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

Abstract 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. Significance Statement Data obtained from measurement campaigns are often influenced by instrumental limitations such as upper and lower detection limits. One such example is atmospheric visibility which is usually represented as a range, from objective measurement of light attenuation by constituent particles. Here, we examine the consequences of characterizing visibility using the extinction coefficient, by considering the presence of a lower limiting value, using two datasets in the Paris region—forward scattering sensor and airport visibility measurement. Through data analysis, numerical simulation, and theoretical formulation, the biases are identified and the underlying unbiased stochastic field is retrieved. This enables a more accurate analysis and simulation of visibility, as well as other geophysical fields with similar instrumental or application limitations.