Statistical Modelling of Spatial and Temporal Variation in Urban Particle Number Size Distribution at Traffic and Background Sites

Ultrafine particles (UFP) pose a risk to human health, but due to the multitude of sources and fast transformation in the urban atmosphere, quantifying the exposure is challenging. Furthermore, physical properties of aerosol particles depend on the particle size. Statistical models are used to quantify spatial and temporal variation of UFP, but rarely used for particle number size distribution (PNSD). The aim of the study was to establish an interpretable statistical model capturing spatial and temporal variation of urban PNSDs using generalized additive models (GAM) and multivariate adaptive regression spline models (MARS). These algorithms automatically fit interpretable, non-linear marginal function to represent relationships between explanatory and response variables. Three different approaches were evaluated to cope with the multidimensionality of the PNSD data (20-800 nm, 34 size bins): a generalized additive model for the particle number concentration (PNC) of every individual size bin (GAM(bins)), a generalized additive model for the parameters of the PNSD function (GAM(pams)) and a multivariate adaptive regression spline model for the PNC of every size bin (MARS(bins)). Reanalysis data of meteorological quantities, urban geometry parameters and approximated traffic counts were used as explanatory variables. Marginal functions of the final models could be attributed to major processes that contribute to spatial and temporal variation of the PNSD, i.e. emissions from vehicle traffic, transport, dilution, accumulation, deposition and new particle formation. Cross-validation coefficients of determination ranged between 0.27 and 0.48 for most size bins. Nonetheless, the modelling approaches resulted in similar root mean square errors (RMSE) and mean absolute error (MAE). Though direct spatial transferability of the models is limited, the presented approaches may be useful for estimating ambient exposure to particles.