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Referring to the engineering reference for the sky temperature: https://www.energyplus.net/sites/default/files/docs/site_v8.3.0/EngineeringReference/05-Climate/index.html

We can see that sky temperature is the radiative temperature of the sky based on the horizontal infrared radiation, which is itself determined by the water vapor in the air and cloud cover (the sky emissivity) - so the q"_sky is the flux between a surface and the sky at the cloud layer.

The air temperature however is ambient to the surface; so we have a local radiative exchange with the ambient air and an additional radiative exchange with the sky and cloud cover.