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How much does time does the ArcGIS solar radiation tool take to give solar map for day of about 50 km area?

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That depends on you data resolution and computer specifications including RAM and processing power. It took me about 1-day to do a college campus at about 2m resolution.

I cannot link to GeoNet as it is behind a log in wall but on this forum I found that,

"We are using the tool to calculate direct and diffuse incoming solar radiation for a valley in the mountains. The cell size of the raster is 1 m x 1 m and it has around 45'000 columns by 42'000 rows - it's quite big. We try to calculate the radiation for the period of a whole year with a time interval of 14 days and 0.5 hours. The output will be a single file."

This took about 1 month on a high spec PC.

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