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I used r.horizon to calculate horizon on a raster every 10° without any offset. I have got 36 files now.

Is the first file from 0° to 10° (then centered on azimuth=5°) or is it centered on 0°, in this case the first file is from 355° to 5° (knowing that GRASS start 0 in the East counterclockwise)?

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Unless I completely misunderstand r.horizon, when creating raster output it calculates the height of the horizon for each point (cell) for the given direction. So if you don't set direction and your horizonstep is 10 degrees you will get the height of the horizon for directions 0°, 10°, 20°, etc. It does not represent the height of the horizon between 355° to 5°, 5° to 15° and so on, but only for the specified azimuth.

If you use r.horizon as input for r.sun you probably should use the same horizonstep for both for it to be useful.

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Note that r.sun does not require r.horizon, it can calculate it by itself (it is just a bit slower then). –  markusN Nov 6 '12 at 15:12

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