I suspect the charring makes it last longer with contact with the water. I know partly burned wood seems to take forever to breakdown in my garden.

I missed this question entirely. The photo is very nice, I like the effect.
Almost any wood except treated lumber or a soft wood like redwood or cedar would be good. The charring would work better if it is done slowly. Lay the wood out on a level surface and apply a layer of dirt on top of it. Use about 1 1/2 to 2 inches at most. Build a fire on top of this soil and allow coals to form. Once you have a good amount of coals, bank it by shoveling ash lightly on top. You can use soil as well. The idea is to keep the coals going without allowing so much air it produces flame. Keep the coals going for several hours. The longer you can keep it going the better as it uses up oxygen and volatiles in the wood. What is produced is a kind of Charcoal. Some wood blackens more than others and some of the wood will distort. Green wood will char but not burn like older wood. What you are doing is replacing wood with carbon which will not decay the way wood will in contact with water.
It appears the wood in the picture has not been treated to go very deeply. I expect they don't need it to last for more than a few years. The part that has been carbonized is fairly fragile and brittle so don't carbonize the wood entirely through.
Another way to char wood is to lay it above the coals but not touching them. You have to keep an eye on it to avoid the fire from catching hold and it must be turned frequently.
A third way to do it is to stack bales of hay with the wood laid between bales. Ignite the bales all around. Once the bales are burning, cover the bales with more bales. An alternate to additional bales is to use sandy soil. The object is to form coals and raise the temperature greatly but never allowing the bales to start flaming which will cause the wood to burn rather than just char. This is how Raku pottery is fired.
This is not a project that can be set up and left alone. You must always have someone there in case the whole thing gets too much oxygen and bursts into flame. Always have water hoses ready and waiting. If sparks are flying there is too much flame some where. You can spray enough water in a fine mist to douse the flames but not the coals. Do not let it get away from you. Check your local fire codes or ask if there is an area where you can burn safely.
A fourth method which is fairly quick and not as hazardous but doesn't produce as much deep carbon is to flame each board with a blowtorch. Keep water handy to extinguish any fire. Use welders gloves. The water inside those boards reaches the boiling point. Don't stack the scorched boards. They could develop a flame. A good way to quench any flame when a board is finished is to douse it in a water barrel.

There are a ton of safety precautions when you are doing a project like this. See what your local fire department says. If you go ahead, make sure you have a competent helper. The only one I would attempt by myself is the blowtorch method.
I recommend using welders gloves for protection from burns. The wood can become extremely hot.
This is not a project to do around idiots and children. It must be done far away from houses, trees or other flammable materials. It may not even be legal where you live.