Urban Meteorology, Pollutants, Geomorphology, Fractality, and Anomalous Diffusion

The measurements, recorded as time series (TS), of urban meteorology, including temperature (T), relative humidity (RH), wind speed (WS), and pollutants (PM₁₀, PM_2.5, and CO), in three different geographical morphologies (basin, mountain range, and coast) are analyzed through chaos theory. The parameters calculated at TS, including the Lyapunov exponent (λ > 0), the correlation dimension (D_C < 5), Kolmogorov entropy (S_K > 0), the Hurst exponent (0.5 < H < 1), Lempel–Ziv complexity (LZ > 0), the loss of information (<ΔI> < 0), and the fractal dimension (D), show that they are chaotic. For the different locations of data recording, C_K is constructed, which is a proportion between the sum of the Kolmogorov entropies of urban meteorology and the sum of the Kolmogorov entropies of the pollutants. It is shown that, for the three morphologies studied, the numerical value of the C_K quotient is compatible with the values of the exponent α of time t in the expression of anomalous diffusion applied to the diffusive behavior of atmospheric pollutants in basins, mountain ranges, and coasts. Through the Fréchet heavy tail study, it is possible to define, in each morphology, whether urban meteorology or pollutants exert the greatest influence on the diffusion processes.