That would be somewhat awkward to implement. Rainwater washes down into the river because of the slopes riverbanks, but in Stonehearth there are only flat surfaces of varying elevation. The water levels could just artificially rise (hard coded rather than simulated) whenever it rained, but that would mean if it rained too often the river would overflow. Normally in real life it just means (due to the sloped riverbanks) the river widens. Unfortunately due to the flat-ness of everything the riverbanks wouldn’t expand, but there would just be a thin layer of water over everything on that ground level.
Also the main source of water for rivers is tributaries, smaller rivers and streams that feed them water directly. Usually only springs directly feed smaller streams, not rivers
There was actually a live stream a while back on which he modeled a set of water pumps and pipes. I would love if the engineer had these rather than the traps and turrets he uses now.