The 2015/2016 freezing season

[TenneyNaumer]

Here is a perfect example of what happens when the Arctic Oscillation Index goes positive -- we're going to see some big melt on the Atlantic side as the warm air pushes into the Arctic:

http://www.cpc.ncep.noaa.gov/products/precip/CWlink/daily_ao_index/ao_index.html

You can see it going in here:

http://mp1.met.psu.edu/~fxg1/SAT_NHEM/animw.html

[crandles]

Speaking of graphs, I noticed the trend on Andrew Slater's freezing degree days chart was dropping through the X-axis, so I decided to update it for Andrew  :

Fun



Compared to 2012 we seem to currently be at about 200 FDD less than 2012 which ended at about 5000FDD. So you might expect about 4% less ice volume growth. Typical recent ice volume growth is around 19,000 Km^3.

4% of that is only 760 Km^3
2015 minimum compared to 2011 minimum was about 1300 Km^3 higher, but end of Feb 16 is similar to end of February 2012.

So on this simplistic analysis, it has been warmer causing slow ice growth but PIOMAS ice growth seems (surprisingly?) much slower than this? Perhaps the higher volume at Sept 15 causes slower growth in the ice so adjust for that in above rough calculation and perhaps you get about what PIOMAS shows? Or is that just fudging a reconciliation with lots of large missing terms (clear or cloudy sky weather, Ocean heat content, ....)?

Perhaps attempts at reconciling other years would reveal whether there must be lots of large missing terms?

Thoughts anyone?
Or maybe someone has done a better exercise is seeing how good FDDs are at predicting volume growth?

[Michael Hauber]

Might also be worth looking at this version of the Andrew Slater Graph.



Still a long way to go before we reach 0 degree freezing days, but there is visible progress towards this potential result.  And an ice free Arctic even in winter is presumably possible on more than 0 freezing days.

[Neven]

Thoughts anyone?
Or maybe someone has done a better exercise is seeing how good FDDs are at predicting volume growth?

It also depends on where the freezing happened. If it froze a lot where the multi-year ice, but not so much where the ice is thinner, volume growth would be slower than the other way around. You'd need an FDD distribution map of sorts, for different years, to be able to really compare.

[seaicesailor]

I am going to pull stuff from university.
The thermal diffusivity of low density but not-so-recently fallen snow is somewhere between alpha = 5*10^-7 m2/s to 10^-6 m^2/s. Numbers depending on many factors (see second and third results of google.com search "thermal diffusivity of snow").
Let's take 5 10^-7 m2/s for these rough estimates, doesn't really matter.

1D heat equation: dT/dt = alpha dT/dz2
Say that temperature raises out there by 10 degC and stays sustained at that level for a couple of months. The depth reached by a significant temperature change as time goes by can be estimated as of the order of:
z ~ ( alpha*t ) ^ 1/2
This is the classic diffusion wave that propagates slower as it goes deeper, hence the fact that 60 cm of snow protect four times longer than 30 cm of snow, not twice.

Let's take a snow depth z = 30 cm from those TOPAZ maps. Then t ~ .1 * 10^6 /.5 = 500,000 seconds = roughly 1/2 day. If we take the ice to be far more conductive than snow, it becomes a perfect sink of heat, and the time to raise the ice surface up by 10C will be just of the order of another day. That is: 30 cm of snow protect about 2 days the ice from feeling the heat out there. The real number can be 1 week or 1/2 day, but cannot be 1 month or 1 hour.

Meaning that after two months of sustained +10C of temperature anomaly, snow represents no protection anymore.
Likewise early snow insulating warmer ice in Fall. My feeling is that is delays the (initially fast) growth of ice a bit, but in a few days nothing protects the ice from the cold winter
If it is 60 cm, it becomes 1 week to 1 month.
If it is 120 cm, it becomes 1 month to the whole season.
And so.
If somebody finds I got some estimate wrong let me know.
It seems in Summer it is different effect (or added to): snow has a very high albedo and takes very long to melt out, delaying surface melt and albedo amplification, early ice thickness reduction, subsequent earlier bottom melt, etc etc etc

PS. I am inclined to believe on the numbers that give more insulating effect of snow: 1 ft -> 1 week, 2 ft -> 1 month, 3 ft -> the whole season. If feels about right when one caves under the thick snow to feel a pretty bearable temperature in a very cold skiing day. But if the max depth over the Arctic is 1 ft, well, a snow bear cannot make much use of it.

[Andreas T]

The key with sea ice is that it has a fixed temperature at the bottom:  melting point at sea water salinity. What you should calculate is heat flux through snow cover and icethickness to the sea water beneath. This is driven by the temperature gradient between top and bottom, i.e. the snow layer keeps the ice surface warmer than the snow surface most of the time. If temperatures rise quickly then that may be reversed for a while but since the ice is warmed from below as well as above in that case this situation won't last long.
The main significance of snow cover in winter is that it lessens ice growth by reducing conduction (diffusion) of heat at any given temperature difference between surface temperature and sea water temperature.

[Pi26]

I am going to pull stuff from university...

But if ice, cold air, cold water and snow are our wortfhul ressources there, exactly as much cold air there gets consumed for producing snow from imported humidity. I think much snow in central arctic shows, that humidity came to far to north and especially late added snow is no real win.
Or is it?

[Frivolousz21]

And there is a huge area of Western Russia that's almost snow free.

Although that might change with that massive Kara vortex blowing up.



2012 and 2015 both had record low snow cover at the end of May over NA. 

For whatever reason likely because of the Pacific ocean and Rocky mtns vortex's can sit over Alaska and pump warm air into the arctic basin. 

Where as the low level thermal boundary over The Russian arctic appears to be much stronger in May preventing WAA from penetrating the arctic basin.

Also the air over Russia is likely much drier than air over NW NA in May.



So Imo the key factor in beating 2012 is record low snow cover over far North NA in May. 

[Frivolousz21]

Looking through the weather archives.

2007 didn't have massive preconditioning.

Between June 3-7th a persistent ridge formed over the Beaufort region and pushed warm air off the NA land region until it was built up over the pacific side of the basin + endless sunny days over  2/3rds of the arctic.  Once albedo lowered and melt ponds formed surface temps ossilated between 0-2C.


Crushing 2.5-3.5M old ice.

Now a combo between increased GHG forcing, thin ice, warmer oceans, and faster snow melt allow major melt with weaker conditions

A 2007 this summer and we would see 2012 get crushed.

[Frivolousz21]

So yeah.

Incredible really.

I used the entire 1970s instead of one of the coldest years so the data wasn't overly skewed.  But it's not even close regardless.

The cold pool has shrunk and modified so much.

It's pretty clear how important snow cover and sea ice is in terms of modifying Spring temperatures in the Northern Hemisphere.

I'd bet by 2030 we will see land snow cover in early May start to resemble the current late May/early June snow cover.

You can imagine how much warmer the atmosphere will be by then around the arctic.

Think about April versus late August and early September.

Same level of solar insolation.

Yet thanks to thermal inertia + albedo modulation the atmosphere is quite different.




Imagine an April and May where oceanic ssts are 3-6C warmer on average than now between 45-65N.

Snow cover will have no chance to reach June.

Surface melt will likely be underway in the arctic basin by May 1st.  I mean real deal surface melt.  With melt ponds forming by May 10th.  Substantial open water by June 1st-15th. 

Completely melted out Beaufort, ESS, and Chukchi by July 1st.





If the ice completely melted out by July 1st in those areas. 

SSTs in those areas would sky rocket with just a few days of sun/WAA.

Easily rocket upwards into the 8-15C range.  Which in turn will modulate the low level air temperature much closer to the remaining ice.  And then a strong breeze from the Chuchki/ESS off the Russian coast over the warn open water will be thrusted into the CAB carrying 8C+ air.  But more importantly much higher dew points

This would cause a pretty massive positive feedback crippling the remaining ice.  Assuming the structural integrity of this ice is somewhat similar to today's.

Widespread melt lakes would form all the way from the pole to Greenlands Northcoast.


How much more energy can melt lakes transmit from the atmosphere to the ice than smaller melt puddles or ponds?



In turn as the sea ice vanishes GIS will likely get punished so much harder.

[seaicesailor]

The key with sea ice is that it has a fixed temperature at the bottom:  melting point at sea water salinity. What you should calculate is heat flux through snow cover and icethickness to the sea water beneath. This is driven by the temperature gradient between top and bottom, i.e. the snow layer keeps the ice surface warmer than the snow surface most of the time. If temperatures rise quickly then that may be reversed for a while but since the ice is warmed from below as well as above in that case this situation won't last long.
The main significance of snow cover in winter is that it lessens ice growth by reducing conduction (diffusion) of heat at any given temperature difference between surface temperature and sea water temperature.

I gave some numbers about how ice surface temperature responds to atmospheric temperature change with 30 cm on top. Meaning that the ice problem stays identical and the heat flux (and hence bottom freezing rate) does not change much whether there is 30 cm of snow on top or zero. So if there are 10 C excess for months bottom freezing is going to reduce the same as it was no snow.
The same cannot be said if there are 60 cm of snow, or above, I think.
We could have a bite to the bottom meltin rate problem (FYI, because the other MYI becomes a problem full of mines).

[epiphyte]

Thoughts anyone?
Or maybe someone has done a better exercise is seeing how good FDDs are at predicting volume growth?

It also depends on where the freezing happened. If it froze a lot where the multi-year ice, but not so much where the ice is thinner, volume growth would be slower than the other way around. You'd need an FDD distribution map of sorts, for different years, to be able to really compare.

...and maybe knock the definition of "freezing" down to -10 degrees C or so while we're at it... ?

[crandles]

Thoughts anyone?
Or maybe someone has done a better exercise is seeing how good FDDs are at predicting volume growth?

It also depends on where the freezing happened. If it froze a lot where the multi-year ice, but not so much where the ice is thinner, volume growth would be slower than the other way around. You'd need an FDD distribution map of sorts, for different years, to be able to really compare.

...and maybe knock the definition of "freezing" down to -10 degrees C or so while we're at it... ?

Neven, yes that would probably have been the next item for list of missing items I started - also snow distribution.

Epiphyte,
-10C would make a big difference but is it valid? I view this as being ocean convecting heat to surface so it has to be really cold to freeze over. But ocean is still losing heat at -5C and the more heat is lost the more ice can form (perhaps added under other ice rather than at open surface because convection creates temperature gradient where surface stays at or above -1.8C but a little lower under some ice temp does get down to -1.8C). Not sure if FDD displayed has been measured from 0C or -1.8C or something else. Seems to me that measure should start from freezing point i.e. ~ -1.8C. But perhaps this measure should be adjusted for sensible heat content of ocean?

Not sure we have adequate data on temperatures at different depths or how far down should be brought into such an adjustment. So I am not sure I am capable of doing such an exercise that attempts to make such adjustments.

[jdallen]

Thoughts anyone?
Or maybe someone has done a better exercise is seeing how good FDDs are at predicting volume growth?

It also depends on where the freezing happened. If it froze a lot where the multi-year ice, but not so much where the ice is thinner, volume growth would be slower than the other way around. You'd need an FDD distribution map of sorts, for different years, to be able to really compare.

...and maybe knock the definition of "freezing" down to -10 degrees C or so while we're at it... ?

Neven, yes that would probably have been the next item for list of missing items I started - also snow distribution.

Epiphyte,
-10C would make a big difference but is it valid? I view this as being ocean convecting heat to surface so it has to be really cold to freeze over. But ocean is still losing heat at -5C and the more heat is lost the more ice can form (perhaps added under other ice rather than at open surface because convection creates temperature gradient where surface stays at or above -1.8C but a little lower under some ice temp does get down to -1.8C). Not sure if FDD displayed has been measured from 0C or -1.8C or something else. Seems to me that measure should start from freezing point i.e. ~ -1.8C. But perhaps this measure should be adjusted for sensible heat content of ocean?

Not sure we have adequate data on temperatures at different depths or how far down should be brought into such an adjustment. So I am not sure I am capable of doing such an exercise that attempts to make such adjustments.

FDD is tied to 0C, as that's a fixed value rather than something as imprecise that can vary substantially as the freezing point of sea water.

http://psc.apl.washington.edu/nonwp_projects/landfast_ice/freezing.php

Rather than a means by which one can determine if things can freeze, it is a proxy for the transfer of heat that represents "pressure" more than "volume".  The heat content of the two sides of the gradient it represents doesn't really factor in, except in so far as a large transfer of heat would likely shift the value FDD value down.

To your point, the -10C limit as discussed here has never appeared to be a causal threshold, but more of a correlative one, which as you point out likely reflects the temperature gradient at which near surface ocean heat convection/conduction balances surface radiative, convective and evaporative heat loss to the atmosphere. The ocean doesn't stop losing heat between -10C and 0C.  It just doesn't lose heat fast enough. 

I also agree, as it is so much at the whim of microclimate conditions, predicting it is far beyond our current sensory and computational resources.

[Jim Hunt]

FDD is tied to 0C, as that's a fixed value rather than something as imprecise that can vary substantially as the freezing point of sea water.

Not according to the NSIDC it isn't:

https://nsidc.org/cryosphere/seaice/processes/thermodynamic_growth.html

The freezing temperature of ocean (saline) water is typically -1.8 degrees Celsius (28.7 degrees Fahrenheit). If the average daily temperature was -5.8 degrees Celsius (21.6 degrees Fahrenheit), this would be -4 degrees Celsius (24.8 degrees Fahrenheit) for one day, as the following equation shows:

( -1.8 ) - ( -5.8 ) = 4 degrees below freezing

4 degrees below freezing / 1 day = 4 cumulative FDD

I do my automated IMB buoy sums on that basis.

[jdallen]

FDD is tied to 0C, as that's a fixed value rather than something as imprecise that can vary substantially as the freezing point of sea water.

Not according to the NSIDC it isn't:

https://nsidc.org/cryosphere/seaice/processes/thermodynamic_growth.html

The freezing temperature of ocean (saline) water is typically -1.8 degrees Celsius (28.7 degrees Fahrenheit). If the average daily temperature was -5.8 degrees Celsius (21.6 degrees Fahrenheit), this would be -4 degrees Celsius (24.8 degrees Fahrenheit) for one day, as the following equation shows:

( -1.8 ) - ( -5.8 ) = 4 degrees below freezing

4 degrees below freezing / 1 day = 4 cumulative FDD

I do my automated IMB buoy sums on that basis.

Then it appears the NSIDC and UW are using slightly different definitions.

[Andreas T]

The key with sea ice is that it has a fixed temperature at the bottom:  melting point at sea water salinity. What you should calculate is heat flux through snow cover and icethickness to the sea water beneath. This is driven by the temperature gradient between top and bottom, i.e. the snow layer keeps the ice surface warmer than the snow surface most of the time. If temperatures rise quickly then that may be reversed for a while but since the ice is warmed from below as well as above in that case this situation won't last long.
The main significance of snow cover in winter is that it lessens ice growth by reducing conduction (diffusion) of heat at any given temperature difference between surface temperature and sea water temperature.

I gave some numbers about how ice surface temperature responds to atmospheric temperature change with 30 cm on top. Meaning that the ice problem stays identical and the heat flux (and hence bottom freezing rate) does not change much whether there is 30 cm of snow on top or zero. So if there are 10 C excess for months bottom freezing is going to reduce the same as it was no snow......

I'm trying to get a handle on this from the IMB data. I looked around for reasonably stable temperatures over a snow cover which extends over at least a couple of temperature sensors. This is 2014C from 24/03/2014 to 13/04/2014, the temperature gradient in the ice is conducting heat from the ice / water interface to the ice surface. x-axis is time , each line is the temp at 10cm spacing from the surface. The red line fluctuates with diurnal cycle of radiative balance but averages below the green and that in turn below the blue line. The difference between the temperature gradient over those 20cm is steeper than that over any 20cm deeper in the ice. Since ice temperature hardly changes, heat flux through the steep gradient and the shallow temp gradient is the same. The steep gradient is in snow, the shallow gradient is in ice (top sounder gives 20cm of snow)
So what is the effect of the snow? Of a roughly 16 degC average temperature difference between sea surface and atmosphere 5degC drop is over 20cm or so of snow. That means without snow the difference through the ice would be roughly 140% of what it is "now", and heat transfer, i.e. ice growth  would be 140%too.
Alternatively the same heat transfer would occur as "now" if no snow but top surface at only -11 degC below sea surface temp. That same top surface temp with snow cover would then reduce heat transfer to 71%.
These numbers are reduced if the thermal inertia of the ice is taken into account, but your calculation seems to be based on thermal inertia alone without taking the heat flux into account.

I hope that helps to make this clearer

[jdallen]

<snippage>
I hope that helps to make this clearer

I'm afraid without additional legend references (which lines belong to what depth gradient?), I find the graph a bit opaque.

[Neven]

Anomalously cold temps (finally) and northerlies, but SIA/SIE in the Bering Sea didn't budge. It seems Baffin and Okhotsk caused the small uptick that has the maximums not coming in (near-)record early this year:



The GFS weather model forecast was for a cooldown in the Arctic (first negative anomaly for the region in a long time), but the forecast has now changed again and though not as 'warm' as in Jan and Feb, things are staying anomalously warm for the coming week. I think that if anyone feels the need, he/she can call the maximum before the start of next week. A new record low for CT SIA, second place for IJIS SIE.

[charles_oil]

Mondays channel 4 UK tv news had  5 minute article about global warming & the warmest Feb.

This link may get you to the catch-up section:
http://www.channel4.com/news/catch-up/

[seaicesailor]

Andreas, it is time, I  put up a model of 1D heat equation with two layers, one snow, the other ice; boundary conditions being the top side unsteady following atmospheric T during winter, and the other isothermal at freezing point, evaluating the thickness growth if possible, based on the latent heat being released and considering as heat sink the ice above but not the ocean under. In the mid interface I will set the condition of conserved heat flux between ice and snow. 2nd order explicit finite differences in spatial direction and Runge Kutta 4th order in temporal evolution, I will use Matlab. A nice exercise, so I can understand the very basics from my own numbers. Simple thermodynamical model which I think is not so far from reality during Winter, totally inappropriate during melting.

No offense, but absence of x axis labels and legend in your plot, I dont understand it.

Let me know if I miss something in the model (blunt first order phenomena, not satanic details and subtleties based on the inhomogenous salinity of sea ice and salt drainage  for instance, that I can't handle as an amateur).

[Andreas T]

Thanks seaice sailor, I agree the back to basics approach would be good.  Lets continue this discussion on another thread, I suggest "what the buoys are telling" http://forum.arctic-sea-ice.net/index.php/topic,327.msg71781.html#msg71781
sorry about the not so well explained graph, it took me a while to find suitable data and make the graph, so I hoped people would be familiar enough with the IMB buoys to guess what it shows 

[seaicesailor]

Thanks seaice sailor, I agree the back to basics approach would be good.  Lets continue this discussion on another thread, I suggest "what the buoys are telling" http://forum.arctic-sea-ice.net/index.php/topic,327.msg71781.html#msg71781
sorry about the not so well explained graph, it took me a while to find suitable data and make the graph, so I hoped people would be familiar enough with the IMB buoys to guess what it shows 

Sounds good. No I am not that familiar with it, last year I brought some data of thise buoys here are they turned out to be months old. Yes we will continue elsewhere thx :- )

[Richard Rathbone]

Andreas, it is time, I  put up a model of 1D heat equation with two layers, one snow, the other ice; boundary conditions being the top side unsteady following atmospheric T during winter, and the other isothermal at freezing point, evaluating the thickness growth if possible, based on the latent heat being released and considering as heat sink the ice above but not the ocean under. In the mid interface I will set the condition of conserved heat flux between ice and snow. 2nd order explicit finite differences in spatial direction and Runge Kutta 4th order in temporal evolution, I will use Matlab. A nice exercise, so I can understand the very basics from my own numbers. Simple thermodynamical model which I think is not so far from reality during Winter, totally inappropriate during melting.

No offense, but absence of x axis labels and legend in your plot, I dont understand it.

Let me know if I miss something in the model (blunt first order phenomena, not satanic details and subtleties based on the inhomogenous salinity of sea ice and salt drainage  for instance, that I can't handle as an amateur).

Make sure your scheme allows for the moving boundary. (could be a satanic detail or could be a blunt phenomenon, depending on just how you set it up)

[seaicesailor]

Make sure your scheme allows for the moving boundary. (could be a satanic detail or could be a blunt phenomenon, depending on just how you set it up)

It is a blunt phenomenon which requires a satanic detail in the numerical method.
The challenge is I find time before next Winter ... if there is ice left.

[Neven]

Okhotsk is going to get torched in the coming week. For a while there was a GFS forecast on ClimateReanalyzer showing a negative anomaly, but this has now completely vanished and we're back at an Arctic-wide +3-4 °C anomaly.

[Neven]

This data has been updated up to 2016 week 1:

[Adam Ash]

Interesting seeing the 4 and 5 yr ice getting squirted out into the Beaufort Gyre wherein it will vanish before it sees the cliffs of Wrangle Island in the early summer mists.

Considering how little 2 and 3 year ice seems to remain at the end of the freezing season it seems that these conditions will continue the erosion of multi-year ice against the CAA to the point that there will be very little left but mush.

[seaicesailor]

This data has been updated up to 2016 week 1:

A lot has circulated sinced then. We have a lot of FMI (first month ice) in Beaufort and Kara. A lot of MYI is being exported to Fram, Barentz and also got closer to Beaufort.

All russian coast remains FYI as expected in many years.
Was it 4m thick or 2m thick anybody?

[Tor Bejnar]

Per the EASE-Grid Sea Ice Age gif, it looks to me that about half the 3-year-old ice present in October 2015 (“week 40”) got exported out the Fram.

[jdallen]

This data has been updated up to 2016 week 1:

A lot has circulated sinced then. We have a lot of FMI (first month ice) in Beaufort and Kara. A lot of MYI is being exported to Fram, Barentz and also got closer to Beaufort.

All russian coast remains FYI as expected in many years.
Was it 4m thick or 2m thick anybody?

There are places where it's above 2M, but for the greater part, most of the Russian side ice is sub-2M.

[Michael Hauber]

By Andrew Slater's graphs it looks like the coldest weather we've had all winter with temperatures going all the way down to normal.

[seaicesailor]

Is it possible to measure the flatness of the freezing curve? Something like #days within 1% of the max?

This is just a nice exercise. I found the MASIE data regionally (not exactly the same as IJIS or NDSIC, which database I could not find; but I hope MASIE is valid for this purpose). I compared the 10-year average of SIE, with same data but excluding outer seas such as Bering, Baltic, Okhostk, and other minor ones like Yellow Sea and Cook Inlet. Probably something of this sort has already been done here. In the plot I also represent the "excluded outer seas" curve raised by 1.5M km2 as well, just for the purpose of comparing visually the shape with the total ice extent average.

These outer seas are the most meridional ones and less protected by land, so it is reasonable to expect they should suffer the gradual raise of NH temperatures the most. I am representing the extreme in which no appreciable ice is even formed there during Winter.

I leave untouched the inner seas because they are higher in latitude and protected by land (except for Barents) and they are more resilient to a raise of temperatures. For melting to gain momentum in the Arctic Ocean, water has to open up and the ice edge begin to retreat; this is a process that we know depends on many factors.

The plot shows that the extent, excluding the outer seas, does not vary by more that 300,000 Km2 (2%) for two months and a half around the maximum (solid double arrow). If we reduce that percentage to 1%, the time is reduced, still close to two months (dash double arrow).

OTOH, the average of total SIE stays within 300,000 Km2 (2%) for only one month and a half, and this time is reduced to one month for 150,000 Km2 (1%)

Later in April, inner seas start to open up. I don't believe that accelerated melting in inner seas can happen anytime earlier than April, since, when open water appears (by drift, cracks or so) the sea water refreezes immediately. Sun and warmth from the continents is needed and does not come until April. I do not see that changing in a long long time. There can be variations year by year though.

Similarly I expect freezing to be over by December in inner seas and not later. Only an extreme source of warmer water due to alterations of Ocean currents or a strong freeing of Ocean heat content by mechanisms I have no knowledge could counteract the loss of heat by radiation during the long Arctic Night. I do not see that changing in a long long time. Of course there can be variations year by year.

Note also that the melting in the inner seas is fairly uncoupled from what happens during the maximum in Winter with the outer seas; sure a very warm winter won't help ice in Summer, but we have the weather.

My conclusion: real melting starting in April in inner seas not anytime sooner, freezing finishing in December in inner seas not any time later, outer seas being more meridional, exposed to open waters, suffering most of NH warmth excess; and, the time of flatter extent near the maximum being dilated by up to one month in future years.

[DavidR]

SeaIce Sailor, Carmiac 

NSIDC Data:
ftp://sidads.colorado.edu/DATASETS/NOAA/G02135/north/daily/data/

CT Area Data
http://arctic.atmos.uiuc.edu/cryosphere/timeseries.anom.1979-2008

IJIS/Jaxa Data
https://ads.nipr.ac.jp/vishop/data/graph/plot_extent_n_v2.csv

It is fairly easy to put this into an excel spread sheet identify the maximum using the  max() function and then use conditional formatting to  identify all days within a certain value of the  max eg  Max() - 0.200 which I  used for the Plateau Hypothesis calculations I  did.

[Peter Ellis]

Is it possible to measure the flatness of the freezing curve? Something like #days within 1% of the max?

The plot shows that the extent, excluding the outer seas, does not vary by more that 300,000 Km2 (2%) for two months and a half around the maximum (solid double arrow). If we reduce that percentage to 1%, the time is reduced, still close to two months (dash double arrow).

There's a thread for the plateau hypothesis somewhere, so this should probably move there.  One useful exercise would be to see if the "plateau" measurement is stable across different definitions of  plateau.

i.e. say you count the number of days each year spends within 0.5% of the maximum, use this to define "plateau length" for each individual year and then rank them from shortest to longest plateau.  Does the ranking change if you set the cutoff at 1% of maximum, or 1.5%, or  2%?

If (as I strongly suspect) the ordering is inconsistent, then this tells you that the measure of "plateau length" is essentially arbitrary and depends only on the cutoff you happen to choose.  In this event, trying to correlate "plateau length" with any other factor such as summer minimum, winter max, volume loss (etc.) would be a futile endeavour.