I've been waiting to make a correction partly because the discussion switched to published papers. And I tried to let Ross make it himself, but what can you do. I just want to have a post and I can reference if he tries the make the same claim again (so I don't have to deal with it).
Ross has attacked the heat map as flawed. In particular he asserts quite strongly that it is not based on supersaturation whereas his charts (jagged line charts) are based on "exact supersaturation". Here's his argument.
Ross's Argument
Ross's argument comes with graphics. His graphics make reference
to a heat map posted here. See Ross's chart below.
View attachment 378853
The argument Ross makes goes as follows:
"The colors in the heat map claim to represent relative levels of supersaturation. Light Green should represent 50% of Red per the legend. My software shows that when the diver surfaces from VPM-B+3 on this dive they have 7 kPa of supersatuation in compartment #16 (C16). The most heavily supersaturated compartment, C9, has 55 kPa of supersaturation. Therefore, C16 should be the color that represents 12% of the highest supersaturation. This can be derived by dividing C16 by C9, or 7 / 55 = 12%. A 12% compartment should be very dark green-black (see legend). But it is NOT! It is colored some shade of light-green which implies a 50% relative supersaturation to the highest compartment. Error! Therefore, these colors are not based on supersaturations. Error!"
The same basic argument with different colors/compartments is repeated below the first.
Problems With Ross's Argument
Ross's argument depends on 2 pieces of information and 2 implicit assumptions.
- The supersaturation of C16 at the surface is 7 kPa.
- The supersaturation of C9 at the surface is 55 kPa
- It is appropriate within the goals of the heat map to divide C16 by C9 to set the relative color of the heat map.
- The color scale is ALWAYS a fraction of the most heavily supersaturated compartment in the profiles shown (more on this later).
Unfortunately, #1, #2, #3, and #4 are all not true. Ross misunderstands, either conceptually or intentionally, the purpose of the heat map when he divides compartments
within the same profile. The purpose of the heat map is to compare supersaturation patterns
between profiles. When developing the heat map I wasn't interested in how superaturation in a single profile's compartments compared to each other. I was interested in how the compartments between 2 or more profiles compared across profiles. This error was spotted and pointed out
here by Victor.
The errors in Ross's calculation of supersaturation are documented below.
Ross's "Supersaturation"
I can repeat Ross's numbers and charts. This only makes sense. We're both using the same tissue model. So what's Ross missing in supersaturation?
Ross makes the claim that C16's supersaturation upon surfacing is 7 kPa and that C9's is 55 kPa. I can get those numbers as well by the following calculation for the dive discussed here:
View attachment 378854
As you can see, Ross used 7 and 55 and my calculation is very close to his.
It's easy to see what Ross overlooks when looking at the chart below.
View attachment 378855
The charts Ross shows in his software as "supersaturation" are really compartment inert pressure (N2 and He) less ambient pressure. It fails to account for a small, but important, part of supersaturation (and therefore bubble formation potential) from the other gases O2, CO2 and H20. Normally, even in his beloved VPM, this is modelled as a constant added to the inert compartment pressures N2 and He. But here, as in the RBW debate a few years ago, Ross seems unaware of what something as basic as supersaturation really means. Certainly his assertion that his charts represent "exact supersaturation" might be seen as exaggerated.
Summary
Ross's error probably doesn't matter much in his software since the charts are more of a "ooh, cool" thing. I'm only pointing it out because HE has made particular assertions of error in the heat maps based on his misunderstanding of supersaturation. In very heaviliy supersaturated compartments the small missing pressure isn't as big a deal. But he chose a compartment to make his argument where it does make a difference. In that context, the fact that he failed to include 13.6 kPa (I believe that is VPM's value for other gases) of pressure is an error of about 200%. Of course, making the 3 other errors didn't help him either.
The heat maps are accurate in their visual portrayal of the relative handling of supersaturation across profiles.
Perhaps Ross would ask the Mods on SB to allow him to remove or correct his posts here:
Inaccurate claim 1 Inaccurate claim 2 Inaccurate claim 3 Inaccurate claim 4
Inaccurate claim 5 Inaccurate claim 6 Inaccurate claim 7
I may have missed others.
Sorry for the long post, but one more point. The heat map, as disclosed previously, will not
always scale based on the highest supersaturation of any profile's compartment. I did that initially but it inappropriately implied (visually) that more supersaturation was present than actually was when compartments were only lightly supersaturated. For example, assume 2 profiles. C16 in the first profile has 0.02 kPa supersaturation and in the second has 0.01 kPa supersaturation. That's VERY LOW. Clearly both compartments are JUST BARELY supersatured. Without some adjustment the first profile would scale "red" (highest supersaturation) and the second light-green (50% of the highest). This would be consistent coloring, but undesireable in my view (and generally would make VPM look worse). To adjust for this, when the highest compartment falls below the supersaturation implied by some multiple (e.g. 90%, etc.) of the N2 M-value at the surface, I scale the colors based on this higher value. That does not inappropriately disadvantage any profile since the colors are all relative anyway (and generally makes VPM look better than without the adjustment), but it scales back the coloring as compartments converge toward an unsupersaturated state. Remember, again, the colorings are
relative. I was just trying to see how the "complex on gassing and off gassing patterns" actually compared between profiles. I had no idea it would highlight anything, but it did.