Derivation of the adaptive anomaly is detailed in this article.
In an attempt to ‘detrend’ the satellite ice record as a preparatory step for spectral analysis, several generilsed forms were tested. A cubic polynomial totally failed to catch the recent easing of the downward trend and only reversed around 2200. It did not fit the curvature of 1997-2007 decade well either.
A simple cosine resulted in a period of about 140 years. This too was a poor match to the curvature of 1997-2007 decade.
Since it has already been observed that there was an apparent folded cosine form in the variability of about 5.4 years (see adaptive anomaly article) this functions : abs(cos(x)) was also tried as a model for the long term variation. It was found to provide a good match to the general curvature of the record. It was thus retained as the detrending function.
The two abs_cos functions were fitted to anomaly time series using non-linear least square fitting. This resulted in a somewhat reduced amplitude for the shorter term which left an obvious variability of that period in the residual . This was probably caused by the lack of a dip in 2001. This amplitude was increased so as to remove the residual in most of the record, at the expense of a mis-match in 2001.
The combined two cosine model fits the recent up-turn well, despite the influence of this short period on the regression being minimal.
The rapid recovery in ice area seen in 2013 and the surprising results from Cryosat2 showing a 50% increase in ice volume in one year seem to concord with this model of an abrupt turn change in direction.
Since this is an abrupt departure from the “death spiral” run-away melting hypothesis, it should rapidly become apparent which model is the more accurate reflection of changes in Arctic ice cover.
The sustained recovery recorded by end of August 2014 seems to concord with this model which anticipates further increase in 2016 before a slight decline in 2017,2018.
The date of two major stratospheric eruptions is marked. Though both were of roughly equal impact in terms of changes to atmospheric optical thickness, the periods following the two events are quite different. It seems unlikely any significant impact occurred in Arctic ice cover as a result.