PMF ANALYSIS OF WIDE-RANGE PARTICLE SIZE SPECTRA COLLECTED ON A MAJOR HIGHWAY ROY M. HARRISON, DAVID C. S. BEDDOWS AND MANUEL DALL OSTO

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1 Supporting Information PMF ANALYSIS OF WIDE-RANGE PARTICLE SIZE SPECTRA COLLECTED ON A MAJOR HIGHWAY ROY M. HARRISON, DAVID C. S. BEDDOWS AND MANUEL DALL OSTO Number of Pages: 16 Number of Tables: 4 Number of Figures: 3

2 Site Details The sampling site is located on the Marylebone Road (A501) roughly 130 m before the major junction with Baker Street (A41) on the west- bound carriageway and between the minor T-junctions made with Luxborough Street and Chiltern Street. Traffic lights at the Baker Street junction cause a stop-start driving pattern on this six-lane urban highway and the traffic flows are monitored using a loop-profiler embedded in the surface allowing speed and vehicle classification (EUR6 scheme) to be determined (see Supporting Information). The speed limit of the Marylebone Road is 48 kph (30 mph) and range of hourly average speeds range from 20.8 to 56.4 kph. Traffic Flow Data Traffic Flow data are measure at the Marylebone Road Super Site using a loopprofiler embedded in the surface and it classifies the data using the EURO6 scheme. The system measures vehicle speed and classifies the vehicles according to vehicle length and vehicle chassis height into the following categories: Two Wheeled Motor Vehicles (TWMV); Cars and Vans; Car + Trailer; Rigid Lorry, Heavy van of length greater than or equal to 5.2m or mini-bus, Articulate Lorry and Coach or Bus The hourly LDV/HDV traffic counts typically vary from 546/89 to 3983/995 with median values of 3047/358. Beddows and Harrison (1) estimated the diesel component of the Light Duty Vehicle (LDV) fleet to be 80%, being made up largely of taxis and light goods vehicles (Maximum Authorised Mass, MAM < 3.5 t). The percentage of Heavy Duty Vehicles (HDV) varies from a minimum of 10% during low traffic flows (e.g. at weekends) to 25% of the hourly fleet composition when the traffic 1

3 is at its maximum, e.g. during rush hour. The HDV fraction is mainly composed of rigid lorries (MAM > 7.5 t) and heavy vans and people-carrying vehicles (PCVs) (3.5 < MAM < 7.5 t) with roughly one quarter of the HDV fleet being made up of articulated lorries and large PCVs. This data was included in the analysis (see Table S1 for a summary of the traffic fleet travelling along the Marylebone Road during the measurement period). Meteorological Data The temperature ranged from 1.3 to 14.3 o C with a median value of 7.2 o C. The interquartile range of barometric pressure was from 1023 to 1036 mb indicating quite a variety of dry and damp weather as reflected by the relative humidity which ranged from 76 to 93% across the interquartile range. Details of PMF Method PMF solves the general receptor modelling problem using constrained, weighted, least-squares (2) for a review of PMF methods. The general model assumes there are p sources, source types or source regions (termed factors) impacting a receptor (in this case the Marylebone Road monitoring site), and linear combinations of the impacts from the p factors to the observed concentrations of the various species or in this case size bins for the SMPS+APS spectra plus auxiliary measurements (including: gas concentrations, meteorological data and traffic measurements) (see equation 1). Mathematically, observation x, or in this case the particle size distribution plus auxiliary measurements, at the receptor is given by the matrix representation whose elements are, 2

4 x = p h= 1 g f hj + e (1) where the j th size bin (or auxiliary measurement) on the i th hour. The term g ik (termed score) is the contribution of the k th factor to the receptor on the i th hour, f kj is the fraction of the k th factor that contributes to measurement j, and e is the residual for the j th measurement on the i th hour. In PMF, only x are known and the goal is to estimate the contributions (g ik ) and the fractions (f ). It is assumed that the contributions and number fractions are all non-negative, hence the constrained part of the least-squares. Furthermore, PMF uses uncertainties measured for each of the x size-bin. Hours with high uncertainty are not allowed to influence the estimation of the contribution and fractions as much as those with small uncertainty, hence the weighted part of the least squares. Given the above, it is task of PMF to minimise the sum of the squares Q, see equation 2. Q = n m i= 1 j= 1 e s 2 (2) where s is the uncertainty in the j th measurement for hour i. PMF also operates a robust mode, meaning that outliers are also not allowed to overly fluence in the fitting of the contributions and profiles. Further details of the PMF method used appear in the Supplementary Information. The matrix S, is derived from the uncertainties entered by the user. These can either be entered directly as a matrix using the X_std-dev file or using one of various ad- 3

5 hoc computations available to PMF. In general, the X_std-dev entries should predict the average size of the residual of the data value in question; this is the golden rule in assigning these values (3). The method chosen for calculating these values is based on the method used by Ogulei et al. (4,5). In this, S is calculated using equation 3, s = t + v max( x y ) (3) Where x are the actual data values and y are the equivalent data values fitted by PMF. Matrices t and v are given by t = T x + x ) (4) ( j v = V (5) Ogulei et al. (3,4) used constant T values between 0.01 and 0.05 in their work which was decided through trial and error. Similarly, the constant V values 0.1 and 0.4 were chosen such that their calculated Q value was the closest to the theoretical value it could be. In this work, the optimum values derived were T = 0.02 and V = 0.09 using 10 factors. The choice of the number of factors is a compromise according to Lee et al. (6). Using too few factors will combine sources of different nature together and using too many factors will make a real factor further dissociate into two or more non-existing factors. Two measures IM and IS were derived from the elements (r ) of the scaled residual matrix R (equations 6 and 7). ( X GF ) S R = / (6) IM = 1 n max n i = 1 r (7) 4

6 IS = 1 n max n 1 i = 1 2 ( ) r r j (8) Each column of R represents the quality of the fitting of each species (in this case particle size bin count dn/dlog(dp) or the auxiliary metric) to the product GF and from this the values of IM and IS are calculated. IM is the maximum individual column mean and IS is the maximum individual column standard deviation. Both serve as indicators to identify the species having the least fit and the most imprecise fit, respectively. Using the critical number of factors, IS and IM drop in value to a plateau and this drop indicates the minimum number of factors that should be used in the model. The maximum number of factors is selected using a third value taken as the maximum element outputted from the rotation matrix (rotmat). This matrix is used for detecting the degree of rotational freedom of the factors. It is only qualitative in nature but can be used to reveal if factors have excessive rotational freedom. In this case, a small number of factors should be used. Choosing the largest element in the rotational matrix can show the worst case in the rotational freedom and on increasing the number of factors a critical point will be reached where the value of the largest element will increase from a plateau. This critical point indicates the upper range of factors recommended in the model. 5

7 For our data, the values of max(rotmat) increased in value when 10 or more factors were used in the model, whereas the values of IS and IM fell to a plateau value after 10 factors. References (1) Beddows, D.C.S.; Harrison, R.M. Comparison of average particle number emission factors for heavy and light duty vehicles derived from rolling chassis dynamometer and field studies. Atmos. Envron. 2008, 42, (2) Reff, A.; Eberly, S.I.; Bhave, P.V. Receptor Modelling of Ambient Particle Matter Data Using Positive Matrix Factorization: Review of Existing Methods. JAWMA 2007, 57, (3) Paatero, P. Private communication (4) Ogulei, D.; Hopke, P.K.; Wallace, L.A. Analysis of indoor particle size distributions in an occupied townhouse using positive matrix factorization. Indoor Air 2006, 16, (5) Ogulei, D.; Hopke, P.K.; Zhou, L.; Pancras, J.P.; Nair, N.; Ondov, J.M. Source apportionment of Baltimore aerosol from combined size distribution and chemical composition data. Atmos. Environ. 2006, 40, S396-S410. (6) Lee, E.; Chan, C.K.; Paatero, P. Application of positive matrix factorization in source apportionment of particulate pollutants in Hong Kong. Atmos. Environ. 1999,

8 TABLE LEGENDS Table S1. Percentile values of the Traffic Flows Measured at London Marylebone Road (LMR). Hourly time resolution Table S2. Percentile values of the gaseous metrics measured at London Marylebone Road (LMR). Hourly time resolution (all concentrations in µg m -3 ) Table S3. Percentile values of the meteorological data measured at Heathrow. Hourly time resolution Table S4. Statistics showing the percentage contribution of each factor to the total number (volume) SMPS-APS spectrum FIGURE LEGEND Figure S1. Figure 1. PMF results derived from the analysis of the merged SMPS- APS particle number data collected at roadside. The wind roses depict the trend in scores with wind direction for a typical day and the associated graphs show the factors derived for the number spectra and auxiliary metrics. [KEY WS - Wind speed; TEMP Temperature; DEWPNT - Dew point; RH - Relative Humidity; BP Barometric Pressure; SPD - Vehicle Speed; PCV - Bus and Coaches; LDV < 5.2m - Cars and vans; LDV > 5.2m - Trucks, rigid lorries and minibuses TOWING - Cars + TRAILER] Figure S2. Weekday and weekend diurnal pattern in traffic Figure S3. Weekday and weekend diurnal pattern in meteorology 7

9 Table S1. Percentile values of the Traffic Flows Measured at London Marylebone Road (LMR). Hourly time resolution Percentile 0% 25% 50% 75% 100% TWMV Cars and Vans Car + Trailer Rigid Lorry, Heavy Van (>=5.2m) or mini-bus Articulated Lorry Coach or Bus LDV HDV TOTAL Fleet Speed (kph) Table S2. Percentile values of the gaseous metrics measured at London Marylebone Road (LMR). Hourly time resolution (all concentrations in µg m -3 ) Percentile 0% 25% 50% 75% 100% CO NO NO NO x (as NO 2 ) O Data available from Quality Assurance procedures are outlined in QA/QC Procedures for the UK Automatic Urban and Rural Air Quality Monitoring Network (AURN), Report to Defra and the Devolved Adminstrations, AEAT/ENV/R/2837, September

10 Table S3. Percentile values of the meteorological data measured at Heathrow. Hourly time resolution Percentile 0% 25% 50% 75% 100% Wind Speed (m s -1 ) Temperature ( o C) Relative Humidity Pressure (mbar) Table S4. Statistics showing the percentage contribution of each factor to the total number (volume) SMPS-APS spectrum Factor Mean St. Dev. Max (12.8) 5.6(10.8) 35.2(59.3) 2 1.7(13.7) 1.5(10.7) 7.9(50.0) (18.8) 18.8(12.1) 77.5(53.2) (3.6) 15.8(2.8) 73.3(18.4) 5 7.6(2.3) 7.9(2.0) 38.8(9.9) 6 2.0(8.4) 2.3(7.2) 12.8(34.8) 7 4.8(4.4) 4.4(4.1) 34.2(29.2) 8 2.7(2.5) 4.1(3.6) 20.2(20.1) 9 6.6(6.7) 7.3(2.6) 59.0(38.2) (26.8) 3.8(18.1) 33.5(83.4) 9

11 FACTOR Weekday Week end

12 FACTOR Weekday Week end Figure S1: Weekday and weekend diurnal pattern in Factors 1 to 10 11

13 Classification Weekday Weekend Speed kph (dotted line indicates the speed limit) TWMV Car or Van < 5.2 m Car + Trailer Rigid Lorry or van > 5.2 m 12

14 FACTOR Weekday Weekend Articulated Lorry Bus or Coach Figure S2: Weekday and weekend diurnal pattern in traffic 13

15 Classification Weekday Weekend wind_speed 1 air_temperature2 dewpoint 3 RH 4 BP 8 14

16 FACTOR Weekday Weekend CO 9 NO 10 NO2 11 NOX 12 O3 13 Figure S3: Weekday and weekend diurnal pattern in meteorology 15