Fractal Dimension Time Series and Interaction Between Entropic Surfaces of Urban Meteorology and Pollutants in a Geographic Basin: Dynamic Effects, Thermal Flows and Anomalous Diffusion

Abstract

In three periods of 3.25 years each, and at the same six different heights of a basin geomorphology, measurements were made, in the form of a time series, of urban meteorological variables (MV) (temperature, relative humidity, wind speed magnitude) and pollutants (P) (PM 10, PM 2.5, and CO). It is verified that each time series has a fractal dimension, and the value of its maximum Kolmogorov entropy is determined. These values generate two entropic surfaces according to measurement periods: one for urban meteorology and another for pollutants. The calculation of the gradient to each entropic surface multiplied by the average temperature of the period according to the measurement location gives, approximately, the average entropic force for each location. Combining these results with an analysis of the ratio between urban meteorological entropies and pollutant entropies, it is shown that in a basin morphology the entropic forces associated with pollutants are dominant, a source of heat, and there is a high probability that they produce extreme events. This condition also favors anomalous subdiffusion.