Chapman function
Encyclopedia
A Chapman function describes the integration of atmospheric absorption
along a slant path on a spherical earth, relative to the vertical case. It applies for any quantity with a concentration decreasing exponentially with increasing altitude
. To a first approximation, valid at small zenith
angle
s, the Chapman function for optical absorption is equal to
where z is the zenith
angle and sec denotes the secant function.
The Chapman function is named after Sydney Chapman
.
Absorption (electromagnetic radiation)
In physics, absorption of electromagnetic radiation is the way by which the energy of a photon is taken up by matter, typically the electrons of an atom. Thus, the electromagnetic energy is transformed to other forms of energy for example, to heat. The absorption of light during wave propagation is...
along a slant path on a spherical earth, relative to the vertical case. It applies for any quantity with a concentration decreasing exponentially with increasing altitude
Altitude
Altitude or height is defined based on the context in which it is used . As a general definition, altitude is a distance measurement, usually in the vertical or "up" direction, between a reference datum and a point or object. The reference datum also often varies according to the context...
. To a first approximation, valid at small zenith
Zenith
The zenith is an imaginary point directly "above" a particular location, on the imaginary celestial sphere. "Above" means in the vertical direction opposite to the apparent gravitational force at that location. The opposite direction, i.e...
angle
Angle
In geometry, an angle is the figure formed by two rays sharing a common endpoint, called the vertex of the angle.Angles are usually presumed to be in a Euclidean plane with the circle taken for standard with regard to direction. In fact, an angle is frequently viewed as a measure of an circular arc...
s, the Chapman function for optical absorption is equal to
where z is the zenith
Zenith
The zenith is an imaginary point directly "above" a particular location, on the imaginary celestial sphere. "Above" means in the vertical direction opposite to the apparent gravitational force at that location. The opposite direction, i.e...
angle and sec denotes the secant function.
The Chapman function is named after Sydney Chapman
Sydney Chapman (astronomer)
Sydney Chapman FRS was a British mathematician and geophysicist. His work on the kinetic theory of gases, solar-terrestrial physics, and the Earth's ozone layer has inspired a broad range of research over many decades....
.