Average Sunspot Number Research Articles

Phase “Rise” of The 11-Year Solar Cycle with Contribution to Global Warming – Examples from The Bulgarian Meteo Stations’ Temperature Data

A high negative correlation between the average Sun Spot Number in phase “rise” in the 11-year cycle of solar activity and the annual average Earth’s surface temperature was observed in the data from several meteorological stations – first in the temperature data from meteorological stations in Bulgaria, and then from many stations from Europe and the world. As solar activity has decreased over the last 70 years – the last few solar cycles up to the 24th number have had a monotonically decreasing number of sunspots – their negative correlation with temperature results in a rising surface air temperature. This increase is related to processes in the Sun’s magnetosphere and has nothing to do with the increasing concentration of greenhouse gases in the surface atmosphere. The increasing concentration of greenhouse gases may be also a consequence of the processes taking place on the earth’s surface as a result of solar activity and is not a cause of the increasing temperature of the earth’s surface.

Data-Driven Forecasting of Sunspot Cycles: Pros and Cons of a Hybrid Approach

Understanding the number of sunspots is crucial for comprehending the Sun’s magnetic-activity cycle and its influence on space weather and the Earth. Recent advancements in machine learning have significantly improved the accuracy of time-series predictions, revealing a compelling approach for sunspot forecasts. Our work takes the pioneering work by proposing a hybrid forecasting approach that combines the Seasonal Autoregressive Integrated Moving Average (SARIMA) with machine-learning algorithms like Random Forest and Support Vector Machine, delivering high prediction accuracy. Despite its high accuracy, we highlight the need for caution in deploying machine-learning-based methods for sunspot-number prediction, demonstrated through a detailed case study with only three extra time stamps leading to a dramatic change. More specifically, when making a forecast of monthly averaged sunspot numbers from 2023–2043 based on data from 1749–2023, we found that the observations in June, July, and August 2023 have a significant impact on the forecast, particularly in the long term. Given the multiseasonal and nonstationary nature of the sunspot time series, we conclude that this kind of phenomenon cannot be simply captured by a pure data-driven model, which can be highly sensitive in the forecast in the long term, and requires a more comprehensive approach, possibly with a model that includes physics.

Key Signatures of Prominence Materials and Category of Cold Materials Identified by Random Forest Classifier

The origin of cold materials identified by different criteria is unclear. They are highly suspected to be erupted prominences. However, some cold materials defined by charge depletion exist in both quiet solar wind and interplanetary coronal mass ejections (ICMEs). Recently, solar observations show failed prominence eruption in coronal mass ejections (CMEs) that the prominence sometimes did not propagate into interplanetary space. This work uses Random Forest Classifier (RFC), which is an interpretable supervised machine-learning algorithm to study the distinct signatures of prominence cold materials (PCs) compared to quiet solar wind (QSW) and ICMEs excluding cold materials (ICMEEs). Twelve physical features measured by ACE at 1 au and the monthly averaged sunspot number are used in this study. The measurements from ACE are proton moments, magnetic field component B z , He/H, He/O, Fe/O, mean charge of oxygen and carbon, C6+/C5, C6+/C4+, and O7+/O6+. According to the returned weights from RFC that are checked by support vector machine classifier, the most important in situ signatures of PCs are obtained. Next, the trained RFC is used to check the category of the cold materials not related to CME observations. The results show that most segments of the cold materials are from prominences, but four of them are possibly from ICMEEs; another one segment is possibly from QSW. The most distinct signatures of PCs are lower (C6+/C5+)/(O7+/O6+), proton temperature, and He/O. Considering the obvious overlaps on key physical features between QSW, ICMEEs, and PCs, the multifeature classifier shows an advantage in identifying them than solid criteria.

Study of the Relationship Between Sunspot Number and the Duration of the ≈ 1.6 – 2.2 Year Period in Neutron Monitor Counting Rates

Neutron monitor counting rates show periodicities in the ≈ 1.6 – 2.2-year range. These periodicities have been associated with a solar origin affecting the cosmic ray propagation conditions through the heliosphere. Our hypothesis is that the periodicities in the ≈ 1.6 – 2.2-years range correspond to a single periodicity that changes its duration over time.López-Comazzi and Blanco (Astrophys. J.927(2), 155, 2022) found that the duration of the ≈ 1.6 – 2.2-year period (tau ) is linearly related to the average sunspot number (SSN_{a}) in each solar cycle. The relationship shows that shorter ≈ 1.6 – 2.2-year periods occur during stronger cycles when SSN_{a} is higher. Therefore, the duration of this period varies from one solar cycle to another. This study focuses on this relation. For obtaining this relation, the values of the duration of the ≈ 1.6 – 2.2-year period in global neutron monitor counting rates (a virtual station determined by averaging of the different neutron monitor counting rates along the world) along the Solar Cycles 20 – 24 have been used. We extend the sample by adding the duration of the ≈ 1.6 – 2.2-year period in Huancayo neutron monitor counting rates along Solar Cycle 19 to this linear relationship. Once the linear relationship is extended, tau for the current Solar Cycle 25 is computed giving ≈ 2.24 years. Drawing on this more accurate relationship given by SSN_{a} = (-120 pm 10) : tau + (320 pm 20), we computed tau for the cycles previous to the existence of neutron monitors (Solar Cycles 7 – 18).These ≈ 1.6 – 2.2-year periodicities in neutron monitor counting rates could be produce by variations in the solar magnetic field due to an internal mechanism of the solar dynamo called Rossby waves. Concretely, the harmonic of fast Rossby waves with m=1 and n=8 fit with the detected ≈ 1.6 – 2.2-year periodicity. In addition, the variation of the solar magnetic-field strength from weaker to stronger solar cycles could explain the different periods detected in each cycle. Based on the detected periodicities using the dispersion relation for fast Rossby waves, a solar tachocline magnetic-field strength of ≈ 7 – 25 kG has been estimated.

Comparison of solar activity proxies: eigenvectors versus averaged sunspot numbers

ABSTRACTWe explore the links between the averaged sunspot numbers (SSN) and a modulus summary curve (MSC) of two largest eigenvectors of the solar background magnetic field (SBMF) derived from principal component analysis. MSC has rather close correspondence with the whole set of SSN revealing close cycle timings, duration, and maxima times for the cycles 12–24, 6, 7, and −4, −3, while for a few cycles in the mid-18th and mid-19th centuries there are discrepancies in the maximum amplitudes, durations, and times of the maxima. Possible reasons of these discrepancies related to uncertainties in the SSN observations in the 18th–19th centuries, in MSC definition and the different solar activity entities they represent: toroidal (SSN) and poloidal (MSC) magnetic fields, are discussed. Wavelet and Fourier spectral analysis of SSN and MSC series reveal within 95 per cent confidence levels the same prominent period of 10.7 yr, whereas SSN series show a period of 101 yr and MSC of 342 yr close to or above 95 per cent red-noise level. The correlation coefficients between SSN and MSC series vary from 0.25 for the whole SSN data set (from 1700), to 0.56 for the data sets from 1860, to 0.67 for the data sets from 1900 when all SSN restorations agree. These SSN and MSC data sets are confirmed to be closely but not identically related representing the solar activity in different entities of solar dynamo. Use of the summary curve and MSC of eigenvectors of SBMF can provide additional information to SSN for better understanding of solar activity.

Periodicities in Solar Activity, Solar Radiation and Their Links with Terrestrial Environment

Solar magnetic activity is expressed via variations of sunspots and active regions varying on different timescales. The most accepted is an 11-year period supposedly induced by the electromagnetic solar dynamo mechanism. There are also some shorter or longer timescales detected: the biennial cycle (2 - 2.7 years), Gleisberg cycle (80 - 100 years), and Hallstatt’s cycle (2100 - 2300 years). Recently, using Principal Component Analysis (PCA) of the observed solar background magnetic field (SBMF), another period of 330 - 380 years, or Grand Solar Cycle (GSC), was derived from the summary curve of two eigenvectors of SBMF. In this paper, a spectral analysis of the averaged sunspot numbers, solar irradiance, and the summary curve of eigenvectors of SBMF was carried out using Morlet wavelet and Fourier transforms. We detect a 10.7-year cycle from the sunspots and modulus summary curve of eigenvectors as well a 22-year-cycle and the grand solar cycle of 342 - 350-years from the summary curve of eigenvectors. The Gleissberg centennial cycle is only detected on the full set of averaged sunspot numbers for 400 years or by adding a quadruple component to the summary curve of eigenvectors. Another period of 2200 - 2300 years is detected in the Holocene data of solar irradiance measured from the abundance of 14C isotope. This period was also confirmed with the period of about 2000 - 2100 years derived from a baseline of the solar background magnetic field, supposedly, caused by the solar inertial motion (SIM) induced by the gravitation of large planets. The implication of these findings for different deposition of solar radiation into the northern and southern hemispheres of the Earth caused by the combined effects of the solar activity and solar inertial motion on the terrestrial atmosphere is also discussed.

Comparative analysis of the associations between solar activity and trends in the incidence of haemoblastoses in Russia, the USA and Canada

Background. Identification of the links between hemoblastoses and environmental factors is necessary for the development of preventive measures.
 Aim. Comparative analysis of the link between hemoblastosis trends in Russia, the USA and Canada and solar activity.
 Material and methods. The open data on the incidence of hemoblastoses in Canada (19832012), the USA (19982012) and Russia (19932018) was used. To estimate solar activity, the average annual number of sunspots (Wolff numbers) was taken. The relationship between the frequency of hemoblastoses and solar activity was studied using the Pearson correlation analysis in 11 iterations (lag 010 years). The results obtained are compared with the data of an earlier study on Russia.
 Results. In Canada, an association with Wolf numbers was found in the frequency of Hodgkin's lymphoma in men (r=0.431, p=0.017, lag 2 years), multiple myeloma in women (r=0.542, p=0.037, lag 1 year), non-Hodgkin's lymphomas in men (r =0.538, p=0.038, lag 5 years) and women (r=0.750, p=0.001, lag 5 years), leukemia in men (r=0.707, p=0022, lag 7 years) and women (r=0.817, p=0.004, lag 7 years). In the United States, a relationship with solar activity was established for fluctuations in the incidence of Hodgkin's lymphoma in men (r=0.577, p=0.050, lag 5 years) and women (r=0.641, p=0.025, lag 5 years), non-Hodgkin's lymphomas in men (r=0.809, p 0.001, lag 3 years) and women (r=0.844, p 0.001, lag 2 years), leukemia in men (r=0.619, p=0.032, lag 1 year). In the Russian population, a relationship between solar activity and the frequency of all forms of hemoblastoses, was previously revealed. Fluctuations in the frequency of leukemia and non-Hodgkin's lymphomas in the populations of Russia, the USA and Canada have a strong positive relationship with solar activity. The strength of this association in Hodgkin's lymphoma and multiple myeloma ranges from moderate to significant. In all the countries studied, an increase in the incidence of multiple myeloma and leukemia was found, and an increase in the incidence of non-Hodgkin's lymphomas was found in Russia and Canada. The trend in the incidence of Hodgkin's lymphoma in Russia and Canada has a significant downward trend.
 Conclusion. Trends in hemoblastoses in Russia, the USA and Canada are strongly related to solar activity.

Locally weighted regression for sunspots estimation and prediction

Locally weighted regression (LOESS) is a modern non-parametric regression method designed for treating cases where classical procedures are not highly efficient or cannot applied efficiently. Sunspots are the darker areas of the solar sphere's surface relative to other regions and are an important indicator of solar activity .The aim of this paper is to model and predict the number of sunspots because of their very importance to understanding the terrestrial consequences of solar activity and its direct impact on weather and communication systems on Earth, which may lead to damage to satellites. In this paper, the number of sunspots represented by annual data for the period from 1900 to 2021 (122 years) as well as monthly data for the period from January 1900 to January 2022 (1465 months) was obtained from the global data center (Sunspot Index and Long-term Solar Observations) (SILSO). The LOESS regression used for estimating and predicting the number of monthly and annual sunspots. The smoothing parameter, as well as the degree of the polynomial that fulfills the lowest for Akaike corrected information criterion. The analysis showed the ability of the LOESS to represent sunspot data by passing diagnostic tests as well as its high predictive ability. From the predictive values for the monthly data, it found that the maximum average number of sunspots will be 123.7 in July 2022, and the lowest average will be in February with 61.3 sunspots. Regarding the annual data, it found from the predictive values that the maximum average number of sunspots will be in the year 2023 with an average of 161.7 sunspots, and the lowest average will be in the year 2029 with an average of 16.1. Keywords: Locally weighted regression; sunspot; solar cycle; prediction.

A Climatology of Long-Duration High 2-MeV Electron Flux Periods in the Outer Radiation Belt.

Since the advent of the Space Age, the importance of understanding and forecasting relativistic electron fluxes in the Earth’s radiation belts has been steadily growing due to the threat that such particles pose to satellite electronics. Here, we provide a model of long‐duration periods of high time‐integrated 2‐MeV electron flux deep inside the outer radiation belt, based on the significant correlation obtained in 2001–2017 between time‐integrated electron flux measured by satellites and a measure of the preceding time‐integrated homogenized aa H geomagnetic index. We show that this correlation is likely due to a stronger cumulative chorus wave‐driven acceleration of relativistic electrons and a stronger cumulative inward radial diffusion of such electrons during periods of higher time‐integrated geomagnetic activity. Return levels of 2‐MeV electron flux are provided based on Extreme Value analysis of time‐integrated geomagnetic activity over 1868–2017, in rough agreement with estimates based on 20‐year data sets of measured flux. A high correlation is also found between our measure of time‐integrated geomagnetic activity averaged over each solar cycle and averaged sunspot numbers, potentially paving the way for forecasts of time‐integrated relativistic electron flux during future solar cycles based on predictions of solar activity.

Eigenvectors of solar magnetic field in cycles 21–24 and their links to solar activity indices

ABSTRACT Using full disc synoptic maps of solar background magnetic field captured from the Wilcox Solar Observatory for 30 latitudinal bands for cycles 21–24, principal components (PCs) or eigenvectors of magnetic oscillations are obtained. The PCs are shown to come in pairs assigned to magnetic waves produced by dipole, quadruple, sextuple, and octuple magnetic sources. The first pair is linked to dipole magnetic waves with their summary curve revealing a reasonable fit to the averaged sunspot numbers in cycles 21–24. This verifies the previous results and confirms the summary curve as additional proxy of solar activity decreasing towards grand solar minimum in cycles 25–27. There is also a noticeable asymmetry in latitudinal distributions of these PCs showing an increased activity in Northern hemisphere in odd cycles and in Southern hemisphere in even ones similar to the N–S asymmetries observed in sunspots. The second pair of PCs linked to quadruple magnetic sources has 50${{\ \rm per\ cent}}$ smaller amplitudes than the first, while their summary curve correlates closely with soft X-ray fluxes in solar flares. Flare occurrences are also linked to variations of the next two pairs of eigenvectors, quadruple and sextuple components, revealing additional periodicity of about 2.75–3.1 yr similar to observed oscillations in flares. Strong latitudinal asymmetries in quadruple and sextuple components are correlating with the N–S asymmetries of flare occurrences skewed to Southern hemisphere in even cycles and to Northern hemisphere in odd ones. Principal component analysis of solar magnetic field raises perspectives for simultaneous prediction of general and flaring solar activity.

Impact of sunspot activity on the rainfall patterns over Eastern Africa: a case study of Sudan and South Sudan

AbstractThe 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.

Sunspot drawings at Kodaikanal Observatory: a representative results on hemispheric sunspot numbers and area measurements

The importance of the periodicity in sunspot appearance was well recognized by the mid-19th century. Several observatories around the globe have made the record of sunspots in the form of drawings and preserved them safely for posterity. At the Kodaikanal Observatory (KO), the sunspot observations have begun in 1905. In those times observations were recorded on photographic plates and after the development of those plates in the laboratory, the drawings of the same were made on the Stonyhurst grids. In these drawings, called sun charts, different features on the sun’s disk, e.g., sunspots, plages, filaments, prominences, etc. were clearly identified and visually marked with different colors. We have collected 111 years of sunspot drawing spanning over 10 solar cycles. These sunspot drawings were carefully stitched to make bound volumes, each for every 6-months. The drawings are kept at the Kodaikanal library for scientific use and analysis. In this article, we describe briefly the process of drawing, methods of counting sunspot numbers and measurement of sunspot area using square grids. We have collected the data for the northern and southern hemispheres separately. From the collected data, we compute the sunspot number and area and compare it with Royal Greenwich Observatory (RGO) and Sunspot Index and Long-term Solar Observations (SILSO) data. The results show that the measurement of the sunspot number is underestimated by about 40%. The KO monthly averaged sunspot number data of both hemispheres is normalized with the RGO monthly averaged total sunspot number data. This procedure provided a good correlated data set that can be used for further scientific work in the future. The sunspot area data from KO is slightly underestimated in the first 5-cycles and seems mildly overestimated in the later 5-cycles. These data sets are valuable additions to the existing data of sunspot records.

Statistical Study of Surface-charging Events in Aurora Region Over One Solar Cycle

High-level surface-charging events are frequently observed on spacecrafts in aurora region. Besides the sunlit condition, two major factors causing charging events are the ambient plasma density and the precipitating electron flux. For the first factor, when the ambient plasma density is relatively low due to weak solar UV output during solar minimum, more surface-charging events are reported to occur for polar satellite. Moreover, the increased energetic electron precipitation during high geomagnetic activities in solar cycle decent years, may also contribute to the charging events. To evaluate these two factors comprehensively, we present a statistical survey of over 2000 surface charging events recorded by Defense Meteorological Satellite Program (DMSP) satellites over one solar cycle. The relationship between charging events and Kp index, F10.7 index, and monthly average sunspot number is investigated. It is shown that the occurrence frequency of charging events is larger at descending years of solar cycle. In addition, the conditional probabilities of the charging events increase as Kp increase. There is a threshold for Kp index, under which most of the charging events cannot occur, and this threshold grows as F10.7 increases. Finally, it is demonstrated that the surface charging potential is strongly correlated with the Kp index. Although there is no obvious correlation between the surface charging potential and F10.7 index, we still observe a decreasing trend of the surface potential range as F10.7 increases.

Relación entre capturas del tiburón Rhizoprionodon terraenovae al sur del Golfo de México y el número de manchas solares

Background. The Antillean or sharpnose shark is one of the main exemplars of shark species in the commercial catch in southern Gulf of Mexico. Oceanic dynamics on the planet Earth varies year-on-year due to the oscillation of solar radiation; fish abundances (and catches) likely respond to these oscillations. Goals. This study focuses on the analysis of landings variability of the antillean sharpnose shark (Rhizoprionodon terraenovae) in the Mexican coast of the Gulf of Mexico, from 1940 to 2006, and its possible connection with solar activity as assessed by the average sunspot number (Zurich Index). Methods. A polynomial curve by least-squares best fitting was used to eliminate the tendency from the sharpnose shark landings time series. Spectral techniques of Maximum Entropy (ME) and Fast Fourier Transform (FFT) were used to analyze the time series of sharpnose shark landings and the Zurich Index. Results. The time series of sharpnose shark landings showed a remarkable spectral peak with a period of about 12.8 years, while the Zurich Index showed a marked peak at a period of 11.6 years. Cross-correlation revealed a delay between the average number of solar spots and sharpnose shark landings. Conclusions. This work is the first to report such a low frequency variability for landings of the Rh. terraenovae fishery in the Gulf of Mexico, using a particular methodology that can provide information for the design of predictive models in the future. The analyzed landing volumes of the sharpnose shark Rh. terraenovae showed as a result a periodical behavior in coincidence with Wolf’s solar activity cycle of 10.6 years.

Predictions of El Niño, La Niña and Record Low Chicago Temperature by Sunspot Number

The El Nino Index, defined as 4 intensities (very strong, strong, moderate, weak) in Oceanic Niño Index (ONI), was positively correlated with the average sunspot number at each intensity. The La Niña Index, defined as 3 intensities (strong, moderate, weak) in ONI, was negatively correlated with the average sunspot number from 1954 to 2017. It appears that very strong El Niño events occur frequently during the maximal sunspot number while strong La Niña events more often occur during the minimal sunspot number. Since greenhouse-gas is continuously increased, it is therefore proposed that the maximal sunspot number is a major parameter for prediction of El Niño while the minimal sunspot number applies in the same way for La Niña. El Nino/La Nina events can be classified as four typical cases depending upon the submarine volcanic activities at seamounts in Antarctica and South America. The Sea Surface Temperature (SST) of the South and Central Americas are warmer than SST of East Australian Current (EAC), due to the strong volcanic eruptions in the Seamounts and the Ridges in South and Central Americas. This results in the Central Pacific Current (CPC) flowing from east to west due to the second law of thermodynamics for thermal flow from hot source to cold sink. In contrast the opposite direction is made if SST in EAC is warmer than SST in the Central/South American Seamounts and Ridges, due to the strong volcanic eruptions in the Antarctic Seamounts and Ridges. Chicago was selected as a case study for the relationship between extreme cold weather conditions and minimal sunspot number. Previous attempts at predicting weather patterns in Chicago have largely failed. The years of the record low temperatures in Chicago were significantly correlated with the years of the minimal sunspot number from 1873 to 2019. It is forecast that there may occur a weak La Niña in 2019 and another record low temperature in Chicago in January of 2020 due to the phase of the minimal sunspot number in 2019. It may be possible to predict very strong El Nino events with the year of maximal sunspot number as El Niño Index (R2 = 0.7363) and the years of strong volcanic eruption in the Galapagos Hot Spot (GHS) (R2 = 0.9939), respectively. An El Niño event is thus expected during the year of strong volcanic eruption in the GHS. Strong La Niña events can be expected during the year of minimal sunspot number with La Niña Index (R2 = 0.9922). Record low temperatures in Chicago can be also predicted (R2 = 0.9995) during the year of the minimal sunspot number, as was recently the case in January, 2019.

Solar total and spectral irradiance reconstruction over the last 9000 years

Context.Changes in solar irradiance and in its spectral distribution are among the main natural drivers of the climate on Earth. However, irradiance measurements are only available for less than four decades, while assessment of solar influence on Earth requires much longer records.Aims.The aim of this work is to provide the most up-to-date physics-based reconstruction of the solar total and spectral irradiance (TSI/SSI) over the last nine millennia.Methods.The concentrations of the cosmogenic isotopes14C and10Be in natural archives have been converted to decadally averaged sunspot numbers through a chain of physics-based models. TSI and SSI are reconstructed with an updated SATIRE model. Reconstructions are carried out for each isotope record separately, as well as for their composite.Results.We present the first ever SSI reconstruction over the last 9000 years from the individual14C and10Be records as well as from their newest composite. The reconstruction employs physics-based models to describe the involved processes at each step of the procedure.Conclusions.Irradiance reconstructions based on two different cosmogenic isotope records, those of14C and10Be, agree well with each other in their long-term trends despite their different geochemical paths in the atmosphere of Earth. Over the last 9000 years, the reconstructed secular variability in TSI is of the order of 0.11%, or 1.5 W m−2. After the Maunder minimum, the reconstruction from the cosmogenic isotopes is consistent with that from the direct sunspot number observation. Furthermore, over the nineteenth century, the agreement of irradiance reconstructions using isotope records with the reconstruction from the sunspot number by Chatzistergos et al. (2017, A&A, 602, A69) is better than that with the reconstruction from the WDC-SILSO series (Clette et al. 2014, Space Sci. Rev., 186, 35), with a lowerχ2-value.

The Ratio Between the Number of Sunspot and the Number of Sunspot Groups

Data from three solar observatories, Learmonth, Holloman, and San Vito, are used to study the variations in the average number of sunspots per sunspot group. It is found that the different types of sunspot groups and the number of sunspots in these groups have different solar cycle and cycle to cycle variations. The varying ratio between the average number of sunspots and the number of sunspot groups is shown to be a real feature and not a result of changing observational instruments, observers experience, calculation schemes, etc., and is a result of variations in the solar magnetic fields. Therefore, the attempts to minimize the discrepancies between the sunspot number and sunspot group series are not justified, and lead to the loss of important information about the variability of the solar dynamo.

Reduction of the dimension of neural network models in problems of pattern recognition and forecasting

Deep neural networks with a large number of parameters are a powerful tool for solving problems of pattern recognition, prediction and classification. Nevertheless, overfitting remains a serious problem in the use of such networks. A method of solving the problem of overfitting is proposed in this article. This method is based on reducing the number of independent parameters of a neural network model using the principal component analysis, and can be implemented using existing libraries of neural computing. The algorithm was tested on the problem of recognition of handwritten symbols from the MNIST database, as well as on the task of predicting time series (rows of the average monthly number of sunspots and series of the Lorentz system were used). It is shown that the application of the principal component analysis enables reducing the number of parameters of the neural network model when the results are good. The average error rate for the recognition of handwritten figures from the MNIST database was 1.12% (which is comparable to the results obtained using the "Deep training" methods), while the number of parameters of the neural network can be reduced to 130 times.

A study of multi-GNSS ionospheric scintillation and cycle-slip over Hong Kong region for moderate solar flux conditions

This study presents the characteristics of Multiple Global Navigation Satellite System (Multi-GNSS) ionospheric scintillation and cycle-slip occurrence through the analysis of Multi-GNSS data collected by a newly installed receiver located at Sha Tin of Hong Kong from 6 October 2015 to 31 December 2016. This period of time was under a moderate solar activity condition with average sunspot number and F10.7 as 44 and 92, respectively. Considering the frequent occurrence of loss of lock in satellites measurements in the presence of ionospheric scintillation, a rate of geometry-free (ROGF) combination is proposed to take the time gap size between two data arcs into account in the cycle-slip detection. The results show that most ionospheric scintillation events and cycle-slips are observed from 20:00 LT to 0:00 LT. Under the strong scintillation (S4>0.6) conditions, it is found that the time series of wide-land (WL) ambiguity NWL and ROGF vary significantly and their range can reach more than 50 cycles and 0.1m/s, respectively. However, the variations of the NWL and ROGF are generally small under weak scintillation (0.2<S4≤0.6) or non-scintillation (S4≤0.2) conditions. A strong correlation of scintillation and cycle-slip occurrence is also verified by the daily and spatial statistics results. In addition, it is found that on average every 1000 strong scintillation events can result in 200, 124, and 171 cycle-slip occurrences in GPS, GLONASS, and BDS, respectively, whereas these values are 7, 12, and 12 per 1000 under weak scintillation conditions. This study suggests that cautions be taken when GNSS measurements are contaminated by the strong ionospheric scintillation in GNSS applications such as real-time kinematic (RTK) and precise point positioning (PPP).

On a role of quadruple component of magnetic field in defining solar activity in grand cycles

In this paper we revise our prediction of solar activity using a solar background magnetic field as a proxy by the inclusion of eigen vectors of solar magnetic waves produced by quadruple magnetic sources, in addition to the principal eigen modes generated by two-layer dipole sources (Zharkova et al., 2015). By considering the interference of two dipole and one quadruple waves we produce the revised summary curve for the last 400 years accounting for the additional minima of solar activity occurred at the beginning of 19th (Dalton minimum) and 20th centuries. Using the dynamo model with meridional circulation and selecting the directions of circulation for quadruple waves, we estimate the parameters of quadrupole waves best fitting the observations in the past grand cycle. The comparison shows that the quadruple wave has to be generated in the inner layer of the solar convective zone, in order to provide the additional minima observed in 19 and 20 centuries, thus, naturally accounting for Gleissberg centennial cycle. The summary dynamo wave simulated for the dipole and quadruple sources reveals much closer correspondence of the resulting summary curve derived from the principal components of magnetic field variations to the solar activity oscillations derived from the average sunspot numbers in the current grand cycle.