Daily mean solar irradiance ($\overline{S}=(S_0/\pi )(H_0\sin \varphi \sin \delta +\cos \varphi \cos \delta \sin H_0)$)

At latitude $\varphi$ and solar declination $\delta$, integrate $S_0\max (0,\sin \varphi \sin \delta +\cos \varphi \cos \delta \cos H)$ over hour angle $H$. Sunset occurs at $H_0=\arccos (-\tan \varphi \tan \delta )$ when this lies in $[0,\pi ]$, with clipping for polar day or night. The displayed daily mean is at the top of the atmosphere; local absorbed heat flux also includes transmission and surface albedo.