Is there any correlation between winter sea ice volume maxima and summer minima ?
Using data for 1979-2016, the correlation between detrended maximum volume and detrended minimum volume is 0.648, which is highly statistically significant (p-value: p < 0.001).
However, this is only true for sea ice volume. For sea ice extent (rather than volume), the correlation between detrended maxima and detrended minima is very weak.
Thank you Steven. That was a concise and meaningful answer to a perfectly reasonable question.
However, an earlier response to Gerontocrat's question was less helpful.
... Sorry to point out the obvious, but there is no need to calculate a statistical correlation between winter sea ice volume maxima and summer minima, because the two are directly related by a simple formula:
summer ice minimum = (previous) winter ice maximum - total spring/summer melt
Instead of answering the question as to the existence (or otherwise) of such a correlation, that was simply a descriptive statement of an obvious equality. A similar example of an obvious equality from the world of finance would be...
Closing share price = Opening share price + Change in share price
Although taken from entirely different spheres, these two equality statements share a common weakness: namely that, in the absence of any reliable form of time travel - other than the usual unidirectional 1 second per second familiar to everyone
- the predictive skill of each is precisely zero.
As Steven goes on to stress, although there is a strongly positive correlation when the metric is volume, that breaks down when looking at either extent or area. In the summer of 2013, Rob Dekker and myself independently wrote articles on this subject for Neven's Arctic Sea Ice Blog.http://neven1.typepad.com/blog/2013/06/problematic-predictions.htmlhttp://neven1.typepad.com/blog/2013/07/problematic-predictions-2.html
Bringing that a bit more up to date, and using Excel's CORREL function on the NSIDC monthly values for both Artic Sea Ice extent and area for September 1979 - March 2017...
Correlation between September extent (year X) and March extent (year X+1) = 0.739
Correlation between September area (year X) and March area (year X+1) = 0.678
However, those seemingly meaningful correlations are largely due to the overall downward trend in the dataset(s).
March extent trend = - 42k sq kms/annum
March area trend = - 32k sq kms/annum
September extent trend = - 87k sq kms/annum
September area trend = - 79k sq kms/annum
Once the data has been de-trended (using a simple least-squares linear regression), the output(s) of the CORREL function change to...
Correlation between September extent (year X) and March extent (year X+1) = -0.068
Correlation between September area (year X) and March area (year X+1) = -0.165
As Steven stated, this represents a pretty weak level of correlation - and it actually comes out as being weakly negative.
N.B. As mentioned earlier, during those array comparisons, the average September value of (year X) would be paired with the average March value of (year X+1). The reason for this particular arrangement was because Gerontocrat's original question concerned the correlation if only the freezing season was considered. Had the question pertained to the melting season, then March and September values from the same year would have been compared.
However, it would not really have made much difference, as the de-trended correlations for the March - September melt season are also very weak...
extent = 0.000
area = -0.022