ARIMA Analysis of PM Concentrations during the COVID-19 Isolation in a High-Altitude Latin American Megacity

Abstract

The COVID-19 pandemic precipitated a unique period of social isolation, presenting an unprecedented opportunity to scrutinize the influence of human activities on urban air quality. This study employs ARIMA models to explore the impact of COVID-19 isolation measures on the PM₁₀ and PM_2.5 concentrations in a high-altitude Latin American megacity (Bogota, Colombia). Three isolation scenarios were examined: strict (5 months), sectorized (1 months), and flexible (2 months). Our findings indicate that strict isolation measures exert a more pronounced effect on the short-term simulated concentrations of PM₁₀ and PM_2.5 (PM₁₀: −47.3%; PM_2.5: −54%) compared to the long-term effects (PM10: −29.4%; PM_2.5: −28.3%). The ARIMA models suggest that strict isolation measures tend to diminish the persistence of the PM₁₀ and PM_2.5 concentrations over time, both in the short and long term. In the short term, strict isolation measures appear to augment the variation in the PM₁₀ and PM_2.5 concentrations, with a more substantial increase observed for PM_2.5. Conversely, in the long term, these measures seem to reduce the variations in the PM concentrations, indicating a more stable behavior that is less susceptible to abrupt peaks. The differences in the reduction in the PM₁₀ and PM_2.5 concentrations between the strict and flexible isolation scenarios were 23.8% and 12.8%, respectively. This research provides valuable insights into the potential for strategic isolation measures to improve the air quality in urban environments.

1. Introduction

Air pollution, a global concern requiring urgent attention, imposes a significant economic strain on public health systems [1]. In 2019, it was responsible for an estimated 4.2 million premature deaths, with 38% due to ischemic heart disease, 20% to heart attacks, and 43% to chronic obstructive pulmonary disease [2]. Particulate Matter (PM), a key air pollutant, has a significant impact on public health. PM, comprising small-diameter particles of inorganic and organic substances, originates from coal combustion, thermal power plants, and industrial activities [3]. The severe effects of PM on the pulmonary and cardiac systems persist even at low exposure levels, particularly for particles with diameters ≤ 10 µm (PM₁₀) and ≤2.5 µm (PM_2.5) [4]. The smallest particles (PM_2.5) evidence the greatest problems, because they can penetrate deep into the lungs and even reach the bloodstream. This phenomenon increases their toxicity, because they can cause or worsen respiratory and cardiovascular problems [5]. This issue is exacerbated in low- and middle-income countries, where a large segment of the population is exposed to PM. As a result, there is a significant economic burden due to the increased mortality and morbidity rates arising from cardiovascular and respiratory diseases [1]. The main sources of PM₁₀ and PM_2.5 in urban environments are primary combustion, such as vehicle emissions, coal combustion, biomass burning, secondary aerosol formation, industrial emissions, and dust sources [6].

The COVID-19 pandemic precipitated an acute respiratory disease, prompting the global implementation of social isolation measures to curb the spread of this novel biological agent [7]. These unprecedented social restrictions profoundly influenced global economic dynamics, social interactions, and urban environments [4]. This period of social isolation provided a unique opportunity to study the impact of human activities on urban air quality. The behavior of pollution emission sources underwent significant changes during the pandemic. Mobile sources (e.g., vehicles) [8,9], stationary sources (e.g., factories) [10,11], and fugitive sources (e.g., construction sites) [12,13] all responded to the isolation measures imposed by COVID-19. Consequently, the urban concentrations of PM₁₀ and PM_2.5 exhibited notable reductions [14,15]. These reductions were attributed to measures such as limiting vehicular traffic, restricting public transportation mobility, and curbing non-essential industrial production [16]. However, not all cities experienced uniform air quality changes. Some reported increases in the PM₁₀ and PM_2.5 concentrations [17,18]. The factors contributing to these increases included heightened household utility usage (e.g., natural gas and electricity) and the economic reactivation following the isolation period [19]. For instance, during the strict lockdowns in Indian cities like Chennai, New Delhi, and Kolkata, the PM₁₀ and PM_2.5 concentrations decreased by approximately 65% and 73%, respectively [20]. In contrast, Saudi Arabia witnessed PM concentration increases, likely due to regional phenomena like sandstorms and urban dust resuspension [17]. In the megacity of Bogota, Colombia, strict isolation measures led to a substantial reduction in PM₁₀, NO₂, and PM_2.5 concentrations—approximately 39%, 63%, and 34%, respectively [7]. While meteorological conditions also played a role, historical observations during this period suggest that changes in human behavior were the primary drivers of the improved air quality [7,21].

The fluctuations in the PM concentrations within our study megacity during the COVID-19 isolation provide a unique lens through which to examine this air pollutant’s behavior under conditions of reduced anthropogenic activity. This analysis holds particular significance given PM’s central role in the megacity’s air quality monitoring and control efforts [22]. PM’s relevance in our megacity stems from its frequent exceedances of the permissible limit values for both PM₁₀ and PM_2.5. While these elevated concentrations are often associated with human activities, they may also result from the unfavorable meteorological conditions that hinder atmospheric dispersion. Factors such as persistent thermal inversions, reduced precipitation, and wind patterns conducive to the influx of external pollutants all contribute to these exceedances [23,24]. Moreover, regional events—such as biomass burning in nearby crops—can introduce external air pollutants [25]. Therefore, our investigation sheds light on the dynamics of PM in a megacity during a unique period of reduced human activity, emphasizing the need for comprehensive air quality management strategies. While there is some literature on air quality changes during COVID-19, few studies have focused on high-altitude urban environments where the atmospheric dynamics can differ significantly.

During efforts to prevent and mitigate air pollution events, governmental entities and research centers have increasingly turned to modeling techniques to generate early warnings of air quality deterioration [26]. These models serve as valuable tools for air pollution control and management [27]. Simulation models such as Weather Research and Forecasting (WRF) or the WRF-CMAQ require a substantial amount of air quality data and meteorological information to achieve accurate predictions [26,28]. To address this need, researchers have explored the individual modeling of air pollutants using time series analysis—a statistical approach based on continuous observations of a variable of interest over a specific time interval [29,30]. Among the time series analysis techniques, Autoregressive, Integrated, and Moving Average (ARIMA) models play a prominent role. ARIMA models allow for the study of air pollutants individually and over time by analyzing correlations within the data series itself [31]. The ARIMA model comprises three key components: (1) an Autoregressive (AR) component, which accounts for the regressors of the time series and reflects the model’s memory [32,33]; (2) an Integrated (I) component, which is associated with the number of differences needed to make the time series stationary (i.e., independent of time) [33]; and (3) a Moving Average (MA) component, which addresses random shocks and inherent variability within the time series [33]. The ARIMA structure facilitates the simulation of parameter behavior in the presence of external variables by capturing linear trends within the time series [34]. By leveraging these models, researchers can enhance our understanding of air pollutant dynamics and contribute to effective pollution management strategies.

The application of ARIMA models in analyzing urban PM concentrations has garnered attention across several studies [35,36]. Notably, the optimal ARIMA simulations of the PM concentrations were observed at an hourly timescale, during short time intervals, and in the urban areas characterized by low pollutant persistence (where the autoregressive [AR] term was less than 4) [26,37]. Sensitivity analyses revealed that the ARIMA models performed well when dealing with a PM concentration series exhibiting substantial temporal variability [38]. This variability in the PM concentrations was closely linked to unfavorable meteorological conditions for air pollutant dispersion [31] and regional particle transport phenomena [39]. Megacities provided an ideal testing ground, where persistent PM₁₀ (with AR terms exceeding 8) and variable PM₁₀ (with moving average [MA] terms exceeding 8) were observed in the areas dominated by impervious surfaces [40]. Furthermore, the ARIMA models were pitted against other modeling approaches (such as Long Short-Term Memory [LSTM], Random Forest Regression [RFR], and Support Vector Regression [SVR]) to explore the concentration behavior of PM during the COVID-19 isolation. The ARIMA models demonstrated a satisfactory performance within this context [41]. Moreover, the historical PM_2.5 concentration series were compared with those observed during the COVID-19 isolation. The latter exhibited higher persistence and variability, underscoring the unique impact of pandemic-related behavioral changes on urban air quality [4].

The objective of this work is to investigate by means of ARIMA models the effect of COVID-19 isolation measurements on the PM₁₀ and PM_2.5 concentrations in Bogota, Colombia—a megacity located at a high altitude. Leveraging the ARIMA models, we explore the following three distinct scenarios for the PM concentrations: (1) the historical series, examining pre-pandemic data; (2) pre-isolation, assessing the PM concentrations before the initial isolation measures; and (3) during isolation, analyzing the impact of various social isolation strategies (strict, sectorized, and flexible) implemented by the city administration. Our study holds practical significance in the field of urban pollution for the following reasons. (1) The Evaluation of ARIMA Models: We assess the utility of ARIMA models in studying urban air quality interventions. These models allow us to dissect the temporal dynamics of the PM concentrations. (2) A High-Altitude Context: Bogota’s unique high-altitude conditions introduce additional complexities. We investigate how COVID-19 isolation influenced the PM levels in this challenging environment. (3) Temporal Structure Analysis: By examining different types of social isolation measures, we gain insights into the temporal behavior captured by our ARIMA models. Lastly, this research contributes to our understanding of the pandemic-induced changes in air quality and informs effective pollution management strategies.

2. Materials and Methods

2.1. Study Site Description

The megacity under investigation is situated in Colombia (South America, 4°35′53″ N–74°4′33″ W). Bogota, the capital of Colombia, is positioned at an average elevation of 2640 masl and is recognized as one of the most densely populated megacities in Latin America, with a density of 272 inhabitants/Ha. This density surpasses the Latin American average by a factor of 2.5 [42]. Owing to its proximity to the equator, this megacity does not experience distinct seasons and maintains an average annual temperature ranging between 14 and 15 °C. Its elevated location results in hourly temperature fluctuations reaching up to 17.9 °C within a single day. The annual precipitation pattern reveals two periods of increased precipitation: March–May and September–November [43]. For the purpose of air quality monitoring, four stations were selected (RMCAB, http://rmcab.ambientebogota.gov.co/home/map (accessed on 1 February 2022). These stations are identified as follows (Figure 1): Centro de Alto Rendimiento—CAR, Kennedy—KEN, Las Ferias—LAF, and Tunal—TUN. The selection criteria for these stations included comprehensive coverage of the megacity and data availability exceeding 90% for the PM₁₀ and PM_2.5 concentrations. The characteristics of these monitoring stations are detailed in

Table 1. Characteristics of selected air quality monitoring stations.

Characteristic	Monitoring Stations
	CAR	KEN	LAF	TUN
Coordinates	4°39′30.48″ N	4°37′30.18″ N	4°41′26.52″ N	4°34′34.41″ N
	74°5′2.28″ W	74°9′40.80″ W	74°4′56.94″ W	74°7′51.44″ W
Atmospheric pollutants	PM10, PM2.5	PM10, PM2.5	PM10, PM2.5	PM10, PM2.5
Meteorological variables	VV, DV, T, Pr, HR	VV, DV, T, Pr, RS, HR, Ps	VV, DV, T, Pr, HR, Ps	VV, DV, T, Pr, RS, HR
Altitude (masl)	2577	2580	2552	2589
Height of sampling (m)	4.6	7.0	4.6	3.0
Type of monitoring station	Background	Background	Traffic	Background
Mean annual relative humidity (%)	67.6	63.1	63.2	62.6
Mean annual precipitation (mm)	1148	797	1147	980
Mean annual temperature (°C)	14.9	15.8	14.4	14.9
Mean annual wind speed (m/s)	1.21	2.15	1.87	1.36
Predominant annual wind direction (°)	204 (SSW)	196 (S)	140 (SE)	175 (S)
Land use (%)	R: 54.9	R: 38.4	R: 53.1	R: 41.9
	I: 4.40	I: 5.80	I: 7.10	I: 0.60
	D: 3.80	D: 37.1	D: 10.0	D: 8.90
	C: 9.60	C: 18.4	C: 5.20	C: 31.3
	P: 8.30	P: 0.20	P: 2.80	P: 17.0
Land category (%)	Urban: 100	Urban: 93.5	Urban: 95.8	Urban: 71.5
		Urban sprawl: 6.55	Urban sprawl: 4.14	Protection: 28.5
Population density (Inhabitants/Ha)	123	268	227	183

Note: VV—wind speed, DV—wind direction, T—temperature, Pr—precipitation, RS—solar radiation, Ps—atmospheric pressure, R—residential, I—industrial, D—residential and services, C—commercial, and P—protection.

.

2.2. Data Collection

The time series data procured from the monitoring stations provided hourly information on the PM₁₀ and PM_2.5 concentrations, relative humidity (%), precipitation (mm), temperature (°C), wind speed (m/s), and wind direction (°). This study spanned a period of five years, from 1 January 2017 to 31 December 2021, a timeline chosen in accordance with the occurrence of the COVID-19 isolation episodes within the megacity. The method employed for the collection of PM₁₀ and PM_2.5 samples, aimed at determining the presence of inorganic compounds in the air, adhered to the guidelines established by U.S. EPA/625/R-96/010a [44]. Furthermore, the monitoring system was designed in compliance with the guidelines set forth in CFR 40, Part 50, Appendices J and L, for the automatic measurement of PM₁₀ (Met One Bam 1020) and PM_2.5 (Thermo Scientific FH62C14-DHS, MA, USA) [45]. The system utilized Beta Ray Attenuation as the principle of measurement.

2.3. Data Analysis

The analysis of the data was conducted in three phases. In the first phase, an exploratory analysis of the hourly time series of atmospheric pollutants and meteorological parameters was carried out. Initially, the non-normal distribution (p-value > 0.050) of the time series was examined using a Kolmogorov–Smirnov test [46]. The correlation between the variables considered was also studied using Spearman’s coefficient [47]. These correlations between PM₁₀ and PM_2.5 and the meteorological parameters allowed for the study of the influence of meteorological conditions and anthropogenic activity due to COVID-19 isolation. Three scenarios of human activity were considered: (1) pre-isolation, (2) isolation, and (3) historical. Descriptive statistics (mean, median, and standard deviation) were calculated for the time series under study. The IBM SPSS Statistics V.25.0 software [48] was used in this study. Lastly, wind roses, pollution roses, and polar roses were developed for the PM₁₀ and PM_2.5 concentrations at each of the monitoring stations using the OpenAir package of the R software [12,15].

In the second phase, the missing data in the time series of atmospheric pollutants and meteorological parameters were filled in. It was previously confirmed that all the time series had more than 75% of the data. The random nature of the missing data was detected using the Visualization and Imputation of Missing Values (VIM) package of the R 4.2.1 software [49]. The missing data were filled in using the Multivariate Imputation by Chained Equations (MICE) and Nonparametric Missing Value Imputation using Random Forest (MissForest) packages of the R 4.2.1 software [50]. The MICE package used various methods (Predictive Mean, Bayesian Linear Regression, and Logistic Regression) to fill in the missing data [51]. The MissForest package filled in the missing data by creating random forests with the observed data, then iterated again until the minimum error was obtained [52].

In the third phase, the ARIMA models were developed for the PM₁₀ and PM_2.5 concentrations. The timescales considered were as follows: daily (24 h moving average), weekly (120 h moving average), and monthly (720 h moving average). The development of the ARIMA models also considered three scenarios: (1) before the first isolation (E1), (2) during the different types of isolation (E2.1 = strict, E2.2 = sectorized, and E2.3 = flexible), and (3) the historical trend (E3) (Table 2). The development of the ARIMA models was based on the methodology reported by Box and Jenkins [53]. This methodology considered the following stages: identification, parameter estimation, assumption verification, and model use [53]. From the temporal length of the isolation scenarios considered (less than 5 months), it was assumed in this study that the weekly timescale was the most appropriate. The ARIMA modeling of the PM₁₀ and PM_2.5 concentrations was performed using IBM SPSS Statistics V.25.0 software [54].

During the development of the ARIMA models, the PM concentration time series underwent differencing and transformation (square root and logarithmic) according to their time structure. This process was performed to obtain a stationary series (independence). Subsequently, the model identification and parameter estimation were carried out, leading to the determination of the p, d, and q orders of the ARIMA models. The previous stages were carried out using the IBM SPSS Statistics V.25.0 Expert Modeler Tool [54]. Once the p, d, and q terms were identified, compliance with the Ljung–Box statistic (p-value > 0.05) was verified in the model obtained. Compliance with the Ljung–Box test indicated that the residuals of the model were equal or close to zero and that its variance was constant, becoming white noise, confirming the development of a model that adequately described the observed variable [33,55]. If the Ljung–Box statistic was not met, the p, d, and q terms of the initial model were modified until a suitable ARIMA model was obtained. Once the ARIMA model was identified, estimated, and verified, the goodness of fit coefficients (RMSE: root mean square error, MAE: mean percentage error, MAPE: maximum mean percentage error, and R²) were reviewed, with emphasis placed on the Bayesian Information Criterion (BIC) [54]. This last statistic allowed the selection of the model with the highest goodness of fit using the fewest possible terms [56]. All statistics were estimated with a confidence level of 95%.

Table 2. ARIMA analysis scenarios for COVID-19 isolation.

Scenario		Start Date	End Date	Characteristics
Pre-isolation E1		1 January 2020	25 March 2020	Without any type of isolation. Usual behavior of anthropic activities.
Isolation E2	Strict E2.1	25 March 2020	27 August 2020	Controlled outflow for primary activities (health, services, and supply). 41% reduction in population mobility [57]. 85–90% reduction in vehicular transport. Staggered reduction in isolation (12 June 2023). 65–70% reduction in vehicular transport [58].
	Sectorized E2.2	5 January 2021	2 February 2020	Weekly isolation by sector in the city. 63.3% of work activity was remote. Access to closed spaces, stores, and public areas continued to be restricted [59].
	Flexible E2.3	10 April 2020	7 June 2020	Reactivation of the economic sectors of manufacturing, construction, restaurants, and educational centers. Control of maximum capacity in transportation, public places, and commercial establishments. By the end of the scenario, general isolation was repealed [60].
Historical E3	Strict E3.1	25 March 2017–2019	27 August 2017–2019	Historical concentrations of atmospheric pollutants for the same periods (without COVID-19). Three previous years according to other authors’ considerations [14,61,62].
	Sectorized E3.2	5 January 2017–2019	2 February 2017–2019
	Flexible E3.3	10 April 2017–2019	7 June 2017–2019

Table 2. ARIMA analysis scenarios for COVID-19 isolation.

Scenario		Start Date	End Date	Characteristics
Pre-isolation E1		1 January 2020	25 March 2020	Without any type of isolation. Usual behavior of anthropic activities.
Isolation E2	Strict E2.1	25 March 2020	27 August 2020	Controlled outflow for primary activities (health, services, and supply). 41% reduction in population mobility [57]. 85–90% reduction in vehicular transport. Staggered reduction in isolation (12 June 2023). 65–70% reduction in vehicular transport [58].
	Sectorized E2.2	5 January 2021	2 February 2020	Weekly isolation by sector in the city. 63.3% of work activity was remote. Access to closed spaces, stores, and public areas continued to be restricted [59].
	Flexible E2.3	10 April 2020	7 June 2020	Reactivation of the economic sectors of manufacturing, construction, restaurants, and educational centers. Control of maximum capacity in transportation, public places, and commercial establishments. By the end of the scenario, general isolation was repealed [60].
Historical E3	Strict E3.1	25 March 2017–2019	27 August 2017–2019	Historical concentrations of atmospheric pollutants for the same periods (without COVID-19). Three previous years according to other authors’ considerations [14,61,62].
	Sectorized E3.2	5 January 2017–2019	2 February 2017–2019
	Flexible E3.3	10 April 2017–2019	7 June 2017–2019

Following the development of the ARIMA models, the time series simulated under scenarios E1, E2, and E3 were examined. With this information on the PM₁₀ and PM_2.5 concentrations, the following analyses were performed: (1) A non-parametric comparison (a Mann–Whitney U test) [63] was conducted on the simulated time series for scenarios E2 and E3 (E2.1–E3.1, E2.2–E3.2, and E2.3–E3.3). This allowed for an evaluation of similar behavior between the time series of the isolation period (with COVID-19) and the historical period (without COVID-19). (2) The percentage changes were calculated for the simulated weekly concentrations in the short and long term. The short-term percent changes were obtained by comparing the weekly PM₁₀ and PM_2.5 concentrations between scenarios E1 (pre-isolation) and E2 (isolation): E1–E2.1, E1–E2.2, and E1–E2.3. The long-term percent change was obtained by comparing the weekly PM₁₀ and PM_2.5 concentrations between scenarios E2 (isolation) and E3 (historical): E2.1–E3.1, E2.2–E3.2, and E2.3–E3.3. The aim was to quantify the change in the trends of the PM₁₀ and PM_2.5 concentrations during the isolation scenarios [64]. (3) The behavior of the p, d, and q terms and the goodness of fit statistics (BIC, RMSE, MAPE, and R²) of the ARIMA models developed for both the short and long term were analyzed. With this, the occurrence of changes in the ARIMA temporal structure of the weekly PM₁₀ and PM_2.5 concentrations during the COVID-19 isolation was evaluated. This was done in relation to the other established analysis scenarios.

3. Results and Discussion

3.1. PM Concentrations

The results showed that the lowest PM concentrations at the monitoring stations were observed during scenario E2.1 (strict isolation): CAR/PM₁₀ = 15.7 µg/m³, KEN/PM₁₀ = 33.9 µg/m³, LAF/PM₁₀ = 17.0 µg/m³, TUN/PM₁₀ = 25.9 µg/m³, CAR/PM_2.5 = 9.38 µg/m³, KEN/PM_2.5 = 16.9 µg/m³, LAF/PM_2.5 = 9.40 µg/m³, and TUN/PM_2.5 =10.3 µg/m³ (Figure 2). This trend was possibly associated with the strict isolation measures and temporary closure of non-primary economic activities observed during this scenario. However, sudden increases in the PM concentrations were observed between the months of March–April and June–July 2020, which were probably associated with regional PM transport events (e.g., forest biomass burning) [25]. The above trend was more evident in PM₁₀ compared to PM_2.5. During the E2.3 flexible isolation scenario, a decrease in the PM concentrations was also observed, although this decrease was smaller compared to the E2.1 scenario (PM₁₀ = 6.92%; PM_2.5 = 5.79%). This lower reduction in the PM concentrations was possibly associated with the controlled reactivation of the economic sectors of manufacturing, construction, restaurants, and educational centers, due to flexible isolation (Table 2) [59].

The findings showed that the highest concentrations of PM at the monitoring stations were observed during the E1 scenario (pre-isolation): CAR/PM₁₀ = 31.3 µg/m³, KEN/PM₁₀ = 47.8 µg/m³, LAF/PM₁₀ = 36.8 µg/m³, TUN/PM₁₀ = 49.9 µg/m³, CAR/PM_2.5 = 20.6 µg/m³, KEN/PM_2.5 = 29.6 µg/m³, LAF/PM_2.5 = 22.9 µg/m³, and TUN/PM_2.5 = 22.1 µg/m³ (Figure 2). During the E2.2 scenario of sectorized isolation, the PM concentrations also tended to increase, although this increase was smaller compared to the E1 scenario (PM₁₀ = 23.9%; PM_2.5 = 45.3%). The E2.2 scenario showed a different behavior in relation to the other isolation scenarios (E2), as increases in the PM concentrations were observed (Table 2). This trend was similar to that observed during the E3.2 scenario of historical behavior, although the increases in the PM concentrations were lower (PM₁₀ = 21.3%; PM_2.5 = 23.0%). The results suggested that this trend was related to the period of occurrence of these two scenarios (E2.2 and E3.2). That is, the two scenarios developed during the first three months of each year, a period of time in which it was common to detect episodes of regional PM transport (e.g., forest fires and Saharan dust) and meteorological conditions where there was a decrease in precipitation and wind speed [23,25]. These meteorological conditions probably did not favor the dispersion of pollutants, which facilitated the formation and accumulation of PM in the urban atmosphere. This behavior has also been reported in cities under similar meteorological conditions [65].

The findings showed strong positive correlations between the PM₁₀ and PM_2.5 concentrations (Spearman rs between 0.71 and 0.89) at all the monitoring stations during the E3 scenario (historical scenario). This trend suggested a similar historical behavior in the formation and transport of PM₁₀ (the coarse fraction) and PM_2.5 (the fine fraction), which has also been reported in other studies [66]. However, during the isolation scenarios (E2), a decrease in the Spearman correlation coefficients (rs between 0.50 and 0.76) was evidenced. The previous trend suggested a change in the activity of PM₁₀ and PM_2.5 pollution sources during the isolation scenarios. On average, there was a 20% decrease in the magnitude of the Spearman correlation coefficients during the isolation scenarios (E2). This decrease in the correlation between the PM₁₀ and PM_2.5 concentrations was possibly associated with the intervention of external factors during the formation and transport of PM. There were studies that associated this trend with the following external factors: (1) differential meteorological conditions that increased the concentrations of a specific PM fraction [48,67]; (2) regional PM transport events, which increased PM concentrations [68,69]; and (3) changes in the baseline level of atmospheric emissions [11,70]. Therefore, the results suggested that the possible changes in the PM concentrations during the isolation scenarios (E2) could not be attributed exclusively to the implemented restrictions (Table 2).

3.2. Meteorological Analysis

The results showed that the lowest relative humidity occurred during the E2.2 scenario of sectorized isolation (CAR = 64.7%, KEN = 59.9%, LAF = 60.2%, and TUN = 57.8%). This scenario also showed the least precipitation (CAR = 15.1 mm, KEN = 20.5 mm, LAF = 10.3 mm, and TUN = 9.20 mm). The E2.2 scenario of sectorized isolation showed a different behavior in the PM concentrations compared to the other isolation scenarios (E2). That is, an increase in the PM concentrations was observed, possibly associated with the decrease in precipitation and relative humidity, which probably led to less favorable conditions for the vertical dispersion of this air pollutant, similar conditions to those reported in Milan (Italy) [60] and Sao Paulo (Brazil) [64] during the COVID-19 isolation. This trend was also similar to that observed during the E3.2 scenario of historical behavior, although the increases in the PM concentrations were lower in the E2.2 scenario (PM₁₀ = 21.3%; PM_2.5 = 23.0%). On the other hand, the findings showed that the highest relative humidity occurred during the E2.1 (CAR = 67.2%, KEN = 63.0%, LAF = 62.6%, and TUN = 62.7%) and E2.3 (CAR = 67.6%, KEN = 63.9%, LAF = 64.3%, and TUN = 63.9%) scenarios of strict and flexible isolation, respectively. These two scenarios were also the ones that showed the highest precipitation (351/233 mm, 983/370 mm, 202/293 mm, and 376/264 mm, respectively). The results suggested that during the E2.1 scenarios of strict isolation and E2.3 of flexible isolation, the decrease in the PM concentrations were, in part, influenced by the observed meteorological conditions, which favored the washing of the pollutants in the atmosphere [17]. However, the effect on the PM concentrations of the restrictions established during these two isolation scenarios (Table 2) should not be forgotten.

On average, the findings showed that wind speeds tended to be slightly higher (4.74%) during the isolation scenarios (E2) compared to the historical scenarios (E3). However, a Mann–Whitney U test allowed the visualization of the non-existence of significant differences (p-value > 0.050) in the wind speed between these two scenarios. In relation to the wind direction, the results showed a predominance from the SE at all study stations. Nevertheless, as there were isolation scenarios less than five months, the predominant wind direction tended to change during these periods (SSE, SSW, S, and NE). The findings showed that during the scenario of the lower concentrations of PM₁₀ and PM_2.5 (E2.1—strict isolation) the predominant wind direction at the monitoring stations was between SSE and SE. During the E2.3 scenario (flexible isolation), a decrease in the PM concentrations was also observed, as was a predominance in the wind direction between SSE and E. In general, the results suggested that during the scenarios of lower PM concentrations (E2.1 and E2.3) the wind tended to come from the east. In contrast, during the scenario of higher PM concentrations (E1—pre-isolation) the predominant wind direction at the monitoring stations tended to be between WNW and SW. During the E2.2 scenario, the PM concentrations tended to increase. Under this scenario, the predominant wind direction tended to be between SSW and WNW. This trend was similar to that observed during the E3.2 scenario of historical behavior, in which an increase in the PM concentrations was evidenced. In general, the findings suggested that during the scenarios of increasing PM concentrations (E1, E2.2, and E3.2) the wind tended to come from the west. This trend was more evident for PM_2.5 than for PM₁₀ (Figure 3). Lastly, the results suggested that the E2.2 scenario of sectorized isolation (where there was an increase in the PM concentration) could have been influenced by the regional transport of PM (with the forest biomass burning). Other authors have also reported scenarios where urban PM concentrations were influenced by adverse weather conditions that caused the dispersion of air pollutants [67,70].

The results showed that the meteorological variable that best correlated with the PM₁₀ (rs ≤ 0.32) and PM_2.5 (rs ≤ 0.32) concentrations during the historical scenario (E3) was wind direction. Significant positive correlations from weak to medium (rs for PM₁₀ up to 0.32 and rs for PM_2.5 up to 0.32) were observed with this variable. However, during the isolation scenarios (E2), these correlations tended to increase. This increase in correlations was greater for PM_2.5 compared to PM₁₀. Significant positive correlations for PM₁₀ and PM_2.5 up to 0.40 and 0.52 (around medium), respectively, were evidenced. The results suggested that during the isolation scenario (E2) there was possibly an external contribution of PM (due to regional transport) in the megacity under study, especially for the concentrations in the southwest (KEN) and south (TUN) of the megacity. From the observed increase in the correlations, the external contribution of PM_2.5 was possibly greater compared to the contribution of PM₁₀. Borhani et al. [66] reported a similar scenario in Tehran (Iran), where during the isolation, regional transport contributed increases in suspended particles, especially for PM_2.5, which came from industrial and stationary emission sources. The findings also suggested that the increase in the PM concentrations during the E2.2 scenario (sectorized isolation) compared to the other isolation scenarios (E2.1 and E2.3) could be related to the episodes of regional PM transport and increases in the PM emission levels in the sectors of the megacity that had no restrictions (Table 2). Lastly, this study showed very weak or non-significant correlations of the PM concentrations with precipitation, relative humidity, wind speed, and temperature during the isolation scenarios considered.

3.3. Short- and Long-Term Analysis

ARIMA models were developed for each of the considered scenarios (E1, E2, and E3). The models were developed under a weekly timeframe (168 h moving average;

Table 3. ARIMA models developed for PM₁₀ and PM_2.5 concentrations during the scenarios considered.

Station		AR (p)	I (d)	MA (q)	Transformation	R2	MAE	RMSE	MAPE	Q’	p-Value	DF	BIC
E1
CAR	PM10	6	1	2	Square root	0.999	0.043	0.057	0.151	18.099	0.053	10	−5.689
	PM2.5	11	2	1	None	0.999	0.039	0.055	0.219	11.461	0.075	6	−5.762
KEN	PM10	2	2	1	None	0.999	0.056	0.079	0.121	20.683	0.147	15	−5.060
	PM2.5	2	1	1	None	0.999	0.059	0.078	0.213	11.037	0.750	15	−5.086
LAF	PM10	3	2	7	None	0.999	0.069	0.099	0.193	14.380	0.072	8	−4.584
	PM2.5	0	2	7	Square root	0.999	0.055	0.073	0.271	17.432	0.096	11	−5.207
TUN	PM10	2	1	1	None	0.999	0.095	0.132	0.199	16.991	0.319	15	−4.027
	PM2.5	2	1	1	None	0.999	0.046	0.067	0.244	19.117	0.208	15	−5.381
E2.1
CAR	PM10	1	1	3	Natural logarithm	0.999	0.028	0.040	0.199	21.192	0.097	14	−6.440
	PM2.5	1	1	8	Natural logarithm	0.999	0.026	0.038	0.347	14.635	0.101	9	−6.525
KEN	PM10	1	2	3	Natural logarithm	0.999	0.042	0.056	0.130	16.815	0.266	14	−5.764
	PM2.5	0	2	6	None	0.999	0.046	0.059	0.296	7.864	0.796	12	−5.628
LAF	PM10	1	2	4	Natural logarithm	0.999	0.030	0.044	0.197	10.617	0.643	13	−6.243
	PM2.5	0	2	6	None	0.999	0.024	0.034	0.316	12.118	0.436	12	−6.746
TUN	PM10	1	1	5	Square root	0.999	0.064	0.092	0.267	17.624	0.128	12	−4.755
	PM2.5	0	2	12	None	0.999	0.033	0.046	0.385	4.195	0.650	6	−6.107
E3.1
CAR	PM10	2	1	1	None	0.999	0.040	0.053	0.183	17.074	0.314	15	−5.869
	PM2.5	1	2	13	Square root	0.999	0.024	0.032	0.225	1.909	0.752	4	−6.854
KEN	PM10	7	1	1	Natural logarithm	0.999	0.046	0.062	0.106	14.788	0.140	10	−5.533
	PM2.5	1	1	13	Natural logarithm	0.999	0.032	0.042	0.146	6.420	0.170	4	−6.318
LAF	PM10	1	1	12	None	0.999	0.043	0.058	0.172	9.572	0.088	5	−5.664
	PM2.5	0	2	15	None	0.999	0.027	0.036	0.257	1.841	0.606	3	−6.598
TUN	PM10	4	1	1	Natural logarithm	0.999	0.052	0.070	0.168	16.950	0.202	13	−5.293
	PM2.5	1	1	5	Natural logarithm	0.999	0.035	0.047	0.233	12.616	0.398	12	−6.115
E2.2
CAR	PM10	0	2	9	Natural logarithm	0.999	0.061	0.083	0.237	10.085	0.344	9	−4.844
	PM2.5	1	2	1	None	0.999	0.033	0.046	0.254	24.188	0.085	16	−6.108
KEN	PM10	0	2	1	None	0.999	0.054	0.075	0.118	25.517	0.084	17	−5.172
	PM2.5	0	2	3	None	0.999	0.056	0.073	0.258	12.180	0.665	15	−5.192
LAF	PM10	1	2	4	Natural logarithm	0.999	0.054	0.075	0.216	17.942	0.160	13	−5.112
	PM2.5	0	2	7	Natural logarithm	0.999	0.047	0.061	0.297	18.559	0.069	11	−5.485
TUN	PM10	4	2	1	Natural logarithm	0.999	0.087	0.125	0.229	6.561	0.087	3	−3.959
	PM2.5	1	1	1	None	0.999	0.043	0.060	0.316	10.774	0.823	16	−5.596
E3.2
CAR	PM10	1	2	1	Square root	0.999	0.040	0.054	0.129	7.891	0.952	16	−5.790
	PM2.5	0	2	2	None	0.999	0.026	0.035	0.157	25.930	0.055	16	−6.676
KEN	PM10	1	1	0	Natural logarithm	0.999	0.053	0.071	0.108	14.318	0.644	17	−5.261
	PM2.5	2	1	1	Natural logarithm	0.999	0.035	0.046	0.141	10.817	0.765	15	−6.094
LAF	PM10	0	2	6	Natural logarithm	0.999	0.052	0.069	0.144	20.223	0.063	12	−5.247
	PM2.5	1	1	8	Natural logarithm	0.999	0.030	0.038	0.186	14.734	0.098	9	−6.403
TUN	PM10	1	1	0	None	0.998	0.058	0.077	0.148	24.639	0.103	17	−5.116
	PM2.5	1	1	7	Natural logarithm	0.999	0.038	0.052	0.184	8.940	0.538	10	−5.809
E2.3
CAR	PM10	1	2	4	None	0.999	0.050	0.074	0.300	20.424	0.085	13	−5.179
	PM2.5	1	1	2	Square root	0.999	0.028	0.039	0.303	18.976	0.215	15	−6.487
KEN	PM10	0	2	14	Square root	0.999	0.053	0.073	0.142	8.073	0.089	4	−5.136
	PM2.5	1	2	1	None	0.999	0.052	0.068	0.316	12.971	0.675	16	−5.369
LAF	PM10	8	2	8	Natural logarithm	0.999	0.037	0.054	0.216	5.448	0.066	2	−5.741
	PM2.5	2	2	2	None	0.999	0.028	0.039	0.394	13.060	0.522	14	−6.440
TUN	PM10	1	1	12	Natural logarithm	0.999	0.075	0.107	0.303	5.307	0.380	5	−4.394
	PM2.5	1	1	15	Square root	0.999	0.034	0.049	0.450	2.709	0.258	2	−5.921
E3.3
CAR	PM10	1	1	4	None	0.999	0.044	0.057	0.172	15.500	0.277	13	−5.694
	PM2.5	2	1	1	None	0.999	0.028	0.035	0.207	18.587	0.233	15	−6.656
KEN	PM10	1	1	1	None	0.999	0.051	0.067	0.110	19.092	0.264	16	−5.375
	PM2.5	1	1	7	Natural logarithm	0.999	0.035	0.046	0.150	8.840	0.547	10	−6.114
LAF	PM10	1	1	12	None	0.999	0.046	0.061	0.159	5.433	0.365	5	−5.514
	PM2.5	2	1	7	None	0.999	0.030	0.039	0.227	16.431	0.058	9	−6.441
TUN	PM10	1	1	11	Natural logarithm	0.999	0.057	0.074	0.164	7.041	0.317	6	−5.128
	PM2.5	1	1	8	Natural logarithm	0.999	0.038	0.050	0.219	8.781	0.458	9	−5.921

Note: AR—autoregressive, I—integrated, MA—moving average, RMSE—root mean square error, MAE—mean percentage error, MAPE—maximum mean percentage error, R2—determination coefficient, Q’—Ljung–Box statistic, p-value—p-value, DF—degrees of freedom, and BIC—Bayesian Information Criterion.

). The results, based on a Kolmogorov–Smirnov test, showed that all the variables exhibited a non-normal distribution (p-value < 0.05).

The results showed that, during scenario 2.1 of strict isolation, the greatest short-term reduction (compared to E1) was observed in the simulated concentrations of PM₁₀ and PM_2.5. On average, the short-term reductions in the PM₁₀ and PM_2.5 concentrations for the LAF, CAR, TUN, and KEN stations were as follows: 55.7/60.6%, 51.9/56.5%, 49.9/54.8%, and 31.6/44.1%, respectively (Figure 4). In relation to the long-term trend (compared to E3.1), the findings showed a smaller reduction in the simulated concentrations of PM₁₀ and PM_2.5 during scenario E2.1. On average, the long-term reductions in the PM₁₀ and PM_2.5 concentrations for the CAR, LAF, KEN, and TUN stations were as follows: 34.2/24.7%, 37.3/25.3%, 24.4/25.2%, and 21.7/37.9%, respectively. The findings confirmed that there was a short- and long-term reduction in the PM concentrations during scenario E2.1 of strict isolation. Indeed, this trend was primarily related to the strict isolation measures implemented due to COVID-19. A Mann–Whitney U test indicated the existence of significant differences (p-value > 0.050) between the simulated PM concentrations for scenarios E2.1 and E3.1. This behavior possibly confirmed the incidence of the implemented strict isolation measures. However, the influence of factors such as the regional transport of PM from hotspots and the emissions from industrial activities external to the megacity was not ruled out [14,71].

The findings showed that the greatest short-term reductions in the simulated PM concentrations during the E2.1 scenario of strict isolation tended to occur for PM_2.5 compared to PM₁₀. On average, the short-term reductions (compared to E1) in the PM_2.5 and PM₁₀ concentrations during the E2.1 scenario were as follows (significant differences, p-value < 0.050): 54/47.3%, respectively (Figure 4). Indeed, this short-term trend in the PM_2.5 concentrations was possibly related to the established strict isolation restrictions. In other words, the strict isolation measures had a greater short-term effect on PM_2.5 compared to PM₁₀. In the long term (compared to E3.1), the reduction in the PM_2.5 and PM₁₀ concentrations was similar (no significant differences, p-value = 0.235): 28.3/29.4%, respectively. The results suggested that this long-term trend was possibly more associated with those regional PM transport processes that typically occurred during the months of March–April and June–July [21]. These regional transport processes possibly tended to increase the PM_2.5 concentrations, which made the decrease in the PM_2.5 and PM₁₀ concentrations similar. Short-term measures were important for assessing immediate exposure and health risks, while long-term measures were essential for understanding trends and the cumulative effects of air pollution over time [64].

In the E2.2 scenario of sectorized isolation, the results revealed a short-term reduction (compared to E1) in the simulated PM concentrations (significant differences, p-value < 0.050). The reduction in the PM₁₀ and PM_2.5 concentrations for the LAF, TUN, and CAR stations were as follows: 29.4/28.0%, 19.3/32.6%, and 13.3/28.5%, respectively. On the other hand, the KEN station did not show a short-term reduction (no significant difference, p-value = 0.670) in the PM₁₀ concentrations (0.01%), although it did experience a reduction in the PM_2.5 concentrations (21.8%). In general, in the long term (compared to E3.2), the PM₁₀ concentrations also tended to decrease during the E2.2 scenario of sectorized isolation (significant differences, p-value < 0.050). The decrease in the concentrations for the LAF, CAR, and KEN stations were as follows: 27.6%, 13.8%, and 3.11%, respectively. At the TUN station, no reduction was observed (no significant difference, p-value = 0.753) in the PM₁₀ concentration; that is, a slight increase of 1.50% in the PM₁₀ concentration was evidenced. In relation to the PM_2.5 concentrations, the results showed reductions of 29.4%, 14.9%, and 9.79% in the concentrations for the TUN, CAR, and KEN stations, respectively. At the LAF station, no reduction was observed (no significant difference, p-value = 0.510) in the PM_2.5 concentration; that is, a slight increase of 0.55% was evidenced.

Therefore, the results revealed that the greatest short-term reductions (compared to E1) in the simulated PM concentrations during the E2.2 scenario of sectorized isolation tended to occur for PM_2.5 rather than PM₁₀. On average, the short-term reductions in the PM_2.5 and PM₁₀ concentrations during the E2.2 scenario were as follows: 29.7/20.7%, respectively (Figure 4). However, at the KEN station, no significant short-term reduction was observed in the PM₁₀ concentrations, but for the PM_2.5 concentrations this reduction was significant during the E2.2 scenario of sectorized isolation. In the long term (compared to E3.2), the reduction in the PM_2.5 and PM₁₀ concentrations were as follows: 18.0/14.8%, respectively. However, at the TUN and LAF stations, no reductions were observed in the PM₁₀ and PM_2.5 concentrations. These short- and long-term trends in the reduction in the concentrations during the E2.2 scenario were possibly related to the established sectorized isolation measures (Table 2). In other words, under this scenario of sectorized isolation, the short- and long-term reductions in the PM_2.5 (45/36.4%) and PM₁₀ (56.2/49.7%) concentrations were smaller compared to the E2.1 scenario of strict isolation.

Additionally, it was observed during the E2.2 scenario of sectorized isolation that in the central (CAR), western (LAF), and southern (TUN) zones of the megacity, reductions in the PM concentrations occurred both in the short and long term. In the southwestern zone (KEN), the smallest reductions in the PM concentrations were observed. Thus, the results suggested that in the center, west, and south of the megacity, the restrictions due to sectorized isolation had a greater effect compared to the southwestern zone. This spatial trend was possibly related to the influence of the sectorized isolation measures and land use [40,72]. Moreover, during this scenario, climatic conditions possibly also influenced the smaller reduction in the PM concentrations. That is, a higher occurrence of low wind speeds (<1m/s), a decrease in precipitation, the development of thermal inversions, and the regional transport of PM were reported [7,73,74].

In the E2.3 flexible isolation scenario, the results evidenced a short-term reduction (compared to E1) in the simulated PM concentrations (significant differences, p-value < 0.050). The average reduction in the PM₁₀ and PM_2.5 concentrations for the LAF, TUN, CAR, and KEN stations were as follows: 50.9/62.2%, 48.6/60.3%, 42.9/50.6%, and 21.5/40.8%, respectively. In the long term (compared to E3.3), the findings also showed a reduction in the simulated PM₁₀ and PM_2.5 concentrations during the E2.3 scenario. On average, the reductions in the PM₁₀ and PM_2.5 concentrations for the TUN, LAF, CAR, and KEN stations were as follows: 26.4/51.4%, 38.3/36.8%, 31.6/26.6%, and 18.4/25.7%, respectively. The findings suggested that there was a short- and long-term reduction in the PM concentrations during the E2.3 flexible isolation scenario. A Mann–Whitney U test suggested the existence of significant differences (p-value > 0.050) between the simulated PM concentrations for the E2.3 and E3.3 scenarios. Indeed, this trend was mainly related to the flexible isolation measures implemented as a result of COVID-19. For example, it was reported that 63.3% of the population worked remotely [60]. However, meteorology possibly also influenced the reduction in the PM concentrations during this flexible isolation scenario.

The results revealed that the greatest short-term reductions (compared to E1) in the simulated PM concentrations during the E2.3 flexible isolation scenario tended to occur for PM_2.5 compared to PM₁₀. On average, the short-term reductions in the PM_2.5 and PM₁₀ concentrations during the E2.3 flexible isolation scenario were as follows: 53.5/41%, respectively (Figure 3). In the long term (compared to E3.3), the reduction in the PM_2.5 and PM₁₀ concentrations were as follows: 35.1/28.7%, respectively. Indeed, these short- and long-term trends in the reduction in the concentrations during the E2.3 scenario were possibly related to the established flexible isolation measures (Table 2), the observed climatic conditions, and the regional contribution of PM. Under this flexible isolation scenario, the short- and long-term reductions in the PM_2.5 (1.01 times lower and 1.24 times higher) and PM₁₀ (1.15 times lower and 1.02 times lower) concentrations were similar or greater comparatively with the E2.1 strict isolation scenario.

3.4. ARIMA Models

The analysis scenarios considered were comparatively evaluated based on variations in the autoregressive (AR), difference (I), and moving averages (MA) terms of the developed ARIMA models.

In relation to the E2.1 strict isolation scenario, the results showed AR = 1 in the ARIMA models developed for the PM₁₀ concentrations. In the short term (E1), the findings showed AR terms between 2 and 6 for the PM₁₀ concentrations (Table 3). The results suggested that, in the short term, strict isolation measures tended to decrease the magnitude of the AR term (phenomenon memory). In other words, strict isolation measures tended to reduce the persistence over time of the PM₁₀ concentrations. Persistence in an ARIMA model refers to the model’s ability to capture and predict the temporal relationship between the past and present values of a time series [31]. High persistence could indicate a time series with a trend or pattern that persisted over time, while low persistence could indicate a more volatile time series or with more abrupt changes [75]. In relation to the PM_2.5 concentrations, the results showed AR terms between 0 and 1 during the E2.1 strict isolation scenario. In the short term, the AR terms varied between 0 and 11. The results suggested that, in the short term, strict isolation measures tended to reduce the persistence over time of the PM_2.5 concentrations. Thus, it was suggested that, in the short term, strict isolation measures generated a greater reduction in the persistence of PM_2.5 compared to PM₁₀. This lower persistence in the finer fraction (PM_2.5) possibly decreased the toxic effects of PM on human health.

Additionally, in the long term, the results showed AR terms between 1 and 7 in the ARIMA models developed for the PM₁₀ concentrations (Table 3). The results suggested that, in the long term, strict isolation measures tended to reduce the persistence over time of the PM₁₀ concentrations. In relation to the PM_2.5 concentrations, in the long term, the findings showed that the AR terms varied between 0 and 1. Thus, it was suggested that, in the long term, the strict isolation measures implemented possibly did not significantly change the persistence over time of the PM_2.5 concentrations. The long-term persistence of the PM_2.5 concentrations could have been influenced by the following complex factors: regional PM transport patterns and meteorological conditions [76].

The results showed that during the E2.1 strict isolation scenario, the I term in the ARIMA models varied between 1 and 2 for the PM₁₀ and PM_2.5 concentrations, respectively. In the short term (E1), a similar trend was observed for the PM₁₀ and PM_2.5 concentrations (Table 3). The results suggested that the strict isolation measures implemented did not comparatively change the decreasing trend in the PM₁₀ and PM_2.5 concentrations observed in the short term (Figure 2). In the long term (E3.1), the ARIMA models showed I terms = 1 and between 1 and 2 for the PM₁₀ and PM_2.5 concentrations, respectively. The results suggested that, in the long term, the strict isolation measures implemented probably had a greater effect on the PM₁₀ concentrations compared to the PM_2.5 concentrations. Namely, during the strict isolation scenario, a greater decreasing trend was suggested for the PM₁₀ concentrations compared to the PM_2.5 concentrations.

In relation to the MA term of the ARIMA models developed during the E2.1 strict isolation scenario, the findings evidenced a variation in its magnitude between 3 and 5 and between 6 and 12 for the PM₁₀ and PM_2.5 concentrations, respectively (Table 3). In the short term (E1), a variation in the MA term was observed between 1 and 7 for the PM₁₀ and PM_2.5 concentrations, respectively. In general, the results suggested that, in the short term, strict isolation measures tended to increase the variations in the PM₁₀ and PM_2.5 concentrations. This increase in the variation of the concentrations was greater for PM_2.5 compared to PM₁₀. The increase in the variations of the PM₁₀ and PM_2.5 concentrations did not indicate an increase in the PM concentrations in the short term [77]. The variations in the concentrations in the short term were probably related to factors such as climatic effects and specific external events that were reported in the previous sections. In the long term (E3.1), a variation in the MA term was observed between 1 and 12 and between 5 and 15 for the PM₁₀ and PM_2.5 concentrations, respectively. In general, the findings suggested that, in the long term, strict isolation measures (E2.1) tended to decrease the variations in the PM₁₀ and PM_2.5 concentrations. It is probable that the PM concentrations were more stable and less prone to sudden peaks during this strict isolation scenario.

During the E2.2 sectorized isolation scenario, the results showed AR terms between 0 and 4 and between 0 and 1 in the ARIMA models developed for the PM₁₀ and PM_2.5 concentrations, respectively. In the short term (E1), the findings showed AR terms between 2 and 6 and between 0 and 11 for the PM₁₀ and PM_2.5 concentrations, respectively (Table 3). The results suggested that, in the short term, sectorized isolation measures tended to decrease the magnitude of the AR term. That is, sectorized isolation measures tended to reduce the persistence over time of the PM₁₀ and PM_2.5 concentrations. It was also suggested that, in the short term, sectorized isolation measures comparatively generated a greater reduction in the persistence of PM_2.5 compared to PM₁₀. In the long term (E3.2), the results showed AR terms between 0 and 1 and between 0 and 2 for the PM₁₀ and PM_2.5 concentrations, respectively. The results suggested that, in the long term, sectorized isolation measures tended to reduce the persistence over time of the PM₁₀ concentrations. In relation to the PM_2.5 concentrations, in the long term, the findings suggested that sectorized isolation measures did not considerably change their persistence over time. The long-term persistence of the PM_2.5 concentrations may have been influenced by complex factors such as regional PM transport patterns and the meteorological conditions observed [78]. The results showed that there were changes in the wind patterns during the sectorized isolation scenario, which likely influenced the dispersion and accumulation of PM_2.5. This behavior could have affected its long-term persistence. Moreover, the long-term persistence in the PM concentrations possibly depended on factors such as the duration and intensity of isolation measures, the composition of PM sources, and the subsequent economic recovery [79].

The results showed that during the E2.2 sectorized isolation scenario, the I term in the ARIMA models was equal to 2 for the PM₁₀ and PM_2.5 concentrations. In the short term (E1), it was observed that the I term varied between 1 and 2 for the PM₁₀ and PM_2.5 concentrations (Table 3). Comparatively, the results suggested that the sectorized isolation measures implemented did not considerably change the increasing trend in the PM_2.5 concentrations observed in the short term (Figure 2). However, with the I terms = 1 in the short term (E1) in some ARIMA models, a lesser increasing trend in the PM_2.5 concentrations was suggested during this scenario. In relation to PM₁₀, the interpretation required further analysis. Namely, in the CAR and LAF stations, an increasing trend (+) was observed, and, in the KEN and TUN stations, a decreasing trend (−) was observed in the concentrations. Therefore, the results suggested that the ARIMA models indicated with the I term the magnitude of the trend in the PM₁₀ concentrations but did not indicate whether the trend was increasing (+) or decreasing (−). In the long term (E3.2), the ARIMA models showed I terms between 1 and 2 for the PM₁₀ and PM_2.5 concentrations. These ARIMA findings could initially suggest that, in the long term, sectorized isolation measures possibly did not change the trend in the PM₁₀ and PM_2.5 concentrations. However, in general, during the sectorized isolation scenario (E2.2), a decreasing trend (−) was observed, and, in the long term, an increasing trend (+) was observed in the PM₁₀ and PM_2.5 concentrations.

In relation to the MA term of the ARIMA models for the E2.2 sectorized isolation scenario, the findings evidenced a variation between 1 and 9 and between 1 and 7 for the PM₁₀ and PM_2.5 concentrations, respectively (Table 3). In the short term (E1), a variation in the MA term was observed between 1 and 7 for the PM₁₀ and PM_2.5 concentrations. In general, the results suggested that, in the short term, sectorized isolation measures did not tend to considerably influence the variations in the PM₁₀ and PM_2.5 concentrations. However, for the PM₁₀ concentrations a slight increase in the variation of their concentrations was observed during the E2.2 sectorized isolation scenario. In the long term (E3.2), a variation in the MA term was observed between 0 and 6 and between 1 and 8 for the PM₁₀ and PM_2.5 concentrations, respectively. In general, the findings suggested that, in the long term, sectorized isolation measures (E2.2) tended to slightly increase and decrease the variations in the PM₁₀ and PM_2.5 concentrations, respectively. In other words, during this sectorized isolation scenario, the PM_2.5 concentrations were slightly more stable compared to the PM₁₀ concentrations.

During the E2.3 flexible isolation scenario, the results showed AR terms between 0 and 8 and between 1 and 2 in the ARIMA models developed for the PM₁₀ and PM_2.5 concentrations, respectively (Table 3). In the short term (E1), the findings showed AR terms between 2 and 6 and between 0 and 11 for the PM₁₀ and PM_2.5 concentrations, respectively. The results suggested that, in the short term, flexible isolation measures tended to increase and decrease the magnitude of the AR term for the PM₁₀ and PM_2.5 concentrations, respectively. Namely, flexible isolation measures tended to increase and reduce the persistence over time of the PM₁₀ and PM_2.5 concentrations, respectively. Under this E2.3 flexible isolation scenario, a greater difference in the persistence of the PM₁₀ and PM_2.5 concentrations was hinted at. It was also suggested that, in the short term, flexible isolation measures comparatively generated a greater reduction in the persistence of PM_2.5 compared to PM₁₀. In the long term (E3.3), the results showed AR terms = 1 and between 1 and 2 for the PM₁₀ and PM_2.5 concentrations, respectively. The results hinted that, in the long term, flexible isolation measures tended to increase the persistence over time of the PM₁₀ concentrations. In relation to the PM_2.5 concentrations in the long term, the findings hinted that flexible isolation measures did not change their persistence over time. Indeed, the long-term persistence in the PM concentrations probably depended on factors such as the duration and intensity of isolation measures, the composition of PM sources, and the subsequent economic recovery [80].

The results showed that, during the E2.3 flexible isolation scenario, the I term in the ARIMA models was equal to 1 for the PM₁₀ and PM_2.5 concentrations. In the short term (E1), it was observed that the I term varied between 1 and 2 for the PM₁₀ and PM_2.5 concentrations (Table 3). Initially, the results could suggest that flexible isolation measures did not considerably change the increasing trend in the PM_2.5 concentrations observed in the short term. However, the trend observed in the PM₁₀ and PM_2.5 concentrations during the E2.3 flexible isolation scenario was decreasing (Figure 2). In other words, the trends in magnitude were similar, but in the short term it was increasing (+) and during the E2.3 flexible isolation scenario it was decreasing (−). In the long term (E3.3), the ARIMA models showed I terms = 1 for the PM₁₀ and PM_2.5 concentrations. These ARIMA findings suggested that, in the long term, flexible isolation measures possibly did not change the decreasing trend in the PM₁₀ and PM_2.5 concentrations.

In relation to the MA term of the ARIMA models for the E2.3 flexible isolation scenario, the findings evidenced a variation between 4 and 14 and between 1 and 15 for the PM₁₀ and PM_2.5 concentrations, respectively (Table 3). In the short term (E1), a variation in the MA term between 1 and 7 was observed for the PM₁₀ and PM_2.5 concentrations. The results suggested that, in the short term, flexible isolation measures tended to considerably influence the variations in the PM₁₀ and PM_2.5 concentrations. Namely, these flexible isolation measures possibly generated a greater variation in the PM₁₀ and PM_2.5 concentrations in the short term. In the long term (E3.3), a variation in the MA term between 1 and 11 and between 1 and 8 was observed for the PM₁₀ and PM_2.5 concentrations, respectively. The findings suggested that, in the long term, flexible isolation measures tended to increase the variations in the PM₁₀ and PM_2.5 concentrations, respectively. This influence on the variation of the concentrations was more evident for PM_2.5 compared to PM₁₀.

4. Conclusions

The findings of this study allowed for the following conclusions to be drawn from the sequentially established COVID-19 isolation scenarios (strict, sectorized, and flexible) in the high-altitude megacity under study. This is based on the analysis of the PM concentrations using ARIMA models.

The results suggest an average order in the observed concentrations of PM₁₀ and PM_2.5 according to the considered isolation scenarios (compared to the historical trend): sectorized (−28.9% and −31.7%) > strict (−29.4% and −28.3%) > flexible (−8.52% and −12.4%). The change in the sequence between the isolation scenarios is likely related to the occurrence of particular weather conditions (wind direction and precipitation) and regional PM transport episodes (forest fires and Sahara dust) during the sectorized isolation scenario. The differences in the reduction in the PM₁₀ and PM_2.5 concentrations between the strict and flexible isolation scenarios were 23.8% and 12.8%, respectively.

The findings reveal that strict isolation measures have a greater effect on the simulated concentrations of PM₁₀ and PM_2.5 in the short term (PM₁₀: −47.3% and PM_2.5: −54%) than in the long term (PM₁₀: −29.4% and PM_2.5: −28.3%). In the short term, these isolation measures have a greater effect on the PM_2.5 concentrations compared to the PM₁₀ concentrations. In the long term, the effects of these strict isolation measures on the PM₁₀ and PM_2.5 concentrations are similar.

The ARIMA models suggest that strict isolation measures tend to decrease the persistence over time of the PM₁₀ and PM_2.5 concentrations both in the short and long term. The models also suggest that these isolation measures do not significantly modify the decreasing trend of the PM₁₀ and PM_2.5 concentrations in the short term. However, in the long term, these isolation measures have a greater effect on the PM₁₀ concentrations compared to the PM_2.5 concentrations, suggesting a greater downward trend of the PM₁₀ concentrations. Lastly, the ARIMA models reveal that, in the short term, strict isolation measures tend to increase the variation in the PM₁₀ and PM_2.5 concentrations, with a greater increase in the case of PM_2.5. Conversely, in the long term, these isolation measures tend to decrease the variations in the PM concentrations, suggesting a more stable behavior that is less prone to sudden peaks.

The ARIMA analysis suggests that flexible isolation measures tend to increase the persistence over time of the PM₁₀ concentrations in the short term, while they tend to decrease the persistence of the PM_2.5 concentrations. In the long term, an increase in the persistence of the PM₁₀ concentrations is suggested, while no changes in the persistence of PM_2.5 are hinted at. Lastly, the ARIMA models reveal that flexible isolation measures tend to increase the variation in the PM₁₀ and PM_2.5 concentrations both in the short and long term.

Finally, this study is relevant because it highlights the effectiveness of isolation measures to reduce urban PM₁₀ and PM_2.5 concentrations. Strict measures produce significant short-term reductions, while flexible measures affect the persistence of PM over time. These findings are significant for visualizing the air quality management strategies in megacities.