Uhh, perhaps you did not understand that the final result is trend+filtered_anomaly, from which you can calculate the begin and endpoint of the melting period.
The only reason for the split is not to filter the "sinusoid" and hope the anomaly will be mostly made up by random noise. A simple average would probably be sufficient, especially for the Antarctic where the "sinusoid" stays fairly constant in amplitude.
Indeed, I did not realise that was what you were suggesting. Thanks for being more explicit.
I have already noted the presence of a pseudo cyclic variation and stated that as being one of main reasons for this filtering exercise. It is clear that 'hoping' the anomaly is random is not justified and that an average , or worse, a running average filter would be an awful choice.
Such processing would inevitably introduce aliasing effects into the result which would be far from obvious. This will at best introduce spurious variations and quite possibly lead to false conclusions being drawn.
This is signal processing 101. The module that most climate scientists seem to have missed out on.
Anomalies can help to
visualise a dataset with a large repetitive pattern, however applying any filter to what is left is highly questionable. It would be more legitimate to filter first, then take the anomaly if that's what you want to
look at.
This is a classic case of applying a "smooth" without recognition of the fact that it is a filter and giving due consideration to the frequency response of what is being done.
Since the signal we are trying to analyse is deviations in annual cycle what is the effect of filtering the residual anomaly?
Thinking about it: due to linearity of convolution filters (and the subtraction of anomaly processing) , filtering before taking anomaly would be the same as filtering the anomaly
and applying the same filter to the annual 'climatology' that was subtracted.
Adding it back would be identical to just filtering the signal but NOT identical to filtering just the anomaly and adding back in the unfiltered climatology.
Doing what you suggest would leave part of the signal unfiltered. I don't that as being beneficial (or even intentional).
Re. LOESS:
About everything looks good: amplitude, phase, zero crossing, begin- and end point.
The fact that this filter always ends up going through the end points is one of the reasons I don't like it. That clearly has no validity. It is seems to be doing something similar to padding the window in a convolution filter ( only worse ).
The fact that it has an indeterminate frequency response is another problem. Fine, the result look "smoother" but what have we done to the data? We don't actually know.
So, thanks for your suggestions, ideas and suggestions are welcome, but I don't think I see any reason that LOESS would be a better choice than gaussian. Rather the opposite.