Everyone knows what GFs are—or do they?
A new paper on DCS risk assessment is currently sparking debate. It is based on the DAN DSL Database and analyzes 127,957 dives from 5,907 divers, concluding, among other things, that supersaturation on reaching the surface is the most relevant risk factor for DCS. So far, so good—this may not be all that surprising, but it’s useful to be able to back up and quantify the increasing risk with numbers.
The paper has several relevant issues, which we address across three blog posts in total.
1. The analyzed DCS cases are not part of the general data collection. We explain why that’s a problem in the first post.
2. Divers contributed very different profiles. We explain why that is critical for the analysis in another blog post.
New DAN DB analysis
In this third and final part, we look at the one result that is interesting despite all the problems with the data collection: dives that ended with DCS show, on average, higher supersaturation at the end of the dive than those where nothing happened.
The figures cited here seem quite high: on average, the collected dive profiles ended with a “DSSG” of about 0.74, whereas the DCS dives averaged 0.86. DSSG? That’s the “DAN Surface Supersaturation Gradient.”
What it is isn’t explained—but it refers to Cialoni et al. 2017 —the previous study analyzing the first nearly 40,000 profiles from the same database. However, the term does not appear there. According to its explanations, that earlier study uses the Surface GF according to Baker, as is also commonly used among divers.
Aside: What is the “Baker” surface GF?
Surface GF, supersaturation on reaching the surface, Baker GF, or Shearwater GF? Before we take a closer look at the data, we’d like to briefly clarify what is meant by these terms.
A gradient factor is a fraction of supersaturation, usually given in %, but sometimes also as a fraction of 1 (GF70 – 70% – 0.7). As a planning setting, gradient factors determine what maximum supersaturation below the limits of the Bühlmann model should be tolerated. When analyzing dive profiles, the gradient factor on reaching the surface—or the maximum GF reached during the dive—can provide an indication of how aggressive or conservative the profile was.
There is an extremely common mistake in explanations of gradient factors: “GFs are percentages of the M-value” appears in many courses, talks, and explanations in various forms. This will matter later. So remember: gradient factors are fractions of supersaturation—not of the M-value.
The M-value is made up of ambient pressure and the tolerated supersaturation at that ambient pressure. Baker also called the supersaturation component the “M-Value Gradient”—which may have contributed to today’s widespread confusion. The M-Value Gradient refers to supersaturation, i.e., the M-value minus ambient pressure. And gradient factors are fractions of that supersaturation.
Difference between the first and second analysis
Back to the question of what the “DSSG” is supposed to be. First, we need to ask whether it’s possible that the DSSG is actually the same value that, in the first analysis, is simply referred to as “GF,” as claimed. The authors of the 2017 analysis of the first part of the database are largely the same as those of the new, expanded analysis of the same database. But the value they use is not compatible between the two studies.
This becomes apparent in how DCS cases are assigned to GF—or to DSSG. Let’s put the two analyses side by side.
from: Cialoni D, Pieri M, Balestra C, Marroni A. Dive Risk Factors, Gas Bubble Formation, and Decompression Illness in Recreational SCUBA Diving: Analysis of DAN Europe DSL Data Base. Front Psychol. 2017 Sep 19;8:1587. doi: 10.3389/fpsyg.2017.01587.
What’s broken here?
The first table shows the distribution of the 320 (or 317—three are missing without further explanation) DCS cases across the maximum GF reached during the dive. The symbols are set ambiguously: you would expect <70 to mean all profiles with GFs below 70, including those below 60 or below 50. Apparently, however, it actually means >60; <70, as shown in some other rows. The percentages only add up to 100% in that case. So let’s assume a few symbols were simply placed incorrectly.
In the second, current table there are much more relevant inconsistencies. For one, all 136,793 profiles suddenly appear, even though about 8,000 of them were supposedly filtered out. But things get really wild in the P(DCS) column. The case counts and dive profiles allow a direct calculation of the univariate DCS rate per DSSG class. However, the results in the paper’s P(DCS) column deviate massively from that. In particular, in the DSSG ≥1 class, 45 DCS cases out of 963 profiles yields a rate of about 4.67%, not 37.532%. The reported P(DCS) column therefore cannot be reproduced from the published table values and should not be interpreted as the DCS probability per DSSG class—whatever it is supposed to represent, it is not a calculated probability from the available data. Quite apart from the fact that it is a major error to treat the DCS cases in this dataset as part of the collected dive profiles…
But leaving that aside, we want to know whether it’s possible that GF and DSSG mean the same thing. And we can clearly answer no with a look at the two tables: while in 2017 there were still 59 DCS cases in total with GFs below 70, in 2026 there are only up to 29 left. “Up to” because “0.7” does not clearly describe whether it means 0.65–0.75 or 0.6–0.7 or perhaps something else… In any case, a significant number of cases would have had to simply disappear. And conversely, it’s the other way around at the higher values: in 2017 there were only 22 cases with GFs above 90; in 2026 there are already 392. But only 308 cases were added…
So the values in the two analyses are clearly not compatible. So what could the “DSSG” be, if it isn’t the GF?
What could have happened?
We see that the values reached for DSSG are higher than the values for gradient factors. Exactly how much higher, and exactly what was calculated, we can’t know. Unfortunately, even after repeated inquiries, the authors did not explain it, and no other study provides a plausible explanation of what exactly is calculated as DSSG. They do mention in the paper that not all datasets truly end at the surface—but correcting for that is a very minor issue and clearly cannot lead to such a shift in values.
So what would be mathematically possible? And what values does DAN use in its public tools?
In their own data-collection tool, the Diver Safety Guardian (DSG), you can view tissue saturation throughout the entire dive. In this image we see what is shown at the start of the dive, before descent: the 16 tissues are already “saturated” to between 20% and over 50%.
In fact, the inert gas pressure in our tissues is matched to the pressure in the surrounding air. With 78% nitrogen in the air, the gas pressure in the tissue is about 0.75 bar (not quite 0.78, because water vapor in the airways also plays a role). If you talk about “saturation,” you would describe this state on land as “fully saturated.” But what is shown here is something else: namely, what percentage of that tissue’s M-value is reached by the current saturation. And because M-values for slower tissues are significantly lower than those for fast tissues, the same saturation state yields higher values in the slow tissues.
The display is a bit unusual, and I don’t consider it the most didactically valuable—but you can, of course, calculate and display supersaturation this way as well. What you must not do, however, is call these values “gradient factors,” because they are not. But when you export a dive’s data from the DSG, exactly these values—the respective highest percentages of the M-value—are output with the label “GF.” A small labeling error, nothing major, but an indication that there is quite a lot of confusion at this point.
The difference between GF and % of the M-value
How do the numbers change if, instead of GF, you report a fraction of the M-value? Unfortunately, you can’t simply convert one value into the other, because you always need to know which tissue you’re dealing with.
This is easier to show in a graphic than to explain.
Here, in four colors, we show what the value “% of the M-value” looks like at the surface for various GFs between 60 and 90. The M-value is always a much higher value than supersaturation. A given fraction of supersaturation—so long as we are below 100%—is always lower than the fraction of the total M-value. The lower the M-value, the lower the tolerated supersaturation, and the larger the difference between the two values becomes.
What is particularly interesting for us is the range of tissues 4–8, which in typical recreational dives are most likely to have the highest supersaturation at the end of the dive. And here you can see how a GF 60 turns into fractions of the M-value of 80 to 85%—and how much the values differ from tissue to tissue.
For practical use in dive computers, GF is clearly the best choice, because it is supersaturation that is risky—and you want a value that means the same thing for all tissues. But for an analysis of profiles?
What does this mean for the paper?
If you want to investigate which tissues reached what supersaturation during a dive, you can, in principle, use either value. Especially in an analysis that takes into account which tissues are involved, both approaches can lead to plausible and relevant results.
But we have seen that the difference between the two values is so fundamental that it is essential to define crystal-clear which value you are talking about. And here, the term “Surface Supersaturation Gradient” is highly misleading, because you would expect it to mean a fraction of supersaturation, not of the entire M-value.
The study’s values now have the potential to be misinterpreted because “DSSG” is not defined. You see a large number of DCS cases in the very high ranges, above 80, and only very few below that. If these values are misinterpreted as GFs, divers could conclude that GFs up to 80 are extremely safe—while the values, translated into GFs, would actually suggest drawing the line closer to 60 or 70. What you can statistically see about the distribution of risk shifts toward higher values.
So, once again, very clearly for those who incorporate studies and database analyses into their choice of GFs: whatever DSSG is meant to be, it is NOT gradient factors, and you should not draw conclusions from it about which GFs are associated with a specific risk.
Maybe DAN will eventually decide to convert the values, or at least clarify how their “DSSG” is calculated. Then, despite all the other issues in this study, these data would be the one block that could lead to relevant insights. At the moment, the only takeaway is unfortunately “higher supersaturation is riskier,” and that—well—is rather banal.
