Spatial and temporal variations in the atmospheric aerosol optical depth at the ARM CART Site Page: 4 of 16
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data using the LMS-Langley technique 6. The results to be presented in this paper are from the
500 nm channel only.
THEORY AND METHODOLOGY
The AOD is a fraction of the total optical depth (TOD). The TOD can be attributed to the solar
irradiance that is scattered or absorbed by all material in the MFRSR viewpath as it is passing
through the Earth's atmosphere. The majority of the materials in this view path include aerosols,
air molecules, ozone, water vapor, and clouds. When calculating the clear-sky AOD, corrections
are required for the Rayleigh scattering by air molecules, ozone absorption, and water vapor
absorption. At the wavelengths mentioned in this paper absorption of light by water vapor is
insignificant; thus the correction for water absorption was not performed. Since we were only
interested in the clear-sky effects of aerosols on radiative transfer the cloudy time periods were
removed after the LMS regression was performed. The TOD is the linear sum of the AOD,
Rayleigh scattering, and ozone absorption2.
Equation 1. The components of Total Optical Depth (TOD)
TOD = AOD + ROD + 030D
Where:
TOD = Total Optical Depth (unitless)
AOD = Aerosol Optical Depth (unitless)
ROD = Rayleigh Optical Depth (unitless)
030D = Ozone Optical Depth (unitless)
TOD was computed by the Langley method described by Cheng and Kopet6 that used the robust
LMS regression technique. The Langley Law describes the attenuation of solar irradiance as it
passes through the atmosphere.
Equation 2. The Langley Law for one wavelength
I= I, * e-T"
Where:
I= Spectral irradiance at the ground surface (W m2 nm1)
Io = Spectral irradiance at the top of the atmosphere (W m2 nm1)
m = Air mass (unitless)
z = total optical depth (unitless)
I is the direct normal irradiance measurement from the MFRSR. The airmass was determined
from the relative position between the Earth and the Sun; i.e. the day of the year and time of day
(or angle to the sun) and is calculated from the equation derived by Kasten9. Io and ti were
computed for AM and PM periods that have an airmass between 1.5 and 6 when performing a
LMS regression analysis on the following equation.
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Nash, T.M. & Cheng, M.D. Spatial and temporal variations in the atmospheric aerosol optical depth at the ARM CART Site, report, February 1, 1998; Tennessee. (https://digital.library.unt.edu/ark:/67531/metadc711006/m1/4/: accessed March 19, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.