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Despite increasing emission controls, particulate matter (PM) has remained a critical issue for European air quality in recent years. The various sources of PM, both from primary particulate emissions as well as secondary formation from precursor gases, make this a complex problem to tackle. In order to allow for credible predictions of future concentrations under policy assumptions, a modelling approach is needed that considers all chemical processes and spatial dimensions involved, from long-range transport of pollution to local emissions in street canyons. Here we describe a modelling scheme which has been implemented in the GAINS integrated assessment model to assess compliance with PM10 (PM with aerodynamic diameter < 10 pm) limit values at individual air quality monitoring stations reporting to the Air-Base database. The modelling approach relies on a combination of bottom up modelling of emissions, simplified atmospheric chemistry and dispersion calculations, and a traffic increment calculation wherever applicable. At each monitoring station fulfilling a few data coverage criteria, measured concentrations in the base year 2009 are explained to the extent possible and then modelled for the past and future. More than 1850 monitoring stations are covered, including more than 300 traffic stations and 80 % of the stations which exceeded the EU air quality limit values in 2009. As a validation, we compare modelled trends in the period 2000-2008 to observations, which are well reproduced. The modelling scheme is applied here to quantify explicitly source contributions to ambient concentrations at several critical monitoring stations, displaying the differences in spatial origin and chemical composition of urban roadside PM10 across Europe. Furthermore, we analyse the predicted evolution of PM10 concentrations in the European Union until 2030 under different policy scenarios. Significant improvements in ambient PM10 concentrations are expected assuming successful implementation of already agreed legislation; however, these will not be large enough to ensure attainment of PM10 limit values in hot spot locations such as Southern Poland and major European cities. Remaining issues are largely eliminated in a scenario applying the best available emission control technologies to the maximal technically feasible extent. [ABSTRACT FROM AUTHOR]