The zenith angle, y(hr) (rad), is the incidence angle for a horizontal surface, i.e. the angle between the sun's direct rays and a line perpendicular to the horizontal surface at a given point. It is computed on a hourly basis as:
l: latitude (rad)
d: solar declination (rad)
tre: rate of earth's turn, equal to 0.2618 rad h-1
hr: solar hour of the day
hr0: hour of solar noon (equal to 12.00)
Sun elevation angle above the horizon, b(hr) (rad), and zenith angle are complementary:
The lower the elevation angle, the more unit area of beam is spread out on the ground, so its flux density on a unit area basis is reduces. As in the figure below, cosine of y is one when the sun is directly overhead; cosine of y is zero when y is 90 degrees and the sun is aligned with the horizon.
Due to haze in the morning and clouds in the afternoon, atmospheric transmission is lower near the margins of the day. Besides that, path length of solar radiation in the atmosphere is longer (Spitters et al., 1986). A modified ("effective") form of the solar elevation, b'(hr) (rad), takes the effect of the daily course in atmospheric transmission into account (Supit and van der Goot, 2003):
This form is currently used to compute hourly values of the photosynthetically active radiation.