PIOMAS: The Porch and the Roof.

I've previously discussed why I think Spring 2010 saw an event as significant as the Arctic sea-ice crash of 2007. As a result of my last post and the ensuing discussion I am more confident that Spring 2010 was a significant event and that this year, as with 2011, we will see further massive volume losses in the coming Spring. However there are some details that need to be addressed in this post before I go on to look at whether calculated thickness from PIOMAS and extent/area has any value.



I should first point out that this is all based on PIOMAS, Cryosphere Today's area metric, and a combination of two extent series, IJIS-JAXA and GSFC, provided by Chris Randles (aka Crandles) at Neven's blog. The three data sources are linked to at the end of this post. I'd like to thank Kevin O'Neill for a fruitful discussion following my previous post on this matter

I accept PIOMAS as producing a conservative indications of volume that can at least be relied upon for qualitative argument, the recent volume drops I'm talking about are large enough to be outside of PIOMAS's uncertainty range. So whilst there may be argument about the magnitude, I don't see reason to doubt the qualitative picture of massive and significant losses of volume. PIOMAS does not include parts of the Sea of Okhotsk and the Gulf of St. Lawrence in its model domain, this does not affect the results as here I'm looking at results during the Spring and Summer that are related to daily anomalies (based on daily averages).

So on with the issue of the porch and the roof. I used the term 'porch' to describe a detail in the series of thickness calculated by extent and volume. I used the term 'porch' because of its similarity with an element of composite video signals, figure 5 here. Kevin O'Neill then pointed out that there is a 'roof' in the series of thickness calculated by area and volume, he also argued that the porch was an artefact of the processing technique used to calculate extent. For the uninitiated, extent and area have specific definitions with respect to Arctic sea-ice. Area is calculated as the total of each cell's area multiplied by its sea-ice concentration, the cells are then added up to give total area. Whereas extent is calculated by adding up the area of all cells with over 15% sea-ice concentration. The professionals (e.g. NSIDC) prefer the extent metric because it is a more robust metric that is less subject to issues such as melt ponds, although it can be affected by sea-ice movement. In the past I've preferred sea-ice area, however am quite open to extent. I did my original work using extent because I'd got the IJIS-JAXA dataset as my only daily dataset. Driven by what I've found using extent I've done some more serious searching and now have an area dataset going back to 1979, the same date PIOMAS volume starts from. Because this dataset continues over the winter, whereas IJIS-JAXA doesn't due to the failure of AMSR-E, and because of criticism of extent that I accept, I'll be moving over to using the Cryosphere Today Area series in future.

I agree with Kevin O'Neill that in the porch what we are seeing is an artefact of the processing technique used to calculate extent, however that does not mean there is no value to the observation of the porch, and its recent disappearance. Furthermore the roof is another artefact, this time of the area calculation, as I will show in the following post, the calculation of thickness from PIOMAS volume and area is itself a specific construct that may actually tell us little about real 'on the ground' thicknesses. To understand what the apparent changes mean we must first understand why we are seeing the artefacts, both porch and roof.

The porch and roof can be seen in the following graph. Bear in mind that as the average over a long period this graph accentuates the features, as will be seen below, each year's roof isn't as tidy a phenomena as in the average.

Figure 1. Average annual cycle for area, extent, volume, and thickness as calculated from area and extent, using the 1980 to 1999 average. Left vertical axis is in 1000 Km, the right vertical axis is in metres. Volume and area are measured from the left vertical axis, thickness from the right.

Here is what I think is happening in that graph: It can be seen that while volume, area and extent all have their maxima in the early part of the year, the maxima for thicknesses are later. Area and extent have their maxima in March, this because the polar night is from September to March and it is during this time that the sea-ice grows. Volume has a later maximum, this is because even while the area and extent are falling as sea-ice recedes from lower latitudes, it is still cold enough over the central Arctic for ice to form and thicken. Thickness based on extent counter-intuitively has its maxima in the late Spring, even more odd is the roof exhibited by area based thickness, which lasts throughout the Summer months. This Spring/Summer peak in thickness is because of the way thickness is calculated, being simply the volume divided by area, or volume divided by extent. The end of the roof and the porch both happen as the sea-ice area/extent reaches its minima and begins to grow, this growth of new thin ice brings down the average thickness. During the Autumn and Winter thickness is at its lowest because there is a large amount of new thinner sea-ice growing in the peripheral seas. Then in the late Winter and early Spring the loss of the thinner peripheral sea-ice causes a growth in average thickness.

Figure 1 is based on the average from 1980 to 1999, calculating the average of all the metrics in that graph for each day gives the series on which the graph is based.

Because the thickness is calculated from the equation:

Thickness = Volume / (Area or Extent)

We can interpret any period where volume and area/extent are changing, but thickness is not, as being a condition in which the change in volume is accounted for by the change in area or extent. So for thickness calculated from area, the roof shows that all the way through the Summer the change in volume is largely accounted for by the change in area (roof), and that for thickness calculated from extent, towards the end of the Summer the change in volume is largely accounted for by the change in extent (porch). During both periods change in thickness is not needed to balance the volume and area (or extent). I've broken these periods into decades, using daily averages for each decade.

Figure 2a, as figure 1 but for the 1980s.

Figure 2b, as figure 1 but for the 1990s.

Figure 2c, as figure 1 but for the 2000s.

A decade probably isn't long enough to keep a statistician happy, but in terms of the porch, its increasing slope is suggestive of an increasing role of thickness loss throughout the latter two decades. This is borne out by observations on which I've previously posted. Then there are the last two years, 2010 and 2011, the following graph is produced in the same manner as the above four, but averaging over two years.

Figure 2d, as figure 1 but for 2010 and 2011.

Again it's reasonable to point out that not only is a two year average not comparable with a ten year, but a two year is even further from statistical significance. However before we leap from that to conclude that nothing odd happened in the last two years, it's worth looking at the longer term context. Furthermore the volume underlying the thickness calculation shows two step drops, one in 2007, the other in 2010, ref.

Figure 3, 1979 to 2012 timeseries of calculated thickness using extent and area. Original size here.

The above graph shows that the porch and roof have been persistent features of the extent and area derived thicknesses from 1979, until the last two years. As mentioned earlier, the roof as seen in the average is tidier than for each year alone, however comparing 2010 and 2011 with the preceding years does support the idea of a change to the annual cycle in the last two years. Because the roof and porch are both formed where area or extent changes are able to account for changes in volume without recourse to thickness change, the loss of those features implies that either volume change has increased, extent or area changes have lessened, or a combination of both factors. At present I am unable to tie it down to either volume or area, so conclude it must be a result of changes in both factors.

Another feature is the apparent timing of the minima. The minima have been at around day 365, the very end of one year and start of the next, however since 2007 the minima appear to have been earlier as implied by the rising trend at the end of the year. What has happened here is that whereas in earlier decades the minima has been extended from around day 300, rising shortly before day 365, in recent years the minima has been around day 300 with an immediate rise thereafter. What is the cause of this? Taking the period between day 300 and day 365, area change over that period shows a gradual increase, with a spike to 1000km^2 in 2007, however volume change over that period jumps to a sustained 1000km^3 increase. As thickness = volume/area the sustained increase in volume gain appears to be responsible for the change in the minima.

It is worth pointing out that 2007 does not stand out in the thickness anomalies, whereas 2010 does. This is because 2007's loss of volume was largely accounted for by a loss of extent/area, whereas the volume loss of Spring 2010 wasn't associated with a commensurate decrease in extent/area, implying a loss of volume.

So the calculated thickness metric needs to be treated carefully as it can produce counter-intuitive results, despite that it can be a useful aid to understanding what is going on in the PIOMAS volume series, and what some of the implications are. In my next post I'll look at whether the thickness figures from PIOMAS and area are actually reliable indicators of thickness of the sea-ice.


For references see the following post.