there is at least some research and some formula, I’m not sure if you can acces this article (but I can 
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Relationship between sunshine duration and solar radiation
Author links open overlay panelHarrySuehrckeaRoss S.BowdenbK.G.T.Hollandsc
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Highlights
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69,000 pairs of sunshine–radiation readings were examined from 670 sites.
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Relationship between atmospheric transmittance and sunshine fraction is non-linear.
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Reason for non-linearity is clouds get optically thicker with decreasing sunshine fraction.
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A generalization of the Angstrom–Prescott equation most efficiently fits data.
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Fundamental connection between diffuse fraction and sunshine–radiation relationship.