Characterization of Atmospheric Visibility through Extinction Coefficient and the Influence of Lower Threshold on Assessment of Multifractal Parameters

Scaling analysis of subjectively defined fields, which are often expressed as a range of values based on the field of application, is not straightforward. To avoid potential biases in statistical analysis, extracting the actual underlying field and understanding the effect of ranged values are important. One such example is atmospheric visibility which is often estimated as a range in meteorological context, as meteorological optical range (MOR). This is estimated from the extinction coefficient σ_e, an objective measurement of light attenuation by constituent gases and aerosols in the atmosphere, and expressed as a range depending on the application needs. Accurate estimation of visibility and its variability is required for the safe functioning of various domains such as transport sectors and free optic communication or for understanding regional variations in air quality and climate. Since MOR is a subjective range, here we attempt to characterize it using the objectively measured σ_e. In this context, we identify and illustrate the effect of a lower threshold in the data, which is not exclusive to the current problem, and examine its consequences in the multifractal characterization of the field. Here, σ_e was extracted from visibility data by a present weather sensor located in the Paris region (France). This was then compared with σ_e extracted from MOR measured at Paris Charles de Gaulle airport during the same period. Variability in σ_e was investigated under the framework of universal multifractals (UMs), which is widely used to characterize geophysical fields that exhibit extreme variability across scales. With direct data analysis and numerical simulations mimicking the behavior, it was found that the multifractal properties exhibited by σ_e are influenced by the upper limit of visibility range in the data. The biases are identified within the theoretical framework of UM, thus expanding the general understanding on the retrieval of the underlying unbiased stochastic field.