Informational and Topological Characterization of CO and O₃ Hourly Time Series in the Mexico City Metropolitan Area During the 2019–2023 Period: Insights into the Impact of the COVID-19 Pandemic

Abstract

The main anthropogenic sources of air pollution in big cities are vehicular traffic and industrial activities. The emissions of primary pollutants are produced directly from the combustion of fossil fuels of vehicles and industry, whilst the secondary pollutants, such as tropospheric ozone ($O_3$), are produced from precursors like Carbon monoxide ($CO$), among others, and meteorological factors such as radiation. In this study, we analyze the time series of $\mathrm{CO}$ and ${\mathrm{O}}_3$ concentrations monitored by the RAMA program between 2019 and 2023 in the southwest of the Mexico City Metropolitan Area, encompassing the COVID-19 lockdown period declared from March to September–October 2020. After removing cyclic patterns and normalizing the data, we applied informational and topological methods to investigate variability changes in the concentration time series, particularly in response to the lockdown. Following the onset of lockdown measures in March 2020—which led to a significant reduction in industrial activity and vehicular traffic—the informational quantities $N_X$ and Fisher Information Measure (FIM) for $\mathrm{CO}$ revealed significant shifts during the lockdown, while these metrics remained stable for ${\mathrm{O}}_3$. Also, the coefficient of variation of the degree $C{V}_k$, which was defined for the network constructed for each series by the Visibility Graph, showed marked changes for $\mathrm{CO}$ but not for ${\mathrm{O}}_3$. The combined informational and topological analysis highlighted distinct underlying structures: $\mathrm{CO}$ exhibited localized, intermittent emission patterns leading to greater structural complexity, while ${\mathrm{O}}_3$ displayed smoother, less organized variability. Also, the temporal variation of the FIM and $N_X$ provides a means to monitor the evolving statistical behavior of the $CO$ and $O_3$ time series over time. Finally, the Visibility Graph (VG) method shows a behavioral trend similar to that shown by the informational quantifiers, revealing a significant change during the lockdown for $CO$, although remaining almost stable for $O_3$.

1. Introduction

Air pollution remains a critical challenge in large urban agglomerations due to its complex causes and wide-ranging effects on human health, ecosystems, and climate systems [1]. Among the major pollutants, tropospheric ozone ($O_3$) and carbon monoxide ($CO$) are particularly relevant in urban areas because of their strong links to anthropogenic emissions, primarily from fossil fuel combustion in the transport and industrial sectors. In cities such as the Mexico City Metropolitan Area (MCMA)—one of the largest urban zones globally with more than 20 million inhabitants—air pollution is driven by high vehicular density (over 5 million vehicles), industrial activities, and unfavorable topography that traps pollutants within a basin-like valley [2,3,4]. $CO$ is a primary pollutant emitted directly from incomplete combustion processes, especially from gasoline-powered engines, industrial machinery, and residential sources such as gas heaters and stoves [5]. In contrast, tropospheric ozone is a secondary pollutant formed by complex photochemical reactions involving precursors like CO, nitrogen oxides ($N{O}_x$), volatile organic compounds ($VOCs$), and solar radiation [6,7].

Long-term monitoring data from the Environmental Monitoring Office (DMA-CDMX for its Spanish acronym) [8] indicate that from 2019 to 2023, daily $CO$ concentrations in the MCMA ranged between 0.6 and 1.2 ppm, with occasional exceedances in traffic-congested zones. Meanwhile, $O_3$ concentrations routinely surpassed the WHO guideline of 70 ppb, particularly in spring months during the afternoon, driven by high solar radiation and stagnant meteorological conditions [2,3,9]. These local trends mirror observations in other urban centers. For instance, cities like Beijing [10] and Delhi [11] have reported similar patterns, where $CO$ emissions are largely attributed to vehicular traffic, while $O_3$ formation depends heavily on the interaction between $VOCs$ and $N{O}_x$ under specific photochemical regimes. Notably, in VOC-limited environments, reducing $N{O}_x$ emissions can paradoxically lead to increased $O_3$ concentrations—an effect observed during the COVID-19 lockdowns in many cities worldwide, including the MCMA. Despite a sharp decrease in $CO$ and $N{O}_x$ emissions during this period, $O_3$ levels remained stable or even increased due to altered atmospheric chemistry and reduced NO titration [12,13,14].

Such anomalies underscore the need for more advanced analytical tools capable of characterizing the temporal dynamics and inherent complexity of air pollution time series, beyond what traditional statistical methods can capture. Time series of atmospheric pollutant concentrations are, by nature, stochastic processes that may exhibit self-similarity and scale-invariant behaviors across different time scales. In many natural systems, such complex signals often follow a multifractal structure characterized by scaling exponents that vary with scale. Several studies have focused on $O_3$ as a primary pollutant, employing multifractal analysis [15,16] and wavelet-based techniques [13,17,18] to examine temporal dynamics.

While these approaches have yielded valuable insights, they present limitations when it comes to fully capturing the evolving complexity and structural patterns in pollutant behavior. To address these analytical gaps, the present study introduces two complementary methods: the Fisher–Shannon information framework [19,20,21] and the Visibility Graph (VG) method [22,23,24]. These techniques, though widely applied in other disciplines, remain largely underutilized in the analysis of atmospheric pollution time series. Their application offers a novel perspective to uncover hidden patterns, quantify degrees of disorder, and understand the structural evolution of pollutant concentrations.

The Fisher–Shannon method has proven effective in various domains, including geosciences [19] and heavy metal dynamics [25]. Notably, a study in Switzerland used this framework to analyze hourly time series of $N{O}_2$, $O_3$, and $P{M}_{10}$, revealing a clear relationship between pollutant concentration disorder and the spatial characteristics of monitoring stations—insightful for distinguishing land-use types and human activity patterns [26].

In parallel, the Visibility Graph method has gained attention as a powerful tool for mapping time series into complex networks. By leveraging the topological features of these networks, VG analysis allows for the extraction of meaningful structural information about the dynamics of the original signal. Applications span diverse fields: from seismic activity analysis [27,28] and sea surface temperature fluctuations during El Niño events [29], to the study of $P{M}_{10}$ dynamics in Guadeloupe [30] and the differentiation of urban vs. rural ozone behaviors [31].

To better understand these dynamics, the present study applies both the Fisher–Shannon and Visibility Graph methods to $CO$ and $O_3$ time series in the MCMA from 2019 to 2023, including the COVID-19 lockdown period. These tools allow us to identify temporal patterns, assess the degree of disorder in pollutant concentrations, and provide insight into how human activity and meteorological variability influence the atmospheric behavior of key pollutants. By comparing findings within the MCMA and contextualizing them with patterns from other urban regions, this study contributes to a broader understanding of pollution dynamics in complex urban environments.

Although there is a substantial body of research in Mexico focusing on air pollutants—including their concentrations, health impacts, and source attribution, no study to date has applied informational or topological approaches such as the Fisher–Shannon or Visibility Graph methods to explore the underlying dynamical complexity of air pollution time series. This study addresses that gap and proposes a novel methodological perspective to analyze urban air quality in the Mexican context.

2. Materials

Dataset

In Figure 1, the monitoring network is shown; it consists of 34 remote stations located MCMA and driven by the Automatic Environmental Monitoring Network program (Red Automatica de Monitoreo Ambiental (RAMA)).

Our study examines the temporal dynamics of CO and $O_3$ concentrations, measured at seven monitoring stations (currently in operation and measuring the desired parameters, see Figure 1) located in the southwestern zone of MCMA, which is characterized by the highest levels of $CO$ and $O_3$. The selection of this zone as the focus of analysis is based on its high vulnerability to the accumulation of atmospheric pollutants, resulting from a combination of meteorological, geographic, and urban factors. According to the Mexico City Secretariat of the Environment [8], in 2022, a predominant north-to-south wind pattern was observed—consistent with previous years—especially from April to November, which facilitates the transport of pollutants toward the southwest. In the remaining months, wind behavior was more variable, with east–northeast and southeasterly flows converging toward the center, creating zones of confluence that further exacerbate pollutant accumulation. These circulation patterns are compounded by local atmospheric conditions, such as intense solar radiation, high afternoon temperatures, and low cloud cover, which enhance the photochemical formation of ozone. Additionally, the basin’s topography—surrounded by mountain ranges—acts as a natural barrier, limiting the dispersion of pollutants and promoting their concentration in this sector. According to the National Air Quality Report [32], the southwestern zone consistently records the highest concentrations of ozone in Mexico City, particularly during the spring months. These conditions, combined with the continuous influx of emissions from vehicular and domestic sources, justify the selection of this region as a critical area to evaluate the spatiotemporal behavior of $CO$ and $O_3$ in the present study.

Figure 1. Spatial distribution of all monitoring stations within the MCMA. The bold contour indicates the boundary of Mexico City. The southwest zone is conformed by the stations highlighted with red stars [33].

Figure 1. Spatial distribution of all monitoring stations within the MCMA. The bold contour indicates the boundary of Mexico City. The southwest zone is conformed by the stations highlighted with red stars [33].

The sampling time is 1 h. Figure 2 shows the time variation of the two pollutants studied. Each hourly value is the spatial average among the stations (See section “Data Availability Statement”). Outliers caused by instrument failures or human errors are eliminated; the single gaps are filled by the mean of the nonzero neighboring values, while longer gaps are filled by using the procedure developed by [34]. The percentage of data missing is less than 0.1%.

At the end of 2020, an increase in air pollutant emissions in MCMA was observed associated with a gradual return to mobility after lifting some of the preventive measures implemented during the COVID-19 pandemic. This increase was related to the reactivation of economic activities, according to the Local Mobility Reports [35], the increase in vehicular traffic, and the more significant influx of people into public spaces, highlighting the impact of urban mobility on air quality in the region. According to the Environmental Monitoring Office (Dirección de Monitoreo Atmosférico in Mexico City, DMA-CDMX), the highest levels $O_3$ are associated with the so-called ozone season, which occurs from February to June. When meteorological conditions favor warm weather and intense solar radiation, the atmosphere’s photochemical activity increases, favoring the formation of ozone. In addition, when a high pressure system is present, the pollutant stagnates, and, as a result, its concentrations increase (https://www.google.com/covid19/mobility/, accessed on 5 August 2025).

3. Methods

3.1. The Fisher–Shannon Method

To quantify the local and global smoothness of the distribution of analyzed time series, Fisher Information Measure (FIM) and the Shannon entropy (SE) are applied, which are defined as follows:

$$\mathrm{FIM}={\int }_{-\infty }^{\infty }{\displaystyle \frac{1}{f\left(x\right)}}{\left({\displaystyle \frac{\partial f\left(x\right)}{\partial x}}\right)}^{2}dx$$

$$\mathrm{SE}=-{\int }_{-\infty }^{\infty }f\left(x\right)logf\left(x\right)dx$$

where $f\left(x\right)$ is the distribution of the series x. However, it most commonly uses the Shannon entropy power (SEP), $N_X$, instead of SE, which is positively defined:

$$N_X=exp\left(2{\int }_{-\infty }^{\infty }f\left(x\right)logf\left(x\right)dx\right)$$

FIM and $N_X$ are not independent of each other due to the isoperimetric inequality:

$$\mathrm{FIM}·N_X\ge D$$

where the spatial dimension is $D=1$ for time series. The accurate estimation of $f\left(x\right)$ is fundamental to obtain reliable values of informational quantities. For calculating FIM and $N_X$, we applied the kernel-based approach because it is better than the discrete-based approach in estimating the probability density function [36]. Thus, applying this method, $f\left(x\right)$ is given by the following formula:

$$f\left(x\right)={\displaystyle \frac{1}{M}}\sum _{i=1}^{M}K\left({\displaystyle \frac{x-x_i}{b}}\right)$$

where M and b denote the length of the series and the bandwidth, respectively, while $K\left(u\right)$ is the kernel, a continuous, symmetric, and non-negative function satisfying the following two constraints:

$${\int }_{-\infty }^{\infty }K\left(u\right)du=1\mathrm{and}{\int }_{-\infty }^{\infty }{u}^{2}K\left(u\right)du={\sigma }^2$$

$f\left(x\right)$ is estimated by means of an optimized integrated procedure using the algorithms of Troudi et al. [37] and Raykar and Duraiswami [38] with the Gaussian kernel:

$$K\left(u\right)={\displaystyle \frac{1}{\sqrt{2\pi {\sigma }^2}}}exp\left(-{\displaystyle \frac{u^2}{2{\sigma }^2}}\right)$$

3.2. The Visibility Graph Analysis

The Visibility Graph (VG) [39] is a method that transforms a time series in a graph or network. The nodes are given by the values of the series, and the links between them satisfy the following geometrical visibility rule:

$$y_c<y_b+(y_a-y_b){\displaystyle \frac{t_b-t_c}{t_b-t_a}},$$

(1)

where $t_a<t_c<t_b$. In practice, two values, $y_a\left(t_a\right)$ and $y_b\left(t_b\right)$, are visible to each other if any other value $y_c\left(t_c\right)$ satisfies Equation (1).

The mathematical representation of the graph is given by the adjacency matrix $A=\left\{a_{ij}\right\}$, which is defined as follows:

$$a_{ij}=\left\{\begin{array}{c}1\mathrm{if}\mathrm{nodes}\mathrm{i}\mathrm{and}\mathrm{j}\mathrm{are}\mathrm{connected}\hfill \\ 0\mathrm{otherwise}\hfill \end{array}\right..$$

(2)

Equation (2) is a used to describe the connections between nodes in a graph and provides a way to encode the visibility relationships between values in a time series, indicating which values are directly visible to each other based on the visibility criterion (Equation (1)).

The degree $k_i$, defined in Equation (3), represents the number of links departing from the node i to any other node of the network. It is one of the parameters used to describe the network derived from the visibility graph.

$$k_i=\sum _{j=1}^N{a}_{ij}.$$

(3)

4. Data Analysis

In Figure 2, the raw data of two gases analyzed are shown. The frequency peaks at 24 h, 12 h, and 8 h, clearly visible in the power spectra, suggest that the temporal fluctuations of the three pollutants are modulated by meteo-climatic cycles (Figure 3). The presence of seasonal components in the time series of CO and O₃ has been reported by [15] in other cities.

Before applying the Fisher–Shannon and the Visibility Graph analyses, we removed the cyclic patterns from the time series by applying the following procedure:

$$Z\left(t\right)={\displaystyle \frac{X\left(t\right)-\mu (h,d,m)}{\sigma (h,d,m)}}$$

(4)

where

• $X\left(t\right)$ is the original hourly value at time t;
• $\mu (h,d,m)$ is the mean of the hourly values calculated for the same hour h, day d, and month m across different years;
• $\sigma (h,d,m)$ is the standard deviation calculated for the same hour h, day d, and month m across different years;
• $Z\left(t\right)$ is the resulting normalized value.

Figure 4 and Figure 5 show, respectively, the normalized time series of $CO$ and $O_3$ and their spectra.

We applied the FS analysis to the normalized series. The two series are characterized by almost identical values of $N_X$ (0.68–0.69) but very different values of FIM (3.65 and 9.68) (

Table 1. Informational and topological parameters for the analyzed normalized series.

Series	${\mathit{N}}_{\mathit{X}}$	FIM	${\mathit{\mu }}_{\mathit{k}}$	${\mathit{\sigma }}_{\mathit{k}}$	${\mathit{CV}}_{\mathit{k}}$
$CO$	0.68	9.68	9.67	7.87	0.81
$O_3$	0.69	3.65	8.29	6.19	0.74

). If the degree of disorder is practically the same for the two series, the degree of organization is the highest for $CO$ and lowest for $O_3$. Looking at the density of the two normalized series (Figure 6), $CO$ is characterized by multiple peaks that may contribute to the larger FIM.

By converting the time series into graphs using the VG method, we calculated the temporal variation of the degree for each series (Figure 7). The degree of a value reflects its capability to be a hub of the series; thus, the larger the degree of a value, the larger its capability to “attract” the other values of the series. Table 1 shows, for the two normalized series, the mean degree ${\mu }_k$, the standard deviation ${\sigma }_k$, and the coefficient of variation of the degree, defined as follows:

$$C{V}_k={\displaystyle \frac{{\sigma }_k}{{\mu }_k}}.$$

(5)

For $CO$, all the three parameters are slighlty larger than the corresponding values for $O_3$, indicating that $CO$ is characterized by more hubs than $O_3$. This further suggests a greater complexity in the network generated by the VG for $CO$ compared to $O_3$, due to the presence of links between values that may be located far apart from each other, if one of them is a hub. The larger ${\sigma }_k$ and $C{V}_k$ of $CO$ could also indicate a greater complexity of $CO$ compared to $O_3$ regarding a more extensive network heterogeneity.

To identify potential patterns related to the COVID-19 lockdown, we analyzed the temporal variations in $N_X$ (Figure 8a), FIM (Figure 8b), and the coefficient of variation in the degree of the network constructed from the time series using the VG method (Figure 8c). By shifting a 6-month time window over the series in 5-day steps, we calculated these three parameters within each moving window, associating the resulting values with the ending time of the window. This choice balances the need for statistical robustness with the ability to resolve temporal changes in the series. Each 6-month window contains approximately 4,320 data points, ensuring a sufficiently large sample size for reliable estimation of the probability density function, on which the FS method is based, and for the calculation of the coefficient of variation of the degree of the visibility network. A larger dataset within each window leads to a more accurate characterization of the signal’s statistical features. Moreover, the 6-month length allows for an adequate number of windows to be positioned before the onset of the COVID-19 pandemic, making it possible to observe and compare the behavior of the FS and VG complexity in both the pre-COVID and COVID-affected periods. Using substantially longer windows would have reduced the resolution in the pre-COVID phase, hindering the detection of the changes that emerged during the pandemic.

In all cases, we observe that during the COVID-19 lockdown, approximately between April and September 2020, the three parameters show a clear difference between $CO$ and $O_3$. In particular, for $CO$, $N_X$ decreases, while FIM and $C{V}_k$ increase. During lockdown, the three parameters for $O_3$ remain almost stationary and do not exhibit any significant anomalous trends. After lockdown, the three parameters for $CO$ and $O_3$ tend to align with each other, indicating a clear correlation. The combined FS and VG analyses reveal that the temporal behavior of CO is shaped by more localized and intermittent emissions, leading to high structural complexity and organization. $O_3$, by contrast, reflects broader-scale chemical processes and environmental modulation, resulting in smoother, less structured variability. These insights help to bridge the gap between pollutant emission mechanisms and their statistical representation, offering a valuable perspective for interpreting air quality time series.

While the combined use of the FS and VG methods has enabled us to uncover complex patterns and meaningful structural differences between $CO$ and $O_3$, it is important to acknowledge certain inherent limitations of the analysis. The use of a 6-month moving window provided a good balance between statistical robustness and temporal resolution; however, this approach may smooth out very short-term events or abrupt changes. Additionally, although the visibility graph technique effectively captures structural properties of time series, it can be sensitive to outliers or noise, potentially affecting metrics such as hub identification or degree heterogeneity. On the other hand, while the data used are of high quality and resolution, they may not fully reflect the spatial variability of emission sources or local meteorological influences. Finally, although a clear signal was identified during the COVID-19 lockdown period, it is possible that other concurrent factors—such as seasonal effects or regional atmospheric processes—also contributed to the observed patterns. Nevertheless, the results provide a solid foundation for advancing the understanding of the temporal dynamics of urban pollutants and exploring new approaches for air quality time series analysis.

5. Conclusions

This study applied two complementary analytical approaches—the Fisher–Shannon information framework and the Visibility Graph method—to analyze the time series of $CO$ and $O_3$ concentrations in the southwest of the MCMA from 2019 to 2023, including during the COVID-19 lockdown. Our results provide clear evidence of differential responses between primary and secondary pollutants. The informational metrics NX and FIM detected a substantial shift in the statistical behavior of $CO$ during the lockdown period. These changes reflect the abrupt reduction in vehicular activity and industrial emissions and reveal a decrease in complexity and disorder consistent with a more homogeneous and less volatile emission profile during that time. Conversely, the stability of $N_X$ and FIM values for $O_3$ suggests that this secondary pollutant is governed by slower, large-scale chemical and meteorological processes that are less immediately responsive to localized emission reductions. The VG method offered a topological perspective on these findings. The coefficient of variation of the node degree $C{V}_k$ in the constructed networks showed changes in $CO$ time series complexity similar to those detected by the Fisher–Shannon metrics. For $O_3$, the VG structure remained relatively stable, supporting the conclusion that its variability is less sensitive to short-term anthropogenic shifts and is instead modulated by regional photochemistry, precursor ratios, and seasonal solar radiation patterns. These findings have important practical and methodological implications. They confirm the usefulness of $CO$ as a near-real-time indicator of changes in urban activity while highlighting the complex, nonlinear nature of $O_3$ formation and the need for integrated mitigation strategies that consider precursor dynamics and meteorological conditions. The informational and topological methods applied here can detect subtle changes in pollutant behavior, offering valuable diagnostic insights that complement traditional air quality assessments. Their scalability and adaptability make them suitable for application in other urban contexts, and they hold potential as early-warning tools for identifying anomalous pollution patterns linked to extreme events or policy shifts. The integration of informational theory and complex network analysis provides a powerful framework to explore the dynamics of air pollutant behavior. In contexts like MCMA, where emissions are intense and meteorological constraints severe, such approaches offer a more nuanced and mechanistic understanding of pollutant variability—one that is essential for designing robust, adaptive, and evidence-based air quality policies.