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}

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