# solar azimuth angle derivations

1. 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}