Checking the validity of the إngstrِmʹs formula with spectral data of direct-beam irradiance obtained in Athens, Greece

This work analyzes the ability of the Ångströmʹs formula to correctly estimate the spectral aerosol optical depth. For this purpose, direct-beam spectra were obtained by a LICOR spectroradiometer in the 300–1100 nm wavelength range at several sites in the Athens basin under cloudless skies and different atmospheric conditions during May 1995. The total optical depth was retrieved by means of the SMARTS radiative transfer code. The objective of this study is to compare the aerosol optical depths (AOD) derived by the Ångströmʹs formula with the spectral aerosol optical depths (SAOD) retrieved through the SMARTS model and, therefore, to check the validity of the former. From this comparison, it is found that the correlation coefficients between SAODs and AODs are higher than 0.9 in most cases. The greatest SAOD − AOD differences are found to take place at the shorter wavelengths. A further analysis of the above differences at 500 and 1000 nm with SMARTS shows very low values, especially at 500 nm, indicating the accuracy of the Ångströmʹs formula fitting. The differences at 1000 nm are much higher due to the water vapor absorption parameter that causes uncertainties in the water vapor optical depth determination. On the other hand, the sole contributors to the total optical depth at 500 nm are aerosols and ozone; as the ozone optical depth can be estimated with a great accuracy, the Ångströmʹs formula gives an accurate fit to the SAOD values estimated by the SMARTS model.