This is not a novel result, for example:

https://wattsupwiththat.com/2018/03/30/tools-to-spot-the-spots/

Nevertheless, this is a solid analysis and exercise in citizen science.~ctm

By: Leron Wells

During my early teenage years as an avid fan of the Space Program I was patiently waiting for NASA to get the Shuttle flying so hopefully they could boost Skylab from its decaying orbit. However, I was very disappointed as I am sure everyone was when it was announced that Skylab would renter the atmosphere sooner than expected and there was no hope of saving it. I became very curious about the 11 year solar cycle when it was announced that the reason Skylab deorbited sooner than the NASA engineers calculated was because of the increased drag associated with the expansion of Earths outer atmosphere caused by the very active Solar Cycle 21.

Now we fast forward 3 decades and much to my surprise I have yet to see any concrete evidence of any correlation of Earths atmospheric temperature with the 11-year solar cycle. There have been many attempts on various surface temperature records with no real positive signature of any meaningful evidence that I have seen, “IMHO”. As a geophysicist with over two decades of experience and having developed numerous spectral applications for finding Oil & Gas, I took it upon myself to see if there was a correlation in the Stratosphere, how hard could it be, right? After all we now have over 40 years of satellite data which should be more than enough data to detect an 11-year cycle.

With permission from RSS I downloaded the binary dataset for both the lower Troposphere and the lower Stratosphere and began writing an application to read and display the data. The RSS binary data has global coverage for every month ranging from December 1978 to February 2019, which equates to 483 months of data. I designed the application to sum the data along latitude bands for each month and to do all spectral analysis calculations and visualizations in the latitude vs. time space.

Figure 1 Lower Troposphere Latitude vs Time

Figure 1 shows the plot of the lower Troposphere of the latest dataset available from RSS as of February 2019. The application has volcano images positioned by their eruption dates for Mt. St Helens, El-Chichon and Mt. Pinatubo as well as the Enso markers for strong, moderate and weak El-Nino’s and La-Nina’s. Also, at the base of the plot is a graph of the sum of all latitudes for each month. It should be noted that this sum does not include any latitudinal weighting so the Global average will be somewhat different than the true global average temperature for the RSS dataset for the Lower Troposphere. The latitude vs time lower troposphere plot “Figure 1”, clearly shows the latitudinal effects of both the ENSO cycles as well as the short-term cooling caused by Pinatubo and El-Chichon.

The lower Stratosphere plot “Figure 2”, shows the rapid warming caused by the SO2 injected into the Stratosphere by both El-Chichon and Pinatubo. Again, the graph below the plot shows the summation for each month and represents the globally averaged anomaly temperature for the most recent RSS binary dataset as of February 2019 for the Lower Stratosphere.

Figure 2 Lower Stratosphere Latitude vs Time

With the latitude vs time plotting accomplished the next step was to take advantage of the latitude vs time space to compute the spectrum for each latitude and generate the same type of plot as the previous temperature plots, but with the main color plot being latitude vs cycle length in years. I used the binned Periodogram algorithm to compute the spectrum for each latitude and display the latitude vs cycle length plot. The color in the latitude plot represents the spectral energy converted to the base 10 logarithm or what we call in Geophysics as DB Down or Decibels from maximum amplitude. This was necessary to normalize each latitude color band to a relative value so that all the spectral features for each latitude and each month would be normalized to the color bar and show the latitudinal spectral features in a pseudo relative manner for the latitude vs cycle length plot.

The equation for the color plotted spectral data is defined as:

logAmplitude = 20 * Log10(currentAmplitude / maximumAmplitude)

The spectral displays have the actual solar cycle length annotated for cycles 21, 22 and 23 as a reference because the average solar cycle length is assumed to be 11, but the exact cycle length varies by some number of years for each cycle. The graph at the base of the cycle length plot is the average cycle energy for the entire dataset represented as a black line, the Northern Hemisphere mid latitudes as a red line and the Southern Hemisphere mid latitudes as a blue line. It should also be noted that the spectrum graph at the base of the plot is not utilizing the logarithmic amplitude, and it is plotted as the actual linear amplitude as spectral power taken directly from the binned Periodogram. This was chosen because the peak of each cycle for the various latitudinal bands are better represented by showing their relative strengths as a linear function.

Figure 3 shows the spectrum plot for the lower Troposphere in the latitude vs. cycle length in years display. There are many localized anomalies that one could spend quite some time speculating about what the source could be, but the very interesting and powerful 13.5-year cycle leads me to believe that it could possibly be associated with the solar cycle with a reactionary time delay. But never the less, there is no 11 year cycle that shows up in the Troposphere. Again, the black line on the lower graph represents the global average, the Red Line represents the middle latitudes of the Northern Hemisphere and the Blue line represents the average of the Southern Hemisphere mid latitudes.

Figure 3 Lower Troposphere Latitude vs Cycle Length (Years)

Figure 4 shows the latitude vs cycle length in years plotted for the lower Stratosphere and clearly shows a very strong 11 year cycle in the Southern Hemisphere and also shows a meandering cycle length in the Northern hemisphere that varies slightly by latitude from 10 to 10.5 years, but is very close to the period that fits within the range of the Solar Cycle lengths for the satellite date range.

Figure 4 Lower Stratosphere Latitude vs Cycle Length (Years)

Conclusion

The spectral methodologies that I have applied to both the Lower Stratosphere and Lower Troposphere RSS data are very robust methodologies and have served me well throughout my career finding cyclical patterns with much less data than what is available in the RSS monthly global satellite record. There was a concern that the effects of Pinatubo and El-Chichon was the cyclical pattern that I was seeing in the spectral display that correlated with the solar cycle period, so just to be sure I muted the period over the range that Pinatubo caused the stratospheric warming and reran the Spectral plot and the results were very similar for both the Stratosphere and the Troposphere.

All the code that generated this data and produced the plots was written from scratch in C# in the community edition Version of Visual Studio 2017, except for the binned Periodogram which I got from Numerical Recipes in C. The next step will be to use the Wiener Levinson algorithm to utilize Predictive Deconvolution to remove the cyclical patterns for each latitude band individually and display the deconvolved results to see the latitude vs Time space with all cyclical patterns removed, so stay tuned for the next iteration. Also, much appreciation to Remote Sensing Systems for providing access to the binary satellite data.

Leron T. Wells III