Solar Variability

The solar electromagnetic and particulate flux reaching the earth exhibits considerable short-term variability, and the (long-term) time-averaged behavior tracks the general tendency, but not the detailed morphology, of solar active regions and sunspots. This narrow bandwidth behavior is well known. As one increases the bandwidth of the observational filter, we begin to see more irregular behavior. Indeed, in the time domain, the temporal variability ranges from minutes to years.

Table 2-3: Forecast of Sunspot number for Solar Cycle 23

Technique

Low End

Maximum

High End

Even/Odd behavior

165

200

235

Precursor

140

160

180

Spectral

135

155

185

Recent climatology

125

155

185

Neural Network

110

140

170

Full climatology

75

115

155

Panel's Consensus of SSN amplitude

130

160

190

Panel's Consensus of SSN peak month

January 1999

March 2000

June 2001

Observed SSN peak

-

~ 120

Observed peak date

-

~ April 2000

-

Note-1: By inspection of Figure 2-9, the peak monthly value of the SSN was observed to be ~ 175 at ~ July 2000. However, the smoothed (12-month "mean") value is seen to be ~ 120. Note-2: Sunspot cycle 23 exhibited two "peaks" in solar activity, where the secondary peak was ~ 115 at ~ December 2001.

Note-1: By inspection of Figure 2-9, the peak monthly value of the SSN was observed to be ~ 175 at ~ July 2000. However, the smoothed (12-month "mean") value is seen to be ~ 120. Note-2: Sunspot cycle 23 exhibited two "peaks" in solar activity, where the secondary peak was ~ 115 at ~ December 2001.

Figure 2-9 is the ISES solar cycle 23 sunspot number progression as of 29 February 2004. It is seen that solar cycle 24 will begin on or about January 2007.

Table 2-4 stipulates the general amplitude of sunspot variability as a function of the filter time constant, using the Wolf number as the gauge of sunspot activity. It is clear that daily values of sunspot number are far more variable than monthly values. While we should always consider the highest bandwidth information when considering real-time forecasting issues, this does not always lead to the desired result. Normally one would like to compare cause and effect using the same filter, thereby enabling an improvement in the correlation expected to exist. This strategy works well at the low-frequency (high bandwidth) end, but this yields little data of interest. We really don't care about a yearly-averaged relationship between SSN and foF2, for example. However, we would like to take advantage of the daily sunspot number and some daily index of ionospheric parameters, such as the midday value foF2. Unfortunately, as we infer from Table 2-4, the day-to-day variability in sunspot number is sizable, and this is not reflected in the degree of ionospheric variability. But, for a number of reasons, we would not expect sunspot number to be highly correlated with ionospheric personality on a day-to-day basis, and certainly not on an intra-day basis. For one reason, the construction of R is based upon a spatial average over the entire solar disk, and this averaging process has a tendency to eliminate very short-term variations of R. Secondly, there is no physical basis for asserting a direct relationship between sunspot number and ionospheric response. If the same question is asked about solar flares, coronal holes, coronal mass ejections, etc, the answer would be different, with the proviso that time lags be considered in some cases.

January

Figure 2-9: Sunspot number variation for solar cycle 23. Monthly averages and smoothed monthly values are given. The dotted lines near the end of the cycle are the upper, median, and lower limits. Data were provided by NOAA-SEC and ISES.

January

Figure 2-9: Sunspot number variation for solar cycle 23. Monthly averages and smoothed monthly values are given. The dotted lines near the end of the cycle are the upper, median, and lower limits. Data were provided by NOAA-SEC and ISES.

Table 2-4: Sunspot Number Variability

Filter Time Constant

Approximate Sunspot Number Range

11 -years

50-100

1-Year

5-150

1-Month

2-175

1-Day

0-350

HF propagation prediction programs in use today all rely on some baseline value of sunspot number (or its proxy), and it is presumed that a running 12-month average of Rz or R/ is to be used as a driver to yield monthly median values of ionospheric parameters (such as foFI) as an intermediate product. This is consistent with the fact that the ionospheric data used to formulate almost all climatological models in use today are based upon an evaluation of monthly medians as parameterized by values of SSN, suitably averaged over a 12-month interval. This construction is quite useful for hindcasting, but not as useful for accurate forecasting. Workers have attempted to use monthly or even daily values of the sunspot number. One should be cautious with such approaches, given the inferences of Table 2-4, and the fact that the database indicates that the sunspot number should be entered is the prescribed way for optimization (i.e., 12-month average centered at the time in question). But many HF practitioners have thrown caution to the winds, and have used monthly values without noticeably poor results. On the other hand, use of daily values is a virtual disaster. In fact, it has been shown that an effective sunspot number formed by taking the average over the last five days can strike a good balance between the chaotic behavior of daily values and the damping effect associated with long-term smoothing. Other workers use trend lines or persistence to estimate the sunspot number.

HF prediction models are not the only examples where sunspot number drivers are used in some fashion. TEC and scintillation models also require some sunspot number representation as a driver. We will discuss prediction models in Chapter 5.

An intermediate-term component of sunspot variability can be found by observing the sun through a hypothetical filter having a time constant of several days. The predominant periodicity to be disclosed in this manner is correlated with the solar rotation period, but is significant only if a distinct (longitudinally-isolated) solar active region with a lifetime > 27 days exists. If the lifetime is much smaller than the solar rotation period, then recurrence is impossible. Also, if multiple active regions are distributed over the solar disk, then recurrence phenomena can be smeared out or distended, even if the individual active regions are long-lived. Recurrence, when observed, can be used to predict future effects on the ionosphere and telecommunications performance. We have already seen from Figure 2-5 that the long-term trends in solar and magnetic activity are correlated. The coronal hole example in Figure 2-6 illustrates multiple 27-day recurrences, with an obvious forecasting potential.

There is a greater likelihood that active regions will be isolated at solar minimum than at solar maximum. Nevertheless, if an especially active longitude is persistent, it may still introduce a resolvable 27-day modulation in solar activity even when the average levels are high. This situation was quite evident during a period in 1990, where solar activity is characterized by the observed 10.7 cm solar flux. From Figure 2-10, we note a steady background level of 150 solar flux units, and a 27-day oscillatory component of ± 40 flux units.

We have already mentioned that the 27-day recurrence of active regions on the sun might provide a basis for updates of the predictions of geophysical disturbances, which are otherwise based upon long-term trends, or climatology. Persistence of features on the sun coupled with solar rotation creates the potential for determination of the geoeffectiveness of coronal holes and resultant solar wind speed changes. Sheeley and his colleagues at NRL [Sheeley et al., 1976, 1978; Bohlin, 1977] have suggested that coronal holes can be long-lived phenomena and should allow predictions of increased solar wind speed to be made for ~ six months in advance. The prediction of solar wind speed, along with an understanding of the interplanetary magnetic field, is quite important in the growth of geomagnetic substorms, and ultimately ionospheric storms. Figure 2-11 shows a very good correlation between the appearance of coronal holes, solar wind velocity, and magnetic disturbance.

Figure 2-10: Variation of the 2800 MHz solar flux during 1990 showing evidence of a 27-day recurrence in solar activity. Raw data were obtained from NOAA-SEC, Boulder Colorado.

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