This is a proposed solution, so feel free to comment or make suggestions to improve this.
When I was playing minecraft, I noticed when I am above or in the water, I can see the darkened-yet detailed ground structure due to the daytime's high light level, but when I enter in the water, everything turns pitch dark-blue and I can barely see anything that's 2-5 blocks away from me. Its default setting for underwater vision would be too frustrating that I can't have any light that is touched by the water (especially with the caves) that I had to put torches next to the waterfall.
My proposed solution would be that the user should be equipped with underwater light goggles (similar idea to red-light helmet, but specifically useful for underwater exploration) so he/she won't have to worry about pitch darkness when underwater. Be warned though, it's time-based duration (in seconds), so if you use the underwater goggle for a long time, then it will be worn out and the vision returns to pitch dark-blue again. Also, the lighting will only be as strong as torch light (required in crafting) to give some decent range of what's close to the player, especially when it comes to looking at fish and avoiding sharks.
*Crafting represents string represents upgrade based system
I am sure this crafting idea almost looks like this type of underwater goggle
is considered cloth and n=0 so duration is 64 seconds
is cobblestone and n=1 so duration is 129 seconds
is iron and n=2 so duration is 258 seconds
is gold and n=3 so duration is 515 seconds
is diamond and n=4 so duration is 1028 seconds
feel free to comment and make suggestions to further improve this idea.