First some definitions, bearing in mind that the source data is gridded, where the region of the Arctic is broken down into grid boxes and concentration of sea ice is determined for grid boxes using satellite readings of microwave emission (some detail here):
Extent is the sum of all grid box areas for grid boxes that have a concentration of sea ice over 15%.
Area is the sum of all grid box areas multiplied by their respective sea ice concentrations.
Compactness is a measure of how dispersed the sea ice is, it is defined as:
Compactness = Area / Extent.
Because extent covers all grid boxes with a concentration of 15% or more, while area is just the total area of the sea ice, extent is always bigger than area. So compactness by definition varies from 1 to 0, 1 is very compact ice, 0 is when there is no sea ice, i.e. area = 0.
So compactness offers us a chance to answer a question that has cropped up over many recent summers. True, it it not usually phrased as a question, but as as a statement along the lines of: "The ice this summer is unusually fragmented". The question being: Is there evidence of increasing fragmentation of ice using the index of compactness?
To do this analysis I have chosen three periods, each is the 7 day average centred on the stated date:
Spring Equinox, 20 March.
Summer Solstice, 21 June.
Autumn Equinox, 22 September.
The latter period, Autumn Equinox, is rather similar to results from late summer, for which I have used the seven day average centred on 1 September, so the Autumn Equinox does not seem to be suffering from the effects of early season ice growth. Rather than use arbitrary periods throughout the summer I prefered these fixed periods simply related to the fixed solar cycle.
Taking the whole Arctic region, as shown in the maps from NSIDC, e.g. here, the evidence of increasingly fragmented ice is not very strong.
The region for the above is the whole domain of NSIDC gridded data, the region shown in this map. In that map you can see the actual grid boxes used at the edge of the ice and land.
OK, so looking at the whole domain of the data we get little indication of a decline in compactness, maybe we need to zoom in a bit. To do that here is the Arctic Ocean, which as usual is defined as Beaufort, through to Barents, Greenland, Central and the Canadian Arctic Archipelago.
Again, nothing really striking and no evidence to suggest masses of 'rotten ice' as has been claimed by many amongst the amateur community in recent summers.
But I haven't been specific enough. The largest region by far within the Arctic Ocean is the Central Arctic. Taking data for the 1981 to 2010 period on 20 March, the Arctic Basin (Beaufort round to Laptev) has an extent of 2.710M km^2 (39%) and the Central Arctic has an extent of 4.310M km^2 (61%). The bracketed percentages are the percentages of the total Arctic Basin area's extent at the same time. So what of the Central Arctic?
This is the source of the lack of strong decline in compactness, as will be seen, and the large total area dominates the behaviour of compactness in the whole NSIDC concentration domain, also in the whole Arctic Ocean.
Taking the peripheral seas of the Arctic Basin, Beaufort Sea, Chukchi Sea, East Siberian Sea, and Laptev Sea, the decline in compactness is substantial.
By late summer, at the Autumn equinox, compactness has fallen from around 0.7 to around 0.5. This means the ratio of area to extent has fallen such that within a grid box where there is ice defined as extent (>0.15 or 15%) one might expect that in the 1980s one would have 3/10 open water. But by the post 2007 period one would expect to see 5/10 open water, or 1/2 open water. This is a difference that could reasonably be expected to be seen using something like MODIS. The exception here of course is 2013, which is quite an outlier.
The presence of such an increase around the Central Arctic implies that were one to break the Central Arctic down into a peripheral Central Arctic and the core, one might see a similar effect around the edges of the Central Arctic region.
So, is there evidence of increasing fragmentation of ice using the index of compactness? Yes, there is in the peripheral seas of the Arctic Basin.