Fix this Analogy

[Fairbanksnchill]

Every day you go to the local buffet to get your three meals. You eat 100 grams of olive oil, 100 grams of celery, and drink 100 grams of lemon water.  Your total calorie consumption for each meal is 895,103 calories.  For the whole day it’s 2,685 Calories (Big C = Kilo calories)
884,000 calories came from the olive oil. 11,089 calories came from the celery. 14 calories came from the lemon water.  The 2,685 Calories is your daily requirement to stay alive. You must eat that many Calories or you will starve to death.
One day you arrive at the buffet for breakfast and they inform you that the olive oil is now all gone.
You must now eat all your daily required Calories from celery and lemon water. From the math you would need to eat 8,072 grams or 17.8 Pounds of celery and your 100 grams of lemon water to wash it down.
For Lunch, since you are already tired of celery, you decide to go 50/50 on celery and lemon water. You eat your 4036 grams of celery (or 8.9 lbs.) and you down a whopping 3,164,324 grams of lemon water (or 6,976 lbs. of lemon water). 

The concept of going from a high calorie diet to a low calorie diet is obviously, insanely, impossible. The math is simple arithmetic. If you understand this example, you now understand why the arctic sea ice is so important to the planet.
The ratios are exactly the same.
1 serving of olive oil is ~79.72 times as many calories as celery.
1 serving of celery has ~784 times as many calories as lemon water.
You can either consume 100 grams of olive oil, or, 7,972 grams of celery, or 6,250,048 grams of lemon water.
 You can either melt 100 grams of sea ice, heat up 7,972 grams of the ocean 1 degree Celsius, or heat up 6,250 Liters (6,250,048 milliliters) of air at 1 atmosphere of pressure by 1 degree Celsius.
The best case example is that all the extra heat will go into the oceans. Under that impossibly unlikely scenario the world will only heat up 80 times faster instead of melting the sea ice.  This has nothing to do with sea ice albedo. It is simply thermodynamics. 

[Avalonian]

To me, this is indeed the scariest part of the whole situation... but something I don't quite understand is what the mixing distance are, and therefore how isolated different parts of the system might be.

So, say the Beaufort is ice-free every year (it's rapidly heading that way, after all). Does the heat that would otherwise melt ice in that area instead melt ice in surrounding areas, or does the temperature of the local water rise roughly in line with this ratio? I'm not aware of sea surface temperatures rising so spectacularly, so presumably some of that energy is dispersed into the surrounding ice and permafrost (or downwards, raising the bulk sea temperatures by a smaller amount)... That old experiment of melting ice cubes in a pan implies that within a single system, heat will go into melting ice before the water temperature rises, but what are the scales of mixing? If the ice is a thousand km away, shouldn't the SST be rising rapidly across the Beaufort? Is that in fact happening?

Extrapolating from there, once the entire Arctic Ocean is effectively ice-free, will the majority of the heat go straight into the water? Or will the air temperature buffer it, since this is in contact with terrestrial ice caps and permafrost, which might need to also melt before the air temperature (and therefore the SST in equilibrium with it) can also rise too much?

Basically, when does the new diet really kick in, in terms of the vanishing ice..?

[oren]

The analogy, like every other, has a limit where it stops becoming useful. Avalonian brings up an excellent point, as the mixing layer in the Arctic ocean is in the order of 80m, while the vanished sea ice in places that become ice free is let's say 1m, you could get a ~1C SST rise rather than 80C.
In reality some Beaufort SSTs if memory serves me correctly can get to a few degrees above 0C when away from ice.

[Fairbanksnchill]

I completely agree with your take on distance and other variables being significant.  I moved up to Fairbanks AK to study the way ice and temperature interact.  The people here know that a clear sky means a significant temperature drop.  They also know that if it's snowing then the weather has warmed up.  The hills around Fairbanks are always warmer than the flat land where the city lies.  There won't be snow or rain if the storm has to go over the Denali range to get to Fairbanks.  There are other more significant examples of terrain effecting weather.  California's wildfires being the most obvious.  If only the wind would change direction, everything would change with it.  In a closed system, condensation causes a vacuum to occur. In a closed system evaporation causes the pressure to rise.  I expect to witness the wind becoming stratified latitudinally when the sea ice is gone.

My own family member told me once that ice could not get below it's freezing temperature.  I would want to believe that I understand most of the fundamental physical phenomenon.  I was gobsmacked trying to explain the enthalpy of fusion to someone who lacked the core education regarding temperature.

One of my most interesting debates has been the claim "The arctic sea ice doesn't matter as much as Greenland and Antarctica".  My claim is that both are mountains. Ice on 10,000 ft elevated mountains doesn't just melt to keep the world cool. 

The catch 22 I am finding with this food analogy is that a person who doesn't understand climate change often doesn't understand food calories either. . .

[Avalonian]

Thank you both for the thoughts! I imagine that a temperature profile through the top 100 m of the open-water Beaufort next summer would be quite instructive. If the heat penetrates reasonably deeply then it's going to enhance bottom-melt elsewhere as it drifts... and if it doesn't then I guess ready-made krill soup will become a local staple. 

[aperson]

This is a very good analogy to think about! The main issue I had with it after consideration is how salinity affects ice ablation. In this example we're only considering the enthalpy of fusion. However, sea ice loss is also driven by ablation from salt interaction. I don't have any sort of quantitative understanding of these effects though to figure out how and to what extent we'd temper this analogy to deal with it.

[dnem]

I think the biggest problem with this analogy has to do with seasonality.  I often see this argument presented as if it it will kick in completely the first moment we have zero arctic ice.  The first moment we have zero arctic ice will come at the end of a long melt season when enormous energy had just been expended melting the previous freeze season's accumulated ice.  Right after the first melt out, we will head back into the long arctic night, and the thermodynamics will reverse as ice again accumulates.  As we step our way down toward a seasonally ice free arctic, each season there is less ice to melt (it's not a monotonic decrease, but on average the trend is toward less and less ice to melt) so more of the available energy that would have gone to melting ice will heat air and water, in amounts determined by many complex two and three dimensional processes. So really, the oil, celery and lemon water buffet is already happening, and the ratios are heading steadily toward more celery and lemon water, but there will not be any abrupt, discontinuous shift in the "diet."  Only when we get to a year round ice free state will there be no olive oil left to eat, and by then, the planet's climate system will have already absorbed all the cumulative energy that would have gone into melting ice as we travel the long (how long?!) road down to an ice free arctic.

[Iceismylife]

I think the biggest problem with this analogy has to do with seasonality.  I often see this argument presented as if it it will kick in completely the first moment we have zero arctic ice.
...

I like to think in terms of something like a commissary.  Take one that serves 1,000 people, 999 workers and 1 free loader.  The free loader gets to eat the above diet, the place orders so much olive oil a day, now the boss got cheating by his wife and is a bad mood.  So everyone is under stress.  They use more olive oil.  There are four sources of olive oil for the free loader to eat from, little ones for the table, a 20 L one mounted on a pivot for refilling the little ones, a 20l one that isn't and a 200L one that is hard to get at.

Now the boss is pissed and going to fire 8 people. when those people get on the above diet then the table oil will be drained every day and the 20L refill one will to.  Then they will start dipping the celery into the other drums to get the oil.

The person running the commissary is ordering less oil to look good for the boss.

We are going to run out of oil. And Ice.

[Alexander555]

How much heat would a landmass absorb ? Like Africa, that's a big landmass. And the equator runs trough it, so there is no real season to cool it down. And how hot will Europe be by the time we have a year round ice free arctic. Let's say that the sea at the equator keeps storing heat year round. The gulf stream brings it in the direction of the arctic. Were it unloads that heat, every year more. So over the atlantic you have heat comming from the equator, and you have that african continent that is loading up heat like a battery. And than you have the Middle-east that is already a dessert. Smells like a hot future for Europe.

[dnem]

This classic graph by Jim Pettit tells the story pretty well.  The total volume of ice melted out each year has stayed pretty constant at about 8-9 thousand km² per year, so, in very crude terms, the amount of energy that goes to melting ice (and not heating water and air) has remained roughly constant as the arctic has steadily melted out. (This of course completely ignores all the complex effects of albedo, heat trapped vs radiated to space, etc.)  When the converging lines meet, the annual melt volume will start to exceed the volume available at the beginning of the season.  When that happens, there will be excess energy available that will go to heating water and air, and not overcoming the enthalpy of fusion of melting ice.

[TerryM]

dnem
Exactly!
All of the energy not being used to melt the ice must heat the top layer of the water, less what is lost heating the air, less what is lost through evaporation, and less what escapes to the lower layers.
As this will occur close to the summer equinox the albedo change will draw additional heat, specifically to that same top, mixing layer of the ocean.
Exciting times to look forward to.
Terry