Average Sunspot Number Research Articles

Validation of NeQuick 2 model over the Kenyan region through data ingestion and the model application in ionospheric studies

NeQuick 2 is an ionospheric electron density model which provides electron density for a given location. Its output depends on solar activity expressed by 12-month running average sunspot number (R12) or solar radio flux (F10.7). To improve the model capabilities to reproduce electron density, data ingestion techniques have been implemented which replace the standard solar activity indices input with effective parameters that allow adapting a model to a certain data sets. In regions like the Sub-Saharan Africa where few observational data were available until recently, the performance of the ingested model needs some validation. This study investigates the performance of NeQuick 2 in the Kenya region, a low latitude region by assisting the model with total electron content measurement from a single GNSS station. These measurements are used to calculate effective ionization level parameters, which enable the difference between the measured and modeled TEC over the station to be less or equal to 0.5 TECU. The results show that by using computed effective parameters values as inputs in nearby stations, the model performance is greatly improved for both the low and moderate solar activity. This work has also demonstrated the capability of the model to describe spatial distribution of the total electron content in the low- latitude ionosphere.

The Revised Brussels–Locarno Sunspot Number (1981 – 2015)

In 1981, the production of the international Sunspot Number moved from the Z\"{u}rich Observatory to the Royal Observatory of Belgium, marking a very important transition in the history of the Sunspot Number. Those recent decades are particularly important for linking recent modern solar indices and fluxes and the past Sunspot Number series. However, large variations have been recently identified in the scale of the Sunspot Number between 1981 and the present. Here, we reconstruct a new average Sunspot Number series $S_N$ using long-duration stations between 1981 and 2015. We also extend this reconstruction using long-time series from 35 stations over 1945-2015, which includes the 1981 transition. In both reconstructions, we also derive a parallel Group Number series $G_N$. Our results confirm the variable trends of the Locarno pilot station. We also verify the scale of the resulting 1981-2015 correction factor relative to the preceding period 1945--1980. By comparing the new $S_N$ and $G_N$ series, we find that a constant quadratic relation exists between those two indices. This proxy relation leads to a fully constant and cycle-independent $S_N/G_N$ ratio over cycles 19 to 23, with the exception of cycle 24. We find a very good agreement between our reconstructed $G_N$ and the new "backbone" Group Number but inhomogeneities in the original Group Number as well as the $F_{10.7}$ radio flux and the American sunspot number $R_a$. This analysis opens the way to the implementation of a more advanced method for producing the Sunspot Number in the future. In particular, we identify the existence of distinct subsets of observing stations sharing very similar personal k factors, which may be a key element for building a future multi-station reference in place of the past single pilot station.

Predictions of Solar Cycle 24: How are we doing?

AbstractPredictions of solar activity are an essential part of our Space Weather forecast capability. Users are requiring usable predictions of an upcoming solar cycle to be delivered several years before solar minimum. A set of predictions of the amplitude of Solar Cycle 24 accumulated in 2008 ranged from zero to unprecedented levels of solar activity. The predictions formed an almost normal distribution, centered on the average amplitude of all preceding solar cycles. The average of the current compilation of 105 predictions of the annual‐average sunspot number is 106 ± 31, slightly lower than earlier compilations but still with a wide distribution. Solar Cycle 24 is on track to have a below‐average amplitude, peaking at an annual sunspot number of about 80. Our need for solar activity predictions and our desire for those predictions to be made ever earlier in the preceding solar cycle will be discussed. Solar Cycle 24 has been a below‐average sunspot cycle. There were peaks in the daily and monthly averaged sunspot number in the Northern Hemisphere in 2011 and in the Southern Hemisphere in 2014. With the rapid increase in solar data and capability of numerical models of the solar convection zone we are developing the ability to forecast the level of the next sunspot cycle. But predictions based only on the statistics of the sunspot number are not adequate for predicting the next solar maximum. I will describe how we did in predicting the amplitude of Solar Cycle 24 and describe how solar polar field predictions could be made more accurate in the future.

Properties and geoeffectiveness of magnetic clouds during solar cycles 23 and 24

AbstractWe report on a study that compares the properties of magnetic clouds (MCs) during the first 73 months of solar cycles 23 and 24 in order to understand the weak geomagnetic activity in cycle 24. We find that the number of MCs did not decline in cycle 24, although the average sunspot number is known to have declined by ~40%. Despite the large number of MCs, their geoeffectiveness in cycle 24 was very low. The average Dst index in the sheath and cloud portions in cycle 24 was −33 nT and −23 nT, compared to −66 nT and −55 nT, respectively, in cycle 23. One of the key outcomes of this investigation is that the reduction in the strength of geomagnetic storms as measured by the Dst index is a direct consequence of the reduction in the factor VBz (the product of the MC speed and the out‐of‐the‐ecliptic component of the MC magnetic field). The reduction in MC‐to‐ambient total pressure in cycle 24 is compensated for by the reduction in the mean MC speed, resulting in the constancy of the dimensionless expansion rate at 1 AU. However, the MC size in cycle 24 was significantly smaller, which can be traced to the anomalous expansion of coronal mass ejections near the Sun reported by Gopalswamy et al. (2014a). One of the consequences of the anomalous expansion seems to be the larger heliocentric distance where the pressure balance between the CME flux ropes and the ambient medium occurs in cycle 24.

PREDICTION OF SOLAR ACTIVITY FROM SOLAR BACKGROUND MAGNETIC FIELD VARIATIONS IN CYCLES 21-23

A comprehensive spectral analysis of both the solar background magnetic field (SBMF) in cycles 21-23 and the sunspot magnetic field in cycle 23 reported in our recent paper showed the presence of two principal components (PCs) of SBMF having opposite polarity, e.g., originating in the northern and southern hemispheres, respectively. Over a duration of one solar cycle, both waves are found to travel with an increasing phase shift toward the northern hemisphere in odd cycles 21 and 23 and to the southern hemisphere in even cycle 22. These waves were linked to solar dynamo waves assumed to form in different layers of the solar interior. In this paper, for the first time, the PCs of SBMF in cycles 21-23 are analyzed with the symbolic regression technique using Hamiltonian principles, allowing us to uncover the underlying mathematical laws governing these complex waves in the SBMF presented by PCs and to extrapolate these PCs to cycles 24-26. The PCs predicted for cycle 24 very closely fit (with an accuracy better than 98%) the PCs derived from the SBMF observations in this cycle. This approach also predicts a strong reduction of the SBMF in cycles 25 and 26 and, thus, a reduction of the resulting solar activity. This decrease is accompanied by an increasing phase shift between the two predicted PCs (magnetic waves) in cycle 25 leading to their full separation into the opposite hemispheres in cycle 26. The variations of the modulus summary of the two PCs in SBMF reveals a remarkable resemblance to the average number of sunspots in cycles 21-24 and to predictions of reduced sunspot numbers compared to cycle 24: 80% in cycle 25 and 40% in cycle 26.

Symplectic geometry spectrum analysis of nonlinear time series

Various time-series decomposition techniques, including wavelet transform, singular spectrum analysis, empirical mode decomposition and independent component analysis, have been developed for non-linear dynamic system analysis. In this paper, we describe a symplectic geometry spectrum analysis (SGSA) method to decompose a time series into a set of independent additive components. SGSA is performed in four steps: embedding, symplectic QR decomposition, grouping and diagonal averaging. The obtained components can be used for de-noising, prediction, control and synchronization. We demonstrate the effectiveness of SGSA in reconstructing and predicting two noisy benchmark nonlinear dynamic systems: the Lorenz and Mackey-Glass attractors. Examples of prediction of a decadal average sunspot number time series and a mechanomyographic signal recorded from human skeletal muscle further demonstrate the applicability of the SGSA method in real-life applications.

Difference between even- and odd-numbered cycles in the predictability of solar activity and prediction of the amplitude of cycle 25

Abstract. It was shown previously that the sunspot number (SSN) at a point 3 years before the minimum is well correlated with the maximum SSN of the succeeding cycle, and a better correlation is obtained when the maximum SSN is replaced by the average SSN over a cycle for which the average SSN is calculated by dividing cycles at a point 3 years before the minimum (Yoshida and Yamagishi, 2010; Yoshida and Sayre, 2012). Following these findings, we demonstrate in this paper that the correlation between the SSN 3 years before the minimum and the amplitude of the coming cycle differs significantly between even-numbered and odd-numbered cycles: the correlation is much better for even-numbered cycles. Further, it is shown that the amplitude of even-numbered cycles is strongly correlated with that of the succeeding odd-numbered cycles, while the correlation between amplitudes of odd-numbered cycles and those of succeeding even-numbered cycles is very poor. Using the excellent correlations, we estimate the maximum SSN of the current cycle 24 at 81.3 and predict the maximum SSN of cycle 25 to be 115.4 ± 11.9. It is of note, however, that a peak of the SSN has been observed in February 2012 and the peak value 66.9 is considerably smaller than the estimated maximum SSN of cycle 24. We conjecture that the second higher peak of the SSN may appear.

Long-term variations in sunspot characteristics

Relative variations in the number of sunspots and sunspot groups in activity cycles have been analyzed based on data from the Kislovodsk Mountain Astronomical Station and international indices. The following regularities have been established: (1) The relative fraction of small sunspots decreases linearly and that of large sunspots increase with increasing activity cycle amplitude. (2) The variation in the average number of sunspots in one group has a trend, and this number decreased from ∼12 in cycle 19 to ∼7.5 in cycle 24. (3) The ratio of the sunspot index (Ri) to the sunspot group number index (G gr) varies with a period of about 100 years. (4) An analysis of the sunspot group number index (G gr) from 1610 indicates that the Gnevyshev-Ohl rule reverses at the minimums of secular activity cycles. (5) Ratio of the total area to area of Ssp/Sum nuclei has long-term variation with a period approximately 8 cycles. Minimum ratio falls on 16–17 cycles of activity. (6) It has been indicated that the magnetic field intensity and sunspot area in the current cycle are related to the amplitude of the next activity cycle.

Highly Geo-effective Solar Transients and Their Associated Geomagnetic Activities

The solar Cycle 23 has shown some peculiar features, i.e. slow and prolonged decline phase. When it is combined with the ascending phase of Cycle 24, it provides a long phase during which the overall magnetic activity was very low. During this interval the average sunspot number appeared on the solar disk was very low and signified the weak polar magnetic fields, and solar wind streams mainly originating from coronal holes. The study investigated the relationship between magnetic structure of coronal holes and/or coronal mass ejection (CME) source region and their influence on Earth's geomagnetic field, i.e. storms and sub storms. The study is performed mainly considering very intense geomagnetic storms that occurred during Solar Cycle 23. The disturbance storm time index Dst is taken as an indicator of geomagnetic activity by setting a value of Dstmin ≤ −200 nT as threshold. By examining halo CMEs that erupted between 2000 and 2008, we selected 07 events associated with M-class and X-class solar flares. Furthermore, as the geomagnetic field (BGeomag) puts a lower cutoff rigidity (Rc) to the entry of cosmic particles in to the earth's atmosphere. It depends upon the nature of geomagnetic activity and also upon the reconnection of field with the plasma regions formed due to the solar ejections. Sometimes when this entry of charged particles exhibits very sudden sharp and short lived increases in cosmic ray intensities, registered by the neutron monitor, it is termed as Ground-level enhancement (GLEs). These enhancements are known to take place during the result of powerful solar eruption. In present investigation GLE event associated with solar flare and coronal mass ejection (CME) occurred during the study period are also studied. The spacecraft data acquired by STEREO mission and those provided by SOHO, ACE and geomagnetic data from the geomagnetic stations like WDC-Kyoto are utilized in the study. It is found that the GLE's are well associated to X-class solar flares. The average speed of GLE associated CME was much faster than the average speed of non GLE associated CMEs.

On the new prolonged solar activity minimum

The current 24th solar activity cycle started in 2008 and continuing to the present is anomalous in comparison with previous cycles. Its unusual properties include a low sunspot number R z for a long time, a weak interplanetary magnetic field, a weak polar photospheric field in the Sun, and others. Beginning in 1000 to the present, five prolonged solar activity minima took place. These minima occurred in time intervals, when the distance between the center of mass of the solar system and the Sun center changed several times from maximum to minimum values for 40–70 years. Since the beginning of the new millennium, exactly such a period started and it can be assumed that we entered a new prolonged minimum which will last for several decades. In the current 24th and subsequent 2–3 solar activity cycles, annual average sunspot numbers will be low, R zmax ≤ (50–70).

Digitized archive of the Kodaikanal images: Representative results of solar cycle variation from sunspot area determination

Photographic images are valuable data resources for studying long term changes in the solar magnetic field and its influence on the Earth's climate and weather. We digitized more than 100 years of white light images stored in photographic plates and films that are available at Kodaikanal observatory starting from 1904. The digitized images were calibrated for relative plate density and aligned in such a way that the solar north is in upward direction. A semi-automated sunspot detection technique was used to identify the sunspots on the digitized images. In addition to describing the calibration procedure and availability of the data, we here present preliminary results on the sunspot area measurements and their variation with time. The results show that the white-light images have a uniform spatial resolution throughout the 90 years of observations. However, the contrast of the images decreases from 1968 onwards. The images are circular and do not show any major geometrical distortions. The measured monthly averaged sunspot areas closely match the Greenwich sunspot area over the four solar cycles studied here. The yearly averaged sunspot area shows a high degree of correlation with the Greenwich sunspot area. Though the monthly averaged sunspot number shows a good correlation with the monthly averaged sunspot areas, there is a slight anti-correlation between the two during solar maximum The Kodaikanal data archive is hosted at http://kso.iiap.res.in. The long time sequence of the Kodaikanal white light images provides a consistent data set for sunspot areas and other proxies. Many studies can be performed using Kodaikanal data alone without requiring intercalibration between different data sources.

Temporal and spatial variation of equatorial ionization anomaly by using multistation ionosonde data for the 19th solar cycle over the Indian region

The paper deals with the study of temporal and spatial variation of equatorial ionization anomaly (EIA) phenomenon along with its dependence on solar activity and season during the 19th solar cycle by using seven Indian ionosonde stations. Present study is an attempt to carry out the comprehensive study of EIA by using the limited number of ground based instruments. This has been achieved by performing the Gaussian fitting over the latitudinal distribution of F2-region critical frequency (foF2) data. Results reveal that the phenomenon of EIA has a strong dependence on solar activity and seasons. The EIA crest exhibits the feature of latitudinal shifting and expansion with increasing solar activity. It is found out that the effect of solar cycle and seasons on EIA is local time dependent. The observations were also compared with the IRI-2001 model predictions and results reveal that the model values are in general agreement with the observed values with some discrepancies, particularly during the high solar activity period and morning sector. The results have been discussed in the light of relative contribution from transequatorial interhemispheric neutral wind and strength of equatorial fountain process during different local time, season and solar activity levels. Furthermore, an attempt is made to parameterize the location and foF2 of the EIA crest by using the regression analysis. These results can be used to predict the latitudinal position and foF2 of the EIA crest for any given 12-month running average sunspot number (R12).

Tendency of Discreteness of the Solar Amplitude and Intercycle Relatedness

We suggest that the average of the sunspot number (SSN) over a cycle offers a more appropriate index than the maximum value of the SSN in the evaluation of the activity of solar cycles. We then show that the average SSN has a tendency to take discrete values, that is, integral multiples of 20. This remarkable finding is supported by the fact that SSNs around the maximum are likely to take some particular values. Further, it is shown that there exists a positive correlation in the amplitude between even-numbered cycles and succeeding odd-numbered cycles and an inverse correlation between (2𝑛

Solar cycle 24: Implications for energetic particles and long-term space climate change

[1] The recent solar minimum was the longest and deepest of the space age, with the lowest average sunspot numbers for nearly a century. The Sun appears to be exiting a grand solar maximum (GSM) of activity which has persisted throughout the space age, and is headed into a significantly quieter period. Indeed, initial observations of solar cycle 24 (SC24) continue to show a relatively low heliospheric magnetic field strength and sunspot number (R), despite the average latitude of sunspots and the inclination of the heliospheric current sheet showing the rise to solar maximum is well underway. We extrapolate the available SC24 observations forward in time by assuming R will continue to follow a similar form to previous cycles, despite the end of the GSM, and predict a very weak cycle 24, with R peaking at ∼65–75 around the middle/end of 2012. Similarly, we estimate the heliospheric magnetic field strength will peak around 6nT. We estimate that average galactic cosmic ray fluxes above 1GV rigidity will be ∼10% higher in SC24 than SC23 and that the probability of a large SEP event during this cycle is 0.8, compared to 0.5 for SC23. Comparison of the SC24 R estimates with previous ends of GSMs inferred from 9300 years of cosmogenic isotope data places the current evolution of the Sun and heliosphere in the lowest 5% of cases, suggesting Maunder Minimum conditions are likely within the next 40 years.

7Be in ground level air in Daejeon, Korea

(7)Be concentrations in the ground level air in Daejeon, Korea were determined during the period of January 1998 to December 2009 by gamma-ray spectrometric analysis of particulate samples collected on filter paper with a high-volume air sampler. The monthly concentrations of (7)Be in the ground level air were in the range of 1.3-7.7 mBq m(-3) with strong seasonal trends of low values in the summer and high values in the spring and autumn. The annual mean values of (7)Be concentrations showed weak reverse correlation with the annual average sunspot number.

Prediction of solar minimum and maximum epochs on the basis of spectral characteristics for the next millennium

A prevision of solar activity minimum and maximum epochs for the next 1000 years was obtained using a sum of sine waves derived from spectral analysis of the time series of 10 years average sunspot number for the period 1016–2006. The predicted 1000 year solar activity evidence the possibility of forthcoming four minima and one maximum. The 10 years average sunspot number activity in each anomalous period was used in linear equations to obtain estimates of the solar irradiance, solar wind velocity, and the southward component of the interplanetary magnetic field.

Variation of F-region critical frequency (foF2) over equatorial and low-latitude region of the Indian zone during 19th and 20th solar cycle

The effect of solar cycle and seasons on the daytime and nighttime F-layer ionization has been investigated over the equatorial and low-latitude region during 19th (1954–1964) and 20th (1965–1976) solar cycle. The F-layer critical frequency (foF2) data observed from the three Indian Ionosonde stations has been used for the present study. The dependence of foF2 on solar cycle has been examined by performing regression analysis between the foF2 values and R 12 (twelve month running average sunspot number). The result shows that the magnitude of the cycle, seasons and the location of station has considerable effects on foF2. There is a significant nonlinear relationship between the foF2 values and R 12 during 19th solar cycle as compared to 20th solar cycle. Further, the nighttime saturation effect is prominently seen during the 19th solar cycle and summer season. It is also observed that the most profound saturation effect appears at the equatorial ionization anomaly crest region. Seasonally, it is seen that all the stations exhibits semiannual anomaly. The phenomenon of winter anomaly decays as we move higher along the latitude and is prominently seen during the intense solar activity.

Ionogram inversion F1-layer treatment effect in raytracing

This paper shows the importance of the F1-layer shape in the electron density profiles obtained from ionograms with different inversion techniques when the profiles are used in ray tracing. This layer often controls the propagation on the path with ranges less than about 2000 km, particularly for spring and summer periods. Ionograms from two different stations, Hainan (19.4N, 109E) and El Arenosillo (37.1N, -6.7E), obtained during the month of July 2002 (average sunspot number: 99.6) during geomagnetic quiet conditions (Ap-index between 9 and 15) are analyzed. The profiles obtained with two different inversion techniques with different options are used together with the ray tracing program of the Proplab-Pro software. This program calculates the features of the received signal as angle of arrival, path length, height of reflection and range for each given profile assumed to define a spherically symmetric ionosphere in the region along the path. For each ionospheric condition (location, day, hour) the difference between range values obtained with Proplab-Pro program using profiles from the two techniques and the different options (POLAN no valley, POLAN valley, POLAN1-layer and NHPC) are considered.

The Shape of The Sunspot Cycle: A One-Parameter Fit

The empirical description of the shape of the sunspot cycle is one of the oldest problems of solar physics. Here we show that an accurate two-parameter fit is achievable where the parameters are correlated (r=0.88) for 23 solar cycles. The correlation between the parameters of our fit provides the possibility of a one-parameter fit if the times of the minima are known a priori. A one-parameter fit can also be derived from truncated dynamo models, but the goodness of the fit is not better than as achieved for the empirical fit. We suggest that the goodness of a one-parameter fit can serve as a criterion to compare different dynamo models. A one-parameter fit provides the possibility to forecast the shape of the coming cycle via a forecast of one parameter which changes synchronously with the secular variation. A previous estimation of the coming decadal average sunspot number is converted into the forecast of the shape of the 24th cycle with a maximum of 118±26 W. The accuracy is limited mostly by the uncertainties of the predicted secular variation and the uncertainty of the time of the minimum.

An optimal method for determining the time of the minimum of the 23rd solar cycle, July 2008

The time of the minimum of the solar cycle is usually determined by the minimum of the average monthly sunspot number smoothed over 13 months, i.e., with a large time delay, not earlier than eight months after the event. A new optimal method which allows one to establish the time of the minimum of the cycle as early as four months after the event is proposed. In the new method, the indicator of the time of a cycle minimum is the time of reaching the minimum level of average monthly values of the solar constant after which four succeeding values of this constant are larger than the pre-ceding minimum level. It is shown that the minimum of the past 23rd solar cycle took place in July, and the new 24th cycle started in August 2008.