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Gradient Factors in a Post-Deep Stops World

World-recognized decompression physiologist and cave explorer David Doolette explains the new evidence-based findings on “deep stops,” and shares how and why he sets his own gradient factors. His recommendations may give you pause to stop (shallower).



by Associate Professor David J. Doolette

Gradient factors are mechanisms which modify the decompression stops prescribed by the Buhlmann ZH-L16 decompression algorithm. ZH-L16 is a “gas content” algorithm, which tracks the uptake and elimination of inert gas in notional tissue compartments and schedules decompression stops to not exceed specified maximum permissible inert gas partial pressures in the compartments. When such maximum permissible inert gas partial pressures are specified for decompression stop depths, they are referred to as M-values.

Gradient factors (GF) modify M-values (and consequently allowed gas supersaturation) to a fraction of the difference between ambient pressure and the original M-value. Thus, GF 80 modifies the M-value to 80% of the difference between ambient pressure and the original M-value. Typical proprietary implementations of the GF method require the diver to select two gradient factors: GF low modifies the M-values for the deepest decompression stop, and GF high modifies the M-value for surfacing (often designated as GF low/high, e.g. GF 20/80). The algorithm then interpolates a series of modified M-values in between these two user-specified points. If the GF low is set less than 100%, this forces deeper stops to limit supersaturation in the fast tissues early in the ascent, and setting the GF high to less than 100% will produce longer, shallower stops to reduce supersaturation in the slower tissues in the latter phase of the ascent

In contrast to gas content decompression algorithms, bubble decompression algorithms (VPM-B is one such algorithm familiar to GUE divers) characteristically prescribe deeper decompression stops. In simple terms, bubble decompression algorithms favor deeper stops to limit supersaturation and thereby bubble formation early in the decompression, whereas traditional gas content decompression algorithms favor a more rapid ascent to maximize the inspired–tissue gradient of inert gas partial pressures to maximize tissue inert gas washout.

New Findings on Deep Stops

Deep stops came to the attention of early technical divers in the form of empirical “Pyle stops,” a practice serendipitously developed by ichthyologist and technical diving pioneer Richard Pyle, arising from a requirement to vent the swim bladders of fish specimens collected at great depth before arriving at his first decompression stop. There followed a strong trend toward the adoption of bubble algorithms, and also for the use of gradient factors to force gas content algorithms to impose deep stops (for instance, using GF low values of 30% or less). Based largely on supportive anecdotes, a widespread belief emerged among technical divers that deep-stop decompression schedules are more efficient than shallow-stop schedules. Efficiency, in this context, means that a schedule of the same or even shorter duration has a lower risk of DCS than some alternative schedule.

However, since about 2005, evidence has been accumulating from comparative decompression trials that shows deep stops are not more efficient, and possibly less efficient, than shallow stops.

However, since about 2005, evidence has been accumulating from comparative decompression trials that shows deep stops are not more efficient, and possibly less efficient, than shallow stops. Most studies have used venous gas emboli (bubbles) as an indicator of comparative risk of decompression sickness (DCS). Blatteau and colleagues compared dives using French Navy air and trimix decompression tables (relatively shallow stop schedules) to experimental schedules with added deep stops and longer total decompression time (similar to Pyle stops). Despite longer total decompression time, the deep stops schedules resulted in either the same or more VGE than the shallow stops schedules, and some cases of DCS.1

Photo courtesy of GUE Archives.

Spisni and colleagues compared trimix dives conducted using a deep stops schedule (ZH-L16 with GF 30/85) to an even deeper stops schedule with longer total decompression time (a UDT version of ratio deco) and found no difference in VGE.2 An as-yet-unpublished study compared trimix dives using a DCAP shallow stops schedule to a ZH-L16 GF 20/80 deep stops schedule with similar total decompression time, and the deep stops schedule resulted in significantly more VGE.3 A large study conducted by the U.S. Navy compared the incidence of DCS in air decompression schedules for 30 minutes bottom time at 170 fsw bottom for a gas content algorithm with the first stop at 40 fsw (shallow stops) or a bubble algorithm with the first stop at 70 fsw (deep stops). The shallow stops schedule resulted in 3 DCS in 192 man-dives and the deep stops schedule resulted in 11 DCS in 198 man-dives.4

What To Do About Gradient Factors

The emerging body of evidence against deep stops suggest common gradient factor setting should be modified to de-emphasize deep stops. Fraedrich validated dive computer algorithms by comparing them to well-tested U.S. Navy decompression schedules, including the schedules from the deep stop study outlined above. For that dive, ZH-L16 with a GF low >55% (e.g. GF 55/70) produced a first decompression stop between 70 and 40 fsw.5 Tyler Coen at Shearwater Research Inc. noted that GF settings recommended by Fraedrich modify ZH-L16 M-values so that approximately the same level supersaturation is allowed at all stop depths. To understand this requires delving a little further into M-values.

The emerging body of evidence against deep stops suggest common gradient factor setting should be modified to de-emphasize deep stops.

M-values are typically a linear function of stop depth. In older algorithms such as ZH-L16, the M-value generating functions have a slope greater than one (in ZH-L16, the slopes are the reciprocals of the “b” parameters), resulting in increasing supersaturation allowed with increasing stop depth. In more modern algorithms developed by the U.S. Navy since the 1980s, including the one used to produce the shallow stops schedule in the study outlined above, the slope of the M-value generating functions are generally equal to one, so that the same level of supersaturation is allowed at all stop depths. This results in modestly deeper stops than older algorithms, but still relatively shallow stops compared to bubble models.

With this information in mind, I set my GF low to roughly counteract the ZH-L16 “b” parameters (I have been using Shearwater dive computers with ZH-L16 GF in conjunction with my tried and true decompression tables for about three years). In ZH-L16, the average of “b” parameters is 0.83. I choose my GF low to be about 83% of the GF high, for instance GF 70/85. Although the algebra is not exact, this roughly counteracts the slope of the “b” values. This approach allows me to believe I have chosen my GF rationally, is not so large a GF low as I am unable to convince my buddies to use it, and satisfies my preference to follow a relatively shallow stops schedule.

This article was prepared by Assoc. Professor Doolette in his personal capacity. The opinions expressed in this article are the author’s own and do not reflect the view of the Department of the Navy or the United States government.

Header image: Joakim Hjelm

1. Blatteau JE, Hugon M, Gardette B. Deeps stops during decompression from 50 to 100 msw didn’t reduce bubble formation in man. In: Bennett PB, Wienke BR, Mitchell SJ, editors. Decompression and the deep stop. Undersea and Hyperbaric Medical Society Workshop; 2008 Jun 24-25; Salt Lake City (UT). Durham (NC): Undersea and Hyperbaric Medical Society; 2009. p. 195-206.

2. Spisni E, Marabotti C, De FL, Valerii MC, Cavazza E, Brambilla S et al. A comparative evaluation of two decompression procedures for technical diving using inflammatory responses: compartmental versus ratio deco. Diving Hyperb Med 2017;47:9-16.

3. Gennser M. Use of bubble detection to develop trimix tables for Swedish mine-clearance divers and evaluating trimix decompressions. Presented at: Ultrasound 2015 – International meeting on ultrasound for diving research; 2015 Aug 25-26; Karlskrona (Sweden).

4. Doolette DJ, Gerth WA, Gault KA. Redistribution of decompression stop time from shallow to deep stops increases incidence of decompression sickness in air decompression dives. Technical Report. Panama City (FL): Navy Experimental Diving Unit; 2011 Jul. 53 p. Report No.: NEDU TR 11-06.

5. Fraedrich D. Validation of algorithms used in commercial off-the-shelf dive computers. Diving Hyperb Med 2018;48:252-8.

Additional Resources:

PADI recently published an excellent post, “Evolving Thought on Deep Decompression Stops,” by John Adsit, on the subject of Deep Stops.

Alert Diver magazine published a profile and interview with Doolette in the Fall of 2016.

The Math behind the ZH-L16 Model: Bühlmann established, by means of many hyperbaric chamber experiments with volunteers, how much supersaturation the individual tissue compartments can tolerate without injury. He expressed the relationship through the following equation:

pamb. tol. = (pt. i.g. – a) ·b


pt. tol. i.g. = (pamb / b) + a

pamb. tol. – the ambient pressure tolerated by the tissue

pt. i.g. – the pressure of the inert gas in the tissue

pt. tol. i.g. – tolerated (excess)pressure of the inert gases in the tissues

pamb – current ambient pressure

a, b – parameters of the model ZH-L16 for each tissue. “a” depends on the measure unit of pressure used, while “b”  represents the steepness of the relationship between the ambient pressure pamb. and the pressure of inert gas in the tissue pt. i.g. The first equation shows which lower ambient pressure pamb. tol. will still be tolerated at the actual pressure of inert gas in the tissues pt. i.g. The lower equation shows which level of supersaturation pt. tol. i.g. can be tolerated at a given ambient pressure pamb for a given tissue.

Dr. David Doolette began scuba diving in 1979 and was introduced to the sinkholes and caves of Australia in 1984. Around this time, he alternated between studying for his B.Sc. (Hons.) and working as a dive instructor, when he developed an interest in diving physiology. He planned and conducted some of the first technical dives in Australia in 1993. Since being awarded his Ph.D. in 1995, he has conducted full time research into decompression physiology, first at the University of Adelaide, and since 2005 at the U.S. Navy Experimental Diving Unit in Panama City, Florida.

He has been a member of the Undersea Hyperbaric Medical Society since 1987, received their 2003 Oceaneering International Award, and is a member of their Diving Committee. He has also been a member of the South Pacific Underwater Medicine Society since 1990 and served as the Education Officer for five years. He is a member of the Cave Diving Association of Australia, the Australian Speleological Federation Cave Diving Group, Global Underwater Explorers, and the Woodville Karst Plain Project. He remains an avid underwater cave explorer, both near his home in Florida and abroad.


My Deep Dive Into The Dunning-Kruger Effect

Tech diver Brendan Lund shares his personal diving journey from summitting Mount Stupid and descending into the depths of Despair on trimix, before finally beginning his ascent on the Slope of Enlightenment. No Kool-Aid was involved in the making of this story.




by Brendan Lund
Images courtesy of Brendan Lund

Lund diving in Socorro, Mexico,

I started diving in 1996 as a poor student in South Africa. I absolutely fell in love with diving, and haven’t stopped since. After moving to the UK in 2001, I finally started earning money and was able to dive more frequently. At this time, the Red Sea was starting to boom, and I was able to book a full week of diving—including flight and accommodation—for as little as 350 GBP! Many trips later, I became interested in tech diving, as it was the happening thing, and in 2004 I decided to begin my tech journey with a leading agency. This also signals the start of my journey with the Dunning-Kruger Effect!

Grokking Dunning-Kruger 

I first saw the Dunning-Kruger effect graph a year or so ago and couldn’t stop thinking about its relationship to my diving. 

What is the Dunning-Kruger Effect? Here’s what Wikipedia has to say:

In the field of psychology, the Dunning–Kruger effect is a cognitive bias in which people with low ability at a task overestimate their ability. It is related to the cognitive bias of illusory superiority and comes from the inability of people to recognise their lack of ability.

As described by social psychologists David Dunning and Justin Kruger, the bias results from an internal illusion in people of low ability and from an external misperception in people of high ability; that is, ‘the miscalibration of the incompetent stems from an error about the self, whereas the miscalibration of the highly competent stems from an error about others’.

The graph below simplifies this concept—again, this is taken from the internet, but the wording pretty much sums up what I have been feeling throughout  this journey:

The less knowledge you have, the more confident you feel. The more you learn, the less confident you feel. 

The View from Mount Stupid

In 2005, I progressed from an advanced nitrox diver to a fully-certified advanced trimix diver. My instructor was a well-known deep diver at the time, and I was super impressed with the courses. I was at the point of Mount Stupid on the graph. These courses were not a pass/fail style of course; you just had to prove you could complete the skill once, and bam! You’re qualified! 

“Wow, I’m the man! I’ve passed my Advanced Trimix Course and dived to 100m.”

I dug out the photo below from a box in the shed. We had someone take an underwater photo of us celebrating our successful completion of our deco procedure course. As you may notice, trim was not a requirement at the time (I’m now hiding my face with embarrassment)! Apologies to my buddies in the photo; it was a while ago, and the instructor is the only one in reasonable trim!

Class celebrating the completion of a deco procedures course.

To say I was chuffed is an understatement! I immediately went tech diving as much as possible. In 2008, I decided to travel the world for a year—diving of course. I met many amazing people and dived everywhere; I also became an instructor with a well-known recreational agency. I was at the top of my game (or so I thought), although I still don’t think I had any trim! I mean, who needs trim, right?

On one of my adventures, I met a guy who was really interested in checking out a new agency that he had heard of. This would be the first time that I heard about Global Underwater Explorers (GUE). After much research and reading internet forums for GUE in 2000, I believe the Dunning-Kruger realisation phase of my journey began: I thought, “There is definitely a lot more to this!”

The Slope of Despair

I’m not going to lie; the more I looked into GUE, the more nervous I got, and the more I slid down the slope of despair. It took me a good six years to build up the courage to sign up for a Fundamentals class, and I showed up on that day feeling very confident in my brand new drysuit and my horseshoe wing. Wow, did I learn that I was way out of my depth! I was in trouble. It was so much harder than I had ever imagined. I don’t think it was so much the course that was hard, but that it was hard for me to overcome my ego and overconfidence.

I received a provisional “Tech Pass” [i.e., I qualified to take GUE’s Tech 1 or Cave 1], and it felt like I had failed! I was at the bottom of the Dunning-Kruger slope of despair.  Was I ever going to get it? I questioned whether I should go back to get my pass, and I have to thank my buddies Nikky and Darren for encouraging me to do so. After lots of practice and some gear tweaks, I felt like I smashed it, and achieved my Tech Pass! Was this the beginning of the slope of enlightenment? Things were starting to make sense!

The Slope of Enlightenment

I have now completed two more GUE classes—DPV1 and Cave 1—and am signed up for Tech 1 next year. The future looks bright! I dive as often as I can with like-minded divers, and I realize that there is always more to learn and areas where I can improve. I am hopeful that I am now on the Slope of Enlightenment; it certainly feels that way.

I highly recommend GUE to any divers that would like to work on themselves. It has definitely helped me on my diving journey, and I now look forward to many more years of diving and learning. I can’t wait to get involved in more projects and extend my skill set.

Additional Resources

It’s Never Too Late To Tackle Fundamentals

Brendan is an events manager based in London and (currently) dives mainly around the southwest coast of England. He started diving in 1996 in South Africa and has dived all around the world. He found a passion for cave diving a few years agohis favourite place to do this is Tulum, Mexicobut still loves wreck diving. Brendan is looking forward to the next challenge, with project work planned with Project Baseline, and Tech 1 is in his diary for next year in Croatia, since Covid-19 postponed it this year.

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