Ultimately, the amount of water that's flowing in a river will at some point be tied to the balance between precipitation and evaporation in its basin. So depending on what the groundwater flow is, there may be lags between what goes on.
I would suggest in the glaciated Rocky Mountain headwaters there's going to be a very short time lag between snow melt or big precipitation events and what happens in the river. You see that in very periodic and big changes in river flow. Somewhere down in the Fort McMurray area there may be a greater lag because, as Dr. Schindler said, you have these vast wetland complexes that act as sponges. They dampen fluctuations that you might otherwise see over a short period. At some point, it's going to be tied to precipitation--snow melt, that sort of thing.