I think a [link to the comment referenced](https://andthentheresphysics.wordpress.com/2019/11/30/tipping-points-elements/#comment-166602) would be helpful. BTW, I _do_ find it annoying that you cannot in _Wordpress_, unlike here, edit comments you've made after submitting them. This means, effectively, that for anything complicated, you write it up in your own _Wordpress_, check it, and the re-paste it. But, alas, the set of rules for comments are more restrictive than the rules for posts, particularly regarding
. That seems to be true here, as well. It's why I'm exploring Overleaf
as a blogging medium, at least for technical things.
Moving on ....
The tendency to use spectral estimation for geophysical inference is to me a real problem. I'm not questioning its appropriateness or power. I'm questioning its opacity. In that respect it is no better than using convolutional neural networks for calculating or estimating things. Unless all the code is offered, with documentation, the results appear as if by magic and are correct only based upon trust in the skill and self-integrity of the scholars.
Still, I've seen spectral methods abused. I'm not saying Mann or anyone did this. But I've seen people try to do Fourier transforms where multi-taper methods are needed. Professor Mann pioneered using EOFs and eigen-decompositions of data (sometimes referred to, inappropriately, as PCA). Still, it is both difficult to follow, unless scrupulous documentation of steps is taken, and doing an uncertainty analysis is difficult.
In fact, I'd say spectral methods are limited because it is not at all clear how to do such an uncertainty analysis which means something in the time domain rather than in the frequency domain.
Mann is not the only one. [Donnelly, _et al_ (2015) of WHOI](https://agupubs.onlinelibrary.wiley.com/doi/full/10.1002/2014EF000274) did the same for determining recurrence rates for hurricanes. I'm not saying there's anything wrong with it. I'm saying that if there were something wrong with it, they don't have the benefit of the community looking in and trying to do an independent assessment. There are independent ways of doing this. But with the energy barrier to understanding what Donnelly, _et al_ did being so high, _who_ is going to invest the effort?
I do disagree with Professor Mann, who I greatly respect, that choice of method is so stylistic. I think there are objective ways of going about this, particularly with a Bayesian approach. And I think Professor Mann's [defense of the hiatus](https://www.nature.com/articles/nclimate2938) was a demonstrated weakness in whatever means of inference he chooses to pursue. (There is no evidence, in hindsight, it was at all real.)
That there is "a world of mathematical analyses applicable to climate and earth sciences" which "has remained unexplored" does not mean these are worthwhile approaches. The same critical criteria need to be applied to them as all others, and, as in the case of models, those methods which are opaque are less useful than ones which are transparent. This is why, for example, despite their limitations, methods of _random forests_ are so attractive to those using them: They can be interpreted.