1. Direct ascent to the surface would have massive supersaturation over a long time specifically in the slower tissues which will have had no opportunity to off gas. Although you are correct that it would certainly have the fastest off gassing, that would not be much comfort compared to the DCS you'd probably also have.
So I ended up implementing the actual calculation. A few notes on the implementation:
* Integration is numeric, in 10s intervals during the dive, followed by 40s intervals for 1 hour after surfacing, and another 23 hours after that with 200s integration steps. The reason I'm having longer steps post dive is merely because I'm using code I had written before, were performance was important. Happy to calculate this again with 10s intervals throughout the dive + 24 hour surface time interval if you want, but it shouldn't make a difference.
* I'm using 9 tissues in this calculation with the following half-times: 2min, 5min, 10min, 20min, 40min, 80min, 120min, 240min, 480min. Again, this is what I had already implemented (I was implementing the RGBM). Happy to change it to ZHL16 tissues or whatever else if you think it's important. Tissues on- and off-gas proportional to the pressure differential in this calculation.
What I found was that which profile has the lowest ISS depends on how oxygen is considered in the calculation.
a) Ignoring oxygen alltogether (i.e. assuming oxygen partial pressure is 0atm in all tissues at all time):
* NEDU shallow profile: 9,684 atm s
* NEDU deep profile: 10,624 atm s
* NEDU bottom time, then ascending within a minute to the surface: 17,681 atm s
-> NEDU shallow best, followed by NEDU deep. No decompression worst by far.
b) Assuming oxygen partial pressures proportional to nitrogen partial pressures (ppO2 = ppN2 / 0.21):
* NEDU shallow profile: 55,022 atm s
* NEDU deep profile: 62,150 atm s
* NEDU bottom time, then ascending within a minute to the surface: 51,302 atm s
-> No decompression best, followed by NEDU shallow, with NEDU deep being the worst
All three have a descent of 3 minutes from 0 to 170 fsw, followed by 30 minutes bottom time at that depth. (I realize this thread is not about the NEDU dive profile or even air diving per se, I just use these as an example here)
So you are right that my intuition was incorrect here. I did not consider the oxygen window when I speculated about the outcome. I believe that this is because the oxygen window adds a non-linear factor to the supersaturation at a given time. The non-linearity comes from the fact that supersaturation is max(0, pressureGradient), and doing a staged decompression can keep more tissues in the 0-case (undersaturation). Hence ISS with oxygen window does not behave the way that I expected.
2. You seem to be missing the in-context point that integral supersaturation is -one- way of comparing two profiles of the same length, to give one possible indication of decompression stress comparison between the two.
I'm not missing this point, that is exactly the point I'm making! Thank you for putting it into clearer words than I did. (my argument for this point was by contradiction, so I can see why it was a little obscured)
That being said, ISS
by itself seems to be a comparably poor way of providing an indication of decompression stress, given that under the right circumstances it will tell you that going straight to the surface after 30 minutes at 170ft results in less decompression stress than a reasonably safe, staged decompression.
3. Nowhere does Simon say or imply that integral supersaturation is the only thing that is important in decompression schedules.
That is literally what he says in the quote I included in my post. Let me quote him here again:
If two dives have identical gas loading, and their respective decompressions (whatever form that takes) leads one to have a higher integral supersaturation than the other, then the former has higher decompression stress and, all other factors being equal, a higher risk of DCS.
He seems to be saying that for two dive profiles that differ only in their decompression staging, the one that has lower ISS has lower risk of DCS and vice versa. I'm not going to give you a mathematical proof about ordered sets here, but I'm pretty sure that Simon's statement that for any two decompressions A, B
ISS(A) < ISS(B) => P(DCS(A)) < P(DCS(B))
implies that there exists a monotonic function f, such that for any decompression x (from the same dive), we have
DCS(x) = f(ISS(x))
Hence ISS, according to Simon's statement, when taken literally, would indeed be the *only* thing that is important for the risk of DCS when it comes to choosing from a number of alternative decompression schedules for a given dive.
I'm pretty sure that Simon did not mean this. That's why I asked him to clarify how to exactly interpret this statement.