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At least 19 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS1973

The solar wind cycle, the sunspot cycle, and the corona.

Recent theories of the solar cycle and of coronal heating strongly suggest that solar cycle variations of different quantities (i.e., sunspots, coronal green line, etc.) ought not to be expected to be in phase with one another. In agreement with this notion it is noted that the shape of the corona typical of a 'maximum' eclipse occurs 1.5 yr before sunspot maximum, compared with 2 yr as might be expected from Leighton's 'standard' model. Further, it is argued that the phase of the solar wind cycle can be determined from geomagnetic observations. Using this phase, a solar cycle variation of 100 km/sec in the solar wind velocity and 1 gamma in the magnetic field intensity becomes apparent. In general, the solar wind cycle lags behind the coronal-eclipse-form cycle by 3 yr, compared with the 2 yr that might be expected from model calculations.

Hirshberg, J.↗
NASA NTRS1996

On the Importance of Cycle Minimum in Sunspot Cycle Prediction

The characteristics of the minima between sunspot cycles are found to provide important information for predicting the amplitude and timing of the following cycle. For example, the time of the occurrence of sunspot minimum sets the length of the previous cycle, which is correlated by the amplitude-period effect to the amplitude of the next cycle, with cycles of shorter (longer) than average length usually being followed by cycles of larger (smaller) than average size (true for 16 of 21 sunspot cycles). Likewise, the size of the minimum at cycle onset is correlated with the size of the cycle's maximum amplitude, with cycles of larger (smaller) than average size minima usually being associated with larger (smaller) than average size maxima (true for 16 of 22 sunspot cycles). Also, it was found that the size of the previous cycle's minimum and maximum relates to the size of the following cycle's minimum and maximum with an even-odd cycle number dependency. The latter effect suggests that cycle 23 will have a minimum and maximum amplitude probably larger than average in size (in particular, minimum smoothed sunspot number Rm = 12.3 +/- 7.5 and maximum smoothed sunspot number RM = 198.8 +/- 36.5, at the 95-percent level of confidence), further suggesting (by the Waldmeier effect) that it will have a faster than average rise to maximum (fast-rising cycles have ascent durations of about 41 +/- 7 months). Thus, if, as expected, onset for cycle 23 will be December 1996 +/- 3 months, based on smoothed sunspot number, then the length of cycle 22 will be about 123 +/- 3 months, inferring that it is a short-period cycle and that cycle 23 maximum amplitude probably will be larger than average in size (from the amplitude-period effect), having an RM of about 133 +/- 39 (based on the usual +/- 30 percent spread that has been seen between observed and predicted values), with maximum amplitude occurrence likely sometime between July 1999 and October 2000.

Wilson, Robert M.↗
NASA NTRS2013

Estimating the Mean Annual Surface Air Temperature at Armagh Observatory, Northern Ireland, and the Global Land-Ocean Temperature Index for Sunspot Cycle 24, the Current Ongoing Sunspot Cycle

As noted by Gray et al., Sir William Herschel was the first to suggest a possible close connection between the Sun and the Earth’s climate. The Sun, being the source of energy that impacts and drives the Earth’s climate system, displays a variety of changes over both short and long term time scales, the most obvious examples being the somewhat regular waxing and waning of sunspots with time (i.e., the sunspot cycle (SC)), first described by Samuel Heinrich Schwabe, a German apothecary and amateur astronomer who observed the Sun from Dessau, Germany, and the now well established variation of the Sun’s irradiance over the SC. Other factors related to the SC have been linked to changes in climate as well. Some of these other factors include the role of cosmic rays and the solar wind (i.e., the geomagnetic cycle) on climate, as well as the apparent close association between trends in global and northern hemispheric temperature and the length of the SC, although some investigators have described the inferred association between climate and, in particular, SC length as now being weak. More recently, Solheim et al. have reported on the relation between SC length and the average temperature in the same and immediately following SC for a number of meteorological stations in Norway and in the North Atlantic region. They noted that while they found no significant trend (correlation) between SC length and the average temperature when measured for the same cycle, in contrast, they found a significant negative trend when SC length was compared with the following cycle’s average temperature. From this observation, they suggested that average northern hemispheric temperature during the present ongoing SC (SC24) will be lower by about 0.9 °C than was seen in SC23 (spanning 1996–2007, based on yearly averages of sunspot number (SSN), and onset for SC24 occurring in 2008). The purpose of this Technical Publication (TP) is to examine the annual variations of the Armagh surface air temperature (ASAT) and the Global Land-Ocean Temperature Index (GLOTI) in relation to SSN and the SC in order to determine their likely values during SC24. Hence, it may provide insight as to whether solar forcing of global temperature is now lessening as a contributor to global warming, thereby indicating a possible cooling in the near term immediate future that potentially could ameliorate the effect of increased anthropogenic warming.

Wilson, Robert M.↗
NASA NTRS2003

Evidence that a Deep Meridional Flow Sets the Sunspot Cycle Period

Sunspots appear on the Sun in two bands on either side of the equator that drift toward lower latitudes as each sunspot cycle progresses. We examine the equatorward drift of the centroid of the sunspot area in each hemisphere from 1874 to 2002 and find that the drift rate slows as the centroid approaches the equator. We compare the drift rate at sunspot cycle maximum to the cycle-period for each hemisphere and find a highly significant anti-correlation: hemispheres with faster drift rates have shorter periods. These observations are. consistent with an equatorward meridional counterflow, deep within the Sun, as the primary driver of the equatorward migration and the period associated with the sunspot cycle. We also find that the drift rate at maximum is significantly correlated with the amplitude of the following cycle, a prediction of dynamo models that employ a deep equatorward meridional flow. Our results indicate an amplitude of about 1.2 m/s for the meridional flow velocity at the base of the solar convection zone.

Hathaway, David H.↗
NASA NTRS2009

Predicting the Sunspot Cycle

The 11-year sunspot cycle was discovered by an amateur astronomer in 1844. Visual and photographic observations of sunspots have been made by both amateurs and professionals over the last 400 years. These observations provide key statistical information about the sunspot cycle that do allow for predictions of future activity. However, sunspots and the sunspot cycle are magnetic in nature. For the last 100 years these magnetic measurements have been acquired and used exclusively by professional astronomers to gain new information about the nature of the solar activity cycle. Recently, magnetic dynamo models have evolved to the stage where they can assimilate past data and provide predictions. With the advent of the Internet and open data policies, amateurs now have equal access to the same data used by professionals and equal opportunities to contribute (but, alas, without pay). This talk will describe some of the more useful prediction techniques and reveal what they say about the intensity of the upcoming sunspot cycle.

Hathaway, David H.↗
NASA NTRS1975

Are climatological correlations with the Hale double sunspot cycle meaningful?

A sunspot cycle which may have been subject to a predicted phase reversal between 1800 and 1880 A. D is discussed. Several climatological parameters normally correlated with this cycle are examined and do not exhibit a corresponding phase reversal during this period. It is proposed that this apparent discrepancy can be resolved by suitable observations during the upcoming half decade.

Goldberg, R. A.↗
NASA NTRS2013

Meridional Flow Variations in Cycles 23 and 24: Active Latitude Control of Sunspot Cycle Amplitudes

We have measured the meridional motions of magnetic elements observed in the photosphere over sunspot cycles 23 and 24 using magnetograms from SOHO/MDI and SDO/HMI. Our measurements confirm the finding of Komm, Howard, and Harvey (1993) that the poleward meridional flow weakens at cycle maxima. Our high spatial and temporal resolution analyses show that this variation is in the form of a superimposed inflow toward the active latitudes. This inflow is weaker in cycle 24 when compared to the inflow in 23, the stronger cycle. This systematic modulation of the meridional flow can modulate the amplitude of the following sunspot cycle through its influence on the Sun's polar fields.

Hathaway, David H.↗
NASA NTRS2013

Meridional Flow Variations in Cycles 23 and 24: Active Latitude Control of Sunspot Cycle Amplitudes

We have measured the meridional motions of magnetic elements observed in the photosphere over sunspot cycles 23 and 24 using magnetograms from SOHO/MDI and SDO/HMI. Our measurements confirm the finding of Komm, Howard, and Harvey (1993) that the poleward meridional flow weakens at cycle maxima. Our high spatial and temporal resolution analyses show that this variation is in the form of a superimposed inflow toward the active latitudes. This inflow is weaker in cycle 24 when compared to the inflow in 23, the stronger cycle. This systematic modulation of the meridional flow should also modulate the amplitude of the following sunspot cycle through its influence on the Sun's polar fields. The observational evidence and the theoretical consequences (similar to those of Cameron and Schussler (2012)) will be described.

Hathaway, David H.↗
NASA NTRS1984

A comparative look at sunspot cycles

On the basis of cycles 8 through 20, spanning about 143 years, observations of sunspot number, smoothed sunspot number, and their temporal properties were used to compute means, standard deviations, ranges, and frequency of occurrence histograms for a number of sunspot cycle parameters. The resultant schematic sunspot cycle was contrasted with the mean sunspot cycle, obtained by averaging smoothed sunspot number as a function of time, tying all cycles (8 through 20) to their minimum occurence date. A relatively good approximation of the time variation of smoothed sunspot number for a given cycle is possible if sunspot cycles are regarded in terms of being either HIGH- or LOW-R(MAX) cycles or LONG- or SHORT-PERIOD cycles, especially the latter. Linear regression analyses were performed comparing late cycle parameters with early cycle parameters and solar cycle number. The early occurring cycle parameters can be used to estimate later occurring cycle parameters with relatively good success, based on cycle 21 as an example. The sunspot cycle record clearly shows that the trend for both R(MIN) and R(MAX) was toward decreasing value between cycles 8 through 14 and toward increasing value between cycles 14 through 20. Linear regression equations were also obtained for several measures of solar activity.

Wilson, R. M.↗
NASA NTRS1994

The shape of the sunspot cycle

The temporal behavior of a sunspot cycle, as described by the International sunspot numbers, can be represented by a simple function with four parameters: starting time, amplitude, rise time, and asymmetry. Of these, the parameter that governs the asymmetry between the rise to maximum and the fall to minimum is found to vary little from cycle to cycle and can be fixed at a single value for all cycles. A close relationship is found between rise time and amplitude which allows for a representation of each cycle by a function containing only two parameters: the starting time and the amplitude. These parameters are determined for the previous 22 sunspot cycles and examined for any predictable behavior. A weak correlation is found between the amplitude accurate to within about 30% right at the start of the cycle. As the cycle progresses, the amplitude can be better determined to within 20% at 30 months and to within 10% at 42 months into the cycle, thereby providing a good prediction both for the timing and size of sunspot maximum and for the behavior of the remaining 7-12 years of the cycle.

Hathaway, David H.↗
NASA NTRS1988

Predicting the maximum amplitude for the sunspot cycle from the rate of rise in sunspot number

The paper examines the relationship between the maximum amplitude for the sunspot cycle and the rate of rise during the ascending phase. It is found that, prior to about 2 yr into the cycle, the rate of rise is not a reliable predictor for maximum amplitude. Only during the second half of the ascent do the fits display strong linearity, having a correlation coefficient of r = 0.9 and a standard error Syx less than about 20.

Wilson, Robert M.↗
NASA NTRS2024

An Interesting Correlation Between the Peak Slope and Peak Value of a Sunspot Cycle

The maximum slope of the sunspot number during the rising phase of a sunspot cycle has an excellent correlation with the maximum value of the sunspot number during that cycle. This is demonstrated using a Savitzky–Golay filter to both smooth and calculate the derivative of the sunspot-number data. Version 2 of the International Sunspot Number (S) is used to represent solar activity. The maximum of the slope during the rising phase of each cycle was correlated against the peaks of solar activity. Using three different correlation fits, the average predicted amplitude for Solar Cycle 25 is 130.7 ± 0.5, among the best correlations in solar predictions. A possible explanation for this correlation is given by the similar behavior of a shape function representing the time variation of the sunspot number. This universal function also provides the timing of the solar maximum by the time from the slope maximum to the peak in the function as late 2023 or early 2024. A Hilbert transform gives similar results, which are caused by the dominance of the 11-yr sunspot-cycle period in a Fourier fit of the sunspot number.

W. Dean Pesnell↗
NASA NTRS2004

An Improved Solar Cycle Statistical Model for the Projection of Near Future Sunspot Cycles

Since the current solar cycle 23 has progressed near the end of the cycle and accurate solar minimum and maximum occurrences have been defined, a statistical model based on the odd-even behavior of historical sunspot cycles was reexamined. Separate calculations of activity levels were made for the rising and declining phases in solar cycle 23, which resulted in improved projection of sunspots in the remainder of cycle 23. Because a fundamental understanding of the transition from cycle to cycle has not been developed, at this time it is assumed for projection purposes that solar cycle 24 will continue at the same activity level in the declining phase of cycle 23. Projection errors in solar cycle 24 can be corrected as the cycle progresses and observations become available because this model is shown to be self-correcting.

Kim, Myung-Hee Y.↗
NASA NTRS2006

On the Relationship Between Spotless Days and the Sunspot Cycle: A Supplement

This study provides supplemental material to an earlier study concerning the relationship between spotless days and the sunspot cycle. Our previous study, Technical Publication (TP)-2005-213608 determined the timing and size of sunspot minimum and maximum for the new sunspot cycle, relative to the occurrence of the first spotless day during the declining phase of the old sunspot cycle and the last spotless day during the rising portion of the new cycle. Because the number of spotless days (NSD) rapidly increases as the cycle nears sunspot minimum and rapidly decreases thereafter, the size and timing of sunspot minimum and maximum might be more accurately determined using a higher threshold for comparison, rather than using the first and last spotless day occurrences. It is this aspect that is investigated more thoroughly in this TP.

Wilson, Robert M.↗
NASA NTRS1988

A prediction for the size of sunspot cycle 22

Based on 'annual' averages, a bivariate analysis of the maximum amplitude of the sunspot cycle against its minimum amplitude and the minimum value of the aa geomagnetic index (in the vicinity of sunspot cycle minimum) results in a fit that closely matches the observable record. The bilinear fit has a high coefficient of correlation (r = 0.982) and a small standard deviation (s = 9.5), suggesting that it may be useful for predicting the size of a sunspot cycle 3 to 4 years before maximum amplitude occurrence. Applying the fit to cycle 22, the annual average of maximum amplitude is found to be 92 + or - 19 (equivalent to 96 + or - 20 in terms of the 13-month running mean or smoothed sunspot number).

Wilson, Robert M.↗
NASA NTRS2006

An Examination of Selected Geomagnetic Indices in Relation to the Sunspot Cycle

Previous studies have shown geomagnetic indices to be useful for providing early estimates for the size of the following sunspot cycle several years in advance. Examined this study are various precursor methods for predicting the minimum and maximum amplitude of the following sunspot cycle, these precursors based on the aa and Ap geomagnetic indices and the number of disturbed days (NDD), days when the daily Ap index equaled or exceeded 25. Also examined is the yearly peak of the daily Ap index (Apmax), the number of days when Ap greater than or equal to 100, cyclic averages of sunspot number R, aa, Ap, NDD, and the number of sudden storm commencements (NSSC), as well the cyclic sums of NDD and NSSC. The analysis yields 90-percent prediction intervals for both the minimum and maximum amplitudes for cycle 24, the next sunspot cycle. In terms of yearly averages, the best regressions give Rmin = 9.8+/-2.9 and Rmax = 153.8+/-24.7, equivalent to Rm = 8.8+/-2.8 and RM = 159+/-5.5, based on the 12-mo moving average (or smoothed monthly mean sunspot number). Hence, cycle 24 is expected to be above average in size, similar to cycles 21 and 22, producing more than 300 sudden storm commencements and more than 560 disturbed days, of which about 25 will be Ap greater than or equal to 100. On the basis of annual averages, the sunspot minimum year for cycle 24 will be either 2006 or 2007.

Wilson, Robert M.↗
NASA NTRS1976

Structure of the extended solar magnetic field and the sunspot cycle variation in cosmic ray intensity

It is proposed that a relation exists between the extent of interplanetary-magnetic-field sectors and observed variations in cosmic-ray intensity at earth. Changes that take place in the sector magnetic fields and solar polar fields during a sunspot cycle are described. It is argued that a geometrical effect arising from changes in sector-field and polar-field extent during sunspot cycles may be the principal cause of the 11-yr modulation of cosmic-ray intensity observed at earth. The fraction of the heliosphere occupied by sector fields is estimated as a function of time through an average sunspot cycle, the solid angle of the heliosphere occupied by the extended solar polar fields is plotted through the same cycle, and monthly averages of observed absolute intensities of primary cosmic rays with a rigidity greater than 0.5 GV are compared with the plot of polar-field extent. It is found that the average sunspot-cycle variation of the solid angle of the extended polar fields is rather similar to the observed variation in the flux of the cosmic rays considered.

Svalgaard, L.↗
NASA NTRS1990

On the maximum rate of change in sunspot number growth and the size of the sunspot cycle

Statistically significant correlations exist between the size (maximum amplitude) of the sunspot cycle and, especially, the maximum value of the rate of rise during the ascending portion of the sunspot cycle, where the rate of rise is computed either as the difference in the month-to-month smoothed sunspot number values or as the 'average rate of growth' in smoothed sunspot number from sunspot minimum. Based on the observed values of these quantities (equal to 10.6 and 4.63, respectively) as of early 1989, it is inferred that cycle 22's maximum amplitude will be about 175 + or - 30 or 185 + or - 10, respectively, where the error bars represent approximately twice the average error found during cycles 10-21 from the two fits.

Wilson, Robert M.↗