July SEARCH Contribution

My July contribution is as follows. Please feel free to comment.

1.    Extent Projection 4.0 +/- 95% confidence interval of 0.9 M Km^2 based on past forecast performance of this technique.

2.    Methods/Techniques - Statistical

3.    Rationale

As previously, I use regression methods to predict the expected deviation from gompertz fit of September Extent. The alternative method I used last year of predicting falls from current area still does not show any skill at this length of time before the minimum.

As last month, I use a linear regression to predict the deviation from Gompertz fit. The regression uses the residual from a gompertz fit of Cryosphere Today area at the end of June.

4.    Executive Summary

I attempt to predict the residual from a Gompertz fit of NSIDC average September Extent by a linear regression that uses Cryosphere Today area at 30 June residual from a Gompertz fit.

5.    Estimate of Forecast Skill

The standard error arising in the linear regression is .38 M Km^2. However, standard error of a method tends to underestimate the errors likely in practice. So I have used only information up to 30 June of the year being predicted to predict each of the last 10 years. As shown in the table this gives RMSE of .46 M Km^2. 0.46 has been doubled to give a 95% confidence interval of 0.92 M Km^2.

Estimates at 31 May of year concerned   

   

Year	Gompertz Fit	Residual Est	Estimate	Error
2002 2003 2004 2005 2006 2007 2008 2009 2010 2011	6.44 6.17 6.06 5.95 5.65 5.62 4.74 4.40 4.58 4.48	-0.32 0.00 0.18 -0.21 -0.25 -0.31 0.19 0.59 -0.37 -0.02	6.12 6.17 6.24 5.74 5.40 5.31 4.92 4.99 4.21 4.45	0.16 0.02 0.19 0.17 -0.52 1.01 0.19 -0.40 -0.72 -0.16
2012	4.29	-0.26	4.03
			RMSE	0.461

6.    Discussion of thickness and limits to method used

 

I have attempted to predict PIOMAS volume minimum and Cryosphere Today area minimum using similar techniques. For PIOMAS volume, I try to predicting the fall from 30 June volume using a multiple linear regression with 3 predictors: 30 June PIOMAS volume, the residual from a gompertz fit of 30 June volume and the decline in volume in June. This gives a prediction of 2.2 K Km^3 +/- standard error of 0.55. This is a substantial 45% decline in the volume from the record low 2011 minimum of 4.02K Km^3.

 

I predict Cryosphere Today area minimum by using a gompertz fit of the minimum daily area and predicting the residual by a linear regression with residuals from a Gompertz fit of CT areas at 30 June. This gives a prediction of 2.6 M Km^2 +/- standard error of 0.27.

 

There is little difference in timing of minimum area and minimum volume so dividing one by the other to get an average thickness gives 0.85m to compare against previous years:

 

2009    2.01m

2010    1.44m

2011    1.38m

 

These years were all record low average thicknesses and they show a rapid decline. The projection suggest a potential 58% decline in average thickness at minimum in 2012 compared with 2009. These are the best statistical schemes I have found but time was limited and there may well be better schemes.

 

A 58% decline in thickness over 3 years or a 45% decline in volume this year should not be translated into a projection of the ice all disappearing by 2015 without a discussion of whether the rate of loss will accelerate or decline. The two major feedback are a positive one: albedo feedback increasing the volume decline in summer and a negative one: faster growth of ice in winter as more heat can be lost through thinner ice. With PIOMAS showing a decline in volume at 30 June 2012 compared with 30 June 2011 of 1.1K Km^3, there is little sign of this negative feedback showing up to any great extent let alone dominating the albedo feedback. However the feedback should be expected to get stronger as the ice gets thinner so just because we have not seen the effect getting stronger does not mean it will not dominate the albedo feedback. The negative feedback is likely to be limited to restoring winter ice volumes not exceeding them because once the faster growth of ice catches up with previous years thicknesses the reason for the faster growth disappears. If this negative feedback works to full effect, would this stop further increases in the volume decline in summer? If the ice volume declines to 2.2K Km^3 this year, I would suggest there would still be further declines in MYI and this may allow faster melt and albedo feedback as a result of that faster melt. While it may be possible to find assumptions that lead to the rate of decline of ice almost disappearing once the ice reaches a minimum volume of around 2K Km^3, I would suggest these assumptions would have to be rather bizarre best case assumptions.

 

These large potential figures of 45% decline in volume in 2012 and 58% decline in thickness from 2009 to 2012 do emphasize how little time there is for negative feedbacks like this to kick in and slow the rate at which ice is being lost.

 

Implications for my statistical method of estimating extent

My method of predicting extent mainly relies on a naive Gompertz extrapolation fitting the extent minimums. Clearly thickness is declining as well as extent. If the rates of extent decline and thickness decline were not interrelated then you could expect a discontinuity in the extent trend when the thickness runs out. In the real world, it may show up as a further acceleration as volume gets very low. The extent prediction method I have used is therefore likely to be conservative as a seasonally ice free state is approached.

 

Worst Case scenarios: 2013 onwards

In the PIOMAS record, 5 of the 32 year show a decline in volume from minimum to minimum exceeding 2.2K Km^3. So even if a negative feedback should kick in to slow the rate of decline, 2013 onwards could already be down to a volume that could disappear if the weather conditions happen to be favourable towards enhancing volume decline.

 

Note, PIOMAS volumes may not be correct. Schweiger et al 2011 Uncertainty in modeled Arctic sea ice volume reports a conservative estimate for October Arctic ice volume uncertainty of 1.35 × 10^3 km^3. So we could be nearer or further from a melt out than indicated by just taking the PIOMAS volumes as true.

 

2012 worst case

A melt out this year seems a remote possibility. If PIOMAS is reporting volumes that are 1K Km^3 too high and a 2 sigma weather towards increased volume decline occurred then the prediction would reduce from 2.2K Km^3 by 1+.55*2 K Km^3 before considering albedo feedback. A melt out this year is therefore only a remote possibility but it is difficult to rule it out at around the 1% or 2% level.

 

Discussion Conclusions

It is very difficult to be 95% confident of whether the arctic ice will substantially melt out this decade and many scientists seem clear this should not be claimed. However, volumes do appear to be approaching levels where there could be a substantial chance of a melt out and perhaps such probabilities could be estimated rather than waiting to obtain 95% confidence. The method I have used to estimate September Extent could be conservative but for the moment I will leave it as it is with a caution that there could be a thick tail all the way down to zero extent. If my estimates of PIOMAS minimum volume and average thickness decline seems credible, then the probability of melt out in the next fews years seems a sufficient risk that it may be sensible to change climate modelling priorities towards ascertaining regional climate effects of a seasonally ice free arctic.

 

Comments

[crandles]

Yes my priction for PIOMAS minimum changed from 2.5 to 2.2 K Km^3. I am a bit worried that looks a bit crazy alarmist but it had a better fit - RMSE of .55 instead of .6. Anyway we will see what the rest of melt season brings.

Wonder if this will provoke any reaction.

[Werther]

Crandles, as I was on line, my 'last words' before nighttime are for you.
Good work, daring on volume. I wonder how extent will look like with such low volume.
I'll have a better read tomorrow.
Sleep well.

[idunno]

Hi crandles,

I have been wondering if the shape of the ice sinewave pattern is changing so that the bottom is getting wider, more than it is getting deeper...

Amongst this spaghetti...

http://arctic.atmos.uiuc.edu/cryosphere/arctic.sea.ice.interactive.html

it seems, for example, that in 1996, the ice level declined, spent a few days bobbing along the bottom, and went up again.

In the recent, post-2007 period, the period at or near the bottom seems much longer. I'd suggest this is possibly a scenario where the melt collects all of the "low hanging fruit" earlier, but then has more difficulty melting the last bastions of ice in the Arctic Basin and Canadian Archipelago. Extra heat accumulated in the Arctic then goes into delaying the refreeze - leading to a graph with an even bigger bottom.

So, beware the fat-arse graph trap!

[Aaron Lewis]

It is in the nature of non-linear dynamic feed back systems that when they are out of control and seeking a new equilibrium, they exhibit behavior that is not predictable from the behavior of the system while it was "in control".

In statistics one must always compare (ice) to (ice). However, these days statistics on the Arctic is always a comparison of (ice) to (ice plus a lot of heat). Some times ice plus a lot of heat is ice, some times it is water, and sometimes it is water vapor. There is no way of predicting what ice plus a lot of heat will be by doing statistics on ice, unless we also do statistics on the heat. Nowhere, do I see a good heat balance on the Arctic. Even the accounting for the GIS leaves out latent heat.

[crandles]

>"beware the fat-arse graph trap!"

Also beware of the differing interpretations of the fat-arse.

One interpretation could be that we are getting down to difficult to melt MYI that takes a few years preconditioning and will then resume sharp downward trend.

Another interpretation might be that the tough to melt ice might be due to deep water meaning that there is little upward heat flux so that it is a near impossible job to melt it all with top melt only. This might mean a very long time before ice free situation is reached.

Another interpretation might be that it is just chance fluctuations that have given appearance of a fattening arse.

>"Nowhere, do I see a good heat balance on the Arctic."

I am taking it that PIOMAS ice volume is as good a measure as we have got. That suggests 1.1 K Km^3 less than last year at 30 June. Higher than the long term average but near the recent average, so no sign that we are slowing down in our rush to ice free there.

[Charles Longway]

Crandles - Great post!!!
Could export displace ice that is in a difficult to melt location? When I looked at the UB map today I see what looks like a wedge of ice pushing south in Fram. With weaker ice, could export cause more damage than in the past. Last year we had the suprise of flash melt, could we have flash export?

http://www.iup.uni-bremen.de:8084/ssmis/index.html

[crandles]

Well I think the ice would move faster if there is less ice resisting such movement. To me this suggests that the area exported might remain fairly similar despite the faster movement so that the volume exported is lower.

I would hope this is a negative feedback. It may already be built into trends but hopefully it could perhaps become a stronger effect as ice retreats.

Yes I agree about seeing a wedge moving towards Fram over past few days. I tend to see this as a weather event. It was certainly predictable from forecast weather patterns, Neven mentioned it. Such weather events have happened in the past and will occur again in future. Is there any reason to think frequency or strength is changing?

[Bob Wallace]

"area exported might remain fairly similar despite the faster movement so that the volume exported is lower"

That would happen if we were transporting more thin, FYI. But if it's thicker MYI going out then volume export will rise.

I suspect the first meltout will follow right after the Great Thick-Ice Flush of 201x.

[Simon]

Really good post, especially the discussion section.

time was limited and there may well be better schemes

With none of the approaches able to rule out a summer melt-out in the next few years, time is rather limited for all forecast attempts. No doubt the best hindcast will come from a physical model, but the statistical answers are available here and now.

So, thanks for a brave, reasoned contribution and post.

[crandles]

Thanks for the thanks. Will just have to see how quickly daring and brave turns to foolish.

[idunno]

Hi all,

SEARCH July is out:

http://www.arcus.org/search/seaiceoutlook/2012/july