Sunspot Data Research Articles

Statistical Investigation of Supersonic Downflows in the Transition Region above Sunspots

Abstract Downflows at supersonic speeds have been observed in the transition region (TR) above sunspots for more than three decades. These downflows are often seen in different TR spectral lines above sunspots. We have performed a statistical investigation of these downflows using a large sample that was missing previously. The Interface Region Imaging Spectrograph (IRIS) has provided a wealth of observational data of sunspots at high spatial and spectral resolutions in the past few years. We have identified 60 data sets obtained with IRIS raster scans. Using an automated code, we identified the locations of strong downflows within these sunspots. We found that around 80% of our sample shows supersonic downflows in the Si iv 1403 Å line. These downflows mostly appear in the penumbral regions, though some of them are found in the umbrae. We also found that almost half of these downflows show signatures in chromospheric lines. Furthermore, a detailed spectral analysis was performed by selecting a small spectral window containing the O iv 1400/1401 Å and Si iv 1403 Å lines. Six Gaussian functions were simultaneously fitted to these three spectral lines and their satellite lines associated with the supersonic downflows. We calculated the intensity, Doppler velocity, and line width for these lines. Using the O iv 1400/1401 Å line ratio, we find that the downflow components are around one order of magnitude less dense than the regular components. Results from our statistical analysis suggest that these downflows may originate from the corona and that they are independent of the background TR plasma.

Statistically Based Weight Pruning in Feed-Forward Neural Networks

A statistically-based algorithm for pruning weights from feed-forward networks is presented. This algorithm relies upon the Generalized Wald and t-test statistics to determine which weights to remove from the network. Because both of these tests use the exact Hessian matrix, an algorithm for learning the exact Hessian matrix for a feed-forward neural network using a single backward pass through the data is presented when the L2 norm is minimized in the energy function. The pruning algorithm is then applied in two simulations: The first simulation investigates the relationship between neural networks and linear regression (Ordinary Least Squares), and the weight covariance matrix is found to be asymptotically equivalent to the White (1980) standard error corrections for heterogeneity of variance. The final simulation applies the algorithm to a network solving the sunspot data and compares the results to those found in the literature, with mixed results.

Effects of solar activity and galactic cosmic ray cycles on the modulation of the annual average temperature at two sites in southern Brazil

Abstract. Quasi-periodic variations in solar activity and galactic cosmic rays (GCRs) on decadal and bidecadal timescales have been suggested as a climate forcing mechanism for many regions on Earth. One of these regions is southern Brazil, where the lowest values during the last century were observed for the total geomagnetic field intensity at the Earth's surface. These low values are due to the passage of the center of the South Atlantic Magnetic Anomaly (SAMA), which crosses the Brazilian territory from east to west following a latitude of ∼ 26∘. In areas with low geomagnetic intensity, such as the SAMA, the incidence of GCRs is increased. Consequently, possible climatic effects related to the GCRs tend to be maximized in this region. In this work, we investigate the relationship between the ∼ 11-year and ∼ 22-year cycles that are related to solar activity and GCRs and the annual average temperature recorded between 1936 and 2014 at two weather stations, both located near a latitude of 26∘ S but at different longitudes. The first of these stations (Torres – TOR) is located in the coastal region, and the other (Iraí – IRA) is located in the interior, around 450 km from the Atlantic Ocean. Sunspot data and the solar modulation potential for cosmic rays were used as proxies for the solar activity and the GCRs, respectively. Our investigation of the influence of decadal and bidecadal cycles in temperature data was carried out using the wavelet transform coherence (WTC) spectrum. The results indicate that periodicities of 11 years may have continuously modulated the climate at TOR via a nonlinear mechanism, while at IRA, the effects of this 11-year modulation period were intermittent. Four temperature maxima, separated by around 20 years, were detected in the same years at both weather stations. These temperature maxima are almost coincident with the maxima of the odd solar cycles. Furthermore, these maxima occur after transitions from even to odd solar cycles, that is, after some years of intense GCR flux. The obtained results offer indirect mathematical evidence that solar activity and GCR variations contributed to climatic changes in southern Brazil during the last century. A comparison of the results obtained for the two weather stations indicates that the SAMA also contributes indirectly to these temperature variations. The contribution of other mechanisms also related to solar activity cannot be excluded. Keywords. Meteorology and atmospheric dynamics (climatology)

Evolution of the Sunspot Number and Solar Wind B $B$ Time Series

The past two decades have witnessed significant changes in our knowledge of long-term solar and solar wind activity. The sunspot number time series (1700-present) developed by Rudolf Wolf during the second half of the 19th century was revised and extended by the group sunspot number series (1610–1995) of Hoyt and Schatten during the 1990s. The group sunspot number is significantly lower than the Wolf series before ∼1885. An effort from 2011–2015 to understand and remove differences between these two series via a series of workshops had the unintended consequence of prompting several alternative constructions of the sunspot number. Thus it has been necessary to expand and extend the sunspot number reconciliation process. On the solar wind side, after a decade of controversy, an ISSI International Team used geomagnetic and sunspot data to obtain a high-confidence time series of the solar wind magnetic field strength ( $B$ ) from 1750-present that can be compared with two independent long-term (> ∼600 year) series of annual $B$ -values based on cosmogenic nuclides. In this paper, we trace the twists and turns leading to our current understanding of long-term solar and solar wind activity.

Bayesian nonparametric spectral density estimation using B-spline priors

We present a new Bayesian nonparametric approach to estimating the spectral density of a stationary time series. A nonparametric prior based on a mixture of B-spline distributions is specified and can be regarded as a generalization of the Bernstein polynomial prior of Petrone (1999a,b) and Choudhuri et al. (2004). Whittle's likelihood approximation is used to obtain the pseudo-posterior distribution. This method allows for a data-driven choice of the number of mixture components and the location of knots. Posterior samples are obtained using a Metropolis-within-Gibbs Markov chain Monte Carlo algorithm, and mixing is improved using parallel tempering. We conduct a simulation study to demonstrate that for complicated spectral densities, the B-spline prior provides more accurate Monte Carlo estimates in terms of $L_1$-error and uniform coverage probabilities than the Bernstein polynomial prior. We apply the algorithm to annual mean sunspot data to estimate the solar cycle. Finally, we demonstrate the algorithm's ability to estimate a spectral density with sharp features, using real gravitational wave detector data from LIGO's sixth science run, recoloured to match the Advanced LIGO target sensitivity.

A Smoothing Technique for the Multifractal Analysis of a Medium Voltage Feeders Electric Current

The current paper presents a data-driven detrending technique allowing to smooth complex sinusoidal trends from a real-world electric load time series before applying the Detrended Multifractal Fluctuation Analysis (MFDFA). The algorithm we call Smoothed Sort and Cut Fourier Detrending (SSC-FD) is based on a suitable smoothing of high power periodicities operating directly in the Fourier spectrum through a polynomial fitting technique of the DFT. The main aim consists of disambiguating the characteristic slow varying periodicities, that can impair the MFDFA analysis, from the residual signal in order to study its correlation properties. The algorithm performances are evaluated on a simple benchmark test consisting of a persistent series where the Hurst exponent is known, with superimposed ten sinusoidal harmonics. Moreover, the behavior of the algorithm parameters is assessed computing the MFDFA on the well-known sunspot data, whose correlation characteristics are reported in literature. In both cases, the SSC-FD method eliminates the apparent crossover induced by the synthetic and natural periodicities. Results are compared with some existing detrending methods within the MFDFA paradigm. Finally, a study of the multifractal characteristics of the electric load time series detrendended by the SSC-FD algorithm is provided, showing a strong persistent behavior and an appreciable amplitude of the multifractal spectrum that allows to conclude that the series at hand has multifractal characteristics.

Prediction of the Length of Upcoming Solar Cycles

The forecast of solar cycle (SC) characteristics is crucial particularly for several space-based missions. In the present study, we propose a new model for predicting the length of the SC. The model uses the information of the width of an autocorrelation function that is derived from the daily sunspot data for each SC. We tested the model on Versions 1 and 2 of the daily international sunspot number data for SCs 10 – 24. We found that the autocorrelation width $A_{\mathrm{w}} ^{n}$ of SC $n$ during the second half of its ascending phase correlates well with the modified length that is defined as $T_{\mathrm{cy}}^{n+2} - T_{\mathrm{a}}^{n}$ . Here $T_{\mathrm{cy}}^{n+2}$ and $T_{ \mathrm{a}}^{n}$ are the length and ascent time of SCs $n+2$ and $n$ , respectively. The estimated correlation coefficient between the model parameters is 0.93 (0.91) for Version 1 (Version 2) sunspot series. The standard errors in the observed and predicted lengths of the SCs for Version 1 and Version 2 data are 0.38 and 0.44 years, respectively. The advantage of the proposed model is that the predictions of the length of the upcoming two SCs (i.e., $n+1$ , $n+2$ ) are readily available at the time of the peak of SC $n$ . The present model gives a forecast of 11.01, 10.52, and 11.91 years (11.01, 12.20, and 11.68 years) for the length of SCs 24, 25, and 26, respectively, for Version 1 (Version 2).

Detailed analysis of dynamic evolution of three Active Regions at the photospheric level before flare and CME occurrence

We present a combined analysis of the applications of the weighted horizontal magnetic gradient (denoted as WGM in Korsós et al. (2015)) method and the magnetic helicity tool (Berger and Field, 1984) employed for three active regions (ARs), namely NOAA AR 11261, AR 11283 and AR 11429. We analysed the time series of photospheric data from the Solar Dynamics Observatory taken between August 2011 and March 2012. During this period the three ARs produced a series of flares (eight M- and six X-class) and coronal mass ejections (CMEs). AR 11261 had four M-class flares and one of them was accompanied by a fast CME. AR 11283 had similar activities with two M- and two X-class flares, but only with a slow CME. Finally, AR 11429 was the most powerful of the three ARs as it hosted five compact and large solar flare and CME eruptions. For applying the WGM method we employed the Debrecen sunspot data catalogue, and, for estimating the magnetic helicity at photospheric level we used the Space-weather HMI Active Region Patches (SHARP’s) vector magnetograms from SDO/HMI (Solar Dynamics Observatory/Helioseismic and Magnetic Imager). We followed the evolution of the components of the WGM and the magnetic helicity before the flare and CME occurrences. We found a unique and mutually shared behaviour, called the U-shaped pattern, of the weighted distance component of WGM and of the shearing component of the helicity flux before the flare and CME eruptions. This common pattern is associated with the decreasing-receding phases yet reported only known to be a necessary feature prior to solar flare eruption(s) but found now at the same time in the evolution of the shearing helicity flux. This result leads to the conclusions that (i) the shearing motion of photospheric magnetic field may be a key driver for solar eruption in addition to the flux emerging process, and that (ii) the found decreasing-approaching pattern in the evolution of shearing helicity flux may be another precursor indicator for improving the forecasting of solar eruptions.

Parity fluctuations in stellar dynamos

Observations of the solar butterfly diagram from sunspot records suggest persistent fluctuation in parity, away from the overall, approximately dipolar structure. We use a simple mean-field dynamo model with a solar-like rotation law, and perturb the $\alpha$-effect. We find that the parity of the magnetic field with respect to the rotational equator can demonstrate what we describe as resonant behaviour, while the magnetic energy behaves in a more or less expected way. We discuss possible applications of the phenomena in the context of various deviations of the solar magnetic field from dipolar symmetry, as reported from analysis of archival sunspot data. We deduce that our model produces fluctuations in field parity, and hence in the butterfly diagram, that are consistent with observed fluctaions in solar behaviour.

Periodicity of sunspot group number during the Maunder Minimum

Applying the Hilbert-Huang Transform (HHT) method to the yearly average sunspot group (SG) number reconstructed by Svalgaard& Schatten, we investigate the periodicity of SG number from 1610 to 2015. Our main findings are summarized below. Periodicities of 3.56 +/- 0.24 (Quasi-Triennial Oscillations), 9.22 +/- 0.13 (Schwabe Cycle), 16.91 +/- 0.99 (Hale Cycle), 49.25 +/- 0.96, 118.64 +/- 2.52 (Centennial Gleissberg Cycle), and 206.32 +/- 4.60 yr are statistically significant in the SG numbers. During the Maunder Minimum (MM), the occurrences of the Schwabe Cycle and the Hale Cycle, extracted from SG numbers, are suspended; before and after the MM, Schwabe Cycle and the Hale Cycle, extracted from SG numbers, all exist. The results of applying the Morlet Wavelet Analysis to the SG number confirm that, for SG number, the occurrence of the Schwabe Cycle is suspended during the MM, and, before and after the MM, the Schwabe Cycle all exist. Then we investigate the periodicity in the annual Be-10 data from 1391 to 1983, which are given in a supplementary file to McCracken & Beer, using HHT and the Morlet wavelet transform. We find that, for the Be-10 data, the Schwabe Cycle and the Hale Cycle persist throughout the MM. Our results support the suggestion that the Schwabe Cycle is too weak to be detected in the sunspot data.

Connection between solar activity cycles and grand minima generation

Aims. The revised dataset of sunspot and group numbers (released by WDC-SILSO) and the sunspot number reconstruction based on dendrochronologically dated radiocarbon concentrations have been analyzed to provide a deeper characterization of the solar activity main periodicities and to investigate the role of the Gleissberg and Suess cycles in the grand minima occurrence.Methods. Empirical mode decomposition (EMD) has been used to isolate the time behavior of the different solar activity periodicities. A general consistency among the results from all the analyzed datasets verifies the reliability of the EMD approach. Results. The analysis on the revised sunspot data indicates that the highest energy content is associated with the Schwabe cycle. In correspondence with the grand minima (Maunder and Dalton), the frequency of this cycle changes to longer timescales of ~14 yr. The Gleissberg and Suess cycles, with timescales of 60−120 yr and ~ 200−300 yr, respectively, represent the most energetic contribution to sunspot number reconstruction records and are both found to be characterized by multiple scales of oscillation. The grand minima generation and the origin of the two expected distinct types of grand minima, Maunder and longer Sporer-like, are naturally explained through the EMD approach. We found that the grand minima sequence is produced by the coupling between Gleissberg and Suess cycles, the latter being responsible for the most intense and longest Sporer-like minima (with typical duration longer than 80 yr). Finally, we identified a non-solar component, characterized by a very long scale oscillation of ~ 7000 yr, and the Hallstatt cycle (~ 2000 yr), likely due to the solar activity.Conclusions. These results provide new observational constraints on the properties of the solar cycle periodicities, the grand minima generation, and thus the long-term behavior of the solar dynamo.

Climatic periodicities recorded in lake sediment magnetic susceptibility data: Further evidence for solar forcing on Indian summer monsoon

The Indian summer monsoon exhibits considerable spatio-temporal variability. It is therefore important to understand its dynamics and the inherent periodicities. In this study, we have performed spectral and wavelet analyses of magnetic susceptibility data for sediments from Thimmannanayakanakere (TK)–a small lake in southern India. The main objective of this investigation is to identify and explain the possible origin of the prominent periodicities present in the magnetic susceptibility data. Significant periodicities in the TK χlf data are centered at 906, 232, 147, 128, 96, 61, 54 and 44 years, which might have a solar origin. The wavelet power spectrum of the raw and detrended χlf data confirms the findings of spectral analysis and also provides temporal variations of the significant cyclicities during the past 3700 cal. years B.P. Positive correlation is documented between sunspot activity and TK χlf data; cross-spectral analysis of the reconstructed sunspot data and TK χlf data suggest that there is a strong coherence between the two datasets as significant periodicities are documented in both. There is a good match between the TK χlf and the reconstructed total solar irradiance data for the past 1200 years. However, an out-of-phase relationship is documented at certain time-intervals, which may be attributed to uncertainties in the age-depth model. The results obtained from this study show that solar variations are the main controlling factor of the southwest monsoon and, like other archives from different regions in India, the TK lake sediments have also recorded these solar signatures.

SOLAR ACTIVE LONGITUDES FROM KODAIKANAL WHITE-LIGHT DIGITIZED DATA

ABSTRACT The study of solar active longitudes has generated great interest in recent years. In this work we have used a unique, continuous sunspot data series obtained from the Kodaikanal observatory and revisited the problem. An analysis of the data shows a persistent presence of active longitudes during the whole 90 years of data. We compared two well-studied analysis methods and presented their results. The separation between the two most active longitudes is found be roughly 180° for the majority of time. Additionally, we also find a comparatively weaker presence of separations at 90° and 270°. The migration pattern of these active longitudes as revealed by our data is found to be consistent with the solar differential rotation curve. We also study the periodicities in the active longitudes and found two dominant periods of ≈1.3 and ≈2.2 years. These periods, also found in other solar proxies, indicate their relation with the global solar dynamo mechanism.

A new nonlinearity test to circumvent the limitation of Volterra expansion with application

In this paper, we propose a quick and efficient method to examine whether a time series Xt possesses any nonlinear feature by testing a kind of dependence remained in the residuals after fitting Xt with a linear model. The advantage of our proposed nonlinearity test is that it is not required to know the exact nonlinear features and the detailed nonlinear forms of the variable being examined. Another advantage of our proposed test is that there is no over-rejection problem which exists in some famous nonlinearity tests. Our proposed test can also be used to test whether the hypothesized model, including linear and nonlinear, to the variable being examined is appropriate as long as the residuals of the model being used can be estimated. Our simulation study shows that our proposed test is stable and powerful. We apply our proposed statistic to test whether there is any nonlinear feature in the sunspot data. The conclusion drawn from our proposed test is consistent with those from other well-established tests.

Relations of latitudinal characteristics of sunspot groups to the 11-year cycle amplitude at different phases

Using sunspot data for cycles 12 to 23, we have investigated relations of some latitude characteristics of sunspot groups to the 11-year cycle amplitude at different phases. We have revealed a high correlation (with correlation coefficients >0.9) between the middle latitude of sunspot groups at phases of rise, maximum, and decay, on the one hand, and the amplitude of the corresponding cycle, on the other hand. We have shown that the maxima of the velocity of the motion of the sunspot formation zone to the equator have a special physical meaning: the rise phase of the 11-year cycle is characterized by significant correlations between the cycle amplitude and the maximum for the lowest boundary, and the cycle decay phase is characterized by the same maximum for the highest boundary. We have built equations allowing one to determine the amplitude of the 11-year cycle on the basis of data on the given latitudinal characteristics of sunspots groups.

Magnetic fields of opposite polarity in sunspot penumbrae

Context. A significant part of the penumbral magnetic field returns below the surface in the very deep photosphere. For lines in the visible, a large portion of this return field can only be detected indirectly by studying its imprints on strongly asymmetric and three-lobed Stokes V profiles. Infrared lines probe a narrow layer in the very deep photosphere, providing the possibility of directly measuring the orientation of magnetic fields close to the solar surface. Aims. We study the topology of the penumbral magnetic field in the lower photosphere, focusing on regions where it returns below the surface. Methods. We analyzed 71 spectropolarimetric datasets from Hinode and from the GREGOR infrared spectrograph. We inferred the quality and polarimetric accuracy of the infrared data after applying several reduction steps. Techniques of spectral inversion and forward synthesis were used to test the detection algorithm. We compared the morphology and the fractional penumbral area covered by reversed-polarity and three-lobed Stokes V profiles for sunspots at disk center. We determined the amount of reversed-polarity and three-lobed Stokes V profiles in visible and infrared data of sunspots at various heliocentric angles. From the results, we computed center-to-limb variation curves, which were interpreted in the context of existing penumbral models. Results. Observations in visible and near-infrared spectral lines yield a significant difference in the penumbral area covered by magnetic fields of opposite polarity. In the infrared, the number of reversed-polarity Stokes V profiles is smaller by a factor of two than in the visible. For three-lobed Stokes V profiles the numbers differ by up to an order of magnitude.

Changes of solar magnetic asymmetry

The results of an analysis of the north–south asymmetry in solar activity and solar magnetic fields are reported. The analysis is based on solar mean magnetic field and solar polar magnetic field time series, 1975–2015 (http://wso.stanford.edu), and the Greenwich sunspot data, 1875–2015 (http://solarscience.msfc.nasa.gov/greenwch.shtml). A long-term cycle (small-scale magnetic fields, toroidal component) of ~140 years is identified in the north–south asymmetry in solar activity by analyzing the cumulative sum of the time series for the north–south asymmetry in the area of sunspots. A comparative analysis of the variations in the cumulative sums of the time series composed of the daily values of the sun’s global magnetic field and in the asymmetry of the daily sunspot data over the time interval 1975–2015 shows that the photospheric large-scale magnetic fields may also have a similar long-term cycle. The variations in the asymmetry of large-scale and small-scale solar magnetic fields (sunspot area) are in sync until 2005.5 and in antiphase since then.

The influence of solar system oscillation on the variability of the total solar irradiance

Total solar irradiance (TSI) is the primary quantity of energy that is provided to the Earth. The properties of the TSI variability are critical for understanding the cause of the irradiation variability and its expected influence on climate variations. A deterministic property of TSI variability can provide information about future irradiation variability and expected long-term climate variation, whereas a non-deterministic variability can only explain the past.This study of solar variability is based on an analysis of two TSI data series, one since 1700 A.D. and one since 1000 A.D.; a sunspot data series since 1610 A.D.; and a solar orbit data series from 1000 A.D. The study is based on a wavelet spectrum analysis. First, the TSI data series are transformed into a wavelet spectrum. Then, the wavelet spectrum is transformed into an autocorrelation spectrum to identify stationary, subharmonic and coincidence periods in the TSI variability.The results indicate that the TSI and sunspot data series have periodic cycles that are correlated with the oscillations of the solar position relative to the barycenter of the solar system, which is controlled by gravity force variations from the large planets Jupiter, Saturn, Uranus and Neptune. A possible explanation for solar activity variations is forced oscillations between the large planets and the solar dynamo.We find that a stationary component of the solar variability is controlled by the 12-year Jupiter period and the 84-year Uranus period with subharmonics. For TSI and sunspot variations, we find stationary periods related to the 84-year Uranus period. Deterministic models based on the stationary periods confirm the results through a close relation to known long solar minima since 1000 A.D. and suggest a modern maximum period from 1940 to 2015. The model computes a new Dalton-type sunspot minimum from approximately 2025 to 2050 and a new Dalton-type period TSI minimum from approximately 2040 to 2065.

On-line Tools for Solar Data Compiled at the Debrecen Observatory and Their Extensions with the Greenwich Sunspot Data

The primary task of the Debrecen Heliophysical Observatory (DHO) has been the most detailed, reliable, and precise documentation of the solar photospheric activity since 1958. This long-term effort resulted in various solar catalogs based on ground-based and space-borne observations. A series of sunspot databases and on-line tools were compiled at DHO: the Debrecen Photoheliographic Data (DPD, 1974--), the dataset based on the Michelson Doppler Imager (MDI) of the Solar and Heliospheric Observatory (SOHO) called SOHO/MDI--Debrecen Data (SDD, 1996--2010), and the dataset based on the Helioseismic and Magnetic Imager (HMI) of the Solar Dynamics Observatory (SDO) called SDO/HMI--Debrecen Data (HMIDD, 2010--). User-friendly web-presentations and on-line tools were developed to visualize and search data. As a last step of compilation, the revised version of Greenwich Photoheliographic Results (GPR, 1874--1976) catalog was converted to DPD format, and a homogeneous sunspot database covering more than 140 years was created. The database of images for the GPR era was completed with the full-disc drawings of the Hungarian historical observatories \'Ogyalla and Kalocsa (1872--1919) and with the polarity drawings of Mount Wilson Observatory. We describe the main characteristics of the available data and on-line tools.

Comment on ‘The Medieval Quiet Period’ – Implications arising from models of solar irradiance

The recent re-evaluation of sunspot data by Clette et al. strongly suggests that the total solar irradiance (TSI) values for the late 20th century were (apart from 1960) not significantly different from those of the periods of sunspot maxima in the 1780s and the 1840s–1860s in the latter part of the ‘Little Ice Age’. In effect, the re-evaluation removed the previously supposed sunspot maximum of the ‘modern’ period. That means that the supposed recovery of TSI levels to values significantly higher in the late 20th century than those of the ‘Medieval Quiet (or Warm) Period’ (Figure 1 of Bradley et al., 2016) must be an artefact of the solar data. Orbital data suggest that the northern hemisphere cooled significantly over the past 2000 years, a trend confirmed by global temperature proxies. Variations about that trend were driven by small variations in sunspot activity that led to the warmth of the ‘Medieval Quiet (Warm) Period’ and the subsequent cooling of the ‘Little Ice Age’. In fact, the ‘Little Ice Age’ contained several short warm periods when sunspots were at a maximum. It seems highly likely given the new sunspot calibration that the mid- to late 20th century warming was yet another of these ‘Little Ice Age’ warm episodes (e.g. no different from that in 1780) superimposed on which was a growing additional warming supplied by expanding emissions of greenhouses gases.