Measurements were conducted as part of the ClearfLo project (http://www.clearflo.ac.uk/), a multinational collaboration to investigate the processes driving air quality in and around London . This study focuses on the winter intensive observation period (IOP), which took place from 6 January to 11 February 2012. Trace element measurements were conducted at kerbside, urban background and rural sites, at or near permanent air quality measurement stations of the Automatic Urban and Rural Network (AURN) or Kent and Medway Air Quality Monitoring Network (see Fig. ). The kerbside site was located at Marylebone Road (MR; lat 51∘31′21′′ N, long 0∘09′17′′ W) at the southern side of a street canyon . Measurements were performed at 1 m from a six-lane road with a traffic flow of ∼73 000 vehicles per day (15 % heavy duty vehicles; traffic counts by vehicle group from road sensors (number of vehicles per 15 min)). A signal-controlled junction at 200 m and a heavily used pedestrian light-controlled crossing at 65 m from the site resulted in frequent braking and stationary vehicle queues in front of the site. The urban background site, the main sampling site during ClearfLo, was located at the grounds of the Sion Manning Secondary School in North Kensington (NK; lat 51∘31′21′′ N, long 0∘12′49′′ W). Although the site is in a suburban area about 4.1 km west of MR that experiences heavy traffic, measurements took place away from main roads, and this site is representative of the urban background air quality in London . The rural site was situated at approximately 45 km to the southeast of downtown London at the Kent Showgrounds at Detling (DE; lat 51∘18′07′′ N, long 0∘35′22′′ E) on a plateau at 200 ma.s.l. surrounded by fields and villages . A busy road with a traffic flow of ∼42 000 vehicles per day is located approximately 150 m south of the site.

Aerosols were sampled by rotating drum impactors (RDIs) with 2 h time resolution and a flow rate of 1 m3h-1, and were segregated by size into PM10–2.5 (coarse), PM2.5–1.0 (intermediate) and PM1.0–0.3 (fine) fractions. Trace element composition of the RDI samples was determined by synchrotron radiation-induced X-ray fluorescence spectrometry (SR-XRF) at the X05DA beamline at the Swiss Light Source (SLS), Paul Scherrer Institute (PSI), Villigen PSI, Switzerland, and at Beamline L at the Hamburger Synchrotronstrahlungslabor (HASYLAB), Deutsches Elektronen-Synchrotron (DESY), Hamburg, Germany (beamline dismantled November 2012). In total 25 elements were quantified (Na, Mg, Al, Si, P, S, Cl, K, Ca, Ti, V, Cr, Mn, Fe, Ni, Cu, Zn, Br, Sr, Zr, Mo, Sn, Sb, Ba, Pb). Details of the RDI-SR-XRF analysis are described in and in previous application examples in and .

Additional measurements discussed in this paper are briefly described here. Aerosol mass spectrometers (Aerodyne Research, Inc., Billerica, MA, USA) were deployed at MR (5 min resolution), NK (5 min sampling interval every 30 min) and DE (2 min resolution) to characterize the non-refractory submicron aerosol components (organic matter, sulfate, nitrate, ammonium, chloride; ); a quadrupole AMS was deployed at MR; and a high-resolution time-of-flight AMS was deployed at NK and DE. Particle light absorption was derived with seven-wavelength Aethalometers (λ=370–950 nm, model AE 31, Magee Scientific; 5 min resolution) at NK (3.5 µm cyclone) and DE (2.5 µm cyclone). The measured absorption was apportioned to traffic and wood burning based on the absorption coefficients at λ=470 and 950 nm, assuming absorption exponents of 1 and 2 for traffic and wood burning emissions, respectively . At MR and NK, NOx measurements were performed with NOx chemiluminescent analysers (API, A Series, model M200A; 15 min resolution). At DE, NO (Thermo Scientific 42i analyser) and NO2 (Aerodyne CAPS-NO2 and QCL-76-D) data were collected and summed to obtain total NOx concentrations (1 min resolution). Wind direction and wind speed data for the two city sites were taken from the nearby BT Tower, where sonic anemometers (20 Hz) were placed at the top of an open lattice scaffolding tower of 18 m height on top of the main structure (190.8 ma.g.l.; lat 51∘31′17′′ N, long 0∘08′19′′ W; 30 min resolution; ), while local data were used at DE. Relative humidity (RH) data at NK were derived with a Vaisala WXT sensor (5 min resolution). Finally, the UK Met Office's Numerical Atmospheric Modelling Environment (NAME) dispersion model provided back trajectory simulations for analysis of air mass origins .

PMF is a powerful source apportionment method to describe measurements, using the bilinear factor model xij=∑k=1pgikfkj+eij, where xij is the jth species concentration measured in the ith sample, gik is the contribution of the kth source to the ith sample (factor time series) and fkj is the concentration of the jth species in the kth source (factor profiles). The part of the data remaining unexplained by the model is represented by the residual matrix eij. The entries of gik and fkj (required to be non-negative) are fit using a least-squares algorithm that iteratively minimizes the objective function Q: Q=∑i=1n∑j=1meijσij2, where σij are the measurement uncertainties.

The PMF model solution is subject to rotational ambiguity; that is, different solutions may be found having similar values of Q . This ambiguity can be reduced within the ME-2 algorithm by adding a priori information into the PMF model (e.g. source profiles) to reduce the available rotational space and direct the solution towards a unique, optimized and environmentally meaningful solution.

In this study, trace element source apportionment is performed using the ME-2 implementation of PMF , with configuration and analysis in the SoFi (Source Finder) toolkit for the IGOR Pro software environment (WaveMetrics, Inc., Portland, OR, USA). The ME-2 solver executes the PMF algorithm in a similar way to the PMF solver but has the advantage that the full rotational space is accessible. One way to efficiently explore this space is with the a-value approach. Here one or more factor profiles are constrained by the scalar a, which defines how much the resolved factors are allowed to deviate from the input “anchor” profiles, according to fj,solution=fj±a×fj, where a can be set between 0 and 1. If, for example, a=0.1, all elements in the profile are allowed to vary within ±10 % of the input factor profile. For clarity, we here use the term “ME-2” to refer to solving the PMF model with the ME-2 solver using the a-value approach, whereas the term “unconstrained ME-2” refers to solving the PMF model using the ME-2 solver but without a priori constraints on the solution.

These algorithms require both a data matrix (xij, 25 elements measured with 2 h time resolution) and a corresponding uncertainty matrix (σij). Uncertainties that uniformly affect an entire row or column of the data matrix (e.g. RDI flow rate, absolute or relative calibration) do not alter the PMF solution and are thus not considered in constructing the uncertainty matrix. Uncertainties are calculated according to Eq. () and account for the detector counting efficiency (σDet,ij) and the energy calibration of an X-ray line as function of detector channel (σEC,ij): σij=σDet,ij2+σEC,ij2, The σDet,ij depend on the efficiency with which one photon is counted by the detector and is defined as the square root of the signal. The σEC,ij were estimated at 0.01 keV for SLS spectra (representing ∼2 channels) and 0.02 keV for HASYLAB spectra (representing ∼1 channel). Gaussian probability distributions representing energy calibration biases (i.e. keV or energy offsets) are constructed using the above values as the standard deviation (SD). From these distributions, several offsets are selected, such that the perturbations are uniformly sampled according to probability, and the XRF spectra are refitted (here 20 offsets). The σEC,ij are defined as the SD of the refitted spectra across these 20 iterations. Entries in xij with a signal-to-noise ratio (SNR) below 2 are downweighted by replacing the corresponding σij with 2/SNRij. This approach, as opposed to downweighting an entire variable (i.e. increasing the uncertainty associated with an entire column rather than a single point; ), allows variables with low average SNR but high SNR periods to remain in the data matrix, as these peaks might contain valuable information regarding sources (e.g. sources systematically sampled from particular wind vectors).

Missing values in one or several entries in xi (e.g. a line fit failure of one or more elements) are set to zero and the corresponding error is set to 109. Missing data points in time (e.g. a power failure during sampling) are removed from the data and error matrices.

The multi-size, multi-site nature of this data set allowed for several methods of constructing the input data set for ME-2 (i.e. single size × single site; single size × multiple sites; multiple sizes × single site; multiple sizes × multiple sites). Although all combinations were investigated, the analysis herein focuses primarily on the single size × multiple sites option. That is, we investigated three data sets, with each containing a single size (PM10–2.5, PM2.5–1.0 or PM1.0–0.3 fraction) and data from all three measurement sites (MR, NK and DE). Combining the sites enabled separation of sources with high temporal covariance but significant spatial variability. Separation of sizes improved source resolution by preventing sources occurring in only a single size fraction from having too small a contribution to Q for the model to resolve. Sources occurring only at one site were resolved, as discussed below.

ME-2 solutions were evaluated using a number of mathematical and physical criteria. The two major aspects of the analysis are (1) selection of the optimum number of factors and (2) evaluation of whether this solution is acceptable as a final solution or requires additional/modified rotational control. The primary criteria used for this evaluation are as follows:Mathematical

Investigation of the decrease in Q/Qexp (Qexp=Qexpected or the number of remaining degrees of freedom of the system) with increasing p (number of factors) due to the increased degrees of freedom in the model . A large decrease indicates significantly increased explanation of the data, while a small decrease suggests that additional factors are not providing new information and a smaller p is sufficient.

Physical

Attribution of elements to sources and element-to-element ratios within a source are consistent with existing measurements (e.g. published source profiles and source-based element-to-element ratios).

The goal of the present analysis is to conduct ME-2 analyses (unconstrained or constrained) that meet the criteria outlined above for each of the three size fractions on the combined data from all three sites. However, for all size fractions, unconstrained ME-2 (i.e. uncontrolled rotations or conventional PMF) yielded factors containing signatures of multiple emission sources (e.g. mixed brake wear and other traffic-related processes, or mixed S-rich and solid fuel) and were therefore considered non-optimal solutions (Supplement Figs. S1–S4). Therefore, we applied rotational controls, using the a value approach (Eq. ). A central challenge of this approach is the construction of appropriate anchor profiles, which cannot be drawn directly from the literature, because the attribution of elements to sources and the element-to-element ratios within a source are not consistent across different studies (e.g. ). Therefore, to find clean model rotations, anchor profiles were determined within the ME-2 analysis as described below.

In brief, this analysis strategy (outlined in Fig. , and illustrated for the current study in Supplement Fig. S5) involves the construction of a basis set of source profiles by iterating between (1) analysis of a subset of data in which one or more factors can be clearly resolved and their profiles added to the basis set and (2) analysis of the full data set using the existing basis set as anchors to determine whether the existing basis set is sufficient or additional anchor profiles are needed. Finally, sensitivity tests are used to assess the uncertainties associated with the final solution. Implementation of this analysis strategy requires four types of ME-2 analyses, denoted ME2_all, ME2_subset, Profile_unresolved, and Sensitivity_test, which are discussed in detail below.

ME2_all refers to the analysis of the entire data set (i.e. all time points). The initial ME2_all analysis in Fig.  is an unconstrained analysis and is primarily used to identify time segments that may be useful for resolving anchor profiles of specific factors. All subsequent ME2_all analyses utilize the profile basis set built up in previous steps by constraining successfully retrieved profiles during these steps. An ME2_all analysis is defined as successful only when the entire data set is well explained according to the criteria given above.

ME2_subset denotes analysis of a subset of the full data set in the rows (i) dimension. This subset need not be a single continuous block and can be constructed, for example, from separate periods in which a particular source is evident. ME2_subset analyses utilize the basis set built up in previous steps and are considered successful (see Fig. ) if the entire subset is well explained according to the above criteria. To maximize adaptation of the basis set to the entire data set (rather than remaining fixed to a previously analysed and quasi-arbitrary subset), the basis set is allowed to evolve after each successful ME2_subset (or ME2_all) analysis – i.e. the ME2_subset output profiles become the new basis set. Strategies used for selecting subsets may vary with the data set; however, it is critical that the entire data set be well investigated, by ensuring that the entire data set is contained in subsets and/or careful inspection of ME2_all residuals. As an example, in the present analysis high signal-to-noise data at MR and NK were analysed separately (subset 1) from low signal-to-noise data at DE (subset 2). The need for a separate DE analysis was indicated by strong residuals in the ME2_all analysis using the basis set derived from subset 1. This indicated that an additional source (industrial) was needed to fully describe the data set. Other subset selection strategies could include, for example, size fraction, air mass origin, wind direction, or suspected source influence.

Profile_unresolved is used to generate an appropriate anchor profile for a factor whose presence is indicated in the solution but cannot be cleanly resolved by ME2_subset. Thus while Profile_unresolved and ME2_subset may employ similar analytical strategies (e.g. analysis of a data subset), Profile_unresolved is distinguished in that (1) success/failure criteria are applied only with respect to a specific factor and that (2) only the profile of this specific factor is added to the basis set for future analyses. As an example, in the present study, a profile for the PM10–2.5 brake wear factor was resolved by analysing NK data using an excessive number of factors. Although non-brake wear factors exhibited non-interpretable mixing/splitting, the brake wear factor was judged clean based on element ratios consistent with literature, a strong temporal correlation with NOx, and low overall unexplained variation in the solution. Other Profile_unresolved methods could include, for example, (1) an average profile over periods where the source of interest dominates the total signal or (2) use or estimation of a profile from the literature.

Sensitivity_test investigates the uncertainties in the ME-2 solution associated with the final basis set (fully constrained ME2_all). The robustness or uncertainty is investigated with anchor sensitivity analyses for each size fraction separately (three sites combined per size). Random profiles of all source profiles in ME2_all are generated over 10 000 runs by varying the relative intensity of fkj with an anchor of ±20 % of the final model solutions. This allowed a systematic exploration of a large area of the solution space around the final solutions. Physically and mathematically meaningful solutions were selected according to the source profile constraints given in Table . By obeying these constraints in this study, one assures that the other source profiles are meaningful solutions as well. In the coarse fraction, 26 % of the runs were classified as good solutions, while 40 and 64 % are good in intermediate and fine fractions. Factor profile and time series uncertainties are defined as 1 SD of the good solutions (note that these uncertainties are rather small (see, for example, small shaded areas in time series in Figs. , , –, ) and an implication of the criteria in Table , even though these criteria are not strongly restrictive). An anchor of ±50 % led to a higher percentage of meaningless solutions, while the uncertainties were comparable to the ±20 % anchor runs. This indicates that the rotational model uncertainties are rather driven by the criteria in Table  than by how much the profiles are allowed to vary. In other words, the percentage of accepted solutions reflects computational efficiency rather than the robustness of the base solution. The brake wear profile constraint ensures a clean factor without mixing of elements related to other traffic processes or resuspended dust that occurs due to the dominant contribution of MR to Q with its high temporal covariance of most elements. The constraints based on literature values guarantee solutions that have environmentally meaningful attributions of elements to sources and element-to-element ratios within a source. Note that the errors reported for this analysis deal explicitly with model errors and do not account for systematic errors in the RDI-SR-XRF system that do not affect the PMF model operation (e.g. flow rate, element calibrations). For a detailed discussion of these sources of uncertainty, see .

The ME-2 analysis on the three data sets resulted in a total of nine source profiles as shown in Fig.  (values in Supplement Tables S1–S3), with the factor time series for each site in Supplement Figs. S6–S8 (PM10–2.5, PM2.5–1.0 and PM1.0–0.3, respectively). The coarse fraction yielded the source factors (notable elements in brackets) brake wear (Cu, Zr, Sb, Ba), other traffic-related (Fe), resuspended dust (Si, Ca), sea/road salt (Cl), aged sea salt (Na, Mg) and industrial (Cr, Ni). The intermediate fraction yielded the same factors except for the industrial, instead yielding an S-rich (S) factor. In the fine fraction a traffic-related (Fe, Cu, Zr, Sb, Ba) factor was found as well as resuspended dust, sea/road salt, aged sea salt, reacted Cl (Cl), S-rich and solid fuel (K, Pb). The other elements (Al, P, Ti, V, Mn, Zn, Br, Sr, Mo, Sn) are not uniquely emitted by a particular emission source and are attributed to several factors. It should be noted that the concentrations for the factor time series reported below reflect only the elements measured by SR-XRF analysis and not the other constituents associated with the various source types. In particular the lighter elements (H, C, N, O) are not included and may in some cases dominate the total mass associated with a source. The relative contribution to the factors discussed herein are also relative to the measured elemental mass resolved. Although the analysis below includes only trace elements, which constitute a minor fraction of the total mass, the results are important for determining source temporal characteristics and interpreting trends in bulk particle properties such as total PM mass.

The trace element source apportionment results indicate the ability to characterize the environment-dependent variability of emissions in and around London. The analyses of data from the combined sites retrieve a single source profile representative of all three sites, thus allowing a direct comparison of the source strengths across sites. Source strengths strongly differ between sites and sizes, as seen in Fig. . Most of the analysed element mass is emitted in PM10–2.5 with 78 % at MR, 73 % at NK and 65 % at DE, while only 17–22 % and 6–13 % is emitted in PM2.5–1.0 and PM1.0–0.3, respectively.

The separate analyses on the three size fractions provide insights into the emissions of sources to specific size fractions (Fig. ). The regionally influenced S-rich and solid fuel factors are restricted to the smaller size fractions with concentration ratios of 1.0–1.8 between sites roughly 50 km apart. These factors, especially solid fuel, are affected by many anthropogenic point sources and are influenced by emissions not only in and around London but also from elsewhere in the UK and northern Europe. In contrast to other sources, solid fuel is expected to be more prevalent in more rural parts of the UK than in the smoke-controlled inner city areas. The industrial factor is restricted to PM10–2.5 and affects the air quality under specific meteorological conditions around the rural site, which is generally a region characterized by much lower pollution.

The other sources, except reacted Cl, emit elements in all three size fractions. London's city centre is a hotspot of anthropogenic activities, resulting in high pollution levels of locally influenced sources directly related to population density. Brake wear, other traffic-related and resuspended dust factor concentrations are drastically different within different micro-environments and size fractions, indicating major heterogeneity in human exposure patterns. Concentrations at the kerbside are up to 7 and 28 times higher than at NK and DE, respectively, and PM10–2.5 concentrations are up to 4 and 14 times higher than PM2.5–1.0 and PM1.0–0.3, respectively. During this winter period the sea salt sources, although from natural origin and strongly meteorologically driven, are enriched in the city in the form of sea salt resuspension from the roads.

Both direct emissions and resuspension have been identified above as important sources of trace elements. The trend in coarse aged sea salt across the three sites provides insight into the relative importance of these processes. We assume that all aged sea salt originates from a regional, site-independent source, and that the concentration gradient in this factor between sites thus reflects the effect of local resuspension processes of naturally deposited aged sea salt. Although sea salt emissions are typically considered a natural process, human activities (vehicle-induced resuspension) enhance the concentrations of the coarse aged sea salt by 1.7–2.2 in the city relative to the rural site (Fig. ). These ratios provide an upper limit for the resuspension enhancement (and thus a lower limit for the enhancement due to direct emissions) for the anthropogenically influenced factors, whose concentrations at DE may already be increased by local emissions. The lower limits for direct emission enhancement ratios in the coarse fraction at MR relative to DE are 3.5 to 12.7 for brake wear, other traffic-related, dust and sea/road salt factors (1.4–5.5 for NK / DE). Direct emissions for the traffic-related factor show similar enhancement in all size fractions, whereas enhancement of the other anthropogenically influenced factors are a factor of 1.5–3.0 lower in the smaller size fractions. These results indicate that direct source emission processes occur mainly for coarse particles and are dependent on the micro-environment. The S-rich and solid fuel factors have negligible resuspension influences (similar concentrations across sites). Air quality in London can be improved by the development of policies aiming to reduce resuspension processes.

Trace elements are often used as chemically conserved source markers. Here we assess the ability of elements measured herein to serve as unique tracers for specific sources. For a tracer to be considered good, we require that a given source has a high relative contribution (>70 %) to a specific element, i.e. that the element is mainly attributed to a single source (Fig. ). We suggest Cu, Zr, Sb or Ba as markers for brake wear in PM10–2.5 and PM2.5–1.0. The relative contributions are >93, 83, 93 and 96 % for Cu, Zr, Sb and Ba, respectively. The attribution of these elements to the traffic factor in PM1.0–0.3 with relative contributions between 69 and 84 % also suggests brake wear emissions in this size fraction. Fe is typically also attributed to brake wear emissions . However, we observed no Fe in the brake wear factors; instead 86 and 65 % of Fe were attributed to other traffic-related processes in PM10–2.5 and PM2.5–1.0 (74 % of Fe to the traffic-related factor in PM1.0–0.3). Furthermore, around 19 % of Fe contributed to the resuspended dust factors in all three size fractions. We therefore recommend attributing Fe only to a specific source in combination with other markers. Si and Ca in all size fractions can be used as a surrogate for resuspended dust with relative contributions between 72 and 75 % for Si and between 80 and 85 % for Ca. Coarse and intermediate fraction Cl (relative contributions >87 %) are markers for fresh sea salt (preferably combined with Na and Mg), while fine-fraction Cl is not a unique source indicator. Depending on the data set it can indicate waste incineration , coal combustion or reacted Cl as NH4Cl particles (current study, relative contribution 59 %). A combination of fine-fraction K and Pb with relative contributions of around 80 % indicates solid fuel in this study, but can also be attributed to wood, coal or peat burning separately. Fine-fraction S can typically be attributed to regionally transported secondary sulfate (here only a 65 % relative contribution). Other elements can also be used as source markers, but rather as a combination of elements than individually, and preferably combined with measurements of other species.

The analysis herein clearly shows the advantages of rotationally controlled analyses relative to an unconstrained PMF solution. Supplement Figs. S1–S4 show the best solutions retrieved from unconstrained analyses for the separate size fractions (four-, four-, and five-factor solutions for PM10–2.5, PM2.5–1.0, and PM1.0–0.3, respectively). The unconstrained PM10–2.5 solution (Supplement Figs. S1 and S4) yields high residuals of Ni, Cr, and Mo and does not resolve a brake wear factor. The unconstrained PM2.5–1.0 solution (Supplement Figs. S2 and S4) likewise does not yield brake wear and additionally fails to resolve aged (reacted) sea salt from regionally transported sulfate and solid fuel, despite strong evidence for this processing in the raw time series. Finally, the unconstrained PM1.0–0.3 solution (Supplement Figs. S3 and S4) mixes secondary sulfur and solid fuel sources. It also fails to explain major events contained in the Cl-rich factor, apportioning significant Na to these events, leading to high Na residuals. Higher-order solutions do not resolve these problems, instead leading to uninterpretable splitting of the dust factor, factors consisting only of single elements, and unstable solutions that are highly dependent on algorithm initialization (seed).