> Having a thickness of zero is only applicable in abstract mathematics, not real world physics.
KK - I do believe that even according to your own arguments, transition between a thickness of 1mm and a thickness of zero is extremely significant, since, it flips the albedo and biases the overall energy equation toward accelerated warming (in summer), or cooling (in winter).
...and regardless of how precisely one can measure it, I hope you would agree that whether one can see or not, change in thickness do occur, and that the warmer it is, the thinner the ice gets.
In this context, I simply don't understand your insistence that the 2D picture is the most important;
- the area cannot change unless the thickness goes from something to 0
- If the thickness decreases year-on-year, as it has done for almost three decades straight,
it makes it more likely that at some point it will go from something to zero.
- When the thickness _does_ go from something to zero, It makes the planet warmer
than it otherwise would have been, compounding the problem.
Yes, when the thickness decreases from 1mm to zero, it is extremely significant. However as you stated, it is due to the large albedo change, with resulted from the areal loss.
I have always maintained that thickness decreases, resulting in thinner ice as the temperature warms. That is my main argument about volumetric losses being greater (percentage wise) than areal losses. Others here have contended that volume can increase, while area decreases, due to very specific circumstances. That may be true, but it is cherry picking the data.
Regarding your individual points:
- thickness must go to 0, in those places where ice area is lost.
- if thickness continues to decrease, at some point it would reach 0
- when thickness goes to 0, the open water would warm, due to more sunlight reaching the surface. It would cool somewhat during night/winter, but that is unlikely to counter the incoming heat.
As you can see, all these arguments support the 2D approach. The 3D picture only come into play, when the third dimension goes to 0, but that is because the area goes to 0 also. Smaller changes in thickness have little overall effect. Let me pose the question in this manner: what would have a great effect; 50% loss in area, with no change in thickness, or 50% thickness loss, with no change in area? After that, a third comparison; 70% loss in both volume and thickness. In all three cases, volumetric changes are similar.