Langley extrapolation

Langley extrapolation is a method for measuring the Sun's radiance with ground-based instrumentation, and thus remove 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.

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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 θ and m vary according to known astronomical laws.

By taking the logarithm of the above equation, one obtains

lnI = lnI₀ − mτ,

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 at the top of the atmosphere.

The requirement for good Langley plots is a constant atmosphere (constant τ). This is a strong requirement and 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.

Solar Cell Calibration

A Langley plot can also be used as a method to calculate the performance of solar cells under space conditions. At the Glenn Research Center, the performance of solar cells is measured as a function of altitude, and hence seen at varying air mass. By extrapolating the current from the cell as a function of the logarithm of the intensity to air mass zero ("AM0"), the performance under space conditions is found [1].

References

• Glenn E. Shaw, "Sun photometry", Bulletin of the American Meteorological Society 64, 4-10, 1983.