## 3 Results and Discussions
### Analysis of the Rasch Measure: Atmospheric Pollution
Thus, in this case, Madrid, the most important  
Figure 4: Temporal evolution of atmospheric pollution levels at the two urban (Badajoz and Caceres) and the one rural (Monfragie) locations, in 2016.  
city in Spain, is located around 250 km to the east of Monfragie, and, in its surroundings there is one of the most important industrial areas of Spain. Emissions of NOx into the atmosphere from a variety of anthropogenic sources, mainly traffic and industrial activities, from the area around Madrid can reach the Monfragie Park in some days. In consequence, many of the ozone episodes in this area occur with a wind flow from the southwesterly direction coming from a region with strong emissions of NOx as Madrid. Another useful output from the Rasch model is the Guttman scalogram [26]. It is a complementary tool to display all days according to their level of atmospheric pollution. As it can be seen in Table 5, days are sorted in a descending order, by their level of atmospheric pollution. Simultaneously, the Guttman scalogram shows all individual pollutants and climatic factors arranged in the order indicated in the first row (Table 5), enabling to show their influence on the latent variable during each day. The Guttman scalogram has the advantage that a single variable is considered to analyze the individual behavior of each day. In the same way, the individual pattern of each individual pollutant or climatic factor can be studied. Pollutants and climatic factors located to the left in Table 5 had higher influence on atmospheric pollution than those located to the right. Thus, a hierarchical order is obtained and the unexpected scores for some items can be easily visualized. For instance, CO, NOx, benzene, and NO scores are usually low for the days with higher atmospheric pollution in Monfragie (Table 5). However, an unexpected high score for benzene on day 261 was detected. Inversely, day 38, located in the bottom of the ranking, where scores of pollutants are very low, had an unexpected high value for SO2. Any other days can be analyzed in a similar way, detecting the particular item in which a low or high value exists with respect to the pattern of the surrounding days. For example, in Monfragie, day 206 (19 August), which is placed at the top of the scalogram (Table 5), had the highest scores for some items (precipitation, ozone, relative humidity, solar radiation, mean air temperature, and barometric pressure); it was the day when the highest atmospheric pollution occurred. If it is compared with days 207 (20 August) and 261 (19 October), which also had the maximum total score but are the second and third in the ranking, it is observed that they all had the maximum score for two items, precipitation and barometric pressure, but for the other items the scores were different. Days 207 and 261 had a lower score in ozone and solar radiation, two of the main items which affect atmospheric pollution in Monfragie; consequently, they are after day 206. Those days at the top in Table 4 had high atmospheric pollution (higher Rasch measure). In contrast, those days at the bottom had low scores for all items; they were the days with the lowest atmospheric pollution (lower Rasch measure). The last in the Guttman scalogram is day 42 (19 February); in consequence, it was the day when the lowest atmospheric pollution took place. In Badajoz, according to the Guttman scalogram, the days when the highest atmospheric pollution was generated had higher scores for the same items (precipitation, ozone, relative humidity, solar radiation, mean air temperature, and barometric pressure) than the rural site (Monfragie), but the participation of SO2 and NO2 in the environmental deterioration was also important during some days, usually located at the top of the scalogram, with high scores.