I was able to use a GroPro hero 4 session underwater taking a photograph every 5 seconds for approximately 1 hr 40 min. It recharges very quickly, which is nice.

See Hugyfot for aluminium housing and additional battery pack. That means 6 hours of video (which is much longer for photography)

http://fotografit.eu/products/90-hugyfot-alu-accessores/1684-hugyfot-gopro-hero-housing-pro/

Btw, how long you need it underwater ?

I have had variable recording lengths of underwater continuous video and time lapse video. The with time lapse video I have gotten about 3.5 hours of recording before either the memory (64G) filled up or the battery died. The cam-do intervalometer requires at least a minute in between each shot. So it would depend on what your application is, but a minute can be a long time. However, with continuous video I have gotten anywhere from 1.5 hrs to 2.5 hours. The issue is water temp as that affects battery performance. 

many thanks to all of you for the useful links and information

Jerome: the site comes handy and I have sent a question (no answer so far), but my main problem is not to vary the intervals between shots, but for the battery to last a whole daylight period in the summer while taking pictures very regularly.

Anna: at 5 sec intervals did the camera shut off in between shots? the overall duration seems pretty low, similar to standard gopros

Dimitri: nice site but prohibitive prices. also I am going to use it in a context where accidents and nicking are real risks, so I cannot afford to look for very expensive solutions. the duration is up to 14-15 hours (of daylight)

Jocelyn: i am only interested in photos (and not of particularly high quality) at a water temperature of 14-15 degrees (at round 15 m). what is the system you have been using?

at the moment I am exploring a solution with a local engineer to incorporate artisanally the switching of f solution with time lapse to standard gopro machines (other than session). if we get anywhere with this I will send a new post. thanks again!

I do not believe so, no.

had a useful and clarifying reply from camdo:

basically, gopro batteries are 3.5-4.5 Wh and standard time-lapse mode requires 1.2-2.1W depending on model (http://cam-do.com/pages/power-consumption-by-gopro-camera-model), so to take pictures with time-lapse with wifi off would allow for 2-3h of operation before the battery fails.

the time-lapse intervalometer of camdo operates from 50sec upwards, so assuming a mean camera connection of 10 sec per frame, it only allows a maximum frequency of 1 frame per minute and at this frequency extends the duration of the battery approximately 6 times (photo only: http://tools.cam-do.com/TimeLapseCalculator.html) at normal ambient temperatures.

finally the have not worked with gopro hero4 session because it does not have the standard hero port 

this means that for photo shooting frequency 2-3h either some home-made solution is required (intervalometer or additional energy source for underwater use).

will keep looking into it, thanks again for the help (and sorry for the muddled reply on variable shooting frequency jerome)     

although it's only a Hero and not a Hero 4 I have used it to monitor the species in my cold saltwater tank at home using video and I am yet to try the time-lapse mode but I think the variable shooting mode is something that the Hero lacks

See this also Yorgo: https://www.tindie.com/products/GroupBinc/gopro-hero-3-extreme-depth-underwater-housing-9000ft-2750m/

Can fit also additional battery.

I have looked on the website Jerome said about in his answer but for many of the products on there quite alot of saving up is required as they do appear to be very expensive, but from my point of view thats good, because you get what you pay for right?

In my experience it was the memory that ran out before the battery. In some models they will not take a large (64 MB) memory card.