The mean extent of Arctic sea ice for September 2011, calculated from the University of Bremen time series (website; technical paper), was 4.6 million km2. A Gompertz curve that I estimated last April based on Uni Bremen data for 1972 through 2010 gave a predicted September 2011 mean of ... 4.6 million km2. Encouraged by this lucky guess (and that’s what it was!), I here offer an even earlier and more naive prediction for the UB September 2012 mean ... 4.3 million km2, with a confidence interval of ±.8 (Figure 1).
Figure 1
Other Gompertz-based predictions made in April (regarding September NSIDC extent, NSIDC area and PIOMAS volume) were not quite so lucky as this UB prediction, but they were all within range. I’ll write a wrap-up post soon about how things came out, including comparisons between Gompertz, linear and quadratic trend models, as well as more sophisticated analyses contributed to the SEARCH Sea Ice Outlook.
Like linear and quadratic models, Gompertz curves are an un-physical, simple way to describe past changes in Arctic ice measures, and to suggest near-term predictions about the future. Extending them more than a few years ahead, as done in Figure 1, is purely speculative. If the curve in Figure 1 accurately describes the path of Arctic sea ice, we would see virtually ice-free September conditions, defined as extent below 1 million km2 (the dark red line) before 2030.
Linear and quadratic trend models are more widely used, but the Gompertz more realistically fits past data. It is the only one of these three that can match both the slow decline seen in early years of the satellite era (especially visible in the longer UB dataset, which goes back to 1972), and the more recent accelerating decline. Linear models decline at a constant rate, which the ice clearly has not done. Quadratic (inverted-U) curves impose a slight but counterfactual increase in the early years.
Both linear and quadratic models also predict extent below zero, in time. An appealing feature of Gompertz models is that they never drop below zero, instead approaching this physical limit asymptotically (although rapidly). While the curve approaches zero smoothly, its implication for real ice might be different. To illustrate an alternative, Figure 2 shows four simulated trajectories based on the model of Figure 1.
Figure 2
For each simulation in Figure 2, I added white noise to represent year-to-year variations in weather. Deviations around the Gompertz curve in Figure 1 pass statistical tests for white noise (Ljung–Box Q), so this seems a reasonable starting point. The added noise has a standard deviation set equal to that of the 2007–2011 period; in other words, it mimics the unpredicted behavior of year-to-year variations in the recent past. Noise-driven predictions below 0 were truncated. Figure 2 suggests the possibility that even if the Gompertz model proves prescient, and virtually ice-free conditions arrive before 2030, we still could often see “recovery” years with more ice.
These Gompertz versions of the “death spiral” are not grounded in physical argument, but provide a visualization of how recent trends might continue. As with the September 2011 results, their predictions are eminently testable. They could provide a challenging benchmark for evaluating the skill of physical (or more substantive statistical) models, as those are improved.
Like linear and quadratic models, Gompertz curves are an un-physical, simple way to describe past changes in Arctic ice measures, and to suggest near-term predictions about the future. Extending them more than a few years ahead, as done in Figure 1, is purely speculative. If the curve in Figure 1 accurately describes the path of Arctic sea ice, we would see virtually ice-free September conditions, defined as extent below 1 million km2 (the dark red line) before 2030.
Linear and quadratic trend models are more widely used, but the Gompertz more realistically fits past data. It is the only one of these three that can match both the slow decline seen in early years of the satellite era (especially visible in the longer UB dataset, which goes back to 1972), and the more recent accelerating decline. Linear models decline at a constant rate, which the ice clearly has not done. Quadratic (inverted-U) curves impose a slight but counterfactual increase in the early years.
Both linear and quadratic models also predict extent below zero, in time. An appealing feature of Gompertz models is that they never drop below zero, instead approaching this physical limit asymptotically (although rapidly). While the curve approaches zero smoothly, its implication for real ice might be different. To illustrate an alternative, Figure 2 shows four simulated trajectories based on the model of Figure 1.
Figure 2
For each simulation in Figure 2, I added white noise to represent year-to-year variations in weather. Deviations around the Gompertz curve in Figure 1 pass statistical tests for white noise (Ljung–Box Q), so this seems a reasonable starting point. The added noise has a standard deviation set equal to that of the 2007–2011 period; in other words, it mimics the unpredicted behavior of year-to-year variations in the recent past. Noise-driven predictions below 0 were truncated. Figure 2 suggests the possibility that even if the Gompertz model proves prescient, and virtually ice-free conditions arrive before 2030, we still could often see “recovery” years with more ice.
These Gompertz versions of the “death spiral” are not grounded in physical argument, but provide a visualization of how recent trends might continue. As with the September 2011 results, their predictions are eminently testable. They could provide a challenging benchmark for evaluating the skill of physical (or more substantive statistical) models, as those are improved.
Your simulated data seem to suggest that it is almost certain we'll see something truly spectacular within the next few years (2007 not just broken but shattered). Makes me wonder if we will get late summer SST's in the shallower peripheral areas of the Arctic Ocean approaching 70 degrees F, which would almost make it a nice beach (!!!!!)
Posted by: Nightvid Cole | October 01, 2011 at 16:59
Great post!
How might one decide if the Gompertz prediction is good or not?
My thinking is that we would need to witness several years outside of the + and - 2 sigma values. However, it's not clear to me how exactly to figure that out.
Of course the reality is that the Gompertz prediction is probably fairly good and may only need some minor adjustments in the future. However, from the data it looks like 2011, 2010 and 2009 fit the Gompertz prediction very closely.
It looks like 2007 and 1996 were the last 2 years to challenge the Gompertz prediction. 2007 illustrated that the prediction might be liberal while 1996 showed that it could be conservative.
Regarding the simulated data.... Nobody should take it to imply anything about the future.
Posted by: Andrew Xnn | October 01, 2011 at 19:05
Regarding the simulations, these are just 4 examples out of infinitely many we could generate from the same model. Nightvid is right that a September mean far below 2007 could happen very soon, although the reverse is true too -- in the near future there could be a few years that looked like a splendid recovery.
I work in Stata, and wrote a do-file to estimate the models and draw the graphs for this post in one step. Each time I re-ran that file, while fiddling with details like graph colors, I would get 4 new and different-looking plots for Figure 2.
It would be easy to set a seed number so the pseudo-random generator always gave the same results, but watching Figure 2 change with each iteration helped me keep the random element in mind.
Posted by: L. Hamilton | October 01, 2011 at 19:34
Great post.
Re "Deviations around the Gompertz curve in Figure 1 pass statistical tests for white noise"
So does this mean that the first 8 or 12 years seeming to have little noise compared to years after is likely to be just a random occurance? Last 3 years having little noise is far too short to deduce anything.
I guess it is rather difficult to say how we should expect the size of the noise to vary over time?
Is it just me imagining things or does it seem like there is a high level of noise in 1991-1996 before a change in direction of the linear trend?
Posted by: crandles | October 01, 2011 at 23:17
The low variation in the first decade might be a physical phenomenon, or a measurement quirk, or just random -- with so little data, null hypotheses are tough to reject.
Looking closely at any one of the 4 simulations, I can also see periods that seem to have more or less variation. But there we know that the errors really are normal, independent and identically distributed.
Posted by: L. Hamilton | October 01, 2011 at 23:39
Hey.... If I want to make some calculations like If we have an ice free arctic from August 1st to October 1st. How much extra solar energy would the arctic have then compared to now?
Posted by: Chris Biscan | October 02, 2011 at 01:04
Larry
Thanks for posting this information. Would you clarify a couple of points? Right now you believe an exponential decay is the closest fit to the data? That would fit with any natural process with a positive feedback loop. How much variability is in your selection of the tail off period? Could you have made the curve drop below 1MsqKM say by 2020? Or is the data sufficient to constrain the selection of the tail period? This drops under the 1M mark on 2025 what would the date be if you used september minimum ice instead of average ice?
Posted by: RunInCircles | October 02, 2011 at 01:35
don't forget sea ice is 3D not 2D.
extent has fallen in a linear sense because only part of the cycle has been effected.
for instance we may reach a point where the volume hits s low the ice sheet fractures so bad early enough that it melt out.
right now its pretty bad for October 1st.
Posted by: Chris Biscan | October 02, 2011 at 03:10
Chris, I haven't forgotten, a post on sea ice volume is not far behind ... waiting for the PIOMAS other shoe to drop.
Runnin, it's not quite exponential decay, but an asymmetrical S-curve with 3 parameters. You can see more details of the estimation method in a SEARCH Sea Ice Outlook contribution (describing models for NSIDC extent, NSIDC area, and PIOMAS volume) I filed last spring.
http://www.arcus.org/files/search/sea-ice-outlook/2011/06/pdf/pan-arctic/hamiltonpanarcticjune.pdf
Parameters for these curves are estimated by nonlinear least squares using the available data, with no fudge factors applied by me. The time window of predictions I show in the graphs is just a balance between what's fun and what's decent, it doesn't in any way affect the results.
Posted by: L. Hamilton | October 02, 2011 at 04:08
"what would the date be if you used september minimum ice instead of average ice?"
If I fit a Gompertz curve to UB one-day minimum instead of September mean, it hits 1m about a year sooner, 2024.
Posted by: L. Hamilton | October 02, 2011 at 04:18
Larry
In my naive state of ignorance I do not know how the Gompertz model applies. My understanding of this model is it was constructed for exponetial growth being choked by resource limitations. The basis would be when you reached a population of x for every birth somebody immediately starved to death. Using the reverse of this logic on sea ice would seem to imply that a fundamental property of the sea ice is that at some minimum level for every gram of ice lost a new gram of ice is forced to grow. It seems clear that there are positive feedbacks in the system so the more ice lost causes the rate of loss to increase. I do not know if there is some point at which negative feedbacks in the system kick in and overwhelm the positive feedback. This would justify the use of an S curve so your choice of mathamatical models may be prescient. I am of the school of thought that the positive feedbacks that are seen in the data are dominant and the loss continues to accelerate exponentially to zero. In any case the acceleration of ice loss or the slowing of ice loss will be clear before this decade is out.
Posted by: RunInCircles | October 02, 2011 at 15:12
Larry;
Again; many thanks for a great post.
Curious to know what the +-2sd error bars are for future predictions.
The Gompertz fit has 3 coefficients; each with their own 95% confidence level. Two of the coefficients have a clear physical basis.
One is the past (~7.5 Mkm2) and the other in the future (somewhere between the year 2012 to 2022 we could witness the fastest rate of decline on average). The 3rd I'm not too sure about what it corresponds to in a physical sense; but it may be the average rate of decline during the above mentioned year and hence it's another future parameter.
Posted by: Andrew Xnn | October 02, 2011 at 16:30
The Gompertz and exponential fits are similar; both using 3 parameters and I get RMSE of 0.43805 and 0.4387 respectively.
This is working with NSIDC monthly average extent figures. The extrapolations are as follows:
Year Gompertz Exponential
2011 4.438316 4.390888
2012 4.187272 4.100645
2013 3.925300 3.784473
2014 3.653758 3.440055
2015 3.374386 3.064867
2016 3.089328 2.656160
2017 2.801126 2.210940
2018 2.512698 1.725945
2019 2.227286 1.197621
2020 1.948378 0.622097
2021 1.679589 -0.004843
2022 1.424517 -0.687792
Yes, even with noise, it probably is going to be clear which is better before the end of the decade. Probably not much before the end of the decade as the gompertz and exponential fits of data upto say 2017 will look similar to each other regardless of the actual data in 2012-2017 as the fits will adjust to fit the data in 2012-2017 pretty well.
Anyway, if anyone wants to play about with seeing how these fits work, I have put it on
https://docs.google.com/spreadsheet/ccc?key=0AjpGniYbi4andHMtYXlSemJVQmdoQlJoTFRmcjh2YlE&hl=en_US#gid=0
Posted by: crandles | October 02, 2011 at 17:41
Andrew, I would say the other parameter is mainly about the rate at which the curve curves if you follow what I mean. Alternately, view the graph on the spredsheet linked above as you change the .10399 parameter from 0.05 to 0.15.
Posted by: crandles | October 02, 2011 at 17:50
Gompertz curves have traditionally been applied to model biological or economic growth, where the first parameter represents a slowly-approached saturation level, and the second is time at the point of inflection. The third parameter controls change in the rate of growth.
In my negative application, the first parameter is a starting level, from which initial departure is slow (but exponentially increasing). The second is the year of steepest decline, and the third controls change in the rate of decay.
Crandles' spreadsheet has a nice graphic where you can experiment with different values. As he notes, there is not much difference between exponential and Gompertz predictions right now, though some might emerge in the future (and they're very different regarding the past).
To visualize how linear, quadratic and Gompertz curves compare with respect to sea ice data, I have a rough graphic here. Was planning soon to fold an updated and cleaner version of this graph into a post.
http://img.photobucket.com/albums/v224/Chiloe/Climate/2011_Gompertz_evaluations.png
Because quadratic curves head way below zero, they don't encourage speculation like the Gompertz simulation in Figure 2 above, where random weather no more radical than past variations occasionally leaves some late-summer ice.
Posted by: L. Hamilton | October 02, 2011 at 18:37
I suspect we'll see a "one hoss shay" total collapse of Arctic ice within my lifetime. If that's personally presumptuous at my ripe old 61, then there will be that collapse by 2025. Everywhere you look up there, ice melts away from long-established margins, and the greenhouse gas forcing keeps growing.
The Vostok ice core data shows a change in state that is like a rocket. So, geologic changes can happen fast enough to be humanly perceptible. And not just earthquakes.
http://www.worldviewofglobalwarming.org/images/vostok.jpg
Look particularly at the change in state around 130,000 years ago. The graph isn't finely grained enough and probably neither is the data. But the change in temps is ~14C over the course of around 3000-5000 years. If that. From an initial forcing that was an order of magnitude smaller than the current one from greenhouse gases.
Posted by: Jeffrey Davis | October 02, 2011 at 19:29
Sorry, I put 2nd and 3rd parameters backward in my explanation above. The 3rd parameter is time at the point of inflection. Here's the equation for UB extent graphed in Figures 1 and 2 above:
ub = b1*exp(-exp(-b2*(year - b3)))
= 7.406*exp(-exp(.1004*(year - 2018.26)))
So 2018 is the year of steepest descent.
It's worth mentioning that if the end stage is noisy, along the lines of Figure 2, then we probably couldn't tell whether Gompertz or exponential had turned out to be "right."
Of course, things might turn out very different from either.
Posted by: L. Hamilton | October 02, 2011 at 20:07
The cold of the winter will most likely draw a line under how much ice volume can be lost as every winter there will be a lot of ice growth.
Posted by: dorlomin | October 02, 2011 at 22:24
Dorlomin
We get to see in the next few years if you are right about lots of ice growth in winter. Keep your eye on Hudson bay. The ice has been melting out earlier and freezing up later. If you look at the suns declination you will see that if the freeze over gets delayed about 3 weeks more then the sun moving back into the northern hemisphere will give an extra shot of energy into low albido waters as the sun moves above -20 degrees in the last week of January. This may rapidly lead to a loss of ice from Hudson bay in February. This will be the clue of what to watch for the arctic winter behavior first at the edges and then moving intoward the pole.
Posted by: RunInCircles | October 02, 2011 at 22:42
Nearly half of the Hudson bay is 3-5C SST above normal.
that is record warm water for this time of year..far south areas of the bay are in the low to mid 50s. Incredible huh?
the cooler areas are now near normal are moving slightly above as climo says they should be heading toward 0c getting ready for ice to start forming.
850 temps 15-20C above normal will move in...and the warm/cool boundary will sit just North of the Hudson after the warm surge is moved out. With most of the Hudson left with regional highs in the 50s to 60s with no snow cover after record highs of upper 60s to low 70s maybe even mid 70s reach the South or SW lake shore.
Unbelievable and unprecedented at this point.
This climate has changed for good. I am tracking this, in it's own thread over at Americanwx.com.
Posted by: Chris Biscan | October 02, 2011 at 23:14
Hudson Bay...
Chris, a couple of days ago my attention was drawn to the Barentz-Kara region. In my post I suggested the anomaly in Hudson/baffin Bay not that unusual. I still think the SST's over there were higher during 2010. The bust to the NH circulation IMO would not come from there this time (at least; not as strong as last fall).
Posted by: Werther | October 03, 2011 at 00:15
Re "The cold of the winter will most likely draw a line under how much ice volume can be lost as every winter there will be a lot of ice growth."
Should we assume volume lost in winter is meant to be volume gained in winter or something else?
Apparently I have indicated "insolation heat should be released rapidly once the sun went down". This sounds sensible to me but I could easily be wrong and I am no expert.
I doubt the winter maximum volume will begin to trend upwards. If the minimum volume is going down and heat content going up then the freeze is likely to be later to start. But we do get some catching up to previous years once the freeze does start as the heat can be lost faster through thinner ice. I do not expect this catching up to overtake because if it catches up then there is no longer a thinner ice reason for the faster release of heat.
So I expect the maximum volume to continue to decline. There may be continued small increases in volume gained in winter but only while the minimum volume is declining faster. That faster decline in summer minimum volume cannot continue for long. So yes, I agree that there is a limit to the volume of ice that can be gained in winter. However, I am not quite sure how the reasoning is as simple as saying "The cold of the winter will most likely draw a line ..."
Of course, it is more complicated. There is noise and more feedbacks than this negative ice thickness feedback. Perhaps snow and fog effects could overwhelm this negative ice thickness feedback or maybe this negative ice thickness feedback just isn't important and the ice volume decline and heat content increase are dominated by albedo feedback even as the ice gets very thin in winter. These scenarios involve fairly rapid transition to ice free year round arctic. I think and hope that they aren't likely.
Posted by: crandles | October 03, 2011 at 00:25
http://ocean.dmi.dk/arctic/satellite/index.uk.php
That one gets cut off..but shows 3-5C ssts in the hudson..
the hudson has been warming from the SW to the NE the last week.
with the very very warm air coming in, we could see this get widespread after a week of 5-18C 850 temp anomalies.
Posted by: Chris Biscan | October 03, 2011 at 01:12
"The cold of the winter will most likely draw a line under how much ice volume can be lost as every winter there will be a lot of ice growth."
BUT it's not a stationary line--as expected from theory and observed on the ground (or should I say, in the air?)--winter temperatures are warming the most.
While we may see rapid seasonal SIE growth for the reasons discussed above, the seasonal growth in ice *thickness* should keep declining for as long as the winter temperatures keep warming. So I don't think we are likely to see increasing winter volume at all.
Posted by: Kevin McKinney | October 03, 2011 at 15:13
L. Hamilton:
The lines in the graphs above are drawn using Arctic wide data. Implicit in the drawing of these graphs is an assumption that all regions in the Arctic are declining at the same rate. Observations do not support this assumption.
The Central Arctic Basin is not showing the same rate of decline as other regions and the factors which influence ice decline do not operate with the same force on the central Arctic Basin as it receives less heat from the sun and ocean currents than other regions. Additionally, the central Arctic Basin receives significant contributions of ice from other regions from ice transport.
Would it be possible to draw lines for the central Arctic Basin alone and see what the shape of the curve is for predicting when the Arctic will be "ice free"?
If this is too radical, could the lines be done for the area above 75 degrees north or as a third alternative, can the lines be drawn excluding regions with significant area outside the Arctic circle from the data?
Posted by: William Crump | October 03, 2011 at 15:42
Re "The lines in the graphs above are drawn using Arctic wide data. Implicit in the drawing of these graphs is an assumption that all regions in the Arctic are declining at the same rate. Observations do not support this assumption."
Surely, the more obvious implicit assumption is of the pencil sharpening example; should you measure the whole pencil or the length of the last 3cm? This surely leads to concluding we should look at volume of whole arctic basin not area nor a central region of the Arctic. That is the most rapid loss version.
Factors like wave action and bottom melt surely do not act on central arctic with the same force now as they do on the edges of the pack. When the central region does become on the edge then your methodology suddenly looks extremely suspect doesn't it?
"as it receives less heat from the sun and ocean currents than other regions. Additionally, the central Arctic Basin receives significant contributions of ice from other regions from ice transport."
looks very one sided to me; are you considering any counterarguments made to you?
Posted by: crandles | October 03, 2011 at 16:14
@William
"as it receives less heat from the sun". Agreed.
"as it receives less heat from ....ocean currents". Hmmm....
"Additionally, the central Arctic Basin receives significant contributions of ice from other regions from ice transport." But so do other parts of the Arctic. In fact, all that this is saying is that the ice is on the move and, in that respect, doesn't make the Basin all that different.
Henry
Posted by: H Barnard | October 03, 2011 at 16:34
"Curious to know what the +-2sd error bars are for future predictions."
Andrew, the 4.3 +/-.8 prediction is just adding and subtracting twice the residual standard deviation (.4) for the whole series; likewise the gray bands.
In the simulations I drew samples from an N(0,.6) distribution, where .6 reflects the higher residual sd seen 2007-2011.
I thought about showing the theoretical confidence bands (which have an hourglass shape centered on the mean year), but they seem less plausible in this context, and lack a rationale for extrapolation.
Posted by: L. Hamilton | October 03, 2011 at 16:36
Will Crump,
"The lines in the graphs above are drawn using Arctic wide data. Implicit in the drawing of these graphs is an assumption that all regions in the Arctic are declining at the same rate."
No, that assumption isn't implicit in the graphs anymore than an assumption that all American citizens always grow richer or poorer at the same rate is implicit in a graph of US economic growth. If you want to repeat your theory ad nauseum, fine, but could you spare us obvious nonsense like that?
Posted by: Jon Torrance | October 03, 2011 at 18:02
Crandles:
The pencil example is illustrative of the problem of using averaged data.
If there are ten pencils that are all being sharpened at different, but steady rates, and a plot of the average rate of the disappearance of all the pencils is made and a forecast line is extended when 50% of the pencils as a group are gone, the forecast line will predict an earlier demise to the pencils than will actually occur.
The best measure of the demise of the pencils as a group is to look at the data for the pencil that is being sharpened at the slowest rate.
The Arctic is certainly more complex than a bunch of pencils, and I believe the demise of ice below 80 degrees north will result in an acceleration of the melt rate of the ice above 80 degrees north; however, I see no reason to believe that the northern-most ice will diminish as fast as ice at lower latitudes. The area and extent data from Cryosphere today and MASIE support the position that the Arctic Basin is declining at a slower rate than other regions.
Why include data for Hudson Bay, Okhotsk Sea, Bering Sea, Baffin Bay or the Greenland Sea regions or any other region that has already reached a "no ice" level at the September minimum in the data base? The Arctic basin makes up more than 80% of the ice at the minimum (2.5 million km2 out of 3.0 km2). It is currently closing in on 3.0 million km2 and will reach its maximum extent of approximately 4.25 million km2 in early December and will stay at this level until almost the end of April. It is not going to disappear as fast as the line drawers would have you believe.
Looking at the map, many regions appear to be well outside the main body of Arctic ice even if you use a broadly measured area of 75 degrees north and higher to define the Arctic Basin.
Jon:
The nonsense is using a bad data base to make predictions when a better one is available. There is no reason to believe that ice melts above 80 degrees north as fast as it does at lower latitudes. Why corrupt the data base for making predictions by including such ice? Why include melt figures for Hudson bay, which is below the Arctic Circle, in predicting the demise of Arctic ice above 80 degrees north? To do so is nonsense.
Posted by: William Crump | October 04, 2011 at 00:06
H Barnard:
If the Arctic Basin is not different, why is the rate of decline in area and extent so much lower than other regions?
At the minimum it had 2.5 million km2 remaining. Per Cryosphere today, this was at most 1 million km2 below the 1979 to 2008 mean. Does any other region show a percentage decline rate this slow?
http://arctic.atmos.uiuc.edu/cryosphere/IMAGES/recent365.anom.region.1.html
Posted by: William Crump | October 04, 2011 at 00:17
Re "The best measure of the demise of the pencils as a group is to look at the data for the pencil that is being sharpened at the slowest rate."
Huh? I think most people would assume that when other pencils have run out, the remaining pencil will get more use and need sharpening more often.
Maybe you have a case for Hudson Bay and Sea of Okhotsk. But these have already reached zero in September so these are not contributing to the annual loss of ice area or volume nor the remaining ice area or volume at the minimum. Therefore dividing the remaining area/volume by the annual loss is not affected by whether we include those areas or not.
Excluding some of the annual losses that are happening now by excluding regions like Kara Sea or East Siberian Sea appears to me to just be hopelessly silly if not just wrong or complete nonsense.
Suppose hardly any ice formed in the East Siberian Sea over winter for whatever reason. Do you think the normal enhanced melt at the edge of the ice pack would simply cease or would it be transferred to where the ice edge is in the central arctic region?
So I think it is much more a case of the remaining pencil getting much more use and needing to be sharpened more often.
Posted by: crandles | October 04, 2011 at 00:32
The PIOMAS data is interesting and confusing. First of all I have taken all of the PIOMAS yearly minimums and divided them by minimum area and minimum extent. Just my way of attempting to understand thickness. So if I divide by area the average thickness this year went down by 9 cm. Whereas last year it decreased by 60 cm. If I use extent this year 5 cm last year 42 cm. The divide by area thickness is 133 cm left and the divide by extent is 89 cm left on average. I am using Larry's UB figures for extent Cryosphere Today numbers for area. PIOMAS shows much less ice volume loss this year from maximum to minimum versus last year. Does anybody out there have insight into the reduced volome melt this year versus last year when clearly area and extent both went down substantially? I have one other nagging question about PIOMAS, what happened in 1981? This yeaar sticks out like a sore thumb being substantially different from any other year around it.
Posted by: RunInCircles | October 04, 2011 at 01:15
William,
While I can see your point, there is an issue with it.
If you were measuring the rate of melt of an ice cube in the sun, then you could take the rate of melt for the ice cube as a whole or you could discount the rate for the outer few mm and base your projection on the fact that none of the inner part of the ice had melted, showing that the rate of melt was zero.
And after ever little bit of further melt that intruded on the centre part, you could simply arbitrarily reduce the size of the bit that you were using to measure the rate of melt.
You could keep doing this until just prior to the final bit melted, predicting that there was going to be no further melt, as the centre bit had not melted one bit during its whole time in the sun.
So: my question to you would be what bit would you use to determine the likely future melting rate and why? If it is the Arctic Basin, isn't that simply an arbitrary decision? Why not choose everything north of 81 degrees? Or 82 degrees? Or 83 degrees 58 minutes and 21 seconds?
In a few years, there will be no ice below 81 degrees. So why include that region when making predictions for the future?
Posted by: David Gould | October 04, 2011 at 01:19
The point that I feel William fails to take into account in his thesis is the effects of wind, ocean currents and the thinning of the mixing layer under the ice.
With the ongoing loss of ice cover in the Arctic, the ice in the Central Basin has thinned by more than half in the past decade alone (Polarstern). A continued erosion in area, extent and volume will see additional warming water and warmer winds brought to the Central Arctic Basin. The winds will more easily break up the scabrous ice, increasing turbidity in the waters underneath the ice, further thinning the mixing layer.
One summer we will be treated to a most spectacular melt...
Posted by: Daniel Bailey | October 04, 2011 at 01:58
RunInCircles - the loss (area, extent, or volume) will vary from year to year. Some years may even see an increase. Year over year numbers are interesting, but can't really tell you anything about trends.
If you look at your thickness results for 2002 versus 2011, what do you see? My numbers (for the end of Sept.) show a fairly steady decrease from 1.7meters to .86meters - a 50% reduction in thickness. I also show 2011 to be slightly thinner than 2010.
Volume alone has decreased by 50% since 2006. It decreased by 10% (400,000 km^3) this year compared to last year. I'm not sure what you expect to see? At yearly minimum there was only 4 million km^3 left. At this year's rate of decrease we'll be at zero ice in ten years time. That's faster than everyone but Maslowski is predicting.
Posted by: Kevin O'Neill | October 04, 2011 at 02:15
William, I think David points out the logical fallacy of your argument, but there's also the physical basis of the measurement you're using. Area (or extent) can remain the same even though the ice is being greatly affected by melt/transport. The area loss in the central basin may be minimal, but the volume losses have been substantial. Your metric of choice ignores this completely.
We focus on extent because we have daily numbers available and a decent time series to compare against. This does not mean extent is the best gauge of the ice's health, condition, or predictor of future sustainability. Any description of sea ice conditions that ignores volume is incomplete at best.
The central basin has long been the oldest and thickest ice in the Arctic. Neven's recent posts on the iceshelves points out that some of this ice has survived longer than the pyramids. In the very near future the oldest ice in the arctic will be 5 years old. Area and extent do not take this into account.
So, while the central basin may appear to be resistant to the forces of warming, it's a mirage. More ice has probably been lost in the central basin than any other area of the arctic - despite what extent or area numbers may lead you to believe.
Posted by: Kevin O'Neill | October 04, 2011 at 02:26
Kevin
My numbers are using vol/UB extent:
2002 193cm
2003 170cm -23cm
2004 168cm -2cm
2005 170cm +2cm
2006 155cm -15cm
2007 151cm -4cm
2008 154cm +3cm
2009 135cm -19cm
2010 94cm -41cm
2011 89cm -5cm
So 40% of the thickness reduction of 104cm occured in 2010. 2007 works out to only 4 cm less than 2006. Moreover I can't place any physical occurance during the melt season which tracks this variability. What conditions should one follow that would correlate with the thickness variability? Now extent is probably the wrong divisor to use. If you use area the thickness reductions are similar with ~40% occuring in 2010. Again what data should we be following that would help us understand the substantial differences in thickness loss?
Posted by: RunInCircles | October 04, 2011 at 02:58
@RunInCircles: I think you're pursuing something some of the rest of us are wrestling with, as well. I would suggest that you consider using volume at the time of minimum area as an indicator of trends in thickness. This is because minimum thickness tends to lag minimum volume, because melting of thicker fringe ice is not yet balanced by increases in volume and area due to very thin new ice. I view volume at minimum area as a better indicator of how much ice thickness is left to melt.
In the case of 2011, it appears that minimum volume and minimum area are about the same time (unlike 2010?). My recollection is that in 2010 thickness at minimum area was around 1.4, and this year sounds like around 1.33, which would be a 5% decrease (and don't forget, we lost some area at minimum this year vs. 2010, which means loss of thickness/volume is in some sense underestimated)
One hypothesis is that the dip in maximum volume from year to year may give a hint as to minimum volume the next year.
Sorry, I'm too tired to clarify further.
Posted by: Wayne Kernochan | October 04, 2011 at 03:21
"Earlier this year, researchers detected a gaping hole in the Arctic ozone layer where over 80% of the existing ozone was completely obliterated. Post-winter ozone depletion in the Arctic is a regular occurrence, but the level of this year's destruction was record-breaking.
Researchers from the Jet Propulsion Laboratory in California believe they have a handle on the mechanism that created the hole. They think unusually cold air in the stratosphere formed clouds which created a form of chlorine that is toxic to ozone molecules. The real mystery is why the stratosphere was so chilly for so long, and whether it could happen again.
One explanation is climate change. As the climate of the earth on ground level warms due to greenhouse gasses and other manmade environmental hazards, the stratosphere actually cools. This cooling may be setting the dominos in motion and leading to the depletion of the ozone layer. The research is still ongoing, and scientists aren't ready to pin down a cause just yet, but record-breaking holes in our planet's protective shield aren't good news for anybody."
http://news.yahoo.com/blogs/technology-blog/massive-hole-ozone-layer-leaves-scientists-baffled-005255319.html
A large hole in the ozone layer over the Arctic allows more heat to escape?
"Earlier this year"? Any idea when? Before/during the melting season?
Can anyone flesh this out?
Posted by: Bob Wallace | October 04, 2011 at 07:51
The models, both the GFS and Euro now have a text book beautiful DPA forming this week.
if this was early September we would have seen 2011 smash the min record.
Posted by: Chris Biscan | October 04, 2011 at 07:58
-7000K prelim on jaxa.
even with a decent fat area of cold air the rapid refreeze is stuck in the mud.
I guess with decently bad winds and warm ssts new ice formation is not easy.
Posted by: Chris Biscan | October 04, 2011 at 08:00
I will say this now...
if what the 00z GFS has comes to fruition then we will see a record amount of Jaxa losses by number of them in one month on the data set as well the record for largest single day drop in October in the pack as well as record for largest single week loss in October, as well as largest multiday losses on the data set.
If this happens we will be near 2007 or behind it by mid October.
How intriguing!!!!!
Posted by: Chris Biscan | October 04, 2011 at 08:25
Bob Wallace, someone sent me a mail with a link to a BBC article on the record ozone loss in the Arctic.
The Alfred Wegener Institute also has a press release out today (in German), referring to a study that just appeared in Nature (also referred to in the BBC article).
Posted by: Neven | October 04, 2011 at 14:03
Chris, I agree. It'll be interesting to see what happens when those highs move in.
Posted by: Neven | October 04, 2011 at 14:04
And coincidentally Canada will stop monitoring ozone levels as of this winter.
Posted by: Neven | October 04, 2011 at 15:16
Hi Larry. What is the linear trend for the residuals from 1972-2011 for the Bremen/Gompertz curve?
In other words, is there sufficient justification to restrict the Std Dev to 2007-11 data, rather than the complete data set? From +/-0.4 to 0.6 is a sizable jump in white noise going forward...
Cheers,
Lodger
Posted by: Artful Dodger | October 04, 2011 at 22:12
The linear trend for the residuals from 1972-2011 for the Bremen/Gompertz curve won't be 0 but it will be very close. If it wasn't close a better fit could be found. But what does that prove in relation to justifying using 2007-11 std dev rather than whole set?
Posted by: crandles | October 04, 2011 at 23:04
Perhaps you are wondering if the 5 year average of the absolute residual is monotonically downward. If so this would be a reliable indicator that the errors are reducing and std dev of last 5 years might be an overestimate.
Unfortunately it isn't monotonically downwards. If you look at the graph you can see that the 1992-1996 has higher errors than either side of this period. We cannot be sure that that level of variability won't return.
Posted by: crandles | October 04, 2011 at 23:30
Where are we going to get ice data now that AMSR-E is broken? Can anybody tell mewhat other systems are available?
Posted by: RunInCircles | October 05, 2011 at 01:46
Hi Daniel,
Funny thing about digging a basement on the sea ice; you'll won't find any Inuit Elders spending their time that way!
The fallacy you are looking for is this:
Uh, no... It receives more:
During the 100 days centered around the Summer solstice, the North Pole receives, on average, 17% more solar energy than at 60 N latitude. Yup, that's May 1 thru Aug 10, the time of mega-melt.
The difference until now is that the sea has been more compact further North. As this changes in the future, the Ice Albedo flip will bite with a vengeance, and there will be sudden catastrophic loss of sea ice in the central basin.
So, the further North you go, the more solar energy you get during melt season... I wonder if Inuit Elders like donuts?
Cheers,
Lodger
Posted by: Artful Dodger | October 05, 2011 at 01:47
Yep, it's true... (hate ta say i told ya this day was coming):
http://nsidc.org/data/amsre/news.html
Posted by: Artful Dodger | October 05, 2011 at 02:06
Interesting point about insolation levels vs latitude during the summer providing greater energy input the further north.
Of course, the same is not true during the rest of the year. So, north of 80 will be able to form more ice during the fall and winter. The currents and wind will tend to transport the ice towards Ellesmere Island, where the thickest ice will pile up.
Eventually, most of the ice north of 80 will be thin enough to melt or drift out during the summer.
Posted by: Andrew Xnn | October 05, 2011 at 03:10
Hi Andrew,
Those symmetries do not quite apply that way... Once the Sun sets, insolation goes to zero, but it can never become negative, regardless of how far the Sun is below the horizon.
To illustrate, if we stretch the time interval to Mar 21 - Sep 21, then avg insolation at 66.7 N is 234.7 w/m^2, and at 90 N it's 255.6 w/m^2.
If we look at an entire 365 day year, avg insolation is just what you'd expect: half that of the 6 months centered around the Summer solstice.
Avg annual insolation is 117.7 w/m^2 at 66.7 N, and 128.1 w/m^2 at 90 N.
Deep fried donuts are called Krispy Kremes, aren't they? Maybe they can open a franchise in the Chukchi sea... ought to be lots of drilling rigs there within 8 years.
Cheers,
Lodger
Posted by: Artful Dodger | October 05, 2011 at 06:27
Lodger,
Thanks for digging up the (Top Of Atmosphere) insolation numbers are various latitudes.
What I find interesting is to think about what this means for when the ice margin moves further and further north. I would expect that the increased insolation during the melting season creates something of a positive feedback due to the albedo effect having more of an impact the further north open ocean emerges during the melting season.
That would be the 8th or 9th positive feedback operating in the Arctic. Can't we find a nice negative feedback for a change ? This way, the quadratic drop-off will not be stopped until there is so little ice left over in September that open ocean heat simply can't get to it any more.
Incidentally, where did you find a calculator that produced these numbers ?
Posted by: Rob Dekker | October 05, 2011 at 07:16
Hi Rob,
There are lots of spreadsheets around to calculate insolation for use in the home/solar panel industry.
I use a customized version of an Excel worksheet created/tagged "05/04/2002, 14:43:50, Famile Erren-Wijlens" called insol.xls
A copy of it is freely available, here:
http://members.lycos.nl/ErrenWijlens/co2/insol.zip
Cheers,
Lodger
Posted by: Artful Dodger | October 05, 2011 at 07:37
At least AMSR2 will be online January-February.
Models still forecasting hardcore DPA.
right when we lose AMSRE
Posted by: Chris Biscan | October 05, 2011 at 08:50
There is a new monthly update online from NSIDC -> Arctic sea ice near record lows:
October 4, 2011
Summer 2011: Arctic sea ice near record lows
The summer sea ice melt season has ended in the Arctic. Arctic sea ice extent reached its low for the year, the second lowest in the satellite record, on September 9. The minimum extent was only slightly above 2007, the record low year, even though weather conditions this year were not as conducive to ice loss as in 2007. Both the Northwest Passage and the Northern Sea Route were open for a period during September...
Chris K
Posted by: www.google.com/accounts/o8/id?id=AItOawkpUaD_uYjZAIrhpA6AA5KyEs-CSoL4zlM | October 05, 2011 at 12:50
The NW passage is still open.
a bit mis-leading.
Posted by: Chris Biscan | October 05, 2011 at 13:40
Chris Biscan | October 05, 2011 at 08:50
"At least AMSR2 will be online January-February."
Humm, probably not...
The JAXA facility where AMSR2 was assembled was damaged in the Japan earthquake on Mar 11, 2011. The AMSR2 instrument was covered with dust, and had to be cleaned and inspected. This process took until June, setting back the GCOM-R1 launch schedule by at least 3 months.
The June 2010 GCOM-R1 Status Report had the launch scheduled for Nov 2011. This is now pushed back, hopefully not much further than Feb 2012.
Then, continuing the GCOM-R1 plan, 6 months for CA/VA (calibration and validation). 1 year after launch before first public release of Level 1 data. 2 years until Level 2 data becomes available.
So, best case scenario: Spring 2013 before AMSR2 data is flowing normally, and 2014 until it is of comparable reliability to what AMSR-E was producing on Sep 30, 2011.
More here:
GCOM-W1 Status (June 29, 2011)
http://weather.msfc.nasa.gov/AMSR/meetings2011/Wednesday/110629_AMSR_E_imaoka.pdf
Posted by: Artful Dodger | October 05, 2011 at 17:07
The demise of Arctic ice in the Gompertz curve above is certainly more believable than the volume trend line forecast analysis that says the Arctic will be "ice free" for the entire month of August, September and October by 2018.
The Arctic Basin (AB) area is 4.25 million km2. The Arctic Basin made up more than 80% of the ice remaining at the minimum.
Why not try drawing a Gompertz curve using area and extent data for the Arctic Basin alone and see what falls out?
Ice coverage in the AB is currently above 3 million km2, about the same as it was on August 1st. Ice coverage in the AB at its lowest point in 2011 was 2.5 million km2 per CT link below, about where it has been for the last 4 years - 2007 was about 2.1 million km2 per the link below.
http://www.arcus.org/files/page/images/639/figure8.png
http://arctic.atmos.uiuc.edu/cryosphere/IMAGES/recent365.anom.region.1.html
The Arctic will not be "ice free" until the Arctic Basin is "ice free".
Why not use data related to the Arctic Basin alone to show when it will be "ice free"?
If you think this is too narrow, then add in the Kara Sea, Laptev Sea, East Siberian Sea,Chukchi Sea and the Beaufort Sea. I see no reason why an Arctic wide data base is superior to this more limited data base.
Posted by: William Crump | October 05, 2011 at 18:57
Notification service: There's an October 2011 Open Thread for all things off-topic.
Posted by: Neven | October 05, 2011 at 21:27
Artful Dodger:
That page is from Hans Erren. He is a long time 'denier on demand', and is also responsible for spreading a lot of bad science on the net. I would distrust anything coming from him.
I use a program downloaded (as fortran source) from http://aom.giss.nasa.gov/srlocat.html .
With that I get for annual insolation:
latitude 66.7 : 208,0 [W/m2]
latitude 90,0 : 173,2 [W/m2]
Opposite to your results.
Posted by: Wipneus | October 07, 2011 at 13:44
>"With that I get for annual insolation:
latitude 66.7 : 208,0 [W/m2]
latitude 90,0 : 173,2 [W/m2]
Opposite to your results."
Annual insolation will be more for 66.7 N than for 90N. We were discussing summer insolation.
Posted by: crandles | October 07, 2011 at 14:31
No, quote from AD:
"Avg annual insolation is 117.7 w/m^2 at 66.7 N, and 128.1 w/m^2 at 90 N."
The numbers are remarkably different IMO.
The numbers for the 21march-21sept (inclusive) are 384,7 (66,7 lat) and 382,0 w/m2 (90 lat).
Quoting AD here:
"To illustrate, if we stretch the time interval to Mar 21 - Sep 21, then avg insolation at 66.7 N is 234.7 w/m^2, and at 90 N it's 255.6 w/m^2"
Posted by: Wipneus | October 07, 2011 at 15:41
Oops yes, sorry.
For AD figures:
255.6 / 2 ~ 128.1 looks sensible for 90N but it certainly shouldn't be 234.7 / 2 ~ 117.7.
For Wipneus figures:
How can 382 w/m^2 for 90N 21 Mar-21 Sept go down to 173.2 for the annual figure? That is less than half! Does it receive negative insolation in winter?
Posted by: crandles | October 07, 2011 at 16:24
Right, those numbers were mistakingly calculated from 21 april-21 sept.
Corrected 21mar-21sept numbers are 360,8 (66,7 lat) and 341,7 W/m2 (90 lat).
Posted by: Wipneus | October 07, 2011 at 16:41
Using the NASA link from Wipneus, I downloaded solar insolation values from March thru Sept for this year. Here is a chart comparing 90 North (red) vs 66.7 North (blue):
For the 96 day period between May 5th to Aug 8th, daily solar insolation (watts/m2) is greater at 90N than 66.7.
In addition, for the roughly 159 days period between April 2nd thru Sept 9th, the total amount of solar insolation is approximately equal.
Of course, during the rest of the year, 66.7 North receives a greater amount, except of course during the height of the polar winter when they both receive zero.
So, if it weren't for all the thermal momentum from snow and ice, it is entirely possible for 90N to have warmer temperatures during the height of the summer.
Posted by: Andrew Xnn | October 07, 2011 at 17:14
Here is my version of the graphic (100 days high summer):
So indeed in high summer, the north pole receives more energy than a place on the polar circle. The difference for these 100 days is about 7%.
Posted by: Wipneus | October 07, 2011 at 18:01
Hi folks,
So, can you see the donut now? The point is that Climate Denier Trolls begin with a false assumption, and then attempt to induce a spurious debate. Critical thinking, people!
Bonus question: Point out the latest fallacy-of-the-day being repeated on this blog.
Posted by: Artful Dodger | October 08, 2011 at 01:50
@William Crump. Here are the annual minimum volumes (per Topaz) for the regions you indicated (Central Basin + Kara + Laptev + East Siberian + Chukchi + Beaufort):
2007 5.294
2008 5.228
2009 4.661
2010 3.937
2011 3.098
This would indicate that the ice will be all gone in 5.6 years (at a rate of 2.196 per 4 years -- yes I'm just subtracting 2011 from 2007, because it's 1:38am and I can't figure out the least squares fit line, but it couldn't make more than a year or two difference).
For comparison, using the entire arctic yields the following:
2007 6.237
2008 6.279
2009 5.325
2010 4.302
2011 3.364
Indicating 4.6 years remaining.
Yes, your measure is more optimistic, but not by much....
Posted by: Bfraser | October 08, 2011 at 10:42
Hi Larry,
A Gompertz fit gives a predicted range for 2012 Sep Avg SIE of 4.3 +/- 0.8 M km^2. So the bottom of the 95% confidence level sits at about 3.5 M km^2
While it's still possible that mean September sea ice extent will drop below 3.5 M, I think it's more likely that 2012 will not be quite low enough to reject the Gompertz hypothesis at 95% significance.
Of course having said that, the winds of September will ...
Cheers,
Lodger
P.S. Note that Larry's SIE prediction on Oct 1st, 2011 is the same as the August 2012 SIO update Median value for SIE, 4.3 M. Well done, Larry ;^)
Posted by: Artful Dodger | August 31, 2012 at 07:05
It looks like all my Gompertz point predictions will be too high this year, although perhaps within confidence limits. PIOMAS is really the one that has been telling the story, steeply down with not that much room until zero!
Posted by: L. Hamilton | August 31, 2012 at 14:40
Indeed. At what point can we reject the null hypothesis? Also, please remind us of how your other curves predicted events. Can we favour any one model yet?
Cheers,
Lodger
Posted by: Artful Dodger | September 01, 2012 at 12:02
Lodger, I've added a note to my "Naive predictions" thread, comparing recent 1-day values with the Gompertz predictions and confidence intervals.
http://neven1.typepad.com/blog/2012/06/naive-predictions-of-2012-sea-ice.html
Posted by: L. Hamilton | September 03, 2012 at 16:00
Hi Neven,
Could I ask you to please remove this spam comment?
Posted by: Maury Microwave | February 23, 2012 at 07:14
Thanks,
Lodger
[Done, N.]
Posted by: Artful Dodger | April 10, 2013 at 07:24