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}