Calculating "sun time" on areas with high mountains? Topography available

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I'm wondering how to proceed if you want to calculate how a location on land will get direct sunshine at a given time on a given date (compared being in the shadow of the mountains)? The area is very dense with high mountains, and located well above the polar circle (69 degrees north). This means the path of the sun will vary greatly (from polar night (below horizon for a few months), to midnight sun (above horizon)).

I have the topography of the area available. I can (probably) get the path (or highest point) of the sun on a given day.

I have absolutely no clue how to tackle this problem.

Ideas? Is this possible with free GIS tools (QGIS)?



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