# Measure for convolutedness of landscape

September 28, 2015 6:08 AM Subscribe

Is there a measure for the convolutedness of landscape where a grassland would be a low number and someplace like Guilin would be a high number?

You could also use rugosity - if you're doing GIS, Google jenness tools rugosity for a relatively easy way to calculate it for a surface.

posted by umwhat at 6:31 AM on September 28, 2015 [1 favorite]

posted by umwhat at 6:31 AM on September 28, 2015 [1 favorite]

i don't know anything about rugosity but it seems to be a cool idea. the fourier transform is very standard physics - a kind of general tool used all over the place - but complicated to understand.

if you just want an arbitrary number that's easy to calculate in practice then, off the top of my head, you could place random lines (of some fixed length - say a mile) on maps of the areas you want to compare (using maps of the same scale and with the same contour levels) and count the number of contour levels that each line crosses. the average of that, for a number of lines in each area, will give a hand-waving measure of how rough the surface is.

posted by andrewcooke at 6:49 AM on September 28, 2015

if you just want an arbitrary number that's easy to calculate in practice then, off the top of my head, you could place random lines (of some fixed length - say a mile) on maps of the areas you want to compare (using maps of the same scale and with the same contour levels) and count the number of contour levels that each line crosses. the average of that, for a number of lines in each area, will give a hand-waving measure of how rough the surface is.

posted by andrewcooke at 6:49 AM on September 28, 2015

My comment on a related question some years ago relates to this: the concept of "fractal dimensionality" is such that if a planar surface has 2 dimensions and a fully-solid tangible object has 3 dimensions, there should exist a range of values between 2 and 3 dimensions to describe the surface in terms of its complexity and form.

posted by zachxman at 7:14 AM on September 28, 2015 [1 favorite]

posted by zachxman at 7:14 AM on September 28, 2015 [1 favorite]

Another choice is the "terrain ruggedness index" proposed here and scripted in AML here.

Alternately, you could areally summarize the slope of the slope to get an indication of ruggedness.

My quick searches didn't turn up many examples of this end, but several applications use similar intermediate values for landslide, landform, and fragmentation indices. Glad to discuss further.

posted by zachxman at 8:06 AM on September 28, 2015

Alternately, you could areally summarize the slope of the slope to get an indication of ruggedness.

My quick searches didn't turn up many examples of this end, but several applications use similar intermediate values for landslide, landform, and fragmentation indices. Glad to discuss further.

posted by zachxman at 8:06 AM on September 28, 2015

I think the first step here would be creating a better definition of "convolutedness". That would inform a better mathematical analog/model for that measure. My opinion (and how easy this is depends on the data you have access to) would be statistical rather than numerical like the others above...

...perhaps the standard deviation of a sufficiently frequently sampled grid of altitude measurements in the area. A very smooth area would give you a very small standard deviation and a very rough, turbulent area would give you a very large standard deviation. The requirement of land to be mathematically continuous (and relatively differentiable) help this be a solid measure. The next step better would be to do the same thing with the derivative of this number with respect to north/south and east/west (or something like the potential or the gradient of the surface).

All of this is assuming a lot of math. Without that math, this gets pretty nuanced/hand-wavy very quickly.

posted by milqman at 8:10 AM on September 28, 2015

...perhaps the standard deviation of a sufficiently frequently sampled grid of altitude measurements in the area. A very smooth area would give you a very small standard deviation and a very rough, turbulent area would give you a very large standard deviation. The requirement of land to be mathematically continuous (and relatively differentiable) help this be a solid measure. The next step better would be to do the same thing with the derivative of this number with respect to north/south and east/west (or something like the potential or the gradient of the surface).

All of this is assuming a lot of math. Without that math, this gets pretty nuanced/hand-wavy very quickly.

posted by milqman at 8:10 AM on September 28, 2015

*standard deviation of a sufficiently frequently sampled grid of altitude measurements*

that's roughly what the ruggedness index above is.

posted by andrewcooke at 8:40 AM on September 28, 2015

Response by poster: So "landscape convolutedness" = "terrain ruggedness". Interesting that putting it another way hits the nail on the head. Unfortunately, not knowing how to put it limited my searching.

I don't do GIS -- I was just wondering if there was a term out there that someone might use if they liked the terrain ruggedness of one area and wanted to know where there might be similar areas.

The PDF zachxman linked to had one map of Montana, but that's all. It would be nice to find a trove of more maps like that. :)

posted by strangeguitars at 9:02 AM on September 28, 2015

I don't do GIS -- I was just wondering if there was a term out there that someone might use if they liked the terrain ruggedness of one area and wanted to know where there might be similar areas.

The PDF zachxman linked to had one map of Montana, but that's all. It would be nice to find a trove of more maps like that. :)

posted by strangeguitars at 9:02 AM on September 28, 2015

At a smaller scale, there's also Roughness length, which matters a lot to wind flow.

posted by scruss at 9:07 AM on September 28, 2015

posted by scruss at 9:07 AM on September 28, 2015

Best answer: If you are interested in this concept from a landscape ecology point of view rather than a mathematical one (i.e. no need to reinvent the wheel), terms we use are 'topographic roughness' or 'topographic complexity'. There are a ton of measures used for this depending on your question and its scale (terrestrial vs. aquatic, remote sensing trees, mountains vs. grasslands). There are also tons of maps.

posted by hydrobatidae at 9:54 AM on September 28, 2015

posted by hydrobatidae at 9:54 AM on September 28, 2015

This thread is closed to new comments.

in simple terms, you can represent "any" curve (or surface) in terms of "fundamental wiggles". a rolling landscape's wiggle's are vary slowly varying, while a mountainous area has lots of high frequency variations.

(well, the power spectrum is a whole series of numbers, but you could construct some measure from that, like the ratio of total power in the high frequencies relative to the low frequencies).

posted by andrewcooke at 6:17 AM on September 28, 2015