As the old saying goes, whiskey is for drinking and water is for fighting over.
I forget the name of it, but there was a reservoir in Wyoming (?) that got taken out a few years ago because the amount of evaporation from it was held against them in an interstate compact as part of their allocation of water from that river. So now they don't have a reservoir and are still allowed to take X amount of water out of the river. Makes perfect sense in a world where you get unreasonable people in the same room.
Roughly 800 million gallons of water evaporates from Lake Sak in a given day. Which is roughly equal to 5% of the water that passes by Bismarck in the Missouri River each day. So that being said, Sakakawea is roughly putting about the same amount of water into the atmosphere as 3.2 million cottonwoods.
Perhaps even more important isn't the big lake, but the increased acreage of smaller wetlands that are much shallower and warmer. I've no numbers on that, but we have definitely been at a recent geologic high in wetlands over the past 20 years.
Note: The effing willows around my dam scoff at your cottonwoods.
I don't know if a person could tease the effect of the lake out of the data because of natural variations and cycles though. Pretty complex problem to tackle and would be open to a lot of "expert" opinions.