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Description
Given aerosol optical depth (AOD), Angstrom alpha and precipitable water (AKA total column water vapor) calculate Linke turbidity factor using Molineaux (1998), Bird-Hulstrom (1980), Berk (1996) and Kasten (1980).
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calculate Angstrom turbidity alpha exponent if not known, from AOD at two wavelengths,
lambda1andlambda2:alpha0 = -log(aod1 / aod2) / log(lambda1 / lambda2)Example with
lambda1 = 1240nmandlambda2 = 550nmalpha0 = -log(aod1240nm / aod550nm) / log(1240 / 550) -
get
aodat 700[nm] fromalphaaod700 = aod550* ((700 / 550) ^ (-alpha0)) -
From numerically integrated spectral simulations done with Modtran (Berk, 1996), Molineaux (1998) obtained for the broadband optical depth of a clean and dry atmopshere (fictious atmosphere that comprises only the effects of Rayleigh scattering and absorption by the atmosphere gases other than the water vapor) the following expression where
Mis airmass.delta_cda = - 0.101 + 0.235 * M ^ (-0.16) -
The broadband water vapor optical depth where
pwatis the precipitable water vapor content of the atmosphere in [cm]. The precision of these fits is better than 1% when compared with Modtran simulations in the range 1 < M < 6 and 0 < w < 5 cm.delta_w = 0.112 * M ^ (-0.55) * pwat ^ (0.34); -
Aerosol
either using (Molineaux 1998)
delta_a = aod700or using (Bird-Hulstrom 1980)
delta_a = 0.27583*aod380 + 0.35*aod500 -
Using the Kasten pyrheliometric formula (1980), the Linke turbidity at M
TL = -(9.4 + 0.9*M) * log(exp(-M * (delta_cda + delta_w + delta_a))) / M
This derivation was developed in collaboration with Armel Oumbe @aoumbe
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