Are 3 dimensions better than 2?

[Jim Hunt]

A place to be nice whilst debating volume/thickness versus area/extent whilst not cluttering up the 2019 melting season thread:

https://forum.arctic-sea-ice.net/index.php/topic,2591.msg193705.html#msg193705

A few facts for you:

http://GreatWhiteCon.info/2019/04/facts-about-the-arctic-in-april-2019/

[Midnightsun]

I was really pondering this while reading the other thread.

Loss of extent/area --> decreased albedo, increased potential for waves --> more melt

Loss of volume should logically lag behind since thin ice melts faster, and thick ice is more resistant to melt, but once it goes it's gone.

So imo, both are important to track but extent comes first.

(Why are climate deniers do obsessed with volume?)

[vox_mundi]

A binary poll might illuminate the consensus.

[Jim Hunt]

A binary poll might illuminate the consensus.

Your wish is my command!

[gerontocrat]

Extent has fallen by nearly 1 million km2 since extent maximum on March 12th to March 31st. That is 10% of the average total season melt c.f. the average of 3%. Area decreased by 862 k.

In the same period volume increased by 209 km3 from 22,209 to 22,218 km3.

As a result thickness increased.

So, did sea ice increase or decrease in that period? Which dimensions will you choose to use to make the call?

 

[Archimid]

Sea ice increased. The surface area that is covered in sea ice decreased.

[Jim Hunt]

So, did sea ice increase or decrease in that period? Which dimensions will you choose to use to make the call?

It increased in the centre, and decreased around the periphery.

Volume! In the centre area and extent are pretty much constant at this time of year.

[Juan C. García]

3 dimensions are real, 2 dimensions is just a concept, an idea, an abstract of reality.

[b_lumenkraft]

So, did sea ice increase or decrease in that period? Which dimensions will you choose to use to make the call?

Depends on what the story is you are telling. i.e.:

If you talk buffer effects of the Arctic sea ice, you'll take volume as a measure.
If you talk albedo, you'll take extend as a measure.

[b_lumenkraft]

3 dimensions are real, 2 dimensions is just a concept, an idea, an abstract of reality.

Word! 

[LRC1962]

So, did sea ice increase or decrease in that period? Which dimensions will you choose to use to make the call?

Depends on what the story is you are telling. i.e.:

If you talk buffer effects of the Arctic sea ice, you'll take volume as a measure.
If you talk albedo, you'll take extend as a measure.

Then you can add a 3rd component and that is mass of 3D ice. As seen in both 2007 and '12 both large melt offs, but for different weather reasons, happened primarily because large volume was hiding little mass.

[Jim Hunt]

If you talk buffer effects of the Arctic sea ice, you'll take volume as a measure.
If you talk albedo, you'll take extend as a measure.

Whilst I agree in general terms, by request there is now a binary poll at the top.

You can't sit on the fence, if you want your vote to count at least!

Also I'd quibble slightly and say "If you want to talk albedo, you'll take area and melt ponds into account."

[b_lumenkraft]

melt ponds

2D or 3D melt ponds??

Yes, i was about to correct 'extend' to 'area', but forgot. 

[Juan C. García]

If you want to calculate the heat absorbed with the albedo, you use 2 dimensions, but if you want to go further and analyse the heat transfer, you have to go 3D.
And with the time series (how is changing day by day) then you are on the 4D. 

[gerontocrat]

As I, with reluctance and sadness, have just resigned from "The Flat Earth Society", I have no choice but to vote for 3 dimensions.

What about the 4th dimension, or even a few more in parallel universes?

[vox_mundi]

As I, with reluctance and sadness, have just resigned from "The Flat Earth Society", I have no choice but to vote for 3 dimensions.

What about the 4th dimension, or even a few more in parallel universes?

4th dimension and alternate realities are covered here:

https://forum.arctic-sea-ice.net/index.php/topic,1578.msg192698.html#msg192698

[Pmt111500]

I occupy a slice in 2d multiverse so it's obvious time is the 3rd dimension.

(Modified: oops this was about ice. Change the first words to "ice occupies" and add "on the positively curved 2d surface" at the proper place.

[b_lumenkraft]

Paladiea, can you or someone briefly elaborate on how density would influence melting, please.

(Repeating myself)^n

https://forum.arctic-sea-ice.net/index.php/topic,2618.0.html

Sorry Jim, it wasn't my intent to overslaugh your great thread.

So, feel free to elaborate in length on the 2Dness of slushed vs. dense ice.

[epiphyte]

All three are needed to derive meaning, and also time. Without all of the dimensions, one sees only a shadow. 

An imperfect analogy, but think of it as a live musical performance - a summation of amplitudes and frequencies, projected onto a surface. Without all of the parameters,  you can't tell Mozart from Metallica.

[Dharma Rupa]

In my own private corner of the Metaverse the spheres start as small circles when you first see them and then grow into large circles which are clearly projections of spheres as you get close enough to really see them.  So I think you have to have at least 4 spatial dimensions.

About ice???  Well, it seems to me our problem is that to properly represent Arctic Ice you need 12 or so dimensions in an Information Space.

(I reluctantly voted for 3, lacking higher available choices.)

[Klondike Kat]

Not even including the much greater uncertainty when adding the third dimension (thickness), I voted for two dimensions.  This should come as no surprise to those who have followed my posts.  Allow me to elaborate.  The albedo effect is based on two dimensions; adding thickness will only change the albedo marginally when the ice is extremely thin, while the difference between any ice and open water is huge.  Weather is unaffected by ice thickness also.  The entire evapotranspiration process is cutoff, when the water is covered by ice.  This effectively changes the Arctic from an ocean system to a desert.  Extent has a much greater effect on wildlife than thickness.  The ice forms an effective barrier between the air and water, and the size of the barrier is largely immaterial.  Animals above cannot feed on those below, and mammals below cannot surface. 

Given the topic at hand, the differences between open water and an ice-covered surface is significantly greater than the difference in ice thickness.

[gerontocrat]

Here are some example graphs on ice area and volume.

Bering Sea.  The data is consistent in that both volume and area are falling quickly and both are well below the 2010's average.

Barents Sea. The data is not consistent. In the last week of March volume loss stalls and rises a bit while area keeps on going down. Volume remains well above the 201's average while area is now well below.

[LRC1962]

Weather is unaffected by ice thickness also.  The entire evapotranspiration process is cutoff, when the water is covered by ice. 

Given the topic at hand, the differences between open water and an ice-covered surface is significantly greater than the difference in ice thickness.

GAC2012, in case one has forgotten, puts a great lie to those statements. The GAC ran onto ice, which if thick and solid would have died out quickly as the temp differential between the outer edge and core would have become the same as both would have been using the same air. What happened in 2012, the ice was thin or if thick very broken, which when the storm first hit dispersed the ice giving access to open water. End result was the temp differential remained high enough the the storm continued doing damage for a very long time. Volume and density do matter very much.
Another factor is waves. Waves hitting a wall of dense thick ice lose all their energy very fast. In 2007, scientists witnessed many times where waves were entering ice fields 100's of miles from the edge and destroying ice over 10 meters thick because the ice was really nothing more then slush. Again volume and density matter.
The last few years we have not seen a GAC nor the kind of wave action that destroys fragile ice and therefore extent has been a very important factor as  far as the shape of ice appears to be in, but if we get another storm like in 2012 or wave action like in 2007, and I feel that we would witness very large fast decline in the ice, because the volume and density of the ice that is around is very very fragile.
BTW I have not voted because it all depends on the weather. Some conditions the 2D metric is far better, but in others the 3D is far better. If we ever can get to the point of getting reliable density measurements, that would be even better.

[Archimid]

This should come as no surprise to those who have followed my posts.

I have followed your posts. You seem to have most things backwards.

The albedo effect is based on two dimensions;

Not true for sea ice, but likely true for ocean water. 

From  NSIDC

Sea ice has a much higher albedo compared to other earth surfaces, such as the surrounding ocean. A typical ocean albedo is approximately 0.06, while bare sea ice varies from approximately 0.5 to 0.7. This means that the ocean reflects only 6 percent of the incoming solar radiation and absorbs the rest, while sea ice reflects 50 to 70 percent of the incoming energy. The sea ice absorbs less solar energy and keeps the surface cooler.

...

Snow has an even higher albedo than sea ice, and so thick sea ice covered with snow reflects as much as 90 percent of the incoming solar radiation. This serves to insulate the sea ice, maintaining cold temperatures and delaying ice melt in the summer. After the snow does begin to melt, and because shallow melt ponds have an albedo of approximately 0.2 to 0.4, the surface albedo drops to about 0.75. As melt ponds grow and deepen, the surface albedo can drop to 0.15

Albedo can vary wildly depending on the characteristics of the ice. Thick, snow covered ice, extremely high albedo. Thin, melt pond areas have almost the Albedo of open ocean. Both snow and melt ponds are extremely relevant to volume.

adding thickness will only change the albedo marginally when the ice is extremely thin, while the difference between any ice and open water is huge. 

Again thick snow covered ice, .9 Albedo. Thin, melt ponded ice, .2-.4 Albedo. Huge difference.

Weather is unaffected by ice thickness also.

 

Maybe. The big differences (humidity, albedo, temperature) between Melt Ponds and snow might have a slight effect on weather, but the conduction difference between 2 meter ice and 5 meter ice may be negligible. However, the difference between .5 meter ice and 5 meter ice is significant

This effectively changes the Arctic from an ocean system to a desert.  Extent has a much greater effect on wildlife than thickness.

Hard to argue with that.

The ice forms an effective barrier between the air and water, and the size of the barrier is largely immaterial. 

The thickness of the barrier determines the transfer of heat between the ocean and the atmosphere. It the ocean temperatures and surface air temperature are the same, the thinner ice will melt faster and will grow faster, depending on the temperatures.

Animals above cannot feed on those below, and mammals below cannot surface.

Sure. I'm sure you are generalizing but it seems like a good assumption. 

Given the topic at hand, the differences between open water and an ice-covered surface is significantly greater than the difference in ice thickness.

If the topic is the melting season, then extent, volume and thickness are about equally important. Each as a simple scalar tells us vital information about a generalized view of the arctic, but nothing specific nor sufficient for most informed analysis. All three together gives us the best picture.

Interestingly, when extent or area are presented as a point on an arctic map, volume and thickness are completely lost. However, when presenting volume/thickness in the same manner we get area for free.

[Klondike Kat]

Sounds like you just supported my statement about albedo, even though you claim you did not.  The range given for sea ice (0.5-0.7) is much smaller than the difference between 0.6 and 0.06.  Do you really think that a 90% drop in thickness can even compare to a 90% drop in extent (or area)?  You seem to be trying awfully hard to refute my statements, when in reality, all you did was provide supporting evidence for my claims.

[jdallen]

Sounds like you just supported my statement about albedo, even though you claim you did not.  The range given for sea ice (0.5-0.7) is much smaller than the difference between 0.6 and 0.06.  Do you really think that a 90% drop in thickness can even compare to a 90% drop in extent (or area)?  You seem to be trying awfully hard to refute my statements, when in reality, all you did was provide supporting evidence for my claims.

OK, this sounds like a setup for a straw man argument.

The fundamental problem is the two metrics *are* linked in ways which would categorically prevent a 90% drop in one without a major reduction in the other.  The relationship is dynamic and can't really be isolated in the way you want.

Your first problem is, the volume of ice in the Arctic is not uniformly distributed.   We will likely see major drops in extent at the end of season - probably not on the scale you suggest of 90% but on the order of 20 to 30% - which will outstrip the related drops in volume.  However that remaining ice will become increasingly important in buffering other changes taking place both in the ecosystem and climatalogically.

The thickness - volume - of that ice is key to its survival.  The durability of that ice increases with age.  If I recall correctly, in 2012, the average melt was on the order of 1.85M.  That's a really important number, as it pretty much identifies at the end of the refreeze what ice is going to survive the melt season or not.  Not extent.  Not area.  It reflects the seasonal uptake in heat, which in more recent years, IIRC has actually dropped back a bit to 1.7-1.8M... which is itself reflected in the recoveries in volume which took place.  (I'll have to check, but 2016 might be an outlier)

I agree, in terms of increasing the potential uptake in heat, reducing extent is a key factor, but you really cannot dismiss volume.  The system is not two dimensional.

[Archimid]

Do you really think that a 90% drop in thickness can even compare to a 90% drop in extent (or area)?

Do you really think you should ignore a 90% thickness reduction (whatever that means)?

[Michael Hauber]

There are two parts to the Arctic.  One part where there is too much heat during the year for ice to survive the melting season, and another part where there is not enough heat during the year to melt the ice.  Extent is the best measure of the shrinking of the zone in which ice can survive, and best measure of the long term trend in reducing the ice, and best predictor of when we will go ice free.  Those who were extrapolating volume/thickness loss around 10 years ago were predicting ice free by about now.  Those who were extrapolating extent predicted that we wouldn't be.  Looks to me like the predictions based on extent were better.

Thickness remembers recent conditions, and encodes information on how warm that part of the Arctic is.  If thickness is very low, that suggests recent temperatures have been warmer, and it is more likely that the ice won't last this specific season.  Thickness is the most important measure for predicting short term changes in ice extent and whether ice will survive the coming melt season.

[oren]

Thickness is the most important measure for predicting short term changes in ice extent and whether ice will survive the coming melt season.

Indeed, thickness predicts short term drops in extent. You can have high temps but if all the ice is 50cm and up, it will take a while for extent to shrink. If lots of ice is very thin, you can get large drops in extent. The 2012 GAC achieved its notorious extent drops by hitting large swaths of thin vulnerable ice.
Thin ice also compacts easier than thick ice, another contribution to potential extent drops. I think this year's recent sharp drops are a combination of thin ice melting in the periphery, and not so thick ice compacting in the inner seas. Plus I assume some wind-driven wave action.
OTOH, a thick ice pack will resist melting and delay extent drops. Some years have seen long stalls at the height of the melting season, due to the ice edge being composed of thick ice (such as the string of thick old ice in the Beaufort/Chukchi in 2018 IIRC).

Ignoring the distribution of thickness (per latitude/location) is like driving blind - expect nasty surprises.

[Archimid]

There are two parts to the Arctic.  One part where there is too much heat during the year for ice to survive the melting season, and another part where there is not enough heat during the year to melt the ice. 

True.

Extent is the best measure of the shrinking of the zone in which ice can survive,

Sorry but no. Extent is binary. Is there ice or is there no ice. That's it. It contains no information on the survival of ice without encoding geographic or temperature data. If you do the same thing to volume and thickness they will show  all the data extent does and then some.

and best measure of the long term trend in reducing the ice, and best predictor of when we will go ice free.  Those who were extrapolating volume/thickness loss around 10 years ago were predicting ice free by about now.  Those who were extrapolating extent predicted that we wouldn't be.  Looks to me like the predictions based on extent were better.

BIG TIME NO! At the same time people were extrapolating no ice by now with volume, other people were extrapolating no ice by 2070 and beyond based mostly on extent. Most of them now admit they were wrong and the estimates have been changed to earlier dates.

If we get a time machine and go to the year if the first BOE, then we can determine who was "more right" or "more wrong".

Thickness remembers recent conditions, and encodes information on how warm that part of the Arctic is.  If thickness is very low, that suggests recent temperatures have been warmer, and it is more likely that the ice won't last this specific season.  Thickness is the most important measure for predicting short term changes in ice extent and whether ice will survive the coming melt season.

Thickness is indeed a very important. Just like volume and extent. Those diminishing the importance of the higher dimensions of the arctic are wrong.

[Klondike Kat]

There are two parts to the Arctic.  One part where there is too much heat during the year for ice to survive the melting season, and another part where there is not enough heat during the year to melt the ice.  Extent is the best measure of the shrinking of the zone in which ice can survive, and best measure of the long term trend in reducing the ice, and best predictor of when we will go ice free.  Those who were extrapolating volume/thickness loss around 10 years ago were predicting ice free by about now.  Those who were extrapolating extent predicted that we wouldn't be.  Looks to me like the predictions based on extent were better.

Thickness remembers recent conditions, and encodes information on how warm that part of the Arctic is.  If thickness is very low, that suggests recent temperatures have been warmer, and it is more likely that the ice won't last this specific season.  Thickness is the most important measure for predicting short term changes in ice extent and whether ice will survive the coming melt season.

So true.  Most people do not realize that volumetric losses will always exceed areal losses, due to the added dimension (unless one dimension is held constant).  Hence, a 50% loss in surface area, equates to a 66% loss in volume (and a 30% loss in either dimension constituting the area).  This is simple mathematics (and physics).  Many erroneously claimed that area must accelerate to "catch up" to volumetric losses, when in realty, the difference between the two indicate similarity and confirmation that the system is behaving as expected.  This is evident by the decrease in volumetric losses recently, as volume slows to match areal losses. 

Using a straight linear regression of the NSDIC leads to an ice-free (less than 1 million km2) minimum in 2060.  Various scientific estimates have different, depending on which years are using in this calculation, or which curve best fits the data.  Even this may be too early, as recent minima have not followed the declining trend of the previous decade. 

I agree that this year's early losses are the recent of melting thin ice.  The maximum this year was significantly higher than the past four, and much of that ice was likely thin, first-year ice.  This made for rather easy melting, when temperatures rose.  The melt will likely decline quickly, as this thin ice has mostly melted.  Summer melt will then be on the low side, as the thickness ice will be more resistant.  Due to this prevalence of thick ice, I suspect the minimum this year will be slightly high than last.

[magnamentis]

There are two parts to the Arctic.  One part where there is too much heat during the year for ice to survive the melting season, and another part where there is not enough heat during the year to melt the ice.  Extent is the best measure of the shrinking of the zone in which ice can survive, and best measure of the long term trend in reducing the ice, and best predictor of when we will go ice free.  Those who were extrapolating volume/thickness loss around 10 years ago were predicting ice free by about now.  Those who were extrapolating extent predicted that we wouldn't be.  Looks to me like the predictions based on extent were better.

Thickness remembers recent conditions, and encodes information on how warm that part of the Arctic is.  If thickness is very low, that suggests recent temperatures have been warmer, and it is more likely that the ice won't last this specific season.  Thickness is the most important measure for predicting short term changes in ice extent and whether ice will survive the coming melt season.

So true.  Most people do not realize that volumetric losses will always exceed areal losses, due to the added dimension (unless one dimension is held constant).  Hence, a 50% loss in surface area, equates to a 66% loss in volume (and a 30% loss in either dimension constituting the area).  This is simple mathematics (and physics).  Many erroneously claimed that area must accelerate to "catch up" to volumetric losses, when in realty, the difference between the two indicate similarity and confirmation that the system is behaving as expected.  This is evident by the decrease in volumetric losses recently, as volume slows to match areal losses. 

Using a straight linear regression of the NSDIC leads to an ice-free (less than 1 million km2) minimum in 2060.  Various scientific estimates have different, depending on which years are using in this calculation, or which curve best fits the data.  Even this may be too early, as recent minima have not followed the declining trend of the previous decade. 

I agree that this year's early losses are the recent of melting thin ice.  The maximum this year was significantly higher than the past four, and much of that ice was likely thin, first-year ice.  This made for rather easy melting, when temperatures rose.  The melt will likely decline quickly, as this thin ice has mostly melted.  Summer melt will then be on the low side, as the thickness ice will be more resistant.  Due to this prevalence of thick ice, I suspect the minimum this year will be slightly high than last.

without going into details, to some of them i agree, to some i do not agree and again about others i know that they're not correct. There is one thing that deserves to be pointed out to round up the picture independently of the other factors and details that were discussed:

while it's true that the early fast melt is due to thin and, what you forgot to mentione, dispersed ice, the assumption that this doesn't mean more than just that is IMO not 100% spot on.

why?

it would be a valid conclusion if we had  just seen a steep decline from seasonal high to now within a common range.

in fact we did not only see a steep decline, but a steep decline into a significant new all time low for the time of the year and this by  a huge margin and continuing and margin increasing and expected to stay more or less in that zone for some time to come.

i'm sure that the early heat in the system and the added moisture due to more open water and due to lower albedo, also due to more open water, has an impact on max thickness of the remaining sea-ice as we speak. perhaps not in the pole region that won't melt out as a whole anyways, but in the region above 80N and below 85N that may or may not melt out any year from now.

of course facts will ultimately tell us all as usual.

[Viggy]

There are two parts to the Arctic.  One part where there is too much heat during the year for ice to survive the melting season, and another part where there is not enough heat during the year to melt the ice.  Extent is the best measure of the shrinking of the zone in which ice can survive, and best measure of the long term trend in reducing the ice, and best predictor of when we will go ice free.  Those who were extrapolating volume/thickness loss around 10 years ago were predicting ice free by about now.  Those who were extrapolating extent predicted that we wouldn't be.  Looks to me like the predictions based on extent were better.

Thickness remembers recent conditions, and encodes information on how warm that part of the Arctic is.  If thickness is very low, that suggests recent temperatures have been warmer, and it is more likely that the ice won't last this specific season.  Thickness is the most important measure for predicting short term changes in ice extent and whether ice will survive the coming melt season.

So true.  Most people do not realize that volumetric losses will always exceed areal losses, due to the added dimension (unless one dimension is held constant).  Hence, a 50% loss in surface area, equates to a 66% loss in volume (and a 30% loss in either dimension constituting the area).  This is simple mathematics (and physics).

I have to assume you are trolling at this point because your argument is that volume lost is greater than area lost because volume has thickness???

And it is impossible to form any simple % correlation between area and volume unless we explicitly know the complete depth profile of the ice and it is somehow uniform across the entire Arctic (which is ludicrous).

‘A lot of people’ may not realize this because apart from using the words ‘mathematics’ and ‘physics’, your argument has no factual basis in either of them.

[Klondike Kat]

There are two parts to the Arctic.  One part where there is too much heat during the year for ice to survive the melting season, and another part where there is not enough heat during the year to melt the ice.  Extent is the best measure of the shrinking of the zone in which ice can survive, and best measure of the long term trend in reducing the ice, and best predictor of when we will go ice free.  Those who were extrapolating volume/thickness loss around 10 years ago were predicting ice free by about now.  Those who were extrapolating extent predicted that we wouldn't be.  Looks to me like the predictions based on extent were better.

Thickness remembers recent conditions, and encodes information on how warm that part of the Arctic is.  If thickness is very low, that suggests recent temperatures have been warmer, and it is more likely that the ice won't last this specific season.  Thickness is the most important measure for predicting short term changes in ice extent and whether ice will survive the coming melt season.

So true.  Most people do not realize that volumetric losses will always exceed areal losses, due to the added dimension (unless one dimension is held constant).  Hence, a 50% loss in surface area, equates to a 66% loss in volume (and a 30% loss in either dimension constituting the area).  This is simple mathematics (and physics).

I have to assume you are trolling at this point because your argument is that volume lost is greater than area lost because volume has thickness???

And it is impossible to form any simple % correlation between area and volume unless we explicitly know the complete depth profile of the ice and it is somehow uniform across the entire Arctic (which is ludicrous).

‘A lot of people’ may not realize this because apart from using the words ‘mathematics’ and ‘physics’, your argument has no factual basis in either of them.

What is so difficult to understand?  Yes, volume lost is greater than area, due to thickness.  Unless thickness remains unchanged over the course of decreasing area, volume must decrease to a greater extent.  This is not rocket science, but elementary mathematics, which you dismiss as nonfactual.  May I remind you that volume equals length x height x depth.  If the length x height decreases by a combined 50% (30% each), and depth decreases by a corresponding 30%, volume will decrease by 66%.

Yes, we do not explicitly know the complete depth profile of the ice.  Hence volumetric numbers are calculated from models, which estimate an average sea ice thickness.  This is another reason why two dimensional measurements are better than three dimensional estimates.

[magnamentis]

There are two parts to the Arctic.  One part where there is too much heat during the year for ice to survive the melting season, and another part where there is not enough heat during the year to melt the ice.  Extent is the best measure of the shrinking of the zone in which ice can survive, and best measure of the long term trend in reducing the ice, and best predictor of when we will go ice free.  Those who were extrapolating volume/thickness loss around 10 years ago were predicting ice free by about now.  Those who were extrapolating extent predicted that we wouldn't be.  Looks to me like the predictions based on extent were better.

Thickness remembers recent conditions, and encodes information on how warm that part of the Arctic is.  If thickness is very low, that suggests recent temperatures have been warmer, and it is more likely that the ice won't last this specific season.  Thickness is the most important measure for predicting short term changes in ice extent and whether ice will survive the coming melt season.

So true.  Most people do not realize that volumetric losses will always exceed areal losses, due to the added dimension (unless one dimension is held constant).  Hence, a 50% loss in surface area, equates to a 66% loss in volume (and a 30% loss in either dimension constituting the area).  This is simple mathematics (and physics).

I have to assume you are trolling at this point because your argument is that volume lost is greater than area lost because volume has thickness???

And it is impossible to form any simple % correlation between area and volume unless we explicitly know the complete depth profile of the ice and it is somehow uniform across the entire Arctic (which is ludicrous).

‘A lot of people’ may not realize this because apart from using the words ‘mathematics’ and ‘physics’, your argument has no factual basis in either of them.

while i agree with your point, not everyone shooting a bit fast or erring to a certain degree is trolling. i did not have the impression that that was intended but perhaps a bit shot from the hip which i'm also a candidate to do at times and i know that i'm serious, even in error LOL.

[Viggy]

What is so difficult to understand?  Yes, volume lost is greater than area, due to thickness.  Unless thickness remains unchanged over the course of decreasing area, volume must decrease to a greater extent.  This is not rocket science, but elementary mathematics, which you dismiss as nonfactual.  May I remind you that volume equals length x height x depth.  If the length x height decreases by a combined 50% (30% each), and depth decreases by a corresponding 30%, volume will decrease by 66%.

Yes, we do not explicitly know the complete depth profile of the ice.  Hence volumetric numbers are calculated from models, which estimate an average sea ice thickness.  This is another reason why two dimensional measurements are better than three dimensional estimates.

So ... im actually a degree’d Aerospace Engineer so even if it was rocket science, I could help you with it 😝

And I am not going to continue a discussion as to why km³ is more than km². It’s as insane as arguing that acceleration is greater than speed.

Any quantity MUST have the same units for you to be able to compare them. Saying volume is greater than extent is absolutely meaningless because extent is expressed in km² and to compare it to a volume, km³, we would need to multiply the extent by 0 (thickness), to convert it to the same comparable units.

‘ANY’ km² x 0 = 0.

And yes, any volume is greater than 0 volume!

[Klondike Kat]

What is so difficult to understand?  Yes, volume lost is greater than area, due to thickness.  Unless thickness remains unchanged over the course of decreasing area, volume must decrease to a greater extent.  This is not rocket science, but elementary mathematics, which you dismiss as nonfactual.  May I remind you that volume equals length x height x depth.  If the length x height decreases by a combined 50% (30% each), and depth decreases by a corresponding 30%, volume will decrease by 66%.

Yes, we do not explicitly know the complete depth profile of the ice.  Hence volumetric numbers are calculated from models, which estimate an average sea ice thickness.  This is another reason why two dimensional measurements are better than three dimensional estimates.

So ... im actually a degree’d Aerospace Engineer so even if it was rocket science, I could help you with it 😝

And I am not going to continue a discussion as to why km³ is more than km². It’s as insane as arguing that acceleration is greater than speed.

Any quantity MUST have the same units for you to be able to compare them. Saying volume is greater than extent is absolutely meaningless because extent is expressed in km² and to compare it to a volume, km³, we would need to multiply the extent by 0 (thickness), to convert it to the same comparable units.

‘ANY’ km² x 0 = 0.

And yes, any volume is greater than 0 volume!

Perhaps if it was rocket science, you would be better equipped to handle the issue.  No one is comparing area and volume directly.  The issue is percent lost, which is unit-less.  In this case, the percent area and volume lost can be compared directly.  Having a thickness of zero is only applicable in abstract mathematics, not real world physics.

[Jim Hunt]

Having a thickness of zero is only applicable in abstract mathematics, not real world physics.

In real world physics what's the equation for the latent heat of fusion?

[gerontocrat]

Having a thickness of zero is only applicable in abstract mathematics, not real world physics.

In real world physics what's the equation for the latent heat of fusion?

See attached.
But as we are talking about sea ice, always a complication...

The content of latent heat in the case of sea ice is a complex one, since thermodynamically it is possible for sea ice and brine to coexist at any temperature, and therefore for sea ice to melt at temperatures other than 0∘C if it is bathed in a suitably concentrated salt solution, such as occurs in the walls of brine cells when brine cell migration is taking place.

[Viggy]

Perhaps if it was rocket science, you would be better equipped to handle the issue.  No one is comparing area and volume directly.  The issue is percent lost, which is unit-less.  In this case, the percent area and volume lost can be compared directly.  Having a thickness of zero is only applicable in abstract mathematics, not real world physics.

Ok let’s talk real world -
Arctic extent peaks in late Feb/early March (see Jaxa/nsidc/gerontocrat’s daily update)
Arctic VOLUME peaks in late April/early May (see Piomas thread)

For the next 2 months, Extent will decrease by 10-20% while Volume will increase by 10-20%

Using your own arguments, percentages to define the change and ‘factual elementary mathematics’, volume doesn’t just decrease more when extent decereases (your hypothesis), it actually increases over the given time frame.

[uniquorn]

Is it real world when all the volume numbers are models?

[Jim Hunt]

See attached.

For the benefit of KK: Q=mL

[b_lumenkraft]

Is it real world when all the volume numbers are models?

Models are not real. The observations feed into the models are though.

[jdallen]

Is it real world when all the volume numbers are models?

Models are not real. The observations feed into the models are though.

Models are estimates derived from the best available data, complete with confidence levels. Even if imprecise, as year over year the use the same inputs and rules, They can be used to identify trends and changes in scale.

[uniquorn]

Agreed. They are estimates until validated.

[Neven]

I believe that for kissing 24 dimensions are best. 



it's a maths joke

[uniquorn]

23 is prime. I'll go with that.   

[magnamentis]

i love this page 

[Klondike Kat]

Cannot argue with any of that!

[wili]

Since we've entered the field (dimensions?) of romance, may I point out that Edwin Abbott managed to create romance in two dimensions (though the third eventually intrudes):

Flatland: A Romance of Many Dimensions is a satirical novella by the English schoolmaster Edwin Abbott Abbott, first published in 1884 by Seeley & Co. of London. Written pseudonymously by "A Square",[1] the book used the fictional two-dimensional world of Flatland to comment on the hierarchy of Victorian culture, but the novella's more enduring contribution is its examination of dimensions.

https://en.wikipedia.org/wiki/Flatland

But in romance and in ice dimensions, quality is at least as important as quantity.