solar zenith angle derivations

1. solar zenith angle from solar elevation angle

   symbol	description	unit	variable name
   \(\alpha_{0}\)	solar elevation angle	\(deg\)	solar_azimuth_angle {:}
   \(\theta_{0}\)	solar zenith angle	\(deg\)	solar_zenith_angle {:}

   The pattern : for the dimensions can represent {time}, or no dimensions at all.

   \[\theta_{0} = 90 - \alpha_{0}\]

2. solar zenith angle from latitude and solar declination/hour angles

   symbol	description	unit	variable name
   \(\theta_{0}\)	solar zenith angle	\(deg\)	solar_zenith_angle {time}
   \(\delta\)	solar declination angle	\(deg\)	solar_declination_angle {time}
   \(\phi\)	latitude	\(degN\)	latitude {time}
   \(\omega\)	solar hour angle	\(deg\)	solar_hour_angle {time}

   \[\theta_{0} = \frac{180}{\pi}\arccos(\sin(\frac{\pi}{180}\delta)\sin(\frac{\pi}{180}\phi) - \cos(\frac{\pi}{180}\omega)\cos(\frac{\pi}{180}\delta)\cos(\frac{\pi}{180}\phi))\]