of small bipolar magnetic regions on basic solar quantities

Understanding the evolution of the solar magnetic field is of great importance for heliosphere, dynamo, and irradiance studies, for example. While the contribution of the field in active regions (ARs) hosting sunspots to the Sun's large-scale field has been extensively modelled, we still lack a realistic model of the contribution of smaller-scale magnetic regions such as ephemeral regions which do not contain any sunspots. For this work, we studied the effect of small and large bipolar magnetic regions (BMRs) on the large-scale solar magnetic field. The evolution of the total and open magnetic flux, the polar fields, and the toroidal flux loss since 1874 has been simulated with a surface flux transport model (SFTM) and the results were compared to analytical considerations and observational data. For this purpose, we constructed semi-synthetic BMR records using the international sunspot number as a proxy. We calculated the emergence rate of all BMRs from a single power-law size distribution, whose exponent varies with solar activity. The spatial distribution of the BMRs was calculated from statistical relationships derived from various solar observations. We included BMRs with a magnetic flux as low as $2 $ Mx in our SFTM, corresponding to regions with lifetimes down to one day. We found a good agreement between the computed total magnetic flux and observations, even though we do not have a free parameter to adjust the simulated total flux to observations, as in earlier versions of the employed SFTM. The open flux, the polar fields, and the toroidal flux loss are also consistent with observations and independent reconstructions. In our model, small BMRs contribute about one-third of the total and open flux at activity maximum, while their contribution increases to roughly half at activity minimum. An even greater impact is found on the polar fields and the toroidal flux loss, for which the contribution of small BMRs is comparable to that of spot-containing ARs at all activity levels. Even so, smaller regions, not included in our simulations, do not seem to play a significant role due to their high tilt angle scatter. Our simulation results suggest that most of the statistical noise is caused by large ARs, while small BMRs have a stabilising effect on the magnetic flux evolution, especially for the polar field reversals. We conclude that small BMRs (here, with magnetic fluxes between $2 $ Mx and $3 $ Mx) may also play an important role in the evolution of the solar magnetic field at large spatial scales. Their impact is largest at low solar activity, but it is also substantial during activity maxima, although the actual relative contributions by small and large regions depend on the steepness of their emergence rate distribution. The inclusion of small BMRs in SFTM simulations will allow the secular variability in solar irradiance to be better constrained and the generation of the poloidal field in the Babcock-Leighton dynamo to be better understood.

Statistical analysis of detected ionospheric anomalies with earthquake magnitudes: A case study of the New Zealand earthquakes of March 4, 2021

Statistical analysis of detected ionospheric anomalies with earthquake magnitudes was carried out on two seismic events of March 4, 2021, (M7.3 Gisborne and M8.1 Kermadec Earthquakes) to ascertain a possible link between observed perturbations and event size. GPS-TEC data were downloaded 20 days pre and 5 days post the events from stations within the epicenter of respective earthquakes. The data were statistically analyzed to detect unusual variations within the investigative window. The investigation revealed that the M7.3 Gisborne EQ shown two variations on –19 and –4 days; both being positive perturbations. However, five anomalies were detected for the M8.1 Kermadec EQ on –15, –11, –5, –3 and –2 days. With exception of the irregularities on –3 days, all others were positive anomalies. The observed anomalies were subjected to further scrutiny using the geomagnetic indices of Kernnifzer digit (kp) and disturbance storm time (Dst.) for geomagnetically induced perturbations while sunspot number and F 10.7 cm were used to monitor solar activities within this same period. The study suggested an increased in detected anomalies with earthquake magnitudes.

Interaction of global electron content with the Sun and solar wind during intense geomagnetic storms

Assessment of solar and solar wind parameters driving the ionosphere model is essential for prediction of the ionospheric weather. In the present paper impact of the different solar, interplanetary and geomagnetic parameters on the global electron content (GEC) during intense space weather storms is investigated. Hourly GEC values are calculated from JPL global maps of total electron content GIM-TEC from 1995 to 2023. The sample comprises 90 intense storms from 1995 to 2023 associated with monthly peak of the weighted accumulation of the geomagnetic Apo(τ, t) index exceeding 90 nT. The 27 day weighted accumulation of the solar sunspot numbers SSN2(τ), solar radio flux F10.7(τ), the solar hydrogen emission Lyman_α(τ) and the composite magnesium MgII(τ) indices are explored as precursors of GEC enhancements. As distinct from the positive ionosphere storm, the solar wind speed Vsw, the solar wind electric field Ey, merging electric field Em and Apo(τ, t) indices proved to be effective as potential drivers of the negative GEC depletion. The positive and negative dGEC deviations from hourly GEC are produced by subtracting a quiet reference GECav averaged during 24h prior the storm normalized by GECav. The hourly storm profiles Vsw(t), Em(t), Ey(t), Apo(τ, t), Dst(t), GEC(t) and dGEC(t) were reduced by method of superposed epochs. The zero epoch t0 = 0 was taken at the peak Apo*(τ, t0) and the storm time lasted for 48h from −12h prior t0 and 35h afterwards. The best correlation of the positive storm dGECp amplitude is obtained with MgII(τ) and the negative storm dGECn with Em* and Apo*(τ, t0) which are used to derive characteristics of five key points of storm-time dGEC(t) model: 1 – onset of the storm profile t1 = t(dGECp); 2 – the amplitude dGECpmax and its time t2(dGECpmax); 3 – the time of transition t3(dGEC = 0) from the positive to negative (±) GEC storm; 4 – minimum negative disturbance dGECnmin and its time t4(dGECnmin), 5 – the end of the storm profile t5(dGECn). Analytical model of dGEC(t) is derived with Epstein step functions fitting 5 key points. Deviations dGEC(t) are inverted to GEC(t) using quiet reference pre-storm GECav. The model is validated for three intense storms on 26–28 February, 23–25 March and 23–25 April 2023. The results show improvement of dGEC forecast with RMS error reduced from 45 to 80% compared to results produced by the international reference ionosphere−plasmasphere model IRI-Plas.

A Multi-Input Convolutional Neural Networks Model for Earthquake Precursor Detection Based on Ionospheric Total Electron Content

Earthquakes occur all around the world, causing varying degrees of damage and destruction. Earthquakes are by their very nature a sudden phenomenon and predicting them with a precise time range is difficult. Some phenomena may be indicators of physical conditions favorable for large earthquakes (e.g., the ionospheric Total Electron Content (TEC)). The TEC is an important parameter used to detect pre-earthquake changes by measuring ionospheric disturbances and space weather indices, such as the global geomagnetic index (Kp), the storm duration distribution (Dst), the sunspot number (R), the geomagnetic storm index (Ap-index), the solar wind speed (Vsw), and the solar activity index (F10.7), have also been used to detect pre-earthquake ionospheric changes. In this study, the feasibility of the 6th-day earthquake prediction by the deep neural network technique using the previous five consecutive days is investigated. For this purpose, a two-staged approach is developed. In the first stage, various preprocessing steps, namely TEC signal improvement and time-frequency representation-based TEC image construction, are performed. In the second stage, a multi-input convolutional neural network (CNN) model is designed and trained in an end-to-end fashion. This multi-input CNN model has a total of six inputs, and five of the inputs are designed as 2D and the sixth is a 1D vector. The 2D inputs to the multi-input CNN model are TEC images and the vector input is concatenated space weather indices. The network branches with the 2D inputs contain convolution, batch normalization, and Rectified Linear Unit (ReLU) activation layers, and the branch with the 1D input contains a ReLU activation layer. The ReLU activation outputs of all the branches are flattened and then concatenated. And the classification is performed via fully connected, softmax, and classification layers, respectively. In the experimental work, earthquakes with a magnitude of Mw5.0 and above that occurred in Turkey between 2012 and 2019 are used as the dataset. The TEC data were recorded by the Turkey National Permanent GNSS Network-Active (TNPGN-Active) Global Navigation Satellite System (GNSS) stations. The TEC data five days before the earthquake were marked as “precursor days” and the TEC data five days after the earthquake were marked as “normal days”. In total, 75% of the dataset is used to train the proposed method and 25% of the dataset is used for testing. The classification accuracy, sensitivity, specificity, and F1-score values are obtained for performance evaluations. The results are promising, and an 89.31% classification accuracy is obtained.

Reconstructing daily group sunspot numbers since the maunder minimum with objective inter-calibration algorithms

We present a new daily Group Sunspot Numbers (GSN) reconstruction from the Maunder minimum to Solar Cycle 24/25. This new reconstruction was obtained as a result of rectifying the raw and uncalibrated GSN database of Vaquero et al. (2016) and incorporating data from previously unconsidered GSN sources. Notably, a pivotal challenge encountered during the reconstruction of this GSN activity record, lay in the inter-calibration of different databases reported by multiple observers. The challenge is further compounded by data gaps that are particularly prevalent during the Maunder minimum. We have applied a novel methodology to solve these obstacles, entailing the calibration and standardization of all GSN databases relative to a reference observer. Our novel approach employs calibration techniques, ensuring standardized visual acuity between all individual observers. Moreover, our methodology accommodates variations in climatic, geographic, and instrumental conditions encountered by observers during their respective sunspot observations, thus establishing a uniform comparative framework. Furthermore, a comparative analysis was conducted with a total of four other different GSN reconstructions, revealing notable distinctions and resemblances that can be explained by the implementation of diverse methodologies in the respective GSN reconstruction processes and steps. In addition to the temporal differences found, both the wavelet and multi-cross wavelet analyses were carried out, which allowed a quantification of the differences and similarities in the spectral contents of various GSN records. The wavelet analysis results show the similarities and differences of the new GSN reconstruction with the inter-calibration algorithm when comparing it both temporally and spectrally with other GSN reconstructions. The periodicities of this analysis are 1.2, 5.5, 10.9, 20.6, 30.9, 58.4, and 119.8 years and 3.47, 5.4, 9.8, 27.8, 66.1, 117.8, and 160.5 days respectively.

SOLAR AND GEOMAGNETIC ACTIVITY IN 19-25 CYCLES

The paper presents the results of the analysis of changes solar and geomagnetic activity in 19−25 Wolf cycles. A forecast of the maximum geomagnetic activity cycle 25 is made. Solar activity is presented by sunspot number RZ, geomagnetic activity is expressed by the energetic index calculated from the data of the "Lviv" and "Belsk" geomagnetic observatories. By annual averages RZ values, the 11-year window was used to obtain the solar activity minimum (around 1711, 1810, 1901, and 2009). The minimum of 2009 was one of the smallest in the observed data, and we took it as the beginning of the 24th cycle and the 100-year solar activity cycle. The maximum of the 24th cycle occurred in 2014 for RZ and in 2015 for energetic index. Cycle 25 began in 2019 according to RZ, and in 2020 cording to energetic index. For cycles 19−25 solar activity is 1−2 years ahead of magnetic activity. The identified quasi-biennial variations over the studied period and the lag of geomagnetic activity from solar activity allow us to predict the magnitude of geomagnetic activity and its maximum in cycle 25. According to our calculations, the maximum of geomagnetic activity will occur around 2026 and its magnitude will be 1.5−2 times higher than the maximum of the 24th cycle.

THE EARTH’S MAGNETIC FIELD AND THE LARGE-SCALE MAGNETIC FIELD OF THE SUN: THE SOLAR-TERRESTRIAL CONNECTION

The paper presents the results of a joint analysis of the Earth's main magnetic field (core field) BIGRF and the large-scale magnetic field (LSMF) of the Sun. Selected 11- and 22-year periods of LSMF and BIGRF variations are well manifested in both fields and are usually modulated by solar activity. Even 11-year cycles for which the direction of the Sun's magnetic field coincides with the direction of the Earth's magnetic field are characterized by the minimum values of sanspot numbers, and odd cycles with opposite directions of magnetic fields have larger values of sunspot numbers. The rotation rate of two- and four-sector structure of the Sun source of LSMF varied with about 11-year and 22-year cycle. Longer changes in the magnetic fields of the Sun and the Earth with a period of about 75 years have also been revealed. The rotation periods of the Sun source global field (28.0-28.5 days) were maximum at the middle of the 20th century in the period 1940÷1960 years. This maximum of solar activity corresponds to temporal gradient of geomagnetic field. It is shown that the gradient of the geomagnetic field BIGRF depends on the rate of change in the length of the day. So, according to the results of the study, the rotation modes of the Sun and the Earth cause different periodic changes in their magnetic fields.

Wavelets in the analysis of local time series of the Earth's surface air

The practical application of local smoothing and wavelet analysis methods for studying the spectral composition and coherent relationships of local average annual surface air temperatures with solar activity and the displacement of the Earth's North Pole is presented. A preliminary analysis of local time series of surface temperatures revealed the presence of emissions and their localization. It is shown that to eliminate the influence of outliers (short-term events) on the reliability of identifying a long-term nonlinear trend, the wavelet decomposition method, which filters high frequencies, is most suitable. Functional approximation models are constructed and compared at different levels of wavelet decomposition of the data. Time or scale smoothing is used to improve the reliability of the wavelet spectrum. Based on data on average annual surface air temperatures in Yalta (44.48⁰, 34.17⁰, = 72.0 m) for the time interval from 1869 to 2022, functional models of long-term trends were built and used to obtain short-term forecasts. Information about the linear relationship of events in the compared time series is obtained and discussed in the analysis of wavelet cross-correlation, wavelet coherence and phase coherence. Local similarities were discovered between data on surface air temperature and solar activity data (Wolf numbers) for a period of ∼(30–70) years, as well as oscillations with period of 11 years, manifested in the constancy of the phase difference and an increase in the modulus of wavelet coherence power over time. Localized similarities were also found in data on surface air temperature in Yalta and in data on displacements of the Earth's mean pole relative to the conventional beginning of EOP (IERS) CO1 in the interval of periods ∼ (30–70) years.

Correlation between Supergranular Lane Widths and Sunspot Number; A Simple Way to Predict the Amplitude of Sunspot Cycle

The network structure seen in the solar images is the outline of supergranulation, which is the large-scale convection in the Sun with a size of about 30 Mm and a lifetime of 24 hr. We have obtained the supergranulation lane widths from the autocorrelation function of image windows from the Ca ii K spectroheliograms. The images are obtained from the 100 yr Kodaikanal data, which contains information on more than nine solar cycles. The lane widths are known to show a positive correlation with the sunspot number. It is now found that the lane widths, obtained near the mid-latitudes during the sunspot cycle minima, are strongly correlated to the following sunspot number maxima. A straight-line fit adequately describes the variation. It is also found that the correlation is weak or insignificant at other times. The strong correlation of the two parameters thus provides a simple way to predict the maximum sunspot number about 4–5 yr in advance. The results are important in space weather predictions and solar irradiance variations.

Causal Analysis of Influence of the Solar Cycle and Latitudinal Solar-Wind Structure on Co-Rotation Forecasts

Studying solar-wind conditions is central to forecasting the impact of space weather on Earth. Under the assumption that the structure of this wind is constant in time and co-rotates with the Sun, solar-wind and thereby space-weather forecasts have been made quite effectively. Such co-rotation forecasts are well studied with decades of observations from STEREO and near-Earth spacecraft. Forecast accuracy is primarily determined by three factors: i) the longitudinal separation of spacecraft from Earth determines the corotation time (and hence forecast lead time) [δ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$\\delta$\\end{document}t] over which the solar wind must be assumed to be constant, ii) the latitudinal separation (or offset) between Earth and spacecraft [δθ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$\\delta\ heta$\\end{document}]] determines the degree to which the same solar wind is being encountered at both locations, and iii) the solar cycle, via the sunspot number (SSN), acts as a proxy for both how fast the solar-wind structure is evolving and how much it varies in latitude. However, the precise dependencies factoring in uncertainties are a mixture of influences from each of these factors. Furthermore, for high-precision forecasts, it is important to understand what drives the forecast accuracy and its uncertainty. Here we present a causal inference approach based on information-theoretic measures to do this. Our framework can compute not only the direct (linear and nonlinear) dependencies of the forecast mean absolute error (MAE) on SSN, Δθ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$\\Delta \ heta $\\end{document}, and Δt\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$\\Delta t$\\end{document}, but also how these individual variables combine to enhance or diminish the MAE. We provide an initial assessment of this with the potential of aiding data assimilation in the future.

Dynamics of dissolved Fe content in tributaries of Lake Teletskoe, depending on solar activity indicators

Relevance. The need to expand and deepen the understanding of the influence of solar radiation indicators on chemical characteristics of surface water, since the dependence of hydrochemical processes on periodic changes in solar activity has so far been studied extremely poorly. In addition, special attention is paid worldwide to the study of iron content in waters of rivers and lakes. Iron increased concentrations are one of the reasons for the "brownification" of surface waters in a significant part of the Northern Hemisphere. Aim. To establish a relationship between iron content and dynamics in the waters of the tributaries of Lake Teletskoe with indicators of solar activity (sunspots number, F-index). Methods. Water samples from the tributaries of Lake Teletskoe were collected into clean new polyethylene bottles in the estuaries of the rivers, from a depth of 0.5 m during the spring-summer high water and autumn low water, in 2016–2020. Content of total and dissolved Fe in the waters was determined by the ISP-MS method and by the AAS method. We used the data on solar activity indicators from the Belgian Observatory, which are freely available. Results. The total Fe content in the rivers of Lake Teletskoe basin for the period from 2016 to 2020 changes from 5 to 340 µg/l. Concentrations of dissolved iron (4 to 200 µg/l) do not exceed Russian standards, but they are often noticeably higher than the global average for river waters established abroad. The highest iron content, as well as the proportion of its soluble forms in the tributaries of Lake Teletskoe and in lake waters, was noted in 2016. It is probably due to the highest rates of solar activity. They cause certain changes in the environment – such as an increase in air temperature and water evaporation, and decrease in river flow, which accompanied by growth in concentrations of chemical elements in surface waters. Since 2016, there has been a steady decrease in dissolved iron concentration in surface natural waters of Lake Teletskoe basin, which may be a consequence of a decrease in solar radiation intensity in recent years.

Solar Flare 1/f Fluctuations from Amplitude-Modulated Five-Minute Oscillation.

We first report that the solar flare time sequence exhibits a fluctuation characterized by its power spectral density being inversely proportional to the signal frequency. This is the 1/f fluctuation, or pink noise, observed ubiquitously in nature. Using GOES16 data, we found that low-energy flares (E≤Emean) display 1/f fluctuations, whereas high-energy flares (E>Emean) show a flat spectrum. Furthermore, we found that the timing sequence of the flares reveals clearer 1/f fluctuations. These observations suggest that the solar flare 1/f fluctuations are associated with low-energy phenomena. We investigated the origin of these 1/f fluctuations based on our recent hypothesis: 1/f fluctuations arise from amplitude modulation and demodulation. We propose that this amplitude modulation is encoded by the resonance with the solar five-minute oscillation (SFO) and demodulated by magnetic reconnections. We partially demonstrate this scenario by analyzing the SFO eigenmodes resolving the frequency degeneration in the azimuthal order number m using the solar rotation and resonance. Given the robust nature of 1/f fluctuations, we speculated that the solar flare 1/f fluctuations may be inherited by the various phenomena around the Sun, such as the sunspot numbers and cosmic rays. In addition, we draw parallels between solar flares and earthquakes, both exhibiting 1/f fluctuations. Interestingly, the analysis applied to solar flares can also be adapted to earthquakes if we read the SFO as Earth's free oscillation and magnetic reconnections as fault ruptures. Moreover, we point out the possibility that the same analysis also applies to the activity of a black hole/disk system if we read the SFO as the quasi-periodic oscillation of a black hole.

Association between gestational exposure to solar activity and pregnancy loss using live births from a Massachusetts-based medical center

BackgroundSolar activity has been linked to biological mechanisms important to pregnancy, including folate and melatonin levels and inflammatory markers. Thus, we aimed to investigate the association between gestational solar activity and pregnancy loss. MethodsOur study included 71,963 singleton births conceived in 2002–2016 and delivered at an academic medical center in Eastern Massachusetts. We studied several solar activity metrics, including sunspot number, Kp index, and ultraviolet radiation, with data from the NASA Goddard Space Flight Center and European Centre for Medium-Range Weather Forecasts. We used a novel time series analytic approach to investigate associations between each metric from conception through 24 weeks of gestation and the number of live birth-identified conceptions (LBICs) —the total number of conceptions in each week that result in a live birth. This approach fits distributed lag models to data on LBICs, adjusted for time trends, and allows us to infer associations between pregnancy exposure and pregnancy loss. ResultsOverall, the association between solar activity during pregnancy and pregnancy loss varied by exposure metric. For sunspot number, we found that an interquartile range increase in sunspot number (78·7 sunspots) in all of the first 24 weeks of pregnancy was associated with 14·0 (95% CI: 6·5, 21·3) more pregnancy losses out of the average 92 LBICs in a week, and exposure in weeks ten through thirteen was identified as a critical window. Although not statistically significant, higher exposure to Kp index and to UV radiation across all 24 weeks of pregnancy was associated with more and less pregnancy losses, respectively. ConclusionWhile exposure to certain metrics of solar activity (i.e., sunspot number) throughout the first 24 weeks of pregnancy may be associated with pregnancy losses, exposure to other metrics were not. Solar activity is a complex phenomenon, and more studies are needed to clarify underlying pathways.

Long-term equatorial ionosphere variations over Ethiopia

This paper focuses on the investigation of the long-term behavior of the equatorial ionosphere in Ethiopia. To explore the extended ionospheric variations, we analyze Total Electron Content (TEC) fluctuations in conjunction with solar activity indices, including F10.7 radio flux, EUV radiation, and Sunspot Number (SSN). The dataset used encompasses GPS-derived TEC records spanning 11 consecutive years from 2007 to 2017, corresponding to the period of solar cycle 24. Our analysis shows that the highest TEC levels generally occur during the post-noon hours, while the lowest values are observed around post-midnight or early morning. Notably, exceptions to this pattern are found in 2011 and 2013 when the highest TEC levels are observed during the December solstice. Otherwise, the seasonal TEC variation exhibits a semi-annual pattern, with peak TEC values occurring during the equinoxes and the lowest values during the solstices. Further examination demonstrates that in both solar activity phases, TEC magnitude is higher during the March Equinox compared to the September Equinox, and slightly higher during the December Solstice compared to the June Solstice. This reveals an asymmetry in the seasonal variations, encompassing the equinoxes, solstices, and the ascending and descending phases of the solar cycle. Our study confirms that long-term fluctuations in ionospheric TEC closely correspond to variations in solar activity indices. Correlation analysis indicates a strong link between all solar activity indices and TEC. Notably, while a negative correlation is observed in 2007, the correlation in 2011 is remarkably stronger. Additionally, we find that the long-term TEC variation exhibits stronger correlations with EUV and F10.7 radio flux than with SSN, with correlation coefficients of 0.86, 0.85, and 0.78, respectively. Lastly, our study extends previous research by identifying the long-term trends of vertical TEC (vTEC) in relation to various driving factors such as F10.7, SSN, and EUV.

Solar activity: Towards a standard classification of solar phases from cycle 1 to cycle 24

This paper aims to develop a standard classification method of solar phases from Cycles 1 to 24. The purpose is to establish new solar cycle cutting criteria. The maximum sunspot number values (SNmax) of previous criteria were examined. In addition, the evolution of sunspot appearance latitudes (maximum latitude (λ_max) and minimum latitude (λ_min)) was taken into account. This has enabled new criteria to be developed. These criteria take into account the actual Sun' behavior. They also resolve past inconsistencies between classification criteria and new sunspot data. Four phases have been retained: minimum, increasing, maximum and decreasing phases. The new sunspot number (SN) data computed by the Belgian Observatory have been taking into account. SN data set have been smoothed to obtain normalized curves that allowing to represent solar sunspot numbers evolution as a trigonometric function. The mathematical hypotheses formulated concern sunspot appearance latitudes and the identification of the solar cycle. The results show that the different phases do not have the same duration. The increasing phase is quite fast compared to the decreasing one. In fact, the method proposed in this work presents a new cutting criterion as follow: (i) minimum phase: SN(t) < 0.122 × SNmax; (ii) increasing phase: 0.122 × SNmax ≤ SN(t) ≤ 0.73 × SNmax; (iii) maximum phase: SN(t) > 0.73 × SNmax and (iv) decreasing phase: 0.73 × SNmax ≥ SN(t) > SNmin (next cycle).

Solar cycle prediction using a combinatorial deep learning model

Abstract The long-term prediction of the solar cycle is of great significance for aerospace, communication, and space missions. For a long time, many studies have used relatively primitive deep learning methods to predict the solar cycle, and most of them do not perform well in the long-term prediction. In this paper, we proposed XG-SN ensemble model. The model used extreme gradient boosting (XGBoost) ensemble learning method, combined with sample convolution and interaction net (SCINet) and neural basis expansion analysis for the interpretable time series (N-BEATS) to make predictions for known solar cycles. 13 months of smoothed monthly total sunspot numbers were selected as the dataset. The model performance was evaluated by mean absolute error (MAE), root mean square error (RMSE), and mean absolute time lag (MATL) between the predicted and actual values. The first two evaluation metrics measured the prediction deviation from the numerical dimension, and the last one measured the prediction deviation from the temporal dimension. The results show that the model achieves the MAE, RMSE, and MATL values of 13.19, 17.13, and 0.08, respectively, in Solar Cycle 13 to 24. Our model is able to better predict in most cycles, ensuring accurate prediction of peaks with little time lag.

A New Index to Describe the Relationship between Solar Extreme Ultraviolet Variation and Solar Activity

In this paper, a new solar activity index based on a novel disturbance extraction method, the spectral whitening method (SWM), is introduced to process the solar EUV data on the Atmospheric Imaging Assembly (AIA) on board the Solar Dynamics Observatory. Our research suggests that the spatial information derived by SWM can well reflect the location of disturbance extraction, which is consistent with the location of the solar active region. It indicates that the disturbance extraction is effective. From AIA 094 Å to AIA 335 Å, SWM results are strongly correlated with solar radio flux F107 and the sunspot number (SSN), especially at AIA 211 Å, where the correlation coefficient reaches the maximum, while at AIA 1600 Å and AIA 1700 Å there are no detectable correlations. The proposed new solar activity index, , has the following characteristics: (1) the new index can reflect the main variations of F107 and SSN, indicating that the index is valid; (2) the new index has higher temporal resolution, which is more conducive to the more detailed study of solar activities on short timescales; (3) the new index reveals that the solar atmosphere still has significant variability during solar minimum characterized by low F107 and SSN; (4) the new index can be used in conjunction with the new magnetospheric and ionospheric indices, which are also derived by SWM to deepen the understanding of the causal chain of space weather and promote the improvement of forecasting capabilities.

Relation between Latitude-dependent Sunspot Data and Near-Earth Solar Wind Speed

Solar wind is important for the space environment between the Sun and the Earth and varies with the sunspot cycle, which is influenced by solar internal dynamics. We study the impact of latitude-dependent sunspot data on solar wind speed using the Granger causality test method and a machine-learning prediction approach. The results show that the low-latitude sunspot number has a larger effect on the solar wind speed. The time delay between the annual average solar wind speed and sunspot number decreases as the latitude range decreases. A machine-learning model is developed for the prediction of solar wind speed considering latitude and time effects. It is found that the model performs differently with latitude-dependent sunspot data. It is revealed that the timescale of the solar wind speed is more strongly influenced by low-latitude sunspots and that sunspot data have a greater impact on the 30 day average solar wind speed than on a daily basis. With the addition of sunspot data below 7.°2 latitude, the prediction of the daily and 30 day averages is improved by 0.23% and 12%, respectively. The best correlation coefficient is 0.787 for the daily solar wind prediction model.

Hemispheric prediction of solar cycle 25 based on a deep learning technique

In the current work, single-and double-layered Long Short-Term Memory (LSTM) model have been developed and compared to find the most suitable one for hemispheric prediction of solar cycle 25. The smoothed Hemispheric Sunspot Number (HSN) reconstructed by Veronig et al. (2021) has been used to achieve the objective. The deep learning models are evaluated over different pairs of train and test set for both the hemispheres using the 5-fold cross-validation scheme, to determine the best effective model for hemispheric prediction of cycle 25. Our analysis reveals that the single-layered LSTM model achieves lower RMSE when predicting the test dataset. To prove the reliability of our suggested LSTM models, we have predicted the hemispheric profiles of solar cycles 21–24. From our analysis, we found that the single-layered LSTM model performed better in comparison to the double-layered LSTM model in predicting past solar cycles 21–24. Hence, hemispheric prediction of solar cycle 25 is carried out utilizing the single-layered LSTM model due to better performance capability during experimental analysis. This work founds that the northern hemisphere will peak with an amplitude of 56 ± 5 during July 2023 + 3 months while the southern hemisphere will have a maximum amplitude of 54 ± 4 during June 2023 + 2 months. So, it can be said that the southern HSN will peak before the northern HSN and that the peak of northern HSN will be slightly higher than the southern one.

Study of the Effect of Solar Indices on the Ionosphere Layer of Mars

This paper studies the effect of the solar indices (total sunspot no., solar wind density and coronal mass ejection linear speed) on F2- layer electron density, as well as, the comparison of seasonal variations of electron density of F2- layer, NmF2, for Mars at local noontime and for maximum and minimum solar cycles. Results show that there is an inverse correlation between sunspot number, solar wind density, CME linear speed and ionosphere electron density for Mars, at maximum and minimum solar cycles. This correlation is clear when electron density is at minimum value. The maximum value of NmF2 was in month 4 (Summer), month 21 (Winter) during maximum solar cycle, and month 1 (Spring), month 24 (Spring) during minimum solar cycle. The minimum value of NmF2 was in month 13 (Autumn) during maximum solar cycle, and month 9 (Summer) during minimum solar cycle. NmF2 was approximately constant in months 1- 8 (Spring and Summer) and gradually decreased in months 9- 13 (Summer and Autumn), then, gradually increased in months 14- 18 (Autumn and Winter) during maximum solar cycle (2012, 2013). In other hand, NmF2 was approximately constant in months 1- 5 (Spring and Summer) and gradually decreased in months 6- 9 (Summer), then, gradually increased in months 10- 16 (Autumn and Winter) during minimum solar cycle (2016, 2017).