Clustering Air Monitoring Stations According to Background and Ambient Pollution Using Hidden Markov Models and Multidimensional Scaling

Abstract

In order to study the cluster of monitoring sites from an urban air quality monitoring network (AQMN) with respect to the background and ambient pollution of key pollutants, a combined methodology is proposed: firstly, to obtain the ambient and background levels of air pollution from every selected pollutant, time series obtained from the AQMN were modeled with hidden Markov models; secondly, to study the grouping of these monitoring sites according to these levels of pollution, both ambient and background pollution, multidimensional scaling (Smacof MDS) was used and the stability of these solutions obtained with a Jacknife procedure (smacof library—R software). Results show that the clustering behaviour of sites is different when studying the ambient from the background pollution. However, sites marked with a distinct pollution contribution could locate them distant from the main cluster of sites as long as they show a marked stability in the MDS solutions.

1 Appendix

The aim of this appendix is to show how the values TS Mean (M) and TS SD (SD) are calculated for the TS of Torneo site (Table 2):

$$ \displaystyle\begin{array}{rcl} M& =& \sum _{1}^{3}\pi _{ i}\,m_{i} = (0.41 \cdot 20.4) + (0.47 \cdot 33.7) + (0.12 \cdot 46.7) = 29.8 {}\\ SD& =& \Biggl [\sum _{1}^{3}(m_{ i}^{2} + sd_{ i}^{2})\,\pi _{ i} - M^{2}\Biggl ]^{1/2} {}\\ & =& \Biggl [(20.4^{2} \cdot 4.9^{2}) \cdot 0.41 + (33.7^{2} \cdot 5.3^{2}) \cdot 0.47 + (46.7^{2} \cdot 6.1^{2}) \cdot 0.12 - 29.8^{2}\Biggl ]^{1/2} {}\\ & =& 10.3 {}\\ \end{array} $$