Long-Period Cycles of the Sun's Activity Recorded in Direct Solar Data and Proxies

Different records of solar activity (Wolf and group sunspot number, data on cosmogenic isotopes, historic data) were analyzed by means of modern statistical methods, including one especially developed for this purpose. It was confirmed that two long-term variations in solar activity – the cycles of Gleissberg and Suess – can be distinguished at least during the last millennium. The results also show that the century-type cycle of Gleissberg has a wide frequency band with a double structure consisting of 50–80 years and 90–140 year periodicities. The structure of the Suess cycle is less complex showing a variation with a period of 170–260 years. Strong variability in Gleissberg and Suess frequency bands was found in northern hemisphere temperature multiproxy that confirms the existence of a long-term relationship between solar activity and terrestial climate.     

On the Possibility for Action Conservation in the Solar Cycle

The sunspot series are investigated in detail by use of a wavelet transform. By simple arguments, we present a reduced sunspot time-series, which can be argued to be approximately proportional to the magnetic flux density at the coronal surface. This reduced sunspot index correctly reproduces the (average) 22 year solar cycle. Closer scrutiny of the sunspot variation shows that the frequency of the solar cycle and the energy in the magnetic field vary consistently with conservation of action, i.e., energy divided by frequency. The analysis is based on the available data beginning with the year 1700, and analyzed by a wavelet transform. The present results relate to observations reported previously in the literature.     

Forecasting Solar Flares Using Magnetogram-based Predictors and Machine Learning

We propose a forecasting approach for solar flares based on data from Solar Cycle 24, taken by the Helioseismic and Magnetic Imager (HMI) on board the Solar Dynamics Observatory (SDO) mission. In particular, we use the Space-weather HMI Active Region Patches (SHARP) product that facilitates cut-out magnetograms of solar active regions (AR) in the Sun in near-realtime (NRT), taken over a five-year interval (2012?–?2016). Our approach utilizes a set of thirteen predictors, which are not included in the SHARP metadata, extracted from line-of-sight and vector photospheric magnetograms. We exploit several machine learning (ML) and conventional statistics techniques to predict flares of peak magnitude \({>}\,\mbox{M1}\) and \({>}\,\mbox{C1}\) within a 24 h forecast window. The ML methods used are multi-layer perceptrons (MLP), support vector machines (SVM), and random forests (RF). We conclude that random forests could be the prediction technique of choice for our sample, with the second-best method being multi-layer perceptrons, subject to an entropy objective function. A Monte Carlo simulation showed that the best-performing method gives accuracy \(\mathrm{ACC}=0.93(0.00)\), true skill statistic \(\mathrm{TSS}=0.74(0.02)\), and Heidke skill score \(\mathrm{HSS}=0.49(0.01)\) for \({>}\,\mbox{M1}\) flare prediction with probability threshold 15% and \(\mathrm{ACC}=0.84(0.00)\), \(\mathrm{TSS}=0.60(0.01)\), and \(\mathrm{HSS}=0.59(0.01)\) for \({>}\,\mbox{C1}\) flare prediction with probability threshold 35%.     

Longterm Prediction of Solar Activity Using the Combined Method

The Combined Method is a non-parametric regression technique for long-term prediction of smoothed monthly sunspot numbers. Starting from a solar minimum, a prediction of the succeeding maximum is obtained by using a dynamo-based relation between the geomagnetic aa index and succeeding solar maxima. Then a series of predictions is calculated by computing the weighted average of past cycles of similar level. This technique leads to a good prediction performance, particularly in the ascending phase of the solar cycle where purely statistical methods tend to be inaccurate. For cycle 23 the combined method predicts a maximum of 160 (in terms of smoothed sunspot number) early in the year 2000.     

A Method of Forecasting Solar Activity Based on Radio Astronomical Observations

We present the results of forecasting flare activity based on the data from microwave spectropolarimetric observations of active regions (ARs) obtained with the RATAN-600 radio telescope and the X-ray data from the GOES satellite as well as monitoring data. The method is designed for short-term (1–3-days) flare forecasts. Proton events are considered as part of the general flare problem. Obtaining a reliable forecast is a difficult process in view of the multi-parameter and multi-dimensional system of plasma parameter variations and multiple non-linear interconnections.We used a modified Tanaka–Enome criterion, as well a database of observational material collected over many years. The forecasting efficiency was analyzed depending on the threshold values of the criterion. We show that the quality of the radio astronomical forecast is determined by the level of sensitivity of the detector at short centimeterwavelengths and by the solar activity level.     

New Evidence for Long-Term Persistence in the Sun's Activity

Possible persistence of sunspot activity was studied using rescaled range and detrended fluctuation analyses. In addition to actual Wolf numbers (1700–2000 A.D.), two solar proxies were used in this research, viz., an annual sunspot proxy obtained for 1090–1700 A.D. and sunspot numbers reconstructed from the decadal radiocarbon series (8005 B.C. – 1895 A.D). The reconstruction was made using a five-box carbon exchange model. Analyses showed that in all cases the scaling exponent is significantly higher than 0.5 in the range of scales from 25 yr up to 3000 yr. This indicates the existence of a long-term memory in solar activity, in agreement with results obtained for other solar indices.     

Light Deflection Near the Sun's Limb: Refraction by the Solar Atmosphere

Light refraction by the Sun's atmosphere is calculated.As detected from the Earth, the refraction can deflect a light ray emitted from the Sun's limb by 13 or a starlight ray grazing the solar limb by 26, an effect 15 times larger than the gravitational deflection.     

On the Sun's limb brightening in the visible

It is shown that in practice the method by Julius (1906) is incapable to determine the limb intensity drop. The brief intensity reversal near the extreme limb as derived from cinematography of flash spectra can be explained by diffraction.     

On the Claimed 5.5-year Periodicity in Solar Activity

Recently, Djurovic and Pâquet (1996) claimed to have found an oscillation with a period of about 5.5 years in several solar and solar-terrestrial parameters, in particular in solar activity as indicated by sunspot numbers. Since the temporal evolution of the solar activity and solar-terrestrial environment is of great interest in many fields, we have examined their claim in detail. We show here that their conclusion is based on an artefact due a questionable method applied, and due to the asymmetric form of the solar cycle. Accordingly, there is no reasonable evidence for the existence of a fundamental 5.5-year periodicity in solar activity.     

The Varying Multipolar Structure of the Sun's Magnetic Field and the Evolution of the Solar Magnetosphere Through the Solar Cycle

The Sun's magnetic field extends far from the photosphere, into the corona, defining a magnetically dominated region before being drawn out radially by the solar wind flow. This region, where the internal sources of the solar field dominate the plasma structures and the energetic particle movement, can be properly considered the solar magnetosphere. The magnetic field in this region can be approximately described by models that extrapolate photospheric magnetic field observations under some simplifying assumptions. In this paper we use a potential field model which describes the solar field up to a source surface at 3.25 R_s, where the field is constrained to become radial. We present the variation of the magnitude and inclination of the various multipolar components throughout the solar magnetic cycle that characterise the changes in the structure of the solar magnetosphere over a period of 22 years. We also present some 3-D images of the coronal magnetic structure to show the global evolution of the solar magnetosphere throughout the solar cycle and discuss the importance of taking this structure into account in order to relate interplanetary and solar features.     

On the Relation Between Solar Activity and Clear-Sky Terrestrial Irradiance

The Mauna Loa Observatory record of direct-beam solar irradiance measurements for the years 1958?–?2010 is analysed to investigate the variation of clear-sky terrestrial insolation with solar activity over more than four solar cycles. The raw irradiance data exhibit a marked seasonal cycle, extended periods of lower irradiance due to emissions of volcanic aerosols, and a long-term decrease in atmospheric transmission independent of solar activity. After correcting for these effects, it is found that clear-sky terrestrial irradiance typically varies by ≈?0.2±0.1 % over the course of the solar cycle, a change of the same order of magnitude as the variations of the total solar irradiance above the atmosphere. An investigation of changes in the clear-sky atmospheric transmission fails to find a significant trend with sunspot number. Hence there is no evidence for a yet unknown effect amplifying variations of clear-sky irradiance with solar activity.     

The Evolution of the Sun's Open Magnetic Flux – II. Full Solar Cycle Simulations

In this paper the origin and evolution of the Sun's open magnetic flux is considered by conducting magnetic flux transport simulations over many solar cycles. The simulations include the effects of differential rotation, meridional flow and supergranular diffusion on the radial magnetic field at the surface of the Sun as new magnetic bipoles emerge and are transported poleward. In each cycle the emergence of roughly 2100 bipoles is considered. The net open flux produced by the surface distribution is calculated by constructing potential coronal fields with a source surface from the surface distribution at regular intervals. In the simulations the net open magnetic flux closely follows the total dipole component at the source surface and evolves independently from the surface flux. The behaviour of the open flux is highly dependent on meridional flow and many observed features are reproduced by the model. However, when meridional flow is present at observed values the maximum value of the open flux occurs at cycle minimum when the polar caps it helps produce are the strongest. This is inconsistent with observations by Lockwood, Stamper and Wild (1999) and Wang, Sheeley, and Lean (2000) who find the open flux peaking 1–2 years after cycle maximum. Only in unrealistic simulations where meridional flow is much smaller than diffusion does a maximum in open flux consistent with observations occur. It is therefore deduced that there is no realistic parameter range of the flux transport variables that can produce the correct magnitude variation in open flux under the present approximations. As a result the present standard model does not contain the correct physics to describe the evolution of the Sun's open magnetic flux over an entire solar cycle. Future possible improvements in modeling are suggested.     

On the Sun's differential rotation and pole-equator temperature difference

The Sun's differential rotation can be understood in terms of a preferential stabilization of convection (by rotation) in the polar regions of the lower part of the convection zone (where the Taylor number is large). A significant pole-equator difference in flux () can develop deep inside the convection zone which would be unobservable at the surface, because can be very efficiently reduced by large scale meridional motions rising at the poles and sinking at the equator. This is the sense of circulation needed to produce the observed equatorial acceleration of the Sun. Differential rotation is generated, therefore, in the upper part of the convection zone (where the interaction of rotation with convection is small) and results as the convection zone adjusts to a state of negligible Taylor number.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

From Predicting Solar Activity to Forecasting Space Weather: Practical Examples of Research-to-Operations and Operations-to-Research

The successful transition of research to operations (R2O) and operations to research (O2R) requires, above all, interaction between the two communities. We explore the role that close interaction and ongoing communication played in the successful fielding of three separate developments: an observation platform, a numerical model, and a visualization and specification tool. Additionally, we will examine how these three pieces came together to revolutionize interplanetary coronal mass ejection (ICME) arrival forecasts. A discussion of the importance of education and training in ensuring a positive outcome from R2O activity follows. We describe efforts by the meteorological community to make research results more accessible to forecasters and the applicability of these efforts to the transfer of space-weather research. We end with a forecaster “wish list” for R2O transitions. Ongoing, two-way communication between the research and operations communities is the thread connecting it all.     

Comparisons of the NOAA-11 SBUV/2, UARS SOLSTICE, and UARS SUSIM Mg II Solar Activity Proxy Indexes

A NOAA-11 SBUV/2 Mgii solar activity proxy index has been created for the period February 1989 through October 1994 from the daily discrete mode solar irradiance data using an algorithm that utilizes a thorough instrument characterization. This product represents a significant improvement over the previously released NOAA-11 SBUV/2 sweep mode-based Mgii data set. As measured by the NOAA-11 Mgii index, the amplitude of solar rotational activity declined from approximately 4–7% peak-to-peak near the maximum of solar cycle 22 in 1989–1991 to roughly 1% peak-to-peak by late-1994. Corresponding to this decrease, the 27-day averaged NOAA-11 Mgii index decreased by 5.8% over this period. The NOAA-11 Mgii data set is compared with coincident data sets from the UARS SOLSTICE and SUSIM instruments. The impact of differences in instrument resolution and observation platform are examined with respect to both the absolute value and temporal variations of the Mgii index. Periodograms of the three indexes demonstrate comparable solar variation tracking. Between October 1991 and October 1994 predominate power occurs near 27 days, with secondary maxima in the power spectra near 29 and 25 days. Overall, there is low power near 13.5 days during this period. Dynamic power spectral analysis reveals the quasi-periodic and quasi-stationary nature of the middle UV variations tracked by the Mgii index, and periods of significant power near 13.5 days in mid-1991 and late-1994 through mid-1995.     

On the Possibility of Deflecting an Asteroid from Collision with the Earth Using the Kinetic Method

The possibilities of deflecting an asteroid from its collision course with the Earth by changing its velocity with an impact are considered. Using the asteroid Apophis as an example, the time dependence of the positions and sizes of the keyholes leading to collision is studied. It has been found that the possibility of deflecting this asteroid usually exists, and the impact can be accomplished in principle, given the capabilities of modern space technology. A change in the velocity should be performed before the encounter of 2029 in order to use the gravitational maneuver effect. The possible accuracy of determining Apophis’ orbit and the keyholes that lead to collision and are associated with the resonance returns are considered.     

On the Prediction of Maximum Amplitude for Solar Cycles Using Geomagnetic Precursors

Precursor methods for the prediction of maximum amplitude of the solar cycle have previously been found to provide the most reliable indication for the size of the following cycle, years in advance. In this paper, we evaluate several of the previously used geomagnetic precursor methods and some new ones, both as single-variate and multivariate regressions. The newer precursor methods are based on the size of the geomagnetic index maximum, which, since cycle 12, has always occurred during the declining portion of the solar cycle, usually several years before subsequent cycle minimum. These various precursor techniques are then applied to cycle 23, yielding the prediction that its maximum amplitude should be about 168 ± 15 (r.m.s.), peaking sometime in 1999–2000.     

Intermittency of the Solar Magnetic Field and Solar Magnetic Activity Cycle

Small-scale solar magnetic fields demonstrate features of fractal intermittent behavior, which requires quantification. For this purpose we investigate how the observational estimate of the solar magnetic flux density \(B\) depends on resolution \(D\) in order to obtain the scaling \(\ln B_{D} = - k \ln D +a\) in a reasonably wide range. The quantity \(k\) demonstrates cyclic variations typical of a solar activity cycle. In addition, \(k\) depends on the magnetic flux density, i.e. the ratio of the magnetic flux to the area over which the flux is calculated, at a given instant. The quantity \(a\) demonstrates some cyclic variation, but it is much weaker than in the case of \(k\). The scaling obtained generalizes previous scalings found for the particular cycle phases. The scaling is typical of fractal structures. In our opinion, the results obtained trace small-scale action in the solar convective zone and its coexistence with the conventional large-scale solar dynamo based on differential rotation and mirror-asymmetric convection.