Multifractal analysis of extinction coefficient and its consequences in characterizing atmospheric visibility

Extinction coefficient (σ_e) is a measure of light attenuation in the atmosphere, due to absorption and scattering properties of constituent gases and aerosols. In meteorological context, σ_e is used to understand transparency of the atmosphere, by estimating visibility or meteorological observable range (MOR). An accurate representation of visibility is required for safe functioning of various domains such as transport sectors, free optic communication, etc., and for understanding regional variations in air quality and climate. As the measurement of visibility is subjective and dependent on the instrument and range of measurement, here we attempt to characterize the same using extinction coefficient. σ_e was investigated under the framework of universal multifractals (UM), which is widely used to analyze and characterize geophysical fields that exhibit extreme variability over measurement scales.

For this study, σ_e was extracted from forward scattering visibility data by disdrometer (Campbell Scientific PWS100) located in the Paris area (France), operated by Hydrology, Meteorology, and Complexity laboratory of École des Ponts ParisTech (HM&Co, ENPC). As governing nonlinear equations of the atmosphere such as Navier-Stokes possess scale invariance, it was assumed here that the behavior of light attenuating particles should inherit similar scaling properties and hence be treated as multifractal fields. σ_e extracted from MOR measured at Paris-Charles de Gaulle airport was also subjected to multifractal analysis during the same time period for comparison. With direct analysis and simulations, it was found that σ_e exhibits multifratcal properties but are influenced by upper limit of visibility range in the instrument used for measurement. From the study, we suggest usage of extinction coefficient (σ_e) for characterizing atmospheric visibility as the former is a more physically relevant quantity which is objectively measured by instruments and directly related to particles in the atmosphere; while emphasizing the need to consider biases from instrumental range.