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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.



  1. MommyRev

    April 8, 2020 at 2:47 pm

    Perhaps the first study of deep stops profile was done by the French Navy while considering whether to move to a bubble model from their gas content model. They compared their model to three different deep stop protocols by measuring post dive venous gas bubbles. They discovered that none of the deep stops models were superior to the gas content model, and one of them was inferior.

  2. Pingback: The Best of InDepth in 2019 - InDepth

  3. Pingback: Decompression Series Part Four: Finding Shelter in an Uncertain World

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Teaching Again as the World Tries to Reopen

Conducting classes and supervising dive ops during the midst of a pandemic can be challenging. Here GUE instructor Francesco Cameli details his experience teaching his first “Fundies” class since lockdown! Welcome to the new normal.




By Francesco Cameli 

Header Photo by Damon Loble.

The world has definitely become a little stranger as we all try to deal with the ongoing COVID-19 pandemic and are forced to adapt our way of life to safeguard ourselves from infection. Needless to say, it has been a challenging time for diving instructors around the world, and certainly here in Southern California.

Whether you like reef structure, macro photography, kelp forests, or deep wrecks, Southern California offers some of the best diving in the world. However, it is often overlooked in favor of warmer waters and more exotic locations. It’s true that conditions here are at times challenging, but as the saying goes, “if you can dive in SoCal, you can dive anywhere.” As such, it has been fertile ground for divers seeking out GUE training in an effort to perfect their underwater skills. 

As we launched into 2020, diving conditions in SoCal were stunning. We were seeing 30 m/100 ft plus visibility days, and the new GUE community-inspired dive boat, Big Blue, had just been delivered and began conducting dive operations. Importantly, our four active local GUE instructors were busy with classes. Then the pandemic hit. In early March, the governor of California issued a stay-at-home order and all activity shut down. As a result, courses—and to a large extent local diving—were placed on hold. 

Francesco and students practicing mask skills. Photo by Sheldon Jones.

As of early July, we have resumed limited diving operations carefully following the recommendations from Divers Alert Network to insure our divers’ safety. We have also begun modified classes. In fact, as luck would have it, I just finished teaching my first Fundamentals class in this new COVID-19 world, and wanted to share my experience of what it was like.

The short answer is that it was not unlike many Fundamentals classes before it. While there were a couple of small changes that I think overall actually made for a better learning experience for my students, there were a few minor drawbacks.

Taking The Plunge

Because of the required social distancing, I experimented with working with the students remotely for all of the lectures and some of the land drills. At first, I was unsure as to how this was going to pan out, but it actually turned out great. You see, typically here in Los Angeles, because of the logistics of going diving, we tend to pre-load the class with all the academics in one marathon day consisting of Modules 1-6 followed by the swim test. That was traditionally how I had been doing it. Frequently though, you could see the students start to struggle with concentration after about four modules. So I would take a break and do the swim test but then, they would be tired from the swim test. Not so anymore! This last class, we scheduled three Zoom meetings, each lasting about two to three hours, where we could go through the modules at a leisurely pace. This allowed each student to meet in the comfort of their home and at a time that suited them.

As these were going so well, I then tried Valve drills, Basic 5, and SMB deployment with us all sitting in our rigs. I have to say, that seemed to be well received, too. I was able to focus easily on each student, and the picture quality meant it was really no different than if they had been standing before me in person. So far, so good! 

Now, because these meetings only took up the equivalent of one day of time, we were left with three days of diving (versus two, normally). The cool part is that we had ample time, thanks to our swift local boat Big Blue to still get three dives in per day. So instead of doing six dives, we did nine. We filled in the missing land drills on the boat, which—as it was travelling with COVID-19 load restrictions—still gave us plenty of room to social distance and work on the drills. 

Everyone of course was wearing a mask at all times and kept a bit more to themselves. The students benefited greatly from these extra dives as we could really focus and spend time on the subject matter that required more attention. I feel, after all, that my students benefit most from the time they get with me in the water, so the more the merrier. 

We were even able to conduct the swim test in the open ocean. The boat leant itself well to the task as 10 times around the boat rather neatly worked out to be 300 yards. As for the breath hold, we deployed 15 m/50 ft of current line with a diver holding the line taught while the students swam from the boat to the buoy.  

Getting Wet

So, what about the diving itself? Well, managing the students on the surface was easy enough. Keeping them 2 m/6 ft or so apart worked while we discussed dives and debriefed. Then once the regulators were in, we would get closer and descend as a team. Honestly, this was no great chore. 

The one slight hiccup I had not anticipated, however, came in the form of the S-Drill COVID-19 style. The donation itself went without an issue, and the switching to a necklace instead of the donated regulator was no problem at all. The full long hose deployment and swimming part were also somewhat unspectacular with the exception of the fact that you could see the cogs turning as the out of gas (OOG) student tried to decide on hose routing once a direction was picked. Because they were simply holding the donated regulator and were in fact breathing from their own necklace, they did not always have the regulator correctly orientated and therefore had to be reminded that the hose would normally be on the right side of their face. This of course is something we never actually think of when the regulator is in our mouths. The biggest confusion, in my opinion, came at the moment when it was time to clean up. 

Francesco with students in formation. Screen grab of a video by Angie Biggs.

What I noticed was that frequently the donating student would try to clean up too soon before the OOG student was back on their primary regulator. I can only assume that they were confused by seeing their team mate holding a regulator in their hand and not breathing from it, which would normally signify it was time for the donating diver to clean up. This small confusion was easy enough to clear up in the subsequent debrief, and the students managed just fine after that. This was a small price to pay, I feel, to ensure that our students remained safe and that we reduced as much as possible the risk of passing COVID-19 through regulator sharing. Just in case, we had disinfectant ready on the boat to re-sanitize a regulator that was unwittingly used not by its rightful owner, but the need never presented.

In conclusion, I think the differences are not so great that the class suffered in any way. As it went, in this case, both students earned a well-deserved tech pass and were rather chuffed (those Brits!) with how the class proceeded. I myself greatly enjoyed the online lecturing and the extra dives. I may well try to find a way to keep conducting fundamentals classes in this manner in the future to maximize water time and split up the modules for better assimilation and retention. 

Happy Diving everyone! 

Photo by Imad Farhat.

Born in France but hailing from Italy via England, Francesco’s passion for the ocean was ignited early on by the work of Jaques Cousteau, and Luc Besson’s film “The Big Blue.” Growing up in the seaside village of Portofino, Italy, Francesco spent just about every daylight hour of his summers freediving. In his 20s and 30s, he found himself locked in a recording studio in London or Los Angeles making records for the likes of Queen and Duran Duran as well as Korn, Stone Sour, Avatar, and others. Francesco rediscovered the ocean on a trip to Kona, which is where his scuba journey began in earnest. Since then, he has averaged over 200 dives a year cultivating his own skills. Once he found GUE, he worked his way through the curriculum and became a GUE instructor in 2019. That year, the passionate and exacting polymath was one of the busiest GUE instructors in Los Angeles, and is now working to become a Tech One instructor in 2020. Some say you can occasionally hear him singing to the fish.                                                                                                           

Big Blue was built by a GUE instructor with the GUE and tech diving community in mind. She’s got a big wide ladder, wide diver spaces to accommodate doubles, CCRs, comfy seating for long rides to far targets and speed. Big Blue is one of the fastest dive boats in the Los Angeles area. What’s more, it offers a tech savvy crew. Visit us at: or on FB!

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