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What will be the maximum PIOMAS volume during 2014?

Record low under 21.827
21.827 to 22.326
22.327 to 22.826
22.827 or over

Author Topic: Predicting PIOMAS [s]Max[/s] now on to minimum volume 2014  (Read 30426 times)

crandles

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Predicting PIOMAS [s]Max[/s] now on to minimum volume 2014
« on: December 19, 2013, 07:05:59 PM »
The data seems to be indicating that relationships are changing over time.

Chris Reynolds suggested using gains early in the freeze season as a guide to gains at the end of the season.

looking at gains from 30 Nov to max compared to gain up to 30 Nov I found a correlation co-efficient for 1979 to 2005 of -0.19 but for 2006 to 2012 of +0.47. I probably need to de-trend the numbers.

Using minimum volume as a guide to the gain from min to max I get correlation coefficients (again I haven't detrended) from 1979 to 2005 of -0.38 and for 2006 to 2012 of -.70

High rates of change in correlation coefficients probably don't make for reliable estimates. In addition the gain to 30 Nov 2013 is high suggesting further rapid increase, but the minimum is high suggesting a low total gain.

I am not really sure if it is possible to make sense of all this. Nevertheless I shall give it a go and probably make a fool of myself:

Many people have suggest the situation has changed at some point between about 1998 and 2007. The changing correlation coefficients might be an indicator of this.

As the area of thick multiyear ice has declined there are increased areas of no and thin ice which can rapidly gain volume early in the freeze season. Later in the freeze season, this slows down as these areas approach their equilibrium thickness. So later in the freeze season, perhaps the volume of ice plays a more important role.

The gain in ice from minimum to 30 Nov increases from 4.7 K Km^3 in 1979 to 6.7 K Km^3 in 2011.

The gain from 30 Nov to max is less clear possibly declining a little from 1979 to 1994 before increasing.

The biggest two gains are after the minimums of 2007 and 2012 which were particularly low minimum volumes so after a high minimum volume I am expecting a fairly low volume gain.

I am therefore not giving too much attention to the high volume gain so far as I expect the volume effect to occur later in the freeze season.

I could be completely wrong, the variations in volume at max may be due to weather rather than any trends or volume gains early in the freeze season may be a better guide, or lots of other things not considered here.

It will be interesting to see what happens.

Other thoughts welcome.

« Last Edit: May 23, 2014, 12:30:59 AM by crandles »

ChrisReynolds

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Re: Predicting PIOMAS Max volume 2014
« Reply #1 on: December 19, 2013, 08:01:01 PM »
The correlation coefficients even when detrended are low, however plotting the early period volume gain (min to 30 November) against total volume gain suggests that there is a positive relationship.



I'm not hazarding a guess in numbers, although I did so in our email exchange. I am however prepared to make a qualitative prediction. The 2014 maximum will be around the level of 2010, likely a bit below, but not as high as 2009, nor as low as 2011.

Neven

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Re: Predicting PIOMAS Max volume 2014
« Reply #2 on: December 19, 2013, 08:32:53 PM »
Nice topic, crandles! If you want I can add a poll to it.

Maximums since 2005 (in km3):

2005: 26181
2006: 25191
2007: 23803
2008: 25159
2009: 25082
2010: 23402
2011: 21961
2012: 21923
2013: 21827

These maximums occurred between April 10th and 24th.
Il faut comparer, comparer, comparer, et cultiver notre jardin

Richard Rathbone

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Re: Predicting PIOMAS Max volume 2014
« Reply #3 on: December 19, 2013, 10:37:41 PM »
I don't see any reason for projecting based on a correlation. I'd just take the average gain, which looks to be 11 - 11.5 to me from the graph Chris posted (x vs. x+y showing a correlation doesn't give any reason for expecting a correlation between x and y).

That puts me in the 22.5-23 bucket, which also looks about right eyeballing the PIOMAS anomaly graphs.

crandles

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Re: Predicting PIOMAS Max volume 2014
« Reply #4 on: December 20, 2013, 04:36:27 PM »
Added a poll to thread now.


Using minimum volume and year as 2 predictors and data for 2006 to 2013, multiple linear regression suggested a maximum value of 20.7 +/- SE of 1. I would be pretty surprised if it was that low.

If I use all the years 1979 to 2013 it suggests 22.6 +/- SE of 0.7

Predicting gain since 30 Nov to Maximum using year and volume at 30 Nov predicts 22.9 +/- SE of 0.6 if I use 1979 to 2013 data.

If I only use 2006 to 2013 years data it predicts 22.1 +/- SE of 0.9.

I think things have changed so I am not paying much attention to results using all years. Using latest data may well be sensible, but the extremely low figure of 20.7 has pushed me towards guessing a record low maximum volume.

Anyway it seems you can get quite different results using similar methods so who knows what will really happen.

ChrisReynolds

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Re: Predicting PIOMAS Max volume 2014
« Reply #5 on: December 22, 2013, 02:31:42 PM »
The Central Arctic is where most of the volume gain over last year is.



And in the Central Arctic the thckness profile is notably biassed to the low end, with a peak about 1.2m.



I'm reading the data as saying that the peak at around 1.2m is all ice that is going to thicken and fill up into higher thickness bands to reach a typical peak thickness of about 2m.



I could be wrong, but I think we'll see most/all of the volume peak of 2013 carried over into the start of the 2014 melt season.

Bob Wallace

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Re: Predicting PIOMAS Max volume 2014
« Reply #6 on: December 22, 2013, 10:55:58 PM »
At this point in time a lot of the thick stuff in the Basin is floating out the Fram.

It seems to be getting replaced by thinner, recently-frozen ice coming in from the periphery.

That's assuming the HYCOM/CICE thickness gif is correct.

Perhaps the pack will solidify as time goes along....

jdallen

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Re: Predicting PIOMAS Max volume 2014
« Reply #7 on: December 23, 2013, 05:33:55 AM »
Looks about right, Chris.  The ice over 2M isn't going to thicken particularly, so the profile next April should look a lot like 2013.  The Fram is a wildcard, but still a nominal loss, much less than loss to insolation.  Mostly what it does during the melt is permit gaps to open.

This winter, I see a key variable to be the weather, in particular, the extent to which warmer temperatures constrain thickening, which may become serious. 
This space for Rent.

ChrisReynolds

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Re: Predicting PIOMAS Max volume 2014
« Reply #8 on: December 27, 2013, 10:02:24 PM »

AndrewP

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Re: Predicting PIOMAS Max volume 2014
« Reply #9 on: January 22, 2014, 07:13:46 AM »
22.8+/- .5

ChrisReynolds

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Re: Predicting PIOMAS Max volume 2014
« Reply #10 on: February 24, 2014, 07:07:57 PM »
Earlier I said:

Quote
The 2014 maximum will be around the level of 2010, likely a bit below, but not as high as 2009, nor as low as 2011.

That's 25.074 to 24.275.

Since mid June last year the interannual difference for daily volume has been tracking around roughly 1.5k km^3 (2013/14 above 2013/13 calculated for each day). 

That suggests Jan 2013 + 1.5, or 23.332 + 1.5 = 24.832k km^3. I suspect it'll be lower rather than higher with regards that figure. So I'll hazard a guess at -

24.9 to 24.3k km^3.

ChrisReynolds

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Re: Predicting PIOMAS Max volume 2014
« Reply #11 on: February 26, 2014, 09:01:58 PM »
Taking the average intermonth changes for the last four years from January to April (monthly averages)...

3.053961118
2.375071141
1.091547312

and adding onto the January average...

17.46258065 - January
20.51654176
22.8916129
23.98316022 - April

Suggests 23.98k km^3 for max (the daily max is virtually the same as monthly for April - cusp of the peak). The std dev is 0.65, so that would be 24.6 to 23.3k km^3. So perhaps I'm too far on the high side in the above comment.

I assume that by this time of the season further gains aren't strongly dependent on the state at minimum - but I've not done the maths on that.

crandles

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Re: Predicting PIOMAS Max volume 2014
« Reply #12 on: February 26, 2014, 11:52:56 PM »
Chris, I still think you are on the high side. I think last few years have shown gains in Beaufort but this year the gains will be much smaller there.

Wondering if there is a forecast technique that works out mode thickness for April in each area. Perhaps knock off a couple of cm or better would be to calculate trend in this value evaluated for this year. The forecast thickness for each cell is then higher of trend mode thickness and current value.

Not sure how well that would work and if it is badly biased it would need correction for the bias. However, I would expect it to give a lower answer than yours.

I might be being silly to think your method gives an overestimate.

Oyvind Johnsen

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Re: Predicting PIOMAS Max volume 2014
« Reply #13 on: February 27, 2014, 11:39:10 AM »
In #2 Neven gives numbers for maximums:

Maximums since 2005 (in km3):

2009: 25082
2010: 23402
2011: 21961


In #10, Chris reynolds writes:
Earlier I said:

Quote
The 2014 maximum will be around the level of 2010, likely a bit below, but not as high as 2009, nor as low as 2011.

That's 25.074 to 24.275.


According to Neven, that should be 25 082 to 21 961.

Which/who is correct?

crandles

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Re: Predicting PIOMAS Max volume 2014
« Reply #14 on: February 27, 2014, 11:48:29 AM »
v2.1 came out since Neven's post.

There is also possibility that one is daily and one is monthly average.

Probably both correct in their own way.

Oyvind Johnsen

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Re: Predicting PIOMAS Max volume 2014
« Reply #15 on: February 27, 2014, 04:22:02 PM »
v2.1 came out since Neven's post.

There is also possibility that one is daily and one is monthly average.

Probably both correct in their own way.

Thanks, at least a partial explanation. But if 24 275 is meant to be the maximum in 2011, the difference from 21 961 still seems to large.

http://psc.apl.washington.edu/wordpress/wp-content/uploads/schweiger/ice_volume/version_diff.png

Anyway, for the poll: Is it daily max?

ChrisReynolds

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Re: Predicting PIOMAS Max volume 2014
« Reply #16 on: February 27, 2014, 06:29:21 PM »
Oyvind,

For the daily series I get 25.074 on 13/4/2009, and 24.275 on 10/4/2013 as the two maxima.

I've just double checked by reloading the whole of PIOMAS V2.1 from 1978, those numbers haven't changed - so I had the correct current version. On checking my 2013 spreadsheet I find that Neven's numbers are indeed for PIOMAS V2.0.

My most recent previous post uses monthly values as stated. The one before that is daily - should have made that clear, sorry for any confusion. But during April the rate of change is slow, so there actually isn't much between the two sets of numbers.

Crandles,

I don't think it will be a massive overshoot. There's been a small down tick in the last week of the January PIOMAS release. However as I say the long term difference from a year ago has been about 1.5 (by eye) and I calculated a bit more than that in the average (1.7 IIRC). When we get February next week that should start to settle things Jan to Feb gains about as much as Feb to April, any major stall this month will have a large impact.

I've attached a graph of difference from a year prior to each stated date.

ChrisReynolds

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Re: Predicting PIOMAS Max volume 2014
« Reply #17 on: February 27, 2014, 06:55:05 PM »
Wondering if there is a forecast technique that works out mode thickness for April in each area. Perhaps knock off a couple of cm or better would be to calculate trend in this value evaluated for this year. The forecast thickness for each cell is then higher of trend mode thickness and current value.

Not sure how well that would work and if it is badly biased it would need correction for the bias. However, I would expect it to give a lower answer than yours.

You might like to try something in the volume domain. I've uploaded a spreadsheet to my Google Drive with monthly volume for each region from 1978 to present.
https://drive.google.com/file/d/0B3pB-kdzoLU3MGQ5QXNMUTVlcG8/edit?usp=sharing

Steven

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Re: Predicting PIOMAS Max volume 2014
« Reply #18 on: February 27, 2014, 10:03:37 PM »
Perhaps it's useful to list some recent volume maxima for the new PIOMAS Version 2.1:

2004:    25.811 k km3 on April 25
2005:    26.181          on April 23
2006:    25.191          on April 15
2007:    23.865          on April 8
2008:    25.159          on April 18

2009:    25.074          on April 13
2010:    24.275          on April 10
2011:    22.677          on April 19
2012:    23.365          on April 24
2013:    23.332          on April 22

Source: the PIOMAS daily series.  The full list of PIOMAS maxima from 1979 is on Wipneus' webpage, link.  (Note that the last 5 years in that file are not updated yet for PIOMAS Version 2.1).

Wipneus

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Re: Predicting PIOMAS Max volume 2014
« Reply #19 on: February 28, 2014, 09:00:55 AM »

Source: the PIOMAS daily series.  The full list of PIOMAS maxima from 1979 is on Wipneus' webpage, link.  (Note that the last 5 years in that file are not updated yet for PIOMAS Version 2.1).

Oops, somehow that totally slipped my mind.

Fixed now.

Google spreadsheet

as text file, import in your own spreadsheet

Oyvind Johnsen

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Re: Predicting PIOMAS Max volume 2014
« Reply #20 on: February 28, 2014, 09:31:46 AM »
Thanks to Steven for listing the maxima, and referring to Wipneus webpage, now updated:-)

Chris Reynolds: The maximum of 24 275 is 10/4/2010, not 2013. Earlier you seem to date the same maximum to 2011, which confused me. Probably typos, and I see now that it has not influenced your arguments about the probable maximum in 2014.

ChrisReynolds

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Re: Predicting PIOMAS Max volume 2014
« Reply #21 on: February 28, 2014, 06:46:42 PM »
Sorry, yes "The 2014 maximum will be around the level of 2010, likely a bit below, but not as high as 2009, nor as low as 2011." should read "The 2014 maximum will be around the level of 2010, likely a bit below, but not as high as 2009, nor as low as 2010."

crandles

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Re: Predicting PIOMAS Max volume 2014
« Reply #22 on: February 28, 2014, 08:01:30 PM »
nor as low as 2010."

Aren't we currently below 2010? You expect it to go higher? or, Should that be 'not as low as 2012 or 2013'?

'around the level of 2010' seems to indicate it shouldn't be 2010.

Steven

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Re: Predicting PIOMAS Max volume 2014
« Reply #23 on: February 28, 2014, 08:50:59 PM »
Taking the average intermonth changes for the last four years from January to April (monthly averages) [...]

Chris, FWIW I think it may be useful to average over more than 4 years.  The ice in January 2014 was thicker than the 2010-2013 average, so the volume increase from January to the maximum may be smaller than the average of those 4 years, due to the fact that thicker ice thickens more slowly?

In fact, January 2014 monthly volume was close to the average over the last 7 years, 2007-2013.  Taking the average volume gain from January to maximum over these 7 years, and adding it to the January 2014 volume, suggests for the 2014 daily PIOMAS maximum:  23.92 +/- 0.59.  (Compared to 24.18 +/- 0.51 when using only the last 4 years.)  Using data for January 31st rather than January monthly average suggests  23.83 +/- 0.40.   

So this would suggest the 2014 volume maximum to be near the 2007 level, i.e. higher than in 2011-2013 and lower than 2008-2010.

Another factor is that the Cryosphere Today sea ice area in April was relatively high in the last few years (see attached figure), presumably mostly due to natural variability.  This certainly affected the maximum volume as well. 

So assuming that the April 2014 sea ice area will be closer to the long term trend line, then the volume maximum may be lower than the estimates given above.  I tried to quantify this by using some multiple linear regression but it wasn't satisfactory.
« Last Edit: March 01, 2014, 02:31:26 PM by Steven »

slow wing

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Re: Predicting PIOMAS Max volume 2014
« Reply #24 on: March 01, 2014, 02:36:18 AM »
24.0 +- 0.7 thousand cubic kilometres, with one sigma confidence limits.

That is, about a 2/3 probability of being between 23.3 and 24.7 thousand cubic kilometres.


This is just from eyeballing Wipneus' volume plot vs. time, which currently goes up to the end of January 2014. I haven't read anything to improve much on that or to convince that the rise from the end of January this year will be significantly biased one way or the other from those of recent years.


That prediction was a bit of fun and very easy to do as it takes advantage of a lot of work from others. Thanks to the likes of Wipneus and Chris Reynolds who present the data in convenient form and thanks especially to the scientists and technicians who have collected and analysed the data and made it available.

« Last Edit: March 02, 2014, 01:18:52 AM by slow wing »

Espen

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Re: Predicting PIOMAS Max volume 2014
« Reply #25 on: March 01, 2014, 12:53:14 PM »
Our friend Andy Lee Robinson is mentioned in an article on DMIs webiste ( in Danish):

http://www.dmi.dk/nyheder/arkiv/nyheder-2014/02/isdroem-akkompagnerer-rekordlille-isvolumen-i-arktis/
Have a ice day!

ChrisReynolds

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Re: Predicting PIOMAS Max volume 2014
« Reply #26 on: March 02, 2014, 08:18:03 AM »
Steven,

You may be correct, the drop in volume difference between 2014 and 2013 at the end of the graph I posted above might be continued through February. April volume outside the Arctic is from about 14% in the early part of the series to 18% of total volume in recent years.

Only a few more days before we find out the state of February, gridded data or not. And actually the matter should be largely decided by March, there's no long term trend in March to April volume gains, and in the post 2007 period (winter 2008 onwards) the March to April average gain is 1.105k km^3 (std dev 0.07k km^3). That's tight enough to decide between those of us who are aiming low and those who are aiming high - excepting unusual weather.

It's worth noting that the total volume difference between Jan 2012 and Jan 2013 is 1.609k km^3, within the Arctic Ocean the difference is 1.352k, outside the Arctic Ocean the difference is 0.257k, in all cases 2013 is a higher volume than 2012. Most of the gain for 2013 w.r.t. 2012 is due to ice within the Arctic ocean, not outside that region where most of the current reduced area/extent seems to be coming from.

EDIT - forgot to add, I used post 2010 year average because we're still in a post 2010 volume loss event ice state.
« Last Edit: March 02, 2014, 12:17:38 PM by ChrisReynolds »

crandles

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Re: Predicting PIOMAS Max volume 2014
« Reply #27 on: March 02, 2014, 12:29:38 PM »
I also like Stephen's answer

"January 2014 monthly volume was close to the average over the last 7 years, 2007-2013", so using 7 years not 4 and "Using data for January 31st rather than January monthly average suggests  23.83 +/- 0.40".

I still think this could be an overestimate as equilibrium thickness in 2014 is likely to be lower than the average for last 7 years. This in addition to Stephen's area argument.

Chris Reynolds Graph:

Steven

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Re: Predicting PIOMAS Max volume 2014
« Reply #28 on: March 02, 2014, 08:09:34 PM »
"Using data for January 31st rather than January monthly average suggests  23.83 +/- 0.40".

I still think this could be an overestimate as equilibrium thickness in 2014 is likely to be lower than the average for last 7 years. This in addition to Stephen's area argument.

I forgot to mention that the number behind the +/- sign is the standard deviation, as in Slow Wing's comment above,  i.e. 1-sigma confidence limits.

Another reason why 23.83k km^3 may be an overestimation: it seems Arctic temperatures in February 2014 were exceptionally high: see attached figure  (source; may take a while to load). 

Temperatures in most regions of the Arctic were much above those in recent years, e.g. compare with the attached figure of the February 2007-2013 average (source).

The PIOMAS volume anomalies for January 2014 were more or less "flat".  Since the high temperatures in February 2014 were more extreme and more widespread than in January, this makes me wonder how close the 2014 volume will approach 2013 by the end of February.  Of course it's possible that other factors helped the ice volume to increase, e.g. the low Fram export and the compaction/fracturing of sea ice.

P.S. Crandles, my name is not Stephen but Steven (Dutch version of the name, rhymes with "raven")  :)
« Last Edit: March 03, 2014, 10:32:13 PM by Steven »

crandles

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Re: Predicting PIOMAS Max volume 2014
« Reply #29 on: March 02, 2014, 08:27:15 PM »
Sorry about name Steven  :-[

Steven

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Re: Predicting PIOMAS Max volume 2014
« Reply #30 on: March 03, 2014, 11:06:06 PM »
Attached is the difference between the two plots in my previous post, i.e. surface air temperatures in the Arctic in February 2014 compared to the 2007-2013 average.  Data from NCEP/NCAR.

Source  (may take a while to load).  The webpage used to create the plot is here.  (Other values of the parameters can be selected.)
« Last Edit: March 04, 2014, 04:34:05 PM by Steven »

ChrisReynolds

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Re: Predicting PIOMAS Max volume 2014
« Reply #31 on: March 04, 2014, 06:14:53 PM »
Steven, Crandles,

The reason I've not commented further is that we'll shortly know what effect current conditions have had on total volume. I'm hoping that the gridded thickness will be updated because otherwise we'll be stuck not knowing if a loss of the 2013 volume gain is due to ice outside the Arctic Ocean or within it.

Either way we'll have at least a partial answer shortly, so pursuing the argument further this close to data release doesn't seem efficient.

I should have made my position clear earlier, but got distracted.

ChrisReynolds

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Re: Predicting PIOMAS Max volume 2014
« Reply #32 on: March 07, 2014, 10:01:24 PM »
Now I've got the data - my predictions above are going to be too high, the PNA pattern has limited thickening, and probably in the Arctic Ocean as well as outside.

So I concede defeat...  ;D

I'm grinning because this opens up the possibility of more crash action in 2014.  8)

werther

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Re: Predicting PIOMAS Max volume 2014
« Reply #33 on: March 07, 2014, 10:30:18 PM »
Concession accepted, Chris (at least by me),
Who could have foreseen such a winter over the Arctic. It now seems as though a lack of winter power is the driver....

ChrisReynolds

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Re: Predicting PIOMAS Max volume 2014
« Reply #34 on: March 07, 2014, 10:34:58 PM »
It's worth pointing out that the 2013 volume increase began as a result of weather (cold in May 2013), and might have ended in February 2014 as a result of weather.

I only say 'might' because I'd still like some gridded data to get a look at the state within the Arctic. But as I've just argued, it's hard to make the case all the volume loss has happened outside of the Arctic ocean.

werther

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Re: Predicting PIOMAS Max volume 2014
« Reply #35 on: March 07, 2014, 10:44:10 PM »
Yeah,
It's been many years since there was 300-500K more ice than usual on the Labrador-Newfoundland coasts and St.Lawrence Bay...
What do the gridded data provide on that?

ChrisReynolds

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Re: Predicting PIOMAS Max volume 2014
« Reply #36 on: March 07, 2014, 10:46:24 PM »
The PIOMAS domain doesn't cover the Gulf Of St Lawrence, so it says nothing, sorry.

werther

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Re: Predicting PIOMAS Max volume 2014
« Reply #37 on: March 08, 2014, 12:17:59 AM »
Well, you dont have to be sorry, I just forgot... this is the domain, isn't it?



So even when St. Lawrence is out of range, there's still a lot of periphery in the Labrador Sea/Newfoundland Coast, Bering and Okhotsk... So your case is likely right. 'Winter power' hasn't been awfully good for the CAB-ice.

ChrisReynolds

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Re: Predicting PIOMAS Max volume 2014
« Reply #38 on: March 08, 2014, 08:28:04 AM »
Yes, that's the domain. I suspect that the Gulf of St Lawrence was missed out because within the domain it becomes a stub whose water doesn't interact with the wider Atlantic so it would be likely to produce incorrect results.

crandles

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Re: Predicting PIOMAS Max volume 2014
« Reply #39 on: April 03, 2014, 04:28:17 PM »
Gains from 28 Feb to 31 March   
2007   1.648
2008   1.943
2009   1.776
2010   2.124
2011   1.67
2012   2.182
2013   1.947
   
average   1.899

This approach didn't do too well for Feb:
Gains from 31 Jan to 28 Feb      
2007   2.479   
2008   2.545   
2009   2.44   
2010   2.707   
2011   2.521   
2012   2.275   
2013   3.17   
      
average   2.591   
actual   1.923   

However I thought that the increase was likely to be less than the average of 2.59 because:

1. Tendency to converge to thermal equilibrium thickness (TET). So if the volume is relatively high, you get a small gain.
2. TET is declining with time as GHG increase, ocean heat increases, ...
3. Weather - it was warm in February except for last few days.

For March reason 1 has pretty much been eliminated by slow growth in Feb. 2 still applies. 3. Weather: Feb 2014 was warmer than any preceding Feb in last 7 years. March 2014 looks about same as 2011 but warmer than March in rest of the last 7 years.

With 1 reason gone and one reason reduced in strength, I don't think we will see the gain being as low as 74% of average of last 7 years but I still expect the gain to be below the average. Half way between these is about the gain of 2011, 1.67. 28 Feb value of 20.86 + 1.67 = 22.53 as forecast for 31 March.

crandles

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Re: Predicting PIOMAS Max volume 2014
« Reply #40 on: April 07, 2014, 11:16:27 PM »
actual just released  31 Mar 14  22.609

gain from 28 Feb 14 of 20.860 is 1.75

Neven

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Re: Predicting PIOMAS Max volume 2014
« Reply #41 on: April 07, 2014, 11:45:10 PM »
Well well, that's the lowest on record for March 31st, right?

I'm off downloading a spreadsheet.  8)

Edit: finished downloading -> second lowest for March 31st.
« Last Edit: April 07, 2014, 11:54:45 PM by Neven »
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crandles

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Re: Predicting PIOMAS Max volume 2014
« Reply #42 on: April 07, 2014, 11:46:49 PM »
        31-Mar   Max        Gain
2007   23.711   23.865   0.154
2008   24.698   25.159   0.461
2009   24.613   25.074   0.461
2010   24.053   24.275   0.222
2011   22.129   22.677   0.548
2012   22.889   23.365   0.476
2013   22.85   23.332   0.482
2014   22.609   

To be lowest ever maximum increase would need to be less than 0.068 and lowest gain in last 7 years is 0.154

To be higher than 2nd lowest maximum gain from 31 March would have to be more than .723 and highest gain in last 7 years is 0.548

Therefore 2nd lowest maximum volume appears highly likely.

Neven

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Re: Predicting PIOMAS Max volume 2014
« Reply #43 on: April 08, 2014, 01:09:44 AM »
Post is up on the ASIB: PIOMAS April 2014
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crandles

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Re: Predicting PIOMAS Max volume 2014
« Reply #44 on: May 08, 2014, 04:46:53 PM »
Daily Max 23.104 day 105 second lowest 0.427 above day 109 2011 at 22.677 (so my 'highly likely' was true).

April Average 22.931 second lowest 0.42 above April 2011

31 March 14 at 22.609 was second lowest 0.48 above 2011.

30 April 14 at 22.94 is third lowest 0.112 above 2013's 22.828 and 0.658 above 2011's 22.282.

So April 2014 has been unusually flat, starting 0.48 above 2011 the difference reduced to 0.427 at maximum then the difference increased to 0.658 at the end of April.


OSweetMrMath

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Re: Predicting PIOMAS Max volume 2014
« Reply #45 on: May 19, 2014, 01:26:40 AM »
Warning: very long. tl;dr: Using the anomaly data has a better outcome in terms of the bias-variance tradeoff than using the data from each month separately.

Chris Reynolds suggested that we move discussion of PIOMAS prediction from the Latest PIOMAS Update thread http://forum.arctic-sea-ice.net/index.php?topic=119 to here, so here I am. To keep everything in one place, I'm going to recapitulate some of the discussion and reproduce the (corrected) relevant graphs.

I started by posting a SARIMA forecast of PIOMAS ice volume based on the PIOMAS monthly data through April. In particular, the forecast predicts a monthly value for September of 4700 km^3, with 95% confidence interval of 3000-6300 km^3. I followed this with a spline regression of the monthly sea ice anomaly, which predicts a monthly value of 4600 km^3. I did not compute a confidence interval, but noted that splines have high variance at the ends of the fitted interval, so the confidence interval for forecast values should be assumed to be very large.

Chris asked whether it makes sense to work directly with the anomaly, arguing that it makes more sense to treat each month separately.

My response was that computing the anomaly is an attempt to treat the time series as consisting of a sum of a trend component and a periodic component, with additional noise. The anomaly computation attempts to subtract out the periodic component, leaving just the trend and the noise. If the seasonal component is approximately periodic, this should give a better estimate of the trend than estimating the trend for each month separately. To back this up, I produced a graph of just the September ice values, along with the ARIMA forecast and spline regression. The ARIMA forecast predicts a September ice volume of 4300 km^3, with 95% confidence interval of 1800-6700 km^3. The spline regression prediction is 3600 km^3.

The confidence interval for the SARIMA forecast using all of the data is smaller than the confidence interval for the ARIMA forecast using just the September data. My claim is that this shows that the SARIMA forecast is better than the ARIMA forecast.

Chris responded by challenging that claim. He pointed out that the September volume is falling faster than the April volume, and therefore the seasonal variability is not periodic. Predictions based on that assumption may be misleading, and therefore the computed confidence intervals for the SARIMA forecast may in fact be too small. (This is a summary of Chris's arguments, so hopefully I'm not misrepresenting him. If I'm missing anything important, I assume he will correct me.)

In response, I will point out that although I'm a new poster here, I've been lurking for several years. At about this time last year, the general consensus was that 2013 was likely to have a lower ice minimum than 2012. Around July 1, Chris Reynolds updated his prediction for the 2013 minimum. Contrary to his previous prediction of a record low, his prediction was now at the high end of predictions for the site, as shown on this post: http://forum.arctic-sea-ice.net/index.php/topic,418.msg8940.html#msg8940. Chris's reasoning was that ice levels around the end of June were high enough, and the amount of ice melt from the end of June to the low in September is regular enough, that there was now essentially no chance of a record low in September. And in fact, this new prediction was highly accurate.

Using the anomaly data (or the SARIMA forecast) is essentially arguing from the same reasoning that Chris used last July. The ice data can be divided into a trend component, a periodic component, and a noise component. If we can estimate the trend and the periodic component, we can forecast future values for the ice as a sum of the trend and the periodic component, subject to the variability due to the noise. Chris's July prediction was an estimate of the periodic component, along with the argument that neither the trend nor the noise could be large enough to set a new record.

Chris's argument now is that the seasonal component is not periodic. Since the September ice level has been falling faster than the April ice level, the seasonal variability is increasing, rather than the constant variability assumed by the model. This is true. On the anomaly graph, it is clear that there is a seasonal component to the anomaly since 2010, so removing a fixed periodic component does not correctly account for the recent seasonal variability.

On the spline forecast graph, it is clear that this means that predictions based on a periodic seasonal anomaly underestimate the April maximum and overestimate the September minimum. (It's less obviously true, but the SARIMA forecast has a similar issue.) The question really becomes whether the error introduced by the imperfect seasonal model is outweighed by the additional data that the seasonal model gives us access to.

If the goal is to predict ahead a full year, then this question should be carefully considered. I suspect that the SARIMA forecast for April 2015 is better than an ARIMA forecast for April 2015 based on just the April data, but to verify this I would want to go back and check the historical prediction accuracy of both forecasts.

On the other hand, my primary goal currently is to predict the September 2014 minimum. If I just look at the ARIMA model (or the spline model) based on the September data, I have my prediction. It can't get any better, even as we get closer to September. On the other hand, the SARIMA model and the spline anomaly model can automatically incorporate all of the monthly data up until September, and in fact already have incorporated all of the data through April. As we get closer to September, the predictions will only get more accurate.

It's true that the spline anomaly model has a bias for September, but even though I haven't computed it, the variance for the spline anomaly model is much smaller than the variance for the spline model for September only. This variance will get smaller as we get closer to September, although the bias remains. This tradeoff between bias and variance is a fundamental tradeoff in statistics. You can minimize one or the other, but you can't minimize both. My claim is that by considering the seasonal anomaly rather than just the data for a single month, you can come closer to making the optimal tradeoff between bias and variance.

OSweetMrMath

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Re: Predicting PIOMAS Max volume 2014
« Reply #46 on: May 19, 2014, 05:08:33 AM »
I've done some computations which back up my claims. I'm thinking about whether I have a good way to graph this and provide visual support. If you just use the September data, perform a spline regression, and use that to predict the following September's PIOMAS ice volume, the RMS prediction error over the last 10 years is 1149 km^3.

If you use all the data through September of one year, compute the anomaly, perform a spline regression, and use that to predict the following September's PIOMAS ice volume, the RMS prediction error over the last 10 years is 1029 km^3. So even a year ahead, the prediction based on the anomaly is more accurate.

The prediction error steadily decreases during the year, until you get to August, when the RMS prediction error is 784 km^3.

The prediction error in August is largely due to the bias. The prediction a year ahead using the anomaly is a combination of the bias and the variance. However, the variance using the anomaly is sufficiently smaller than the variance using just the September data that the prediction is better, even though the bias is larger using the anomaly data than using the September data only.

Using the anomaly wins the bias-variance tradeoff.

crandles

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Re: Predicting PIOMAS Max volume 2014
« Reply #47 on: May 19, 2014, 05:59:05 PM »

The question really becomes whether the error introduced by the imperfect seasonal model is outweighed by the additional data that the seasonal model gives us access to.

It's true that the spline anomaly model has a bias for September, but even though I haven't computed it, the variance for the spline anomaly model is much smaller than the variance for the spline model for September only. This variance will get smaller as we get closer to September, although the bias remains. This tradeoff between bias and variance is a fundamental tradeoff in statistics. You can minimize one or the other, but you can't minimize both. My claim is that by considering the seasonal anomaly rather than just the data for a single month, you can come closer to making the optimal tradeoff between bias and variance.

Thanks for these posts OSweetMrMath.

The idea of a trend that is an autoregressive moving average is interesting. So far I have looked at the difference between exponential, gompertz and linear as an indicator of likely error from choosing the wrong form of extrapolation while generally liking the gompertz version as mirroring the shape that GCM type models seem to produce.

It seems possible that the error from the model being the wrong type of model could be larger than the noise in the system type error estimate that are usually quoted as the error range. So quoting an error range that assumes that the system is correct may not be ideal for saying this is the best method to use. Don't you have to calculate the size of the bias and adjust for that?

I do understand it is better to use all the data rather than a subset, but it seems to me that using it in the wrong way might potentially be a bad idea.

A better alternative might be to have a seasonal component where the amplitude of this seasonal component varies with time.
Piomas2.1meltfreeze by crandles2011, on Flickr
The green melt is generally above the purple freeze but that is just the trend.

Those lines are fairly horizontal until ~2007 and then there is an increase in the amplitude of the seasonal component. This increase in amplitude of the annual swing could be modelled as linear or exponential or in several other ways but lacking sufficient data I suggest we assume linear for the moment.

The graph above just shows the total amplitude of the swing but to really get a good fit of all the data, presumably you would want to know when during the year it occurs. We know about the June Cliff:


so just applying a single linear increase in amplitude from ~2007 may not be ideal. However perhaps the linear increase in amplitude for each day of the year can be calculated empirically from the data for those days.

Doing this you end up with a large number of variables with which to fit the data. Could there be too much risk of over-fitting?

Even if it doesn't over-fit the data, it might end with a small error range that is further out than if a better system had been used (like a Gompertz or exponential or whatever it eventually looks like)?

« Last Edit: May 19, 2014, 06:12:21 PM by crandles »

ChrisReynolds

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Re: Predicting PIOMAS Max volume 2014
« Reply #48 on: May 19, 2014, 07:37:28 PM »
Thanks OMrSweetMath,

I'm too tired after a long day at work, so will reply in more detail tomorrow but for now....

Your summary is very fair, thanks for the work you've put into that.

Thanks for doing the math on using all available months anomalies, and only September to predict September. All months seems to win.

Crandles re-overfitting. I'm not too worried about that for a one year prediction, if hindcasts consistently succeed and at some point in the future forecasts fail, then this could be providing useful information about a change of behaviour.

My only disagreement is with the interpretation of my prediction method last year and its success. I see the success as telling us that (contrary to what I was told at the time) sea ice behaviour had not changed and 2013 was typical of past behaviour. With regards the method itself, it uses the observation that CT Area losses have not changed from late June onwards since 1979. If a trend is being used it is the trend of losses prior to late June. But the prediction merely starts from late June, using initial conditions regardles of trend. So I don't think that it is correct to say that "Using the anomaly data (or the SARIMA forecast) is essentially arguing from the same reasoning that Chris used last July."

I'm still minded to pursue to Extent / Volume relationship, to attempt to predict extent at min. That relationship would take care of the trend of loss of extent. The residuals of which may be amenable to further 'explanation' - e.g. NCEP/NCAR, temperatures, pressure, (what other factors?). In essence I'd be using the initial condition in April instead of the trend model providing an initial condition.

I think that OMrSweetMath has already shown that the residuals of the applied SARIMA model might be of similar interest.

OSweetMrMath

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Re: Predicting PIOMAS Max volume 2014
« Reply #49 on: May 20, 2014, 05:42:51 AM »
crandles,

The big difference between the ARMA family of models and say, an exponential or Gompertz fit is that ARMA models try to determine a correlation structure for the noise in the model, while the other models assume that the noise is uncorrelated. It's a little buried in the model, but the SARIMA model is basically a linear (or low order polynomial, in general) plus periodic model. So the ARMA family isn't a different model for the trend, it's a different model for the noise.

In general, if there is an error in the specification of a model, this will be reflected in the estimated noise. To some extent, this protects you from a misspecified model, because the predictions from the model will have a larger error range due to the larger estimated noise.

This isn't perfect, however. The accuracy of the error estimate depends on the goodness of fit of the model. If the variance of the estimated noise is not constant, then the error estimate should be based on the variance local to the predicted value, not the variance estimated by the model. The variance from the model assumes the variance is constant and therefore may underestimate the variance at the predicted value. (This in fact is happening with the SARIMA model, and the confidence intervals are too small.)

As for changing the seasonal component with time, there are some older posts by Tamino where he briefly discusses that. I ran across them the other day while I was working on my models. You can search on his site for them, or I can try to dig them up. My attitude is first, any time you want to make a model more complex, you should have a physical justification or the data should really unambiguously support the change.

Second, and I think this is more tied to your concerns, the more complex the model is, the more important it becomes that the model is correct. Otherwise, things can devolve into an exercise in meaningless curve fitting. When you fit more parameters, the error in each parameter increases. This comes out in the prediction error, so you don't come out ahead unless the more complex model sufficiently reduces the noise.

When I look at the seasonal component of the PIOMAS data, the seasonal differences are increasing, especially after 2010. But I feel like I don't have a handle on it from a modeling perspective. It might be possible to model the change in behavior in a way that improves model performance, but I don't see how to do it.

Chris Reynolds:

You say "sea ice behaviour had not changed and 2013 was typical of past behaviour." I say the seasonal behavior of ice is periodic and to understand the trend, we can remove the periodic component. The future behavior of the ice is then predicted by the trend plus the seasonal behavior. You may say that doesn't mean the same thing, but I think we are saying the same thing.

The component of the prediction error which I want to explain is the part which is attributable to the weather for the next two months. Given that future knowledge of the weather isn't available, I'm not convinced that it's possible to explain the residuals in a way that meaningfully improves prediction accuracy. It's possible that there are interrelationships between the different measures of the ice which are worth pursuing, but I'm not particularly motivated by it.