Wednesday, 6 February 2013

Open Water Formation Efficiency Part 1.

What is the link between volume and area changes in Arctic sea ice? For some time I've been intrigued by the concept of 'OpenWater Formation Efficiency' (OWFE) and the relationship between sea ice thinning and the consequent increased exposure of open water, with its attendant impacts; summer albedo feedback and autumn heat loss to the atmosphere. In this first post I try to outline the base relationship and data that goes into calculation of OWFE from PIOMAS gridded data, but the OWFE itself will shown be in part two.

All this is new data to me, so any explanations I put forward are tentative and need more examination.
Looking at the changes in the ice pack it seems to me that we have three distinct regions:
  • The Atlantic, a region of relatively little shift in the ice edge as it is pinned by the abyssal drop of warm Atlantic waters out of contact with the ice, the abyssal drop is seen in the graphic below as the deep blue region over the central Arctic Ocean, with an edge poleward of Svalbard, Franz Josef Land and Zevernya Zemlya.
  • The Siberian sector, an area with rapid recession of the ice both in recent years, and within the melt season itself rapid early onset recession. The seas here are generally shallow and are characterised by vigorous winter ice growth enhanced by the transpolar drift drawing ice out of this region and poleward.
  • The American sector (by which I'm referring to the American continent), an area containing the last bastion of older ice off the northern coasts of Greenland and the Canadian Arctic Archipelago (CAA), also the Beaufort Sea, which shows recession between the Siberian and Atlantic rates.

Fig 1, Google Earth plot showing regions used.

So the longitude divisions are as follows: Atlantic: 330.000 to 99.999 deg. Siberian: 100.000 to 189.999 deg. American: 190.000 to 329.999 deg. And the regions are bounded by the 65degN line of latitude, meeting at the common point of the north pole.

All data is from PIOMAS gridded data, source, areas have been multiplied by grid cell area and concentrations from area.h files when calculating %OW, this converts grid cell thickness into volume, which is a de-facto grid weighting. Average thicknesses are then retrieved by dividing by total area in the given month. Average thinning is calculated as the difference between April and September weighted thickness for the region under consideration, which is then divided by April area (the area of maximum ice extent, which is used because thinning that results in open water is included). All thicknesses are in metres.

Linear trend lines added to scatter plots to allow the relationship to be discerned, as it's not clear in some plots, and once added to some plots it seemed daft not to do for all of them. A linear trend is used as a conservative choice in preference to a power or polynomial trend because of the difficulties deciding which of these is appropriate.

Due to earlier difficulties with area weighting the graphics I posted at Neven's Sea Ice Blog should be binned - sorry!

I've calculated the percentage of open water (%OW) in a given year as the September area difference from the April area, i.e. calculate sea ice area at April within 65degN for a given year, then calculate the difference (%) for the September sea ice area within 65degN. Here's a plot of %OW.

Fig 2, Timeseries of %OW for the three regions.

First I'll look at thinning from April to September, April is the peak volume for the whole pack, including areas south of the 65degN parallel. However there is some thickening in the central Arctic through to May (gridded PIOMAS map plots). That noted April still seems like the most intuitive place to start considering the melt season.

Fig 3a, Timeseries of thinning from April to September, 'axis title' should read 'thinning m'.

Fig 3b, Scatterplot, Atlantic sector thinning from April to September versus % of open water in September.

Fig 3c, Scatterplot, Siberian sector thinning from April to September versus % of open water in September.

Fig 3d, Scatterplot, American sector thinning from April to September versus % of open water in September.

What's notable, and is a recurrent theme in the rest of the post, is the lack of change in thickness related to %OW in the Atlantic. This lack of change in %OW can be seen in figure 3a, but why should it be so? I suspect that this for the reason stated in the first bullet point above: The Atlantic is a killing ground for ice with net ice import, ice is continually melted against the Atlantic and is exported through Fram in this sector, so the regular influx of ice brings with it the thinning signature from its source regions. However the ice edge is relatively stable, being pinned by geographical issues, mainly the drop of warm Atlantic water into the abyssal deeps, so the relationship between ice thickness and %OW is not able to manifest itself. This reasoning of course excludes the Barents and Kara Seas.

The American and Siberian sector show both an increased amount of thinning in recent years and a relationship between thinning and %OW such that more thinning during the season corresponds with more open ocean. I assume that the greater variability of the Siberian thinning (spread of figure 3c) is because thinner ice is more prone to weather impacts driving %OW. The American sector contains much more multi-year sea ice, furthermore, in common with the Atlantic, the American Sector is a net importer of ice, via the transpolar drift from the Siberian sector. These factors should buffer ice in the American sector against rapid response to weather.

Why should there be greater thinning during the melt season? The main reason is the change from older to younger ice and resultant decrease in albedo and increase in net energy absorption. I've blogged about this previously here.

Now to look at April thickness.

Fig 4a, Timeseries of April thickness.

Fig 4b, Scatterplot, Atlantic sector April thickness versus % of open water in September.

Fig 4c, Scatterplot, Siberian sector April thickness versus % of open water in September.

Fig 4d, Scatterplot, American sector April thickness versus % of open water in September.

The timeseries of March thickness shows a lesser trend for the Atlantic (~0.5m from start to end), with Siberian and American accounting for much of the loss of thickness, about 1m from start of the period to end. It's worth pointing out that whilst in 2010 the American thickness shows a clear drop, which persists in subsequent years, whereas for Siberia the volume drop occurs in 2011 and 2012 with 2010 itself being locally high. For Siberia the years 2007, 2011 and 2012 are the ones below 2m thickness in April. Atlantic shows a large but not unprecedented drop in 2012.

The Siberian sector shows a clustering of three outliers to the left of the main grouping in its scatterplot, these years are 2007, 2011 and 2012. 2007's presence shows the role of preconditioning in that year, as the drop is in April thickness and precedes the events of that summer. In my next post I'll mention such clustering, and gaps, in a proper OWFE plot, March thickness loss can be used as an indicator in model runs to flag Rapid Ice Loss Events (RILEs), the concurrent behaviour of OWFE plots also reflects these RILEs. The separate grouping in the American sector is a direct consequence of the volume loss of 2010, more detail here.

Leaving aside the Atlantic, once again Siberian sector shows a behaviour suggestive of non linear relationship between %OW and April thickness. But again this is damped in the American Sector, which does not appear to have begun to participate in the same process, again I suspect that this is because of thicker older ice, preferential loss from that old ice (which does not expose open water) and ice import, although I could be wrong on this, see end of post.

Finally, September thickness.

Fig 5a, Timeseries of September thickness.

Fig 5b, Scatterplot, Atlantic sector September thickness versus % of open water in September.

Fig 5c, Scatterplot, Siberian sector September thickness versus % of open water in September.

Fig 5d, Scatterplot, American sector September thickness versus % of open water in September.

All regions show a drop in September thickness from 2010 onwards, this suggests that whatever happened in 2010 had subsequent impact through the summer with widespread impacts. This has already been shown in breakdown of volume by thickness bands, on which subject; in due course I'll breakdown those volume/thickness sets into regions as done here.

Once again for Siberia and America we see the sort of clustering and break in distribution noted previously, this is due to the drop in thickness seen in figure 5a. But it is amplified from the March drop due to the increasing seasonal thinning seen in figure 3a, but I think that the lack of a post 2010 jump in thinning shows that the April thickness deficit is being amplified by thinning increases, not caused by them.

The apparently non linear nature of some the relationships needs to be noted. In particular the Siberian sector  shows a relationship with the linear trend whereby it starts above, is below in the middle, and ends above the trend line; this implies non linear behaviour. Specifically it implies that for April and September thickness - as the thickness reduces the increase of %OW becomes more aggressive. This behaviour is weakly apparent in the American sector %OW increase with respect of both April and September thickness, will it become more strongly apparent? As most of the volume loss has been from thick ice categories, i.e. older ice declining, and the American sector contains what's left of that, we should see an increase in %OW as that declines further. However this interpretation could be flawed.

Comparing figure 4a and 5a it is apparent that April thickness for both the Siberian and American sectors are  very close, albeit that there is a marked drop in Siberian sector April thickness after 1988 (why?). Yet by September the Siberian sector is about 50cm thinner than the American, this is supported by figure 3a, where although both are rising, the Siberian sector is constantly above the American.

So perhaps the behaviour of the Siberian sector is unique to its bathymetry, with shallow seas as opposed to the deeps below much of the American sector of the Arctic ocean? If so could this be a source of the GCM's 'long tail' of ice persisting for years without a rapid crash? The American sector ice, specifically what's off the Canadian Arctic Archipelgo could indeed be more resistant to melt that overall volume trends indicate. However models show that net OWFE, which is derived from %OW, thinning, and is measured against March thinning is also non linear with March thickness (there's little difference between March and April thickness).

This blog is a sort of online open notepad for me, so rather than wait until I'm sure I have the answers to such questions I'll publish and not deny others the fun of puzzling it all out. A regional breakdown of my volume/thickness data from the PIOMAS gridded data will be of great use, but as I have a day job that'll have to wait a bit, I need some time to put my feet up. But as I already have the OWFE stuff worked out, and the main reference read, I'll post about that in a few days.

OK anonymous - hit me with those typos you've found! ;)


crandles said...

I'm lost early on:

>"The Atlantic, a region of relatively little shift in the ice edge as it is pinned by the abyssal drop of warm Atlantic waters out of contact with the ice"

Isn't the Atlantic sector the region where the ice edge has moved most? Isn't that because of warmer Atlantic water?

>"What's notable, and is a recurrent theme in the rest of the post, is the lack of change in thickness related to %OW in the Atlantic."

Isn't this because the edge is retreating, removing thin ice and keeping the remaining area at fairly similar thickness. In other sectors the edge isn't retreating in April so the thinning shows up.

crandles said...

Fig 4a, Timeseries of April thickness in September.
Fig 5a, Timeseries of September thickness in September.

Should the 'in September' at end of each of these titles be dropped? If not, I don't understand what that is about.

Chris Reynolds said...


I've deleted the errant 'in September' from each point you mentioned.

As the Atlantic sector ice edge in April isn't geographically constrained it has moved more than that in the siberian sector, in April.

The calcuation of ice thickness is based on - sum of volume of ice for each grid cell / total area for that year's april. So I don't think the thinning is due to retreat of the winter ice edge. But it is very early in the morning and I'm rushig off to work. I'll think about it.

crandles said...

My explanation was probably a bit off track:

The April to Sept thinning graph looks rather horizontal for Atlantic sector. Your April area denominator is getting smaller in later years, therefore it appears that the volume loss (numerator) is really dropping off.

I think that is potentially significant and could be showing 1) that when we get to deeper water the ice becomes harder to melt and/or 2) with a smaller area over which to melt, less volume gets melted.

Either way that might sound like the ice may last longer than trends but I think Wipneus' trends for each cell shows there is sufficient thinning at all locations.

So I think the April area in the denominator is dominating this graph rather than thicknesses.

Simpler graphs might help avoid such problems.

E.g. start with a couple of simple 6 line timeseries graphs:

Volume in April and Sept for each sector. (Or maybe (April-Sept) Volume and either April or Sept Vol.)

Area in April and Sept for each sector.

Chris Reynolds said...


Yes, these say nothing about volume, as I said I'll be calculating and posting tables of volume per thickness band. Rather than mess around amending code in the OWFE code I've done I'd rather wait until I re-jig the volume/thickness code to do areas. That will have much more utility. It's not a major task and I plan to do it this weekend. I'm just pondering whether to break 65 to 90 degN into two bands. But I suspect it's best to keep it simple. The three areas I've used seem to work adequately.

I'm not convinced that the denominator (area) is dominating as you describe. The flatness of figure 3b is a consequence of the flatness of Atlantic thinning in figure 3a. Were there a trend the scatter plot would tease out this relationship, but there is very little trend in thinning, so there's very little slope.

As the % open water increases it drags the data points on the scatter plot upwards, but due to figure 3a showing little trend in thinning, the scatter is merely smeared upwards as the ice thins - the data points still occupy the same range on the thinning axis.

All of the ice pack is experiencing volume reduction, but not all the ice pack shows the behaviour in figure 3b.

PS on the subject of breaking down the areas, it's noteworthy that in this Atlantic sector Barents & Kara are probably accounting for much of the recession. Cryosphere Today.

I tend to agree that the plot from Wipneus trumps this, but I am persuaded that we're in a RILE that may end up in a rapid transition, so I try to use new data to challenge that idea.