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Dave C

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Volume Predictions.
« on: April 08, 2013, 08:55:37 AM »
This is my initial attempt to make a simple ice model that can make near-term ice volume predictions as measured by PIOMAS. My current prediction for minimum ice volume this year is 3.21k km3. Volume loss does not seem to be following an exponential decrease, but a slowing linear decrease.

My general hypothesis is that 2007 permanently changed ice patterns in the arctic. Arctic ice is a moving target. Every preceding year is less likely to reflect current conditions. An accurate assessment is a balancing act between measuring the actual system and having enough data points. Also, the trends in summer and winter are different enough that I think you should look at them separately. The sun seems to have an increasingly large effect on melt, which means that summer/winter trends are diverging. If you do overweight the recent past then the trend lines(relative to 10 or 30 year) for ice melt are decreased since we have been on a slight ice melt plateau over the last 5 years.

I also tend to focus on the quantified metrics. I'm sure some details are important but in general I assume that various less measurable tendencies will be roughly reflected in the primary numbers. This could be falling prey to the availability fallacy but to adequately look at every factor would be a full time job. This could certainly change in the future, but in the last few years the statistical predictors seem to have done better than the "measure all the details" predictions.

In the last 10 years there have been 2 huge years, 7 average years and 1 recovery year.
Winter tends to get ignored, but accounts for almost as much variation as the summer melt season. 2007 and 2010 had very low winter recovery. They were well on their way to a huge loss by this time of year. By contrast, 2008 and 2013 have had easily the highest winter volume gains. 2008 was the only recovery year. 2013 is pretty unlikely to gain 600 km3 like 2008, but is even more unlikely to be a record shattering year like 2007 and 2010. 2013 is currently on pace to tie the volume gain record, gaining about 18.7 with the likely maximum volume being close to 22.

Arctic Sea Ice Volume by PIOMAS
Year---Avg----Max----Min---Melt---Gain
2003---19.0---27.3--10.2---17.1---16.5
2004---18.5---25.8---9.9---15.9---15.6
2005---17.9---26.2---9.2---17.0---16.3 
2006---17.2---25.2---9.0---16.2---16.0
2007---15.5---23.9---6.5---17.4---14.9 
2008---16.6---25.2---7.1---18.1---18.7
2009---16.1---25.1---6.9---18.2---18.0
2010---14.0---23.4---4.4---19.0---16.5
2011---13.2---22.0---4.0---17.9---17.5
2012---12.7---21.9---3.3---18.7---17.9

-There seems to be a step-change after 2007 in winter gain through January.
-Recovery in winter is counter-cyclical. The years following big volume losses have tended to have larger gains.
-Summer melt does not seem to be affected by volume losses or winter gains.
-Recovery has been increasing. Volume losses are occurring because summer melt is still larger.
 
This graph is of adjusted winter volume gain and summer melt. Red is melt, blue is gain. Curved lines are 2 and 3 year moving averages. The two steeper lines are the 10 year linear trends. The 3 other lines are 5 or 6 year trends. Each grid line represents a year, with the dots from 2003-2013. The Y axis is in .5 increments.

http://s16.photobucket.com/user/iciclespike/media/ice.jpg.html?sort=3&o=0

Summer loss seems to have plateaued, as reflected in the 2 and 3 year moving average. For this reason it fits the data better to use a 5 year linear trend to predict summer melt rather than a 10 year linear or exponential trend. The prediction for this year is 18.65k km3 of melt.
There is a correlation between winter gain and the previous year's volume loss with a -1 slope. So when looking at winter gain trends you need to add the previous volume anomaly to reduce noise. Winter gain is increasing, but is harder to predict since it is more variable than summer loss. None of the linear curves seem to fit well. If I had to guess I'd predict a slope between the 6 and 10 year slope with gain and loss converging around 2015.

If you assume that this winter wasn't a large deviation from current trends then winter gain is increasing faster than recent summer gain. If these trends hold then the arctic ice would stabilize in the next few years. Of course this will be temporary, with the global heat increase eventually overwhelming the primary negative feedbacks of less sun and higher winter freezing.

Why cracking probably won't have a large effect-
-Ice is always flowing, whether there is cracking or not. This video shows ice flow over the years. Notice that ice always flows through the strait, even in winter.
http://www.climatewatch.noaa.gov/video/2011/old-ice-becoming-rare-in-arctic
-There has been very little increase in yearly ice volume through the Fram strait as ice has gotten thinner. Faster ice movement seems to have been equally balanced by less available ice(especially less multiyear ice) to exit the strait.
https://sites.google.com/site/arctischepinguin/home/piomas/grf/fram.png
-There was extensive cracking in winter of 2008. That year was the only recovery year in the last decade. It's possible that cracking only indicates thin ice, and is not an indicator of a large melt.
-The AMSR2 diagrams show less ice in the Fram strait than in February and only slightly more than a couple weeks ago. The NSIDC shows that ice is currently average in the Fram strait. These two results seem to indicate that there is not much extra ice transport right now.
-Ice cracking in the winter increases volume. February was a record shattering month for ice gain, yet the temperature was not that far below average. So ice loss due to cracking will have to overcome the extra ice gained by cracking in the winter.

My guess is that the ice cracks before it melts every year. But if the sun isn't shining then it seems that it would not make a difference whether the ice cracks in February or April. As a mild concession to cracking, I'll predict .1k km3 additional expected volume melt this year.

I think the volume anomaly graph supports my claims about melt trends-
https://sites.google.com/site/arctischepinguin/home/piomas/grf/piomas-trnd3.png

-The ice anomaly pattern in winter vs summer is increasingly diverging. This adds to the reason to consider winter and summer separately since different processes are occurring.
-Less multiyear ice, ice area and thinner ice means that the solar cycle has a stronger effect, as seen by the steeply downsloping trends in the last few years that match the solar cycle. That the remaining ice is closer to the north pole should also increase the solar effect.
-There is less ice to melt later in the summer and the solar decline is larger so the VA slopes up more.
-More ice regrows in the winter, so the VA slopes up more at the end of the year.
-Transport does not seem to be having an effect. Transport should vary with weather, but variation in the VA is going down. This is partly why I am skeptical that the arctic will have a huge melt year this year.
-While weather seems to be having less of an effect, it still can produce variation. February of this year was probably the largest February ice gain on record. You can also see a downward blip caused by the storm last August.
 
This year the linear trends and an exponential or ice cracking model are making significantly different predictions. I'm currently predicting 18.75k km3 of melt. An exponential trend is predicting 20, which is much higher than the previous record high of 19.0. If melt is higher than 19.5 I'll admit that I was wrong and that this year is different than all previous years. However, if melt is under 19.0 then that would cast  doubt on the exponential and ice-cracking theories.

My model is pretty simple. It's likely that there is some complex curve that fits the data better. However, if the inputs really are changing by year then no amount of curve fitting will guarantee accurate predictions unless you find a way to predict the underlying factors. I've looked for measurable, predictable factors that could reduce the standard error in the ice volume trend predictions. I haven't been able to find much. It might be that whatever is causing the ice loss is not currently quantifiable.

ChrisReynolds

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Re: Volume Predictions.
« Reply #1 on: April 08, 2013, 10:07:31 AM »
That's not a model, you've not even factored in the confidence ranges.

"Summer loss seems to have plateaued, as reflected in the 2 and 3 year moving average. "

How about understanding why the summer loss has changed and what that may mean for this year and the future?  Never mind.  :-X

Dave C

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Re: Volume Predictions.
« Reply #2 on: April 08, 2013, 02:27:23 PM »
As far as I'm aware, there are no good models of arctic ice loss. We haven't reached the point where it is worth the bother to include confidence ranges.

I make a lot of verifiable statements in my post. How about explaining which ones you think are incorrect? Or, if you think you have a better prediction, how about posting it?

Obviously I am an amateur just trying to figure out how arctic ice works. But given their utterly embarrassing track record the professionals have no room for arrogance.

Wipneus

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Re: Volume Predictions.
« Reply #3 on: April 08, 2013, 04:05:29 PM »
Quote
This year the linear trends and an exponential or ice cracking model are making significantly different predictions. I'm currently predicting 18.75k km3 of melt. An exponential trend is predicting 20, which is much higher than the previous record high of 19.0.

I disagree using to using the word "significant" here. Exponential decline has a confidence range that is at least -2 to +2 [1000 km3]. Even if your current prediction has no uncertainties to speak of, the two predictions do not differ "significantly".

Richard Rathbone

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Re: Volume Predictions.
« Reply #4 on: April 08, 2013, 04:34:01 PM »
The problem with not quantifying confidence ranges, is that come next year either you can say you would have been right, but for some weather event, or a critic can say you would have been wrong apart from some weather event.

You need to give reasoning not just for why you think a particular loss will happen, but reasoning for how far either side of that could be down to the weather. That could just be a standard deviation around a trend, or some mechanistic argument about just how much extra energy could be absorbed if the skies were extremely clear/cloudy at the right/wrong time.

Without that, in 9 months time, when you come to look at the performance of your model, you don't know whether you got the prediction right from weather cancelling out bad mechanics in your model, or you got it wrong due to weather confounding good mechanics.

A melt of 19 wouldn't cast any doubt on the exponential trend, except in the eyes of a denialist, because its well within the range of normal weather driven variation. If a melt of 19 was combined with the type of weather that  is associated with high melt, then it would give reason for closer examination, but without additional context, 19 is one of the possible melts for this year being predicted by the exponential trend.

Its key in developing a model, not just to know where you think the outcome will be and why, but also to know how far out you could be and why. How large a bet would you place on the melt being 19.5 or less? (I'm not actually offering to bet, but thinking about it is a good way to get your mind into the gear of just what your confidence ranges are).

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Re: Volume Predictions.
« Reply #5 on: April 08, 2013, 04:51:42 PM »
Although the topic is welcome I miss the physics. I think looking at volume loss without estimating yearly export, bottom melt and radiation all attempts are close to line chart gymnastics. Saying the sum of all three drivers will be close to last year can't be that wrong. On the other hand you're 60% right by saying tomorrow's weather will be like today without any model.

Sure, there is no data and I wish there were not seven but seven thousand IMB buoys drifting in the ocean. At least the professionals give more and more insights how models fail to capture reality: http://www.the-cryosphere.net/7/555/2013/tc-7-555-2013.pdf

Here the ensemble suggests volume loss will flatten soon, but the authors wanted to know why exactly and revealed some interesting connections. (quite some math included)

Jim Hunt

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Re: Volume Predictions.
« Reply #6 on: April 08, 2013, 05:38:17 PM »
Hi Dave,

If you're interested in discovering more about some of the complexities involved in developing useful models of sea ice volume you might wish to take a good look at some existing threads on here, such as:

http://forum.arctic-sea-ice.net/index.php/topic,108.0.html

and/or

http://forum.arctic-sea-ice.net/index.php/topic,155.0.html

 :-X
Reality is merely an illusion, albeit a very persistent one - Albert Einstein

Richard Rathbone

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Re: Volume Predictions.
« Reply #7 on: April 08, 2013, 06:24:41 PM »
Thats a nice piece of work, a***. Using the models as a way of teasing out mechanisms, which is just the sort of thing they should be good for.

Richard Rathbone

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Re: Volume Predictions.
« Reply #8 on: April 08, 2013, 08:46:03 PM »
My take away quote from the West et al paper

"Given the causes discovered, we cannot conclude, from the HadGEM1 projections, that a slowdown in ice loss is to be expected soon, particularly as the slowdown has already started in the present year of the experiments. However, the model has provided clues as to what mechanisms might be causing a slowdown, with one to be observed at any point in the future."

i.e. they reckon the ice is probably soon gone but are covering themselves just in case reality starts throwing up the features seen in the models which result in keeping the ice for rather longer.


Bob Wallace

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Re: Volume Predictions.
« Reply #9 on: April 08, 2013, 09:59:58 PM »
Where is this slowdown seen?

Certainly not in the PIOMAS annual minimum.

eta:  And not in the PIOMAS monthly figures.  There was a small up-bump during the winter of 2012 but by the end of the melt season a new record low was reached.  The up-bump of this year could simply be more noise in the system.

(It takes, what, 18 years to establish a global temperature trend?  There's a lot of noise in the ice system as well.  Probably best to not make too much out of short term variability.)
« Last Edit: April 08, 2013, 10:06:09 PM by Bob Wallace »

ChrisReynolds

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Re: Volume Predictions.
« Reply #10 on: April 08, 2013, 10:05:17 PM »
Interesting paper and conclusion.

Pursuing my interest in autumn/winter volume increases in response to low sea ice area, I'm wondering if there will be a reduction of winter and summer losses in the next few years.

I've taken the year, split it into melt and growth periods, and used past behaviour to derive some equations for seasonal loss and gain. Combining those equations to create a 'toy model' reveals a oscillatory tail when sea ice volume response to area at minimum is factored in, and a crash when it's not.
http://dosbat.blogspot.co.uk/2013/04/long-tail-or-fast-crash.html

Richard Rathbone

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Re: Volume Predictions.
« Reply #11 on: April 08, 2013, 11:43:39 PM »
I think you need more than just maximum volume as a determinant of summer melt. I have a strong suspicion you'd find a much better correlation with time than maximum volume, but the answer you'd get from putting that in your simple model is that its all going to go any year now. Why don't you include something of your open water formation efficiency investigations into how you model the melt?

I don't like using a small effect to drive a large effect in the crudest part of the model. The last thing you want is to have maximum gain in the part of the system you are least certain about. The September volume is changing faster than the March volume, so you can live with modelling the freeze in a relatively crude way.  Your model is more sophisticated in how it treats the freeze, but the observations call for a model which is more sophisticated in how it treats the melt.

crandles

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Re: Volume Predictions.
« Reply #12 on: April 09, 2013, 12:55:59 AM »
I think you need more than just maximum volume as a determinant of summer melt. I have a strong suspicion you'd find a much better correlation with time than maximum volume, but the answer you'd get from putting that in your simple model is that its all going to go any year now.

I would suggest both a linear time component and an exponential decline based on linear dependance on maximum volume seems the most physically plausible suggestion without introducing too many parameters.

The answer you get from that is an even steeper decline than just an exponential fit.

Dave C

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Re: Volume Predictions.
« Reply #13 on: April 09, 2013, 07:00:52 AM »
If you have a 4.5k km3 confidence interval, why bother to make a prediction at all?

The standard deviation of my graph for melt is .42, the largest deviation .73. There isn't enough data to assume a normal distribution, but I would be surprised if melt was over 19.5.
As for ice cracking, according to this chart only 1k km3 of ice gets transported through the Fram strait during the melt season. That is of course a tiny fraction of the annual melt. Even if we had a huge transport year then it would still be unlikely to significantly affect overall volume loss.

Another interesting fact is that 2010 had much lower ice transport than 2008, 2009, 2011 and 2012, yet was the record breaking year for volume melt. The likely reason is that each year ice transport is subject to a strong negative feedback. The less ice there is, the less ice will flow through the fram strait. 2010 started with significantly less ice. That is also the reason that JulyAugustSeptember transport is so low each year.
https://sites.google.com/site/arctischepinguin/home/piomas/grf/fram2.png

Re the cryosphere paper- What I was thinking about doing was to try to assign some sort of weight to each factor that affected ice loss. But if ocean heat transfer is the dominant factor then this seems hardly worth the effort. I can't think of any simple way that ocean currents could ever be modeled/measured. Rather ironic though that the model in this paper agrees with me that arctic melt is going to slow in the near future.

It remains to be seen whether this is a real slowdown or not, but I don't remember anyone predicting 6 months ago that we would have record ice gain this winter.
« Last Edit: April 09, 2013, 07:32:27 PM by Dave C »

anonymous

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Re: Volume Predictions.
« Reply #14 on: April 09, 2013, 10:53:21 AM »
It remains to be seen whether this is a real slowdown or not, but I don't remember anyone predicting 6 months ago that we would have record ice gain this winter.

Dave, since you are predicting even less volume for this summer, doesn't that include even more gain next winter?

crandles

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Re: Volume Predictions.
« Reply #15 on: April 09, 2013, 12:06:28 PM »


Larger: http://farm9.staticflickr.com/8224/8334481723_947248554a_b.jpg

I think the light orange and light green are reasonable fits for the orange and green lines being melt and maximum respectively.

Why only use the last 10 years when using data back to 1979 gives a clearer indication of the shape.

Extrapolating curves is dangerous and you need all the help you can get which is nicely shown by

this


Dave C

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Re: Volume Predictions.
« Reply #16 on: April 09, 2013, 04:49:14 PM »
Arcticio-No. I am predicting the opposite. My formula for winter gain is the winter gain trend(which I'm still working on) - this year's volume anomaly. So years with less volume loss have less winter gain the next year. The expected volume for 2013 based on the trend line was 2.6. I am predicting 3.21, for a positive anomaly of .61. The expected value based on my tentative winter gain line was 18.5. So my current prediction for winter gain next year is 17.89, much lower than this year.

Crandles- Those curves look similar to what I am predicting. Based on them what would you predict for summer ice loss and winter gain this next winter?

I use the last 10 years since I think that the inputs affecting arctic ice are different now than they were 10-30 years ago. Also, if the curves aren't linear, I am less likely to get the slope wrong if I cut off data past 10 years ago.

Richard Rathbone

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Re: Volume Predictions.
« Reply #17 on: April 09, 2013, 06:19:24 PM »
You misread the paper.

The modellers are wrote up a detailed examination of why their model predicts a slowdown in ice loss. They look at what happens in the model to cause this, and what is happening in the real world, and conclude that their model is unlikely to reflect reality.

Their model predicts a slowdown in ice loss, but they don't.

They are modellers saying the same thing as data extrapolators. They don't believe the model predictions for slowdown in ice loss either.

ChrisReynolds

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Re: Volume Predictions.
« Reply #18 on: April 09, 2013, 07:41:38 PM »
Richard,

I am working on the OWFE stuff. Yes you do need more than max volume for summer melt, hence the low R2, however it seemed a reasonable version 1 first order proxy for the presence of MYI, as the volume loss has been virtually exclusively from MYI. I am pondering looking at the issue of MYI fraction using June area (~10M km^2) minus previous year's minimum area to give a ballpark index of MYI. I am pondering other refinements as well.

Crandles,

I want to avoid time domain dependence altogether. This is because I want to project beyond current conditions using the assumption that whatever feedbacks are to come are already active. My previous claim that area/extent decline is merely epiphenomenal of volume decline has led me to concentrate on volume as the core of the 'model'.

Is this worth doing a separate thread on?

Dave C,

The graph Crandles presented shows that maximum volume and seasonal melt converge in 2017. In other words it projects a virtually sea ice free arctic in that year (+/- a bit) and increasing open water periods during summer thereafter.

crandles

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Re: Volume Predictions.
« Reply #19 on: April 09, 2013, 07:52:55 PM »
Those curves look similar to what I am predicting. Based on them what would you predict for summer ice loss and winter gain this next winter?

Maximum estimated with trend having both linear and exponential component:

2012 21.813 Unfairly close to actual of 21.923 because 2012 data used in tuning
2013 20.988 Clearly too low having already reached 21.612 so sensible to assume this decline is too fast
2014 20.094
2015 19.126
2016 18.075

Melt volume depending solely on linear function of max volume giving an exponential pattern:
22.78 - 0.213*max vol

So 2013 22.78-.213*20.988 = 18.31
2014 22.78-.213*20.094 = 18.50
2015 22.78-.213*19.126 = 18.71
2016 22.78-.213*18.075 = 18.93

This gives minimum volumes of
2013 2.68
2014 1.59
2015 0.42
2016 -0.85

I don't believe it will be that fast for a number of reasons including:

1. Ice over deeper water may well have lower upward heat flux and be harder to melt
2. So far have melted areas that have net transport of ice out of those areas. Where there is net transport in, it will be harder to generate open ocean because that keeps getting filled with ice from other areas.
3. A lot of melt happens around edge of pack with wave action etc. As the ice retreats the length of the edge declines so the rate of volume loss may decline. This seems supported by the volume anomalies reducing after June.

Maximum this year will be higher than the trend prediction of 20.988 which could be some of these effects coming into play.

I don't have a good feel for the strength of these effects nor can I see sufficient data to try to extrapolate them.
 

ChrisReynolds

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Re: Volume Predictions.
« Reply #20 on: April 09, 2013, 09:36:31 PM »
Crandles,

I've tried incorporating some normally distributed noise (sigma that of detrended sea ice area) in the sea ice area in the model, scroll down the pink bands to the bottom set and you'll find it. I wanted to know what effect it would have and if it could lengthen the decline, it can but it also brings about Tietsche et al like resurrections of the ice in about 3 to 4 years, which IIRC is similar to the recovery time in Tietsche et al. Another ammendment is that when volume at min tries to drop below zero it is set to zero to stop the model crashing with a physically untenable state.

Spreadsheet here.
https://docs.google.com/file/d/0B3pB-kdzoLU3YWs3U0lNV2xITG8/edit?usp=sharing
Press F9 to update which re-seeds the random numbers (or weather).

Dave C

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Re: Volume Predictions.
« Reply #21 on: April 10, 2013, 04:05:18 PM »
Crandles-

If you make a conservative assumption of 21.8 max this year, then your model seems to be predicting a 3.66 minimum volume this year.

Even I wouldn't go that high. Do you think that melt increases at all as volume goes up? Would you make other adjustments to your model when anomalies happen?

Considering the high value it predicts this year and the negative feedbacks you've mentioned, would you consider changing the equations you use?

Maybe I'm overweighting this year. My impression though is that your equations are too conservative in the next couple years, but too aggressive after that.

crandles

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Re: Volume Predictions.
« Reply #22 on: April 10, 2013, 07:19:32 PM »
The maximum is going to be close to 21.8 this year which will be above trend. That will flatten the trend so that the 2014 maximum prediction will be above 21 and it will take longer to get down to 18.8 where it practically melts out. That with other factors I mentioned agrees with your ' too aggressive after that'.

The 2013 prediction of 2.68 may well be aggressive for 2014. So I don't think I agree with too conservative for 2014 or 2015.

The melt pattern is practically flat up to 2007 then turns upward as volume declines. So we only have 5 years data after the flat part. An extra years data can therefore make a significant change in perception of amount of upturn in volume melted.

As volume further declines, there is less ice at edges to melt but more time where the melt can get at central areas. I think this make it hard to be sure the pattern I am trying to extrapolate will continue.

As for 2013 predict at 3.66 that is 0.4 above 2012 when the last PIOMAS volume number is almost the same as 2012. With the cracking this year, I can imagine that the minimum volume might be less than 2012 but I can easily imagine it being 0.4 above. So 3.66 might be a little high but I don't really see any reason to think it is way too high.

Richard Rathbone

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Re: Volume Predictions.
« Reply #23 on: April 10, 2013, 08:39:34 PM »
Chris

Ice goes down faster in your model than reality, because the melt has been accelerating in reality but you are using an average in your model.

You are starting from conditions about 35 years ago, using averaged melt rates appropriate perhaps to 15 years ago and consequently the melt is more aggressive at the beginning in your model than it was in reality. (and you have the opposite problem at the end of it being too ready to slow down or bounce back).

ChrisReynolds

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Re: Volume Predictions.
« Reply #24 on: April 10, 2013, 09:11:03 PM »
Richard,

Using a best fit from a full set of data doesn't necessarily mean you're using the average from the middle of the set. In this case the pulling ahead of recent years may be having such an effect. But that isn't really what I set out to do, I was interested in how the melt season and freeze season processes interact, and if the freeze season gains were powerful enough to overcome melt season loss increases and cause a tail to sea ice.

Up to now I've used a quadratic, but have been doing some more thinking today about whether I can see any physical justification for that. I can't. It seems to me that the increase of volume gain due to low sea ice at the end of the previous season should be linear, assuming no change in equilibrium growth thickness of sea ice, a reasonable assumption as long as winter warming doesn't increase too much. Winter thinning has been occurring, but much of this is due to loss of MYI.

When I use a quadratic equation it has a tendency to overcome melt season losses leading to a longer time to zero, and pulsed recoveries thereafter. When I use a linear equation (ax +b) the freeze season gains are not enough to overcome the melt season losses, and the sea ice crashes to zero about 4 to 5 years earlier, the end being a very rapid loss of ice by the annual minimum. By adding noise in the form of an offset to sea ice area (normal distribution sigma that of detrended CT Area), the timings and loss profiles vary significantly.

I am now pondering whether it is possible to get a more physics based approach to work. But I am not interested in modelling sea ice, merely trying to get a handle on whether we face a fast crash or a tail.

Richard Rathbone

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Re: Volume Predictions.
« Reply #25 on: April 10, 2013, 10:27:40 PM »
For tail vs. crash, I look for factors that close the energy balance as the ice decreases.

The arctic is accumulating heat. Why would it stop accumulating heat? Not only is it accumulating heat, the trend is that as ice goes down, rate of accumulation goes up.

Less ice means more freeze, but it also means even more melt.

ChrisReynolds

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Re: Volume Predictions.
« Reply #26 on: April 11, 2013, 09:44:11 AM »
True to Arctic system is gaining heat, but more open water at the end of the season might act to counter that. We'll have to wait and see. Key to the issue is how early open water appears and I think we'll see an exciting experiment on that issue in Beaufort this year, despite the influx of MYI that's happened over the winter.

wanderer

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Re: Volume Predictions.
« Reply #27 on: April 11, 2013, 10:44:35 AM »
So total volume is about the same it was last year - but comparing sea ice thickness it
doesn't look the same at all:

April 7th 2012:

April 7th 2013:

And let's not forget that CO2 and methan concentrations are higher than last year...

wili

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Re: Volume Predictions.
« Reply #28 on: April 11, 2013, 05:02:00 PM »
Thanks for those maps, W. Keep in mind that even that thickest ice is cracking, so it is probably not quite as solid ice as it used to be. I think this is likely to be true throughout the icepack. Everything is newer, saltier, and less solid.

Another point that neven highlighted on the blog, Tremblay (iirc) in the fourth video on the recent blog post, at about the 20th minute, points out that the evaporation and heat loss from leads leads to a kind of chimney effect that draws heat up from over 100 m below. That is this phenomenon draws the warm Atlantic water, that is usually stratified far below the ice, up next to the bottom of the sea ice, thus weakening the ice further, leading to more cracking, and more 'chimneys'...a classic feedback.

What I'm wondering if anyone knows whether there are measurements of how much warmer that under-layer of  warm water of ultimately Atlantic origin is than it used to be. Should this mechanism play a role in models for ice loss?
"A force de chercher de bonnes raisons, on en trouve; on les dit; et après on y tient, non pas tant parce qu'elles sont bonnes que pour ne pas se démentir." Choderlos de Laclos "You struggle to come up with some valid reasons, then cling to them, not because they're good, but just to not back down."

Dave C

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Re: Volume Predictions.
« Reply #29 on: April 12, 2013, 01:54:24 PM »
You can make an approximate "safety zone" based on the most likely shape of the minimum ice extent. There is more doomed ice by the islands, but less in the Beaufort and Chukchi areas. There is less ice in the Fram, and there seems to be slightly less ice in danger of being exported from the Fram. Overall there appears to be slightly more ice in the danger zone than last year.
However, you also have to consider ice flow into/out of the danger zones. My guess is that the influence of the Beaufort area is overrated. It is more likely that the extra ice surrounding the islands will slow ice movement than less ice/more cracking in the Beaufort will increase ice movement. There is a decent chance that the increased ice in the melt zones will be roughly balanced by lower transport through the Fram strait.

http://s16.photobucket.com/user/iciclespike/media/piomasthicknessdifference.jpg.html?sort=3&o=0

http://s16.photobucket.com/user/iciclespike/media/2012.jpg.html?sort=3&o=2

http://s16.photobucket.com/user/iciclespike/media/2013.jpg.html?sort=3&o=1

ChrisReynolds

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Re: Volume Predictions.
« Reply #30 on: April 12, 2013, 07:46:49 PM »
"You can make an approximate "safety zone" based on the most likely shape of the minimum ice extent."

A reasonable proposition. But how do you come to the most likely region at minimum?

crandles

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Re: Volume Predictions.
« Reply #31 on: April 12, 2013, 07:57:57 PM »
"You can make an approximate "safety zone" based on the most likely shape of the minimum ice extent."

A reasonable proposition. But how do you come to the most likely region at minimum?

Ice over 1.67m thick in March and not near land at low latitude? Perhaps with adjustment for drift?

ChrisReynolds

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Re: Volume Predictions.
« Reply #32 on: April 12, 2013, 09:11:40 PM »
Crandles,

I'm not convinced it's that simple, try the last three years, green line is September ice edge (PIOMAS).







What I've been looking at is a combination of DAM and PIOMAS over 2m (my blue area). I'm pondering that DAM multi year ice seems to correspond with regions that melt out slowly if at all by the end of the season. But this doesn't account for large regions of FYI that hasn't melted by the end of the season, which is where the ice over 2m thick seems to come in. But it's all speculative and I really need to see how this year turns out.

I wonder whether it would be worth calculating the statistical occurrence of melt out (zero thickness for a grid cell) for initial thicknesses, at what point does the probability drop, and how does it drop?

EDIT - one area we could simplify is the Atlantic, as those plots show it can be considered an invariant edge, as an approximation.

Dave C

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Re: Volume Predictions.
« Reply #33 on: April 12, 2013, 10:40:54 PM »
"You can make an approximate "safety zone" based on the most likely shape of the minimum ice extent."

A reasonable proposition. But how do you come to the most likely region at minimum?

I just looked at the september minimum for the last 6 years, with the shape most heavily weighted towards last year. I forgot to shift it to the right based on current ice patterns, so for the most accuracy you would shift it slightly.

ChrisReynolds

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Re: Volume Predictions.
« Reply #34 on: April 13, 2013, 10:42:16 AM »
Dave C,

Not unreasonable, as I think you have noted earlier; it is important to use post 2007 years as arguably this is a new regime. One possible issue I see is the role of MYI in last year's record.

In 2012 ice recession was delayed by the large region of low concentration ice off Siberia. The DAm shows this to have been associated with a remnant of MYI.
ftp://ccar.colorado.edu/pub/tschudi/iceage/gifs/age2012_31.gif

My argument is that this delayed melt will have impacted the minimum, saving ice from melt that would have occurred if the MYI wasn't there.

We'll see a test of whether this argument is correct because the MYI is much more concentrated this year, with much more FYI across most of the pack, by March the thickness distribution of 2013 is far more thin biased than in previous years. All of which means that contrary to your position I expect a new area record this year (1.75 to 2.00M km^2 CT area daily) .

PIOMAS Volume/CT Area = calculated thickness.

This metric is just under 1.5m thick around the time of minimum, therefore that implies around 3 to 2.6 k km^3 PIOMAS volume at time of minimum for 2013, based on my area estimate.

Dave C

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Re: Volume Predictions.
« Reply #35 on: April 22, 2013, 06:53:43 AM »
Chris,

I haven't really looked at area and extent much. I want to look at the correlations between volume, area, extent, thickness, shape, etc before making any predictions. Since I am currently predicting a new volume record(barely), I suppose it's possible that I would predict a new area record.

Your volume prediction of about 2.8 isn't that far from my prediction of 3.2. A lot of people seem to think this is going to be a monster melt year though. I don't agree, which is why I made this thread.
« Last Edit: April 25, 2013, 06:19:33 AM by Dave C »

ChrisReynolds

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Re: Volume Predictions.
« Reply #36 on: April 23, 2013, 06:16:37 PM »
Dave,

Sorry for not replying earlier.

I've made myself very unpopular when I ridiculed people's claims that we could see an ice free June or July. So I've decided to let such people be educated by the ice itself.

I agree, it's not going to be as great a loss as some claim. For much of the pack ice conditions aren't that much different from last year, and the fracturing has been due to a combination of thin ice and the low AO over the winter. link. Where I do think we'll see something remarkable is that I see a strong role in previous melts for MYI. This year the MYI extent is at record lows and is not spread throughout the pack where it can retard melt. Furthermore the FYI that's grown in the leads opened up during the late Feb / early Mar fracturing will melt early forming leads in the pack.

But none of this adds up to ice free this year. As I've said elsewhere; if NSIDC monthly average for Sept is under 1M this year I'll stop blogging. I won't be stopping blogging because it's not going to happen.

crandles

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Re: Volume Predictions.
« Reply #37 on: April 24, 2013, 02:13:40 PM »


Larger: http://farm9.staticflickr.com/8519/8678052864_d69f582e1d_b.jpg

March volume over 0.8m thick has a better correlation than volume over 0.7m or 0.9m with minimum PIOMAS volume. (Or any other volume over xm thick shown)

Volume over 0.8m shows a very slight decline from 2012. Volumes over smaller thicknesses do not show such a decline.

However, I think it can be seen that a previous years minimum volume is a better indicator of volume over xm than volume over xm is an indicator of the next minimum volume.

Despite that, one approach is to use a linear fit of volume over 0.8m. A different approach looking at correlation of each cells thickness with minimum volume in order to use this to weight the changes in thicknesses of each cell similar to Lindsay and Zhang ( http://www.arcus.org/files/search/sea-ice-outlook/2011/06/pdf/pan-arctic/lindsayzhangpanarcticjune.pdf ) Surprisingly? this doesn't seem to work as well as volume over 0.8m. Or maybe I have yet understood Lindsay and Zhang properly yet.

Both these seem to overestimate the minimum thickness for years 2007 onward. So perhaps some further reduction in those estimates is required. So I may fit a curve and use residual from trend in volume over 0.8m to estimate the residual from trend of the fit of the minimum volumes.

Quite a few further things to try yet.....

But comment are welcome.

ChrisReynolds

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Re: Volume Predictions.
« Reply #38 on: April 24, 2013, 07:27:35 PM »
I'll reply tomorrow Crandles, tired so am going to have a night off.

Vergent

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Re: Volume Predictions.
« Reply #39 on: April 24, 2013, 08:21:36 PM »
CRandles,

Nice graphic, but;



How do you account for the disparity between yours and Chris's >2.0m volumes? Chris shows a 2.5k decline over last year. Also, you are showing a slight '79-13 decrease in <2.0m volume(total volume minus >2.0m volume). Chris shows a two fold increase(from 7k to 14k).

Am I misreading something here? Is Chris using > and you using >?

Vergent
« Last Edit: April 24, 2013, 08:42:28 PM by Vergent »

crandles

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Re: Volume Predictions.
« Reply #40 on: April 24, 2013, 08:44:03 PM »
Chris Reynolds over 2m category counts all the ice volume where the ice is over 2m thick. You can tell that because 14.25+6.47 = 20.72 = volume for Mar 2013.

My version is only counting the excess over 2m thick. (i.e. (Thickness - 2m)*area )

My figure for volume for March 2013 in excess of 2m = 1.399807 K Km^3
I have the area where thickness is over 2m as 2.538173 M km^2

2*2.538173 +1.399807=6.476152

Chris's figure of 6.476153 seems to agree exactly.

Basically I am using a childishly simple assumption of xm melted from all locations and any surplus heat where thickness is less than xm does not melt any ice. I have calculated these x thicknesses as:

1979   1.16672
1980   1.19612
1981   1.39164
1982   1.09065
1983   1.10815
1984   1.16688
1985   1.21084
1986   1.083
1987   1.2126
1988   1.2073
1989   1.1797
1990   1.2683
1991   1.32515
1992   1.10714
1993   1.39995
1994   1.20674
1995   1.39575
1996   1.02725
1997   1.2232
1998   1.3277
1999   1.3276
2000   1.2703
2001   1.1374
2002   1.2705
2003   1.3026
2004   1.221
2005   1.3473
2006   1.2832
2007   1.424
2008   1.414
2009   1.4324
2010   1.6325
2011   1.5414
2012   1.669

Fitting a 4 parameter exponential trend through this gives a thickness melt of 1.773 for 2013. Using that gives larger error bars than other methods but I may yet find the residuals from trend in this to be in some way a useful estimate of residuals from a gompertz fit of minimums with time.

Re Edits: Sorry about earlier silly information in last paragraph. I has used a 3 parameter exponential when I needed a 4 parameter exponential to look anything like sensible.
« Last Edit: April 24, 2013, 09:31:27 PM by crandles »

Vergent

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Re: Volume Predictions.
« Reply #41 on: April 24, 2013, 09:32:14 PM »
CRandles,

That clears it up. Thank you. An interesting new partition of data.

Vergent

SATire

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Re: Volume Predictions.
« Reply #42 on: April 24, 2013, 11:52:31 PM »
just 2 comments on the predictions:

First, if PIOMAS simulated volume is declining a bit further this year (e.g. like the exponential, the gompertz or even linear - the difference doesn't matter significantly at all now), that would be no surprise since that is just the trend of the last years.

Second comment: Since e.g. the trend for Sept. volume is allready quite close to zero (allready this year within 95% confidence margins), everything but a record low in observables like area or extent would be a surprise. Volume just can not be close to zero without area/extent also.

The most probable reason for missing a record low area or extent therefore could be that PIOMAS simulation is just not right - the real ice volume could be very well different from the volume modelled by PIOMAS. To be clear - "volume prediction" here is a prediction of a sea ice volume predicted by a model, which is not proven yet. That is double uncertainty of course - loosing any ground to real observables. Please do not get me wrong, I "like" PIOMAS predictions because of plausibility in the past - but it is not an observable, nature is different of course.

So - if PIOMAS would be right - the trend of PIOMAS volume represents a soon crash of extent and area. Just because zero volume results in zero area and zero extent and if math is worth something, the decline of the latter must be way steeper than the former considering a definite thickness of ice to be recognised. 

If you instead prefer to rely on observables - area and extent from satellites should be used and thickness determined by measurements must be applied. In that case the negative feedback has been allready observed seen since 2007 - the autumn zero will be reached soon and spring zero is very unlikely any time soon. And of course the formulars inside PIOMAS would need to be adjusted to match reality in that case. Nature will tell us in 10 years what is right - therefore the last chance to predict something useful is now and the future of nature will jugde. I go with the crash of area and extent because I bet on the PIOMAS trend.

crandles

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Re: Volume Predictions.
« Reply #43 on: April 25, 2013, 12:22:45 AM »
The most probable reason for missing a record low area or extent therefore could be that PIOMAS simulation is just not right - the real ice volume could be very well different from the volume modelled by PIOMAS. To be clear - "volume prediction" here is a prediction of a sea ice volume predicted by a model, which is not proven yet. That is double uncertainty of course - loosing any ground to real observables. Please do not get me wrong, I "like" PIOMAS predictions because of plausibility in the past - but it is not an observable, nature is different of course.

If you instead prefer to rely on observables - area and extent from satellites should be used and thickness determined by measurements must be applied. In that case the negative feedback has been allready observed seen since 2007 - the autumn zero will be reached soon and spring zero is very unlikely any time soon. And of course the formulars inside PIOMAS would need to be adjusted to match reality in that case. Nature will tell us in 10 years what is right - therefore the last chance to predict something useful is now and the future of nature will jugde. I go with the crash of area and extent because I bet on the PIOMAS trend.

Yes I agree there is a important distinction between a prediction of the actual ice volume and a prediction of what the PIOMAS system is in due course going to say the volume is. It is easier to get closer to the latter and I think that is what I am trying to do in this thread and a thorough post on what I was doing should have addressed this. Oops  :-[ sorry.

I see this as a first stage. Once I have predicted 'what the PIOMAS system is in due course going to say the volume is' then I will attempt a conversion to area and extent. It may or may not be better to try to estimate area or extent directly but you have to attempt to both ways to gain a good idea. (And then you are probably wrong because you haven't found the best tricks, err I mean techniques  ;) )

>"And of course the formulars inside PIOMAS would need to be adjusted to match reality"

Don't forget that PIOMAS does assimilate information from satellites like SST and ice extent, so that already has the effect of pulling PIOMAS towards reality.

ChrisReynolds

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Re: Volume Predictions.
« Reply #44 on: April 25, 2013, 08:17:51 PM »
Given that PIOMAS is the most comprehensive and detailed proxy for volume it seems to me to reasonable to proceed with using it. However PIOMAS may not be giving a correct measure of volume. There are of course two outcomes of this given PIOMAS current trends: 1) Real world area crashes to zero giving PIOMAS an unexpected volume crash because PIOMAS was over projecting volume, or 2) A tail appears, in which case it may take years to determine whether this tail is due to ice dynamics in the real world or PIOMAS under projecting volume. Either way the regular assimilation of SIC means PIOMAS won't show no ice when there clearly is some, or ice where there clearly isn't.

Crandles.

I must admit I'm struggling to grasp exactly what you're doing. Surely if you're checking agreement between ice volume for thicker than 0.8m and the long term net volume decline you're going to be picking up the preferential decline in thick ice, this alone would increase any agreement over the long term (assuming you're talking about agreement of trend).

Similarly you say: "Volume over 0.8m shows a very slight decline from 2012. Volumes over smaller thicknesses do not show such a decline." smaller thickness would just pick up the net increase in volume for total ice column thickness of <2m thick.

So I suspect I'm not following you at all.


crandles

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Re: Volume Predictions.
« Reply #45 on: April 26, 2013, 12:04:38 AM »
Hi Chris, see my comment saying

My version is only counting the excess over 2m thick. (i.e. (Thickness - 2m)*area )

You are using a cookie cutter on a plan of the ice. I am slicing it height wise.

I am not checking agreement, I am looking for ways of doing a volume prediction per title of this thread.


I am trying to use the location/ distribution of volume information available for March 2013 and previous Marchs' to better estimate September 2013 minimum volume per PIOMAS. Any techniques that might usefully use that information to arrive at a better PIOMAS volume estimate can be discussed here. I am starting with a childishly simple attempt to find a better correlation with minimum volume than time or total volume. If better correlation can be found then perhaps an estimate of PIOMAS minimum with smaller error bars can be made.

Basically I am using{/starting with?} a childishly simple assumption of xm melted from all locations and any surplus heat where thickness is less than xm does not melt any ice.

The number derived by doing this is not going to be perfect.

However it does turn out that the volume in excess of 0.8m in March turns out to have a better correlation with the minimum volume than the total March volume correlation with the minimum volume. So perhaps it is better to use the volume in excess of 0.8m thick to estimate the minimum volume than to use total volume.

Other adjustments might well further improve the correlation. I have some ideas for a more complex version than the childishly simple assumption which seems to have some benefit but I am far from saying I have optimised these yet. Before going into these I want to see if you follow what I am doing.

Agres

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Re: Volume Predictions.
« Reply #46 on: April 26, 2013, 04:04:59 AM »
The volume of ice is going to fall off the charts.

These days, what really counts is the total surface area of the ice (e.g., is it fractured into little pieces) and how much heat can be transported into the Arctic.  With Eurasia, North America, North Pacific, and the North Atlantic all acting as solar collectors for the Arctic basin, local incident radiation is not the most important factor.  And, ice export (to the south) is really heat import from the south, as warm water (from the south) flows in to replace the exported ice.  Some of that warm water from the south is sun warmed runoff from Eurasia and North America, and some is North Atlantic Drift flowing in under the fresher surface water. 

These days, plumes of water vapor, from the equatorial Pacific, hitting the south coast of Alaska and Western BC, are now warmer and wetter.  More heat is getting over the mountains and into the Arctic proper.  There were days last winter when Fairbanks Alaska was warmer than the Napa Valley in California.

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Re: Volume Predictions.
« Reply #47 on: April 26, 2013, 04:54:23 AM »
........... There were days last winter when Fairbanks Alaska was warmer than the Napa Valley in California.


There were also many mornings in February, this year, that Narsarsug, Greenland was much warmer than where I live in the Hill Country of Texas!!

We are entering, or have entered, a completely new climate regime for the entire Northern Hemisphere.  In the past, transitions between climate regimes were measured in centuries and averaged over decades.  Now we may well be in a state of transitioning between climate regimes on an annual basis.  This makes predictive modelling difficult, if not impossible, since there is no  stable baseline from which to compare current events.
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ChrisReynolds

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Re: Volume Predictions.
« Reply #48 on: April 26, 2013, 07:58:16 AM »
Crandles,

Thanks. I got what you were saying, should have been clearer, my problem is in trying to grasp the physical meaning behind it.

"However it does turn out that the volume in excess of 0.8m in March turns out to have a better correlation with the minimum volume than the total "

I still have the feeling that your 0.8m break point may be showing a better correlation with max volume in large part because most of the past preferential loss of thicker ice. As we're entering a new phase of FYI dominance, I wonder whether correlations derived over the former period will hold up so well in the latter.

crandles

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Re: Volume Predictions.
« Reply #49 on: April 26, 2013, 01:45:52 PM »
Crandles,

Thanks. I got what you were saying, should have been clearer, my problem is in trying to grasp the physical meaning behind it.

"However it does turn out that the volume in excess of 0.8m in March turns out to have a better correlation with the minimum volume than the total "

I still have the feeling that your 0.8m break point may be showing a better correlation with max volume in large part because most of the past preferential loss of thicker ice. As we're entering a new phase of FYI dominance, I wonder whether correlations derived over the former period will hold up so well in the latter.

It shows a better correlation with max volume because the data is from the same period. I suspect you meant it shows better correlation with previous minimum than next minimum. Yes I agree with you there is a risk that the correlation becomes less good. However, I think we can get to better physical reasoning that might keep the relationship sensible.


As I indicated it is childishly simple to assume 0.8m melts from all locations. The good thing about it is that it is a single parameter to tune and little overfitting risk.

More realistically there a couple of potential improvements:

1. Less thickness melts when the ice is over 2m thick than when it is 1.5m thick because of higher albedo meaning less heat is absorbed.
2. When ice is 0.1m thick rather than 0.8m thick, it melts out quickly and builds up heat from solar absorption. While there is only 0.1m in that cell to melt, the heat may help melt ice in nearby cells by water traveling under ice and/or further away by heating atmosphere and winds travels over ice.

We could end up with a formula for predicting the volume that remains looking something like

if(thickness>variable1,(Thickness-variable1)+((thickness/variable1)^0.04-1),0)+(max(0,0.3-thickness))^0.2

If variable1 is a fixed 0.8m for each year then there are 4 parameters (variable1=0.8, 0.03,0.3, and 0.2). That is rather high even without having the 0.8m increase each year. The third part does not seem to help much so I may drop the third part to implement an increase in variable1 with time.

I have a lot to do yet to try to optimize this (while trying not to overfit it). So to attempt some discussion before going down the wrong path seemed sensible.


With more realism added as discussed above then I hope it is possible that there will be better correlation with next minimum rather than last minimum. In past, area of minimum was a good indicator of area of MYI which was thick and therefore a good indicator of volume in excess of x metres at next maximum. That becomes less good as MYI disappears, but the physical reasoning I am basing my prediction on shouldn't get worse and may get better as the ice is more homogeneous FYI. Is the curve getting smoother? It looks as if it might be, but maybe I am biased because I am working on it.