Functional kriging prediction of pollution concentrations: Overcoming the big N problem

Particulate matter (PM) is considered to be the air pollutant that most commonly affects people's health, especially in large cities. Consequently, the prediction of PM concentrations is of particular interest in the field of air pollution control. In this article we focus on the spatio-temporal geostatistical approach to predicting PM₁₀ at non-monitored sites of large urban areas. However, due to both the bad performance and also the prohibitive computational burden of the traditional spatio-temporal kriging equations in the case of massive databases (the “big N problem”), we use functional kriging prediction, which has emerged as a promising strategy in such situations. functional kriging prediction deals with single entities (functional data) representing the observations recorded at each observed location. This means that spatial kriging based on such functional observations, along with a trace semivariogram, allows the prediction of functional data at the non-observed locations of interest, thus overcoming the “big n problem”. This promising approach has been applied in the city of Madrid (Spain), where in 2010 the atmosphere monitoring pollution system (AMPS) of the city was reorganized and some stations monitoring PM₁₀ were removed from the system. We use the 2010-2015 PM₁₀ functional data corresponding to the monitoring stations (MS) operating after the reorganization of the AMPS to predict the PM₁₀ functional data at the locations where the stations were removed. This way suspicions of the ecologists associations, that the Municipality of Madrid removed the stations located at the most potentially polluted sites, can be verified. Our results reject such suspicions.