**1. Introduction**

Nowadays, most cities have an increasing environmental problem related to air pollution [1–4]. This specific pollution is a continuing threat to human health and welfare, with a range of different sources generating different pollutants which have distinct health effects on urban populations [5–7]. Detailed air quality monitoring data for pollutants, such as carbon monoxide (CO), nitrogen oxides (NO and NO2), sulphur dioxide (SO2), ozone (O3) and particulate matter (PM10 and PM2.5), are becoming more important because of the health problems said pollutants can cause in living beings [6]. The measurements of pollutants provide real-time data to inform the public and provide a mechanism of alerting local residents of a possible hazard. In particular, pollutant sources from traffic emissions, such as NOx, which represents a combination of nitrogen oxide (NO) and nitrogen dioxide (NO2), are typically emitted at ground level from vehicles and are associated with health-related problems [8].

Despite a reduction in emissions from the transport sector, an increasing trend in NO2 concentrations has been observed in a number of different European countries; for example, the United Kingdom and Ireland [9,10]. Therefore, meeting the standards and air quality guidelines by European and national environmental agencies for pollutants such as NO2 is becoming more challenging [9], as exceedances of pollutant concentrations can lead to short-term, chronic human health problems [11].

On the other hand, it is understandable that occasional values in polluted air samples behave as outliers in an urban environmental database. They can be classified as local outliers [12,13] or global outliers. Unlike global outliers, local outliers can be detected by comparison with near neighbours. For the purpose of air pollution studies in urban areas, global outliers that deviate from the guide values indicate that there may be a significant source of pollution. Observations which are not excessively high but are different from neighbouring values may also contain information on unusual processes such as pollution. Outliers may merely be noisy observations, or alternatively, they may indicate atypical behaviour in the system. These abnormal values are very important and may lead to useful information or significant discoveries, but also contribute to the selection of the most suitable mitigation techniques or measures [14].

Different techniques of functional data analysis (FDA) have been used in vectorial problems. This new methodology appeared due to the inefficiency of the classical data mining techniques treating vector data [15]. FDA is applicable in a multitude of fields, such as environmental [16–19] and medical research [20], and is applicable for sensors [21,22] and industrial methods [23,24]. The functional model is based on two ideas that make it unique: it takes into account the time correlation structure of the data and leads to a global view of the problem through curves analysis instead individual observations. This analysis is focused on the comparison of the curves using the functional depths, a variable that measures the centrality of a given curve within a set of curves [25]. Functional depth has already been used in several environmental problems [26,27].

The aspiration of this research is to create a model to detect air pollution episodes and identify outliers in gaseous emissions, and to validate this method using real world data from a suburban air quality monitoring site in Dublin, Ireland. Although many methods are known to identify outliers (from the classical Grubbs test [28] to a test proposed in 2019 by [29]), they are all based on the vector approach. This study was carried out, on one hand, with conventional methods, and on the other hand, with a functional approach; a comparative study between the two methodologies is presented. Each method will be presented and the findings will outline the most effective method for detecting outliers in air pollution monitoring data to enhance its capacity for informing new measures to improve local air quality.
