3.2.3. Trend Analysis

Using the hourly NO2 concentration data, a trend analysis was undertaken to examine the diurnal patterns and identify outliers. Figure 10 shows the box plots of hourly emissions over 365 days and represents the mean, the confidence interval of this mean, quartiles and abnormal values in red that. This way it is possible to studying individually the distribution of the NO2 emissions in each hour of the day.

**Figure 10.** Hourly box plot of NO2 concentrations from Blanchardstown air quality monitoring station. Software: Python [57].

In Figure 11, where only the mean values have been represented, two maximum values were analysed, at 9 a.m. and 7 p.m., which correspond to heavy traffic hours in this area of Dublin. These two hours, as can be seen in Figure 10, also have high variability (wide boxes), and around them there are numerous outliers.

**Figure 11.** Mean hourly NO2 concentrations from Blanchardstown air quality monitoring station. Software: Python [57].

It can also be seen in these figures that the absolute minimum is 4 a.m., which also corresponds to the hour with the least variability in the NO2 concentration. If a daily analysis approach is considered throughout the year (Figure 12), it is clear that Wednesday, Thursday and Friday are the days with the highest NO2 concentrations.

**Figure 12.** Daily analysis of NO2 concentrations at Blanchardstown air quality monitoring station. Software: R-programming [56].

Blanchardstown contains the largest shopping centre in Ireland and the most major motorway nearby; because of this, there is a lot of traffic when rush hour and evening shopping are combined in this area. On the other hand, there are lower concentrations during the weekend, although not as low as expected. This is because the largest shopping centre in the country is very busy at weekends, especially during Christmas period.

In this case, a SPC gives us more information than the previous analysis, such as the differences in the NO2 levels between days or hours. However, it still does not take into account the complete daily behaviour of NO2 emissions from correlated hourly measurements.

### *3.3. Functional Analysis of NO2 in Dublin*

The subsequent step in the functional methodology is to compare the results between the classical analysis and the SPC. In the functional methodology, the first thing to do is to build a sample of curves based on the discrete values measured every hour. Figure 13 shows the 365 functions generated with 24 hourly data. Once the data are transformed into functional data, i.e., daily curves of 24 values, each of them takes into account the correlation between the hourly NO2 values and can be analysed for outliers.

**Figure 13.** Data represented in functional form (functions): 365 daily curves of NO2 emissions. Software: R-programming [56].

The results obtained with the functional analysis, taking into account the depths, allow us to identify days with abnormal functional values, even if, discreetly, they are not outliers. Despite not exceeding the daily limit values, the concentration of NO2 over a whole day may have an abnormal behaviour. For this reason the vectorial analysis, like SPC, does not ge<sup>t</sup> to detect these days. In a different way, the functional approach detects any deviation from normal daily behaviour in the emissions of NO2, without relying on any distribution restrictions. This is shown in Figure 14 where the functional outliers found in this case study are presented.

**Figure 14.** NO2 functional data; and in the dark grey and dotted line, the functional outliers detected. Highlighted is the 11th day which is also an outlier. Software: R-programming [56].

The data analysed were not discretely outside the limits values; however, functionally excessive variations were observed on specific days. It can be deduced that there were no NO2 pollution problems in 2013 because hourly, daily and annual NO2 concentration limits were not exceeded. But it is also important to analyse whether there are hours or days with anomalous trends of NO2 concentrations, although they remain within legal limits. The NOx (NO, NO2) is an pollutant not coming from a natural source ([58]), and for this reason also, its involvement in the mechanisms of depleting the ozone layer are very unfortunate. The FDA methodology has proven to be very effective in detecting days with trends that are not the same as the rest of the data. It is important not only to analyse whether the contamination is within the allowed limits, but also to find days that are different than expected.

For example, on the 11th day, detected by the functional approach and highlighted in the Figure 14, with the results obtained through the SPC, as can be seen in Figure 8, this day has a higher mean, but it is within the limit values. Neither using the classical analysis (Figure 1) with individual time series nor the one with the corresponding statistical parameters, it could be considered an outlier. Figure 14 shows a strength of the functional approach by detecting this curve as an atypical day; it will be possible to study the reasons that lead the NO2 to behave this way on this particular day. In fact, there are several studies that demonstrate the greater power of the functional approach for detecting outliers than other methodologies (see [17,59]). There are also studies that, specifically, show that the depth measure used here (*h-modal*) is the one that achieves the lowest error rates [50].

To find a reason that explains the anomalous behaviour on those days, it would be necessary to have greater traceability of the most important sources of NO2 emissions. It would be necessary to have data relating to the weather conditions, traffic movements, industry sources affecting the study area, etc. For example, incorporating weather conditions, i.e., temperatures, sunshine hours and precipitation, could improve the assessment of outliers. The detection of outliers and air pollution episodes can help to separate the causes of normal and specific variability, and is a first step towards the effective design and implementation of mitigation measures. Although the only reason for these outliers is possibly not the weather conditions, as can be seen in Table 2, those days were colder than usual; had very little precipitation; and in general, had fewer sunshine hours than the average for the month.

**Table 2.** Sample of other environmental characteristics from Dublin (temperature, sunshine and precipitation) which may impact hourly NO2 concentrations measured at Blanchardstown air quality monitoring station. The averages shown represent the monthly average of each variable.

