Edited quote

Since the third term is a calculated average (and not a finite measure as the other two) then flipping them around makes no sense.

At least we have identified where we disagree,

I submit that mathematically all are true.

E*T=V

E = V/T

T = V/E

It does not matter to their mathematical relationship which one you solve for, the relation stays the same. In your examples you solve for T based on set values for E and V, and you get a T that is greater than E. But that is not an inherent requirement. It is simply an artifact of the values you set for E and V. You could set E and V to different values and find that the resulting T is less than E.

For example: As you found

If E = 0.99 and V = 0.98

then T = V/E = 0.9898

T decline (=1 - 0.9898) is greater than E (1-0.99).

But

If E = 0.9898 and V = 0.98

then T = V/E = 0.99

T decline (=1 - 0.99) is

~~greater~~ **less** than E (1-0.9898)

It does not matter which is directly measured and which is inferred. Mathematically they are all equally real. (And BTW, Thickness IS measured. Volume is calculated from Extent and Thickness).

But if you want to define E and V and then calculate T, that is fine. Doing so does not require T to be smaller or larger than E. All that matters is the relative sizes of the E and V values you choose. Specifically, if E - V is larger or smaller than 1 - E

For example, if E = 0.9 and V = 0.85,

T = V/E

T = 0.94

T is larger than E

E - V = 0.05

1 - E = 0.1

E-V is less than 1-E, so T is greater than E

if E = 0.95 and V = 0.85,

T = V/E

T = 0.89

T is less than E

E - V = 0.10

1 - E = 0.05

E-V is larger than 1-E, so T is less than E

RE: Oren. Close but no cigar. You are using E + T = V.

It is E * T =V.

Multiplication vs. Addition.

Addendum to the end game scenario. Extent losses are largely due to the loss of thin ice at the edge of the pack.

As the pack shrinks, that edge area becomes an increasing proportion of the total pack area. Circumference to area ratio gets larger.

(This is analogous to the surface to volume ratio that lets insects do things we can't, and also why insects have to be small to do what they do, but I digress)

So, as the percentage of the total ice pack subject to edge area losses gets larger, the percentage rate of Extent losses will increase.

***Not sure about this next statement. Math fatigue setting in.***

The straight line trend for Extent losses will begin to curve downward unless it is counteracted by a decline in rate of thickness loss around that edge, which does not seem likely.

*** Then again, the absolute amount edge = Extent loss would not increase, and in fact with smaller absolute edge area, absolute Extent losses would decrease. But the amount of extent loss would be higher ratio relative to the amount of previous year Extent. So it may just come down to whether you report Extent losses as absolute number of km2 or % of previous year. Math fatigue now math exhaustion. This is becoming a "how many angels fit on the head of a pin discussion". Who cares. It does not matter.

What matters is that the ASI is nosediving. Because of albedo and other effects, how the Extent trend will evolve is of interest. Thanks to Notz and Stroeve and their colleagues, we have insight on how the ASI situation will dramatically evolve over the next 10-30 years. It is a scary, ominous story. Maybe if the immediacy of ASI collapse is better understood it will help us make difficult decisions to reduce the damage we are doing to ourselves.