April 30, 2018

Elevation II: Erosion

Erosion is a feature of both soil type and river volume. Certain soils erode faster than others, and yield different features. For now, I'm mostly concerned with how erosion affects the height of a 20-mile hex.

I think I like this model the best. This paper gives very good results and is easy to implement into my system.
\[\partial h = \partial t (u - k \sqrt{A} s)\]

where $\partial t = 2.5(10)^5$ years is the geological scale, $u = 5(10)^{-4}$ m/y is the tectonic uplift, $k = 5.61(10)^{−7}$ y$^{-1}$ as the erosion rate, $A$ is the total area drained, and $s$ is the slope between two nodes.

Strictly speaking, $u$ is a function of the tectonic collisions. For now, I'll set the value to a constant and see what happens. It'll be a bit more work to let the cells know if they sit above a collision boundary, etc.

No discussion of erosion would be complete without at least a mention of Wilbur. I'm not sure what model it uses to create its drainage networks and erosion, but it does give very pretty results and allows you to play with some of settings to get the type of surface you want.

For now, I don't want to bother with deposition (so no river deltas, a mainstay of fantasy maps), so I'll only bother in the case where $\partial h > 0$. I'm still working on the raw heightmaps, so it'll be a while before I have enough to test this model anyway.

I also need to create the precipitation maps before I do any major irreversible work on erosion, because the amount of rainfall will affect how much volume the rivers actually have, of course. This will be considered as a modifier to $A$, as the original model is precipitation-independent. Once that happens, I'll push out an update to this post. I'm working on this draft as I'm fiddling with settings, so I'm dangerously close to an unedited stream of conscious.

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