Jim, Those are utility functions I wrote that I forgot to include. I will attach them in a bit. But now that you mention it, I should probably use the LogisticSigmoid instead as that is built in!
In the meantime you can blank those out as they are only used to shape the TSI time-series from a sinusoid to a modulated sine. The sigmoid serves the same role as a tanh function as it provides a gradual envelope from one peak-to-peak level to another level. The sig2 combines two back-to-back sigmoids to provide a modulated peak or valley on an envelope. That is how I got the dip in TSI around 1970.
Ostensibly, I should find an algorithm that can interpolate the QBO, TSI, and CW time series with enough resolution that the DiffEq solver can continuously integrate across the time span.