Langley Analysis

Langley Analysis computes the values necessary to calculate air mass of a column and the total optical depth of a column. Langley Analysis can only be run on clear, sunny days. The output of a Langley Analysis is in nine columns. The files are in the form:

allYYMMDD.lang

where YYMMDD is the date analyzed. If there no date listed, that means that the conditions were not correct to run Langley. For example, it may have been a cloudy day.

When looking at the data, the columns (from left to right) are:

Date (in Julian time--followed by .25 for a morning regression or .75 for an afternoon regression)
Channel number (each stands for a different wavelength)
- 2 is for 415.6nm
- 3 is for 500.5nm
- 4 is for 616.6nm
- 5 is for 670.6nm
- 6 is for 868.8nm
- 7 is for 939.7nm
Number of data points available for the regression
Number of data points actually used for the regression
Total Optical Depth (known as t, or tau)
Extrapolated Irradiance at the top of the atmosphere (known as I₀)
Standard deviation of the residual variance from the data to the regression line of the ln(intensity)
Distance from the earth to the sun in AU
Estimate of the Solar Constant: I₀*distance²

Langley Analysis files

Once the total column optical depth has been found using Langley analysis, several other values can be calculated. Solar radiation that is not absorbed by water vapor or oxygen (ozone) can be calculated using the equation:

I=I₀ext(-tm)

where:

I is the solar irradiance at the point of measurement
I₀ is the solar irradiance at the top of the atmosphere
t is the total column optical depth (from Langley analysis)
m is the air mass

A formula for air mass is:

m = [sin(el) + 0.50572(6.07995+el)^-1.6364]^-1

where el is the elevation of the sun in degrees. Programs for obtaining the elevation of the sun are available for download from the Atmospheric Science Research Center in Albany, NY. For Unix systems, the program is called airmass and is available here. For PC's the program is called asunpos.f and it is in the /pub/progs/ directory of this anonymous ftp site.

The total optical depth can be separated into its various components (Rayleigh scattering, ozone absorption, water vapor absorption and aerosol extinction) using the following equations: