As we approach Solar minimum, I thought it might be worthwhile to examine what Dr Landscheidt had to say about future of Solar Cycles and how things look for upcoming solar cycle 24.
Perhaps the best approach is to take a close look at this definitive paper:
EXTREMA IN SUNSPOT CYCLE LINKED TO SUN’S MOTION
(Received 21 May 1999; accepted 13 September 1999)
Partitions of 178.8-year intervals between instances of retrograde motion in the Sun’s oscillation about the center of mass of the solar system seem to provide synchronization points for the timing of minima and maxima in the 11 -year sunspot cycle. In the investigated period 1632-1990, the statistical significance of the relationship goes beyond the level P = 0.001. The extrapolation of the observed pattern points to sunspot maxima around 2000.6 and 2011.8. If a further connection with long-range variations in sunspot intensity proves reliable, four to five weak sunspot cycles (R < 80) are to be expected after cycle 23 with medium strength (R ~ 100).
The part I bolded is a most interesting prediction of upcoming solar activity.
As we have not yet reached solar minimum, and no high latitude cycle 24 spots have yet appeared, we may still be 12 to 18 months from minimum if recent cycles are anything to go by, and I venture a speculation that if no cycle 24 spots appear in the very near future then perhaps Dr Landscheidt should have also mentioned the other possible date of the upcoming solar max using his methods, 2013.6 (see details of his methods in the paper), which if it turns out to be true means a very long cycle which could indicate a very low sunspot max.
The following is a rather lengthy look at this interesting paper.
After introducing 11 and 22 year cycles, some historical work, and changes in the rate of solar rotation, he dicusses the interaction of the Sun’s orbital angular momentum and it’s spin momentum:
Yet the Sun’s spin momentum, related to its rotation on its axis, is only one component of its total angular momentum. The other factor is the Sun’s orbital angular momentum linked to its irregular oscillation about the center of mass of the solar system. The contribution of the orbital momentum to the total angular momentum is not negligible. The maximum value reaches 25% of the Sun’s spin momentum. In addition, there is strong variation. The orbital angular momentum varies from â€”0.1 x 10^47 to 4.3 x 10^47 g cm2 s1 or reversely, which is more than a forty-fold increase or decrease. If there were transfer of angular momentum from the Sun’s orbit to the spin on its axis, this could make a difference of more than 5% in its equatorial rotational velocity (Blizard, 1982). Such acceleration or deceleration has been actually observed (Landscheidt, 1976). This seems to be indicative of a case of spin-orbit coupling of the spinning Sun and the Sun revolving about the center of mass involving transfer of angular momentum (Landscheidt, 1986b, 1988). Coupling could result from the Sun’s motion through its own ejected plasma. The low corona can act as a brake on the Sun’s surface (Dicke, 1964).
After introducing the 178.8 yr cycle and some early cycles work, Dr Landscheidt gets into the real ‘meat’ of his paper, describing the 178.8 yr return period of retrograde events:
Jose (1965) did not relate the 178.8-year cycle to special events in the Sun’s motion. He only observed that the Sun’s path about the center of mass and functions like the rate of change in the orbital angular momentum form patterns that repeat at intervals of 178.8 years. Yet there are special events in the Sun’s motion that constitute a 178.8-year repeat pattern. Jose was the first to point at these phenomena. Around 1632, 1811, and 1990 the Sun’s motion relative to the center of mass was retrograde and the orbital angular momentum, which had been positive for centuries, became negative. The next retrograde Sun event (RSE) will occur around 2169. If there is a relationship between the Sun’s motion and solar activity, the intervals of 178.8 years between RSEs might provide synchronization points for the magnetic sunspot cycle, especially as Jose has shown that there is a cycle of 178.8 years in sunspot activity.
Here is a graph of the angular momentum for the three periods discussed above:
In particular, note the red arrows that mark the -ve angular momentum points at 1632, 1811, 1990, and 2169. Notice also how similar the three full 178.8 year cycles look when displayed this way – at first glance they look the same, but there are subtle differences if you look closely.
Dr Landscheidt goes on to discuss some interesting evidence connecting RSEs with solar plasma instabilities, going into some detail about the remarkable flare events in the period around the 1990 RSE.
He then mentions the lack of data to check longer time scales and some historical solar work, and continues:
…It has been shown, however, that there is a close connection between variations in the Sun’s positive orbital angular momentum and solar activity. As positive momentum is the prevailing condition for centuries, it may be expected that a switch to negative momentum has a disturbing effect which also affects the Sun’s activity, though perhaps in a different way.
According to Pimm and Bjorn (1969), 49% of the variance in sunspot number can be related to the Sun’s positive orbital angular momentum and the curvature of its path around the barycenter. This is based on a correlation coefficient r = 0.7. Further 9.8% of the sunspot variance can be explained by Sun-centered Coriolis acceleration (Blizard, 1987). I showed in the early eighties that there is a secular cycle in the time rate of change of the Sun’s orbital angular momentum that is in phase with the secular Gleissberg cycle which modulates the amplitudes of the 11-year sunspot cycle. Since A.D. 300, the solar motion cycle has correctly indicated all maxima and minima in the Gleissberg cycle, though the length of this cycle varies from 40 to 120 years. An evaluation of this connection by a /2-test [R2-test?] yields highly significant results far beyond the level P = 0.001 (Landscheidt, 1986a, 1987).
See these papers for more on his analysis of the Gleissberg cycle mentioned in the bolded part above:
Swinging Sun, 79-Year Cycle, and Climatic Change
SOLAR ROTATION, IMPULSES OF THE TORQUE IN THE SUN’S MOTION, AND CLIMATIC VARIATION
The secular solar motion cycle points to waning sunspot activity past 1990 and a deep sunspot minimum around 2030.
I have bolded this part where Dr Landscheidt predicts a marked reduction in solar activity from 1990 to a deep minimum in 2030, which to my mind indicates that after a few decades of global warming the Earth may soon turn the corner towards global cooling – and since 2000 the Earth’s temperature does seem to be moving sideways rather than upwards, so we may be in fact now be moving along the top of the temperature curve prior to a coming downturn:
And continuing with cycle 23:
Forecasts in 1984 (Landscheidt, 1986a, 1987), based on these data, seem to be in accordance with the actual development after 1990. Though a panel of experts on solar cycle forecast (Joselyn et al, 1997) predicted in 1996 and even two years later that cycle 23 would have a large amplitude similar to the preceding cycles (highest smoothed monthly sunspot number R = 160), the course of the data in the first three years of the cycle shows that a peak around R â€” 100 is more realistic. The Sunspot Index Data Center, Brussels, now expects a maximum at R = 97. Even more conspicuous is the weakness of eruptional activity in cycle 23.
Here is a graph of soon to be complete sunspot cycle 23, which peaked at about 120 (smoothed) in April 2000, although the strongest month of the series by far was was July 2000:
He goes on to discuss predicting solar eruptions such as X-ray flares and geomagnetic storms and confirmation of same, even predicting where in relation to the direction of the center of mass of the solar system (CM) such flares will occur under certain circumstances.
He then moves on to discuss Retrograde Sun and Sunspot Extrema, and power of two divisions (harmonics) of the 178.8-year period:
In the light of these effects linked to change in the Sun’s positive angular momentum and the observed coincidence of outstanding solar eruptions and reversals of the sign of momentum, it seems promising to see whether the 178.8-year intervals between consecutive RSEs (RSI) can be related to sunspots, though perhaps in a different way as with regular positive momentum. It attracts attention that half of the RSI – 89.4 years – falls within the range of the length of the Gleissberg cycle. It is also noticeable that the fourth part of the RSI – 44.7 years – has not only the length of the double Hale cycle, quoted in the literature (Schove, 1983), but also indicates periods of strong sunspot activity covering several decades. After 1700 the fourth parts of RSIs fell at 1766, 1856, and 1945. In each case, this was the start of a sequence of two to three strong 11-year cycles. In the case 1856 the strong activity additionally included two earlier cycles. The whole interval and its half and fourth parts point to the geometric progression 1, inversely related to powers of 2. This elementary progression plays a fundamental role in natural sciences and is also part of the Titius-Bode Law of planetary distances and von Weizsacker’s nebular theory which explains the power 2 progression and its role in the formation of the distance pattern (Nieto, 1972).
Continued investigation along these lines shows that the 8th part and the 16th part of the RSI are closely connected with sunspots.The 8th part, equal to 22.35 years, is close to the mean length of the complete magnetic cycle of 22.1 years. The 16th part of the RSI, equal to 11.175 years, and the mean length of the 11-year sunspot cycle of 11.05 years, based on continuous observations available since 1700, are equally close to each other. This match disappears when a geometric progression is chosen that is based on powers of 3. Fairbridge and Hameed (1983) have shown that there is significant phase coherence of 11 -year sunspot minima in two consecutive 178-year intervals even if they are not related to special initial events. The minimum phases observed in the first interval show a repeat pattern in the second interval, though only a rough one. The level of significance is P = 0.02.
Some fascinating corespondences between various cycles discussed above – to summarise:
1 RSI = 178.8 years: interval between successive RSE’s
1/2 RSI = 89.4 years: weak approximation of Gleissberg cycle (80 yr)
1/4 RSI = 44.7 years: marks start of 2 to 3 cycles of strong solar activity
1/8 RSI = 22.35 years: close to mean length of Hale magnetic cycle (22.1 yrs)
1/16 RSI = 11.175 years: close to mean length of the sunspot cycle of (11.05 yrs)
He discusses this a bit further, then presents some results of his investigations:
Figures l(a) and l(b) show the result for the respective RSIs. Initial phases of these intervals are indicated by arrows and the label RS. Sixteenth parts of RSIs (SP) are marked by filled triangles. Nearly all of the 33 SPs coincide within a relatively small range with sunspot extrema. In both of the RSIs investigated, the first 13 SPs go along with sunspot minima. A switch to maxima in the earlier RSI after the 13th SP is exactly repeated in the later RSI. Only after 15 conforming SPs there is a divergence including the last two SPs.
Figure 1. Distribution of 16th parts (filled triangles) of 178.8-year intervals between retrograde phases in the Sun’s motion about the center of mass of the solar system (arrows) in relation to extrema of the 11-year sunspot cycle in the periods 1632-1810 (a) and 1811-1990 (b). The associations in both of the 178.8-year intervals show the same pattern with the exception of the last two extrema. Such divergence seems to balance the accumulating difference in length between 16th parts (11.175 years) and sunspot cycles (11.05 years). The extrapolation of the pattern, covering nearly 360 years, points to future sunspot maxima around 2000.6 and 2011.8.
In the first cycle the SPs fall back at minima, whereas in the second cycle the association with maxima continues. Such a divergent course was to be expected. The difference of 0.125 years between the mean length 11.05 years of the sunspot cycle and the length 11.175 years of SP is small, but accumulates over longer periods and must be balanced. Especially secular periods of weak sunspot activity with longer cycles as after 1790 or between 1880 and 1930 and of strong activity with shorter cycles as after 1940 make compensations necessary.
Figure 2. Frequency distribution of 16th parts of 178.8-year intervals from 1632 to 1990 within the normalized 11-year sunspot cycle. The close association with sunspot minimum and maximum is statistically significant beyond the level P = 0.001.
The association of a sunspot maximum with the recent RSE 1990 differs from the two preceding RSEs that were related to minima. This indicates that changes in the association are predominately linked to compensation processes, though there may be a basic association pattern that prevails as long as the differences between the length of sunspot cycles and SPs do not accumulate to such a degree that compensation becomes inevitable.
Two RSIs are not enough to decide what the basic association pattern looks like. The investigation is still in the stage of gathering data and establishing morphological relationships which precede the emergence of hypotheses and elaborated theories. We need to fully characterize the Sun’s behaviour first before we can explain it. Yet it may be speculated that phase locking plays a role in establishing the association between sunspot extrema and RSIs. The waxing and waning sunspot activity constitutes an oscillation as well as the Sun’s motion about the center of mass. These oscillations may be considered coupled as they belong to the same system, the Sun’s dynamics. As coupled oscillators obey the principle of least action, they are bound to establish a state of minimal energy waste. Complete or partial phase locking contributes to such an economical state. In the phase locking process, consecutive RSEs, which are produced by the Sun’s oscillations at equal distances, could be looked at as fixed points which serve as synchronizing signals. As symmetry breaking occurs in such cases (Strogatz and Stewart, 1993), it may be expected that on occasion the emerging pattern deviates from the most frequent outcome.
He goes on to further discuss the distribution shown in figure 2 above, and observes that:
The SPs around maxima concentrate on a range of 8 to 12 months before and after the maximum and shun the exact maximum phase. The association of SPs with the sunspot minimum shows a similar pattern. There are accumulations around 5.3 and 7.6 years, 1 year before and 1.3 years after the minimum, but the exact minimum phase is empty, and in the year afterwards only two SPs are to be found. Conspicuous is the skewed distribution around the minimum. Eighteen harmonics fall before it and only 7 after it. This could be important for prediction experiments. That there are only 6 connections with maxima and 25 with minima could be an effect of the relatively short time series of RSIs.
He then discusses the statistical significance of the results before moving on to forecasting:
5. Forecasts of Sunspot Extrema
This statistical corroboration, linked to a physical background, justifies a forecast experiment. Though there are no reliable indications in the pattern when a switch from sunspot maxima to minima will occur, recent data can be used to decide whether the next SPs will go along with minima or maxima. The last minimum occurred in 1996.4. Even if the current cycle 23 had a length of only 10 years, which is not likely because of its relative weakness, the next minimum would fall at 2006.4. This is 4.9 years away from the next SP in 2001.5. Minima observed since 1632 did never deviate more than 1.8 years from the SP date. So the next SP should be associated with a maximum. Figure 2 shows that in most cases the actual maxima fall in a range 8 to 12 months before the exact SP date. So the imminent maximum will probably occur around 2000.6 Â± 0.16 years. Even if cycle 24;.had also a length of 10 years, the following minimum would occur in 2016.4. This does not match the SP in 2012.7. So another maximum should be expected around 2011.8 Â±0.16 years.
Note that his prediction of cycle 23 max for 2000.6 Â± 0.16 (May-Sept) max was a little late (April) if looking at the smoothed vales but spot on for the highest month (June).
Now, to rehash what I wrote earlier, as we have not yet reached solar minimum, and no high latitude cycle 24 spots have yet appeared, we may still be 12 to 18 months from solar minimum if recent cycles are anything to go by, meaning the solar min may not be until mid to late 2008, and I venture a speculation that if no cycle 24 spots appear in the very near future, aside from the next solar max being at 2011.8 Â±0.16 years as mentioned above, perhaps Dr Landscheidt should have also mentioned the other possible date using his methods: 2013.6 Â±0.16 years – the longer we go without any cycle 24 spots the more likely the second date becomes – which if it turns out to be true means a very long cycle which could indicate a very low sunspot max.
He next looks at cycle intensity.
6. Intensity of Sunspot Activity
Further inspection of the data indicates that not only the epochs of sunspot extrema, but also the intensity of sunspot activity may be read from RSIs. Figure 3 shows superimposed smoothed sunspot data from the two investigated RSIs. Prevalent antisymmetry of the trendlines in the consecutive RSIs is obvious. Details of these oppositely directed trends can be identified in Figure 1. Only the short period between the 130th and 145th year of the respective RSIs is an exception. The parallel course was initiated just at the time of the switch from minima to maxima after the 13th SP. It is a striking feature that in both of the RSIs the sunspot numbers reach the highest observed values a decade after the switch: R = 159 in 1778 and R = 201 in 1957. If this is a substantial repeat pattern, the sunspot amplitudes in the running RSI should roughly follow the course in RSI 1632 to 1810. A forecast experiment could help to decide whether this is correct. It should be expected that the current cycle with medium strength (R ^ 100) is followed by four to five weak cycles (R
Figure 3. Superimposed smoothed sunspot numbers within consecutive retrograde Sun intervals 1632 -1810 and 1811-1990. The two curves, representing long-range trends in sunspot intensity, show prevalent antisymmetry, details of which are apparent in Figure 1. The exceptional parallel trend between the 130th and 145th year of the intervals is linked to the coherent switch from minima to maxima visible in Figure 1. Both of the curves reach their highest point at the end of the parallel trend. This corresponds with record sunspot numbers R = 159 in 1778 and R = 201 in 1957. If the connection is real, the interval that began in 1990 should roughly reflect the course of the interval starting in 1632. After cycle 23 of medium intensity, four to five weak cycles (R < 80) should follow.
If Dr Landscheidt is correct, then the Earth is likely to enter into many decades of cooler temperatures, with the very real threat that conditions could become more like the Little Ice Age a few centuries back.
He then discusses the weaknesses of this examination and finishes off with a full list of sources cited.