## 3 Results and Discussions
### Analysis of the Rasch Measure: Atmospheric Pollution
\begin{tabular}{c} **Benzene** \\ \end{tabular}  } & \multirow{2}{*}{\ \begin{tabular}{c} **NO\({}_{\times}\)** \\ **NO** \\ \end{tabular}  } & \multirow{2}{*}{ \begin{tabular}{c} **NO\({}_{\times}\)** \\ **CO** \\ \end{tabular}  } \\ \hline \multicolumn{11}{c}{**Badajoz**} \\ \hline
159 & 5 & 5 & 5 & 5 & 5 & 1 & 3 & 3 & 4 & 4 & 2 & 1 & 1 & 1 \\
206 & 5 & 5 & 5 & 5 & 5 & 2 & 4 & 4 & 1 & 1 & 1 & 1 \\
237 & 5 & 5 & 4 & 5 & 5 & 5 & 2 & 5 & 3 & 1 & 2 & 1 & 1 \\....................................  
benzene, NO, NO\({}_{\rm x}\), and PM\({}_{10}\) in the rural location, but their influence on atmospheric pollution is lower than the other pollutants and climatic factors. Another ranking of all days according to their Rasch measure can be obtained. Figure 3 displays a continuous distribution of days, with most of them aggregated. However, some days, located to the left in the continuum, have very low score, suggesting their low atmospheric pollution. Conversely, the days located to the right in the continuum are those in which high atmospheric pollution occurred. It is important to denote that the pollutants levels at the three locations were usually very low and consequently, the atmospheric pollution level was also very low. This fact is reflected in the variable maps: the mean Rasch measure for days is lower than the mean Rasch measure for pollutants and climatic factors (Figure 3). The separation between both Rasch measures is greater at the rural site, Monfragie, than at the urban locations, and, in turn, the separation was greater at Badajoz than at Caceres (see Tables 1 and 2). That means Caceres is the location where there were more days in which the probability to find high atmospheric pollution was more important, followed by Badajoz (despite this city has more population and, consequently, the number of motor vehicles is considerably higher), and as it could be expected, Monfragie has very low probability to find high atmospheric pollution. Figure 4 shows the mean atmospheric pollution level, the Rasch measure, for each month during 2016. Higher values are evident for both urban locations and, in turn, the Rasch measure was considerably higher in Caceres during many months, basically in spring and summer, when atmospheric pollution was more important because of the increasing contribution of the ground-level ozone. During summer, atmospheric pollution levels in the three sites were more similar, coinciding with maximum solar radiation, mean air temperature, and, in consequence, higher contribution of the tropospheric ozone. In contrast, in winter, when the ozone levels are lower, other individual pollutants generated in urban areas, as NO\({}_{2}\), PM\({}_{10}\), or benzene, acquire a highest relative level, because of the increased emissions from heatings or heavier traffic in cities compared to the vacation period, as it has been also observed in other locations [24]; in consequence, atmospheric pollution levels are considerably higher in the urban sites than in the rural one. As it was previously mentioned, ozone is the only individual pollutant which exerts an important influence during a large number of days in Monfragie, and, additionally, this number of days is greater than in Badajoz or Caceres (Figure 3). The existence of higher ozone concentrations in rural areas, with low anthropogenic activities, than in urban areas has been also reported in other regions [25]. One of the main reasons of this fact is the impossibility to generate the titration effect of NO emissions because this ozone precursor is not as important in rural areas as it is in urban ones [24]. Moreover, although most emissions of ambient air pollutants are from local or regional sources, under certain atmospheric conditions ozone precursors can travel long distances.