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ChrisReynolds

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Re: Volume Predictions.
« Reply #50 on: April 26, 2013, 07:37:07 PM »
Crandles,

It shows a better correlation with max volume because the data is from the same period. I suspect you meant it shows better correlation with previous minimum than next minimum.

OK, We're very much talking at cross purposes here. I didn't think you were using different periods or comparing previous or following minima,

From the post where you calculated agreement between my numbers and yours it seems clear to me that what you're doing is effectively slicing off all the ice over a certain thickness and considering the volume of the ice sliced off, not the remainder that's left.

What I am suggesting is that as the loss of volume from 1978 to recently has almost totally come from thick (presumably MYI) ice, then leaving the remainder out could be expected to better reflect the total trend of loss of volume. Think of it the other way, where you slice off the top and look at the remainder, while 'throwing away' the upper portion. In such a case the volume decline would be more like the area decline, since you'd have a volume of Xm X Area.

1. Less thickness melts when the ice is over 2m thick than when it is 1.5m thick because of higher albedo meaning less heat is absorbed.

Well technically PIOMAS doesn't factor in lower albedo for thinner (presumably FYI) ice.

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

Bear in mind that the thicknesses we get for PIOMAS grid cells are effective thicknesses. My imperfect understanding is that this is the integral of the thickness distribution within the grid cell. As the ice thins more of the thickness distribution 'crosses zero' hence represents open water in leads within the cell (and 'rotten ice'). I think that should impact albedo and heat absorption by the ocean, but the maths is over my head so I am unsure.

Sorry to be stupid, but I still don't really get the rationale behind what you're doing, so can't comment on the formula you've posted. I can parse that formula, but it means nothing to me.

crandles

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Re: Volume Predictions.
« Reply #51 on: April 26, 2013, 08:51:11 PM »
OK, We're very much talking at cross purposes here. I didn't think you were using different periods or comparing previous or following minima,

From the post where you calculated agreement between my numbers and yours it seems clear to me that what you're doing is effectively slicing off all the ice over a certain thickness and considering the volume of the ice sliced off, not the remainder that's left.

What I am suggesting is that as the loss of volume from 1978 to recently has almost totally come from thick (presumably MYI) ice,


I am considering the ice sliced off (in excess of x meters) as the part that doesn't melt in any particular year. The up to 1.1m (or perhaps up to 1.7m) is what I am considering to be the part that melts in the melt season. Clearly the really thin ice does melt.



Above graph shows I have calculated amount in excess of various fixed thicknesses for all years. I am comparing this to volume at minimum. i.e. the in excess of part is the ice that remains at end of melt season. That is consistent with it being the thin ice that melts.

If you prefer you could calculate volume up to x m thick and compare to volume melted from max to min. That creates an increasing exponential whereas I think we are more familiar with exponential or gompertz type declines.


I think in reality albedo changes with thinner ice, not just with a MYI /FYI difference. If we build in that thick ice does not melt as much as thinner ice then I think we are getting somewhere nearer to being realistic. If PIOMAS doesn't distinguish FYI from MYI then we should also be able to get away with that. Are you sure PIOMAS doesn't have different albedo for different thicknesses? The thickness information is clearly available for PIOMAS to use. I do accept what you said and pointed out as showing that PIOMAS doesn't differentiate FYI from MYI.


I was going to ask if you knew how to get thickness distribution for a single PIOMAS cell. I am thinking that the SEARCH contribution I linked earlier must have used such information. Otherwise  it would look like that contribution correlated series of 1s changing to 0 at some point with minimum area series. That would seem a bit odd to me. That contribution seemed to work very well, unlike my attempt aimed at estimating PIOMAS min volume. So it is possible that could point towards a way of manipulating thickness data to get better correlation.

ChrisReynolds

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Re: Volume Predictions.
« Reply #52 on: April 26, 2013, 11:35:40 PM »
Crandles,

I've just done the image posted in this comment, It'll be part of a blog post in due course. But I think you'll find it useful.
http://farm9.staticflickr.com/8115/8684706810_9bb4de3e11_o.png

Calculated as follows: Any areas of less than 5cm effective thickness considered to be ice free. Bucket ice thicknesses into 5cm batches and calculate the percentage of the total area of the buckets that becomes ice free in Sept, w.r.t. April thickness area. Plotted percentage melt to open water as a function of April thickness.

Grey are all years (1978 to 2012) plotted to give an idea of range. Red is average of all years, green is average of 2007 to 2012, blue is average of 2010 to 2012.

I'm too tired to pay full attention to your comment, will read it tomorrow. If needs be I can either email the source spreadsheet, or post on my Google docs if anyone else wants the source numbers.
« Last Edit: April 27, 2013, 08:01:21 AM by ChrisReynolds »

Wipneus

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Re: Volume Predictions.
« Reply #53 on: April 27, 2013, 08:38:13 AM »

Calculated as follows: Any areas of less than 5cm effective thickness considered to be ice free. Bucket ice thicknesses into 5cm batches and calculate the percentage of the total area of the buckets that becomes ice free in Sept, w.r.t. April thickness area. Plotted percentage melt to open water as a function of April thickness.


Interesting curve, but I am not sure that I understand what is plotted (maybe more coffee needed):

1) You take they number of grid cells in a bin (say 100), see which have melted to "zero" (less than 5cm). If 80 are zero the percentage is 80.
2) You calculate area of the gridcells in a a bin and calculate area of all cells that have melted to "zero". Calculate the ration of those numbers.
3) You calculate the average thickness of the cells in a bin in September and divide that to the average of the bin.
4) as 3) but multiply by the area of the grid cells.
5) as 1, 2, 3 or 4, but put the effect of the concentration  in the calculation.
6) something else?
 

ChrisReynolds

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Re: Volume Predictions.
« Reply #54 on: April 27, 2013, 08:39:58 AM »
Albedo: Dr Zhang has confirmed to me that PIOMAS doesn't differentiate between FYI and MYI albedo. Strictly speaking this could still mean that albedo changes with thickness. However it seems strange he didn't go on to expand on that. The basic sea ice model is from Winton 2000 "A Reformulated Three-Layer Sea Ice Model", who states:

Fs(Tˆs) and ][Fs(Tˆs)]/]Ts would typically be calculated using downward short- and longwave radiative fluxes, bulk formulas for latent and sensible heat fluxes, the Stefan–Boltzmann formula for the upward longwave, and the computed surface albedo for the upward
shortwave. This part of the calculation is unchanged from Semtner (1976).

Semtner 1976 states that two albedos are used, those of snow and ice. The fraction of solar radiation penetrating into the ice is set to 0.17, and the solar radiation flux into snow free ice contains no thickness element.

I was going to ask if you knew how to get thickness distribution for a single PIOMAS cell.

I don't know that this is possible for us, although Dr Zhang might be able to help. I'm having difficulties grappling with what is going on in Thorndike. A critical point is that the thickness distribution when integrated between maximum thickness and zero always equals 1. I think that this thickness distribution is a set profile which multiplies with the effective thickness of the ice in a gridbox. to give a thickness profile for that box. However Dr Zhang talks about open water in a grid box as leads. This would surely not imply that the integral of the thickness profile always equals 1.

I'm still grappling with this issue.

ChrisReynolds

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Re: Volume Predictions.
« Reply #55 on: April 27, 2013, 09:02:07 AM »
Wipneus,

ThicknessBucket = Round(AprilThicknessArray(n) / 0.05, 0)
      If AprilThicknessArray(n) > 0.05 Then
         TotalAprilArea(ThicknessBucket) = TotalAprilArea(ThicknessBucket) + GridArray(n, 3)
         If SeptThicknessArray(n) < 0.05 Then
            MeltedArea(ThicknessBucket) = MeltedArea(ThicknessBucket) + GridArray(n, 3)
         End If
      End If

GridArray, is an array of grid box constants, where GridArray(n, 3) is grid box area. n goes from 1 to 43200 and is the number of the grid box.

So it's your option 2. i.e. effective thickness in April weighted by area of the cell, and area of grid boxes that have melted out (below 5cm thickness) in the September average.

I left concentration out totally. Using April concentration (X each grid box area), for both the melt and the total area gives a very similar result. So it would perhaps be better to say they're effective thicknesses area weighted by grid box area, not ice area.

crandles

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Re: Volume Predictions.
« Reply #56 on: April 27, 2013, 12:04:31 PM »
Chris,

Thank you for your replies and the interesting graph.

Can you easily amend routine to calculate the average thickness that melts for each 5cm bin?

Just 2012 would do and I understand that you are not accounting for drift. I am interested to see if it reaches a peak for the 1.65 to 1.70 thickness band for 2012 and whether it then declines or stays at approx same melt thickness.

Even though PIOMAS does not change albedo with thickness, the melt thickness may decline as the thicker ice is further into the pack.


Drift can cause some thick cells to move to edge of pack and melt out while some thin cells will get thicker ice drifting into them and not melt out. High thicknesses presumably go wild in recent years because there is very little ice in these thicknesses. So I think the shape of your graph is generally as expected. The detail is interesting eg not much change from earlier years to later years whereas I would have expected a clear trend between 1.1 and 1.7m.

Wipneus

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Re: Volume Predictions.
« Reply #57 on: April 27, 2013, 01:27:11 PM »

Semtner 1976 states that two albedos are used, those of snow and ice. The fraction of solar radiation penetrating into the ice is set to 0.17, and the solar radiation flux into snow free ice contains no thickness element.


I found this: ftp://psc.apl.washington.edu/zhang/IDAO/GIM_code/

In budget.F "surface heat budget and ice growth rate" :

:
C CUTOFF SNOW THICKNESS
      HCUT=0.15

(...)
:
      ALB(I,J)=0.75E+00
      IF(TICE(I,J).GT.TMELTP) ALB(I,J)=0.66E+00
:
C MODIFY ALBEDO FOR SNOW COVER FROM Flato and Hibler (Ridging and strength...)
      ASNOW=0.8E+00
      IF(TICE(I,J).GT.TMELTP) ASNOW=0.7E+00
      IF(HSNO(I,J).GT.HCUT) THEN
      ALB(I,J)=ASNOW
      ELSE
      ALB(I,J)=ALB(I,J)+(HSNO(I,J)/HCUT)*(ASNOW-ALB(I,J))
      IF(ALB(I,J).GT.ASNOW) ALB(I,J)=ASNOW
      END IF

My explanation:

Over 15cm snow albedo is taken as 0.70
0 cm snow albedo is either 0.75 or 0.66 depending on ice temperature
snowdepth between 0 and 15: albedo is linearly interpolated.
« Last Edit: April 27, 2013, 05:14:29 PM by Wipneus »

crandles

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Re: Volume Predictions.
« Reply #58 on: April 27, 2013, 02:40:52 PM »
Presumably you meant

Over 15cm snow albedo is taken as 0.70 or 0.80 depending on ice? temperature
0 cm snow albedo is either 0.75 or 0.66 depending on ice temperature
snowdepth between 0 and 15: albedo is linearly interpolated.

OK Thanks. Interesting.

Compare


PIOMAS range of 0.66 to 0.8. 0.8 seems reasonably for coldest snow. 0.66 as lowest level seems a bit high?

Wipneus

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Re: Volume Predictions.
« Reply #59 on: April 27, 2013, 03:53:02 PM »
Presumably you meant

Over 15cm snow albedo is taken as 0.70 or 0.80 depending on ice? temperature

Yes, my mistake.

PIOMAS range of 0.66 to 0.8. 0.8 seems reasonably for coldest snow. 0.66 as lowest level seems a bit high?

Well this is not PIOMAS but probably a precursor, thickness profiles are mentioned in the comments but not implemented. Further, this is the ice part, albedo of the open water part is taken elsewhere as 0.2.

ChrisReynolds

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Re: Volume Predictions.
« Reply #60 on: April 27, 2013, 04:01:42 PM »
Wipneus,

I'll try again later but at present that link (ftp) isn't working for me. Nonetheless, thanks for pointing me to the temperature dependence of ice albedo, this is designed to simulate melt ponds, hence if the ice surface is greater than the melting point of ice, albedo lowers as melt ponds form. However I can only back up what Crandles shows using the graph - I can dig out the reference for that if needs be.

Now I think about it, isn't pond formation a major player in the albedo difference between MYI and FYI? FYI tends to be flatter so more prone to melt pond formation. How much of the albedo difference is due to melt ponds, and how much due to dielectric constant differences between MYI and FYI?

As ice thickness can be seen as a proxy for age, thickness plays a major role in ice temperature, and that affects which albedo is chosen, I think I was arguably wrong to say PIOMAS doesn't model albedo changes with ice age. It is possible to view the melt pond formation parameterisation as also introducing an ice albedo effect that is indirectly affected by (implicit) ice age.

Doesn't help with the spring melt anomaly, as most of this is happening while NCEP/NCAR temperatures are below zero. I still think that anomaly is due to simple ice thickness and that thinner ice thins more over the season than thicker (see below).

Crandles,

I can do so, but before I do here's why I've not done so earlier.

As part of my trying to get to grips with the spring melt anomaly in PIOMAS I've done scatter plots of thinning through the season as a function of initial thickness.
http://farm9.staticflickr.com/8263/8606025700_a494abf6b7_o.gif
EDIT - animated gif corrected.

I decided not to proceed with average thinning as the spread of thinning for a set initial thickness (under about 2.5m) means an average seems to me to be pretty meaningless. The graph I presented above is more meaningful because it's just looking at what grid cells 'bottom out' to zero.

I had been pondering doing some form of pdf of melt thickness based on initial thickness bands.
« Last Edit: April 27, 2013, 04:34:29 PM by ChrisReynolds »

Wipneus

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Re: Volume Predictions.
« Reply #61 on: April 27, 2013, 04:32:47 PM »
I'll try again later but at present that link (ftp) isn't working for me


Somehow the colon (:) after "fpt" is shown in the text, but not in the link. Let me try again, otherwise insert it yourself:

ftp://psc.apl.washington.edu/zhang/IDAO/GIM_code/

I found the link on http://psc.apl.washington.edu/zhang/Global_seaice/codes.html, link "Global sea Ice Model (GIM_seaice_model)"
« Last Edit: April 27, 2013, 05:13:35 PM by Wipneus »

Wipneus

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Re: Volume Predictions.
« Reply #62 on: April 27, 2013, 04:35:15 PM »
Aha, don't use hyperlinks for ftp links, there is a special one for that:

ftp://psc.apl.washington.edu/zhang/IDAO/GIM_code/

ChrisReynolds

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Re: Volume Predictions.
« Reply #63 on: April 27, 2013, 04:38:44 PM »
Thanks Wipneus.

crandles

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Re: Volume Predictions.
« Reply #64 on: April 27, 2013, 05:25:23 PM »

I can do so, but before I do here's why I've not done so earlier.

As part of my trying to get to grips with the spring melt anomaly in PIOMAS I've done scatter plots of thinning through the season as a function of initial thickness.
http://farm9.staticflickr.com/8263/8606025700_a494abf6b7_o.gif
EDIT - animated gif corrected.

I decided not to proceed with average thinning as the spread of thinning for a set initial thickness (under about 2.5m) means an average seems to me to be pretty meaningless. The graph I presented above is more meaningful because it's just looking at what grid cells 'bottom out' to zero.

I had been pondering doing some form of pdf of melt thickness based on initial thickness bands.


The scatter plots are nice. However, I think it is a bit hard to know what proportion of points are on the y=x line and therefore how much below the y=x line the average is. An average y for each 5cm bucket plotted in a different colour would be a useful addition to those scatter plots IMHO.

pdf is more comprehensive. However, given the problem of ice moving how much of the variation is caused by ice movement and how much is real? Given that problem is a pdf worth the effort? Sometime a simple average might suffice?


Re albedo. We know PIOMAS doesn't melt enough ice in the melt season and PIOMAS using albedos' that are too high may explain why. Of course this doesn't explain why PIOMAS doesn't form enough ice in winter.

ChrisReynolds

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Re: Volume Predictions.
« Reply #65 on: April 27, 2013, 09:40:36 PM »
I'll do an average seasonal melt per thickness 'bucket' tomorrow.

ChrisReynolds

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Re: Volume Predictions.
« Reply #66 on: April 28, 2013, 09:52:58 PM »
Crandles, Anyone Else,

As promised: Graph of average loss of thickness during the season:
http://farm8.staticflickr.com/7056/8689225963_e27a8619ef_o.png

If April thickness is greater than 0.05m then ice present so average calculated, if less than that assume open ocean, and not included in calculation. Average is area weighted, calculated volume loss between April and Sept and divided by the area of ice in April. Concentration has not been used as concentration for that plot, concentration has however been used in a parallel calculation on the spreadsheet, which is available here:
https://docs.google.com/file/d/0B3pB-kdzoLU3V0sxQlNNR01SQXM/edit?usp=sharing

You will need Excel to view, this is a multi-sheet file with the VBA macro source code used to generate the figures included. Download the file and open, no need to give permission to macros unless you want to view the code.

Edit - Grey, all years for 1978 to 2012, lighter plots more recent, darker earlier. Red = average of 1978 to 2012. Green = average 2007 to 2012. Blue = average 2010 to 2012.
« Last Edit: April 29, 2013, 06:14:14 PM by ChrisReynolds »

Richard Rathbone

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Re: Volume Predictions.
« Reply #67 on: April 28, 2013, 10:38:38 PM »
Interesting that there's a peak around 1.9m

I'm not sure how much that shape is due to ice drift, and how much is due to albedo variation with thickness.

crandles

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Re: Volume Predictions.
« Reply #68 on: April 29, 2013, 12:07:33 AM »
Thank you Chris.

Yes. interesting that a lot of years have their peak at around 1.9m.

Also interesting that recent years are doing worse with 1.4 to 1.85m. I would guess that these thicknesses used to be around the edge of the pack but now there are more particularly more in the middle of the pack that don't get high rate of melt that those on the edges get.

There seems to be a minimum around 3m, not really sure why it would begin to increase again above that thickness.

Wipneus

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Re: Volume Predictions.
« Reply #69 on: April 29, 2013, 08:12:48 AM »
Chris's graphic on April 26 is consistent with a melting peak of 1.9m plus a statistical spread.

Here I'm not so sure, the right hand side has contributions of far less grid cells. The lessening of numbers may have to do with the apparent lessening decline in thickness.

Wipneus

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Re: Volume Predictions.
« Reply #70 on: April 29, 2013, 04:25:58 PM »
Looking again at the scatter plots, it is clear the peak is there indeed.

Here is my version over the first 10 years:



My simplest explanation of the graph:

1) thickest ice (over 2.5 m or so) melts/declines about 1 meter;
2) The thinner ice will melt progressively more as the ice gets thinner, albedo effect (eg from lower concentration) and easier transport may the phenomena;
3) 1 + 2 are maxed by the available thickness.

« Last Edit: April 29, 2013, 04:40:17 PM by Wipneus »

Richard Rathbone

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Re: Volume Predictions.
« Reply #71 on: April 29, 2013, 05:26:10 PM »
Thank you Chris.

Yes. interesting that a lot of years have their peak at around 1.9m.

Also interesting that recent years are doing worse with 1.4 to 1.85m. I would guess that these thicknesses used to be around the edge of the pack but now there are more particularly more in the middle of the pack that don't get high rate of melt that those on the edges get.

There seems to be a minimum around 3m, not really sure why it would begin to increase again above that thickness.

Thicker ice will tend to melt less because its in the coldest areas and albedo feedback is less pronounced. However, the cells with the thickest ice in them can only lose from drift, while other cells can gain as well as lose. Losses from drift will be highest for the cells that started with the thickest ice.

ChrisReynolds

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Re: Volume Predictions.
« Reply #72 on: April 29, 2013, 07:32:49 PM »
Both of these plots are as posted above, in both plots grey are for all years for 1978 to 2012, lighter plots more recent, darker earlier. Red = average of 1978 to 2012. Green = average 2007 to 2012. Blue = average 2010 to 2012. i.e. RGB in order as a mnemonic.

% Ice Loss: Percentage of ice melted by September as a function of April thickness.
http://farm9.staticflickr.com/8115/8684706810_9bb4de3e11_o.png

Thickness Loss: Thickness loss from April to September as a function of April thickness.
http://farm8.staticflickr.com/7056/8689225963_e27a8619ef_o.png

Note that if you open these up in seperate windows you can flick between them as they're scaled the same in terms of April thickness.

Basically these are showing the same thing. This can be appreciated because in % Ice Loss under 2m thick shows a substantial increase in percentage of ice melt, while in Thickness Loss under 2m shows an increasing clustering to the line where loss of thickness equals April thickness. By about 1m in every year the average melt equals the April thickness, in % Ice Loss the rate of change slackens and the plots tend to about 90% or more of melt out. This is due to increased open water formation efficiency, the thinner ice is the more easy it become for a given loss of thickness during the melt season to expose open water.


I think that ice drift accounts for the high thickness losses for thick ice >3m, firstly it's hard to envisage a thermodynamic reason for such massive melts of ice in situ, secondly I suspect that for some of these categories there is relatively little area (or volume) involved.

With regards the 1.9m peak, I think Wipneus is correct, if I can add something Dr Zhang pointed out regards the spring volume loss anomaly. The thicknesses we are using are 'effective thickness', in the PIOMAS model itself there is a sub-grid paramerisation of ice thickness which creates a range of thicknesses. As ice below about 2m thins it opens up simulated 'leads' within the pack, these will accelerate the absorption of solar energy and create more warming. I think this accounts for the smearing of data points seen in Wipneus's plot and in the animated gif I've done.
http://farm9.staticflickr.com/8263/8606025700_a494abf6b7_o.gif
The smearing is the spreading of seasonal melt thicknesses upwards towards the open water limit from the grouping of thickness loss around 1m seen for ice above 2m thickess in April.

Need I mention the thinner ice state suggested by PIOMAS's March data?

crandles

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Re: Volume Predictions.
« Reply #73 on: April 30, 2013, 02:56:41 PM »
Thought I would try the split a different way. We don't know the drift, but suppose we assume that the thickest cell in Sept comes from the thickest cell in March, second thickest from 2nd thickest etc.

for 2012 I arrive at the following
Thick to   Area   TotVol   TotVolR   Ini Thick   Thin   % melt
0.05   1338488.288   16545.83803   16545.83803   0.012361586   0.012361586   100.0000%
0.1   349587.3879   25831.49755   25831.49755   0.073891389   0.073891389   100.0000%
0.15   336754.9516   42631.70729   42631.70729   0.126595636   0.126595636   100.0000%
0.2   294609.803   52179.3818   52179.3818   0.177113529   0.177113529   100.0000%
0.25   276275.8961   61156.7591   61156.7591   0.221361183   0.221361183   100.0000%
0.3   194866.6748   53706.19516   53706.19516   0.275604822   0.275604822   100.0000%
0.35   227709.4263   74391.30807   74391.30807   0.326694021   0.326694021   100.0000%
0.4   241220.3136   90361.50925   90361.50925   0.374601574   0.374601574   100.0000%
0.45   219503.8121   92622.518   92622.518   0.421963141   0.421963141   100.0000%
0.5   235056.3633   112228.685   112228.685   0.477454358   0.477454358   100.0000%
0.55   268362.8659   140815.3308   140815.3308   0.52471988   0.52471988   100.0000%
0.6   237381.0765   136376.6232   136376.6232   0.574505033   0.574505033   100.0000%
0.65   266619.141   166824.0161   166824.0161   0.625701574   0.625701574   100.0000%
0.7   231502.085   156604.7576   156604.7576   0.676472342   0.676472342   100.0000%
0.75   202745.7456   146981.0189   146981.0189   0.72495242   0.72495242   100.0000%
0.8   229421.8294   177857.6043   177857.6043   0.775242725   0.775242725   100.0000%
0.85   268480.8769   221427.2317   221427.2317   0.824741167   0.824741167   100.0000%
0.9   254711.6734   223046.5668   223046.5668   0.875682547   0.875682547   100.0000%
0.95   185850.4688   171917.6993   171917.6993   0.925032369   0.925032369   100.0000%
1   145417.8952   141624.7278   141624.7278   0.973915401   0.973915401   100.0000%
1.05   178764.4419   183543.668   183543.668   1.026734769   1.026734769   100.0000%
1.1   198881.7529   213667.6905   213667.6905   1.074345371   1.074345371   100.0000%
1.15   226180.0704   255113.8324   255113.8324   1.12792357   1.12792357   100.0000%
1.2   309467.4092   363263.8888   363263.8888   1.173835687   1.173835687   100.0000%
1.25   268639.8897   328920.5858   328920.5858   1.224392201   1.224392201   100.0000%
1.3   293382.2236   374560.707   374560.707   1.276698712   1.276698712   100.0000%
1.35   423915.0662   562358.282   562358.282   1.326582438   1.326582438   100.0000%
1.4   412347.9689   566259.1729   566259.1729   1.373255637   1.373255637   100.0000%
1.45   325303.2283   462940.5216   462940.5206   1.423104603   1.4231046   100.0000%
1.5   268526.6294   395910.7579   395910.7254   1.474381735   1.474381614   100.0000%
1.55   272067.0575   415034.4915   415033.8886   1.525486016   1.5254838   99.9999%
1.6   281900.6744   444161.1722   444154.2597   1.575594571   1.57557005   99.9984%
1.65   252065.3089   409652.9944   409600.5886   1.625185934   1.624978028   99.9872%
1.7   307887.5891   515259.3501   514810.0142   1.673530757   1.672071342   99.9128%
1.75   291663.8623   502984.8638   501237.9211   1.724536114   1.718546539   99.6527%
1.8   300251.0802   533217.732   527869.3767   1.775906123   1.758093181   98.9970%
1.85   351469.3812   641616.3382   626477.4762   1.825525558   1.782452497   97.6405%
1.9   387084.9673   725373.2899   692889.9532   1.873938156   1.79002031   95.5218%
1.95   313042.1227   602893.8062   557577.7416   1.92591911   1.781158832   92.4836%
2   454830.0789   898320.8011   792424.7492   1.975069026   1.742243501   88.2118%
2.05   474348.2658   960625.3621   777444.5445   2.025147832   1.638974147   80.9311%
2.1   438427.8602   909319.6427   662005.6523   2.074046212   1.509953432   72.8023%
2.15   337283.0208   716060.7821   469605.9499   2.123026473   1.392320161   65.5819%
2.2   219371.0086   476822.9105   288480.8133   2.173591276   1.315036181   60.5006%
2.25   199111.0977   442473.588   255371.0621   2.222244732   1.282555644   57.7144%
2.3   173286.0554   394206.6567   222851.735   2.274889667   1.286033862   56.5317%
2.35   160854.3512   374009.2973   207906.9153   2.325142556   1.292516577   55.5887%
2.4   147646.9876   350488.7676   192098.3317   2.373829451   1.301065025   54.8087%
2.45   101366.7313   245525.1713   133706.8529   2.422147467   1.319040786   54.4575%
2.5   96435.92985   238531.0569   129572.4957   2.473466656   1.34361224   54.3210%
2.55   95745.73192   241636.5669   129114.9448   2.523731994   1.348519064   53.4335%
2.6   77537.50125   199539.8626   104513.9467   2.573462639   1.347914815   52.3775%
2.65   82515.7487   216481.3708   110567.4945   2.623515804   1.339956266   51.0748%
2.7   95046.68667   254356.4804   126197.4178   2.676121487   1.327741368   49.6144%
2.75   77713.26775   211770.6413   101043.2009   2.725025565   1.300205277   47.7135%
2.8   99070.22813   275191.7228   126047.5895   2.77774391   1.272305433   45.8036%
2.85   104285.1829   294841.9859   129707.9737   2.827266326   1.243781428   43.9924%
2.9   146490.4388   421056.2451   177151.8653   2.874291651   1.209306674   42.0732%
2.95   90427.35078   264146.4217   106674.0585   2.921089908   1.179665859   40.3844%
3   52919.73302   157346.5263   61786.8044   2.973305369   1.167556994   39.2680%
3.05   71473.74192   216115.8695   82211.45337   3.023710018   1.150232955   38.0405%
3.1   45144.25787   138735.433   50121.33602   3.073157905   1.11024831   36.1273%
3.15   46831.3276   146327.2392   51057.24492   3.124558851   1.090236975   34.8925%
3.2   34027.77775   108006.941   36452.11749   3.174081533   1.071245903   33.7498%
3.25   29315.81395   94543.45663   31130.60061   3.224998521   1.0619047   32.9273%
3.3   24351.15335   79698.49832   25774.61683   3.272883923   1.05845569   32.3402%
3.35   18924.53932   62953.33566   19681.05978   3.326545211   1.039975634   31.2629%
3.4   13498.0326   45593.42897   14128.84863   3.377783291   1.046733924   30.9888%
3.45   14794.66827   50638.46538   15092.34285   3.422750983   1.020120395   29.8041%
3.5   10798.4844   37490.43733   10792.13057   3.471824003   0.9994116   28.7864%
3.55   16149.01895   56891.61362   16119.21589   3.522914537   0.998154497   28.3332%
3.6   13184.14672   47237.15746   12370.84906   3.582875589   0.938312453   26.1888%
3.65   10446.84395   37849.72893   8920.593893   3.623077852   0.85390324   23.5684%
3.7   6522.5746   23958.50832   5315.861655   3.673167389   0.814994382   22.1878%
3.75   9158.907475   34125.82382   7288.487543   3.72597102   0.795781327   21.3577%
3.8   5352.803975   20227.99683   4172.190337   3.778953409   0.779440151   20.6258%
3.85   11007.33195   42102.88909   7880.683638   3.824985863   0.715948576   18.7177%
3.9   3345.37105   12944.04301   1579.945508   3.869239861   0.472278107   12.2060%
3.95   3339.3747   13054.24405   1260.216281   3.909188162   0.377380915   9.6537%
4   1682.28585   6656.931476   494.2847234   3.957075116   0.293817322   7.4251%
4.05   631.89425   2537.962824   106.7516709   4.016436016   0.16893914   4.2062%
4.1   4329.76755   17667.07206   768.433727   4.08037426   0.177476901   4.3495%
4.15   785.602225   3236.126848   111.5083329   4.119294402   0.14193994   3.4457%
4.2   306.7995   1275.452745   11.59784946   4.1572843   0.0378027   0.9093%
4.25   631.86175   2670.020497   -20.26612964   4.225640336   -0.032073677   -0.7590%
4.3   306.89925   1316.268357   -55.85191933   4.2889266   -0.1819878   -4.2432%
4.35   632.093325   2738.627658   -108.9458104   4.332631828   -0.17235716   -3.9781%
4.4   306.98955   1345.556073   -67.50780022   4.383068   -0.2199026   -5.0171%
4.45   632.09305   2786.763261   -168.8297887   4.40878643   -0.267096417   -6.0583%
4.5   1750.22315   7838.501543   -617.6614332   4.478572657   -0.35290439   -7.8798%
4.6   650.2729   2969.818834   -853.7173838   4.5670346   -1.31286016   -28.7464%
4.9   1430.333725   6967.13555   -2043.381911   4.870986   -1.428605   -29.3289%
5.3   2875.5719   15192.07068   -4234.493532   5.283147565   -1.472574388   -27.8731%


It is melting practically all up to 1.72m. Maximum thinning is 1.79 out of 1.87 then it rapidly falls to 1.30m of thinning of 2.15m thick, steadies at 1.3m thinning then continues to fall.

I am inclined to think that this is a better way to do the split to get reduced effects of drift. Any thoughts?

There is a lot of area which only thins by 1.3m. 1.3m is a lot less than the max thinning of 1.79m. As this is not due to albedo changes presumably it is mainly due to centre of pack location?

Not sure I want to repeat this for all years. Not sure if it is easy enough to adjust your macro to sort Mar and Sept by thickness before calculating thinning and the rest of the work to extract these numbers?

ChrisReynolds

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Re: Volume Predictions.
« Reply #74 on: April 30, 2013, 06:56:02 PM »
Sorry, but I'm far from convinced. Certainly not convinced enough to put time into writing a sorting routine and proceeding from there.

First, it seems to me that by sorting prior to calculating the thinning it is far from guaranteed that the calculated thinning will have any relationship to real thinning. I think it does matter if you're calculating a thinning from grid boxes separated by hundreds or thousands of km.

Secondly, I'm far from convinced that the result has any physical meaning. I don't like the high melt out values you get - almost all ice less than 1.8m melts out. Given the state of the pack in recent years there doesn't seem to be such September lows that this finding is realistic. And I'm struggling to see what the negative percentages for thicker ice categories actually mean. I can't get that table of numbers to load into Excel, so can't look at the numbers in detail as I'd like.

Thirdly, movement of ice is part of the pack. It clearly affects some years more than others (high thinning of thickest ice implies movement out of the area in April - maybe this is the -ve percentages you get? - areas receiving that old ice.) I'm not convinced it's a substantial problem that needs to be factored out. We don't have the ice movement data for post 2004 years so it's an issue we have to live with.

Richard Rathbone

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Re: Volume Predictions.
« Reply #75 on: April 30, 2013, 09:42:03 PM »
Is PIOMAS actually saying that the thickest ice in Sept 2012 was thicker than the thickest ice in March 2012?

ChrisReynolds

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Re: Volume Predictions.
« Reply #76 on: April 30, 2013, 10:05:11 PM »
No it's not. The odd grid cell could feasibly be thinner in April than Sept, due to ice movement. But this is not typical of the pack as a whole.

Is this a result of what's been discussed, if so could you explain?

Richard Rathbone

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Re: Volume Predictions.
« Reply #77 on: April 30, 2013, 10:58:30 PM »
No it's not. The odd grid cell could feasibly be thinner in April than Sept, due to ice movement. But this is not typical of the pack as a whole.

Is this a result of what's been discussed, if so could you explain?

Crandles' negative numbers imply that the thickest cells in Sept 2012 were thicker than the thickest cells in March 2012. If they weren't thicker, then there's an error in his calculation somewhere.

crandles

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Re: Volume Predictions.
« Reply #78 on: April 30, 2013, 11:49:20 PM »
No it's not. The odd grid cell could feasibly be thinner in April than Sept, due to ice movement. But this is not typical of the pack as a whole.

Is this a result of what's been discussed, if so could you explain?

Crandles' negative numbers imply that the thickest cells in Sept 2012 were thicker than the thickest cells in March 2012. If they weren't thicker, then there's an error in his calculation somewhere.

True. There are 9 thickness categories derived from just 14 cells. Look at the areas involved, they are tiny compared to other thickness categories.

Thickest cell in March 5.28m. Thickest cell in Sept is 6.75m. There is bound to be some cells thickening and forming pressure ridges. 14 out of 43200 cells is saying it is pretty rare.

crandles

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Re: Volume Predictions.
« Reply #79 on: May 01, 2013, 12:37:39 AM »

First, it seems to me that by sorting prior to calculating the thinning it is far from guaranteed that the calculated thinning will have any relationship to real thinning. I think it does matter if you're calculating a thinning from grid boxes separated by hundreds or thousands of km.

Secondly, I'm far from convinced that the result has any physical meaning. I don't like the high melt out values you get - almost all ice less than 1.8m melts out. Given the state of the pack in recent years there doesn't seem to be such September lows that this finding is realistic. And I'm struggling to see what the negative percentages for thicker ice categories actually mean. I can't get that table of numbers to load into Excel, so can't look at the numbers in detail as I'd like.

Thirdly, movement of ice is part of the pack. It clearly affects some years more than others (high thinning of thickest ice implies movement out of the area in April - maybe this is the -ve percentages you get? - areas receiving that old ice.) I'm not convinced it's a substantial problem that needs to be factored out. We don't have the ice movement data for post 2004 years so it's an issue we have to live with.

Yes it is far from perfect. The alternative of same cell to same cell suffers from drift moving thicknesses around. This has 2m of melt from cells 2.35m thick and only 1.57m from cells 1.8m thick. Both methods are going to have some weirdness with low area high thickness categories. The sorted method gets rid of too much of that wild variations. I am not really interested in what is happening with those wild swings so I agree it isn't a substantial problem that needs to be eliminated. I am more interested in categories with large areas. With large area categories, there will be some that is wrong but I am hoping it doesn't change the averages too much. Seems like it should be easier to model and predict what we will get with 2013. Easier to model may not be the best way to estimate if it is unrealistic. You might be right about it being unrealistic.


For 2012 thinning seems likely to be somewhere between

Initial thickness  1.8m      2.35m
Thinning:
(a) Cell to same cell 1.57m   2m

(b) Thickness Sorted 1.76m  1.3m

I think it will be nearer b than a but perhaps you think differently.


Here is that table in an excel file. (You should be able to copy paste to a text editor save as txt and then import with space separators?) I have probably messed up the calculations. Forgot to keep track of area of september cells.
« Last Edit: May 01, 2013, 12:49:05 AM by crandles »

crandles

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Re: Volume Predictions.
« Reply #80 on: May 01, 2013, 12:51:11 PM »
Using my sorted by thickness I have done 2012 and 1979 on similar basis.



Interesting?

The thickness that melts does not seem to have increased. That is partly explained by melting further into the pack which is harder to melt. Also there is a lot more area of the thinner categories that have a high melt thickness.

Highest area categories in 2012 were 1.35, 1.4, 2, 2.05 and 2.1. Not really sure if this is physical and further thinning of these large area categories 1.95-2.1 is going to result in a lot more melt out.

ChrisReynolds

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Re: Volume Predictions.
« Reply #81 on: May 01, 2013, 10:26:49 PM »
Crandles.

Just got in from an on-site job (now 2100 left at 0700  :( ), got a similar day likely tomorrow. Will reply over the weekend, and may decide to make the time to do what you're asking for.

Richard Rathbone

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Re: Volume Predictions.
« Reply #82 on: May 01, 2013, 11:27:33 PM »
There's something not right in the way the calculations are being done. Whether or not its physically plausible to have the thickest ice in September be twice as thick as the thickest ice in March, that extreme zigzaging is mathematically impossible if the sorting has been done correctly.

You have thickest in September about 12m, 2nd thickest about 6m, 3rd thickest about 9m and 9 should have been sorted to be thicker than 6.

Its not just at the highest point, there are about 20 similar inconsistencies all the way down to about 1.6m September thickness.

crandles

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Re: Volume Predictions.
« Reply #83 on: May 02, 2013, 12:49:44 AM »
Sorry, that is me not properly keeping track of area.

Here are the last few entries in the table:
MarThick   MarArea   SepThick   SepArea   Thinning
5.5021 741.6836 6.735 995.284 -1.2332
5.5180 1005.592 7.010 1031.19 -1.4923
5.5241 488.8000 7.139 744.790 -1.6149
5.5426 569.3727 7.314 988.437 -1.7722
5.5568 922.2687 7.492 1208.38 -1.9357
5.5663 704.0086 7.536 1791.48 -1.9699
5.5708 934.2085 8.119 1005.59 -2.5483

The sorting looks ok but I am comparing cells of different area. I have not dealt with this properly.
Ideally, the last march cell should be compared against 934.2/1005.59 of the last Sept cell and the previous cell against two par cells but I haven't worked out a way to cope with possibilities of several cell matching one cell.

I have just done a 1 cell to 1 cell match. I have calculated volume in Mar and a volume in Sept for each category and worked out a volume reduction %. That is wrong due to different areas involved in the comparison. Then gone to a thinning figure by dividing by the March area which compounds the problem.

Personally I am not too worried about the high thickness categories that have little area, I mainly want to see the shape for the more popular categories. If there are lots of cells in a thickness category there is more opportunity for large and small areas to balance out. There are still errors there but here are some of the cumulative areas for Mar and Sept:

1.45   52660454 52476419
1.50   52931140 53004817
1.55   53176771 53217102
1.60   53401107 53435458
1.65   53620941 53672039
1.70   53837966 53897925
1.75   54002209 54059946
1.80   54172132 54228535
1.85   54385303 54422292
1.90   54561965 54573170
1.95   54762316 54728702
2.00   54902490 54863100
2.05   55028668 55013301
2.10   55130760 55144060
2.15   55243120 55254879
2.20   55356328 55373119
2.25   55483266 55507382
2.30   55628940 55635004
2.35   55789085 55789683
2.40   55952937 55947242
2.45   56095815 56099137
2.50   56225812 56241026

Sorry if you find the errors distracting. Not quite sure how to fix it easily.



Richard Rathbone

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Re: Volume Predictions.
« Reply #84 on: May 02, 2013, 03:30:21 AM »
What I'd do is pick a common scale for area. Convert both series to that scale using interpolation where necessary. Then use the difference as a measure of melting.

crandles

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Re: Volume Predictions.
« Reply #85 on: May 02, 2013, 11:26:30 AM »
What I'd do is pick a common scale for area. Convert both series to that scale using interpolation where necessary. Then use the difference as a measure of melting.


I am trying to keep the total volume reduction correct. Average thickness of Mar - Average thickness of Sept is a better measure of the thinning.

So I haven't fixed the problem just hidden it better as I did with 2012:


Richard Rathbone

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Re: Volume Predictions.
« Reply #86 on: May 02, 2013, 08:24:42 PM »
Its an interesting contrast between the two. Some quite different behaviour in the 1.8-3.5m range.

The summer ice seems able to ridge up a lot more than the winter.

Conserving the volume reduction is just a matter of choosing your interpolation method for putting both series onto a common scale. Using area as the common scale is going to conserve it to first order, but you might need something fancy rather than just linear interpolation if you wanted to eliminate the higher order errors. I'm not sure the underlying data is accurate enough to warrant that though.

crandles

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Re: Volume Predictions.
« Reply #87 on: May 03, 2013, 12:09:23 AM »
I have fixed the problem - wasn't too difficult: a couple hundred vlookup to provide information to do a few adjustments did the trick. I should be able to do the last 10 years without it taking too long.

Wipneus

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Re: Volume Predictions.
« Reply #88 on: May 03, 2013, 08:32:29 AM »
Following my own train of thoughts a little more.

Attached my scatter plot of grid cell April-thickness vs decline, with some annotations.

The apparently biggest blob, marked region 5, shows a lot of ice that declines about 1 meter with a broad spread.
It is not so visible, but actually most of the dots are on the y=x line, representing grid cells where the ice declines fully. I recognize 3 regions:
1. the ice is less than about 1 meter thick and will disappear when declining as fast as region 5;
2. ice is somewhat thicker and will need some augmented melting and/or advection. This can be explained by increasing mobility and decreasing concentration as the thickness falls below 1 meter during the melt season;
3. ice is really thick. Perhaps some unusual circumstances have led to the full decline (thinking cyclone here).

To complete the classifications there are regions 4 and 6. In 4 the decline is unusually large and in 6 it unusually small or even negative.

Next post will show some maps to see if this provides some insight.
 

Wipneus

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Re: Volume Predictions.
« Reply #89 on: May 03, 2013, 08:52:27 AM »
Continued from previous post where I classified grid cells based on April and September thickness.

Mapping the classes show considerable year-to-year variability, but after 2000 the area with enhanced decline grows considerable (and normality shrinks)

Attached is 1990:

Next post will show 2010,2011 and 2012. The forum seems to have some trouble with all of them at the same time.

Wipneus

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Re: Volume Predictions.
« Reply #90 on: May 03, 2013, 08:55:39 AM »
continued....

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Re: Volume Predictions.
« Reply #91 on: May 03, 2013, 10:54:04 AM »
Attached my scatter plot of grid cell April-thickness vs decline.

Have you thought of coding years as colors (rainbow)? I think, blob #5 would tell something about the resistance of MYI.

crandles

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Re: Volume Predictions.
« Reply #92 on: May 03, 2013, 04:18:45 PM »
With the area mismatch solved, here is years 2005 to 2012 (and 1979).



Chris, Thank you for the offer, but I can do this back several more years without it taking too long now.

crandles

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Re: Volume Predictions.
« Reply #93 on: May 03, 2013, 04:45:17 PM »
Wipneus,

Thanks for the maps interesting and useful.

I think it can be seen that region 6 partial or negative is due to transport of thicker ice into the region.

Region 3 exceptional thick melt out. Ice is compressed usually against land into thick ice but surrounded by land and areas that melt out, this also melts out. I think this is an effect that is not modeled by my sorted by thickness approach. There may also be transport out of area, which I think my thickness sorted method copes with better.

Region 4 partial decline large. Next to land may have large thickness melting. These areas may have transport of ice into cells so doesn't fully melt.

Region 5 Simply centre of pack so 1m melt rather than larger melt that edge of pack causes.

Region 1 Peripheral area which start thin and always melt out.

Region 2 Slightly less peripheral so a little thicker but melt out because more melt at edges.

Tor Bejnar

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Re: Volume Predictions.
« Reply #94 on: May 03, 2013, 07:53:10 PM »
I’m greatly appreciating these PIOMAS Decline analyses. If the graphed data points were plotted in a color based on plot density (red for highest density, blue for lowest density), we would graphically see that Areas 1 2 and 3 represent a lot of data (as Wipneus indicates).

I am surprised that for ice over 2.5 meters thick, only about a meter of ice melts.  Given this analysis, I suspect much of this ice has protected edges (minimally affected by wave action and mixed/warmed water) and is furthest north (shorter summer).  I imagine much of the scatter is due to ice movement.

I think all the maps (1990 and 2010-12) show Fram Strait containing MYI along the east coast of North Greenland in September that wasn’t there in April.  So why does the fast ice of late winter not include lots of recently exported MYI?  (MYI is exported through the Fram all year long.)  Might it be because ocean currents drag the MYI remaining near the coast southward during the early winter, preventing it from becoming part of the fast ice, and MYI exported after fast ice has formed goes southward further away from the coast?
Arctic ice is healthy for children and other living things.

SATire

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Re: Volume Predictions.
« Reply #95 on: May 03, 2013, 08:49:54 PM »
Wipneus,
that is quite shocking. Regions 5 and 6 are fading out - in 2011-12 region 6 can be explained by transport. You are making visible how the ice dies: From top (Bering) to bottom (Fram) - the regions 5&6 are progressing continuously to Fram-export :-(

ChrisReynolds

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Re: Volume Predictions.
« Reply #96 on: May 03, 2013, 09:53:22 PM »
Thanks Wipneus,

Very good stuff. Interesting to see how the bar of MYI that delayed 2012's melt and caused the low concentration that was hit by the August storm is visible (dark green in 2012 plot).

Crandles,

It would have been several days before I'd have done anything. I've just had to do another long day to make sure I didn't have to work during the Bank Holiday.

Richard Rathbone

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Re: Volume Predictions.
« Reply #97 on: May 03, 2013, 10:14:36 PM »
Nicw graphs. The maps give really good context for the plots.

Wipneus

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Re: Volume Predictions.
« Reply #98 on: May 04, 2013, 08:23:42 AM »
I wonder if attaching a real big .png with the complete set of years is useful.

Let me try: FAILED (disconnected)

Converted to low quality (80 70 60) .jpg, cutting size to half.

See if that works: YES.

Now trying the .png again with a http connection: WORKS
« Last Edit: May 04, 2013, 08:48:15 AM by Wipneus »

Richard Rathbone

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Re: Volume Predictions.
« Reply #99 on: May 04, 2013, 03:43:00 PM »
Its looks very similar to me to the ice age category maps.

The message I take from seeing the same story in melt and age categories is that the arctic doesn't have a way to regenerate MYI any more. The stuff that thickens in the summer is the stuff on the way out of the Fram, and the zone that bulks up during winter is next year's high melt zone.