Digital Diatribes

A presentation of data on climate and other stuff

December 2008 Update on Sunspot stats

Posted by The Diatribe Guy on January 6, 2009

We are truly in a remarkable time as it relates to the current solar cycle.  By a number of measures, we are witnessing a once-in-a-lifetime event…  maybe.

It certainly is “once in a lifetime” if you are post-middle age.  We ahve not seen measures in solar activity like we are seeing now for some time.  However, if history is any guide, this may not be the last time we see this kind of event in next 50-100 years.  So, for the younger people among us, this may simply be an indication of things to come.

I say this not because of some expertise in solar science, but simply based on a review of the data.  Now, the caveat here is that, while we have somewhat reliable data going back to the 1700s (certainly not as technologically savvy as modern times, but if you read my Eddy reviews in the Landscheidt category, you will see that he is fairly confident that overall conclusions can be drawn from data since the 1700s), the solar cycles are long enough that we still have only a limited amount of data points in which to draw conclusions.  I state this caveat because it is the honest thing to do.  I will calculate averages and standard deviations on available data.  Also, I will be calculating averages and standard deviations on data points where part of the data is overlapping into other data points, so there is bias introduced.  We need to understand the limitations and know that our conclusions based strictly on the data are necessarily limited by time.

That said, there are a number of very interesting observations that we can make that indicate the special nature of our time.  The Sunspot data can be located by clicking the link on the right, under RESOURCES, of the NOAA Sunspot data.

1) Current six-month average = 1.7.  This is the lowest 6-month average since the period ending November 1913.

2) Current 12-month average is 2.8.  This is the lowest such average since the period ending March 1914.

3) Current 24-month average is 5.2.  This is the lowest such average since the period ending November 1914.

4) Current 36-month average is 8.5.  This is the lowest such average since the period ending December 1934.

5) Current 48-month average is 13.8.  This is the lowest such average since the period ending October 1935.

6) Current 60-month average is 19.1.  This is the lowest such average since the period ending March 1936.

7) Current 72-month average is 26.5.  This is the lowest such average since the period ending November 1936.

This is truly remarkable.  All the way up to the 6-year average, we see numbers that have not been witnessed in over 70 years, and in the first few cases, almost 95 years.  Only when we finally get to a 7-year average do we get into our generation:

8 ) The 84-month average is 37.6.  This is the lowest such average since the period ending March 1978.

There are two components to the solar cycle:  magnitude and length.  The above average measure the most recent magnitudes.  Obviously, since the cycle has a maximum and a minimum, the recent averages drop as the cycle lengthens.  So, it is not pure coincidence that these low measures are happening as we see an equally impressive length of the current cycle.

Now, I am measuring cycle length from the 12-month average minimum to 12-month average minimum.  I understand that this is not the actual declared start of the new cycle, but mathematically it is a convenient way of segregating the cycles.   So, when I speak here of length, know that the count starts from the minimum value of the 12-month average. 

With th latest month, a new lowest value on the current cycle was established, so we are still waiting to declare a minimum of the 12-month average.  This puts the current cycle length at 147 months since the previous 12-month minimum.  The last time a cycle reached 147 months was the period ending March 1856.  That cycle finally ended at 149 months.

I decided to see if I could identify some interplay between the cumulative length of successive cycles.  In the 22 cycles identified in the NOAA data (minimum to minimum) the average length is 131.5.  The shortest cycle was 109 months, and the longest was 163 months.   The standard deviation was 14.2 months.  This puts the current cycle at just over one standard deviation from the mean as it relates to the overall cycle length.   This does not seem overly unique from that perspective.  Cycle 22 was 115 days, which is just over one standard deviation from the mean in the other direction. 

What makes the current cycle seemingly unique is that seven of the last eight cycles are below the average.   So, now that we see a longer cycle, it looks like an unusual event.   To me, it’s more of an indication of a longer-period cyclical event.  That period may have now come to an end.

I decided to look at successive lengths.  Sure enough, as you start adding cycle lengths together, the standard deviation increases, but as a percentage of the average period it declines dramatically.  The standard deviation of individual cycles is 14.2, which is 10.8% of the mean.  The standard deviation of two successive cycles is 22.2 months, which is 8.4% of the mean.  This trails down to a 34.9 month standard deviation for nine successive cycles, which is only 2.9% of the mean.  Some of this is to be expected strictly on a random basis.  However, the extent of the reduction leads me to believe that there is something to the fact that there is some overall balancing act going on where successive short cycles necessarily lead to longer cycles, and vice-versa.  This idea has been posited by Jose and Landscheidt, so I’m stealing it from them.   I prefer “borrowing.”

The results of looking at the successive cycles provides interesting results:

Two successive cycles:
Min: 220
Max: 315
Average: 263.7
Standard Deviation: 22.2
Current Previous 2 cycles: 239 (second lowest historically, just over 1 standard deviation from average).
The lowest 2-cycle length of 220 was followed by combined lengths of 274, 315, 301, and 275. Our current length following the 239 length is at 262 and counting. We see the current 2-cycle lengths at the moment approaching the mean.

Three successive cycles:
Min: 355
Max: 464
Average: 397.5
Standard Deviation: 25.7
Current Previous 3 cycles: 378 (within one standard deviation).
The current 3-cycle length is at 386 and counting. This is still 11.5 months short of the mean. Assuming a tendency towards the mean, that means the current cycle still has some legs (or lack of them, as the case may be) or that future longer cycles are in store.

Four successive cycles:
Min: 490
Max: 590
Average: 532.1
Standard Deviation: 26.3
Current Previous 4 cycles: 504 (The last six averages are the six lowest).
Notice that the overall dispersion between min and max is actually less on the four-cycle average than it is on the three-cycle average. The last four-cycle length is once again more than a standard deviation away from average. The current 4-cycle length is at 525 days and counting. If the current cycle were to end today, the next cycle length would need to be 146 months to reach the average.

Five successive cycles:
Min: 616
Max: 706
Average: 665.7
Standard Deviation: 27.6
Current Previous 5 cycles: 626 (Second lowest historically. This is about 1.5 standard deviations from the mean.)
The dispersion of only 90 days between max and min on the 5-cycle length is the lowest dispersion outside of the single cycle length. The current 5-cycle length is at 651 and counting. This is still 14.7 months below average. If the current cycle would end today, the next cycle length would be 141 to reach average.

Six successive cycles:
Min: 751
Max: 855
Average: 798.8
Standard Deviation: 30.9
Current Previous 6 cycles: 751 (The lowest historical value. This is about 1.6 standard deviations from the mean.)
The current 6-cycle length is at 773 and counting. This is still 25.8 months below average. If the current cycle would end today, the next cycle length would be 148 to reach average.

Seven successive cycles:
Min: 873
Max: 989
Average: 931.5
Standard Deviation: 33.4
Current Previous 7 cycles: 873 (The lowest historical value. This is about 1.7 standard deviations from the mean.)
The current 7-cycle length is at 898 and counting. This is still 33.5 months below average. If the current cycle would end today, the next cycle length would be 159 to reach average. This has happened before. But if there is truly a tendency to the mean, this starts to point to the possibility of either another very long cycle, or successive longer-than-average cycles.

Eight successive cycles:
Min: 994
Max: 1128
Average: 1065.3
Standard Deviation: 34.8
Current Previous 8 cycles: 994 (The lowest historical value. This is a full 2 standard deviations from the mean.)
The current 8-cycle length is at 1020 and counting. This is still 45.3 months below average. If the current cycle would end today, the next cycle length would be 168 to reach average. This has not happened during the period recorded in the data set. Again, if there is truly a tendency to the mean, this would necessarily mean that we can expect longer cycles on the way, probably successively. The fourth – sixth cycles in the data show that this is a historic possibility. There were cycles of lengths 163, 152, and 149 in direct succession. This is an average of 154.6. We don’t need an average quite that long to reach the 131.5 month average. If the current cycle plus the next two average 142 months, we will reach our average. Interestingly, those three cycles were on the heels of three cycles even shorter than our previous three cycles. If I replace the previous three cycles with 135, 109, 111 then we would need the next three cycles to average about 150 months to attain the overall average. The data set does not extend back far enough to see what the cycle lengths were previous to that time period, so we can’t compare the tendency of that “rebound effect” over the 8-cycle period.

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One Response to “December 2008 Update on Sunspot stats”

  1. […] December 2008 Update on Sunspot stats […]

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