solar azimuth angle derivations
solar azimuth angle from latitude and solar declination/hour/zenith 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} \(\varphi_{0}\) solar azimuth angle \(deg\) solar_azimuth_angle {time} \(\omega\) solar hour angle \(deg\) solar_hour_angle {time} \begin{eqnarray} \varphi_{0} & = & \begin{cases} \sin(\frac{\pi}{180}\theta_{0}) = 0, & 0 \\ \sin(\frac{\pi}{180}\theta_{0}) \neq 0 \wedge \omega > 0, & -\frac{180}{\pi}\arccos(\frac{\sin(\frac{\pi}{180}\delta)\cos(\frac{\pi}{180}\phi) - \cos(\frac{\pi}{180}\omega)\cos(\frac{\pi}{180}\delta)\sin(\frac{\pi}{180}\phi)}{\sin(\frac{\pi}{180}\theta_{0})}) \\ \sin(\frac{\pi}{180}\theta_{0}) \neq 0 \wedge \omega <= 0, & \frac{180}{\pi}\arccos(\frac{\sin(\frac{\pi}{180}\delta)\cos(\frac{\pi}{180}\phi) - \cos(\frac{\pi}{180}\omega)\cos(\frac{\pi}{180}\delta)\sin(\frac{\pi}{180}\phi)}{\sin(\frac{\pi}{180}\theta_{0})}) \end{cases} \end{eqnarray}