I have rarely (as in, "never that I can remember") seen a published adventure or RPG supplement which dealt with the changing nature of a river as you travel up or downstream, with varying currents, depth, and hazards. For the most part, in an RPG, a river is a blue line on a map, and any interpretation of what that blue line means is left to a GM's personal experience. For me as a teenager, that meant a blue line on a game map meant a body of water that was too deep and wide to cross without a bridge except by very strong and unencumbered swimmers, navigable by ocean-going ships, and potentially hiding giant water monsters of some sort.
Working off of this table (and converting units to imperial units, because metrics just doesn't say "fantasy", also rounding roughly for simplicity's sake):
We get the following for inches of rain per year:
|Tropical Dry Forest||50-100|
|Tropical Montane Forest||100-140|
Now, about 2/3 of this water will return to the atmosphere as vapor, from direct evaporation into the air or transpiration as a result of plant photosynthesis. The rest of it is absorbed into the ground (where it slowly flows and returns to the surface as springs) or runs off into streams. An inch of rain on one square mile of land produces 2,323,340 cubic feet of water, so each inch of annual rainfall translates into about 1.5 cubic feet of water per minute flowing off of each square mile of land year round (again, majorly simplifying).
And this is about as far as I've gotten. The Dungeoneer's Survival Guide has some flow velocities based on the slope of the stream, and I originally considered this might be good enough to work with, since knowing total flow and flow velocity will give you the numbers you need to work out the size of the stream. For example, if you know you have 1000 cubic feet of water flowing each minute, and you know it's flowing at 20 feet per minute, you can easily see that the stream will have a cross section of 50 square feet. While I was trying to figure out how to structure that cross section (is it 5' deep and 10 across? 2 deep and 25 across? deeper? shallower?), I came across a discussion of water flow that showed that velocity is based on slope *and* cross section...a wide, shallow stream will move slower than a deeper one of the same cross-sectional area. While I could ignore this, and it might not even matter for small rivers that only drain a couple dozen hexes, I'm afraid that really long rivers like the Streel River of the Known World/Mystara would end up ridiculously deep and wide as they flowed slowly through plains and marsh in the final few miles to the ocean. Like miles wide.
So I'm looking into some numbers, trying to come up with a simpler solution for RPG rivers than applying Manning's equation with its fractional exponents to every hex. I'll be back later.