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It is the complement to the solar altitude or solar elevation, which is the altitude angle or elevation angle between the sun’s rays and a horizontal plane. [1] [2] At solar noon, the zenith angle is at a minimum and is equal to latitude minus solar declination angle. This is the basis by which ancient mariners navigated the oceans. [3]
This is the coordinate system normally used to calculate the position of the Sun in terms of solar zenith angle and solar azimuth angle, and the two parameters can be used to depict the Sun path. [3] This calculation is useful in astronomy, navigation, surveying, meteorology, climatology, solar energy, and sundial design.
A 2021 publication [8] about solar geometry first calculates the x-, y-, and z-component of the solar vector, which is a unit vector with its tail fixed at the observer's location and its head kept pointing toward the Sun, and then uses the components to calculate the solar zenith angle and solar azimuth angle. The calculated solar vector at 1 ...
The optical depth for a slant path is τ = mτ′, where τ′ refers to a vertical path, m is called the relative airmass, and for a plane-parallel atmosphere it is determined as m = sec θ where θ is the zenith angle corresponding to the given path.
For a plane-parallel atmosphere, the airmass factor is simple to determine if one knows the solar zenith angle θ: m = 1/cos(θ). As time passes, the Sun moves across the sky, and therefore θ and m vary according to known astronomical laws. Direct solar radiation as a function of secant of solar zenith angle at Niamey, Niger. December 24, 2006.
Approximate dates when the solar zenith angle reaches a minimum of 0 degrees vs latitude superimposed on an equirectangular world map. The example in blue shows the dates of Lahaina Noon at Honolulu, Hawaii, USA.
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It is the sum of direct irradiance (after accounting for the solar zenith angle of the Sun z) and diffuse horizontal irradiance: [8] = + Global tilted irradiance (GTI) is the total radiation received on a surface with defined tilt and azimuth, fixed or Sun-tracking.