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crandles

I've re-voted for the same options as last time; second lowest option in each case. The SEARCH July report key statement makes it look like I should go for less than 4m but in fact that key statement was in an email in early June sending the June report contribution so it applies to the june report where the statistics I presented suggested 4.3m.

The discussion in the July report may well make it look like I am suggesting that the statistics calculating to 4.0 is too high, but I am regarding this as a low probability risk of the statistics being way too high. That doesn't necessarily pull a huristic central estimate down.

Maybe I am trying to blacksliding a little having seen my estimate be the lowest in the July report.

Seke Rob

Maybe some voters are confused over monthly or daily for NSIDC looking at the vote spread. These were the last 2 values in the OP.

2010: 4.93 million square km
2011: 4.61 million square km

I've voted 4.25-4.50 for monthly extent minimum and 2.8-3.0 for daily CT.

Jeffrey Davis

I think the final totals will be greater than 2007 and 2011. Based on nothing more than it looks like the slope has been turning more shallow.

Seke Rob

The NSIDC Extent daily for reference: http://nsidc.org/data/seaice_index/images/daily_images/N_stddev_timeseries.png

Neven

I voted the same for CT min daily area as last month: between 3.0 and 3.2 million square km.

For NSIDC min monthly extent I went up a notch: between 4.5 and 4.75 million square km.

Wipneus

Same as in June:

CT minimum: 2.50 +/- 0.41 [10^6 km2]
NSIDC Sept: 3.98 +/- 0.67 [10^6 km2]

See http://neven1.typepad.com/blog/2012/06/2012-polls-part-1.html?cid=6a0133f03a1e37970b0167678329f6970b#comment-6a0133f03a1e37970b0167678329f6970b

Chris Biscan

I wouldn't let the idea of this next pattern to slow things down.

The ice is destroyed all over the pack but 3-4 mil km2 in the Eurasian Basin and North of CA/Greenland.

if NSIDC averages over 4.50.4.75 for the month I would be very surprised.

crandles

Wipneus, that looks very good and seems to give a very narrow 2 sigma range. Particularly so as you appear to only use data to Sept 2011. Why not submit it to SEARCH?

Your exponential extrapolation of PIOMAS minimum gives 1K Km^3 lower than Sept 2011. If June 2012 is 1.1K Km^3 lower than June 2011 and the rate of decline in June 2012 is much higher than previous years, wouldn't a lower prediction for PIOMAS minimum be more appropriate if you are allowed use of data up to June 2012?


Normally I would be a bit wary of exponential extrapolation of volume as this gives a much earlier date for ice disappearing than gompertz extrapolation of any extrapolation of area or extent. It seems to be taking the worst case possibility. However, the data to June suggests it isn't bad enough. Perhaps that is adequate reason to go with the worst case extrapolation?

Dave Leaton

Based on a simple linear extrapolation + look at the ice, I came up with 2.89 for area. I'd like to know who polled more than 4.0. That would require an average daily drop for the next sixty days of around 26636 km2, which is more than 3 STD below average daily for those sixty days (44826).

For what it's worth, the current sixty-day area drop (Cryosphere) is now the second largest in the record for any sixty-day period:

-6.0621495 (1985 - Days 151-210)
-5.9827003 (2012 - Days 133-192)

Wipneus

crandles:

the rate of decline in June 2012 is much higher than previous years, wouldn't a lower prediction for PIOMAS minimum be more appropriate if you are allowed use of data up to June 2012?

Perhaps, but you probably have noticed that the trend of the ratio in decline of June to that of July is to increase. So 2012 July's decline may be a bit smaller.

Perhaps that is adequate reason to go with the worst case extrapolation?

Gompertz and exponential 1-year-ahead extrapolations are both not too bad. But there is a noticeable tendency to estimate too high for the gompertz fit. In only one of the last ten years the estimate is a fair bit too low:
https://sites.google.com/site/arctischepinguin/home/piomas/piomas-trnd9-1.png

The exponential extrapolations highs and lows are more evenly:

https://sites.google.com/site/arctischepinguin/home/piomas/piomas-trnd6-1.png

It does not matter much for the final estimate of area and extent: as the rates of decline for them is relatively smaller than of volume, so is the propagated error.

Jim_pettit
Dave Leaton: I'd like to know who polled more than 4.0. That would require an average daily drop for the next sixty days of around 26636 km2, which is more than 3 STD below average daily for those sixty days (44826).

Indeed. Over the last ten years, an average of 2.92M km2 of ice area has been lost between Day 194 and area minimum (range: 3.18M km2 [2009] to 2.41M km2 [2006]). If that average applies this year, SIA minimum would end up around 2.68M km2, while even the smallest post-Day 194 drop on record--1997's 2.3M km2--would still yield a minimum of 3.25M km2. That's nowhere near a record, of course, but it's far less than the 4 million km2 prediction. (Just for fun: if 2012 could equal the largest post-Day 194 drop--1982's 3.57 million--it would end up with a truly astounding 2.03 million km2.)

On a side note, 2012 SIA has been in first place for the last 13 consecutive days, and 29 of the last 34 (2012 spent five days in second place behind 2010 toward the end of June). Barring any unforeseen circumstances, it should stay in first for at least another four or five days. After that, a series of big daily drops in 2007 may knock 2012 out of first.

crandles

>"Perhaps, but you probably have noticed that the trend of the ratio in decline of June to that of July is to increase. So 2012 July's decline may be a bit smaller."

I don't think I have specifically looked at declines in June versus declines in July. I thought my regression suggested that when June volume decline was large, the minimum was usually lower than the gompertz fit.


>"Gompertz and exponential 1-year-ahead extrapolations are both not too bad. But there is a noticeable tendency to estimate too high for the gompertz fit. In only one of the last ten years the estimate is a fair bit too low:"

I don't think I follow this. Switching between the two graphs, I see gompertz prediction going a little too low on 2 occassions whereas the exponential goes too low on three occassions, two of which are much worse than the gompertz curves with errors of over 4K Km^3 for 2011. The gompertz worst misses are going too high by 2.5K Km^3.

For 2011 prediction in range 2.5-6.7 from gompertz extrapolations looks a better tighter range than -2 to 5.9 for exponential extrapolations.

For 1 year ahead, gompertz is better in 2000, 2001, 2006, 2008, 2009

while exponential is better in 2003, 2005, 2007, 2010, 2011.

For 1999, 2002 and 2004 I cannot tell from the graphs.

5 each seems a draw, but the winner would depend on how the shape of the actual varies, which seems a bit artificial. (ie there is only 1 prediction a fair bit too low as only 1 actual year is quite a bit higher than both neibouring years.)

AFAICS all the exponenial extrapolations are below gompertz extrapolations by a pretty minor amount for the first few years but they increasingly separate with the exponential always being more alarmist.

This may be just about justified for the past on a least square error basis, but there are reasons why that may not be the case for the future.

Wipneus

crandles:

This is how I count the results of the last ten years:

numbers of "predictions" too low, about right, too high:

gompertz 1 5 4
exponent 3 4 3

Just counting, comparing the size of the error probably requires weighting by the std errors. I don't think they are the same.

crandles

I think we both agree that there is very little in it and maybe exponential has done marginally better in past few years but it is so marginal it could easily change such that gompertz is better for future.

The linear not through origin relationship of area/extent to volume is interesting. Any thoughts on why that works like that? Clearly we know thickness is being lost faster than area, which is what the line pointing above the origin means. However a curved relationship would seem more natural, and I don't see a way of explaining the linear relationship with some explanation of ice tending to break up once it gets down to a certain thickness. If anything, the linear relationship seems to suggest the ice can continue getting thinner until it all disappears.

This seems strange to me. But if you have found a good method great. Understanding it would be an extra bonus.

Are you thinking about submitting it? I think you should.

AmbiValent

I chose the second lowest in both cases again, though I now believe it's going to be rather the lower half of that interval.

As for exponential vs gompertz, I think exponential is more in line with the processes during melt season to September, and gompertz would only fit better if refreezing is added e.g. for December.

Jim_pettit

A monster drop in CT SIA of nearly 240k km2, the second largest one-day decrease this year. Area now stands at 5.36M km2, which is lower than the minimums seen in 1979, 1980, 1983, and 1986. The anomaly is back down to (or up to, depending how one sees it) -1.93M km2. 2012 is very safely in first place for the time being, more than half a million square kilometers ahead of second place 2011.

Wipneus
The linear not through origin relationship of area/extent to volume is interesting. Any thoughts on why that works like that?

Yes, I too found that interesting and I am still puzzling to find what it means.
The thickness graphs, hint that there is some break after 2009, but that is only two data points. I am very curious to see the 2012 data:

https://sites.google.com/site/arctischepinguin/home/piomas/aib/pvar.png
https://sites.google.com/site/arctischepinguin/home/piomas/aib/pvext.png

Werther

Wipneus,
Wouldn't that break you mention be thickness decoupling from extent? I mean, it seems obvious to me that extent doesn't actually describe the state of the pack anymore...

Chris Reynolds

I've been without proper 'net access for the last two weeks and will have no access for the next two as I await the installation of phone etc. Just had a very quick scan of what's happening at present.

On the basis of what I'm seeing (low concentration over large areas compared to previous 10/7/XX post 2007) I've just voted 'below 2.8M' for CT's area. I've not entered a vote for NSIDC extent because of the fragmentation I expect later in the season making that metric too uncertain. I think we're in for another crash this year.

I'm saying 'bye' for a while, and saying it in envy. :(

Fufufunknknk

The problem with the poll is that there should be at least one more category, probably three more, below what you have listed. Personally, I think you're going to list 'above 6 million', I think at least down to 3.0 million.

Kalle GZ

A huge drop on CT, putting it far in first place, while IJIS is showing 2012 slipping away from 2011 and is now near 2007. Looks like we are going to see a big drop on CAPIE today.

Neven

Chris Reynolds, good luck with everything! I will probably be without an internet connection at my holiday destination in September and have to think of a way to cover the final phase of the melting season...

Kalle, CAPIE is very low. More in tomorrow's update.

Wipneus

Werther:

Yes, the graphs try to capture that relation (or coupling) between area/extent and volume.

Alberto Silva

Ouch!

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

Hmpitcher

hello all, (note: In the discussion below i have treated loss of ice volume as a positive number)

i have followed your discussions with interest and no small amount wonder at the civility and intelligence shown by one and all. i hope to finally have something positive to add to the discussion. specifically, to the problem of projecting the minimum sea ice volume. Using the piomas data set through 6/30/12, i constructed data inputs in excel for 3/31 (day 90) for the 34 years 1979 to 2012. i did the same for 4/30, 5/31, 6/30, 7/31, 8/31, and 9/15. i then ran a variety of regression models in excel (i will move to R shortly) and found the following to work well. 7/31 on 6/31 and 5/31; ie explain july 31 as a function of june 30 and may31 levels. The results for July31, Aug 31, and sept 15 are table 1A. the equations fit so well (table 1b) that i wonder if i have inadvertently picked up some characteristic of piomas process.
Table 1A
dep.var. 31-Jul
Coefficients Standard Error t Stat P-value
Intercep -1.958376655 1.076168499 -1.819767682 0.078786697
6/30 1.304233372 0.111008976 11.74890014 9.44756E-13
5/31 -0.425587792 0.128211544 -3.319418664 0.002375901

dep.var. 31-Aug
Coefficients Standard Error t Stat P-value
Intercept 0.161541168 1.01483997 0.159178957 0.8745947
7/31 1.332404399 0.177414035 7.510140897 2.26132E-08
6/30 -0.365845088 0.167221772 -2.187783823 0.036611428

dep.var. 15-Sep
Coefficients Standard Error t Stat P-value
Intercept 0.009715172 0.130989372 0.074167638 0.941369338
8/31 1.157851368 0.052767924 21.9423333 4.97293E-20
7/31 -0.144396653 0.050174141 -2.877909827 0.0073092
Table 1b
31-Jul
Adjusted R Square 0.993343819
Standard Error 0.283087527

31-Aug
Adjusted R Square 0.990494797
Standard Error 0.321661296

15-Sep
Adjusted R Square 0.999092654
Standard Error 0.100109097
Below i provide the estimated values and errors for the three periods for the years 2007 t0 2011. (Y^ y-hat is the estimate and Y -Y^ is the error.)
table 2
7/31 Y^ Y-Y^
2007 9.06199196 -0.09799196
2008 11.05346432 -0.003464315
2009 10.18669655 -0.412696551
2010 6.594701414 0.320298586
2011 6.106160145 0.306839855
8/31
2007 6.400591738 0.251408262
2008 8.503539746 -0.680539746
2009 7.096067803 0.199932197
2010 4.664496229 -0.018496229
2011 4.216233809 0.069766191
9/31
2007 6.417370876 0.154629124
2008 7.47200341 -0.21800341
2009 7.046065868 -0.148065868
2010 4.390589773 0.077410227
2011 4.0462504 -0.0262504
below i show the results of using the estimates to project the arctic sea ice volumes for 7/31, 8/31, and 9/15, respectively 4.9, 2.6 and 2.3 x 10^3 km cubed.

table 3
proj 7/31/12
Intercept -1.958376655
6/30 1.304233372 11.163
5/31 -0.425587792 18.1
4.897641441

proj 8/31/12
Intercept 0.161541168
7/31 1.332404399 4.897641441
6/30 -0.365845088 11.163
2.603251448


proj 9/15/12
Intercept 0.009715172
8/31 1.157851368 2.603251448
7/31 -0.144396653 4.897641441
2.316690391
i have a couple of figures that i had hoped to include in this note but can't manage to get them to copy. Figure 1 would show the differences by month (ie. there would be a series for april 30 - march 31 may 31- april 30, etc). examination of this chart shows a couple of interesting things: first, the change in ice loss volume is focused in the months of June--now the largest loss month and May. Second the estimated losses for July, August and September are all well within the historical values for these months. {I do worry that the size of the June loss means that the historical relationship for July is corrupted by the fact that the remaining ice is "harder" to melt. The second chart shows the levels at the end of each month for 1979, 1991, and 2002 to 2012. one sees in this chart that the seasonal pattern is now stronger (more ice melts from day 90 to day 257) and the thing that i hadn't realized before was how long the ice would be close to the minimum level.

my summary of these results is as follows: We have a significant risk of a large downward break in sea ice volume If this occurs this year, then the stage will be set for an effectively ice free arctic within the next several years. If it doesn't then we will need to work hard at the underlying micro structure of the areas where the sea ice stays high.
my summary of these results is as follows: We have a significant risk of a large downward break in sea ice volume. i don't need to belabor the import of a sea ice volume below 2.5 to the group. If this occurs this year, then the stage will be set for an effectively ice free arctic within the next several years. If it doesn't then we will need to work hard at the underlying micro structure of the areas where the sea ice stays high.
my research questions for a post ice free arctic would focus on the consequences of this state of affairs on the Greenland ice sheet. we are presently melting just short of 20x 10^3 cubic km of ice as part of the annual cycle. (we could figure out what the net is (at least a ballpark number and then begin to think harder about just how fast the sheet might melt)
I would love it if somebody could talk the folks at Piomas into doing a mid month estimate. my gmail account is hmpitcher. If somebody can tell me how to make the charts available i will do so likewise for the excel spreadsheet (2007)

crandles

If the spreadsheet is small enough google docs does a pretty good conversion of excel and is shareable. There are various limits like 40,000 formulae, 400,000 cells. I don't know if you are willing to join, upload, share with those having the link and provide the link.

Your 2.3 is fairly close to my 2.2 K Km^3 +/- standard error of 0.55.

(Not quite sure how .28 .32 and .1 combine to your std err for the sept est at the moment.)

Espen Olsen

The Dark Purple color on today's map on The Cryosphere Today is almost gone, I wonder how that map will look like in a month from now?

http://arctic.atmos.uiuc.edu/cryosphere/

AmbiValent

Even without deep purple, there'll be smoke on the water...

Another century (108k), ice area now 5.250 m

Seke Rob

Espen, 2007 and 2012 compared for the 13th per CT.

http://igloo.atmos.uiuc.edu/cgi-bin/test/print.sh?fm=07&fd=13&fy=2007&sm=07&sd=13&sy=2012

Planned to be dropped into a FS blog thread... they love me for that [discussion pointless there] The 3 monkeys have a 4th (I do not hate), but they do anyway.

crandles


Thickness for PIOMAS Volume at minimum

How about this formula for working out the expected thickness for a PIOMAS volume which then allows you to calculate the estimated area?

(As it happens 2.59 is pretty close to the 2.6 I estimated in my SEARCH contribution.)

Espen Olsen

Seke Rob;

I prefer to compare 2011 with 2012 because they are more alike, especially volume wise, the difference between them is striking when using the dark purple (above 80%) as measurement:
http://igloo.atmos.uiuc.edu/cgi-bin/test/print.sh?fm=07&fd=13&fy=2011&sm=07&sd=13&sy=2012

L. Hamilton

I dusted off & updated this graphic from last August. Current SIA is already below the annual minimum reached in 5 previous years.
http://img.photobucket.com/albums/v224/Chiloe/Climate/sea_ice_N_min_to_date.png

And as everyone knows, way below any previous area on this date.
http://img.photobucket.com/albums/v224/Chiloe/Climate/sea_ice_N_this_date.png

DMI is running pretty even with last year.
http://img.photobucket.com/albums/v224/Chiloe/Climate/sea_ice_DMI_this_date.png

Wipneus

crandles:

Your graph is too small for me to read the formula.

crandles

Sorry.

Should have put a link to
http://farm8.staticflickr.com/7106/7574777208_5b13b38e84_b.jpg

and/or written out

(.079P+1.744)*tanh(.216P)

where P is the PIOMAS volume.
(.079P+1.744) is the straight line that the curve tends to for high P because tanh(x) tends to 1 for high x (negligably less than 1 for x=7 or more).

It is very doubtful that there is any logic to a hyperbolic tan function and a different function that tends to 1 for high P may well be preferable.
HTH

RMSE on the thickness fit is .124. Maybe I will eventually work out how to combine that error to the 0.55 std err in estimating PIOMAS minimum at 2.2 K Km^3.

crandles

tanh(0) is 0 so the curve will pass through origin.

Wipneus

crandles:

It is very doubtful that there is any logic to a hyperbolic tan function and a different function that tends to 1 for high P may well be preferable.

Indeed. Worse, if you have selected such function observing the very low years 2010 and 2011, those years get a relevance they may not deserve.
From the meteo minded people on this blog I understand the low values of these years are well explained by unfavorable weather conditions.
Again, I'd like to see 2012.

My favorite fit of thickness would be const*volume^0.5, where 0.5 is the result of some fitting as well.

For a power function, vol^K , there is some justification. A melting perfect cube of ice would have thickness as vol^(1/3).

so the curve will pass through origin

That is not required I think.

crandles

>>so the curve will pass through origin

>That is not required I think.

So you think it possible to have zero ice volume but for there to be some thickness or some volume but zero average thickness?

Or are you saying there could be a discontinuity when volume gets down to something like .5 K Km^3 with a change in slope so the function does go though the origin?

Trouble with that discontinuity is that it is more likely to be a thickness where ice just breaks apart and there are increasing areas of below that thickness as volume goes down.

So a smooth curve passing through origin seems to me to be more likely than a discontinuity in the curve.


Wipneus
>>so the curve will pass through origin

>That is not required I think.

So you think it possible to have zero ice volume but for there to be some thickness or some volume but zero average thickness?

What I am saying is that when volume (and area) "go to" zero, there is no requirement for volume/area to go to zero.

If a mathematical argument is not convincing:

When area is down to the last square km, which for all practical purposes is zero, that last km2 can still have a finite thickness and have a dot on our y-axis somewhere above zero.

No discontinuities.

crandles

That volume may be practically zero but it isn't zero.

If our last 2 m^2 area by 1m thick was held in place and all melted by melt on the sides then yes it could stay at 1m thick all the way down to 0 volume.

However if it is floating, when it gets down to .99m by .99m by 1m thick, it is going to rotate so it is 1m by .99m by .99m thick. This situation has a series of downward steps in thickness that approximates a curve that goes through the origin.

That last example is rather artificial because the shape of sea ice is very thin so that top and bottom melt are going to melt through it before side melting does. Now use the same trick this time assuming no side melt and all melt is top or bottom melt. If you start with a retangular block, then you get a straight line through origin. If you assume something more realistic like a lens shape then you get a curve but it still goes through origin.

While you can certainly get discontinuities with glacier calving events, I still think the origin is our best known point. Hence the shape I have tried to fit.

Wipneus

crandles:

While you can certainly get discontinuities with glacier calving events, I still think the origin is our best known point. Hence the shape I have tried to fit.

Well your shape predicts that when volume "goes to" zero, area stops declining and increments. In the limit of zero volume (and of course thickness), area is:

1/(1.744*0.216)=2.6546 10^6 km2.

Does not seem realistic.

crandles

You are right it doesn't seem realistic.


Thickness Versus Area at Minimum

But the straight trendline runs out of area before it runs out of thickness which isn't realistic (and surprised me). So perhaps the curve shown fitted on Thickness for Volume basis is sensible for the moment but will have to curve back towards the origin.

Wipneus

crandles:

Now take that (thickness-area) graph, and fit a straight line through the origin. The fit is a little less good, but not bad IMHO.

That line would be my thickness ∼ sqrt(volume) model.

crandles

That is certainly a possible interpretation. Doesn't seem like we have the data to decide on whether to prefer straight line through thickness v area origin or the switchback curve I suggested in the last post yet.

For 1979 Piomas volume 16855 km^3. Thickness = Volume^0.05 gives thickness 3.25m which is pretty close but for Volume =4079 km^3 gives thickness 3.02m so thickness is not declining anywhere near fast enough.

Thickness = (Volume / 2.5*10^9)^0.62

gets answers in the right ballpark for 1979 and 2011 but it is not a straight line but a curve that curves the opposite way to my curve and looks too steep for the early years.


Given that we don't know which to choose between straight line and my curve, what should we do? Probably don't want to go to one extreme or the other so I am inclined to stick with my thickness for volume fit rather than use the straight line.

FrankD

what should we do?

crandles, I'm not sure how valid this is, but since you reason (and I agree) that 0,0 is kind of mandatory (in the modelling sense, not that we have to go to zero area & volume), why not include it as a data point for your fit-curve?

That should have the effect of flattening out your curve, while still providing a relatively good fit (?), and curve the "right" way.

Espen Olsen

Urgent: Please read: Arcticicelost80 on ASI 2012 update 7: Steady as she goes

crandles

Sorry Wipneus, I was being a bit thick in trying to interpret your thickness ∼ sqrt(volume) model

Try again


Thickness versus Area at Minimum

Frank,

The RMSE for my red curve excluding the last point (nearest origin) being a 2012 estimate is 0.209

The RMSE for the green straight line is 0.226.

The red needs to have lower RMSE than the green because it has more degrees of freedom. Perhaps that difference isn't sufficient and I should prefer Wipneus's stright line.

Adding the 0,0 point with no error reduces the error for both proportionately.

I could curve the red line back to the origin in numerous different ways. There is no data to judge between these ways of curving it back. Because there is no such data to judge between these ways adding the 0,0 point does not do anything to tell me whether to straighten or accentuate the curve.

Johannes

CT area now 3,787 million km2. So far 4,6% of readers have been voted wrongly (more than 3,8 million km2).

Seke Rob

It would be interesting to get a summary of the poll, and if available, how many late revisions were made [up/down] with all that imagery of the last few weeks boding little uplifting news. My favorite comparitive 2007-2012

http://igloo.atmos.uiuc.edu/cgi-bin/test/print.sh?fm=08&fd=02&fy=2007&sm=08&sd=02&sy=2012

And for Espen, 2011-2012

http://igloo.atmos.uiuc.edu/cgi-bin/test/print.sh?fm=08&fd=02&fy=2011&sm=08&sd=02&sy=2012

Eyeball mark II, the higher concentration purple looks a little less than in 2011. The outline IS smaller and thinner. Look at how low the concentration is up against Ellesmere.

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