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 is important. One such example is atmospheric visibility which is often estimated as a range in meteorological context, as meteorological observable range (MOR). This is estimated from 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, free optic communication etc. 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 lower threshold in the data, which is not exclusive to the current problem, and examine its consequence in multifractal characterization of the field. Here, σ e was extracted from visibility data by a present weather sensor located in 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 (UM), which is widely used to characterize geophysical fields that exhibit extreme variability across scales. With direct data analysis and numerical simulations mimicking the behaviour, it was found that the multifractal properties exhibited by σ e is influenced by the upper limit of visibility range in data. The biases are identified within the theoretical framework of UM, thus expanding the general understanding on retrieval of underlying unbiased stochastic field.