Langley extrapolation
Encyclopedia
Langley extrapolation is a method for measuring the Sun's radiance
with ground-based instrumentation,
thereby removing the effect of the atmosphere
. It is based on repeated measurements with a sun photometer
operated at a given location for a cloudless morning or afternoon, as the Sun
moves across the sky
. It is named for American astronomer and physicist Samuel Pierpont Langley
.
It is known from Beer's law that, for every instantaneous measurement, the direct-Sun radiance I is linked to the solar extraterrestrial radiance I0 and the atmospheric optical depth
τ by the following equation:
where m is a geometrical factor accounting for the slant path through the atmosphere, known as the airmass factor
.
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
and 
vary according to known astronomical
laws.
By taking the logarithm of the above equation, one obtains
and if one assumes that the atmospheric disturbance τ does not change during the observations (which last for a morning or an afternoon), the plot of ln I versus m is a straight line. Then, by linear extrapolation
to m = 0, one obtains I0, i.e. the Sun's radiance that would be observed by an instrument placed above the atmosphere.
The requirement for good Langley plots is a constant atmosphere (constant τ). This requirement can be fulfilled only under particular conditions, since the atmosphere is continuously changing. Needed conditions are in particular: the absence of clouds along the optical path, and the absence of variations in the atmospheric aerosol layer. Since aerosols tend to be more concentrated at low altitude, Langley extrapolation is often performed at high mountain sites. Data from NASA
Glenn Research Center
indicates that the Langley plot accuracy is improved if the data is taken above the tropopause
.
s outside the Earth's atmosphere. At the Glenn Research Center
, the performance of solar cells is measured as a function of altitude. By extrapolation, researchers determine their performance under space conditions http://rt.grc.nasa.gov/power-in-space-propulsion/photovoltaics-power-technologies/technology-thrusts/solar-cell-measurement-and-calibration/.
Radiance
Radiance and spectral radiance are radiometric measures that describe the amount of radiation such as light or radiant heat that passes through or is emitted from a particular area, and falls within a given solid angle in a specified direction. They are used to characterize both emission from...
with ground-based instrumentation,
thereby removing the effect of the atmosphere
Atmosphere
An atmosphere is a layer of gases that may surround a material body of sufficient mass, and that is held in place by the gravity of the body. An atmosphere may be retained for a longer duration, if the gravity is high and the atmosphere's temperature is low...
. It is based on repeated measurements with a sun photometer
Sun photometer
A sun photometer is a type of photometer conceived in such a way that it points at the Sun.Recent sun photometers are automated instruments incorporating a Sun-tracking unit, an appropriate opticalsystem, a spectrally filtering device, a photodetector, and a...
operated at a given location for a cloudless morning or afternoon, as the Sun
Sun
The Sun is the star at the center of the Solar System. It is almost perfectly spherical and consists of hot plasma interwoven with magnetic fields...
moves across the sky
Sky
The sky is the part of the atmosphere or outer space visible from the surface of any astronomical object. It is difficult to define precisely for several reasons. During daylight, the sky of Earth has the appearance of a pale blue surface because the air scatters the sunlight. The sky is sometimes...
. It is named for American astronomer and physicist Samuel Pierpont Langley
Samuel Pierpont Langley
Samuel Pierpont Langley was an American astronomer, physicist, inventor of the bolometer and pioneer of aviation...
.
It is known from Beer's law that, for every instantaneous measurement, the direct-Sun radiance I is linked to the solar extraterrestrial radiance I0 and the atmospheric optical depth
Optical depth
Optical depth, or optical thickness, is a measure of transparency. Optical depth is defined by the negative logarithm of the fraction of radiation that is not scattered or absorbed on a path...
τ by the following equation:
where m is a geometrical factor accounting for the slant path through the atmosphere, known as the airmass factor
Airmass
In astronomy, air mass is the optical path length through Earth’s atmosphere for light from a celestial source. As it passes through the atmosphere, light is attenuated by scattering and absorption; the more atmosphere through which it passes, the greater the attenuation. Consequently, celestial...
.
For a plane-parallel atmosphere, the airmass factor is simple to determine if one knows the solar zenith angle
Celestial coordinate system
In astronomy, a celestial coordinate system is a coordinate system for mapping positions on the celestial sphere.There are different celestial coordinate systems each using a system of spherical coordinates projected on the celestial sphere, in analogy to the geographic coordinate system used on...
θ: m = 1/cos(θ). As time passes, the Sun moves across the sky, and therefore
and vary according to known astronomicalAstronomy
Astronomy is a natural science that deals with the study of celestial objects and phenomena that originate outside the atmosphere of Earth...
laws.
By taking the logarithm of the above equation, one obtains
and if one assumes that the atmospheric disturbance τ does not change during the observations (which last for a morning or an afternoon), the plot of ln I versus m is a straight line. Then, by linear extrapolation
Extrapolation
In mathematics, extrapolation is the process of constructing new data points. It is similar to the process of interpolation, which constructs new points between known points, but the results of extrapolations are often less meaningful, and are subject to greater uncertainty. It may also mean...
to m = 0, one obtains I0, i.e. the Sun's radiance that would be observed by an instrument placed above the atmosphere.
The requirement for good Langley plots is a constant atmosphere (constant τ). This requirement can be fulfilled only under particular conditions, since the atmosphere is continuously changing. Needed conditions are in particular: the absence of clouds along the optical path, and the absence of variations in the atmospheric aerosol layer. Since aerosols tend to be more concentrated at low altitude, Langley extrapolation is often performed at high mountain sites. Data from NASA
NASA
The National Aeronautics and Space Administration is the agency of the United States government that is responsible for the nation's civilian space program and for aeronautics and aerospace research...
Glenn Research Center
Glenn Research Center
NASA John H. Glenn Research Center at Lewis Field is a NASA center, located within the cities of Brook Park, Cleveland and Fairview Park, Ohio between Cleveland Hopkins International Airport and the Cleveland Metroparks's Rocky River Reservation, and has other subsidiary facilities in Ohio...
indicates that the Langley plot accuracy is improved if the data is taken above the tropopause
Tropopause
The tropopause is the atmospheric boundary between the troposphere and the stratosphere.-Definition:Going upward from the surface, it is the point where air ceases to cool with height, and becomes almost completely dry...
.
Solar cell calibration
A Langley plot can also be used as a method to calculate the performance of solar cellSolar cell
A solar cell is a solid state electrical device that converts the energy of light directly into electricity by the photovoltaic effect....
s outside the Earth's atmosphere. At the Glenn Research Center
Glenn Research Center
NASA John H. Glenn Research Center at Lewis Field is a NASA center, located within the cities of Brook Park, Cleveland and Fairview Park, Ohio between Cleveland Hopkins International Airport and the Cleveland Metroparks's Rocky River Reservation, and has other subsidiary facilities in Ohio...
, the performance of solar cells is measured as a function of altitude. By extrapolation, researchers determine their performance under space conditions http://rt.grc.nasa.gov/power-in-space-propulsion/photovoltaics-power-technologies/technology-thrusts/solar-cell-measurement-and-calibration/.