A recursive estimation approach to the spatio-temporal analysis and modelling of air quality data

This paper presents the methodology for the spatial and temporal interpolation of air quality data. As a practical example, the methodology is applied to the daily nitric oxide NO concentrations measured at 23 stations around Paris. Analysis of the temporal and spatial variability of observations of NO in the Paris area is divided into: (i) time series analysis of AirParif data; and (ii) development of combined spatial and temporal analysis techniques using NO observations from 19 stations. The first part of the paper shows how advanced methods of nonstationary time series analysis can be used to interpolate the data sets of NO concentrations over periods where measurements are missing and to decompose the time series into trend and harmonic components. The results of this analysis applied to 19 stations around Paris are then used in further spatio-temporal analysis of the data. This consists of two steps: (i) preliminary analysis of spatial relations within the data sets; and (ii) the development of a spatio-temporal model for log-transformed NO measurements. The results of the analysis indicate that the simple spatio-temporal model consisting of trend and noise efficiently represents the spatio-temporal variations in the data and it can be applied to predict air pollution variations in time and space at un-sampled locations.