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APPLICATION OF COMPLEX NETWORKS TO THE DESCRIPTION OF OZONE DYNAMICS
Rafael Carmona-Cabezas, Eduardo Gutiérrez de Ravé, Francisco J. Jiménez-Hornero
Keywords: Ground-level ozone, air pollution, Visibility Graphs, complex networks, time series 1. Introduction
Many studies have been performed about ground-level ozone over the last decades. The importance of ozone characterization and analysis lies on the fact that it is one of the main photochemical oxidants (due to its abundance). This irritant gas has serious repercussions for human health and harvests when its concentration is high (Doherty et al., 2009). The exposed damages have an economic impact, since every year they lead to losses of several billions of dollars (Miao et al., 2017). Ozone is a secondary pollutant, whose chemical formation and destruction mechanisms are known to be photochemical and nonlinear processes (Graedel and Crutzen, 1993). These mechanisms a r e highly dependant on meteorological variables, such as the temperature, wind direction and, mainly, solar radiation, and it depends as well on chemical precursors, such as nitrogen oxides (Sillman, 1999). As a matter of fact, all these factors make the analysis of the temporal evolution of ozone a very complex task.
2. Materials and methods
Here, authors propose the use of a recently created method to transform time series into complex networks, called Visibility Graph (VG) (Lacasa et al., 2008). After performing this transformation, it is possible to extract some properties from the signal (ozone concentration time series in this case) by analyzing the resulting network. This has been applied to ground- level ozone concentration time series corresponding to the pollution in the city of Córdoba, from 2013 to 2016.
In order construct the visibility matrix which contains the information of all the nodes of the new system, it is necessary to stablish a criterion to discern whether two points would be connected or not. This criterion reads as follows: two arbitrary data from the time series (𝑡a, 𝑦a) and (𝑡b, 𝑦b) have visibility (and would become two connected nodes in the graph) if any other data point (𝑡c, 𝑦c) between them (𝑡a < 𝑡c< 𝑡b) fulfills:
𝑦 <𝑦 +(𝑦 −𝑦)𝑡𝑐−𝑡𝑎 (1) 𝑐 𝑎 𝑏 𝑎𝑡𝑏−𝑡𝑎
From it, the parameter that is mainly studied from the visibility graph is the so-called degree (k) (the number of nodes seen by each point) and its probability distribution P(k). From its logarithmic regression, the 𝛾 coefficient can be obtained, which is known to be related to the fractal properties of the signal.
3. Results and conclusions
Results show that indeed, it is possible to describe the seasonal dynamics of the pollutant by cheching the degree (average and standard deviation) of the resulting complex network. The
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