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# External Longwave Radiation (Sky temperature)

Hello everyone,

I have a small doubt regarding the longwave radiational part of the surface energy balance equation. As per the documentation, E+ calculates external longwave radiation using the following equation: q"_LWR = q"_gnd + q"_sky + q"_air

In the case of a flat roof, we can ignore q"_gnd (ground), then q"_LWR = q"_sky + q"_air if q"_sky (= esigma(T_sky^4 - T_surf^4)) is the net thermal radiative flux between a horizontal surface and the sky (Walton 1983) and q"_air (= esigma(T_air^4 - T_surf^4)) is the net thermal radiative flux between a horizontal surface and the ambient air.

Then how do we define q"_sky or T_sky? Is it like T_sky is the effective temperature of a region above a certain height above ground and space? and T_air is the ambient air which is below that certain hight? Are there any criteria for that specific height?

Otherwise, it is redundant to also include a radiation term for the air (q"_air) if we consider q"_sky is the net thermal radiation from a horizontal surface to the sky.

Any help is highly appreciated! Thanks

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Referring to the engineering reference for the sky temperature: https://www.energyplus.net/sites/defa...

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.

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