Descriptive statistics for all the pollutants are summarized in Table 2: the measures of central tendency are median and mean; the measures of dispersion are standard deviation (SD) and interquartile range (IQR); the measure of normality is the Shapiro–Wilk (S–W) test; and the measure of spatial autocorrelation and clustering is global Moran’s I.
The two PM size fractions exhibited similar values in both seasons (mean and median), with greater variation in the winter (SD and IQR), whereas δC exhibited larger values and greater variance in the winter. δC exhibited negative values, indicating that elemental carbon was always greater than organic carbon. The distributions could be considered statistically normal (S–W ≥ 0.95), and both PM fine fractions, as well as δC, exhibited significant spatial autocorrelation (Moran’s I) and clustering (Florax et al. 2003) in both seasons. Spatial autocorrelation was lower for both PM size fractions in the summer.
Summer LUR models
Lag and error SAR models for summer 2015 are summarized in Table 3.
All three summer models yielded identical sets of significant predictors. These sets comprised: two industrial indicators, i.e., industrial land use (within a 1000-m buffer) and the respective PM emitters (in all cases within a 3000-m buffer); one traffic indicator, i.e., collector roads within a 500-m buffer; and elevation. In terms of goodness of fit, the adjusted pseudo R2 lay around 0.60 for both PM2.5 models, around 0.70 for the PM10 models, and around 0.80 for the δC models. Consistent with AIC, these results indicate a slightly better performance of the lag model for PM2.5 and δC, whereas the error model performed slightly better for PM10. RSS exhibited consistent values for PM2.5 and δC in contrast with higher values for PM10. The intercept for PM2.5 was high in SARerr (+ 29.7% compared to the maximum observed PM2.5 concentration) while it was similar to the median observed value (Table 2) for SARlag. Likewise, the intercept for PM10 in SARerr was higher than SARlag (+ 56.4% vs + 9% compared to the maximum observed PM10 concentration). For δC, the intercept of SARerr was as well high compared to the maximum observed δC. For these reasons, SARlag was the preferred model in all cases, and will be used to estimate fine-scale concentration levels.
Winter LUR models
Lag and error SAR models for winter 2016 are summarized in Table 4.
The winter models for all pollutants yielded similar sets of predictors, which were also consistent with the summer models. Significant predictors were: industrial indicators, i.e., land use within 1000 m; the respective PM emitters within 6000 m; traffic indicators, i.e., local roads within 100-m or major roads within a 750-m buffer; and elevation; in addition, commercial land use within 500 m was marginally significant only for PM2.5. The rank order of significance of the predictors varied across models.
Overall, the winter models achieved greater goodness of fit than the summer ones, with adjusted pseudo R2 around 0.86 for PM2.5 and δC, and in the high 0.70 s for PM10. The two PM2.5 models were similar, with slightly lower AIC and RSS for SARlag. The intercept of SARerr was again high (+ 83% compared to the maximum observed PM2.5 concentration) while it was + 7% for SARlag. For PM10, the SARlag model achieved lower AIC and RSS, as well as a lower intercept. For δC, the two models were very similar, with lower RSS, AIC, and intercept for SARlag. Hence, SARlag was, again, the preferred model in all cases, and will be used to estimate fine-scale concentration levels for the winter.
Estimated concentration surfaces
Using the coefficients yielded by the SARlag models summarized in Tables 3 and 4, PM2.5, PM10, and δC concentrations were estimated, for summer 2015 and winter 2016, for the whole city. The estimation scale was the Dissemination Block (DB) level (Statistics Canada 2011), i.e., more than 7100 points within the urban area.
Descriptive statistics were calculated on the estimated DB level concentrations (Table 5) in order to compare them with the observed ones (Table 2) as a map accuracy assessment.
With respect to central tendency, the tables show that the medians of the estimated values were similar to those of the observed ones, with the estimated values slightly lower (< 5%), with the exception of winter PM10 (+ 8%) and summer δC (− 42%). Estimated mean values were similar to the observed ones, again with the single exception of summer δC (− 29%). The interquartile range was generally lower in the estimated values (by 19% to 38%), with the exception, again, of winter PM10, where it was 8% higher. As well, the standard deviation of the estimated values was similar to that of the observed values. Overall, the pollutants’ estimations exhibited slightly lower values than the observed concentrations and with lower dispersion. Notably, the sample size of the estimated values was over 70 times larger than the observed ones, which may affect the comparability of the statistics.
DB-level PM2.5 and PM10 estimated concentration maps obtained from SARlag model coefficients are shown in Fig. 2 for summer 2015 and in Fig. 3 for winter 2016. DB-level δC estimated concentration maps, obtained with the same method, are presented in Fig. 4.
The estimated concentration surfaces for the two PM size fractions exhibited consistent patterns, with elevated values over the industrial areas and the road network. PM2.5 exhibited a higher background level outside these areas, with a more diffused pattern. For both fine fractions, maps show slightly higher concentrations in the eastern part of the city, according to the prevailing winds, captured by the spatial autoregressive term, which are westerly in the summer and northwesterly in the winter.
Winter and summer surfaces are mapped using a consistent classification for each pollutant. For both fine fractions, the estimated winter spatial patterns exhibited association with industrial zones and with the road network. The association with the local road network was more pronounced in winter than summer. They both exhibited higher concentrations over the east.
The summer estimated concentration surface of δC presented slightly positive values and exhibited a sharp contrast between low concentrations in the west quadrants versus high concentrations in the east quadrants: the industrial areas emerged clearly even from the eastern polluted background. The winter map exhibited a more consistent pattern of pollution over all quadrants. In the winter, pollution also radiated more gradually from industrial areas.
PM models for summer 2010 and winter 2011
A corresponding campaign was conducted for PM2.5 and PM10 in summer 2010 (August 4–18) and winter 2011 (January 29–February 11), deploying 50 monitors within the city limits with the allocation strategy described above. Due to power outages, equipment failures, and other interferences, the campaign yielded only 27 valid samples in the summer and 29 in the winter. Due to the unpredictable nature of the malfunctions, the spatial sample was more random than planned (Zhang et al. 2015; Bertazzon et al. 2016). Descriptive statistics are summarized in Table 6.
In summer 2010, both PM fractions exhibited greater (mean and median) values than in winter 2011, yet both fine fractions exhibited greater variability (IQR, standard deviation) in the winter. Both fine fractions could be considered normal in the winter (S–W ≥ 0.95) but not in the summer (S–W ≤ 0.95). Neither fine fraction exhibited significant spatial autocorrelation in either season.
In light of these results, standard regression methods, i.e., OLS, were employed to estimate the LUR models, summarized in Table 7.
Summer 2010 LUR models yielded one industrial indicator and two traffic indicators. For both PM size fractions, adjusted R2 lied in the low 0.70 s and residual spatial autocorrelation was not significant. RSS for PM10 was approximately twice as large as for PM2.5. Similarly, the intercept of PM10 was approximately twice as large as that of PM2.5.
Winter 2011 LUR models were less consistent. For both fine fractions they featured two industrial indicators, i.e., industrial land use (over buffers ranging greatly in size) and PM emitters over identical buffers; the third predictor was major roads for PM2.5, and park land use, with negative coefficient, for PM10. For both fine fractions, adjusted R2 lied around 0.50 and residual spatial autocorrelation was not significant. RSS of PM10 was approximately four times larger than that of PM2.5, and the intercept of PM10 was approximately twice that of PM2.5.