When the water temperature rises above 8 degree Celcius the carps organism really starts to work.
As most of his food also starts to bloom with higher water temperatures and as shallow areas tend to warm up faster, id say look for shallow areas at the beginning of the year, reed beds etc.
If the sun is shining on a big shallow area and the wind is also going to that spot, id say thats a winner. In general, carps tend to follow the wind in big lakes. The sides where the wind hits the bank are most likely to hold more carp then others as the wind is bringing the warmer surface water there.
At about 20°C water temp the carps go into spawning mood and start to get really careless and head for the shallows.
After that they will scatter and wont be found as easily as they then tend to go deeper.
During that early period of the year when the water is still cold a sunny midday should be best imho.
When they are spawning time doesnt matter really as theyll be in the shallows all day.
After the spawning theyll most likely be found in the shallows only in the very early morning.
In one sentence: carps love warmth
Im not an experienced bowfisher, but as a long time carpfishermen (with rod and reel) and as an instructor about fish biology in several workshops and classes id think that the things stated above should be equally true for carp in youre part of the woods.
Good luck!
P.S. Just looked at the pics. During the spawning im nearly certain those little bays at the upmost end next to the river going into the lake would be realy good (if the carp can get in there and those bays are fairly shallow but deep enough that they can get in there.)
Another guess would be the big bay left to where the water runs out of the lake again as the water had the most time to heat up there while going through the lake (again if its shallow enough).
But its really hard to say by only looking at pictures...