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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]
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.
"AM1.5", 1.5 atmosphere thickness, corresponds to a solar zenith angle of =48.2°. While the summertime AM number for mid-latitudes during the middle parts of the day is less than 1.5, higher figures apply in the morning and evening and at other times of the year.
Similar equations are coded into a Fortran 90 routine in Ref. [3] and are used to calculate the solar zenith angle and solar azimuth angle as observed from the surface of the Earth. Start by calculating n , the number of days (positive or negative, including fractional days) since Greenwich noon, Terrestrial Time, on 1 January 2000 ( J2000.0 ).
The solar azimuth angle is the azimuth (horizontal angle with respect to north) of the Sun's position. [1] [2] [3] This horizontal coordinate defines the Sun's relative direction along the local horizon, whereas the solar zenith angle (or its complementary angle solar elevation) defines the Sun's apparent altitude.
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.
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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.