Guest post by Paul L. Vaughan, M.Sc.
“Eyeball” methods of measuring solar cycle length (SCL) by looking at successive minima or maxima only take a measurement on average every 11 years. They ignore all of the sunspots occurring during the interim.
In contrast, wavelet methods utilize all sunspots, producing objective estimates of instantaneous solar cycle length at the temporal resolution of the data.
Graph legend notes:
1) measurements based on successive solar:
min = minimum
max = maximum
FCLT = Friis-Christensen, Lassen, & Thejll
( pv08 = my 2008 “eyeball” adjustments to FCLT )
JA = Jan Alvestad
3) Wavelet measurements based on all sunspots are denoted SCL[w], where w = Morlet wavenumber. (Large w indicates coarse resolution, while small w indicates fine resolution.)
Here’s a look at the rate of change of solar cycle length (SCL’):
Friis-Christensen, Lassen, & Thejll were completely off my radar when I produced results presented here and here . Comments appearing in the latter thread reminded me of the existence of their work. I had considered their work a few years ago, finding:
1) Their measurement methods were wholly unsatisfying.
2) Leif Svalgaard was steamrolling their claims (and Leif was making substantive points).
Wavelet methods are simple. The Morlet wavelet is nothing more than a sine & cosine wave multiplied by a bell-shaped curve to taper the edges. All a wavelet algorithm does is iteratively calculate correlations (to see what matches the wavelet shape) and perform scaling, coordinate, & units conversions. That’s it.
Most of the confusion which arose in the discussion here was a result of participants not realizing that the spacing of the sine & cosine waves in a wavelet can be adjusted to see at varying resolution (Morlet 2pi being a coarse view).
Generalizations about SCL do not apply to SCL’.
Just as sine & cosine waves have zero correlation, oscillations of SCL & SCL’ are nearly orthogonal. Consider why data reduction methods like PCA (principal components analysis) have been developed and why differential equations include (rather than omit) terms with neighboring low-order derivatives.
Perhaps Friis-Christensen, Lassen, & Thejll were looking at the right variable, but not thinking about orthogonality & differential equations?
Raw (not anomaly) ERSSTv3b data are from KNMI Climate Explorer.
[1a] indicates smoothing over the annual cycle.
ERSST = extended reconstructed sea surface temperature
0-90N = northern hemisphere