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Langley extrapolation
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Langley extrapolation : ウィキペディア英語版
Langley extrapolation

Langley extrapolation is a method for determining the Sun's radiance at the top of the atmosphere with ground-based instrumentation, and is often used to remove the effect of the atmosphere from measurements of, for example, aerosol optical thickness or ozone. 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.
==Theory==
It is known from Beer's law that, for every instantaneous measurement, the ''direct-Sun radiance'' ''I'' is linked to the ''solar extraterrestrial radiance'' ''I''0 and the atmospheric optical depth \tau 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 θ and ''m'' vary according to known astronomical laws.
By taking the logarithm of the above equation, one obtains:
and if one assumes that the atmospheric disturbance \tau 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 with a slope equal to \tau. Then, by linear extrapolation to ''m'' = 0, one obtains ''I''0, 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 \tau). 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.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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