Concentration during Odd-Even Rule in Delhi Using Causal Analysis

PM2.5 concentration observed during odd-even rule in Delhi is analysed for assessing its effectiveness in curbing the levels. The local and regional influence is analysed by using similarity and causality analysis. Causality analysis is usually carried out by using nonlinear dynamical technique which predicts one variable using another. In this study a simple approach is presented based on nearest neighbour method. It is observed that PM2.5 in Delhi has regional influence in addition to local sources. Although the effectiveness of odd-even rule is not observed in curbing the PM2.5 levels, it is suggested that extended implementation of the rule may provide more insight to the impact. Similarity analysis suggested that PM2.5 concentrations in Delhi have somewhat similar temporal behaviour with neighbouring locations in the southeast (SE) and west (W)-southwest (SW) sector. The control policies in Delhi need to be adopted keeping in mind the local and regional influences on PM2.5 levels in the area.


INTRODUCTION
Delhi, the national capital of India, is tagged as one of the world's most polluted cities with respect to PM 2.5 concentration (WHO, 2016).Air pollutant concentrations are mostly observed to exceed the standards by Central Pollution Control Board (CPCB) and World Health Organization (WHO).PM 2.5 is one of the critical parameters, exposure to which causes bronchitis, allergies, stroke, lung cancer, heart disease, pulmonary disease and even premature deaths due to these diseases (Chowdhury and Dey, 2016).In Delhi, several studies have reported high PM 2.5 concentration exceeding the CPCB standards of 60 µg m -3 at almost all the sites (Tiwari et al., 2014;Trivedi et al., 2014;Pant et al., 2015).According to WHO (2016), average PM 2.5 concentration of 122 µg m -3 was observed at 10 locations in Delhi.This is more than the standard limit stipulated by CPCB and WHO.In a survey on PM 2.5 levels in Delhi, it was observed that the annual PM 2.5 averages of Delhi were higher than that of Beijing (The Financial Express, 2015).Delhi has many power plants (two coal based and four natural gas based).Road transport is intense in the area due to being a metropolitan, political, industrial and commercial hub.Diesel and gasoline based cars, private vehicles, heavy duty vehicles, Compressed Natural Gas (CNG) based public transport vehicles, utility vehicles and metro rail define the transportation system in the city (Pant et al., 2015).In-spite of the several control measures including EURO III and EURO IV norms incorporated to curb the pollution levels, Delhi has not yet witnessed a decline in the air pollutant concentrations (Kumar et al., 2015).There is continuous uproar at public and political level on the rising air pollution levels.Considering this, government of Delhi decided to bring down the air pollution levels by adopting the control strategies such as odd-even rule.The odd registration number vehicles were allowed on the road on odd date and even registration number can ply on the road only on the even date.CNG vehicles and women were exempted from the rule.With this it was expected to reduce the number of plying vehicles on the road which ultimately will bring down the air pollution levels.Similar rules were imposed in many places around the world like Beijing, Paris and Mexico.A question however remains on the effectivity of odd-even rule in bringing down the particulate matter levels in the area.
It is of debate that whether the rising levels of air pollution in Delhi can be attributed to the burning of stump and other waste in the neighbouring states?The related question has been raised in various forums (First Post, 2016).
To study this, one needs to carry out analysis of contributions from regional sources through suitable techniques in addition to the local analysis.To study local source contributions, source apportionment studies based on chemical mass balance, factor analysis and positive matrix factorization are applied that uses chemical composition of particulate matter (Lu et al., 2016;Parthasarathy et al., 2016).For this, however one needs to sample the particulate matter using monitoring instruments that incorporate filter papers which can further be utilized for chemical characterization.These samplers however do not provide continuous data rather the sampling period is sporadic and therefore do not provide full temporal and spatial coverage.Online continuous monitors do not provide or use filter papers but provide particulate matter concentration data which is continuous and covers many sampling locations.Unlike the above source apportionment techniques, another way to get the information from these data is the use of back-trajectory analysis which can trace back the source regions of the pathways and provide the information on prospectus sources.Growing number of studies have carried out source apportionment of particulate matter in Delhi and other cities of India.Pant et al. (2015) have provided a detailed literature review on such studies.Recently Ghosh et al. (2014) carried out the study on assessing the regional and subregional contribution to aerosols in Delhi from neighbouring country of Pakistan and adjacent states of Punjab, Haryana and Uttar Pradesh.Trajectory clustering and concentrationweighted trajectory showed the significant contribution of these areas to aerosol concentrations in the Delhi region.A more rigorous study and review on the air pollution problem in Delhi is given in a recent study by Kumar et al. (2015).
Recently temporal analysis of air pollution is carried out from local and regional perspective by Chen et al. (2016) and Xu et al. (2008).Here only the data on local air quality along with the regional air quality is required for this purpose.For similarity analysis, cross correlation spectral matching (CCSM) was used to compare the local air quality with regional air quality.The correlation coefficient is computed, the interpretation of which is like usual correlation coefficient.Further, causality analysis was proposed for detecting the causality between the two variables based on convergent cross mapping (CCM) approach, which was initially proposed by Sugihara et al. (2012).By analysing the temporal patterns in two variables, the interactions among them can be understood by output convergence map.Sugihara et al. (2012) proposed using nonlinear dynamical technique to obtain the predictive mapping for the two variables.The technique is however computationally cumbersome and require the selection of few parameters such as time delay lag, which may be subjective.Although Chen et al. (2016) argued that the selection of parameters does not influence the results; one other limitation of this technique is the assumptions of nonlinear attractor dynamics of the system, which is always not present.
Whether the odd-even rule has resulted in the much needed benefit of curbing the rising PM 2.5 pollution, the study is initiated to analyse the temporal patterns in the levels during the period of implementation.To study the local and regional influences on PM 2.5 levels in Delhi, similarity analysis and causality analysis are carried out on hourly data during the odd-even periods in and around Delhi.A method based on nearest neighbour techniques is proposed to carry out causality analysis instead of using nonlinear dynamical systems approach.

DATA USED
Central Pollution Control Board (CPCB), Delhi, has close watch on air pollution levels in many cities in India.In Delhi, it has kept continuous monitoring system to monitor various pollutants such as PM 10 , PM 2.5 , Ozone, NO x , SO 2 , CO etc.The data generated provides a platform to analyse it from various perspectives like source apportionment including the assessment of contributions from local and regional sources, long term temporal and spatial distribution and exposure studies.With the objective of assessing the influence of imposed odd-even rule in Delhi, hourly PM 2.5 data during January 1-15, 2016 and April 16-30, 2016 is considered.During this period, the odd-even rule was implemented in Delhi.The data is selected from the CPCB operated sites namely, Mandir Marg, Shadipur, RK Puram, Punjabi Bag and Dwarka.The data is available from the website of CPCB.In order to assess the regional contribution, PM 2.5 data is also obtained for the adjacent and surrounded areas in three states, Haryana, Rajasthan and Uttar Pradesh.In these states, monitored PM 2.5 data is available for cities rather than the stations.The study area map of four states along with the cities where monitored data are available is given in Fig. 1.Hourly PM 2.5 data averaged over the city is available on CPCB website.The sites belonging to Delhi are given in the lower map of Fig. 1.The distance of Mandir Marg with Shadipur, RK Puram, Punjabi Bag and Dwarka is about 6.2, 12, 12, 22 kms, respectively.The distance of Shadipur with RK Puram, Punjabi Bag and Dwarka is about 13, 5, 20 kms, respectively and the distance of RK Puram with Punjabi Bag and Dwarka is about 16.5 and 17 kms, whereas the distance of Punjabi Bag and Dwarka is about 21 kms.With total 7 locations from surrounding states and 5 local sites, analysis is performed separately for the two odd-even implemented periods, with January 1-15 as Period I and April 16-30 as Period II.15 days data before the Period I and Period II are also considered to study the variations in PM 2.5 levels.These two data sets are termed as pre-period I and pre-period II data.Further details on number of data points in each period is given in Table 1(a).

Similarity Analysis
Similarity analysis is carried out by computing the crosscorrelation function between variables Y and X over different points or lags t as; where r is the cross-correlation between y and x, y is the PM 2.5 concentration observed at Delhi and x is the PM 2.5 concentration observed at the neighbouring sites.The details of the method are given in Van Der Meer and Bakker (1997).

Causality Analysis
Causality analysis is carried out by Sugihara et al. (2012) and Chen et al. (2016) using convergent cross mapping approach for complex ecosystem and air quality index, respectively.Here two time series variable's data is required to analyse the interactions according to an output convergence map.The whole idea of the technique is to check; whether the predictability of one variable using the other variable can be ascertained.This is carried out by examining the predictability over time series of varying length L, which suggests the convergence of the output over L. Convergence means that cross-mapped estimate improves in estimation skill with time-series length L. The feedback relationships can also be studied between the two variables which reveal bidirectional causality (Chen et al., 2016).Sugihara et al. (2012) performed this analysis through the technique of dynamical systems theory.One limitation of this technique is the assumptions of nonlinear attractor dynamics of the system, which is always not present.Rather a simple model can be utilized to examine the predictability of one variable through another.Nearest neighbour approach provides a way to carry out such analysis by just computing the distance between the two time series variables and utilizing the minimum distance information at a point to estimate the corresponding variable.Below the methodology is given for the proposed method.
Let X is the time series of one variable which can be used as input to obtain the output variable Y.In this case PM 2.5 over different sites in Delhi can be considered as Y, whereas X is the time series of locations in the neighbouring states.X = x 1 , x 2 , …, x n and Y = y 1 , y 2 , …, y n .Here the length of X and Y is same.To obtain Y from X, distance matrix |Y -X| can be constructed over i = 1, 2, …, n.The k minimum distances and the indexes of the k nearest neighbours are noted down.The median of corresponding Y of k nearest neighbour indices represent Yest.The prediction capability of the approach can be obtained from using Index of Agreement (IOA) as, where P i is the predicted variable and O i is the observed variable.O ̅ is the mean of the observed variable.IOA ranges from 0 to 1 and presents the influence of one variable on the other.Lower IOA indicates predicted values have better agreement with observed values and vice versa.This modified index is not sensitive to extreme values (Legates and McCabe Jr, 1999).

RESULTS AND DISCUSSIONS PM 2.5 Concentration during the Study Period
The missing values in hourly PM 2.5 concentration observed during January 1-15, 2016 and April 16-30, 2016 were replaced by the average of the respective period.At few of the sites, high number of missing values can be observed.These were replaced with the average concentration of the respective site.It can be seen from Table 1(b) that PM 2.5 concentration during Period I is almost 2.5-5 times the 24hourly standard limit of 60 µg m -3 as stipulated by CPCB (2010).During Period II, it is almost 1.3-3.1 times the standard limit.For pre-period I, PM 2.5 is observed to be 1.9-4.3times higher than CPCB standard, whereas for preperiod II, it is 1.7-2.2times higher.Period II has less exceedance than Period I.During Period I, peak winter is observed in Delhi.Atmospheric conditions during this time do not allow the dispersion of air pollutants although the emissions are quite similar to other seasons.It may also be noted that the data is of hourly frequency, the standard is however available for 24-hourly concentration, that is deemed to be lower than for the high resolution data.
Comparing the average PM 2.5 concentration at different sites in Delhi to neighbouring locations, it can be observed from Table 1(c) that for Period I, PM 2.5 at Mandir Marg, RK Puram and Punjabi Bag is >200 µg m -3 and exceedance to standard is ≥ 4 times.Faridabad and Kanpur also showed the similarity in average and exceedance to standard.PM 2.5 at Shadipur and Dwarka is < 200 µg m -3 and exceedance to standard is ≤ 4 times, which is quite similar to Jaipur, Jodhpur and Lucknow.The percentage of missing values is quite high at Jaipur and Panchkula.For Period II, PM 2.5 concentration is observed to be < 200 µg m -3 .Shadipur, RK Puram, Punjabi Bag and Dwarka have PM 2.5 > 100 µg m -3 and exceedance to standard is ≥ 2 times, which is observed to be similar to Gurgaon, Faridabad, Jaipur and Kanpur.From both the periods, PM 2.5 at Faridabad and Kanpur is observed to be critical and quite similar to Delhi.Panchkula showed quite dissimilar behaviour in terms of average PM 2.5 concentration and exceedance to standard with PM 2.5 in Delhi.
The hourly variation of PM 2.5 at different locations is given in Fig. 2(a), which shows that the concentration is higher during night time and morning hours i.e., 0 h to 10 h and then decreases afterwards till 17-18 h.Thereafter it again increases.The concentration deteriorates immediately after the peak activity hours.In order to understand the diurnal variations further, average concentration is computed for 0-6 h, 7-11 h, 12-17 h and 18-23 h (Fig. 2(b)).Highest concentration is observed during 0-6 h followed by 18-23 h.During 12-17 h, lowest concentration is observed.This

Analysing PM 2.5 Levels during Odd-Even Rule
To analyse the PM 2.5 concentration during odd-even rule, pre-period I i.e., December 17-31, 2015 and pre-period II i.e., April 1-15, 2016 data were selected at the respective sites.A comparison analysis is given in Table 1(b).Comparing the average concentration during and before the implementation of the rule, it can be seen that the concentration has in fact increased during the odd-even rule at almost all the sites.It may however be noted that the number of missing values are quite higher during the pre-periods at most of the sites.This may be the reason for lower concentration before the implementation of the rule.So any conclusion based on too much missing data points will not be reasonable.A rigorous study therefore needs to be carried out to assess the influence of odd-even rule.Another contention is the accumulation or persistence of air pollutants.The persistence of PM 2.5 at a site in Delhi is shown in Chelani (2013).As can be seen, during the pre-period I and per-period II, PM 2.5 concentration has exceeded the CPCB limits from 1.7 to 4.3 times.Due to the persistence in air pollutants, higher concentrations tend to be followed by higher concentration and vice versa.If the

Period I Period II
persistence assumption for PM 2.5 concentration is extrapolated for entire Delhi, the effect of implementation of any policy instrument cannot be seen in near short duration, rather it needs to be implemented for the longer time span, which will allow accumulated pollutants to move out of Delhi environment.

Similarity Analysis
In order to assess the local and regional contribution of sources, similarity analysis is carried out.The crosscorrelation coefficient amongst the study locations and with the neighbouring locations is given in Table 2(a).It can be seen that the inter-locations correlation is strong (> 0.65) in Delhi except for Shadipur which has moderate correlation only with RK Puram.Although statistically significant at alpha (α) = 0.05 and/or 0.01 level of significance, the correlation between the sites in Delhi and neighbouring states is not strong.As can be seen from Tables 2(a) and 2(b), PM 2.5 at Mandir Marg, RK Puram and Punjabi bag is correlated with Faridabad; RK Puram with Jodhpur, Kanpur; Punjabi Bag with Kanpur and Dwarka with Lucknow.During Period II, significant but moderate (correlation < 0.5) inter-location correlation is observed like Period I except for Shadipur.PM 2.5 at Mandir Marg is observed to be significantly correlated with Gurgaon, Jaipur and Panchkula.PM 2.5 at Punjabi Bag is correlated with Faridabad and Jaipur.PM 2.5 at RK Puram is correlated with Gurgaon and Jaipur.Significant correlation is marked with bold in Tables 2(a) and 2(b).When looking at the wind pattern at all the locations, there is not much change in the predominant wind direction during Period I and Period II.Mostly SE to NW sector is observed to be predominant at all the sites.All the neighbouring locations are located in this patch (SE-W) except Panchkula which is in north direction.PM 2.5 concentration levels in Delhi have somewhat similar temporal behaviour with neighbouring sites located in the SE and W-SW sector.This correlation is however not strong but moderate (correlation < 0.5).Correlation of PM 2.5 at Panchkula is observed only with Mandir Marg and Dwarka that too with moderate correlation coefficient during Period II only.

Causal Analysis
Causality analysis is carried out further to assess the regional contribution to PM 2.5 levels in Delhi.As illustrated above, PM 2.5 is predicted at all the sites in Delhi using the PM 2.5 concentration at all the neighbouring locations one by one using nearest neighbour analysis.IOA is computed simultaneously over different time lengths.Figs.3(a)-3(c) and 4(a)-4(c) shows the variation of IOA over L for Period I and Period II, respectively.Ideally as the time length increases, prediction skill should improve.The summary of the causal behaviour is given in Table 3.If IOA increases with increase in IOA and stabilizes for last few time lengths, it indicates the convergences.Any increase in IOA over time  During Period I (Figs.3(a)-3(c)), all the locations have convergent cross mapping from Faridabad, Jaipur, Jodhpur and Kanpur.A sudden decreasing shift in IOA is observed for predicting PM 2.5 at Mandir Marg from Jaipur but convergence is achieved after L = 150.Prediction skill in terms of IOA gets stabilized for last two time lengths at L = 300 and L = 350.Convergence is therefore achieved for Mandir Marg from Jodhpur also.No convergence is observed for predicting PM 2.5 in Delhi from PM 2.5 at Lucknow.In order to understand the convergence pattern in terms of direction of the neighbouring location from Delhi, the stations are grouped in three sectors/directions; SE (Faridabad, Kanpur, Lucknow), W-SW (Gurgaon, Jaipur, Jodhpur) and N (Panchkula) as given in Table 3. Panchkula which is in the upward direction has shown convergent mapping for Mandir Marg only.This means that one can obtain predictions of PM 2.5 at most of the locations in Delhi from PM 2.5 at neighbouring locations from W to SW and SE sector.Predictability of Y from X however does not necessarily mean that X can be obtained through Y.It is also of interest to know whether the reverse mapping is convergent.Hence IOA is also obtained for predicting the neighbouring state's PM 2.5 from Delhi.For Faridabad, feedback mapping is    mapping is observed for Mandir Marg, Shadipur and Dwarka only.This indicates that Kanpur and Lucknow have less influence on PM 2.5 levels at all the locations in Delhi.As Faridabad is closer to Delhi, it has more influence than Kanpur and Lucknow in the SE direction.W-SW locations i.e., Gurgaon, Jaipur and Jodhpur influence the PM 2.5 levels in Delhi as predictions skill converges.Feedback mapping is observed from very few sites.The analysis suggested that the PM 2.5 concentration in neighbouring locations shows influence on PM 2.5 levels in Delhi which also has some reverse impact on the PM 2.5 levels of neighbouring locations.This is particularly observed for the neighbouring locations from SE and SW sector.The contribution of dust from surrounding areas is reported in many studies (Marrapu, 2012;Chelani, 2013;Kumar et al., 2015).In addition to the local sources, regional pollution therefore also influences the PM 2.5 levels in Delhi.The influence of Delhi's PM 2.5 on the PM 2.5 levels in the neighbouring areas is however less pronounced.
The above analysis by using similarity and causality analysis showed that the PM 2.5 concentration in Delhi is influenced by regional PM 2.5 levels in addition to local sources.Nearby stations such as Faridabad and Gurgaon with the stations in W-SW directions (Jaipur and Jodhpur) have more influence on PM 2.5 levels than the stations in SE direction (Kanpur and Lucknow).Northerly station Punchkula does not influence the PM 2.5 in Delhi.Hourly analysis suggested sudden fall in average PM 2.5 levels after the peak activity hours.High concentration in the morning hours is observed mainly due to low mixing height and the influence of local sources during the activity hours.Similarity analysis showed that although the correlation between the two locations is significant but not strong (< 0.5).Statistically, the temporal behaviour of PM 2.5 levels in Delhi is not similar to the temporal behaviour of PM 2.5 in neighbouring locations.This is the reason that bidirectional coupling is not consistent while predicting the PM 2.5 concentration at many neighbouring locations using PM 2.5 of Delhi.
Further, PM 2.5 pollution cannot be brought down immediately even if a combination of control instruments is adopted in Delhi as the above analysis suggested regional contribution in governing the PM 2.5 levels in the area.Hence, in addition to the adoption of strategies related to local source pollution, regional contribution should also be considered.

CONCLUSION
PM 2.5 concentration observed during two periods of oddeven rule in Delhi is analysed for assessing the effectiveness of the rule and influence of local and regional PM 2.5 concentration.It is observed that PM 2.5 concentration is Fig. 4(c).Index of Agreement over varying time length L for Period I for the neighbouring locations in N direction.higher during Period I, which was in winter than Period II which was in summer.While comparing the PM 2.5 levels in Delhi with neighbouring locations, it is observed that Faridabad and Kanpur are critical and quite similar in terms of average PM 2.5 and exceedance to standard concentration to Delhi.Hourly analysis showed the deterioration in PM 2.5 after the peak morning activity hours.While analysing the effectiveness of odd-rule in curbing the particulate matter levels in ambient air, it is observed that the concentration has in fact increased during the odd-even rule.The high number of missing values at few locations prevented to arrive at any conclusion.The extended implementation of the rule may enhance the insight into the success or failure of the proposed rule.Similarity analysis using cross-correlation function suggested that PM 2.5 concentrations in Delhi have somewhat similar temporal behaviour with neighbouring locations in the SE and W-SW sector.The correlation is however not strong but moderate.Causality analysis using proposed method based on nearest neighbour searching suggested that the PM 2.5 concentration in neighbouring locations, particularly from SE and W-SW sector shows influence on PM 2.5 levels in Delhi.The reverse or feedback coupling is however not consistent.This suggests the regional influence on PM 2.5 in Delhi in addition to the local sources.

Fig. 1 .
Fig. 1.Study area map with location of Delhi, sampling stations in Delhi and neighbouring cities in three states; Rajasthan, Haryana and Uttar Pradesh.

Fig. 2
Fig. 2(a).Hourly variation of PM 2.5 concentrations at different locations in Delhi during Period I and Period II.

Fig. 3
Fig.3(a).Index of Agreement over varying time length L for Period I for the neighbouring locations in W-SW direction.

Fig. 3
Fig. 3(b).Index of Agreement over varying time length L for Period I for the neighbouring locations in SE direction.
the convergence in mapping; N indicates no convergence; Y and N after / represents reverse mapping; -indicates no data.

Fig. 4
Fig.4(a).Index of Agreement over varying time length L for Period II for the neighbouring locations in W-SW direction.

Fig. 4
Fig. 4(b).Index of Agreement over varying time length L for Period I for the neighbouring locations in SE direction.

Table 1 (
a).Details on sampling dates and number of samples in each period at each location in Delhi.

Table 1 (b).
Statistical summary of PM 2.5 concentration in Delhi during Period I and Period II.

Table 1 (
c). Statistical summary of PM 2.5 concentration in neighbouring locations of Delhi during Period I and Period II.

Table 2 (
a). Similarity analysis for Period I.The significant correlation either at α = 0.05 or α = 0.01 is marked with bold.

Table 3 .
Convergent mapping of PM 2.5 in Delhi from the neighbouring locations.