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Sorry about the formatting, the editor was driving me nuts.


Great stuff, Chris!



I admire your courage, but the prediction is somehow similar to my gut feelings.

Regards Espen

Ned Ward

Nicely done, crandles. I like it!


Thank you for the encouraging comments.

I just have this nervous reaction to "I admire your courage" thinking it sounds like something Sir Humphrey would say to Prime Minister Hacker
( http://en.wikipedia.org/wiki/Yes_Minister )

to terrify him into changing his mind. Should I nervously be asking why is that?


I guess it won't help if we start calling you Prime Minister Randles. :-B

With the current forecast I'd say 4.45 is a very good prediction, perhaps slightly too low.


While I would not want to seek that office for personal agrandisment, if friends and family were to persuade me that that was the best way I could serve my country .....

...... then

I would know they were joking and I definitely don't want to seek that role.

(I am sure Sir Humphrey's suggested reply in party games was much longer and more flowery which left Hacker desparately trying to write it down at the speed Sir Humphrey was talking leading to a fumbled reply to the question.)

Rob Dekker

Chris, this is really interesting !
Especially I like that you incorporate a physical effect (albedo effect) into the extrapolation.

Even after reading your post a few times, I'm not sure if I understand exactly what you did. In that regard, I have a few questions about what graph actually shows.

I understand that the red line shows the amount of 'open' ocean over the three month period multiplied by (sine curve) of solar input. Correct ?

But how did you exactly calculate that area ? Did you use the 10-CT(area) as a graph (meaning did you do a day-by-day calculation of CT(area) over June,July,Aug ?

Also, about the blue curve w.r.t. the red curve : Doesn't this show that the "the higher the amount of solar input was until Aug 31, the LESS September will show additional melt" ? Which suggests that we are looking at some form of negative feedback kicking in in September, no ?

Or do I see all this incorrectly ?


Yes, for each day in Jun, July, Aug I have calculated (10 - area) subject to a minimum of 0. These numbers have been multiplied by the sine wave then summed these values over the 92 days. (I then divided by 300 just for graph scaling. The y axis units aren't mentioned as they are different for the two lines.)

The blue line is my 31 Aug weighted average minus NSIDC Sept average extent. I should have labeled it more clearly as that.

The area is less than extent pulling the weighted average down so that for most of the time except towards end my weighted average is less than September average extent leading to negative values for the blue line.

So no, the higher the energy that is/can be captured, the more melt in September.

If you want blue line to represent melt in September it should all be shifted upwards into positive values.

Sorry if that was unclear. Hope it is clearer now.

Rob Dekker

Thanks Chris. Yes. Clear on the red line.

On the blue one, I'm sorry, but I still a bit confused. How exactly do you calculate the "31 Aug weighted average" ? and does that already include the red line ?
And if not, then how does the red line get into your final forecast formula ?

Also, how did you choose the number 300 (or is that number irrelevant for your formula) ?


The 31 Aug weighted average is
(6.6 * GSFC-Jaxa Extent + 1 * CT Area)/7.6

so does not include the red line at all.

The red line gets into the forecast by a linear regression between the two. i.e. regression is tuned on 1979 to 2010 and extrapolated to 2011. (This works even if one slope is much steeper than the other.)

The 300 is completely irrelevant and not used at all in any of my calculations. It is only used for drawing the graph.

Hope that helps.

It might also be worth me saying what I see.

In general shape/trend the red and blue lines fit quite well but that is almost certainly due to overfitting the numerous parameters like 10 for area and 92 for period. As mentioned differrent steepness does not matter. Far more important is that the year to year variability is partially explained.

From that perspective you can see that the fit is clearly better that predicting the change based simply on time. The numbers show it is better to use this measure of open ocean than using 31 Aug area. (Since submitting I have seen Tamino say using average July area is better than using average August area which makes sense as July is nearer to June-Aug than Aug is.)

How much of the variability should I expect to explain?
The potential energy captured shouldn't be the only source of noise; there is also:

1. Winds can be dispersive or compacting.
2. Cloud cover can vary changing actual energy captured vs potential energy captured.
3. Ocean heat transport might vary.
4. Heat captured might melt more area if the relevant ice is thin.
5. Isolated areas may melt out almost regardless of energy available.
6. Other aspects of weather like temperature.
7. Other distribution issues like energy near ice being more likely to melt more ice.

and probably a few other factors.

Given so many factors it is perhaps surprising that so much of the variability from year to year is explained by what I have done.

This seem to imply that the potential energy captured is a major cause of the variability.

I said this wasn't necessarily a contradiction "at all" of "and in particular, bottom melt due to ocean heat transport" impling ocean transport being more major than albedo effect.

That is possible for two possible reasons:

1. I could be wrong, my fit could simply be overfitting. Or perhaps other reasons for me being wrong in the interpretation.

2. Ocean heat could be more important than albedo effect for total effect but be very smooth while a lot of the noise for year to year variability comes from potential energy captured.

Rob Dekker

Thanks Chris. Sorry for the late reply. It's busy.
What I was hoping to find in your method was a quantification of the albedo effect. Something like "this much area of open water in July will lead to that much extra area melt in September".
I see your red and blue graph, and the strong correlation they suggest, which should be a main indicator, if not the answer I'm looking for. However, despite you explanations, I do not understand how the red graph ends up in the end result of your projection method.

I think you lost me when you mentioned "The red line gets into the forecast by a linear regression between the two". Do you mean the difference between two regressions (one with CTarea and one with some normalized form of the red line ?
And how does linear regression between "the two" actually work into an adjusted projection for September ? I'm confused.

Do you have a separate post on your blog where you have a more detailed explanation of the method you are using ?


Rob, sorry nothing more detailed than this.

I use Excel LINEST function which tells me the numbers in the post repeated here.
0.003079557 -0.79059
0.000605136 0.113406
0.463310596 0.148322
25.89825285 30
0.569747071 0.659983

What these numbers mean is in the table above these numbers in the post. The top line of this tells me the optimum linear fit is to take red line numbers (before dividing by 300) multiply by 0.003079557 and add -0.79059.

So I do that to the 2011 red line number and use that as the predicted change from the 2011 31 Aug weighted average number.

Perhaps I should have graphed the red line with that linear transformation rather than the divide by 300 transformation.

Quantification of albedo effect. Quantification would be good but it is a lot easier to arrive at this relative measure than to quantify things. Anyone got a good measure of cloud cover over open water in Arctic? How does that affect absorbtion of energy by ocean? How about proportion of energy absorbed by ocean that goes into melting ice? Not easy questions though perhaps someone with a good model could come up with some estimates.

Importantly, also remember that all I have done is found a correlation and that doesn't prove causation. I am merely speculating as to cause and this seems to have lead me to finding a better correlation but this still only means I have found a correlation that does not prove causation.


Update with data to 7/9:

Method unchanged other than using 99 days to 7/9 instead of 92 days to 31/8. Prediction is 4.45 unchanged from 31 Aug prediction.

Rob Dekker

Thanks a lot ! This clarifies a lot. At least I think I understand now what you did.

Of course, we don't know if the correlation you found shows causation, but let's turn it around for a moment : Let's calculate if the correlation leads to reasonable numbers if we assume the cause is the albedo effect.

I'm going to do a first very course estimate.

Bare with me here, since this turned out to be quite a long post :

First of all, I'm going to ignore the constants that you add or subtract, and focus only on the correlation of the slope of the (red and blue) graphs.

Constants addition and subtraction after all can be caused by many things (such as turn of the radiation balance (turning point of melt/freeze) being off-set with the sine wave, or your choice of '10' in the 10-area red graph), none of which affects the slope and thus the correlation that you observe.

Let me note that your red graph (before dividing by 300) essentially represents the total amount of excess energy absorbed by the oceans during summer due to open ocean, like this :

energy absorbed by open ocean = R * 3600 * 24 * A * P

where :

R is the red graph number before you divided it by 300


P is the clear sky insolation at the surface at summer soltice (June 21). That number is actually something like 350 W/m^2 (500 W/m^ TOA insolation attenuated by 30% atmospheric absorption).


A is the albedo effect defined as the excess fraction of average summer insolation that is absorbed by ocean water, in excess of the fraction absorbed by ice.

For example, if the actual ice albedo is 0.6 and open ocean albedo is 0.1 and the Arctic is always under clear skies, then the albedo effect A is 0.5. If there are alway clouds around, then insolation on the surface is low, and A becomes low (close to 0), since it does not matter if there is open ocean or ice under these clouds.

Next, let T be the thickness of ice (in meter) in the ice margin in September, then the amount of energy needed to melt B m^2 (using heat of fusion and density) of ice is :

energy to melt B m^2 of ice = B * T * 334 kJ * 0.9 * 1000

Now that we defined R, B, A, P and T, let's see what your correlation tells us.

You noted that this red graph number (R) is equal to the blue graph graph number (B) (if you ignore the constant additions and subtractions) if it is multiplied by 0.003079557 (or divided by 325). In other words, your correlation tells :

R/325 = B

So if we assume causation, then the energy number from above causes an excess ice area loss in September of :

R/325 * T * 334 kJ * 0.9 * 1000 = B * 3600 * 24 * A * P

which can be simplified to (also set P=350, from above) :

T * 0.03 = A

Tada !
If we roughly assume that ice in the ice margin in September is 1 meter thick, that the albedo effect A is 3%.

Actually this is very much a lower bound for the Arctic albedo effect, considering the fact that most ocean-absorbed heat in the summer will to melting neighboring ice right away (and thus is already included in your normal regressions for area on Aug 31), instead of waiting until September to bottom-melt.

Remember Tiesche et al ? Remember that their GCMs calculated 10W/m^2 albedo effect in July (when insolation is close to 350W/m^2) ? Well, if your correlation is indeed caused by the albedo effect, then you have just shown that Tietsche et al underestimated the albedo effect quite a lot, since your correlation shows that 10W/m^2 albedo effect already goes to September melt (let alone the heat lost during July and August melt of neighboring ice).

Also, your correlation (if causation holds) shows that 1 km^2 of open ocean in early July will cause 0.03 km^2 of additional ice to (bottom) melt out in September, and if ice becomes thinner in the future, that bottom-melt in September due to summer albedo effect will increase....

So this is a very exciting finding Chris !
I think you are on to something here.

Rob Dekker

Oops. Typo in the correlation equation (should replace B by R on the RHS). This is the correct one :

R/325 * T * 334 kJ * 0.9 * 1000 = R * 3600 * 24 * A * P


Re "So this is a very exciting finding Chris !
I think you are on to something here."

Thank you. I think this is what I meant when I said " might merit further investigation."

But, I think you are on to something here.


Is 1m for ice thickness at the margin a rather high estimate if thickness at pole is only around 0.9m ?

Seke Rob

To think that the 'near' NP webcams only moved 4.5 degrees from April to September (NOAA1 still works). This is not transported-in sea ice from far away fringes.


I have gone back to 15th August to run the model from there. Instead of my slope being 0.003079557 for 31 Aug, it comes out at 0.004281767 for 15th Aug using 76 days to 15th Aug.

Rob, do you want me to go back further to see if I get higher numbers or is it sensible to limit this analysis to after dates when bottom melt dominates or is there some other limiting factor to when this analysis is appropriate?

Kevin O'Neill

Chris & RD

There could well be other factors at work. The melt-season stratospheric temperatures over the Chukchi plummeted after 2006. This is likely an indication of reduced ozone. The reduction in ozone should lead to increased UV at the surface.

A comparison of ice concentrations per CT for Aug 1, 2006 vs Aug 1, 2007 shows the largest changes in the area with the large stratospheric temperature anomalies.

Here's the comparison where I highlighted the quadrant with the negative stratospheric air temp anomalies:



I fully agree that there are almost certainly other factors at work.

How would you except such a stratosphere change to alter the correlation between late season melt and area earlier in the melt season? Would it just tend to make correlation of melt against year better than against area earlier in the melt season?

If the correlation with area remains much better than correlation with year, is this a sign that the albedo effect dominates other effects like stratosphere changes? Perhaps a step change at 2007 in the correlation could improve the fit and the measured albedo effect? But unless the stratosphere change is clearly a major effect then I would be a little dubious about doing that.

Such a step change might dominate effect after 2007 and maybe just using correlation before 2007 might be better if there is reason not to just use the whole period. At the moment I am struggling to see such a reason.

Lucia (The Blackboard)


The melt-season stratospheric temperatures over the Chukchi plummeted after 2006. This is likely an indication of reduced ozone.

Do we have relevant data going back in time?
I think chris has a plausible phenomenological explanation, and it has some data support -- but the data are noisy. If we look to numerical values of AIC coefficients, we find area is a good predictor, but not so much better than other predictors that we can say area is definitively "best".

It would be nice to test any alternate explanations (or even just supplemental explanations) that arise. If stratospheric temperatures are known or if ozone temperatures are known-- or there is any other relevant data available to test, that would be useful. Inclusion might 'explain' just enough of what now looks like noisy residuals to be able to really say that upcoming losses are most strongly correlated with area rather than extent or volume both of which come up as models that can't be excluded relative to area. (Mind you: area looks better. It's just the Akaike criteria don't say it's a clear winner.)

Kevin O'Neill


As Chris and Rob showed, the albedo effect coefficient has to be far larger than currently estimated to account for the implied energy required to melt the volume of ice lost in the past few years. Nor does it really account for the apparent step change that occurred in 2007; every year begins with an arctic basin covered in ice.

The post 2006 volume loss changes are in the early part of the melt season - when we'd expect the albedo effect to be minimized.

Volume Loss by Month

1979-2006 2007-2011
+0.196 -0.178 April
-1.674 -2.540 May
-4.957 -6.209 June
-6.565 -6.094 July
-2.896 -2.539 August

On the other hand, the temperature anomalies are greatest in the spring and slowly decrease throughout the summer. So, if ozone depletion has an effect it should be larger early in the melt season. Further evidence is that the region with the greatest extent loss is the region with the stratospheric temperature anomaly.

The large stratospheric temperature anomalies began in March 2007 and help to explain the appearance of a step change. In reality, there is no step function - the increased UV just made a significant and continuing increase to the energy budget. Or at least that's my conjecture :)

Lucia, I'm sure the NCEP/NCAR data can be downloaded - look around here http://www.esrl.noaa.gov/psd/cgi-bin/data/composites/printpage.pl

Rob Dekker

Chris wrote Is 1m for ice thickness at the margin a rather high estimate if thickness at pole is only around 0.9m ?

That true. I also realized that since your correlation is a predictor of extent (not area) that the summer albedo energy that leaks over to September only needs to knock out some low concentration ice in the ice margin (say reduce 50% concentration ice to below the 15% threshold). Thus the effective ice thickness in that extent that melts out in September will be even thinner (probably 25 cm or so).

That would imply that A (the albedo effects that leaks over to September) will be more like 1% or so. Thus it is in the single digits Watt/m^2. Quite surprising actually that so little 'late' energy can still knock out so much ice (some 400k km^2 in your graph), but that's what your correlation and this analysis shows.

The main 'groundwork' albedo effect (bottom melt due to adjacent open ocean) however seems to occur earlier (in August and even July) when the sun is still strong.

Rob Dekker


A drop in stratosphere temperatures is normally an indication of INCREASED ozone (or other GHG) concentration, which also leads to warming in the troposphere. For example, the reduce ozone over the Antarctic compensates for increased CO2, and this effect has been associated with the relative absense of warming over Antarctica.

Also, AFAIK, the radiative effects of ozone are more pronounced in reducing space-bound IR radiation than in reducing incoming UV, especially in the Arctic, where cloud cover and low angle insolation combined with Relaigh scattering cause significant reduction in UV reaching the surface.

So decreased ozone should cause a cooling Arctic, AFAIK.

Rob Dekker

Chris, regarding your note Instead of my slope being 0.003079557 for 31 Aug, it comes out at 0.004281767 for 15th Aug using 76 days to 15th Aug.

Assuming that this number obtained the best correlation between your red and blue graphs, I think that finding suggests that 40% of 'late' (after the sun lost power) energy obtained from summer albedo effect is spent on melting ice between Aug 15 and Aug 31. In effect, I think this means that we can expect extent reduction in September to be 60/40, or 1.5 times the extent reduction between Aug 15 and Aug 31.

Of course, this is assuming that effective ice thickness (concentration in the ice marging) on Aug 15 is the same as on Aug 31, which, with the scatterred ice pack in 2011) is probably a reasonable assumption.

As for your note : do you want me to go back further to see if I get higher numbers or is it sensible to limit this analysis to after dates when bottom melt dominates or is there some other limiting factor to when this analysis is appropriate?

You can go back further, and the number surely will get higher. After all, heat obtained by open ocean is to a great extent (probably 75%) to bottom melt ice nearby.
However, if you go back too far (say into July) then you are overlooking solar input after your cut-off date, which means that your correlation (between the red and the blue graph) will start to break down, and you need to rely more on the 'average' regressions after your cut-off date. It may be fun to see how the R factor changes, but I think if you go back too far, you will find that this correlation starts to break down.

Still, I think it's a great method if you need to make a 'prediction' at any given day, since it actually includes a physical effect, instead of relying on 'average' regression runs.

Rob Dekker

I wrote I think this means that we can expect extent reduction in September to be 60/40, or 1.5 times the extent reduction between Aug 15 and Aug 31.

but I am not sure if that was a correct conclusion. Let me think about your finding and I will get back to you on this.

Kevin O'Neill

Rob D.

I think the idea that ozone depletion is responsible for the recent increase in Antarctic sea ice is becoming less accepted. Simulations with well-modeled upper atmospheres have not supported the idea. From Has the ozone hole contributed to increased Antarctic sea ice extent? Sigmond & Fyfe, Sept 2010:

In this study we consider the impact of stratospheric ozone depletion on Antarctic sea ice extent using a climate model forced with observed stratospheric ozone depletion from 1979 to 2005. Contrary to expectations, our model simulates a year‐round decrease in Antarctic sea ice due to stratospheric ozone depletion...

Our model results strongly suggest that processes not linked to stratospheric ozone depletion must be invoked to explain the observed increase in Antarctic sea ice extent.


Speaking of ozone depletion in Assessing and Understanding the Impact of Stratospheric Dynamics and Variability on the Earth System Gerber et al, 2011, you'll find this:

Just a few years ago, the claim that the halogenated compounds, which used to be contained within everyday aerosol spray cans, could move an entire storm track would have seemed rather preposterous. It is now speculative, but not unreasonable, to ask whether they might help melt an ice sheet.


My assumptions rested on a constant source of UV (the sun), decreased absorption (ozone depletion), and relatively clear spring skies (which we've had) over the area between 72N to 80N and 157E to 238E (East Siberian, Chukchi, and western Beaufort Seas). This is the area in which we've seen the greatest ice losses. While my first inclination - lacking any other plausible connection - was to an increase in UV, I'm now inclined to agree with you that UV cannot account for the difference. One of my assumptions appears to have been completely wrong. This caught me pretty much by surprise: What the SORCE SIM observations tell about solar spectral irradiance. http://www.agci.org/dB/PPTs/10S1_0615_JHarder.pdf

That still leaves me with the question: Why is there a stratospheric temperature anomaly, spatially and temporally, over the very same area seeing the largest decrease in sea ice loss? It still seems beyond coincidence. Especially after reading Dramatic interannual changes of perennial Arctic sea ice linked
to abnormal summer storm activity
, Screen et al, 2011. Screen shows a comparison of 'Ice Gain Years' and 'Ice Loss Years' (Fig. 3) using a metric of Composite Mean Cyclone Count. Note the geographical differences; they coincide very nearly with the geographical region exhibiting the post-2006 stratospheric air temperature anomaly. In fact, if you look at any of the maps showing differences between IGYs and ILYs the same spatial pattern emerges.

I suspect there are dynamic changes at work. Whether this involves a stronger or shifting polar vortex, an increase in polar stratospheric clouds, tropospheric - stratospheric coupling, etc., these types of dynamic changes are not understood in enough detail to offer definitive answers. For example read comments #39 and #40 here: http://scienceblogs.com/stoat/2011/09/why_does_the_stratosphere_cool.php#c5153843

Rob Dekker

Kevin, thanks for these refs. I did not study any of them in detail, and even if I did, I may not be able to tell you much more than you already know.

You notion of a stratospheric anomaly coinciding with sea ice loss is interesting, but unless you can quantify the effect, I think it would be difficult to draw any conclusions of cause and effect and significance. Also, did you find any research on the cause of this anomaly ?

Rob Dekker

Hi Chris,
Regarding your finding :
I have gone back to 15th August to run the model from there. Instead of my slope being 0.003079557 for 31 Aug, it comes out at 0.004281767 for 15th Aug using 76 days to 15th Aug.

This means that in my equations, for Aug 15 cut-off, B = R/233 and thus A = 0.044 T, and you have just increased the lower bound for albedo effect by 40%.

Since the albedo effect itself does not depend on ice thickness, this means that if the ice is thin in the ice margin (large areas of low concentration ice extent) and there was more open ocean in summer, that September bottom melt will be greater.

But the difference between your Aug15 and Aug31 runs also shows that the most significant albedo-caused bottom melt happens earlier (end of August) rather than later (deeper into September).

Of course, anyone with common sense could have told you this, but it's interesting that you can actually quantify bottom melt in late summer as a function of open ocean in high summer, using the correlation you found. And that's pretty neat, especially for projections into September.

I'd say that your findings still confirm my earlier expectation that bottom-melt in 2011 will be a significant factor in September, and because of the thin ice in the margin, we may get extent reduction until later than normal and consequently a late extent minimum.

Kevin O'Neill

Rob -

A lot of work has been done on albedo. You might want to look at Hydraulic controls of summer Arctic pack ice albedo, Eicken et al, 2004 and several of the references listed therein.

Of the three surface types, the albedo of open water and bare firstyear and multiyear ice are remarkably stable at 0.07, 0.60, and 0.65, respectively (Grenfell and Perovich, 1984; Pegau and Paulson, 2001; Perovich et al., 2002b). The albedo of ponded ice is more variable, typically ranging from 0.2 to 0.4 (Perovich et al., 2002b). Melt ponds mostly cover between 10 and 50% of the ice surface (Romanov, 1995; Tschudi et al., 2001; Perovich et al., 2002a), and their areal fraction controls the integrated ice surface albedo ...
Rob Dekker

Hi Kevin,
Yes, a lot of work has been done on the plain surface albedo effect, but local/temporal cloud cover dampens how much this results in excess heat building up in the newly created open ocean in summer.

Tietsche et al estimates this effect as 10 W/m^2 (3% of July "above cloud insolation") for open ocean while other studies suggest that this number may be much higher in reality.

Even fewer (no?) studies quantify how much of the excess heat obtained by open ocean (versus ice cover) would result in late summer bottom-melt, and this is why I found Chris's findings so interesting.

By the way, thanks for the link to Connolley's site on stratospheric cooling. Very good comments from many contributors, and if I have a bit of time, I may kick in a comment as well.

But once again, I think there may be a lot more mondaine explanations for loss of Arctic sea ice than the ozone relationship. I recall that on RC you actually posted one of the studies that suggest a spectrum of common sense explanations that had very little to do with ozone.

Rob Dekker

This is the paper you referred to at RC : Rampal et al 2011

I think this paper has it spot-on. GCMs do not capture the observed thinning of ice over the past decades, and these guys suggest that this may be because GCMs do not model increased ice dynamics of reduced ice thickness well.

That leaves us with the chicken-and-egg problem : If ice dynamics sensitivity increases due to ice thickness reduction and ice thickness reduction causes increased ice dynamics, what caused the downward spiral ? If we can't answer that question, then we can't really project into the future either...

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