The Gleissberg Cycle of Solar Activity: Part 1

What is the Gleissberg Cycle?

The Gleissberg cycle of solar activity spans roughly 80 to 90 years. Because it is not regular, it is probably better described as quasi-periodic or as a pseudo-cycle.

You can easily discover it for yourself.

How to Plot the Gleissberg Cycle

I found the newly corrected sunspot series here:  SILSO sunspot data (by remembering the name “Clette”, a scientist who has been doing research in this field for a long time.)

I entered the monthly data into a spreadsheet and plotted it.

SSN 175-2015

The 11-year cycle is apparent but the Gleissberg Cycle is not.

To display the Gleissberg Cycle, I standardized the values as described below and then cumulated the standardized values. In the following graph, the 11-year cycles appear in clusters of increasing or decreasing numbers of sunspots. A full cycle up and down is defined as a Gleissberg Cycle after Wolfgang Gleissberg.

gleissberg

To obtain Z-scores, I calculated the mean and standard deviation (using the functions AVERAGE() a.nd STDEV()). The Z-scores for every month, is defined as:

Z-score = (DATA-AVERAGE) / STDEV.

The key to the graph is this: After calculating Z-scores I cumulated the scores by recording the first Z-score by itself. Then for the second data point, I added the second Z-scores and so on. At some points the up scores added to the down scores should cancel and the line values should be zero (the line should cross the X-axis).

This method is very crude because the vertical position and the location of the high and low points depends on the starting value. The starting point itself is arbitrary, determined by the point in time when the observers started recording carefully enough and regularly enough for today’s scientists to report sunspot numbers instead of groups of sunspot numbers.

One way to improve would be to add 100 years or so of data going back to the Maunder Minimum, a period of 650 years from 1645 to 1715 when few sunspots were observed.

Because the Maunder Minimum was such a long period with few sunspots the graph would start around zero and a starting point near zero would be roughly correct according to our best current knowledge.

Results

The 11-year solar cycles can be seen, usually 4 to 7 one after the other increasing and decreasing. The peaks occurred around 1790, 1880, and 2005, 90 and 125 years apart. The troughs are 105 years apart.

The average of these intervals (90, 125 and 105) is 107 years, rather longer than the usual value cited of 87 or 88 years.

The cause of the Gleissberg Cycle is speculative. Possibly the process is chaotic, resulting from changes in magnetism deep in the Sun that cause turbulence at the surface. The chaotic nature of the cycle may result from two dynamos within the Sun that are interacting. The Gleissberg Cycle may be displaying the beat frequency of these two dynamos. Alternatively, the gravitational pull of the planets may affect the Sun’s activity.

Next I will try to improve the graphic by adding more data. SILSO provides annual data back to the 17th century.

Discussion

To analyze the graphic we should keep in mind that it displays a metric for CUMULATIVE number of sunspots.

I interpret this as long-term (century) increases and decreases of the amount of energy entering the oceans and the ice caps of the Earth. The reason is that the atmosphere and uppermost few meters (yards) of land can store very little energy. I mention “ice” because when ice melts it absorbs a lot of energy as latent heat.

So during the upward swing of the Gleissberg Cycle I expect a lot of solar energy entering the oceans in the tropics and a lot of melting ice at or near the poles.

Ocean currents tend to distribute energy from tropical to polar regions. So I would expect to see ice melting in the Arctic Ocean. I would expect to see less ice melting in the Antarctic. Why?

First, the southern oceans are bigger and so the heat is distributed less densely.

Second, the existing ice is more extensive than in the Arctic and therefore the Antarctic ice reflects more light back into space preventing it from converting into heat energy. In effect, the 100-year length of the Gleissberg Cycles  is not long enough to have much impact on the Antarctic ice cap.

Further, ice in the Antarctic is mostly land-based and is therefore less affected by ocean heating. By contrast, ice at the margins that is not grounded on the seafloor would be subject to increased melting.

These theoretical predictions are confirmed by observations.

Finally, I conclude that even if one solar cycle of 11-years does not greatly affect climate, a series of 5 sunspot cycles either up or down may be expected to have a cumulative effect. What makes it so difficult to determine the effect is the fact that ocean currents must be integrally involved because only the oceans can store solar energy for 50 years and then release it.

The oceans therefore act as a low-pass filter for variability in solar output.

There is an interesting paper by Nir Shaviv, Using the Oceans as a Calorimeter to Quantify the Solar Radiative Forcing. He estimated that the variation in ocean temperature within one solar cycle is about 0.1 degree Celsius.

We can see from inspection of the Gleissberg Cycle graphic that from 1935 to 2005 the time span is about 70 years compared to 7 solar cycles, giving a duration of 10 years per cycle. The vertical span of the upward swing is 7 bars, and each cycle averages one vertical bar.

If each cycle from top to bottom represents 0.1 degree Celsius, that would give a span of 0.7 degrees Celsius between 1935 and 2005. This may be compared with the rise in ocean heat content estimated to have raised the temperature by about 0.8 degrees Celsius per decade, 056 degrees C in 70 years (1935-2005). This rough comparison suggests that from 1935 to 2005 the Earth’s oceans should have heated by 0.7 degrees Celsius from excess solar energy alone, whereas the oceans heated only 0.56 degrees Celsius.

This analysis seems to be flawed because that would be too great a rise in temperature. The variation in one 11-year cycle may overlap the variation in the next. Assuming only 50% of the figure estimated by Dr Shaviv (o.o5 degrees Celsius) the heating from solar variation over 7 cycles would be 0.35, 60% of total observed oceanic heating.

This analysis suggests that the percentage of total heating by increased solar activity between 1935 and 2005 was between 60% and 100%.

There remains the possibly that much of the increase in solar energy:

… was reflected back into space by ice and clouds

… melted ice without increasing temperature

… evaporated water at the surface that rose into the upper troposphere and was there emitted into space

OR Sunspots are not so tightly correlated with the Sun’s energy flux as hitherto believed.

Still the Gleissberg Cycle is important because at least some approaches to analyzing Sunspots cycles suggest that solar energy accumulates over many cycles sufficient to affect global warming.

This is a highly controversial subject that I leave until later in this series.

Part 2 will attempt to extend the analysis back to 1610. This will correct some of the bias at the beginning of the series because the zero point on the graph will coincide with a time when there were few sunspots observed.

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