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Ned W

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Volume vs extent, by the numbers
« on: July 26, 2017, 05:59:01 PM »
The "extent vs volume" problem keeps coming back.  I thought we could use a thread that looks at that problem from an empirical, quantitative angle.  There are other angles (which metric is "better" or "more important" or whatever) but I won't address those much here.

In this post I'll use monthly mean data on volume (PIOMAS) and extent (NSIDC).  It will be a very long post.

First, let's look at the relationship between June and September monthly means, and use that relationship to forecast the 2017 September mean for each metric:


Fig 1.


Fig 2.

(If I'd waited a week to do this, we could have a more accurate forecast using July instead of June numbers, but for now let's go with this.)

To show them on the same graph, we can scale them to their respective 1980-1989 baselines.  In other words, each data point here shows the September monthly volume or extent in year X, as a fraction of the average September monthly volume or extent during the 1980s:


Fig 3.

Clearly the two series seem to be diverging.  This is a problem because when volume reaches zero, extent should also be zero. 

The trend lines in Fig 3 are simple quadratic extrapolations.  Note the following:

  • Both the linear and quadratic terms are highly significant for both the volume and extent models. 
  • One could create alternative versions of this post using other models for extrapolation -- linear, Gompertz, etc. -- but for now I will just use quadratic models in all cases, for consistency. 

Each year, when a new September data point is added, those extrapolations change -- sometimes a little, sometimes a lot.  Let's look at the history of those changing extrapolations:


Fig 4.

In Fig 4, the left-most data point in each series (2002) represents the extrapolated year in which September ice volume or extent first reaches zero, based only on data through Sept. 2002.  The next data point represents the same forecast using data through Sept. 2003, and so on.  The end of the solid line is the most recent "real" forecast (using data through Sept. 2016) and the dashed line gives the estimate of what it would look like when 2017 is added.

Clearly, the two series, volume and extent, are giving us very different stories about what the future looks like:

Using PIOMAS volume, a naive quadratic extrapolation suggests that we will have an ice-free September around 2022.  There are two important points to remember:
  • This is the monthly average, not the daily minimum.
  • This is actually zero ice, not some other nominal threshold.
So that is a forecast of literally no ice for the entire month of September, in only five years from now.  (It's worth noting that as recently as 2011 and 2012, this PIOMAS-based extrapolation was forecasting an ice-free September in 2017, i.e., this year.).

In contrast, using NSIDC extent, the same quadratic extrapolation suggests that a totally ice-free September won't happen until approximately 2041.

Worse yet, over the past decade the gap between volume and extent has been widening, not narrowing:


Fig 5.

In 2008 there was only an eight-year gap between the two forecasted "zero years", but now that gap is up to 19 years.

Figure 6 summarizes the recent years' forecasts for ice-free conditions in September, with the (expected) 2017 forecasts in solid gold (volume) and solid green (extent):


Fig 6.

It's of course possible that the PIOMAS-based forecast could be completely correct, in which case extent decline would have to speed up dramatically over the next five years. 

Alternatively, it's also possible that the NSIDC-based forecast could be completely correct, in which case the volume decline would have to slow down by a lot.

Another possibility is that both series converge on an intermediate date for the first ice-free September.  That could happen many ways; two examples are shown in Fig 6. The solid blue dots show weighted averages of the 2017 forecasts -- one using equal weights (i.e., a simple average of the 2017 forecasts from PIOMAS and NSIDC) and the other weighting each series based on its historical variance in forecast dates.  Because PIOMAS has less variance in its recent past, it is weighted more heavily, and the "convergence" date is thus closer to 2022 than 2041.

I'm not going to get into all the various arguments in favor of one or the other (PIOMAS is just a model, not a measurement!  Extent neglects the third dimension! etc. etc. etc. ad nauseam).  I am personally inclined to doubt the PIOMAS-based "ice-free September in 2021" forecast, for the following reasons:

  • Just a few years ago it was predicting that we'd have an ice-free September this year. That seems unlikely to happen.  Its prediction for an ice-free September has been moving into the future by one year per year.
  • It seems probable that there would be individual ice-free days long before the first ice-free month, and we have not yet come even remotely close to a single ice-free day.
  • It seems to me that the volume/extent gap would likely begin narrowing long before we reach "zero ice", but instead that gap has been widening.

Aside from not believing the "ice-free September in 2021" forecast, I'm basically agnostic about the relative credibility of PIOMAS volume vs NSIDC extent. 

oren

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Re: Volume vs extent, by the numbers
« Reply #1 on: July 26, 2017, 06:23:23 PM »
Ned, thanks for opening this thread, and thank you for your detailed post. I have been trying to figure the volume vs. extent thing for a while, especially as in how to use PIOMAS to forecast extent, and it's been very difficult.
I don't have much to add at this point, besides making some suggestions and ideas:
* Using JAXA data instead of NSIDC might give better results due to improved grid resolution. (Or might not, as PIOMAS uses NSIDC grid and concentration data).
* NSIDC monthly mean is calculated very strangely, and in addition around the minimum the average of both volume and extent hides a lot of information. I would use the daily numbers with a 7-day average around the beginning of September.
* The physical behavior is very different for Sea of Okhotsk vs. the CAB for example. And in general, for seas which were seasonally ice -free, have become seasonally ice-free, or are still far from that. Separating the calculation into regions could clarfiy some of these physics, and potentially explain the conundrum.

mhampton

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Re: Volume vs extent, by the numbers
« Reply #2 on: July 26, 2017, 07:40:31 PM »
I think the choice of linear or quadratic model is not appropriate, given that negative values don't make any sense.  Whatever model is used should at least respect that property of the data; otherwise it makes sense that ice-free predictions will tend to be premature.

gerontocrat

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Re: Volume vs extent, by the numbers
« Reply #3 on: July 26, 2017, 07:46:50 PM »
The conumdrum has been bothering me for years. I am so glad that this thread has been opened. My simplistic view is that one day thickness will decline during the melt to the point that extent has to give way. Earlier this year I thought it might be 2017. Ho hum.
BUT as the ice thins does reliabilty of volume measurements decline?
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EgalSust

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Re: Volume vs extent, by the numbers
« Reply #4 on: July 26, 2017, 10:13:09 PM »
Thanks for the fantastic analysis, Ned W! Must have been a lot of work!

If I'd dare to wish something, it would be a Gompertz-curve -based analysis. To me the IPCC models seem to look like Gompertz-ish more than anything else... Would be interesting to see if the results would differ that much from the linear-based ones...

Dharma Rupa

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Re: Volume vs extent, by the numbers
« Reply #5 on: July 26, 2017, 11:16:11 PM »
I've seen enough thin skins of ice to think it believable to have a volume close to 0 and almost 100% of the Arctic covered with ice, though I'd be more inclined to expect that in November than September.

When talking about convergence of volume and extent I think you need to question whether our measurement skills are up to the task.

oren

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Re: Volume vs extent, by the numbers
« Reply #6 on: July 27, 2017, 12:30:01 AM »
Ned your analysis inspired me to make the following, several regional graphs of the daily PIOMAS volume vs. NSIDC area for Day 250/Sep 6th.
Some insights: the relation between changes in volume and changes in area is very visible. But there seems to be another factor as well - a thinning of the surviving ice, leading to a higher area/volume ratio as the years go by.
I also note the Beaufort/Chukchi combo are "virtually volume-free most years" since 2007, when a lot of the MYI ice was lost. The ESS/Laptev combo are virtually volume-free since ~2010.  Kara/Barents are virtually volume-free since 2005.
Mind you,"virtually volume-free" is quite far from "virtually area-free".
In the CAB, area is almost flat over the years, despite the shrinking volume. The record low year for CAB area is actually 2016, not 2012. (For Sept 6th)
So the conundrum is partially explained by two factors:
* A thinning of surviving ice in peripheral seas, leading to a slower area/extent loss compared to volume loss. Eventually, remaining area/extent will catch up and crash.
* A resistance of the surviving CAB ice that has thinned by 50%, almost without losing area/extent. Yet. Eventually, area will start declining as well, but not as fast as volume.


Notes:
Why area - because I had it ready in an excel and because it might be better correlated with volume.
Day 250 and Sep 6th are shifted by 1 day in some years, but the error is negligible.
It would have been better to use a 7-day average for the area and volume, but I skipped the effort.
All of the above analysis assumes that PIOMAS has it right, and especially that it is free from a long-term bias towards lower volume.

oren

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Re: Volume vs extent, by the numbers
« Reply #7 on: July 27, 2017, 12:31:06 AM »
CAB graph.

RealityCheck

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Re: Volume vs extent, by the numbers
« Reply #8 on: July 27, 2017, 01:25:24 AM »
Hi All
I think this thread and postings to date exemplify the best of ASIF. Solid data-based analysis, interpreting data to extract information and insights, clarifying relationships, etc. Data will always have inherent limitations, so we work with what we can get. But useful insights can still be extracted. Many thanks to Ned for taking the initiative on this.
Sic transit gloria mundi

Tor Bejnar

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Re: Volume vs extent, by the numbers
« Reply #9 on: July 27, 2017, 01:38:58 AM »
Yes: great work, Ned and oren!I think oren's data can be used to create the maps I longed for in this post:
... a map outlining the several Arctic regions with a single thickness number (in meters) in each that represents the typical thickness loss for that region [edit: average for that region that year/decade], perhaps with a map for each year (or decade).  These maps might be overlain on minimum (or average minimum) extent map.
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greatdying2

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Re: Volume vs extent, by the numbers
« Reply #10 on: July 27, 2017, 03:23:01 AM »
IMHO, like all good paradoxes, the divergence between extent and volume exposes an underlying truth. In each grid cell, volume has a continuous value whereas extent is binary. Because ice splits into ever thinner pieces as it melts, extent in each grid cell flips from 1 to 0 only when the volume curve drops almost to zero.

Furthermore, grid cells are highly correlated with their neighbours, based on weather patterns and regional features (latitude, proximity to land, bathymetry, currents, etc. -- have a look at Wipneus' regional graphs).

So... why should we not expect volume to drop faster than extent -- until volume is near zero? Indeed, this is exactly what we observe in almost every region that already melts out. I expect extent to catch up to volume only when CAB volume approaches zero, and then I expect it to catch up very quickly indeed.
« Last Edit: July 27, 2017, 03:35:28 AM by greatdying2 »
The Permian–Triassic extinction event, a.k.a. the Great Dying, occurred about 250 million years ago and is the most severe known extinction event. Up to 96% of all marine species and 70% of terrestrial vertebrate species became extinct; it is also the only known mass extinction of insects.

DavidR

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Re: Volume vs extent, by the numbers
« Reply #11 on: July 27, 2017, 03:25:43 AM »
If we think in terms of the physical processes there is absolutely no reason for extent and volume to predict the same year for zero ice.  If we look at  the winter maximum extent has declined by  about 6% while volume has declined by  33% since 1979.

As an example lets start with a 1 Km^3 volume of of ice, and ignore ice less than 10cm thick as NSIDC does.  The smallest  possible value for extent and area is about 0.13 km^2 assuming the ice existed in the thinnest stable column. The largest  possible values are 10000 km^ 2  for area and around 60000 km^2 for extent, assuming well distributed pancake ice 10 cm thick. 

For the minimum values a 20% drop in volume would see a negligible drop in extent and area. For the maximum values area and extent would disappear 100%. These are obviously  extreme values and the arctic sits somewhere between them.  However it is clear that both area and extent can expand or not decrease for a long while as the volume decreases.  If we look  at the Greenland sea at the moment  we can see vast areas of fairy floss ice that has great extent but  almost no volume.

We should therefore expect predictions based on either area or extent to completely miss the year of zero extent. 

The decline in volume is based on the energy in the system, this determines the volume of ice that will form and melt each year.  With increasing global temperatures this is constantly increasing in the Arctic and the volume of ice is declining based on those figures.  The rate of volume decline since 2000 is 50% greater than the rate of decline since 1979.

With no prospect of the rate of global temperature increase declining, we are nowhere near a point of equilibrium where melt equals formation each year. In fact it is quite obvious from the trend lines that  the gap between melt and formation is increasing. Annual variations may put the zero year anywhere between 2020 and 2025 but I can't see any prospect of September sea ice after that.
« Last Edit: July 31, 2017, 12:27:39 AM by DavidR »

Dave C

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Re: Volume vs extent, by the numbers
« Reply #12 on: July 27, 2017, 01:29:16 PM »
Diverging Volume vs Extent predictions would only be an issue if ice is actually exponentially declining. It definitely is not. Even a linear decline is becoming more questionable. Since 2010 volume has not declined at all.

It is becoming increasingly untenable to use pre-2007 data to try to predict future trends. The maximum, thickness, percent melt and melt midpoint have changed a lot since then among other things.

http://forum.arctic-sea-ice.net/index.php/topic,2098.0.html

Ned W

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Re: Volume vs extent, by the numbers
« Reply #13 on: July 27, 2017, 02:16:27 PM »
Lots of great comments -- thanks.  Oren, those regional graphs seem like a good idea.  I've got some things I want to check out and test.

RealityCheck

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Re: Volume vs extent, by the numbers
« Reply #14 on: July 27, 2017, 09:36:49 PM »
Hi Ned
How would ijis data affect your results I wonder? Would the correlations be as strong? Just a thought...
PS thanks to Oren for your graphs also...
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dlen

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Re: Volume vs extent, by the numbers
« Reply #15 on: July 27, 2017, 10:26:03 PM »
I'd like to put in two aspects.
1. The thickness as parameter to make a guess for the first ice free september
2. An acceleration to be expected in the decrease of the area / extent.

1.
Look at the following plot for september values:



The mean thickness is just the ratio of volume/area.
Then look at the noise. The area graph is the noisiest, the volume graph is a bit smoother, and the mean-thickness graph has least noise in it - which is logical, because area and volume fluctuations are related and cancel out when calculating thickness.
This is the first reason to take the mean thickness as the parameter with the best predictive value.
The second is, that the vanishing of the sea ice cover is first and foremost a one-dimensional process, dominated by the heat flow from above and below. Volume or extent are only mediately connected to the process.

2.
Why is an acceleration of area decrease to be expected?
I suppose,
  • The thickness decreases more or less linearly with time,
  • The ice cap can be approximated by a more or less circular disc,
  • Its slope, i.d. the thickness decrease over distance from the center, is largest in the vicinity of the edge
Then, with a smaller ice cap, the edge proceeds more to regions with a smaller slope and the same thickness decrease - with a smaller edge slope - yields a higher radius decrease and finally a higher area decrease.
« Last Edit: July 27, 2017, 10:34:00 PM by dlen »

pikaia

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Re: Volume vs extent, by the numbers
« Reply #16 on: July 27, 2017, 10:56:48 PM »
Suppose that the thickness, length and width of the ice sheet all decline linearly. When the thickness has gone down to 50% of its original thickness, the area will have gone down to 25% of its original value, and the volume will have gone down to 12.5%. As a result it will look as if the volume is going to reach zero before the other measures, but it will not, because the curve is a different shape, and will level off while thickness continues to decline at the same steady rate.

If you want to extrapolate you should ideally use a quantity which is expected to decline at a constant rate. Area, volume and thickness do not meet that criterion, so extrapolation from them is dangerous.

Tor Bejnar

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Re: Volume vs extent, by the numbers
« Reply #17 on: July 28, 2017, 12:28:04 AM »
Visually projecting dlen's mean thickness graph suggests (to me) that 2017 ice thickness may reasonably be (at minimum) about what 2012's was (per climate change, not requiring a matching weather experience), and given volume is about the same as 2012's was (at least for the day-of-year two weeks ago), area could end up being similar to 2012, too.  (Minimum extent has a great deal to do with weather during the last month - gathering the floes in or pushing them out.)

I'd love to see the mean thickness graph for the CAB-only, as some of us think its experience will be more predictive of the future than the Arctic-wide experience.
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Let It Go

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Re: Volume vs extent, by the numbers
« Reply #18 on: July 28, 2017, 02:29:52 AM »
I'd like to put in two aspects.
1. The thickness as parameter to make a guess for the first ice free september
2. An acceleration to be expected in the decrease of the area / extent.

The mean thickness is just the ratio of volume/area.
Then look at the noise. The area graph is the noisiest, the volume graph is a bit smoother, and the mean-thickness graph has least noise in it - which is logical, because area and volume fluctuations are related and cancel out when calculating thickness.
This is the first reason to take the mean thickness as the parameter with the best predictive value.
The second is, that the vanishing of the sea ice cover is first and foremost a one-dimensional process, dominated by the heat flow from above and below. Volume or extent are only mediately connected to the process.


Great idea to suggest thickness as the main parameter.
However since we have much noise in outer regions where sometimes ice melts and sometimes it doesn't. Wouldnt it be a better idea to focus only on thickness in the CAB.  Or perhaps to even only focus on the thickness of non-FYI (that one is probably really hard to find)

I'm very interested to see what these graphs will look like.

pikaia

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Re: Volume vs extent, by the numbers
« Reply #19 on: July 28, 2017, 09:53:43 AM »
I would like to see what the graphs of thickness and volume look like if you use some power of the value, such as the square, or maybe the 3/2 power. It looks like you would get a good approximation to a straight line, which you can extrapolate with rather more confidence.

oren

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Re: Volume vs extent, by the numbers
« Reply #20 on: July 28, 2017, 10:02:26 AM »
Note that thickness graphs may very well exhibit an inflection point when the MYI is replaced by FYI. Check out the change in dlen's first chart around 2007. So an extrapolation might be problematic without taking that into account.
Regardless, I have some new ideas for analysis, will post later today.

Ned W

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Re: Volume vs extent, by the numbers
« Reply #21 on: July 28, 2017, 02:45:00 PM »
OK, I am finally catching up with some of the suggestions here.  Based on some excellent comments from Oren and others above, here's what I've done:

(1) Extracted the daily regional numbers for PIOMAS volume and NSIDC extent.  The regional daily volumes for PIOMAS were from Wipneus's file (thanks!) and I used the same set of regions to extract NSIDC extent from their daily GeoTIFF files.

(2) Averaged the daily values in the first week of September, for each year 2000-2016.

(3) Aggregated the volumes and extents for the Russian Arctic Ocean basins (Chukchi, ESS, Laptev, Kara, and Barents -- I think that's all of them, right?)  These represent a large area that still had ice in Sept 2000 but has very little ice in Sept now.  Thus, I see it as an early indicator of what might happen to the rest of the Arctic (CAB) in the future.  Aggregating the data across those five basins smooths out some of the noise and minimizes the problems of ice advecting into or out of a smaller area during the week in question.

(4) For further smoothing, used a LOESS function with a five-year time scale.

(5) Because extent and volume have different units, I rescaled all four series (volume and extent, raw and LOESS) such that the LOESS version is 1.0 in Sept 2000.  Thus, the lines represent the change relative to the smoothed extent or volume in 2000.

OK, so here's the result:



It was not exactly what I expected, I guess.  PIOMAS volume and NSIDC extent seem to have declined very similarly from 2000-2008, but then PIOMAS settles in at around 10% of its 2000 volume while NSIDC is between 20% to 40% of its 2000 extent.

Shared Humanity

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Re: Volume vs extent, by the numbers
« Reply #22 on: July 28, 2017, 03:11:22 PM »
OK, I am finally catching up with some of the suggestions here.  Based on some excellent comments from Oren and others above, here's what I've done:

(1) Extracted the daily regional numbers for PIOMAS volume and NSIDC extent.  The regional daily volumes for PIOMAS were from Wipneus's file (thanks!) and I used the same set of regions to extract NSIDC extent from their daily GeoTIFF files.

(2) Averaged the daily values in the first week of September, for each year 2000-2016.

(3) Aggregated the volumes and extents for the Russian Arctic Ocean basins (Chukchi, ESS, Laptev, Kara, and Barents -- I think that's all of them, right?)  These represent a large area that still had ice in Sept 2000 but has very little ice in Sept now.  Thus, I see it as an early indicator of what might happen to the rest of the Arctic (CAB) in the future.  Aggregating the data across those five basins smooths out some of the noise and minimizes the problems of ice advecting into or out of a smaller area during the week in question.

(4) For further smoothing, used a LOESS function with a five-year time scale.

(5) Because extent and volume have different units, I rescaled all four series (volume and extent, raw and LOESS) such that the LOESS version is 1.0 in Sept 2000.  Thus, the lines represent the change relative to the smoothed extent or volume in 2000.

OK, so here's the result:



It was not exactly what I expected, I guess.  PIOMAS volume and NSIDC extent seem to have declined very similarly from 2000-2008, but then PIOMAS settles in at around 10% of its 2000 volume while NSIDC is between 20% to 40% of its 2000 extent.

This has happened in these seas because there is essentially no MYI here anymore. What we are seeing is that the annual freeze and melt drive both volume and extent identically. If you were to include SIA in this graph, you would see that it tracks equally well with volume and SIE.

Ned W

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Re: Volume vs extent, by the numbers
« Reply #23 on: July 28, 2017, 03:31:59 PM »
Chris Reynolds's "slow transition" thread is obviously relevant to this.

https://forum.arctic-sea-ice.net/index.php/topic,933.0.html

Shared Humanity

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Re: Volume vs extent, by the numbers
« Reply #24 on: July 28, 2017, 03:38:25 PM »
Chris Reynolds's "slow transition" thread is obviously relevant to this.

https://forum.arctic-sea-ice.net/index.php/topic,933.0.html

Yes. Far more than relevant. I would call it explanatory.

Ninebelowzero

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Re: Volume vs extent, by the numbers
« Reply #25 on: July 28, 2017, 03:59:34 PM »
Good thread. Saves having to to post a "stupid question" about volume and area. :)


But  what happens when  the multiyear ice disappears from the Central Arctic? 8)

Shared Humanity

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Re: Volume vs extent, by the numbers
« Reply #26 on: July 28, 2017, 04:28:12 PM »
Good thread. Saves having to to post a "stupid question" about volume and area. :)


But  what happens when  the multiyear ice disappears from the Central Arctic? 8)

I would think the same kind of behavior with both volume and SIE expanding and contracting through the freeze and melt seasons. Count me as one who believes that year round ice free is a long way off and, after our first BOE, we could have succeeding years where substantial amounts of ice survive the melt season, dependent on weather.

Dharma Rupa

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Re: Volume vs extent, by the numbers
« Reply #27 on: July 28, 2017, 04:54:15 PM »
Count me as one who believes that year round ice free is a long way off and, after our first BOE, we could have succeeding years where substantial amounts of ice survive the melt season, dependent on weather.

All the short-term evidence agrees with you.  All the paleontological evidence is more ambiguous, but tends to disagree with you.

We live in interesting times.

Shared Humanity

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Re: Volume vs extent, by the numbers
« Reply #28 on: July 28, 2017, 05:02:29 PM »
Why do I believe that year round ice free is a long way off?

Hudson Bay is ice free annually but freezes over each winter despite being at a much lower latitude than the CAB. The Bering Sea is even a better example. Despite being very stormy and subjected to warm Pacific Ocean waters, portions of it continue to freeze each winter. The CAB will behave in a similar fashion for decades, IMHO.

magnamentis

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Re: Volume vs extent, by the numbers
« Reply #29 on: July 28, 2017, 05:27:28 PM »
Why do I believe that year round ice free is a long way off?

Hudson Bay is ice free annually but freezes over each winter despite being at a much lower latitude than the CAB. The Bering Sea is even a better example. Despite being very stormy and subjected to warm Pacific Ocean waters, portions of it continue to freeze each winter. The CAB will behave in a similar fashion for decades, IMHO.

there are only 2 or 3 users who ever seriously mentioned all year ice free and i'm not even sure whether they really meant winters included or it was a lapsus. that said of cours i think it's nothing like going out to a limb to say that it will probably take centuries for that to happen if not much longer. after all, whenever things happened in the past it took thousands or millions of years and i do not believe that humans can heat up the planet much beyond a certain point. either they will vanish and nature takes over again or the amount of energy needed will exeed any imaginable pollution.
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Dharma Rupa

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Re: Volume vs extent, by the numbers
« Reply #30 on: July 28, 2017, 05:37:55 PM »
Why do I believe that year round ice free is a long way off?

Hudson Bay is ice free annually but freezes over each winter despite being at a much lower latitude than the CAB. The Bering Sea is even a better example. Despite being very stormy and subjected to warm Pacific Ocean waters, portions of it continue to freeze each winter. The CAB will behave in a similar fashion for decades, IMHO.

You might be right, but I think Hudson Bay will freeze over in winter long after the CAB remains ice free all winter.  The Bering is more like the Hudson than the CAB.

Basically, I think deep sea swells and overturning will take over for the bulk of the Arctic well before the coastal waters can ignore the cold continents.

This is why I see the possibility of a volume near 0% with extents near 100% -- maybe, for a year or two -- although I see it just as likely that the volume and extent both crash to near 0 year round in the same year.


magnamentis

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Re: Volume vs extent, by the numbers
« Reply #31 on: July 28, 2017, 06:15:17 PM »

This is why I see the possibility of a volume near 0% with extents near 100% -- maybe, for a year or two -- although I see it just as likely that the volume and extent both crash to near 0 year round in the same year.

this is an interesting theory of yours even though i don't think so, at least not far south hudson compared to high arctic which is in the dark for months. however every theory as long as it's not proven faulty is worth to be considered a possibility and i by far can't tell. perhaps more profound input will show by the pros in this forum, oceanographers as well as by weather and climate scientists. not sure whether this topic has been explored to a level that allows for a final answer, interesting it remains.
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wili

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Re: Volume vs extent, by the numbers
« Reply #32 on: July 28, 2017, 06:30:29 PM »
"...volume near 0% with extents near 100%..."

I think this is an important possibility to keep in mind.

A very simple model would be meter square chunk of ice in the middle of a cold swimming pool. Obviously very low 'extent.'

But probably a fraction of that ice, if shaved down to slushy consistency could basically cover the same cold swimming pool.

So, in principle, and for some limited period of time, I could imagine that you could see actual increases in extent/area even as volume went down.

We're just measuring a different kind of ice then.

It is like confusing price and affordability. Before the great crash of 2008, economists were saying, "Don't worry, the price of oil/gas will inevitably come down again."

They were right, but, at least in the immediate aftermath, that wasn't much of a comfort to the millions of un- and under-employed and broke, who couldn't afford even the much cheaper gas prices.

We think of price as measuring affordability, but it doesn't always. Similarly, our 'measure' of extent no longer means quite what it used to (though it will continue to serve some of the albedo function of previous extent figures, I suppose).
« Last Edit: July 28, 2017, 06:37:30 PM by wili »
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Re: Volume vs extent, by the numbers
« Reply #33 on: July 28, 2017, 07:14:47 PM »
You might be right, but I think Hudson Bay will freeze over in winter long after the CAB remains ice free all winter.  The Bering is more like the Hudson than the CAB.

Basically, I think deep sea swells and overturning will take over for the bulk of the Arctic well before the coastal waters can ignore the cold continents.
Interesting ideas.
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Re: Volume vs extent, by the numbers
« Reply #34 on: July 28, 2017, 09:27:43 PM »
Another great graph, Ned!

A couple of things I see in Ned's (today's) graph or am guessing:
  • nearly all the ice in these regions melted out in 2012, and the following several years 'rebounded' to the 2010 & 2011 values
  • functionally, the MYI in these regions all melted out by 2007 or 2009, and hasn't rebounded
I wish we had 1990s or 1980s information for these regions:  I wonder what portion of average 1980's min. volume this century's data represents.  25%? 10?  (Arctic-wide, I've read "25%" on these threads, but that includes the CAB which may have lost proportionally less.)

Projecting these to the CAB: I think we are still on the pre-2008 downward slope.  As soon as a couple of years from now (I project), with exceptional weather, we could have a 2012-like Russian-Arctic-Seas experience - functional ice freedom.  (followed by years of non-ice-free minimums)
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Re: Volume vs extent, by the numbers
« Reply #35 on: July 29, 2017, 12:26:45 AM »
"...volume near 0% with extents near 100%..."

I think this is an important possibility to keep in mind.

A very simple model would be meter square chunk of ice in the middle of a cold swimming pool. Obviously very low 'extent.'

But probably a fraction of that ice, if shaved down to slushy consistency could basically cover the same cold swimming pool.

So, in principle, and for some limited period of time, I could imagine that you could see actual increases in extent/area even as volume went down.

We're just measuring a different kind of ice then.

It is like confusing price and affordability. Before the great crash of 2008, economists were saying, "Don't worry, the price of oil/gas will inevitably come down again."

They were right, but, at least in the immediate aftermath, that wasn't much of a comfort to the millions of un- and under-employed and broke, who couldn't afford even the much cheaper gas prices.

We think of price as measuring affordability, but it doesn't always. Similarly, our 'measure' of extent no longer means quite what it used to (though it will continue to serve some of the albedo function of previous extent figures, I suppose).

+1
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Yuha

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Re: Volume vs extent, by the numbers
« Reply #36 on: July 29, 2017, 02:03:41 AM »
Here's another simplified model:

Suppose we have ice with maximum thickness of 4 meters but having a continuum of all thickesses from 0 to 4m with equal area of each thickness, so that the ice thinner than 1m covers 25% of the area, ice thinner than 2m covers 50% of the area and so on.

Suppose then that all ice melts at equal rate in terms of loss of thickness. When 1 meter of thickess has melted, all ice initially thinner than 1m has melted completely, 2m thick ice has been reduced to 1m thick and so on.

Under this model the melting proceeds as follows:

loss of    loss of  loss of
thickness  area     volume
 25%        25%      44%
 50%        50%      75%
 75%        75%      94%
 90%        90%      99%
100%       100%     100%


So we get the kind of behaviour we are observing: volume is initially dropping much faster than area but both reach zero at the same time.

This model is obviously not a realistic model of arctic sea ice but it does suggest that volume dropping faster than area is a natural property of this kinds of systems.

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Re: Volume vs extent, by the numbers
« Reply #37 on: July 29, 2017, 04:33:29 AM »
Here's another simplified model:

Suppose we have ice with maximum thickness of 4 meters but having a continuum of all thickesses from 0 to 4m with equal area of each thickness, so that the ice thinner than 1m covers 25% of the area, ice thinner than 2m covers 50% of the area and so on.

Suppose then that all ice melts at equal rate in terms of loss of thickness. When 1 meter of thickess has melted, all ice initially thinner than 1m has melted completely, 2m thick ice has been reduced to 1m thick and so on.

Under this model the melting proceeds as follows:

loss of    loss of  loss of
thickness  area     volume
 25%        25%      44%
 50%        50%      75%
 75%        75%      94%
 90%        90%      99%
100%       100%     100%


So we get the kind of behaviour we are observing: volume is initially dropping much faster than area but both reach zero at the same time.

This model is obviously not a realistic model of arctic sea ice but it does suggest that volume dropping faster than area is a natural property of this kinds of systems.
+1
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Pmt111500

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Re: Volume vs extent, by the numbers
« Reply #38 on: July 29, 2017, 07:45:45 AM »
Here's another simplified model:

Suppose we have ice with maximum thickness of 4 meters but having a continuum of all thickesses from 0 to 4m with equal area of each thickness, so that the ice thinner than 1m covers 25% of the area, ice thinner than 2m covers 50% of the area and so on.

Suppose then that all ice melts at equal rate in terms of loss of thickness. When 1 meter of thickess has melted, all ice initially thinner than 1m has melted completely, 2m thick ice has been reduced to 1m thick and so on.

Under this model the melting proceeds as follows:

loss of    loss of  loss of
thickness  area     volume
 25%        25%      44%
 50%        50%      75%
 75%        75%      94%
 90%        90%      99%
100%       100%     100%


So we get the kind of behaviour we are observing: volume is initially dropping much faster than area but both reach zero at the same time.

This model is obviously not a realistic model of arctic sea ice but it does suggest that volume dropping faster than area is a natural property of this kinds of systems.
+1
And add in statistically determined replenishment speeds of thickness categories (then there's no need to ponder whether thick ones get ejected to warmer sands like they do in the proper models), and +- realistic melt amounts every summer (some 1st year ice still survives so it's somewhere  a bit above... say 1 3/4 m in CAB,  i guess, could be higher) to see how much slower area goes towards zero than the thickness. Extent is mainly for shipping.
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Re: Volume vs extent, by the numbers
« Reply #39 on: July 29, 2017, 08:42:33 AM »
Here's another simplified model:

Suppose we have ice with maximum thickness of 4 meters but having a continuum of all thickesses from 0 to 4m with equal area of each thickness, so that the ice thinner than 1m covers 25% of the area, ice thinner than 2m covers 50% of the area and so on.

Suppose then that all ice melts at equal rate in terms of loss of thickness. When 1 meter of thickess has melted, all ice initially thinner than 1m has melted completely, 2m thick ice has been reduced to 1m thick and so on.

Under this model the melting proceeds as follows:
...
So we get the kind of behaviour we are observing: volume is initially dropping much faster than area but both reach zero at the same time.

This model is obviously not a realistic model of arctic sea ice but it does suggest that volume dropping faster than area is a natural property of this kinds of systems.

Absolutely. And the arctic does have a distribution of thicknesses rather than a uniform surface, this is easily observable in satellite images and melt progression, and is modeled by PIOMAS accordingly.

Getting back to the discussion about CAB-only thickness, I made some charts for several dates (end-Jan, end-March, end-May and mid-July) but basically found nothing interesting - no trend, no insights except for the late area growth Jan 2016 and 2017. I believe the September CAB result is highly affected by April-July behavior in the adjacent Inner Basin seas.
I ran into several data issues:
* I am using area from NSIDC regional daily data (Sea_Ice_Index_Regional_Daily_Data_G02135), and for some reason it has different total areas of the CAB until 2007 (2.907 m km2) and since 2008 (3.185 m km2). I only present data from 2008 onwards.
* I cannot find a regional area/extent breakdown from IJIS/JAXA, not sure if it exists. I do have Wipneus' UH regional breakdown, but it only starts Aug 2012.
* I lack access to the daily PIOMAS distribution of thicknesses in each region. This could provide some insights.
If anyone can shed light on these data issues it will be much appreciated.

Pmt111500

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Re: Volume vs extent, by the numbers
« Reply #40 on: July 29, 2017, 09:39:52 AM »
I'm afraid none of these thoughts are helpful...


I ran into several data issues:
* I am using area from NSIDC regional daily data (Sea_Ice_Index_Regional_Daily_Data_G02135), and for some reason it has different total areas of the CAB until 2007 (2.907 m km2) and since 2008 (3.185 m km2). I only present data from 2008 onwards.

That's an odd one and sounds like someone has been shocked by 2007 minimum and changed the definition of CAB, maybe Barents/East Siberian/Beaufort has been simultaneously enlarged, if so this would be easily corrected?

JAXA area/extent might be used internally but deemed inferior to the NSDIC one. Provides a backup for scientists if NSDIC gets terminated as it could well be?

PIOMAS isn't likely calculated daily anyway as it incorporates a whole bunch of measurements, and some terms of employment for scientists may include non-disclosure agreements that prevent them from publishing full details. Maybe there's some shipping company that has required daily data to be secret.


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Re: Volume vs extent, by the numbers
« Reply #41 on: July 29, 2017, 10:59:12 AM »
PIOMAS isn't likely calculated daily anyway as it incorporates a whole bunch of measurements, and some terms of employment for scientists may include non-disclosure agreements that prevent them from publishing full details. Maybe there's some shipping company that has required daily data to be secret.
PIOMAS has daily data since 2000. The data is publicly available on an FTP web site, but the full files are binary and I haven't managed to crack them yet due to time and programming skill deficiencies. Instead I use those files provided by the tireless Wipneus on his website.
(Such discussion probably belongs in the Developers Corner, I'm just frustrated by lack of time to be a proper developer)

Steven

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Re: Volume vs extent, by the numbers
« Reply #42 on: July 29, 2017, 12:01:38 PM »
I ran into several data issues:
* I am using area from NSIDC regional daily data (Sea_Ice_Index_Regional_Daily_Data_G02135), and for some reason it has different total areas of the CAB until 2007 (2.907 m km2) and since 2008 (3.185 m km2).

That is due to the "pole hole".  Between July 1987 and December 2007, the surface area of the pole hole was 0.31 million km2.  From January 2008 onward it is only 0.029 million km2:

https://nsidc.org/the-drift/data-update/sea-ice-index-updated-with-a-new-arctic-pole-hole-and-residual-weather-masks/


* I lack access to the daily PIOMAS distribution of thicknesses in each region.

I'm not sure about daily data, but Chris Reynolds used to have at least monthly data for the regional PIOMAS volume distribution in several thickness bins, for example the file "Regional Volume Breakdowns v2.1.csv" on his website (file last updated October 2015):

https://drive.google.com/drive/folders/0B3pB-kdzoLU3T2RSSGIxYkJVMlU

Bill Fothergill

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Re: Volume vs extent, by the numbers
« Reply #43 on: July 29, 2017, 05:03:57 PM »
That is due to the "pole hole".  Between July 1987 and December 2007, the surface area of the pole hole was 0.31 million km2.  From January 2008 onward it is only 0.029 million km2:
Yep, and from Nov 78 until Jun 87 it was a whopping 1.19 million km2.

Every time I modify my NSIDC spreadsheet, I always end up having to recheck the pole hole size from here ...

 http://nsidc.org/data/docs/noaa/g02135_seaice_index/#coverage_resolution

(Some day, these values might actually lodge in my cranium - but I'm not holding my breath...)

oren

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Re: Volume vs extent, by the numbers
« Reply #44 on: July 29, 2017, 11:22:30 PM »
Thanks for the pole hole info. I updated the area data and produced CAB charts for 2000-2017 for several dates, including average thickness. (The last chart ends at 2016).
A negative trend for thickness can be easily seen for all dates, but is strongest for for mid-July (for which 2017 is at record low). Still., 2+ meters average in mid-July explains why the CAB is still mostly melt-resistant.
In September, a low area may result in a higher average thickness (thin ice melts first).
Note the left axis units are 1000 km3 for volume and m for thickness.
Tomorrow I hope to analyze what's happening in the adjacent seas.

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Re: Volume vs extent, by the numbers
« Reply #45 on: July 30, 2017, 01:11:15 AM »
Oren:

Tomorrow I hope to analyze what's happening in the adjacent seas.”
Please don’t bother. The only piece of shrapnel worth considering is the CAB (see also http://www.metrolyrics.com/fit-but-you-know-it-lyrics-streets.html ).

Have you actually tried to extract the average ice thickness from PIOMAS, or, is the thickness an artifact of your method?

oren

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Re: Volume vs extent, by the numbers
« Reply #46 on: July 30, 2017, 07:06:11 AM »
Oren:

Tomorrow I hope to analyze what's happening in the adjacent seas.”
Please don’t bother. The only piece of shrapnel worth considering is the CAB (see also http://www.metrolyrics.com/fit-but-you-know-it-lyrics-streets.html ).

Have you actually tried to extract the average ice thickness from PIOMAS, or, is the thickness an artifact of your method?
At this stage I show PIOMAS volume divided by NSIDC area. Hopefully at some point I will be able to use the whole PIOMAS distribution.

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Re: Volume vs extent, by the numbers
« Reply #47 on: July 30, 2017, 03:18:09 PM »
(Such discussion probably belongs in the Developers Corner, I'm just frustrated by lack of time to be a proper developer)

See Zack Labe's open source python code linked to from this thread:

PIOMAS gridded thickness and regional volume
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Re: Volume vs extent, by the numbers
« Reply #48 on: August 01, 2017, 06:01:49 PM »
There's been some discussion about "flattening" (or not) on the 2017 melt season thread, and up above on this thread as well.  To avoid "broken trends" here are LOESS smoothed versions of the September monthly volume and extent series:





The LOESS function uses a 10-year timescale, in order to show decadal-scale variability.

For the raw data (blue) I included 2017's projected values at the end in pale blue.  I also included those 2017 projections in calculating the LOESS function.

Finally, here are both volume and extent on the same graph, scaled relative to their 1980-1989 decadal averages (to be precise, scaled relative to the 1980-1989 averages in the LOESS versions of each series).



I like that graph; it carries a lot of information.

Bill Fothergill

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Re: Volume vs extent, by the numbers
« Reply #49 on: August 01, 2017, 06:13:31 PM »
Nice one, Ned.

I had just created virtually identical rolling 10-year graphs for September PIOMAS and September NSIDC extent, but you beat me to the draw.