Wednesday, October 16, 2013

How Twisty Are Rivers?



The River Jurua, in the Amazon Basin.
The objection has been raised (Hi Kyle!) that my attempt at river generation from a random walk is producing too many twists and that the rivers should be straightened out. I should note that the
example I posted was more twist-laden than a few other attempts I made, and it's quite possible to create a fairly straight section of river as well. Still, let's take a little time look at how to evaluate river bends in terms of their realism.

There are really two relevant parameters for classifying the meanders of rivers: sinuousity, and curvature radius. The former tells us how much curvature is present, and the latter tells us the distance scale on which that curvature exists. Most river valleys are relatively straight or gently bending, and so it is only the river itself that is subject to meandering within the valley.

Here's a plot of river sinuosity as a function of the local land gradient.
http://hydrosciences.colorado.edu/symposium/abstract_images/thumbnails/River_500x500.png
http://hydrosciences.colorado.edu/symposium/abstract_details_archive.php?abstract_id=183

Unsurprisingly, the more swiftly the river is descending, the less likely it is to meander. Values range between 1.2 and 2.4, with most rivers clustering above or below the value 1.5 in temperate zone. (The other cluster up above 2.0 consists of rivers in tropical rainforests.) The mean central angle of a river with a sinuosity of 1.5 is between 150 and 180 degrees. That's considerably snakier than a sine curve!

The mean radius of curvature is a little harder to explore, given more limited data. Here's the mean radius of curvature for the Colorado River:
http://www.utexas.edu/depts/grg/hudson/grg394k/studentprojects/may/mradofcurv.jpg
This is roughly in the neighborhood of 1 km, suggesting that river curves are features on the scale of about a mile or so. This is, naturally enough, the distance scale of the river valley bed.

The natural conclusions are:
  • Rivers curve quite a bit, frequently making the equivalent of near U-turns.
  • The distance scale for these turns is fairly narrow, in particular, much narrower than 6 miles, making these features wash out except on a lower-scale map.
From a game-map standpoint this creates a dilemma, in that a map with granularity of 6 miles can't really represent the lower-scale sinuosity of the river within its bed. It seems important to be able to explicitly locate places where land is surrounded on three sides by a river, for the sake of building your own Conwy! I hate to reduce the presence of bends to something abstractly "hidden" in a hex that shows a straight river, which takes away from the fun of trying to place a stronghold location on the hex map by looking at features on the map itself.

There's a similar problem associated with the difficulty of locating a "rock dome" suitable for a high castle. You can just say that any castle in the mountains is on a dome, but most castles were built on isolated hills and domes that were not otherwise close to other mountainous features. Moreover, since rivers don't go in mountain hexes, this would make it impossible to have an elevated castle on a river (like Conwy).

Thoughts?

2 comments:

  1. I am not particularly bothered by the serpentine rivers. In my attempts to make regions I had both extremes. After reading this post, I tried making a map where I advanced the river two hexes in the rolled direction, but I ended up filling half the region with water, and boxed in my attempt to create an alternate river exit. I then tried to only double the hex travel after the 4th roll, but it still gets messy. I think there should be some player agency in how much or little river there is. Perhaps choose once per region to advance a river hex twice in the rolled direction, or something. It should still be random and stuff, but I found that sometimes I just wanted the river to leave the region! Perhaps we can have two river patterns to pick from? All before resources and terrain are rolled.

    I like how the rivers look as they are, regardless of scale. Having a meandering river is just part of random generation.

    Also, how does terrain elevation progress if you start with hills as the ideal terrain? (i.e. Dwarves)

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  2. It's becoming a running gag that, every time I walk past Kyle in Glaske, he yells something about rivers at me.

    For terrain in hills, I'd currently just have them either stay hills forever, or (with a rising gradient result) stay hills in the first hexes adjacent to the river, but then turn into mountains everywhere beyond. With the "descending" gradient result, I'd probably shift into forests (instead of swamps), to represent forested slopes.

    I don't mind adding some user control to the process, as long as it doesn't result in only one "right" choice to build a region that everyone feels obligated to do to have high-value land. In particular, it's important to build the river first, and then add resources, so that the "best choice" for defending a fortress isn't always the same as the "best choice" for including all the resources. Rivers are pretty important for stronghold design, since the number of fortress walls they protect will affect siege durations and naval resupply.

    One aspect of hills/mountains that I should think more about is adding a gradient that runs parallel to the river, instead of perpendicular, so half the river has mountains around it and half of it has open grassland or forest. That would represent a river in the process of leaving the mountains, right at the foothills.

    This is the geography of the city of Boulder, where I did my PhD on long-range Rydberg spectroscopy. And also the geography the mines of Moria, where I did my undergraduate work on symbiotic balrog-goblin ecosystems.

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