Sampling occurred from mid January to mid May 2008 and had a fixed and a mobile component. The fixed component comprised a city-centre and an urban background site (Figure 1a) and was intended to: (a) provide a broad understanding of temporal variation in UFP in two different settings within the study area and (b) enable pre-processing of the mobile data. UFP one minute mean number concentration counts were taken continuously throughout the five-month sampling period. After quality control, usable data covered a 14 week period. The mobile component comprised 232 3-minute mean spot measurements made over a 32 km² transect from Manchester city centre to the suburbs. The transect-based study area was a compromise between the need to maximise coverage of: land-use types; distances from the city centre; and cohort residences within an ongoing asthma and allergy birth cohort 6. Mobile sites were chosen at two different spatial resolutions. The first was designed to help capture large (city) scale patterns and involved making spot measurements using a pseudo-regular grid. To aid the logistics of spatial sampling five sub-areas were used. The second was designed to allow the consideration of medium scale patterns and used a mixture of random and stratified random sampling (by land-use zone) in one sub-area (Figure 1a).

All mobile-site data were collected on weekdays 10 am-3 pm under mainly dry and wind-free meteorological conditions. This targeted sampling campaign was chosen so as to minimise unwanted temporal and meteorological variability (particularly wind and precipitation) so that the data could be considered a snapshot of a UFP spatial process. An average of 25 sites was visited on any given sampling day and duplicate measurements were found at most sites for later cross validation. All sites had at least one UFP measurement and the final dataset consisted of 402 measurements in total. For both fixed- and mobile-site UFP data, corresponding meteorological data were also found. For the former, Met Office data were used, and for the latter local meteorological measurements were found using a hand-held (kestrel ^®) device. UFP measurements were found using TSI ^® WCPCs (model 3781) at the fixed-sites and hand-held TSI ^® P-TRAKs (model 8525) at the mobile-sites both of which have high sampling rates.

Even with a targeted sampling campaign, some unwanted temporally and meteorologically induced variability in the mobile-site UFP data is expected. Consequently, this data is pre-processed to produce spatial data more suitable for research aims. Air pollution studies that have used some sort of data pre-processing prior to a predictive regression fit include those of 78910, but none provided a methodology transferable to this research. As such, a novel pre-processing methodology is presented and involves an investigation of patterns in the fixed-site UFP data at two temporal scales.

Small-scale diurnal trends in the fixed-site UFP data were analysed in order to provide the basis for pre-processing the mobile-site data to an equivalent time of day between the 10 am-3 pm sampling frame. A nonlinear, local regression (LR) fit 11 was found for individual averaged weekdays. It was assumed that this LR fit represents the same underlying diurnal pattern in UFP variability at each mobile-site and adjustments could therefore be made assuming a proportional relationship.

Wintertime conditions seem to provide highest UFP concentrations and relationships have also been found with temperature and wind speed 1213. Therefore it was also necessary to carry out large-scale, temporal and meteorological mobile-site data pre-processing. This accorded to separate multiple linear regression (MLR) fits to each fixed-site UFP dataset, specified with three temporal indicator covariates (day of week (T1), sampling week (T2) and day/night (T3)); two meteorological continuous covariates (wind speed (WS) and temperature (TP)); and two meteorological indicator covariates (precipitation (PC) and a WS-PC interaction term). This provided two forms of large-scale data pre-processing results: a detrended and an adjusted UFP spatial dataset.

Duplicate mobile-site samples were earmarked for cross validation and then screened resulting in 169 duplicate measurements for 169 sites. This data was then divided into two equally-sized cross-validation datasets, A and B.

Average diurnal patterns in the fixed-site UFP data indicates higher concentration counts and higher variability at the city-centre site compared to the urban site (Figure 1b). An LR fit to an average of the two time-series datasets was used for the small-scale UFP adjustments (Figure 1b with a 4-hour smoothing bandwidth). Mobile-site UFP data can now be adjusted to reflect sampling at a user-specified time of 12 pm using: . Here UFP_ADJ_SS and UFP_ACT are the adjusted and actual values, respectively; and UFP_PRED_1 and UFP_PRED_2 are LR predictions found at the actual sample time (e.g. 11.09 am) and at 12 pm, respectively. UFP_PRED_1 and UFP_PRED_2 must correspond to the weekday that UFP_ACT was sampled on.

For Step 2, a MLR model is fitted to each of the fixed-site datasets, where UFP and meteorological measurements are taken in a 'raw' hourly-averaged form. A stepwise fitting procedure is followed and the reduced MLR fits retain five of the original seven UFP covariates (Figure 1c). Each covariate only relates to variation that needs to be filtered from the small-scale adjusted data (Step 1). In this respect, the resultant regressions are not expected to fit well, as the underlying sources of UFP are not being modelled. Next the mobile-site UFP data is detrended using one of the fixed-site regressions according to whether a mobile site is classed as urban or city centre (based on proximity). For clarity, a mobile-site detrending involves; (i) specifying one of the fixed-site regressions with covariate data particular to the mobile-site, (ii) calculating the UFP prediction and (iii) subtracting this prediction from the actual mobile-site UFP value. The key assumption is that the coefficients of the fixed-site regressions are transferable to the mobile-sites.

Detrended data of step 2 (option A) provides pre-processed data loosely centred on a mean of zero, which is suitable for modelling UFP variability but unsuitable for UFP prediction. Consequently, the (small-scale adjusted) mobile-site data of step 1 is adjusted a second time to provide a fully-adjusted pre-processed dataset. These large-scale adjustments are directly based on the fixed-site detrending regressions and are similar in concept to the small-scale adjustments of step 1, i.e. proportionality is assumed. In this case, user-specified UFP covariate values are chosen so that adjusted datasets can be found for any particular time (for T1, T2 and T3) and meteorological condition (for WS, TP and WS-PC). This could be such that the lowest, average, or highest expected UFP concentrations are found. For this article, an adjusted dataset is found where average UFP concentrations are expected.

Original unadjusted data and pre-processed data are both affected by spatial drivers of UFP concentration patterns. However, since unwanted temporal and meteorological influences have been removed in the pre-processed data, pre-processed cross-validation dataset A should relate more strongly to pre-processed cross-validation dataset B, than is the case for the unadjusted cross validation datasets. Therefore our pre-processing strategy can be validated by using scatterplots and associated diagnostics (Figure 2a). A strong relationship between the two cross-validation datasets should result in a mean error () of zero (reflecting an even scatter around the 45° line), an MLR-intercept of zero, an MLR-slope of one and a correlation coefficient of 1. All diagnostics indicate that the detrended pre-processed data performs better than the unadjusted data and as such should be preferred for subsequent research modelling aims. Similarly positive cross-validation results were found for the adjusted pre-processed data.

Geographically weighted local variance surfaces 14 are presented for unadjusted and detrended UFP data in Figure 2b. The local variances are found using an inverse distance weighting (IDW) function (bandwidth = 25%). As expected, both surfaces indicate areas of high and low UFP variability in the city-centre and suburban areas, respectively. Alternative measures of local variability and different optimisation algorithms are being developed, building on existing work in this area 15.

Relationships between UFP and a number of urban covariates are also being explored and can be used to provide input into a land-use regression approach 16. Covariates include road and traffic patterns, population density, building heights, distance to city centre, exposure-relevant land-use zones and associated surface cover properties. Depending on the nature of any spatial dependence found in the UFP data, these covariates may also provide input to a geostatistical approach 17. Figure 2c shows exploratory IDW mean surfaces for spatial trends (bandwidth = 35%). The unadjusted and adjusted data exhibit a clear spatial trend from the city centre to the suburbs, the nature of which is entirely reasonable and suggestive of city-scale patterns, which may underlie the metre scale variability reported elsewhere 1. The adjusted data has a much reduced UFP variance over the unadjusted data, partially reflecting its on average specification.