Langley extrapolation

As time passes, the Sun moves across the sky, and therefore θ and m vary according to known astronomical laws.

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

Since aerosols tend to be more concentrated at low altitude, Langley extrapolation is often performed at high mountain sites.

A Langley plot can also be used as a method to calculate the performance of solar cells outside the Earth's atmosphere.

At the Glenn Research Center, the performance of solar cells is measured as a function of altitude.

[3] Sun photometers using low cost light-emitting diode (LED) detectors in place of optical interference filters and photodiodes have a relatively wide spectral response.

They might be used by a globally distributed network of students and teachers to monitor atmospheric haze and aerosols, and can be calibrated using Langley extrapolation.

[4] In 2001, David Brooks and Forrest Mims were among many[5][6] to propose detailed procedures to modify the Langley plot in order to account for Rayleigh scattering, and atmospheric refraction by a spherical Earth.

in equations (1) and (2), as the AOT (Atmospheric Optical Thickness), and the handbook refers to I0 as the EC (extraterrestrial constant).

The manual suggests that once a photometer is constructed, the user waits for a clear day with few clouds, no haze and constant humidity.

Direct solar radiation, at the various wavelengths indicated in nanometers , as measured at Niamey Niger on 24 December 2006, with a Multi-Filter Rotating Shadowband Radiometer (MFRSR). Measurements are plotted as a function of time in UTC.
Direct solar radiation as a function of secant of solar zenith angle at Niamey, Niger. December 24, 2006. From ARM data, from an MFRSR instrument. Wavelength in units of nanometers is indicated. Log is base 10.
Points are Langley extrapolation to top of atmosphere of direct solar radiation measured at Niamey, Niger 24 December 2006. Compared with Planck functions with the wavelength in micrometers .