However in playing around with the data, trying to settle on a method that will produce a sound answer, I have ended up being diverted by an idea I thought worth pursuing.
I have used sea ice extent data for the whole period from 1979 to 2014, for the whole Arctic, the data gap in 1987 and 1988 has been left as is, with no attempt to refill. The day to day change in extent is calculated as the difference between the 'current' and previous day for each day of the data, leaving only the data gap and 1 January 1979 as having no presence in the resulting dataset. Then histograms have been calculated based on the data for four periods, the 1980s, the 1990s 2000 to 2006, and 2007 to 2014. The histograms are then scaled according to the number of datapoints in each period in order to adjust for the different lengths of all four periods, and produce a probabilistic distribution of occurrence.
The first result looks like this:
What is most apparent is that there has been a small but evident drop in the smallest day to day changes in extent. What is less immediately obvious is that this is due to a small increase in higher losses. To bring this detail out I have calculated each of the above curves as a difference from the 1980s plot. For completeness I show the 1980s plot below, but by definition this is 0 for all points.
Now what is going on is clear, we have the drop in small day to day changes, this is a result of the increase in day to day extent changes around 0.1M km^2, a figure commonly known as a 'century' amongst sea ice amateurs. It is worth observing that the sum of the curves for the 1990s, 2000 to 2006, and 2007 to 2014 is 0 (zero), in other words the drop in low day to day extent changes is totally due to the increase in higher day to day extent changes.
The changes are small, that doesn't surprise me, in fact little about this surprises me, which is why I have never bothered posting it. But as a result of looking at Pete's question, an assumption of mine; that there seems to have been a broadening of the seasonal cycle, seems to be rather shaky. I've coded the processing of individual years for all regions of the Arctic Ocean as follows, but for this short post I'll stick to the same periods used above and have worked things out manually in a spreadsheet.
Taking Arctic Ocean extent, I have used the January to March average as a baseline to bring the different periods up to similar levels and leave the summer decline to do what it will so to speak.
From the above, with the early plots more or less lined up the summer drop in extent is seen in its true context; summer losses have increased massively in the most recent period compared to the 1980s, and indeed the other periods. It is this increase in loss rate that causes the shift in the distributions of day to day extent changes outlined at the start of this post.
More than that, eyeballing such graphs has led me to conclude in the past that the season has broadened, with a longer melt season for any given extent. However if I calculate the range for each of the above periods as the difference between maximum an minimum, then halve this range and apply to the maximum or minimum, I can calculate a mid point for each period's seasonal cycle. Then I can calculate the difference between the passing of the mid point in the summer and in the autumn, and from that calculate the difference between the two dates and get the time taken to go from mid point to mid point.
So here are the times between mid points calculated for each of the above four periods.
|2000 to 2006||113|
|2007 to 2014||113|
At best there is a week (7 days) between the 1980s and 2007 to 2014, with 2007 to 2014 having the same mid point span as 2000 to 2006, not what my eyeball says about the above graph.
I need to think about this a bit more, my method may be flawed (not in execution, rather in design and interpretation). However at present I am thinking that the steepening of loss rate and growth rate has not caused a widening of the melt/freeze season, rather this visual interpretation is false and is an outcome of the progressively deeper seasonal cycles with successive years.