It was definitely quite a bit of effort to get every line of sight. We felt it was necessary if we were going to try and prove that there are none longer.
Regular viewshed algorithms really aren't built for it, and being able to do it cheaply while also maintaining a cluster of compute that can shut down at any time is also its own mess (these were all spot instance so we could get 75+% off).
The 530km number takes into account both the curvature, along with refraction. It's a simple elevation adjustment when you are doing your angle of elevation calculations.
If you want a synopsis of how we calculate lines of sight and all the parameters we use I have a shorter, less whitepaper-y blog post here:
I think I came up with that name from a game of telephone of sources claiming to have the longest line of sight. There's a lot of really random sources on the Internet that mention the line of sight but do not cite the data or analysis. I have seen Hindu Tagh thrown around as well so if it's more accurate we want it there.
Part of our motivations were to stop the game of telephone and become an authoritative source on this stuff.
Good idea, I'll add it to the FAQ later today. Under a section of "why don't these results match the other tools". The projection error is separate as you mentioned.
The error I've experienced hunting bugs tends to be within about .5-2%. That's a vibe, not an empirical "I've calculated the error to be 1.5%". We definitely expect that bound to tighten as we get access to more computational resources.
I do not think this is numerical however. I think it's more directly related to rasterization, interpolation, and not enough angle coverage. We have fairly good numerical and viewshed tests to double check we don't have weirdness going on there.
There's two forms of interpolation going on here that I'm not sure you or Dr Dueschle are using. We interpolate a "band of sight" of single a degree for our azithmual projection, but uniquely we also rotate the DEM elevations around all the observers rather than the observer around to see all the elevations.
The effects of the first can be lessened by lowering the band of sight such that we only process half a degree at a time so that we make sure we get more coverage further away. We plan on running some more experiments by rotating to cover more points.
The algorithm is already fairly expensive to run against the whole world so we weren't particularly interested in that level of coverage for the full earth.
For total viewshed area, our algorithm comes in at roughly a percent or so difference which was what we used as our benchmark for correctness.
All this to say, no, we don't think you both are wrong, we've been looking at making ours more accurate. At a world scale that's quite computationally expensive, so we didn't use that methodology for our initial launch. We see our results as validation of yours, not as something we've disproved.
The short answer: yes, this is partially the reason.
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Regular viewshed algorithms really aren't built for it, and being able to do it cheaply while also maintaining a cluster of compute that can shut down at any time is also its own mess (these were all spot instance so we could get 75+% off).
The 530km number takes into account both the curvature, along with refraction. It's a simple elevation adjustment when you are doing your angle of elevation calculations.
If you want a synopsis of how we calculate lines of sight and all the parameters we use I have a shorter, less whitepaper-y blog post here:
https://ryan.berge.rs/posts/lines-of-sight/