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Article

Scaling Correlation Analysis of Particulate Matter Concentrations of Three South Indian Cities

by
Adarsh Sankaran
1,
Susan Mariam Rajesh
1,
Muraleekrishnan Bahuleyan
1,
Thomas Plocoste
2,*,
Sumayah Santhoshkhan
1 and
Akhila Lekha
1
1
TKM College of Engineering, Kollam 691005, India
2
KaruSphère Laboratory, Department of Research in Geoscience, 97139 Les Abymes, Guadeloupe, France
*
Author to whom correspondence should be addressed.
Pollutants 2024, 4(4), 498-514; https://doi.org/10.3390/pollutants4040034
Submission received: 20 August 2024 / Revised: 6 November 2024 / Accepted: 11 November 2024 / Published: 13 November 2024
(This article belongs to the Special Issue Stochastic Behavior of Environmental Pollution)
Browse Figures
Figure 1
<p>Overall methodological framework.</p> "> Figure 2
<p>Fluctuation functions of PM2.5 and PM10 for the three cities. Upper panels show the plots of PM2.5 and lower panels show the results of PM10.</p> "> Figure 3
<p>Comparison of Renyi exponent plot and multifractal spectrum of PMs for the three cities.</p> "> Figure 4
<p>Renyi exponent and multifractal spectrum of gaseous pollutant time series for the three cities.</p> "> Figure 5
<p>Renyi exponent and multifractal spectrum of meteorological time series for the three cities.</p> "> Figure 6
<p>MFCCA of PM2.5 with meteorological parameters for Chennai. Last column depicts scaling correlations between the paired variables.</p> "> Figure 7
<p>MFCCA of PM2.5 with gaseous pollutants for Chennai. Last column depicts scaling correlations between the paired variables.</p> "> Figure 8
<p>MFCCA of PM10 with meteorological parameters for Chennai. Last column depicts scaling correlations between the paired variables.</p> "> Figure 9
<p>MFCCA of PM10 with gaseous pollutants for Chennai. Last column depicts scaling correlations between the paired variables.</p> "> Figure 10
<p>Comparison of Renyi exponent plot and multifractal spectrum of precipitation data of the three cities.</p> "> Figure 11
<p>MFCCA of rainfall (R) with PMs for Chennai. Last line depicts scaling correlations between the paired variables.</p> ">
Versions Notes

Abstract

:
Analyzing the fluctuations of particulate matter (PM) concentrations and their scaling correlation structures are useful for air quality management. Multifractal characterization of PM2.5 and PM10 of three cities in India wase considered using the detrended fluctuation procedure from 2018 to 2021. The cross-correlation of PM concentration in a multifractal viewpoint using the multifractal cross-correlation analysis (MFCCA) framework is proposed in this study. It was observed that PM2.5 was more multifractal and complex than PM10 at all the locations. The PM–gaseous pollutant (GP) and PM–meteorological variable (MV) correlations across the scales were found to be weak to moderate in different cities. There was no definite pattern in the correlation of PM with different meteorological and gaseous pollutants variables. The nature of correlation in the pairwise associations was found to be of diverse and mixed nature across the time scales and locations. All the time series exhibited multifractality when analyzed pairwise using multifractal cross-correlation analysis. However, there was a reduction in multifractality in individual cases during PM–GP and PM–MV paired analyses. The insights gained into the scaling behavior and cross-correlation structure from this study are valuable for developing prediction models for PMs by integrating them with machine learning techniques.

1. Introduction

Air pollution is a major concern driven by anthropogenic emissions and meteorological changes. In the literature, particulate matter with an aerodynamic diameter less than or equal to 2.5 and 10 µm (PM2.5 and PM10) is widely known to have health impacts [1,2]. Therefore, a thorough understanding of air pollution time series is essential for improving predictability and providing early warnings. Particulate matter (PM) of various sizes poses additional challenges in maintaining air quality standards in cities [3,4]. The time series of air pollutants exhibit complex behavior and fluctuations, making predictions challenging [5]. Hence, it is therefore crucial to know their stochastic behavior.
Scale invariance is a fundamental property that enables predictions by deriving information on shorter time scales from longer time-scale data, which can be studied using techniques such as fractal analysis [6]. Understanding the scaling behavior of PM data is beneficial for air pollution management [7]. However, a single fractal exponent has been found insufficient to describe complex geophysical processes. Consequently, multifractal detrended fluctuation analysis (MFDFA), proposed by Kantelhardt et al. [8], has become popular for assessing the scaling behavior of such systems. Due to the influence of multiple associated factors like meteorological variables, diffusion, dilution, and anthropogenic forcing, PM time series are often complex in characteristics with many scaling exponents. Numerous studies have investigated the scaling behavior of air pollutant concentrations at various locations around the world, utilizing a wide range of approaches, from traditional methods to detrended techniques like MFDFA and complex network-based frameworks [9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29]. These studies have yielded varying conclusions regarding the relative degrees of multifractality for PM10 and PM2.5 [27,28,29]. Factors such as influences on PM concentrations, their relationships with PM across multiple time scales, and the duration of these influences have been found to impact the multifractality of PM [27]. The variability in PM concentrations is influenced by both meteorological factors and gaseous air pollutants, whether primary or secondary in nature [30]. Therefore, understanding the scaling behavior and fluctuations of gaseous air pollutants and meteorological factors is equally important for gaining deeper insights and improving the accuracy of PM modeling.
Exploring scale-dependent correlations from a multifractal perspective could offer valuable insights into the predictability of PM concentrations. Unfortunately, such studies are rare on a global scale, and research on the multifractality of air pollutants within the Indian context is particularly scarce. Considering the Indian conditions, only a very limited number of studies has attempted multifractal analysis of PM [31,32,33], while not many studies have attempted scaling correlation analysis. Manimaran and Narayana [31] analyzed the multifractal characteristics and cross-correlation behavior of Air Pollution Index (API) data through the multifractal detrended cross-correlation analysis (MF-DCCA) method. They considered API data of nine air pollutants at the Hyderabad University campus from 2013 to 2016. They reported anti-correlation and multifractality in behavior for all 36 cases. PM2.5 and PM10 exhibited behavior anti-correlated with that of all air pollutants. Chelani and Gautam [33] investigated the multifractality of wet and dry seasonal PM2.5 data of five cities in India using MFDFA.
To study the associations among various geophysical variables, the detrended cross-correlation analysis (DCCA) propounded by Podobnik and Stanley [34] is widely used. Its multifractal extension, MF-DCCA [35,36], and the improved alternative, multifractal cross-correlation analysis (MFCCA), are dependable methods for performing scale-dependent correlation studies [37,38]. This study employed MFCCA for the first time to analyze scaling correlations within air pollution research. Additionally, it uniquely and comprehensively examined the scaling correlations of both gaseous pollutants and meteorological factors with PM variants across different cities, providing a distinctive perspective in the Indian context. In summary, the specific objectives of this study are: (i) to analyze the multifractality of PM2.5, PM10, and five meteorological variables and gaseous pollutant data from three south Indian cities; (ii) to examine the scale-dependent correlations of PM, meteorological variables, and gaseous pollutants from a multifractal perspective using the sign-conserved MFCCA approach.

2. Materials and Methods

2.1. Stations and Data

In this study, three cities of south India were considered: Chennai (6.5 million inhabitants), Hyderabad (9.4 million inhabitants), and Vishakhapatnam (2.4 million inhabitants). Chennai and Hyderabad exhibit a more metropolitan character; Chennai is located on the coast, whereas Hyderabad lies inland within the Indian subcontinent. Rapid urbanization, high population density, and extensive use of motorized vehicles are typical features of both cities [30]. Vishakhapatnam, on the other hand, is a port city supported by steel and petroleum industries. Chennai experiences a tropical wet and dry climate with hot and humid conditions. Its maximum temperature hovers around 40 °C, and the minimum is around 20 °C. The city receives an average annual rainfall of approximately 1400 mm, primarily during the northeast monsoon (September to December) and the southwest monsoon (June to September). Similar to Chennai, Hyderabad also has a tropical wet and dry climate. Here, maximum temperatures can exceed 40 °C, and the minimum can drop below 15 °C, displaying a wider temperature range due to the city’s distance from the ocean. Hyderabad receives an average annual rainfall of about 800 mm, with significant rainfall from June to October. Vishakhapatnam has a summer tropical wet and dry climate, with an average annual rainfall of roughly 950 mm and temperatures generally in the range 25–30 °C throughout most of the year.
A wide network of sites operated by the Central Pollution Control Board (CPCB) of India (https://cpcb.nic.in/) exists in India to monitor ambient air quality. These sites feature industrial and chemical production facilities and urban characteristics, with pollution primarily arising from vehicles. The data of PM, gaseous pollutants, and meteorological variables at diverse time scales ranging from minutes to days can be downloaded from the Central Control Room for Air Quality Management operated by CPCB (https://airquality.cpcb.gov.in/ccr/#/caaqm-dashboard-all/caaqm-landing, accessed on 5 November 2024). The data are made available to the public after rigorous quality checks. The measurements of daily PM2.5 and PM10 concentrations, meteorological parameters (solar radiation, SR; air temperature, temp; wind speed, U; relative humidity, RH; rainfall, R), and gaseous pollutants (NOx, O3, SO2, CO) from 2018 to 2021 were used. Many researchers have used data from the CPCB to analyze and model PM concentrations [30,39,40]. Analysis of the data revealed that less than 10% was missing. These missing data were replaced using the predictive mean matching (PMM) method [41] in R programming.

2.2. MFDFA and Parameters

The MFDFA algorithm is very popular in the non-linear dynamics field and the method is well described in the literature [42]. It involves (i) computing the accumulated deviation of the ‘profile’ of the time series, which is the series of deviations from its mean, (ii) dividing the profile into a certain number of non-overlapping segments of length s (referred to as scale), Ns; and (iii) performing a least square fitting of each non-overlapping segment using a polynomial m to remove local trends. Here, the deviation of the polynomial fit from the ‘profile’ provides the detrended time series; (iv) finding the variance of the series, known as the ‘fluctuation function’ Fq(s), which is raised for different moment orders ‘q’ and averaged over all segments. The scaling and multifractal behavior is confirmed if Fq(s) follows a power law with s.
The slope of Fq(s) versus s plot at logarithmic scale denoted by h(q) is called the generalized Hurst exponent (GHE), for different moment order q. The value of GHE for q = 2, denoted as h(2), can be considered as equivalent to the classical Hurst exponent (H), which indicates the long-term or short-term memory persistence of the series. The q-weighted function of GHE τ ( q ) = q h ( q ) − 1 is often called the q-order mass exponent ( τ ( q ) ) . The derivative of the q-order mass exponent gives the singularity exponent (α) α = d τ d q , which helps to comment on the multifractality of the time series. The singularity spectrum is defined by the plot between f(α) versus α, where f ( α ) = q α − τ ( q ) is a useful measure to investigate the strength of multifractality of the series. The singularity spectrum will be a single peaked parabolic curve with an apex at unity. The larger the base width (W) of the spectrum, the higher will be the multifractality. For a multifractal time series, the left- and right-hand wings of the spectrum correspond to the negative and positive q-order, respectively. The shape of the singularity spectrum f(α) curve contains significant information about the distribution characteristics of the examined dataset, and describes the singularity content of the time series. The Asymmetry Index (AI) is defined as the ratio between ( Δ α L − Δ α R ) and ( Δ α L + Δ α R ) , where Δ α L and Δ α R refer to the width of the left and right wing of the singularity spectrum. A positive AI value indicates a left-hand deviation of the multifractal spectrum, likely resulting from some degree of local high fluctuations, while a negative AI value indicates a right-hand deviation with local low fluctuations. The value of the singularity exponent for a zero moment order (known as the Hölder exponent, α 0 ) indicates the complexity of the time series.

2.3. MFCCA

MFCCA can also incorporate the sign of the fluctuation function into the generalized moments to estimate the detrended covariance function and facilitate the determination of individual persistence and the joint persistence between two series. In the MFCCA algorithm, the fluctuation function in each is calculated as follows [37,38,43]:
f f X Y 2 ( ν , s ) = 1 s ∑ k = i s ( X ( ( ν − 1 ) + k ) − p X , υ m ( k ) ) × ( Y ( ( ν − 1 ) + k ) − p Y , υ m ( k ) )
F X Y q ( s ) = 1 2 N s ∑ υ = 0 2 N s − 1 s i g n f f X Y 2 ( υ , s ) f f X Y 2 ( υ , s ) q / 2
The cross-correlation coefficient is defined as the ratio between the detrended covariance function F X Y and the detrended variance functions F X and [43]:
ρ X Y = F X Y q F X q F Y q
Theoretically, the value of ρ X Y lies in the range [−1, 1]. The cross-correlation helps to find the estimation of the scale-dependent correlation between two candidate time series, which can provide better insight into the physical association between the variables.
The seasonal trend decomposition (STL) method is a very popular and efficient data pre-processing method widely used in time series analysis [44]. Complex time series are often characterized by features like trend, noise, periodicity, or seasonality. Using the STL method, the Y t signal can be decomposed as:
Y t = S t + T t + R t
where S t is the seasonality, T t is the trend, and R t is the remainder.
This classical and robust method has already been applied in various fields, including air pollution studies [45,46,47]. Complex time series, such as those of air pollutants or meteorological variables, are often characterized by seasonality, which may, in turn, influence the multifractality of the series. To capture the true multifractal dynamics, it is recommended to use STL as a preprocessing tool. The overall methodological framework developed for this study is presented in Figure 1.

3. Results and Discussion

3.1. MFDFA

Multifractal analysis of PM2.5, PM10, four gaseous pollutants, and four meteorological variables was performed using the popular MFDFA method. Fixing the appropriate scale range is crucial during the implementation of the MFDFA algorithm. The minimum and maximum scale ranges can be appropriately set by following guidelines from the literature [38,48,49,50]. A commonly accepted rule of thumb is that the minimum scale, smin, should be greater than (m + 2), where ‘m’ is the polynomial order. The maximum scale, smax, is recommended to be chosen through a rigorous trial-and-error process when selecting the scale range. Fluctuation functions are developed by fixing the statistical moment orders from −4 to 4, and a first-order polynomial (m = 1) was chosen for the MFDFA application. Accordingly, a minimum scale range to a maximum range up to L/4 (approximately an annual scale in this case), where L represents the data length, was considered suitable and sufficient to capture the fractal properties. Figure 2 shows the fluctuation functions of PM2.5 and PM10 for the three cities. The same procedure was carried out for each parameter studied. The key multifractal properties H, W, AI, Δh(q), ΔH and α0 were estimated and are presented in Table 1.
The results of the multifractal analysis showed that the PM and the related series mostly possessed long-memory persistence (H > 0). The multifractality was evident in all the time series (W ≠ 0). Both the PM series showed negative asymmetry. Figure 3 and Table 1 show that the PM2.5 of all the cities showed more multifractality and complex behavior when compared with PM10 (WPM2.5 > WPM10; ΔHPM2.5 > ΔHPM10). This can be explained by the difference in particle properties. Indeed, PM10 is mainly primary pollutants directly emitted into the atmosphere, while PM2.5 can also be secondary, resulting from chemical reactions between compounds [51,52]. However, the literature lacks consistency regarding the relationship between the degree of multifractality and particulate matter size. Some studies suggest that the multifractality and complexity of PM10 are significantly stronger than those of PM2.5 [28]. Other studies have reported that the multifractality of particulate matter decreases with increasing particle size [29], while some have found that both PM10 and PM2.5 exhibit very similar multifractal behavior. This suggests that both types of particulate matter are influenced by the same natural sources and anthropogenic emissions during the measurement period [27]. A positive AI value indicates that the spectrum is left-skewed, while a negative AI value suggests a right-skewed spectrum. This skewness indicates complexity at the level of large fluctuation amplitudes and multifractality, with insensitivity to small amplitude fluctuations. PM2.5 was found to exhibit negative asymmetry, whereas PM10 showed positive asymmetry. A similar sign pattern was observed in the Δh(q) values. There is a strong correlation of 0.93 between H and α0.
The multifractal intensity varied between pollutants from one city to another (see Figure 3 and Figure 4). Nevertheless, certain trends can be observed and quantified thanks to the results in Table 1. Overall, we note that parameters such as H, W, AI, Δh(q) and ΔH were higher in absolute value for PM2.5, PM10, NOx, and CO in Chennai and Hyderabad. This can be attributed to the fact that these highly urbanized cities have dense road traffic and numerous industries (automotive, chemical, pharmaceutical, biotechnology, etc.). Chennai is considered as a significant industrial hub in India. Regarding O3, the parameter values were higher in Vishakhapatnam, which has more moderate traffic compared to the other two cities. Consequently, the effects of O3 titration by NOx [53] will be less significant in this city, making the fluctuations of this gas more pronounced. For SO2, the parameters were higher for Vishakhapatnam and Hyderabad. This can be explained by the fact that Vishakhapatnam has numerous factories in the oil, steel, and fertilizer sectors. These industries are significant emitters of SO2. In general, the connection between urbanization indices, traffic data, industrial emissions, and PM2.5 and PM10 concentrations is very strong, as described in various multiscale studies [30]. In megacities like Chennai, which are highly urbanized with heavy traffic flow, CO is identified as a major driver of pollution. Adarsh et al. [30] reported that, regardless of the city, PM variability was primarily attributed to MVs such as relative humidity and solar radiation. They found that the dominant GPs influencing PM concentrations showed more spatial variability than MVs. In Chennai and Hyderabad, CO is a common factor affecting PM concentrations, while in more industrialized cities, NOx and SO2 are the main contributors. In summary, the origin and source of gaseous pollutants significantly influence the composition of PM concentrations.
Regarding the meteorological parameters in Figure 5, the U time series exhibited a lesser degree of multifractality at all stations, which contradicts the notion of the complex behavior of wind velocity. This could be due to stable wind patterns at these locations or the influence of external factors. In Table 1, we observe that the multifractal intensity of U was higher in Hyderabad. This can be explained by the fact that, unlike other cities near the coast of the Bay of Bengal, Hyderabad is located inland. Therefore, it can be inferred that the complexity of the series might depend on location and other climatic parameters. All the series exhibit strong, long memory persistence, with the highest persistence observed in the T series. This behavior can be attributed to urbanization and the urban heat island (UHI) effect [54,55,56]. This effect reduces the nighttime cooling of temperatures because the heat stored in building materials is released. Thus, the magnitude of temperature and its spatial variations may influence fluctuations in PM concentration, leading to increased complexity and multifractality.

3.2. Scaling Correlation Analysis Using MFCCA Method

The MFCCA method was applied using a range from weekly to annual scales. The value of q = 2 is known to provide a good estimate for analyzing multifractality [36], for which the properties were extracted. Figure 6, Figure 7, Figure 8 and Figure 9 illustrate the results of the MFCCA analysis and comparison between PM2.5/10, meteorological parameters, and gaseous pollutants for Chennai. The plots for other cities are included in the Supplementary Materials (Figures S1–S8). The multifractal parameters calculated for Chennai are presented in Table 2. For Hyderabad and Vishakhapatnam, these parameters are listed in Tables S1 and S2 of the Supplementary Materials. In Table 2, it is evident that even when considering the joint influence, the series remained persistent. The joint persistence was found to be nearly half of the individual persistence (Hxy > 0). In this scenario, the multifractality was also conserved, although the assessment showed an overall reduction in the multifractal property. The overall linear correlation between PM and MV/GP was weak across the scales. Regardless of the asymmetric nature of individual series, five out of eight spectra displayed negative asymmetry.
Figure 6, Figure 7, Figure 8 and Figure 9 show that the GHE values of PM were consistently lower than those of MVs and GPs, especially for positive q-orders. The meteorological variables showed higher persistence than PM10 for all moment orders. In general, joint multifractal spectra were smaller in base width when compared with individual spectra. This indicates a lower multifractality by considering the joint effect of PM-MV pairs in the multifractal analysis. Correlations were negative in PM-RH and PM-U relationships across all the scales for Hyderabad city, while they were negative for Chennai city. However, the correlations were positive in the PM10-SR relationship over the scales at Hyderabad while they were of mixed nature for PM2.5. In general, the correlation patterns showed an increasing trend for PM-U and PM-SR relations, whereas there was a reducing trend of correlations across scales in the PM-RH and PM-T relationships.
The overall nature of scaling correlations in PM-MV and PM-GP relationships is examined in Table 3, revealing no specific pattern in their nature and trends. In some paired relationships, the correlation was positive, while in others, it was negative across all scales. However, there was a predominance of mixed correlations (positive at some scales and negative at others). Specifically, 29 out of 48 cases (60%) exhibited mixed correlations. Generally, in all 48 cases, the correlations were found to be weak to moderate, regardless of their positive or negative nature.
For a given pair, the relationship did not necessarily exhibit a consistent nature across all cities. The mixed nature of correlations is noted among PM-SO2 relationships, irrespective of PM type or city location. Similarly, except for PM2.5 in Chennai, the relationship between PM and temperature also showed a mixed type. This dynamic nature of correlations may result from the dominant role of gaseous pollutants when considering PM-MV links and vice versa. This is typical of multiscale processes, which are also influenced by local meteorological factors or emissions. Such relationships can be further deciphered using time-frequency methods like wavelet coherence or time-dependent intrinsic correlations [30,57,58,59,60]. Understanding the interplay between different meteorological factors or gaseous pollutants is crucial in deciphering the physical reasoning behind the dynamic multifractal relationships of PM concentrations.

3.3. Effect of Precipitation on PM Concentrations

One of the meteorological parameters that can have a significant impact on particle deposition on the ground is rainfall. Indeed, rainfall (R) can cause the wet scavenging process of particles present in the atmosphere, i.e., wet deposition [61,62,63]. This is the reason why we treat this variable separately. Figure 10 shows the results of the MFDFA analysis for R. Multifractality was observed for the three cities (Δh(q) and W ≠ 0). However, Chennai exhibited a different dynamic. To quantitatively compare the cities, the multifractal parameters are presented in Table 4. The precipitation time series were weakly persistent in Chennai and Hyderabad (H > 0.5), while the series was anti-persistent in nature (H < 0.5) in Vishakhapatnam. The highest multifractality was noted in Vishakhapatnam (W = 2.522), while the lowest was in Chennai (W = 1.595). A positive asymmetry was observed in the spectrum of all cities (AI > 0).
Let us now stochastically analyze the impact of R on PM2.5 and PM10 concentrations for each city. Figure 11 illustrates the results of the MFCCA analysis between the R-PMs pair, and the multifractal parameters are presented in Table 5. In Figure 11, the multifractal cross-correlations of Chennai showed a distinctly different pattern compared to that of Hyderabad and Vishakhapatnam. For PM2.5 and PM10, Wxy in Chennai stood out with significantly lower values. The scaling correlations showed an increasing pattern with scale for the data of Chennai city. Here, the association was negative for smaller scales but positive for larger scales. For the other cities, the association between PMs and precipitation was negative across the entire scale range. Regarding persistence, we note that Hxy PM2.5 > Hxy PM10 in Hyderabad and Vishakhapatnam. This indicates that PM2.5 persisted longer in the atmosphere after rainfall events. This can be explained by particle size. PM10, being larger, is more easily trapped by water droplets, promoting wet deposition. During dry deposition, PM10 also more easily settles to the ground by gravity [64]. According to the authors, the fact that for PM10, Hxy was higher than PM2.5 in Chennai can be explained by the fact that Hx PM10 > Hx PM2.5. In other words, even before rainfall, the persistence of PM10 was more significant than PM2.5, which was not the case for the other cities. Several direct and indirect factors may explain this behavior: emission sources, weather conditions, or topography.
This study examined the multifractal-based scaling correlation of PM of different cities in India with a set of gaseous pollutants and meteorological variables. As one of the initial attempts on multifractal cross correlations of PM, this study is not free from limitations, but allows for further improvements. To draw strong conclusions, similar studies should be conducted for different cities with diverse geographical locations, varying data lengths, and different temporal resolutions (such as hourly and daily). From a methodological perspective, the different variants of scaling correlation analysis should be applied and the efficacy of the methods investigated. Furthermore, this study did not account for the impact of precipitation in the form of wet and dry periods, which affects particle deposition in the atmospheric boundary layer, and such studies are in progress. The diverse nature of correlation measures among different pairs aids in developing machine learning-based hybrid models or decomposition models for PM predictions [65]. Understanding fractality will help develop prediction models and inform policy makers. The findings can enhance understanding of the mechanisms controlling PM dynamics and improve the management of early-warning systems. Despite the broad understanding of this issue, a real prediction model utilizing feedback is still an open problem to be investigated.

4. Conclusions

This study examined the multifractality and cross-correlation of PM (2.5, 10), gaseous pollutants (NOx, O3, SO2, CO), and meteorological variables (SR, T, U, RH, R) in three Indian cities, using daily data from the 2018–2021 period. MFDFA analysis revealed that both air pollutants and meteorological variables exhibited strong long-term persistence and multifractality, except for rainfall of Vishakhapatnam, which displayed an anti-persistence character. The persistent nature of air pollutants underscores the poor air quality in Chennai, Hyderabad, and Vishakhapatnam. Due to the characteristics of the particles, PM2.5 showed higher multifractality compared to PM10 in all cities. For gaseous pollutants, trends varied from city to city based on anthropogenic emissions. Regarding meteorological variables, the temperature series displayed the highest persistence. All series demonstrated multifractal behavior in pairwise analysis using MFCCA, but there was a reduction in multifractality compared to individual cases during PM-MV and PM-GP paired analysis. The PM-MV and PM-GP relationships across all cities showed weak to moderate correlations across different scales. These correlations displayed a mixed nature (positive or negative) across various scales with no clear trend in most cases. Regarding the analysis of the PM-R pair, the results showed the importance of atmospheric washing in the persistence of PM in the atmosphere and the variation in its multifractality. Capturing the dynamics in these correlations will be beneficial in developing potential multiscale models aimed at capturing the highly complex fluctuations of PM concentrations. To refine the impact of dry and wet deposition on PM concentrations in India, a seasonal analysis will be conducted in our next study.

Supplementary Materials

The following supporting information can be downloaded at: https://www.mdpi.com/article/10.3390/pollutants4040034/s1, Figure S1: MFCCA of PM2.5 with meteorological parameters for Hyderabad. Last column depicts scaling correlations between the paired variables; Figure S2: MFCCA of PM2.5 with gaseous pollutants for Hyderabad. Last column depicts scaling correlations between the paired variables; Figure S3: MFCCA of PM10 with meteorological parameters for Hyderabad. Last column depicts scaling correlations between the paired variables; Figure S4: MFCCA of PM10 with gaseous pollutants for Hyderabad. Last column depicts scaling correlations between the paired variables; Figure S5: MFCCA of PM2.5 with meteorological parameters for Vishakhapatnam. Last column depicts scaling correlations between the paired variables; Figure S6: MFCCA of PM2.5 with gaseous pollutants for Vishakhapatnam. Last column depicts scaling correlations between the paired variables; Figure S7: MFCCA of PM10 with meteorological parameters for Vishakhapatnam. Last column depicts scaling correlations between the paired variables; Figure S8: MFCCA of PM10 with gaseous pollutants for Vishakhapatnam. Last column depicts scaling correlations between the paired variables; Table S1: Multifractal parameters for different variables at Hyderabad: Hx stands for persistence property of PM, Hy stands for the persistence property of the variable (MV or GP), Hxy stands for the joint persistence; Wx is the spectral width of PM, Wy is the spectral width of the variable (MV or GP), Wxy is the spectral width of the joint spectra; AIx is the asymmetry index of the spectrum of PM, AIy is the asymmetry index of the spectrum of the variable (MV or GP), AIxy is the asymmetry of the joint spectra; ρs stands for the seasonal correlation, ρa stands for the annual correlation and ρ is the overall correlation; Table S2: Multifractal parameters for different variables at Vishakhapatnam: Hx stands for persistence property of PM, Hy stands for the persistence property of the variable (MV or GP), Hxy stands for the joint persistence; Wx is the spectral width of PM, Wy is the spectral width of the variable (MV or GP), Wxy is the spectral width of the joint spectra; AIx is the asymmetry index of the spectrum of PM, AIy is the asymmetry index of the spectrum of the variable (MV or GP), AIxy is the asymmetry of the joint spectra; ρs stands for the seasonal correlation, ρa stands for the annual correlation and ρ is the overall correlation.

Author Contributions

Conceptualization, A.S. and T.P.; methodology, A.S.; software, A.S.; validation, S.M.R. and M.B., formal analysis, S.M.R., M.B., S.S. and A.L.; data curation, S.M.R. and M.B.; writing—original draft preparation, S.M.R. and M.B.; writing—review and editing, A.S. and T.P; supervision, A.S. All authors have read and agreed to the published version of the manuscript.

Funding

This research received no external funding.

Data Availability Statement

The data that support the findings of this study are available from the Central Pollution Control Board (CPCB) of India (https://cpcb.nic.in/, accessed on 5 November 2024). Data can be downloaded from the Central Control Room for Air Quality Management operated by CPCB (https://airquality.cpcb.gov.in/ccr/#/caaqm-dashboard-all/caaqm-landing, accessed on 5 November 2024).

Conflicts of Interest

The authors declare no conflicts of interest.

References

  1. Polichetti, G.; Cocco, S.; Spinali, A.; Trimarco, V.; Nunziata, A. Effects of particulate matter (PM10, PM2.5 and PM1) on the cardiovascular system. Toxicology 2009, 261, 1–8. [Google Scholar] [CrossRef] [PubMed]
  2. Wang, J.; Ogawa, S. Effects of meteorological conditions on PM2.5 concentrations in Nagasaki, Japan. Int. Environ. Res. Public Health 2015, 12, 9089–9101. [Google Scholar] [CrossRef] [PubMed]
  3. Liu, Z.; Wang, L.; Zhu, H. A time-scaling property of air pollution indices: A case study of Shanghai, China. Atmos. Pollut. Res. 2015, 6, 886–892. [Google Scholar] [CrossRef]
  4. Sofia, D.; Giuliano, A.; Gioiella, F.; Barletta, D.; Poletto, M. Modeling of an air quality monitoring network with high space-time resolution. Comput. Aided Chem. Eng. 2018, 43, 193–198. [Google Scholar] [CrossRef]
  5. Blessy, A.; Paul, J.J.; Gautam, S.; Shany, J.V.; Sreenath, M. IoT-based air quality monitoring in hair salons: Screening of hazardous air pollutants based on personal exposure and health risk assessment. Water Air Soil Pollut. 2023, 234, 336. [Google Scholar] [CrossRef]
  6. Mandelbrot, B.B. The Fractal Geometry of Nature; Freeman Press: New York, NY, USA, 1982. [Google Scholar]
  7. Plocoste, T.; Calif, R.; Jacoby-Koaly, S. Temporal multiscaling characteristics of particulate matter PM10 and ground-level ozone O3 concentrations in Caribbean region. Atmos. Environ. 2017, 169, 22–35. [Google Scholar] [CrossRef]
  8. Kantelhardt, J.W.; Zschiegner, S.A.; Bunde, E.K.; Havlin, S.; Bunde, A.; Stanley, H.E. Multifractal detrended fluctuation analysis of nonstationary time series. Physica A 2022, 316, 87–114. [Google Scholar] [CrossRef]
  9. Lee, C.K. Multifractal characteristics in air pollutant concentration time series. Water Air Soil Pollut. 2002, 135, 389–409. [Google Scholar] [CrossRef]
  10. Lee, C.K.; Ho, D.S.; Yu, C.C.; Wang, C.C. Fractal analysis of temporal variation of air pollutant concentration by box counting. Environ. Model. Soft. 2003, 18, 243–251. [Google Scholar] [CrossRef]
  11. Lee, C.K.; Juang, L.C.; Wang, C.C.; Liao, Y.Y.; Yu, C.C.; Liu, Y.C.; Ho, D.S. Scaling characteristics in ozone concentration time series (OCTS). Chemosphere 2006, 62, 934–946. [Google Scholar] [CrossRef]
  12. Yuval, D.; Broday, M. Studying the time scale dependence of environmental variables predictability using fractal analysis. Environ. Sci. Technol. 2010, 44, 4629–4634. [Google Scholar] [PubMed]
  13. He, H.D.; Pan, W.; Lu, W.Z.; Xue, Y.; Peng, G.H. Multifractal property and long-range cross-correlation behavior of particulate matters at urban traffic intersection in Shanghai. Stoch. Environ. Res. Risk Assess. 2016, 30, 1515–1523. [Google Scholar] [CrossRef]
  14. Chelani, A.B. Long-memory property in air pollutant concentrations. Atmos. Res. 2016, 171, 1–4. [Google Scholar] [CrossRef]
  15. Dong, Q.; Wang, Y.; Peizhi, L. Multifractal behavior of an air pollutant time series and the relevance to the predictability. Environ. Pollut. 2017, 222, 444–457. [Google Scholar] [CrossRef] [PubMed]
  16. Gao, X.; Wang, X.; Shi, H. Multifractal cascade analysis on the nature of air pollutants concentration time series over China. Aero. Air Qual. Res. 2019, 19, 2100–2114. [Google Scholar] [CrossRef]
  17. Wang, Q. Multifractal characterization of air polluted time series in China. Phys. A Stat. Mech. Appl. 2019, 514, 167–180. [Google Scholar] [CrossRef]
  18. Li, X. On the multifractal analysis of air quality index time series before and during COVID-19 partial lockdown: A case study of Shanghai, China. Phys. A Stat. Mech. Appl. 2021, 565, 125551. [Google Scholar] [CrossRef]
  19. Nikolopoulos, D.; Moustris, K.; Petraki, E.; Cantzos, D. Long-memory traces in PM10 time series in Athens, Greece: Investigation through DFA and R/S analysis. Meteorol. Atmos. Phys. 2021, 133, 261–279. [Google Scholar] [CrossRef]
  20. Plocoste, T.; Carmona-Cabezas, R.; Jiménez-Hornero, F.J.; Gutiérrez de Ravé, E.; Calif, R. Multifractal characterisation of particulate matter (PM10) time series in the Caribbean basin using visibility graphs. Atmos. Pollut. Res. 2021, 12, 100–110. [Google Scholar] [CrossRef]
  21. Plocoste, T.; Carmona-Cabezas, R.; Jiménez-Hornero, F.J.; Gutiérrez de Ravé, E. Background PM10 atmosphere: In the seek of a multifractal characterization using complex networks. J. Aerosol Sci. 2021, 155, 105777. [Google Scholar] [CrossRef]
  22. Masseran, N. Multifractal characteristics on temporal maximum of air pollution series. Mathematics 2022, 10, 3910. [Google Scholar] [CrossRef]
  23. Masseran, N. Power-law behaviors of the severity levels of unhealthy air pollution events. Nat. Haz. 2022, 112, 1749–1766. [Google Scholar] [CrossRef]
  24. Shi, K.; Liu, C.; Li, Y.; Du, J. The difference of multifractality of black carbon, NOx and CO at traffic site and its implications for air pollution sources. Stoch. Environ. Res. Risk Assess. 2021, 35, 1715–1723. [Google Scholar] [CrossRef]
  25. Wang, Q.; Zhao, T.; Wang, R.; Zhang, L. Backward trajectory and multifractal analysis of air pollution in Zhengzhou region of China. Math. Prob. Eng. 2022, 2022, 2226565. [Google Scholar] [CrossRef]
  26. Shen, C.; Huang, Y.; Yan, Y. An analysis of multifractal characteristics of API time series in Nanjing, China. Phys. A Stat. Mech. Appl. 2016, 451, 171–179. [Google Scholar] [CrossRef]
  27. Plocoste, T.; Pavón-Domínguez, P.; Sankaran, A.; Euphrasie-Clotilde, L. Investigation of PM2.5 and PM10 Dynamics in the Caribbean Basin Using a Multifractal Framework. Water Air Soil Pollut. 2024, 235, 732. [Google Scholar] [CrossRef]
  28. N’Gobi, G.K.; Agbazo, M.N.; Leode, A. Fractal description of the temporal fluctuation of PM2.5 and PM10 concentrations and their cross-correlation at Cotonou autonomous port and the “Boulevard de laMarina” area (Benin Republic, West Africa). Pollution 2023, 9, 628–645. [Google Scholar] [CrossRef]
  29. Fuwape, I.; Ogunjo, S.; Akinsusi, J.; Rabiu, B.; Jenkins, G. Multifractal detrended fluctuation analysis of particulate matter and atmospheric variables at different time scales. Meteorol. Atmos. Phys. 2023, 135, 27. [Google Scholar] [CrossRef]
  30. Adarsh, S.; Plocoste, T.; Rajakrishnan, A.; Thodika, R.C.; Rema, R.A.; Dharman, S.; Madhukumar, M. Multiscale coherence analysis of PM2.5 and PM10 concentrations of four Indian urban areas using wavelet transform. Urban Clim. 2024, 56, 102056. [Google Scholar]
  31. Manimaran, P.; Narayana, A.C. Multifractal detrended cross-correlation analysis on air pollutants of University of Hyderabad Campus, India. Phys. A Stat. Mech. Appl. 2018, 502, 228–235. [Google Scholar] [CrossRef]
  32. Chelani, A.B.; Gautam, S. Lockdown during COVID-19 pandemic: A case study from Indian cities shows insignificant effects on persistent property of urban air quality. Geosci. Front. 2022, 13, 101284. [Google Scholar] [CrossRef] [PubMed]
  33. Chelani, A.B.; Gautam, S. Fractality in PM2.5 Concentrations during the dry and wet season over Indo-Gangetic Plain, India. Water Air Soil Pollut. 2023, 234, 502. [Google Scholar] [CrossRef]
  34. Podobnik, B.; Stanley, H.E. Detrended Cross-Correlation Analysis: A New Method for Analyzing Two Nonstationary Time Series. Phys. Rev. Lett. 2008, 100, 084102. [Google Scholar] [CrossRef] [PubMed]
  35. Zhou, W.X. Multifractal detrended cross-correlation analysis for two non-stationary signals. Phys. Rev. E 2008, 77, 066211. [Google Scholar] [CrossRef]
  36. Oświȩcimka, P.; Drożdż, S.; Forczek, M.; Jadach, S.; Kwapień, J. Detrended cross-correlation analysis consistently extended to multifractality. Phys. Rev. E 2014, 89, 023305. [Google Scholar] [CrossRef]
  37. Wątorek, M.; Drożdż, S.; Oświęcimka, P.; Stanuszek, M. Multifractal cross-correlations between the world oil and other financial markets in 2012–2017. Energy Econ. 2019, 81, 874–885. [Google Scholar] [CrossRef]
  38. Adarsh, S.; Plocoste, T.; Nourani, N.; Vahab, S.; Salim, A. Assessment of multifractal fingerprints of reference evapotranspiration based on multivariate empirical mode decomposition. Atmosphere 2023, 14, 1219. [Google Scholar] [CrossRef]
  39. Kumar, K.; Pande, B.P. Air pollution prediction with machine learning: A case study of Indian cities. Int. J. Environ. Sci. Technol. 2023, 20, 5333–5348. [Google Scholar] [CrossRef]
  40. Mohan, A.S.; Abraham, L. An ensemble deep learning model for forecasting hourly PM2.5 concentrations. IETE J. Res. 2023, 69, 6832–6845. [Google Scholar] [CrossRef]
  41. Rubin, D.B. Statistical matching using file concatenation with adjusted weights and multiple imputations. J. Busi. Econ. Stat. 1986, 4, 87–94. [Google Scholar] [CrossRef]
  42. Ihlen, E.A.F.E. Introduction to multifractal detrended fluctuation analysis in MATLAB. Front. Physiol. 2012, 3, 141. [Google Scholar] [CrossRef] [PubMed]
  43. Kwapień, J.; Oświęcimka, P.; Drożdż, S. Detrended fluctuation analysis made flexible to detect range of cross-correlated fluctuations. Phys. Rev. E 2015, 92, 052815. [Google Scholar] [CrossRef] [PubMed]
  44. Cleveland, R.B.; Cleveland, W.S. STL: A Seasonal-Trend Decomposition Procedure Based on Loess. J. Off. Stat. 1990, 6, 3–33. [Google Scholar]
  45. Li, E.; Mu, X.; Zhao, G.; Gao, P. Multifractal detrended fluctuation analysis of streamflow in the Yellow River Basin, China. Water 2015, 7, 1670–1686. [Google Scholar] [CrossRef]
  46. Plocoste, T.; Pavón-Domínguez, P. Multifractal detrended cross-correlation analysis of wind speed and solar radiation. Chaos 2020, 30, 113109. [Google Scholar] [CrossRef]
  47. Yin, H.; Jin, D.; Gu, Y.H.; Park, C.J.; Han, S.K.; Yoo, S.J. STL-ATTLSTM: Vegetable price forecasting using STL and attention mechanism-based LSTM. Agriculture 2020, 10, 612. [Google Scholar] [CrossRef]
  48. Pamula, G.; Grech, D. Influence of the maximal fluctuation moment order q on multifractal records normalized by finite-size effects. Europhys. Lett. 2014, 105, 50004. [Google Scholar] [CrossRef]
  49. Baranowski, P.; Gos, M.; Krzyszczak, J.; Siwek, K.; Kieliszek, A.; Tkaczyk, P. Multifractality of meteorological time series for Poland on the base of MERRA-2 data. Chaos Solitons Fractals 2019, 127, 318–333. [Google Scholar] [CrossRef]
  50. Sankaran, A.; Krzyszczak, J.; Baranowski, P.; Devarajan Sindhu, A.; Kumar, N.P.; Lija Jayaprakash, N.; Thankamani, V.; Ali, M. Multifractal Cross Correlation Analysis of Agro-Meteorological Datasets (Including Reference Evapotranspiration) of California, United States. Atmosphere 2020, 11, 1116. [Google Scholar] [CrossRef]
  51. Kulmala, M. How particles nucleate and grow. Science 2003, 302, 1000–1001. [Google Scholar] [CrossRef]
  52. Schlesinger, R.B. The health impact of common inorganic components of fine particulate matter (PM2.5) in ambient air: A critical review. Inhal. Toxicol. 2007, 19, 811–832. [Google Scholar] [CrossRef] [PubMed]
  53. Venter, Z.S.; Aunan, K.; Chowdhury, S.; Lelieveld, J. COVID-19 lockdowns cause global air pollution declines. Proc. Nati. Acad. Sci. USA 2020, 117, 18984–18990. [Google Scholar] [CrossRef] [PubMed]
  54. Khare, V.R.; Vajpai, A.; Gupta, D. A big picture of urban heat island mitigation strategies and recommendation for India. Urban Clim. 2021, 37, 100845. [Google Scholar] [CrossRef]
  55. Veena, K.; Parammasivam, K.M.; Venkatesh, T.N. Urban Heat Island studies: Current status in India and a comparison with the International studies. J. Earth Syst. Sci. 2020, 129, 85. [Google Scholar] [CrossRef]
  56. Mohan, M.; Kikegawa, Y.; Gurjar, B.R.; Bhati, S.; Kandya, A.; Ogawa, K. Urban heat island assessment for a tropical urban airshed in India. Atmos. Clim. Sci. 2012, 2, 127–138. [Google Scholar] [CrossRef]
  57. Aiswarya, R.; Resmi, A.R.; Rahsha, C.T.; Dharman, S.; Adarsh, S.; Mamatha, M. Analyzing the effect of air pollutants on particulate matter concentrations of the tropical coastal city of Thiruvananthapuram, India by wavelet coherence. IOP Conf. Ser. Earth Environ. Sci. 2023, 1237, 012017. [Google Scholar] [CrossRef]
  58. Fattah, M.A.; Morshed, S.R.; Kafy, A.A.; Rahaman, Z.A.; Rahman, M.T. Wavelet coherence analysis of PM2.5 variability in response to meteorological changes in South Asian cities. Atmos. Pollut. Res. 2023, 14, 101737. [Google Scholar] [CrossRef]
  59. Plocoste, T. Multiscale analysis of the dynamic relationship between particulate matter (PM10) and meteorological parameters using CEEMDAN: A focus on “Godzilla” African dust event. Atmos. Pollut. Res. 2022, 13, 101252. [Google Scholar] [CrossRef]
  60. Johny, K.; Pai, M.L.; Adarsh, S. A multivariate EMD-LSTM model aided with Time Dependent Intrinsic Cross-Correlation for monthly rainfall prediction. Appl. Soft Comp. 2022, 123, 108941. [Google Scholar] [CrossRef]
  61. Sonwani, S.; Kulshrestha, U.C. PM10 carbonaceous aerosols and their real-time wet scavenging during monsoon and non-monsoon seasons at Delhi, India. J. Atmos. Chem. 2019, 76, 171–200. [Google Scholar] [CrossRef]
  62. Liu, Z.; Shen, L.; Yan, C.; Du, J.; Li, Y.; Zhao, H. Analysis of the Influence of Precipitation and Wind on PM2.5 and PM10 in the Atmosphere. Adv. Meteorol. 2020, 2020, 5039613. [Google Scholar] [CrossRef]
  63. Plocoste, T.; Carmona-Cabezas, R.; Gutiérrez de Ravé, E.; Jiménez-Hornero, F.J. Wet scavenging process of particulate matter (PM10): A multivariate complex network approach. Atmos. Pollut. Res. 2021, 12, 101095. [Google Scholar] [CrossRef]
  64. Çapraz, Ö.; Deniz, A. Particulate matter (PM10 and PM2.5) concentrations during a Saharan dust episode in Istanbul. Air Qual. Atmos. Health 2021, 14, 109–116. [Google Scholar] [CrossRef]
  65. Adarsh, S.; Sulaiman, S.; Murshida, K.K.; Nooramol, P. Scale-dependent prediction of reference evapotranspiration based on Multivariate Empirical Mode Decomposition. Ain Shams Eng. J. 2018, 9, 1839–1848. [Google Scholar] [CrossRef]
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Figure 1. Overall methodological framework.
Figure 1. Overall methodological framework.
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Figure 2. Fluctuation functions of PM2.5 and PM10 for the three cities. Upper panels show the plots of PM2.5 and lower panels show the results of PM10.
Figure 2. Fluctuation functions of PM2.5 and PM10 for the three cities. Upper panels show the plots of PM2.5 and lower panels show the results of PM10.
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Figure 3. Comparison of Renyi exponent plot and multifractal spectrum of PMs for the three cities.
Figure 3. Comparison of Renyi exponent plot and multifractal spectrum of PMs for the three cities.
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Figure 4. Renyi exponent and multifractal spectrum of gaseous pollutant time series for the three cities.
Figure 4. Renyi exponent and multifractal spectrum of gaseous pollutant time series for the three cities.
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Figure 5. Renyi exponent and multifractal spectrum of meteorological time series for the three cities.
Figure 5. Renyi exponent and multifractal spectrum of meteorological time series for the three cities.
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Figure 6. MFCCA of PM2.5 with meteorological parameters for Chennai. Last column depicts scaling correlations between the paired variables.
Figure 6. MFCCA of PM2.5 with meteorological parameters for Chennai. Last column depicts scaling correlations between the paired variables.
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Figure 7. MFCCA of PM2.5 with gaseous pollutants for Chennai. Last column depicts scaling correlations between the paired variables.
Figure 7. MFCCA of PM2.5 with gaseous pollutants for Chennai. Last column depicts scaling correlations between the paired variables.
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Figure 8. MFCCA of PM10 with meteorological parameters for Chennai. Last column depicts scaling correlations between the paired variables.
Figure 8. MFCCA of PM10 with meteorological parameters for Chennai. Last column depicts scaling correlations between the paired variables.
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Figure 9. MFCCA of PM10 with gaseous pollutants for Chennai. Last column depicts scaling correlations between the paired variables.
Figure 9. MFCCA of PM10 with gaseous pollutants for Chennai. Last column depicts scaling correlations between the paired variables.
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Figure 10. Comparison of Renyi exponent plot and multifractal spectrum of precipitation data of the three cities.
Figure 10. Comparison of Renyi exponent plot and multifractal spectrum of precipitation data of the three cities.
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Figure 11. MFCCA of rainfall (R) with PMs for Chennai. Last line depicts scaling correlations between the paired variables.
Figure 11. MFCCA of rainfall (R) with PMs for Chennai. Last line depicts scaling correlations between the paired variables.
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Table 1. Multifractal properties of different variables for the three cities.
Table 1. Multifractal properties of different variables for the three cities.
VariableHWAIΔh(q)ΔHα0
(a) Chennai
PM2.50.5251.042−0.286−0.5870.5810.683
PM100.6420.647−0.316−0.3610.3410.736
RH0.8130.3800.8350.5820.2000.823
T0.8140.7360.8850.9660.4500.830
U0.6710.2410.8150.4560.0910.670
SR0.7430.3230.9200.6190.1560.749
NOx0.6641.5950.2460.2911.0650.870
O30.7000.5260.2000.2070.2530.739
SO20.7590.2310.7250.3650.1120.770
CO0.7140.8680.3800.3000.5420.786
(b) Hyderabad
PM2.50.7610.7980.2850.3490.4840.859
PM100.6580.5540.2380.2070.3330.730
RH0.7101.1020.7050.8970.7100.748
T0.8070.9390.1540.1770.5840.943
U0.6500.5530.2770.2840.3130.711
SR0.6910.7180.3260.3200.4270.766
NOx0.9610.8890.5740.6230.5741.022
O30.8621.0470.3570.4010.7070.997
SO20.7960.834−0.135−0.1300.5691.008
CO0.7780.6370.1390.0830.3290.827
(c) Vishakhapatnam
PM2.50.7490.6170.1690.1370.4000.849
PM100.7290.5360.2140.1700.3330.804
RH0.7280.4120.5180.3820.2360.763
T0.8610.717−0.193−0.2050.4441.007
U0.7340.3230.0730.0210.1780.773
SR0.6120.5850.1700.1200.3400.682
NOx0.7220.468−0.238−0.2220.2480.790
O30.6531.4110.3520.5440.9390.820
SO20.9090.5440.3120.2560.3560.991
CO0.8570.6650.2520.2660.3900.936
Table 2. Multifractal parameters for different variables at Chennai: Hx stands for persistence property of PM, Hy stands for the persistence property of the variable (MV or GP), Hxy stands for the joint persistence; Wx is the spectral width of PM, Wy is the spectral width of the variable (MV or GP), Wxy is the spectral width of the joint spectra; AIx is the asymmetry index of the spectrum of PM, AIy is the asymmetry index of the spectrum of the variable (MV or GP), AIxy is the asymmetry of the joint spectra; ρs stands for the seasonal correlation, ρa stands for the annual correlation and ρ is the overall correlation.
Table 2. Multifractal parameters for different variables at Chennai: Hx stands for persistence property of PM, Hy stands for the persistence property of the variable (MV or GP), Hxy stands for the joint persistence; Wx is the spectral width of PM, Wy is the spectral width of the variable (MV or GP), Wxy is the spectral width of the joint spectra; AIx is the asymmetry index of the spectrum of PM, AIy is the asymmetry index of the spectrum of the variable (MV or GP), AIxy is the asymmetry of the joint spectra; ρs stands for the seasonal correlation, ρa stands for the annual correlation and ρ is the overall correlation.
Variable PairHxHyHxyρsρaρWxWyWxyAIxAIyAIxy
PM2.5-RH0.5620.8140.6880.2530.2420.2151.0540.3270.6390.210−1.3550.313
PM2.5-T0.5620.8150.688−0.149−0.108−0.1571.0540.7240.5930.210−1.1030.064
PM2.5-U0.5620.6580.610−0.161−0.068−0.1441.0540.3120.4220.210−0.6980.284
PM2.5-SR0.5620.6990.631−0.095−0.408−0.1901.0540.4030.3850.210−1.0430.107
PM2.5-NOx0.5620.6560.6090.0290.1900.1621.0540.6060.3280.210−0.062−0.206
PM2.5-O30.5620.7400.651−0.106−0.0530.0041.0540.3040.3950.210−0.676−0.076
PM2.5-SO20.5620.7120.6370.0080.112−0.0121.0540.9420.6990.210−0.569−0.455
PM2,5-CO0.5620.7310.6460.2450.1810.1901.0540.2330.3470.210−1.406−0.141
PM10-RH0.6470.8140.7300.3350.1770.2300.6440.3270.4440.000−1.3550.071
PM10-T0.6470.8150.731−0.376−0.294−0.2730.6440.7240.4370.000−1.103−0.244
PM10-U0.6470.6580.6520.0430.3400.0520.6440.3120.2140.000−0.6980.173
PM10-SR0.6470.6990.6730.0830.1450.0130.6440.4030.3180.000−1.043−0.041
PM10-NOx0.6470.6560.651−0.054−0.2720.0280.6440.6060.2300.000−0.062−0.183
PM10-O30.6470.7400.693−0.0670.1140.0670.6440.3040.2760.000−0.676−0.104
PM10-SO20.6470.7120.6790.023−0.0660.0220.6440.9420.6060.000−0.569−0.403
PM10-CO0.6470.7310.689−0.027−0.397−0.0420.6440.2330.0520.000−1.406−3.526
Table 3. Nature of scaling correlations between different paired variables for the three Indian cities. If the correlation is positive over the complete scale range, it is marked as P, while negative correlation over the complete scale range is marked as N, and if the scaling correlations are positive at some scale and negative at some other scale, they are marked as mixed (M).
Table 3. Nature of scaling correlations between different paired variables for the three Indian cities. If the correlation is positive over the complete scale range, it is marked as P, while negative correlation over the complete scale range is marked as N, and if the scaling correlations are positive at some scale and negative at some other scale, they are marked as mixed (M).
Variable PairChennaiHyderabadVishakhapatnam
PM2.5-RHPNM
PM2.5-TNMM
PM2.5-UMNM
PM2.5-SRNMM
PM2.5-NOxMMP
PM2.5-O3MPM
PM2.5-SO2MMM
PM2.5-COMPP
PM10-RHPNM
PM10-TMMM
PM10-UMNN
PM10-SRMPM
PM10-NOxMPP
PM10-O3MMP
PM10-SO2MMM
PM10-COMPP
Table 4. Multifractality of precipitation data for the three cities.
Table 4. Multifractality of precipitation data for the three cities.
CityHWAIΔh(q)Δfα0
Chennai0.6641.5950.2460.2911.0650.870
Hyderabad0.6922.3920.3890.3681.9391.106
Vishakhapatnam0.4642.5220.133−0.1431.9811.028
Table 5. Multifractal cross-correlation between precipitation and PMs data for the three cities: Hx stands for persistence property of PM, Hy stands for the persistence property of R, Hxy stands for the joint persistence; Wx is the spectral width of PM, Wy is the spectral width of R, Wxy is the spectral width of the joint spectra; AIx is the asymmetry index of the spectrum of PM, AIy is the asymmetry index of the spectrum of AI, AIxy is the asymmetry of the joint spectra; ρs stands for the seasonal correlation, ρa stands for the annual correlation and ρ is the overall correlation.
Table 5. Multifractal cross-correlation between precipitation and PMs data for the three cities: Hx stands for persistence property of PM, Hy stands for the persistence property of R, Hxy stands for the joint persistence; Wx is the spectral width of PM, Wy is the spectral width of R, Wxy is the spectral width of the joint spectra; AIx is the asymmetry index of the spectrum of PM, AIy is the asymmetry index of the spectrum of AI, AIxy is the asymmetry of the joint spectra; ρs stands for the seasonal correlation, ρa stands for the annual correlation and ρ is the overall correlation.
CityVariable PairHxHyHxyρsρaρWxWyWxyAIxAIyAIxy
ChennaiPM2.5-R0.5620.7270.6440.0640.3830.0121.0541.3460.8000.210−0.251−0.229
HyderabadPM2.5-R0.8620.6410.751−0.181−0.199−0.1040.6993.3641.349−0.211−0.344−0.251
VishakhapatnamPM2.5-R0.8070.5180.663−0.306−0.042−0.1250.5843.8671.339−0.039−0.2750.021
ChennaiPM10-R0.6470.7270.6870.0440.020−0.0440.6441.3460.8360.000−0.251−0.195
HyderabadPM10-R0.7850.6410.713−0.245−0.216−0.1450.5323.3641.336−0.117−0.344−0.251
VishakhapatnamPM10-R0.7530.5180.636−0.281−0.465−0.1630.4493.8671.2620.026−0.2750.000
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Sankaran, A.; Rajesh, S.M.; Bahuleyan, M.; Plocoste, T.; Santhoshkhan, S.; Lekha, A. Scaling Correlation Analysis of Particulate Matter Concentrations of Three South Indian Cities. Pollutants 2024, 4, 498-514. https://doi.org/10.3390/pollutants4040034

AMA Style

Sankaran A, Rajesh SM, Bahuleyan M, Plocoste T, Santhoshkhan S, Lekha A. Scaling Correlation Analysis of Particulate Matter Concentrations of Three South Indian Cities. Pollutants. 2024; 4(4):498-514. https://doi.org/10.3390/pollutants4040034

Chicago/Turabian Style

Sankaran, Adarsh, Susan Mariam Rajesh, Muraleekrishnan Bahuleyan, Thomas Plocoste, Sumayah Santhoshkhan, and Akhila Lekha. 2024. "Scaling Correlation Analysis of Particulate Matter Concentrations of Three South Indian Cities" Pollutants 4, no. 4: 498-514. https://doi.org/10.3390/pollutants4040034

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