## 4 Conclusions  
The successful formulation of the Rasch model to define a measure of atmospheric pollution, integrating different measurements of individual pollutants (CO, SO2, NOx, NO2, NO, O3, PM10,and benzene) and climatic factors (precipitation, relative humidity, solar radiation, mean air temperature, and barometric pressure), is the novel aspect of this work. Moreover, this probabilistic and objective model, based on the data, can detect the influence of each pollutant or climatic variable on the environmental deterioration and the pollution measurement for each day.  
After applying the Rasch method, it was highlighted how climatic variables are the main items affecting the atmospheric pollution in the three study locations, with the lack of precipitation being the most important factor. Most of the considered individual pollutants do not influence significantly the atmospheric pollution, which is probably due to the low levels measured in the locations. Only ozone is important in all sites and, particularly, in the rural one, despite it is a National Park. In consequence, measures to reduce air pollution in both cities, Badajoz and Caceres, should be addressed to reduce the emissions of ozone precursors from traffic, restricting the use of vehicles with internal combustion engines and promoting the use of less polluting vehicles such as those with electric motors. In the Monfrague Park, the transport of ozone precursors from other areas made it difficult to propose local measures to reduce the episodes of air pollution.  
An additional output of the Rasch model is the Guttman scalogram, which constitutes a useful tool to detect unexpected values of any pollutant or climatic factor during each day, or, inversely, the individual pattern of each pollutant or climatic factor during all considered days. Usually these unexpected values are due to local transitory circumstances, such as episodes of intense rainfall or, in contrast, the occurrence of days with Saharan dust intrusion that occurs in summer, increasing the level of particulate matter.  
The use of the Rasch model as a measurement tool constitutes a logical and objective way to define a coherent variable (atmospheric pollution level as the Rasch measure) and it is a powerful tool to better know the interrelationships between all different variables or factors which can affect complex processes as the dynamics of environmental contamination. Since georeferenced information was used, it can be implemented in a geographical information system (GIS) to generate different types of maps. In the future, the combination of the Rasch model and GIS capabilities can be a powerful tool to develop an appropriate environmental and managing policy.  
[PERSON] conceptualized, collected, and analyzed the data, performed the analyses, and wrote the manuscript. [PERSON] also performed the analyses and validation. [PERSON] and [PERSON] collected the data and optimized the manuscript.  
This research was funded by the Junta de Extremadura and the European Regional Development Fund (ERDF) through the projects GR18086 and GR18081 linked to the VI Regional Plan for Research, Technological Development and Innovation from the General Government of Extremadura 2017-2020. We also acknowledge the support received from the Air Quality Surveillance Network of Extremadura (REPICA), project 1855999 FD022, partially financed by the European Regional Development Fund (ERDF).  
The authors declare no conflict of interest.