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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]
The cosine of the hour angle (cos(h)) is used to calculate the solar zenith angle. At solar noon, h = 0.000 so cos( h ) = 1 , and before and after solar noon the cos(± h ) term = the same value for morning (negative hour angle) or afternoon (positive hour angle), so that the Sun is at the same altitude in the sky at 11:00AM and 1:00PM solar time.
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.
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 ).
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 following formulas assume the north-clockwise convention. The solar azimuth angle can be calculated to a good approximation with the following formula, however angles should be interpreted with care because the inverse sine, i.e. x = sin −1 y or x = arcsin y, has multiple solutions, only one of which will be correct.
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The equation above neglects the influence of atmospheric refraction (which lifts the solar disc — i.e. makes the solar disc appear higher in the sky — by approximately 0.6° when it is on the horizon) and the non-zero angle subtended by the solar disc — i.e. the apparent diameter of the sun — (about 0.5°). The times of the rising and ...