Sea Ice Prediction Network 2014 Submissions

[DavidR]

The Sea Ice Prediction Network has released its call for July submissions with a required submission date of 9 July. Public as well as scientific submissions are invited. It's not a poll as you are expected to explain how you achieved your figures. 
http://www.arcus.org/sipn/sea-ice-outlook/2014/july/call

Those who have made submissions are encouraged to post their executive summaries here for discussion. 

[DavidR]

Submitter: David Rennie

Prediction:  September monthly average projection 3.2 M Sq Km.

Uncertainty: Projection uncertainty/probability estimate 2.5 – 3.7 M sq Km.

Executive summary

July should see a loss of extent of around 1.7 M Km2 by July 16th followed by a loss of over 2M km2 from then until Aug 1st resulting in an end of month extent of below 5.8 M Km2.

Starting with the April PIOMAS volume distribution and the April NSIDC average ice extent the estimated extent loss for each 10 cm thickness of ice loss is calculated. This calculation is then correlated with the reported 5 day average NSIDC ice extent loss. The calculation shows that the extent loss is closely correlated with the initial thickness distribution until the end of July. However the final September average figure is heavily dependent on August weather. 

The minimum average thickness loss over the past three years is 2.00 meters. This year that melt would result in an extent of around 4.35 M km2. With 1.37 m of melt as of July 1st, a melt  of only 2.00m seems highly unlikely.

[crandles]

CT Area seems to be about 5th-8th lowest recently suggesting quite a high minimum this year. However the increased area that has thickness less than could be melted suggests some downside risk. If a low minimum is reached that would appear to vindicate your method.

If there is a large area of meltable thickness then it seems likely that quite a bit of it is further into the ice pack than typical. That could make it harder for heat to reach so that it might not melt.

In addition, with area relatively high compared to extent, this suggests less leads, polynia ext within the pack again making it harder for heat to reach the more difficult to reach areas with less than 2m thickness.

I think I might be inclined to consider this makes it a low possibility that the minimum will be a low as you say and a higher possibility of being higher than you suggest.

It seems to be working out well for you so far and I am not surprised you are seeing this as vindication. I think there is a risk of interpreting luck and/or non risky part of your prediction coming true as more vindication than there really is so far. Having said that, certainly so far so good for your predictions.

Could you say how you worked out the 2m and the 1.37m in you last paragraph.

[DavidR]

Crandles,
I  started with this graph posted by Chris Reynolds on Dosbat.

I converted the volume at each point to an area and simply assume that the thinnest  ice will melt  out first.  Based on that I plot the decline as each 10 cm melts out. Last year the melt reached 2m while in 2012 it reached 2.37m.  The July 1st, 5 day average equates to  1.37  on this graph.  In 2012 the July 1st  value equated to 1.33. 
The massive drop in June 2012 is clearly shown in the much higher values between 0.5 and 0.8 m.  Based on these numbers, my estimate put the crossover in extent between 2012 and 2014 as occurring at the end of the first week of June, which proved to  be correct.

As you  can see there is a massive amount of ice in the 1.6-2.0 m range all of which I  expect to melt out this year.  In fact I  expect the extent to have dropped to about the 1.9m point by the end of this month and to  melt  out to  about 2.15 by the end of the season. 

2 m will take us to  2007 levels, 2.1 m will take us to  2012 levels.

[DavidR]

This histogram provides the extent  values I created from the Chris's graph.


Melt at the beginning of June is represented by the 0.55 range, the end of June by 1.35, at  almost  every point between there was significantly more extent in 2012.

This shows the predicted values through June:


This shows the NSIDC reported values:


As you  can see the prediction matches reality well with the exception of the late June melt this year.

[Tor Bejnar]

Last year, using a primitive method, I compared 2012 melt from August 1 to the minimum, noting what August 1 thickness functionally melted out, and guessed the same August 1 thickness would melt in 2013.  It did not happen, not by a long shot.  Weather is so important. 

Although Northern Hemisphere spring snow cover seems to be a fair predictor of ice minimum, I wonder if NH snow coverage is a proxy for Arctic sea ice snow coverage… (with reference to Healy research: http://arcticspring.org/dispatches/closing-circle)

[DavidR]

Tor,
I  agree that  the weather in August  is critical to the final outcome.  However 2m of melt over the season seems to be a fairly consistent  minimum at the moment.   I feel safe predicting 2 m of melt  in any  season. This year,  that  takes extent to 2007  levels.

I  expect significantly more as we are already well ahead of 2013.  Both 2011 and 2013 had, by my  measure, 73 cm of melt after July 1. If that  occurs this year it will takes the melt  to 2.1 m and extent to  2012 levels.  If the weather in August  favors melt who  knows where we will end up.

[Tor Bejnar]

My guesses for ice area and extent minimums in the two sets of ASIF polls indicate I 'believe' Arctic sea ice coverage will tie with 2012.  (I think of myself as being pessimistic, but not expecting a new record may make me an optimist!)  I know, however, that I do not possess the tools (time being one of them) to make any serious stab at a worthy prediction.  I appreciate those co-ASIFers who do make the attempt and show us their reasoning and calculations.

[ChrisReynolds]

In both CT Area and Wipneus Area - area is just not falling while extent is falling. The resultant compaction seems to me to be increasing albedo, and may be indicative/causative of relatively little volume loss over June/early July.

I find myself on the verge of reducing prospect of matching 2007/2011.

SIPN deadline is Wednesday. PIOMAS data still not updated! 

[ChrisReynolds]

Latest PIOMAS update, anomaly plot attached.

Initial message deleted - I'm looking deeper at the numbers, the plot still stands.

[ChrisReynolds]

Attached are thickness distribution for all PIOMAS domain, by June this is dominated by the Arctic Ocean. Also regional average thickness for the last three years.

My prediction, using the method for June SIPN but using June PIOMAS data gives the following result for September NSIDC extent.

Upper...    5.708
Lower...    4.634
Central..    5.171

I'm ditching the top half as a concession to thinner ice in the main peripheral seas, apart from the Atlantic sector. Also as a concession to most of the increase of volume being in the Central Arctic - which plays a role in the very lowest extents, but not in higher extents.

So, unless I change my mind by tomorrow night, right now I intend to submit 4.6 to 5.1M km^2 September extent to SIPN for my July prediction. This rejects 2012, 2007, and at the high end 2009 and 2013.

Year   NSIDC Ext   
2007   4.300   
2008   4.730   <
2009   5.390   
2010   4.930   <
2011   4.630   
2012   3.630   
2013   5.350   

So I reinstate my earlier comment -

Now new record in 2014 (which I already thought).
No chance of matching 2007 or 2012.
And I see little chance of a re-run of 2013

[Neven]

Latest PIOMAS update on the ASIB.

[DavidR]

Chris,
Can you  explain why  the thickness distribution you originally posted for April, shown in my  earlier post is significantly  different  from the one you  posted today.  Are the figures revised every  month, if so this would make predictions based on the original April figures very  dodgy.

I  can understand that  2014 might involve some minor revisions in the following  months but  I  can't understand why 2011 - 2013 would have such  drastic revisions.

My  technique put estimated volume at 24020 and extent at 14296 based on the April figures which are a little higher than the actual figures of 22911 and 14069.  I  can't see that  your revised figures could account for all the volume or extent at the start of the melt  season.

Thanks

[ChrisReynolds]

David,

Sorry, that's for June not April - I was in such a rush to get to bed last night I forgot to change the title.

[DavidR]

Thanks Chris,
That makes sense, the original graph is stretched to the left and the first part of the melt has disappeared.  It fits with my  view that  there is very little loss at the thick end of the spectrum so the average thickness loss above 2.2 is much less than the average thickness loss below 2.2. Which is one reason I  think the June volume is so  high.

[crandles]

I assumed Chris Reynolds graph was June not April.

Didn't use to update every month, but yes they are updating every month now. See the PIOMAS thread for maps each month:
http://forum.arctic-sea-ice.net/index.php/topic,119.msg30183/topicseen.html

I think this update clarifies my opinions greatly:

The large area of ice of meltable thickness was a reason why we might have a large melt this year. With CT area relatively high I was doubtful of this but it remained a possibility. That possibility now appears to have been removed:

David R was presumably expecting much larger areas up to 0.9m thick to remain at June compared to 2012 as his histogram of areas showed much larger areas 1.6m to 2.2m thick.

While 1.37m thick ice at March has been removed from the edges, nowhere near that amount is removed from the remainder. So it isn't a case of expecting the 1.6-2.2m range to be 1.37m thinner.

Nevertheless it is a remarkable change from lots more area in the 1.6-2.2m range at March than 2012 to noticeable less area up to 0.9m thick at June than 2012. So why has there been so much less thinning this year than 2012?

Several suggestions could be put forward like: a fast start to melt season being crucial, low area is needed for albedo feedback....

While these help to explain, I am not sure they adequately explain the dramatic turnaround. Hence I am drawn to Rob Dekkers (extent-area) metric see
http://neven1.typepad.com/blog/2013/07/problematic-predictions-2.html

Extent has been relatively low while area has been relatively high so (extent-area) has presumably been particularly low. Because these holes in the ice are surrounded by ice, the heat absorbed by these areas are more important than heat absorbed at the periphery which are not surrounded by ice because that heat might move away from the ice.

This seems set to continue.

With area close to 5th to 8th position, 8th place CT area just higher than 2013 now seems about the level to expect. Extent might well be similar - about 8th lowest.

Volume is more stable and is currently in a clear 5th place. 2007 is in 6th lowest place and that is about the level I now expect.

(Views subject to change if I manage to do some more detailed calculations of cumulative (extent-area) and area.)

[DavidR]

Crandles,
Its like this, over the season we move along the bottom axis from 0- 2 metres, which has, in the past three years,  always melted out.  As we move along, the ice melts and extent disappears. We can convert the extent loss to determine our position on the bottom axis. 

Based on the April data, on July 1st, at 1.37 cm  we were 4 cm closer to 2m than 2012, when we were at 1.33 metres, 7 cm closer  than 2011, when we were at 1.30 and 10cm closer than 2013 when we were at 1.27m. To not hit 2 m this year,  July  needs to  be much less conducive to ice melt  than any of those years. 

I  just can't see that happening given that  a lot of the melt must  be coming from water temperature.

Extent is currently  well  below the value predicted by the model despite it being higher than 2011 and 2012.

[crandles]

David,

I may have been unduly harsh on your method. I think it does well for predictions about the early part of the season, but it does badly later on when albedo feedback becomes more important.

In the April graph, 2014 clearly has most area with thickness between 1.5 and 2.2m. While in June there is still more area in the 1.3 to 1.8m thickness than 2012. In that thickness range, there is no longer more area than 2011. It clearly hasn't done as much thinning as 2011. We are already seeing less ice volume loss and I expect that trend to continue. If we melt less ice volume in the latter part of the season then the area and extent reductions will also be low.

[Steven]

My prediction, using the method for June SIPN but using June PIOMAS data gives the following result for September NSIDC extent.

Upper...    5.708
Lower...    4.634
Central..    5.171

I'm ditching the top half as a concession to thinner ice in the main peripheral seas, apart from the Atlantic sector......

Chris, the calculated values in the above quote seem to be too high?


If I understand correctly, your method is based on the June monthly average PIOMAS volume for the Arctic Ocean  (excluding Hudson, Baffin, Bering and Okhotsk).    Linear regression on these June volume data (using the 1979-2013 period) suggests about 4.7 million km² for the September 2014 NSIDC extent.    Since your method uses the residuals of the 2007-2012 period, I guess it yields a prediction of about 4.4 million km² or so?  (rather than 5.171?)
 
 

[DavidR]

Crandles,
One of my  assumptions for my  forecast is that  short term variations in melt  rate tend to  even out over the season until Aug 1st (1.77-1.85cm),  after that  the August weather is the major influence. 
After August 1 the additional loss has varied from 18 cm - 52 cm just in the last three years.
My predictions are based on an average year to  Aug 1 and and average melt after that.  Based on the last three years an average melt  to  Aug 1st is 1.82 cm which would take us to  the same position as 2012 at  6200 Km^2.   
Currently the extent  is less than predicted by the model so I  remain confident of getting to  at least that  point  by Aug 1st. 

[ChrisReynolds]

My prediction, using the method for June SIPN but using June PIOMAS data gives the following result for September NSIDC extent.

Upper...    5.708
Lower...    4.634
Central..    5.171

I'm ditching the top half as a concession to thinner ice in the main peripheral seas, apart from the Atlantic sector......

Chris, the calculated values in the above quote seem to be too high?


If I understand correctly, your method is based on the June monthly average PIOMAS volume for the Arctic Ocean  (excluding Hudson, Baffin, Bering and Okhotsk).    Linear regression on these June volume data (using the 1979-2013 period) suggests about 4.7 million km² for the September 2014 NSIDC extent.    Since your method uses the residuals of the 2007-2012 period, I guess it yields a prediction of about 4.4 million km² or so?  (rather than 5.171?)
 
 

Steven,

Thanks. There is an error but I can't get the time to review and correct so I have withdrawn my July submission. The error was caused by working late at night after two 12 hour days - this and the fact that I can't find time now to do any reading on the Arctic mean I am on the verge of retiring my blog.

[SteveMDFP]

 ...
the fact that I can't find time now to do any reading on the Arctic mean I am on the verge of retiring my blog.

Dang.  You've done really good work.  I can understand the need to take a sabbatical.  I hope the blog retirement isn't permanent.

[iceman]

I hope the blog retirement isn't permanent.

Second that.  Dosbat is a tremendous resource for anyone wanting to do a deep dive, and also feeds a good deal of substantive discussion on the forum pages.

[Steven]

Chris, I also think your blog is excellent, and hope that you keep posting new things on your blog. 

Here are some data from the spreadsheet I used yesterday night  (perhaps of interest for double-checking the results, hopefully I calculated correctly).

x-variable: June PIOMAS volume for Arctic Ocean,  excluding Hudson, Baffin, Bering, Okhotsk.
y-variable: September NSIDC sea ice extent

Regression equation (using the 1979-2013 period):  y = 0.2808 * x + 0.1355
Predicted y-value for September 2014:  y = 4.70.

Extent is expressed in million km², volume in 1000 km³.

Code: [Select]

year, x, y, predicted y (hindcast), residual

1979,   27.833,   7.20,   7.95,   -0.75
1980,   27.301,   7.85,   7.80,    0.05
......
2007,   17.797,   4.30,   5.13,   -0.83
2008,   18.964,   4.73,   5.46,   -0.73
2009,   18.180,   5.39,   5.24,    0.15
2010,   16.215,   4.93,   4.69,    0.24
2011,   15.293,   4.63,   4.43,    0.20
2012,   14.902,   3.63,   4.32,   -0.69
2013,   16.003,   5.35,   4.63,    0.72
2014,   16.265,     ? ,   4.70

Taking the minimal and maximal residuals of the 2007-2012 period, and adding them to the above y-value 4.70, gives the lower and upper bounds: [3.87,4.94].  Mid-range: y = 4.41.

[Steven]

From the twitter account of Michel Tsamados, co-author of the Schroeder et al. paper  "September Arctic sea-ice minimum predicted by spring melt-pond fraction".

https://twitter.com/micheltsamados

Latest prediction (based on pond fraction 1 May - 25 June 2014):   5.5 +/- 0.44 Mill. km2

Pond fraction very low till mid June, but rapid increase since mid-June and reached 2001-2013 mean around 25 June. These are model results.

[ChrisReynolds]

Steven,

I agree with your calculations, the problem was that a out of a run of links to a table, the 2014 June data link had gone astray and referenced incorrect data - short of going through the whole sheet it would have been difficult to find. My full range would be as you state, this brings the following years into play..

Year ,   NSIDC Ext   
2007,   4.300   <
2008,   4.730   <
2009,   5.390   
2010,   4.930   <
2011,   4.630   <
2012,   3.630   
2013,   5.350   
"<" indicates within range of my prediction.      


Thanks everyone for all the votes of support, it's appreciated.

Average views of my blog posts are currently running at 200 views per post, the traffic coming in from searches and other blogs doesn't account for this, a substantial number of people are accessing via favourites or feeds, so I am aware that what I blog is appreciated.

Some months ago I was promoted, now I find I just don't have the time to study the Arctic as I did. That's why I gave up on the NSIDC regional extent and area data and let Wipneus run with it. I will continue to post monthly status reports until September, and decide then. But I won't be giving up my interest, if I do mothball the blog for while I will continue to comment here. It's just that when so many people read my blog I feel a duty to make sure I know enough to be worth reading, and I haven't been able to fit in properly reading a scientific paper since April. That's not good enough.

[ChrisReynolds]

From the twitter account of Michel Tsamados, co-author of the Schroeder et al. paper  "September Arctic sea-ice minimum predicted by spring melt-pond fraction".

https://twitter.com/micheltsamados

Latest prediction (based on pond fraction 1 May - 25 June 2014):   5.5 +/- 0.44 Mill. km2

Pond fraction very low till mid June, but rapid increase since mid-June and reached 2001-2013 mean around 25 June. These are model results.

Thanks for this, very useful, you might want to consider re-posting in the 2014 Season thread.

[Steven]

Chris, for what it's worth, personally I wouldn't use the 2007-2012 residuals, but also include the 2013-residual, or perhaps use a somewhat longer period  (if that makes a difference).  The 2013-residual would result in a value that is maybe unlikely to occur, but I think the same can be said about the 2007-residual. 

It has been relatively cold this melt season so far.  And the compactness indices are high (area divided by extent).

Your method uses the June monthly average volume.  I guess that the June 30th daily volume would give a somewhat higher value for the prediction, but unfortunately no gridded daily values are available.

The Schroeder et al. submission based on May/June melt ponds is 5.5 million km2.  I think that is rather high.  For what it's worth, my own guesstimate in last month's forum poll (on June 9th) was 5.0, and for this month's poll I'm thinking to post a similar value, probably a bit lower. 

[ChrisReynolds]

As described in my submission the 2007 to 2012 residuals were used because of the clear difference of atmospheric set up after 2007. This was broken in 2013, I omitted that year as an outlier, the main problem with including that year is that it makes the range so large there is little point in making a prediction - after all one could make a prediction with bounds being 3.0 to 6.0M km^2 - which would be certain to be successful, but offer no information (i.e. low information gained).

The trick is trying to implement some understanding of what is happening in the Arctic to make predictions that test the theory relied upon to formulate the prediction, on the basis that prediction is the purest test of a theory.

In that sense my prediction was testig two theories -
1) The decline in area and extent is due to the decline in volume.
2) After 2007 a new weather pattern has asserted itself that has enhanced summer ice loss.

This year is cooler. However so far the SLP is looking far more like 2007 to 2012 years than a 2013 type year. It is possible that my conclusion that we had got rid of the 2013 volume pulse will prove to have been too hasty.

The daily PIOMAS data was only updated to day 120 (end March), so unfortunately as it's not been updated since then I have been unable to use it. Otherwise I would have, I have the code to use daily data and provide a daily breakdown of volume into regions for the available data, 2000 to 2014.

[DavidR]

My  SIPN prediction for July  is displayed in the following graph.  The dates listed are based on averages achieved in 2011-2013.  At 14 July  extent had just past 1.60m so I  expect the July 16 figure to  be about 1.64.



As you  can see the prediction put 2014 extent above 2013 for just  this week, which is where it is. 2012 was predicted to be 800 k km^2 lower and 2011 550 k Km^2 lower. 
The actual  5 day average figures for Jul 12th has 2014 only 500 k Km^2 behind both 2011 and 2012 indicating that 2014 is actually melting significantly  faster than the model predicted compared to  both 2011 and 2012. 

[DavidR]

The actual  values for July are shown here. As you can see so  far the projection matches the reality pretty well!


2011 (34cm) and 2013 (40 cm) melted fast  in the first  two  weeks of July  while 2012 (25 cm) and 2014 (~27 cm) were relatively  slow.  However 2014 started a full 10 cm ahead of 2013 which  is why they are currently  close.

[OSweetMrMath]

I have to admit I'm confused by your sea ice prediction graph. The x axis is labeled as average ice thickness loss, in meters, but you talk about the graph like the x axis is time. I can't interpret the graph, so I don't understand your predictions.

[DavidR]

OSweetMrMath
As each 10 cm of ice thickness melts out a certain extent of ice is lost. The first graph plots the expected sea ice extent as each 10 cms in the PIOMAS  April distribution (shown in my earlier post) melts out.  The dates provided are average correlations with the actual extent in 2011-2013.  In the last three years the July 16 correlations were 1.64, 1.57, 1.67.  2014 is currently above 1.60m
The July 1 correlation is 130 cm and for Aug 1st its 182.
 The second graph shows the actual melt from July 1 to July  30.

[OSweetMrMath]

Let me try to restate your thinking, as I understand it. The sea ice starts with a certain thickness at every point, and then over time the thickness decreases by the same amount everywhere. When the lost thickness equals the starting thickness at a location, the ice has melted at that location and that location no longer contributes to the sea ice extent.

The top graph shows the ice extent corresponding to a particular thickness loss. Thickness loss is more or less constant year to year, so you can predict how much thickness loss will occur by a future date based on previous years' losses.

Thickness loss so far this year is consistent with previous years. But because of the distribution of the ice, there is a relatively large extent right now, but the extent will plunge to record lows by the end of the season.

The second graph shows the extent changing by time, which supports your prediction for the melt pattern.

Assuming that summary is basically correct, I have two questions. First, where are you getting your thickness loss data from? I would expect that to come from PIOMAS, but they only update monthly and you have a thickness loss number for July 16th.

Second, the radically different shape of the extent vs. thickness loss graph for 2014, compared to previous years, implies that the ice has a fundamentally different character this year. If that's true, what reason is there to expect the thickness loss to be consistent with previous years?

[sofouuk]

another question is whether the ice really melts in the way that DavidR thinks it melts - I doubt it, tho that doesn't necessarily make the model useless. if something like the predicted later season losses does occur it will be impressive

[DavidR]

If you look at the fourth post in this thread, I  have presented the April PIOMAS data for thickness as generated by Chris Reynolds for the past  4 years.  You  can see that at  various low thicknesses (eg 0.4 - 0.8m)there was a lot  more ice in 2012 than in 2014. 

I  start  by estimating the extent each 10cm of thickness represents.  I  then produce a prediction  by successively  subtracting those amounts from the NSIDC average extent for April.  To  get  my  loss estimates I take the 5 day NSIDC average and calculate where that sits on the prediction.
The prediction says that  1.5 m of loss will result in 8725 k Km^2 and 1.6m of loss will result in an extent of 8293 k Km^2.   On 13 July the 5 day NSIDC average was 8334 k Km^2 so I estimate that  at 1.59 m lost.

I am only using an average, I  don't actually think that the rate of loss is consistent everywhere. The PIOMAS data makes it clear that the thicker ice melts more slowly, and the varying rates of loss over summer make it  clear that weather has an important impact,. However I  find it interesting that  by Aug 1st the thickness lost  calculated by  my  method only varies from 1.77 - 1.85 m.  After August 1st anything can happen, as the variation is 18 - 52 cm  in just  3 years.  My SIPN prediction is based on an estimated 30 cm after that date.

[crandles]

Let me try to restate your thinking, as I understand it. The sea ice starts with a certain thickness at every point, and then over time the thickness decreases by the same amount everywhere.

IIUC:
I am not sure he is assuming that exactly. An alternative which is also incorrect to some extent is that the thinnest ice is always on the outside of the pack and the outside of the pack is the only ice that melts.

These two versions are extremes - slice the histogram horizontally or vertically. It is of course nearer to being accurate if you slice off the histogram at an angle.

First, where are you getting your thickness loss data from? I would expect that to come from PIOMAS, but they only update monthly and you have a thickness loss number for July 16th.

I think it is coming from extent data not PIOMAS.

Second, the radically different shape of the extent vs. thickness loss graph for 2014, compared to previous years, implies that the ice has a fundamentally different character this year. If that's true, what reason is there to expect the thickness loss to be consistent with previous years?

Yes, at April there was a greater area of ice of thickness that can melt out. The thinner ice melts out by mid July and then there is nearly twice the area of previous years so presumably this goes nearly twice as far into the pack where it melts at a slower rate, but the model assumes it melts at the same rate so that it all melts out.

Furthermore, subsequent to the April PIOMAS data we have May PIOMAS data showing that ice of the thickness that can melt out in August has been melting at a slower rate than previous years but the model has not been adjusted for this.

Is this a reasonable summary of the situation?

[DavidR]

Crandles,
I think you're over-complicating it.  I  am not making any assumptions about how the ice melts or where it is. My  prediction is addressing the questions. 

If all the PIOMAS areas that were less than m.cc mtrs thick, in April, melted out,  how much extent would be left?
If the extent on a certain date was X K km^2 what thickness loss in the model would account for that loss of extent?

Putting those two together gives a prediction that is, up until July 16th, close enough to reality to suggest it has some value.

[crandles]

I wasn't saying you were making any assumption. I was just pointing out to OSMrMath that there were a range of ways the histogram could be sliced that would all be consistent with your assumption of the thinnest ice melting out first.

Slicing horizontally clearly melts too much volume, slicing vertically clearly melts too little volume so it is more sensible to think in terms of a sloping line. This sloping line may well change shape over the course of the season. Presumably calculating the volume loss from vertically slicing the histogram wouldn't be too difficult then comparison to PIOMAS volume loss figures would give an indication of how much of the volume loss is melting the thinnest ice and how much of the volume loss goes into thinning the ice that hasn't melted out at that stage. This might be useful?

Your model can be stated simply as you have done. However if someone asks if they are understanding it correctly, there might be a slight nuance to their understanding that might requires more detailed explanation. Also, to explain where I think the model is going wrong also requires more explanation. So there can be reasons for extra explanations which is not necessarily 'over-complicating it'.

I think your model does well in the early part of the melt season. You have said that anything can happen in August. This doesn't necessarily mean that random weather dominates in August and it is impossible to predict better with other prediction methods.

You have said your model expects an average melt rate. We know that we have had slow volume loss so your model expects high volume loss to catch up to average. I think the slow volume loss can be attributed to 1) relatively high area and 2) area being high relative to extent meaning low level of holes in the pack. So I think the low volume loss was predictable and is set to continue.

You seem to be restating what your model does and saying it is doing pretty well so far rather than addressing questions and criticisms of the model. I am not quite sure whether you are brushing aside the criticisms with a response that your model is doing well so far or whether the lack of response means you are accepting the criticisms or whether you want to see the outcome before declaring what you think of the criticisms or something else?

[DavidR]

Crandles,

I  sort of think of it as a piece of string attached to the thickest ice.  As I  pull on the string the thin ice disappears quickly but the thicker ice hardly  varies.   

My perception is that global warming is highly  important  up until the beginning of August , but that  after that  weather is the important  input.

I  am not brushing aside criticism, simply  trying to  restate the simplicity of the model.   We don't have low volume loss,  we have predictable volume loss.  We have lost  more volume than the model predicts.   Extent  loss is greater than the model predicts. 

You  say that the model does well in the early  part  of the melt  season, but when does the 'early  part' stop.  The model predicts that  2013 extent will  be lower than 2014 extent  in the current  week as it is. When do  you  expect the model to  stop reflecting reality and if I  may  say  so  what  evidence do you  have that  it  will. 

Neither of us will  have any  corroborating  evidence until about Aug 1st when I  predict  SIE  will  be lower than 2012.  If I  am wrong we can  discuss why I  am wrong  but  you  present no evidence to  support  your claim that  I  will  be wrong.

My  only  claim is that the model is reflecting  reality and therefore it must  be presenting  a valuable  reflection  of reality.

If the rest  of the melt season is 'average' then the extent  loss will be spectacular. 
 

[crandles]

We don't have low volume loss,  we have predictable volume loss.  We have lost  more volume than the model predicts.   Extent  loss is greater than the model predicts. 

You  say that the model does well in the early  part  of the melt  season, but when does the 'early  part' stop.  The model predicts that  2013 extent will  be lower than 2014 extent  in the current  week as it is. When do  you  expect the model to  stop reflecting reality and if I  may  say  so  what  evidence do you  have that  it  will. 

Neither of us will  have any  corroborating  evidence until about Aug 1st when I  predict  SIE  will  be lower than 2012.  If I  am wrong we can  discuss why I  am wrong  but  you  present no evidence to  support  your claim that  I  will  be wrong.

My  only  claim is that the model is reflecting  reality and therefore it must  be presenting  a valuable  reflection  of reality.

If the rest  of the melt season is 'average' then the extent  loss will be spectacular.

>"We don't have low volume loss,  we have predictable volume loss."
Agreed

>"We have lost  more volume than the model predicts."
I prefer to look at all the volume loss not just the volume loss in the parts that have melted out.

>Evidence
I have previously linked to Rob Dekkers model using (extent-area) and extent.

http://neven1.typepad.com/blog/2013/07/problematic-predictions-2.html

I have also in past years done analysis of correlation of volume loss in the latter part of the season with cumulative area in the earlier part of the season. While far from perfect, for the latter part of the season they do show good correlation with over 30 years of data. I should dig this out but I think it represent evidence that August and September loss is more predictable than your model is able to do.

When does it diverge? Sorry I am not providing a specific date but my answer is that it already has in the way(s?) I expected. That needs some explanation. If there is lots more area than usual that is of a thickness to melt out next then the area reaches further into the ice pack than in previous years and will likely take longer to melt out. Similarly if there is less area than in previous years, it should take less time to melt out. Therefore compared to your predictions, I expected the extent to melt out faster at the start of the season than your slow predictions and slower towards the end of the season.

In addition to this the area is relatively high compared to the years you are comparing with and (extent-area) is low. This means that I expect the volume decline to be slower than normal. For the early part of the melt season the two effects work against each other and they can largely cancel out. For the latter part of the season the two effects combine.

That is what I expected. Now how does the evidence stack up? The extent decline is pretty close to what you expected while PIOMAS shows the volume decline being slow.

This doesn't mean I am right, we both seem to be seeing evidence in our favour. (Might just be that the predictions are not much different for extent so far but maybe confirmation bias by one of us is perhaps also involved?)

I am not trying to criticise to be be nasty. Just saying it is good doesn't spur development.

[ChrisReynolds]

A lot depends on the compactness decreasing, must admit I've not had the chance to look at that for days. But CT Area anomalies are still on track for a re-run of 2013, I think they'll drop but not by so much as to mean massive losses (above normal losses) in the rest of the season.

Sticking to NSIDC Extent. Here are the Sept average extents from 2000 to 2007.

Actual monthly avg of daily NSIDC Extent   
2012   3.370
2007   4.161
2011   4.330
2008   4.555
2010   4.599
..............5.000
2009   5.055
2013   5.077
2005   5.318
2002   5.625
2006   5.749
2004   5.776
2000   5.944
2003   5.972
2001   6.568

Taking the 16 July 2014 extent of 8.073, I've taken the losses from 16 July in each year to minimum (daily) from 2000 to 2013, and applied those losses to the current 16 July extent. The results are in order of projected low, as in the above table of annual minimum.

Projected Loss   
2012   3.836
2008   3.938
2004   4.356
2002   4.375
2007   4.410
2010   4.482
2000   4.557
2009   4.615
2005   4.634
2003   4.808
2011   4.849
..............5.000
2013   5.111
2006   5.334
2001   5.617

I've noted where 5.000 would come in each series. Putting blinkers on and restricting to NIDC Extent this suggests we'll finish 2014 somewhere in the top 6 lowest years.

Doing a similar calculation between 16 July daily Extent and NSIDC September Extent and only 2007, 2008, 2012 fall below my upper bound June SIPN prediction of 4.62. I do not expect that to be successful. Putting the projections in order (as above but using Sept extent).

September extent projections
2012   4.097
2008   4.114
2007   4.549
......SIPN June upper bound: 4.62.
2004   4.630
2002   4.711
2010   4.813
2005   4.885
2000   4.933
.....Withdrawn SIPN July upper bound: 4.94
2009   4.950
2003   4.986
2011   5.148
2013   5.384
2006   5.505
2001   5.799

My withdrawn July SIPN prediction would have had an upper bound of 4.94, that would have stood more of a chance.

[OSweetMrMath]

Okay, my revised understanding of DavidR's model is that in April, the volume data is used to determine the extent of ice of a given thickness. Then, the extent loss by a particular future date is approximately equal to the the initial extent of ice less than a specific thickness. The relationship between the date and the thickness used to estimate the extent loss is more or less constant from year to year.

The model as stated is not making any physical predictions about where or how the ice melt occurs. Instead, it is based on the correlation between initial ice extent by thickness and the observed extent later in the season.

This appeals to me more than my previous understanding of the model. I tend to think that there's enough uncertainty in the entire system that precise predictions of the melt process are unlikely to be accurate. A prediction based on observed correlations rather than a detailed ice melt model may be less informative, but it is more likely to be robust.

That said, I'm still concerned that this year's distribution is sufficiently different than previous years that the observed relationships may not continue to hold. The fact that the predicted behavior is different than previous years, with a much greater extent loss predicted for the next several weeks than has been previously observed, suggests to me that the model may be overfitting the data.

On the other hand, my general prediction for ice loss is that at some point the ice will have a generally unpredicted collapse in volume. There will be future years which look like 2007 or 2012, and most observers will not see them coming. It could be that DavidR's model will hold, and this year will set a new record minimum extent. Put me on the side that doesn't see it coming. My prediction is still that this year will be below 2013, but well above 2012 or 2007.

[DavidR]

Yes the question is very much how robust  the model is. 

If reality gets close to my prediction for Aug 1, I  might extend the data set for next  year if not it will just  be a failed hypothesis.

[DavidR]

Unfortunately, as at  July 16th my  SIPN prediction remains on track.    
The table below compares the actual  July  16th , 5 day  average for NSIDC extent and the predicted values after 1.6 m of PIOMAS thickness loss.
The original model suggested that  the thickness loss on July  16th would be 1.62 m,  in 2014 it was 1.64.    

2011      2012       2013       2014  Year

7.749     7.487     8.250     8.293  Model 1.6 M Loss

7.525     7.616     8.080     8.073  NSIDC Jul 16th 5 Day Average

-0.224      0.129     -0.170   -0.220  Variance

Three of the four years have a variation from the Model of between 170 and 224 K km^2 lower than the model , only 2012 had an extent significantly  higher than the prediction. 

I  find it remarkable that after three months of melt the predicted values are so close to  reality and particularly that  2011, 2013 and 2014 are so  close they are essentially  identical.

[crandles]

The 1.6 to 1.7m thickness band has more volume/area for 2014 than 2012, but little difference. It is after the 1.7m that there is more than double the area. David do you expect this to melt away at twice the rate 2012 melted away? It seems to me that the other years in Chris Reynolds graph that you used also had substantially more area of this thickness yet it was 2012 that melted volume at the fastest rate.

Expecting the rate of volume melt to be double the fastest previous year seems a little extreme. It might be tenable if there had been a lot of thinning of the ice 1.7-2.1m thick but I think the indications are that the thinning has been slow.

Your prediction after 1.7m is so substantially different that we will soon see.

[DavidR]

Crandles,
I  am just  presenting the data in an understandable way. You  can see from the histogram,  that  there was much more ice between 0.4 and 1.0 m  and also  between 1.2 and 1.6 in 2012 than in 2014 and these periods coincide with the periods when 2012 melt  has exceeded 2014 melt.  Between 1.6 and 2.2 m of thickness there is vastly  more extent (2.6 M Km^2 more ) this year  than existed in 2012 and I  expect  most of this to  melt out this year.  If it  melted out  at half the rate of 2012 , 2014 would be  below 2012 by  Aug 16th.

My model  shows 2012 as having the fastest  loss of thickness over the next  15  days,  28 cm  versus 15 for 2013 and 17 for 2011.   However 2012 had less than half the volume of ice to  lose at that  thickness  than 2014.  So even if the next  two weeks in 2014 is as slow as 2013, we should expect extent  to  drop to  6.7 M km^2, which is above the 2012 figure of 6.33.  However if 2014 melts as fast  as 2012 the extent would drop to  5.2 m Km^2.  which is more than 1.1 M km^2 below 2012. 

My estimates are based on averages,  and clearly  the std deviation is very high even at this point.  I  haven't altered my  estimates from information that  was available in April, and I  see no point  in changing them now.   

I  thought this exercise was useful precisely  because the thickness distribution in 2014 was markedly  different from 2012.  So far the model  has matched reality. We are now getting to the crunch and its going to  be interesting to  see how the end game plays out.  An average result  from now until the end of the melt  season would validate, or invalidate my model.  Anything wildly  different from the model will  not  tell us much. 

My  prediction for extent,  if we had a year  like 2012, is that  we would be lucky  to  have an extent that didn't start with a 1,  such is the volume of ice thickness left  in the Arctic.   

[DavidR]

Crandles,
One of the things to  consider is that  my  model  assumes the maximum possible ice retention.  It  assumes  that  we progressively  loose the thinnest  ice. 

If however we lose less thinner ice and some thicker ice to  acheive the same extent then the volume of ice lost must  be greater.

A simplistic example . If we lose 1,000,000 km^2  extent of 1 metre thick ice that  equates to  1000 km^3 of volume, if however we lose the same extent  of 2 metre thick ice that  equates to  2000 km^3 of volume.

The best case scenario for ice retention is the one used by  my  model all the rest are worse and make the likelihood of further extent  loss more probable.

[DavidR]

July  22nd, and one could consider my  predictions as being highly unlikely. However because my  primary  metric is the April PIOMAS thickness the current position is that  thickness loss will  need to  be less than 2/3rds of that occurring in 2012 for the August 1st  extent to be greater than 2012 extent. 
After that extent drops much  more easily than in 2012 for several 10's of centimeters total thickness  loss.

[crandles]

because my  primary  metric is the April PIOMAS thickness the current position is that  thickness loss will  need to  be less than 2/3rds of that occurring in 2012 for the August 1st  extent to be greater than 2012 extent. 

At the end of June volume per PIOMAS was 14.632 (day 181 2014)
on day 181 2012 PIOMAS volume was 12.295

On 1 August 2012 (day 213) volume per PIOMAS was 6.538 so to catch up we would need to lose volume of about 8.094 versus the 2012 loss of 5.757 so 40.5% more volume loss than 2012

I think 2012 will have been one of the higher volume losses so 13.5% more than that seems unlikely to me.

To take things to extremes: Suppose histograms showed 20 time more volume of a certain thickness in one year for one of your 10cm bands than another year. Would you expect the rate of volume loss to be anywhere near 20 * faster in that year compared to the other. (You seem to expect 2.5* more ice of certain thicknesses to mean 2.5* faster volume melt.)