In desperation I asked Fermi whether he was not impressed by the agreement between our calculated numbers and his measured numbers. He replied, “How many arbitrary parameters did you use for your calculations?” I thought for a moment about our cut-off procedures and said, “Four.” He said, “I remember my friend Johnny von Neumann used to say, with four parameters I can fit an elephant, and with five I can make him wiggle his trunk”.
So said Freeman Dyson, one of the brighter stars in the physics firmament. When we try to understand the star which supplies all the energy Earth needs to maintain life on its surface, we have a problem. The problem is it keeps surprising us with its unpredictable changes in activity levels. It’s doing this at the moment in solar cycle 24. The top solar physics institutions made various predictions about the timing of the start of the cycle, and how high the ampliitude would be. They’ve been proved very wrong. A couple of individual solar physicists did predict a low solar cycle (low for the modern era anyway), including Leif Svalgaard, who predicted a max monthly sunspot number of around 70 for this cycle back in 2004. Leif based his prediction on phenomenological observation of the solar polar field strength, which has been diminishing for a long time now. Even this is looking a bit high at the moment though. I predicted 35-50 SSN in 2008 based on a planetary method.
In this post, we take a cycles analysis approach to looking at solar activity since 1600. Regular contributor Tim Channon has done work in the past in acoustics, and as part of his toolbox, he developed some software which uses clever techniques to break down complex sound envelopes into underlying frequencies and amplitudes. For fun and interest, we fed it with the Lean 2000 TSI reconstruction data to see what would happen. The result is shown in the graph below the break.
The R^2 value for the correlation in the top graph between the Lean 2000 TSI reconstruction and the curve generated by Tim’s cycles analysis software is 0.99 – or in layman’s terms “Near enough perfect”.
The software decided to use seven cycles to get a best fit, and so following Johnny von Neumann’s metaphor, we were able not only to get Nellie to wiggle her trunk, but hold a brush with it and paint Lean’s TSI curve while doing a belly dance.
So, given the number of ‘arbitrary parameters’ to play with, this stuff is easy, right?
Well I haven’t seen anyone else manage it, so hats off to Tim Channon and his remarkable software.
Beyond that though, there is the question of whether there is any scientific value or merit in this kind of curve fitting exercise, or as Leif Svalgaard would have it, “cyclomania”. :)
It seems to me the answer to this depends on how ‘arbitrary’ the parameters really are. It has long been thought that the Sun’s activity and Earth’s climate exhibit some longer term cycles beyond the well known ~11 year Schwabe Cycle and the solar magnetic ~22 year Hale Cycle. There is also the ~80 year Gleissberg Cycle, and the ~200 year de Vries Cycle. There are also a couple more lesser known ones. The 55.15 year cycle identified by Roy Martin, and the ~110 year cycle noted recently by Roger Andrews in his SST vs Air temperature analysis. Roger notes in comments that not only is the periodicity right, but the phase is pretty close too.
Another point I want to stress here is that the cycles, which when combined reproduce the Lean TSI curve so perfectly, were not ‘picked’ by a human with pre-conceived ideas or knowledge of real natural cycles in terrestrial climate or solar activity. The software did the choosing, testing and refining all by itself.
Look again at the legend at the bottom of the lower graph, where the frequencies of the cycles Tim’s software found are enumerated:
11.09, 11.51, 57.2, 78.94, 112.5, 238.86, 426.47 years.
Most of these are close to periods recognised by solar physicists, climatologists and planetary cycle periods identified by researchers here on this blog.
Given that the Lean TSI reconstruction is no doubt imperfect, there remains the question of how a curve generated by nearby exact planetary synodic frequencies would look compared to it. This is a project I’ll be undertaking soon.
What happens when you project the synthesized curve further backwards and forwards in time?
Watch this space, it’ll be worth your time, I promise.