Robustness of Land-Use Regression Models Developed from

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Robustness of Land-Use Regression Models Developed from Mobile Air Pollutant Measurements Marianne Hatzopoulou, Marie-France Valois, Ilan Levy, Cristian Mihele, Gang Lu, Scott Bagg, Laura Minet, and Jeffrey Robert Brook Environ. Sci. Technol., Just Accepted Manuscript • DOI: 10.1021/acs.est.7b00366 • Publication Date (Web): 27 Feb 2017 Downloaded from http://pubs.acs.org on March 18, 2017

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Environmental Science & Technology

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Robustness of Land-Use Regression Models Developed from Mobile Air Pollutant Measurements

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Marianne Hatzopoulou1*, Marie France Valois2, Ilan Levy3*, Cristian Mihele3, Gang Lu3, Scott Bagg4, Laura Minet1, Jeffrey Brook3**

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Department of Civil Engineering, University of Toronto, Toronto, Ontario, Canada, M5S 1A4

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Division of Clinical Epidemiology, McGill University, Montreal, Quebec, Canada, H4A 3J1

Air Quality Processes Research Section, Environment Canada, Downsview, Ontario, Canada, M3H 5T4 4

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School of Urban Planning, McGill University, Montreal, Quebec, Canada, H3A 0C2

*Current address: Technion Center of Excellence in Exposure Science and Environmental Health, Technion Israel Institute of Technology, Haifa, Israel **

Corresponding author, Air Quality Research Division, Science and Technology Branch, Environment Canada, 4905 Dufferin St., Toronto, Ontario, Canada, M3H 5T4. Telephone: (416) 739-4916. E-mail: [email protected]

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Abstract

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Land-Use Regression (LUR) models are useful for resolving fine scale spatial variations in average air pollutant concentrations across urban areas. With the rise of mobile air pollution campaigns, characterized by short-term monitoring and large spatial extents, it is important to investigate the effects of sampling protocols on the resulting LUR. In this study a mobile lab was used to repeatedly visit a large number of locations (~1800), defined by road segments, to derive average concentrations across the city of Montreal, Canada. We hypothesize that the robustness of the LUR from these data depends upon how many independent, random times each location is visited (Nvis) and the number of locations (Nloc) used in model development and that these parameters can be optimized. By performing multiple LURs on random sets of locations, we assessed the robustness of the LUR through consistency in adjusted R2 (i.e., coefficient of variation, CV) and in regression coefficients among different models. As Nloc increased, R2adj became less variable; for Nloc=100 vs. Nloc=300 the CV in R2adj for ultrafine particles decreased from 0.088 to 0.029 and from 0.115 to 0.076 for NO2. The CV in the R2adj also decreased as Nvis increased from 6 to 16; from 0.090 to 0.014 for UFP. As Nloc and Nvis increase, the variability in the coefficient sizes across the different model realizations were also seen to decrease.

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1. Introduction

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Exposure to traffic-related air pollution has been associated with various acute and chronic health effects. In particular, a number of studies have established positive associations between various health outcomes (e.g. cancers, hearth attacks, asthma) and exposure to nitrogen dioxide (NO2), an accepted marker of traffic-related air pollution.1-4 More recently, exposure to UFP has been associated with an increased risk of cardiovascular morbidity. 5,6

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The development of air pollution exposure surfaces in urban areas based on land-use regression (LUR) is one of the most common methods used to derive air pollution exposure in epidemiological studies.7-11 LUR methods are attractive for their lower computational requirements compared to dispersion or chemical transport models and for their ease of implementation when Geographic Information Systems (GIS) data are available.12 Until recently, NO2 was considered as the pollutant of choice in the development of LUR models for trafficrelated air pollution primarily because urban NO2 concentrations are dominated by vehicleinduced emissions of nitrogen oxides13 and because it is possible to conduct ambient monitoring with relatively inexpensive passive samplers.10, 11, 14-17 Along with the use of passive samplers, long-term monitoring (on the order of weeks) also characterizes these earlier NO2 LUR studies. The mean over several seasons is typically calculated and then a long-term exposure surface is generated. LUR usually offers a good fit for NO2 with coefficients of determination ranging from 54% to 89% with a number of monitoring sites ranging from 18 to 161.17-19 More recently, LUR was also applied for UFP in several cities including Vancouver,20 Toronto,21,22 Montreal,23 Barcelona, 24 and Amsterdam.25 In general, these models have demonstrated that the spatial variations in UFP can be captured using land-use and traffic predictors with coefficients of determination exceeding 50%. Further advances in LUR development have demonstrated the possibility of reducing estimation error through the development of hybrid approaches, which include a combination of LUR and Bayesian Maximum Entropy interpolation of the residuals.26,27

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Mobile monitoring emphasizes sampling on the roadway and provides the opportunity to achieve unparalleled spatial coverage compared to fixed-site sampling. Klompmaker et al. argue that short-term monitoring campaigns may be an efficient means of developing LUR models.18 In contrast, the relatively short sampling durations at each location (on the order of seconds at each road segment) raise an important question that relates to the number of observations or visits needed in order to achieve a stable average at each location. Often, we note that when mobile monitoring is used to develop LUR models, instruments are set-up at a 1Hz sampling frequency, collecting sec-by-sec readings which are ultimately merged with location data collected via GPS. In this case, either single road segments are used as individual sampling locations (whereby all readings collected at a road segment are averaged)21,22,28,29 or sec-by-sec readings are averaged at specified distance intervals across the road network (e.g. every 100m).30-32 The development of LUR models becomes highly sensitive to the number of sampling points per location (or road segment, distance interval) thus leading to the exclusion of locations with a low number of 3



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observations.22 For example, in the development of a UFP LUR for Montreal, Weichenthal et al., collected data for road segments (with multiple visits) but ultimately restricted the model to segments with more than 250 seconds over the multiple visits (440 segments) and discarded the remaining segments.23 Similarly, in Toronto, Sabaliauskas et al. designed 10 routes to collect UFP concentrations second-by-second. Measurements were aggregated into 112 road segments, with an average of 5 to 10 minutes of sampling per segment; all of which were considered in LUR model development.21 To date, LUR studies which involve either mobile monitoring or fixed monitoring with portable samplers, have covered varying numbers of sites and overall sampling durations of 5 minutes,22 15 minutes,24 30 minutes,18 1 hour,20 3 hours,33 and 5.5 hours.34 The number of sites or roads visited varies largely across the studies and while most studies attempt to justify the number and location of sampling sites as well as the sampling duration, there is a paucity of research investigating how robust or vulnerable LUR methods are to sampling protocols.

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This study explicitly aims at investigating the effect of sampling protocols on the resulting LUR model by developing a LUR analysis of NO2 and UFP in Montreal, Canada using data collected by a mobile laboratory in 2009. This study also attempted to maximize the representativeness of the discrete mobile measurements to the long term mean for multiple pollutants, while balancing cost, and assessed this factor in Levy et al.28 For this purpose, data for approximately 3,000 road segments were collected with multiple visits per segment across the different seasons in 2009. By drawing random sub-samples of segments and of visits per segment, we evaluated the robustness of LUR models across the various sub-samples. We hypothesize that the robustness of the LUR from these data depends upon the number of visits per location as well as the number of locations and that these parameters can be optimized to guide future collection and use of mobile measurements for LUR development.

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2. Materials and methods

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2.1 Air pollution data

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Concentrations of 19 different air pollutants were collected on the Island of Montreal using the mobile laboratory, CRUISER, during three different seasons (winter, summer, and fall) in 2009. This paper focuses on total particle counts, referred to hereafter as UFP, and NO2. We focused on these two pollutants because they are both markers of traffic-related air pollution and therefore have been mostly used in previous LUR studies. In addition, they were both measured at a 1-sec interval and they had the highest total number of data points collected thus enabling the robustness analysis which involves sub-sampling. The measurement details are described in Levy et al.28 Briefly, 1-second time resolution UFP was measured using either a GRIMM model number 5.403 or a TSI model number 3775. The inlet to these condensation particle counters had a 2.5 µm size cut and thus all particles below this size were counted. However, the added

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contribution to total numbers made by particles in the accumulation mode is expected to be a very small fraction of the total and UFP associated with combustion were expected to dominate the total numbers35-37 and thus be the main factor leading to spatial and temporal variability. NO2 was determined by subtracting separately measured, time synchronized values of 1 second NO and 1 second NOx (NO+NO2) using two instruments operating on the basis of chemiluminescence (Thermo Scientific / TECO 42CTL). The NOx instrument utilized a photolytic NO2 converter so that actual NO2 values (interference free NO2 ambient concentrations) were obtained.38

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The number of mobile measurement days in winter, summer and fall was 11, 17 and 6, respectively (the long term representativeness of the measurements compared to the Ville De Montreal long term air quality monitoring sites was examined extensively in our earlier paper.28 Two driving routes: 1) east Montreal and 2) central + west Montreal, which passed along or near highways, main roads and local streets, as well as residential, commercial and industrial areas were established in advance (Figure 1). The east route was used for approximately two thirds of the time due to interest in assessing the impacts on concentrations of and potential exposures to industrial emissions along with traffic. Based on geolocated 1-second UFP and NO2 data, the average, standard deviation and coefficient of variation were determined by road segment and day of measurement. A road segment extends from one intersection to another. For the analyses presented here, different numbers of available days were further averaged to produce segmentspecific multi-day values. Approximately 3,000 road segments were visited, some up to 35 times.

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Table S1 in the supporting information presents the numbers of road segments for which NO2 and UFP data were collected including the number of visits (Nvis), which typically corresponds to the number of days. After filtering all segments that had 3 or more visits, we retained over half of the segments and noted a similar distribution of road types as the original sample (the original sample has 12% expressways, 37% major roads, 41% local roads and the sample of segments with 3+ visits has 15% expressways, 30% major roads, 45% local roads). We therefore used the sample of segments with 3 or more visits as a base against which models based upon segments with more than 3 visits, up to a maximum of 16 or more visits, were compared. We chose the segments with more than 3 visits as a base because this cut-off maintains the road class distribution and spatial coverage of the population of approximately 3,000 road segments visited.

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Figure 1. Island of Montreal featuring data collection routes including the number of visits per road segment

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2.2 Generating land-use predictors

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Each road segment was associated with a number of land-use and built environment characteristics. These include variables computed as distances between the mid-point of the road segment and sources of UFP and/or NO2 (distance from the Montreal International Airport and distance from the Port of Montreal) and variables computed within buffers of sizes 50, 100, 150, 200, and 300m created around the midpoint of each segment. These variables include: number of bus stops, length of bus routes (in meters), number of industrial chimneys, length of rail lines (in meters), number of restaurants, length of expressways (in meters), length of primary highways (in meters), length of secondary highways (in meters), length of major roads (in meters), length of local roads (in meters), length of trails (in meters), total length of roads (in meters), population (number of individuals), number of commercial buildings, buffer area (in m2) occupied by different land-use types (commercial, governmental/institutional, open areas, parks/recreational, residential, resource/industrial, water body), number of trees, average building height (in meters), building footprint (in m2). Geographic analyses (buffering and intersections) were conducted using ArcGIS (version 10). GIS layers for the building footprint, rail network, road network, and land-use were obtained from DMTI Spatial Inc. for the year 2008. Layers for bus stops and bus

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lines were obtained from the local transit provider, the Société de Transport de Montreal, also for 2008.

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For the purpose of more directly linking the effect of traffic on observed UFP and NO2, we made use of a coupled traffic simulation and vehicle emission model we previously developed for the Greater Montreal Area.39 The traffic simulation model allocates passenger car traffic on the road network at different times of day by applying a stochastic user equilibrium algorithm. It uses as input household travel survey data collected in 2008 on a 5% sample of the Montreal population in addition to information on the road network (road classifications, number of lanes, capacity, speed limits, and turning restrictions). The model generates outputs at the level of the road segment for vehicular composition (light-duty vehicles and sports utility vehicles including the model year), volume, and speed. In order to refine our measure of road traffic, we used the output of the same traffic assignment model and transformed traffic volumes, compositions, and speeds into a measure of daily NOx emissions per road segment (in grams). In order to estimate emissions, we derived emission functions from the model MOVES (motor vehicle emissions simulator), the latest EPA emission inventory model. MOVES was calibrated for the Montreal vehicle fleet and driving characteristics and reflected local fuel composition and vehicle fuel efficiencies. The emission functions were multi-dimensional, representing the variations of emission factors (in g/vehicle.km) as a function of vehicle type, age, road type (highway, arterial, local), speed, and ambient temperature and relative humidity. The methodology for emission modeling is documented in Sider et al.39 Using the same buffer sizes mentioned previously, we calculated the total NOx emissions (in grams) within each buffer based on the number and proportion of segments falling within.

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In general, the variables compiled are consistent with those documented in other studies.20-24 We also included variables that have not been traditionally used in LUR models (such as building height and NOx emissions), which we expected would have significant associations with ambient UFP and NO2.

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2.3 Regression analysis

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Comparing models for segments with 3+ visits and segments with 16+ visits

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For both pollutants, we first developed regression models using all segments with 3 or more observations (Nvis=3+) as well as for segments with 16 or more observations (Nvis=16+). A natural log transform was applied to the mean NO2 and UFP (average across all the visits) after examining the density plot of both variables, resembling a lognormal distribution. The same methodology was adopted for both pollutants in the development of the linear regressions. For each potential predictor, we developed a univariate model in addition to a scatterplot (with 50% LOESS line) and graphs of the natural cubic spline (NS) fit for 2, 3 and 4 degrees of freedom. All variables were continuous. Variables that were associated with ambient UFP or NO2 7



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concentrations in simple linear models (i.e. 95% confidence intervals excluded the null) were retained for evaluation in multivariable models. These remaining variables were evaluated in multivariate models by adding variables one at a time (starting with those that had the highest effect in the univariate models) and then including or excluding a variable if it did not increase the adjusted R2 by 0.5%. If more than one buffer size was examined for a given variable, the buffer size with the strongest association was retained for analysis. Similarly linear and nonlinear effects were tested for each variable. All coefficient sizes are reported as mean percent change for a change in the interquartile range (unless otherwise specified). Models developed for segments with more than 3 visits and models developed for segments with more than 16 visits were compared based on the values of the adjusted R2, coefficients, sets of predictors, and coefficient sizes. Only statistically significant variables with interpretable coefficient signs in terms of their association with UFP/NO2 were kept in the models.

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The comparison of the model with 3+ visits with the model based on 16+ visits was undertaken to assess the changes in the set of predictors, their effects, and the overall predictive power of the model when a criterion is established requiring a minimum number of visits (i.e., 16) is used to derive segment-specific averages. Following this comparison, the regression models developed for segments with more than 16 visits were then used as a new base against which models developed with varying samples of segments and of number of segment visits were developed.

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Investigating the effect of number of segments (Nloc) using segments with Nvis= 16+

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The emphasis in this sensitivity analysis is on examining whether various samples of segments will have an effect on the predictive power of the model with or without the same set of predictors. First, using the regressions developed for segments visited at least 16 times (Nvis= 16+), we tested the effect of estimating the same land-use regression models (i.e., those based upon the same set of predictors) on a sub-sample of these segments rather than the entire set. We therefore randomly drew a) 60 samples of 100 segments (i.e., Nloc=100) each; b) 60 samples of 150 segments (i.e., Nloc=150) each; c) 60 samples with Nloc=200; d) 60 samples with Nloc=250; and another set of e) 60 samples with Nloc=300. Each sample (i.e., sub-population of segments) was constrained by the road classification strata (expressways, major, local), maintaining the same distribution of roads as the one for the entire set of segments with more than 16 observations. Every time a new sample was drawn, the same predictors originally present in the model with all segments (with Nvis= 16+) were imposed. This analysis was conducted for NO2 and UFP.

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Having the same set of predictors allows for an easy comparison between the sets of models (cases a to e); however in order to test whether the same conclusions would hold true when a new set of predictors is explored every time a new regression is estimated, we conducted the same analysis but only with two sets of segments characterized by Nloc=100 and Nloc=300. In this

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analysis, we adopt the same method introduced earlier for building the regression, by exploring the entire set of potential predictors every time a new regression is developed with a different sample of segments. We compared the R2adj of the different models and most importantly, we examined the differences in the final predictors selected and in their coefficient sizes. We hypothesize that as we move from samples of 100 to 300 segments, the predictor sets for the different models of 300 segments will look similar. This would mean that the LUR model is stable when various sets of 300 segments each are selected, suggesting that there is a “universal” set of predictors. This analysis was only conducted for UFP with the assumption that a similar trend would be observed for NO2. We also only drew 7 different samples of 100 segments and 7 different samples of 300 segments.

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Investigating the effect of number of visits (Nvis) using segments with Nvis= 16+

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In order to evaluate the effect of Nvis on the models and regression coefficients, we drew 10 random samples of 6, 8, 10, 12, 14, and 16 observations (or visits) for each segment using the entire set of segments with 16 or more visits and calculated each segment mean UFP from the prescribed number of sampled visits. This analysis was only conducted for UFP due to the slightly larger number of observations available compared to NO2. The samples of visits were constrained by seasonality, we always drew half of the visits from summer and part of the fall and the other half from fall and winter. We also did not allow for the same visit to be drawn twice in the same regression. This latter constraint meant that a segment with just 16 visits would have the same mean UFP in the 10 samples of 16 visits but there would be slightly varying means in the 10 samples of based upon smaller numbers of visits. We compared models based on the values of the adjusted R2 coefficients and in terms of the variation in the values of the regression coefficients.

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3. Results

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3.1 Distribution of road segments

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Table S2 in the supporting information presents the distributions of NO2 and UFP across all segments, segments visited 3+ times (1,821 segments with UFP data and 1,739 with NO2 data), and segments visited 16+ times (611 segments with UFP data and 557 with NO2 data). We observe that segments visited 16+ times have lower mean NO2 and UFP concentrations. Indeed, an examination of the types of roads remaining in the sample of segments visited at least 16 times reveals that highways, which make up about 12% of the segments in the original sample, are no longer present in the sample of segments with 16+ visits. While the original sample is roughly composed of 12% highways, 37% major roads, and 41% local roads (the remaining include trails and other paths), the sample of segments with 16+ observations is roughly

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composed of 25% major roads and 64% local roads (the remaining include trails and other paths). This was a result of the design of the mobile sampling campaign, which had an enhanced focus on East Montreal (Figure 1) where there is a greater contribution from industry in addition to traffic, and where our driving route was designed to be more representative of exposures (e.g., more measurements in residential areas). For comparison purposes, note that the overall road type distribution in the Greater Montreal Region includes about 10% highways, 15% major roads, and 75% local roads. Although the sample of segments with 16+ observations no longer reflects the original sample of segments (or the road class distribution in the Montreal region), it does not pose a significant limitation to the study since our analysis focuses on an intercomparison of models developed from the sample of 16+ segments.

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3.2 Comparing models for segments with 3+ visits and segments with 16+ visits

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The results of the linear regressions developed for UFP are presented in Table 1. We clearly observe that the regression model estimated for segments with at least 16 observations achieved a higher adjusted R2 with fewer explanatory variables compared to the model developed with segments having 3+ visits. In both models, traffic emissions of NOx had the highest effect indicating the strong positive association between traffic and UFP. Other positive effects include the length of bus routes and number of bus stops. Distance to the airport was a common variable to both models, with a positive sign indicating that segments distant from the airport which also coincide with the east end of Montreal, are more polluted. The effect of the airport itself as a source of UFP emissions was not detected, probably due to the clustering of segments with those that are closer to the airport being located on the west side of the island which is mostly residential (and located upwind of the airport most of the year). In both models, the number of trees has a small, albeit significant negative effect. In the model for segments visited at least 3 times, the number of trees was included within a small buffer, and therefore captures the effect of on-street trees. This variable continues to be significant even after parks are included in the model. In the model for segments visited at least 16 times, the number of trees within a larger buffer (150 m) was a significant variable while park area did not have an effect which indicates that in this case, the number of trees is possibly serving for both parks and on-street trees. It is also important to note that the adjusted R2 in the model with Nvis = 3+ is smaller than the one obtained in the model with Nvis = 16+. This could be due either to the longer-term average of the segments with Nvis = 16+ or to the more constrained set of roads in the model with Nvis = 16+. For this reason, we decided to use the model with Nvis = 16+ as a base against which various models based on sub-populations can be compared.

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The results of the linear regressions developed for NO2 are presented in Table 2. Although the models for NO2 were not constrained by the same variables as the UFP models, the final set of variables was relatively similar. Emissions of NOx, lengths of major roads, number of bus stops, and length of bus routes were all associated with positive effects. The distance to the Montreal

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airport had a positive and significant effect in the model for segments visited at least 16 times and a negative effect in the model for segments visited at least 3 times. Note that the models developed for NO2 relied on a sample size of 480 (instead of 557 which includes all segments with NO2 and 16+ visits) due to missing land-use data for a small number of segments. The two models based on Nvis = 3+ and Nvis = 16+ are not as different from each other in terms of R2 as the models for UFP. This illustrates the nature of UFP (very high temporal and spatial variability) compared to NO2. The fact that NO2 models had lower R2 values than UFP models is presumably due to the lack of background-adjustment in the case of NO2.

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Table 1. Multivariate model for ln(UFP) for segments visited at least 3 times (n=1,821) and for segments visited at least 16 times (n=611) Nvis = 3+; n=1,821

For ln (UFP) for increase of IQ if not otherwise indicated Mean Percent Change 95% CI 43.94 36.79, 51.45 15.58 11.88, 19.40 -23.03 -27.24, -18.58 7.71 3.86, 11.70 3.72 2.59, 4.86 12.22 8.57, 15.99 19.60 15.05, 24.32 10.67 7.20, 14.26 -3.62 -5.89, -1.30 -3.98 -6.29, -1.61 4.96 1.58, 8.44 For ln (UFP) for increase of IQ if not otherwise indicated Mean Percent Change 95% CI 94.93 83.08, 107.55 10.05 6.88, 13.32 6.48 2.63, 10.47 13.87 11.52, 16.27 -5.49 -8.52, -2.35 15.94 11.64, 20.40 8.33 3.31, 13.59 4.69 1.58, 7.89

AIC: 1910.60 Adjusted R2: 0.60

Annual NOx emissions from traffic - 500m Total length of C1, C2, C3, C4 and C5 roads - 150m Land Use - residential - 50m Number of STM bus stops - 500m Number of commercial buildings - 500m Land Use - resource and industrial - 500m Population - 500m Distance to Montreal Airport (m) Number of trees - 50m Land Use - parks and recreational - 500m Number of restaurants - 50m Nvis = 16+; n=611

AIC: -218.63 Adjusted R2: 0.74

Annual NOx emissions from traffic - 150m Length of bus routes - 150m Number of STM bus stops - 150m Land Use - resource and industrial - 500m Number of trees - 150m Number of commercial buildings - 500m Number of chimneys - 500m Distance to Montreal Airport (m)

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Table 2. Multivariate model for ln(NO2) for segments visited at least 3 times (n=1,739) and for segments visited at least 16 times (n=480) Nvis = 3+; n=1,739

For ln (NO2) for increase of IQ if not otherwise indicated Mean Percent Change 95% CI 38.65 31.70, 45.95 4.36 0.70, 8.16 -17.96 -23.80, -11.68 -12.75 -16.93, -8.36 5.60 1.23, 10.16 10.42 7.03, 13.90 3.55 2.09, 5.03 28.93 23.37, 34.75 -4.26 -7.62, -0.78 10.83 6.82, 14.98 -0.0025 -0.0047, -0.0002 For ln (NO2) for increase of IQ if not otherwise indicated Mean Percent Change 95% CI 47.19 28.82, 68.19 12.22 7.58, 17.06 -11.96 -17.96, -5.51 -10.13 -15.28, -4.67 5.78 0.46, 11.37 0.07 0.01, 0.13 7.83 2.57, 13.37 11.36 3.84, 19.42 1.99 -0.73, 4.79 -1.85 -3.29, -0.39 5.45 1.10, 9.99 8.89 3.57, 14.49 2.48 -3.59, 8.94

AIC : 2159.73 Adjusted R2: 0.51

Annual NOx emissions from traffic - 500m Length of arterial roads - 500m Land Use - residential - 50m Length of local roads - 50m Number of STM bus stops - 500m Length of bus routes - 150m Number of commercial buildings - 500m Population - 500m Distance to Montreal Airport (m) Land Use - resource and industrial - 500m Land Use - government and institutions - 50m Nvis = 16+; n=480

AIC: 60.64 Adjusted R2: 0.55

Annual NOx emissions from traffic - 150m Length of bus routes - 150m Land Use - residential - 50m Length of local roads - 150m Length of arterial roads - 500m Length of major arterial roads - 50m Number of commercial buildings - 150m Number of chimneys - 500m Number of STM bus stops - 50m Land Use - parks and recreational - 250m Distance to Montreal Airport (m) Average building height - 500m Building footprint - 500m

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3.3. Investigating the effect of number of segments (Nloc) using segments with Nvis= 16+

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The analysis of the effect of number of segments (Nloc) on the regressions of ln(NO2) and ln(UFP) was conducted for 60 sets, each including 100 road segments and repeated another four times, each time with 60 sets with Nloc=150, 200, 250, and 300. Figure 2 presents the variation of the adjusted R2 coefficient reflecting the 60 different regression models of ln(UFP) estimated based on samples of 100, 150, 200, 250, and 300 segments while Figure 3 presents the results of the same analysis for NO2. It is important to note that in each case, NO2 and UFP, the predictors were constrained to be the same as the predictors of the base model developed based on all segments visited at least 16 times.

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In the case of UFP and with 100 segments, we observe a significant variability in the adjusted R2 ranging between 0.56 and 0.85 (with a coefficient of variation = CV = 0.088), distributed around the adjusted R2 of the base model with Nvis ≥ 16. With an increase from 100 to 300 segments in each sample, the distribution of values for the adjusted R2 of the 60 models has a smaller range 12


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(between 0.69 and 0.79) and CV equal to 0.029 indicating that with 300 segments, we achieve models that are very similar to the base model with Nvis ≥ 16. With 100 segments, the large range in possible R2 values indicates the potential that any given selection of 100 segments has a greater likelihood of yielding a model with poorer predictive ability. The same analysis conducted with NO2 reveals a similar effect of increasing the sample size from 100 to 300 segments. With 100 segments, the range of adjusted R2 values extends from 0.39 to 0.73 with a CV equal to 0.115, dropping to 0.076 with 300 segments. The fact that the initial model for NO2 (based on all segments with Nvis ≥ 16) has a lower R2 than the UFP model and the larger sensitivity of the NO2 regression to the number of segments reflects the nature of NO2, affected not only by traffic and the built environment but also by “more regional effects” with an influence on the chemistry of NO2.

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Figure 2. Variation of adjusted R2 across 60 models for UFP estimated for samples of 100, 150, 200, 250, and 300 segments. The dotted line represents the Adjusted R2 for the sample of all segments with Nvis ≥ 16.

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Besides the examination of the variation in the R2 values across models as a function of Nloc, we also investigated the variation in the size of the regression coefficients across the different models since the UFP and NO2 models were estimated with the same variables included in the base model, but their coefficients could vary to optimize fit to the data (i.e., the particular segments selected). Figures S1 (UFP) and S2 (NO2) in the supporting information illustrate the variation in the size of the coefficients (in mean percent change MPC for an increase in the IQR). In the case of both NO2 and UFP, we observe that as the number of segments increases, the variability in the coefficient size decreases. With 300 segments, the coefficients estimated in 20 different models, are entirely included within the confidence interval of the coefficient in the model with all segments.

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In order to investigate the stability in the set of predictors, we conducted the same analysis with Nloc=100 and Nloc=300 but without constraining the set of predictors to be the same as the base set. Instead, we searched for a new set of predictors every time a regression is estimated. Figure 4 illustrates the variation of adjusted R2 in the samples of 100 and 300 segments indicating a larger variability in the samples of 100 segments compared to the samples of 300 segments. Compared to the models constrained to the same predictor set (i.e., comparing Figures 2 and 4), we notice that models that search for a new predictor set have a smaller variability in the R2adj (Figure 4). This is expected since the search for new predictors allows for optimizing the model every time.

Figure 3. Variation of adjusted R2 across 60 models for NO2 estimated for samples of 100, 150, 200, 250, and 300 segments. The dotted line represents the Adjusted R2 for the sample of all segments with Nvis ≥ 16.

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In terms of the predictors themselves, we observe that the same set which was included in the model with all segments having 16 or more visits (Table 2) is generally appearing in the different models however, the combinations of variables are slightly different and the buffer sizes for the same variables may vary from one model to another. Variables with large effects in the original model with all segments (e.g. NOx, resource and industrial, length of bus routes) appear in most instances while variables which had a small effect in the original model (e.g. distance to Montreal airport, number of chimneys, and number of trees) appear in only a few model instances. Figures S3 and S4 in the supporting information illustrate the number of models in which selected variables appear, Figure S3 illustrates the variables with large effects in the original model while Figure S4 illustrates the variables with small effects in the original model.

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This analysis sheds light on the robustness of the LUR model illustrating that with 250 to 300 segments sampled randomly across the area, it is possible to achieve an adjusted R2 close to the R2 of the model developed with all segments (this conclusion is substantiated by Figures 2 and 4). This finding holds whether a new set of predictors is identified every time or when the predictor set remains the same. We also demonstrate that even when a new set of predictors is searched for, generally the same predictors that were in the original model with all segments are included in the different models, with slight variations in the variable combinations across the models. This is particularly true in the case of the 300 segments (rather than the 100 segments) whereby both the R2 and the predictor set are more tightly distributed around -and similar to- the R2 and the predictor set of the model with all segments having Nvis=16+. This would suggest that the potential for a more ‘universal model’ is greater with more segments.

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Figure 4. Variation of adjusted R2 for UFP estimated for samples of 100 and 300 segments without constraining the models to the predictor set in the sample of all segments with Nvis ≥ 16. The dotted line represents the Adjusted R2 for the sample of all segments with Nvis ≥ 16.

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3.4 Investigating the effect of number of visits (Nvis) using segments with Nvis= 16+

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The analysis of the effect of the number of visits was conducted only with UFP data because a larger number of segments with Nvis greater than 16 exists. This is important because we examined the effect of Nvis going up to 16 visits which means that at that point, we need to draw for each segment, various random samples of 16 visits. For segments with just 17 visits, the samples of 16 visits would only vary by one segment meaning that characterizing the distribution of results is more uncertain. For UFP, our sample of segments with 16+ visits has a median number of visits equal to 18 with a 75th percentile of 19 and a maximum of 34. Figure 5 illustrates the variations in the adjusted R2 across 10 different samples each with Nvis equal to 6, 8, 10, 12, 14, and 16 visits. We clearly observe that with Nvis = 6, none of the ten models were able to achieve an adjusted R2 equal to 0.74 (the value derived from the model estimated for all visits – the base model). Models with Nvis = 10 and 12 achieve higher values for the adjusted R2 however they remain below the values for the base model. At Nvis = 16, the adjusted R2 values for the ten samples are all included between 0.7 and 0.74 with a few of them overlapping with the adjusted R2 for the base model. The CV in the R2adj decreases as Nvis increases from 6 to 16; from 0.090 to 0.014. Recall that the models estimated for these sub-samples include the same set of variables present in the base model.

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As in our sensitivity analysis for Nloc, we also examined the variability in the size of the regression coefficients across the different samples with varying Nvis. We observe that with 6 and 10 visits, the coefficient sizes are highly variable, with large confidence intervals as illustrated in Figure S5 in the supporting information. As Nvis increases, the variability in coefficient sizes decreases as do the confidence intervals. The latter begin to overlap significantly with the confidence intervals for the variables in the base model (with all segments). At Nvis = 16, most coefficients across the different model realizations have values and confidence intervals which are very close to the base model.

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Figure 5. Variation of adjusted R2 for UFP as a function of Nvis with models estimated using data for 6, 8, 10 visits, 12, 14, and 16 visits (randomly sampled from the total number of visits) The dotted line represents the Adjusted R2 for the sample of all segments with Nvis ≥ 16

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4. Discussion

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While the recent literature swells with LUR studies with varying numbers of sampling locations and durations, little is known about the effect of those two parameters on the resulting LUR. Our data collection campaign presented a unique opportunity to investigate the effect of number of

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locations and number of visits since a relatively large pool of road segments was visited numerous times.

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In general, the predictors included in our models are consistent with those from other cities.20-24 A novel variable that is present in our model is the estimate of average NOx emissions from road traffic. Since it is challenging to collect detailed traffic count data across large geographical areas, we used an estimate of simulated NOx emissions from traffic extracted from a transportation-emissions model. Our measure of NOx emissions reflected traffic volume as well as traffic speed and fleet composition. An important limitation of our emission estimates is that they only reflect the contribution of household travel and do not include trucking and other commercial movements. Data regarding the latter are often proprietary and difficult to simulate. Despite this limitation, we believe that NOx emissions represent a better proxy for the effect of traffic since they incorporate the effects of traffic volume, composition, and speed into a single measure. Ideally, emissions of UFP would also be computed however their emission rates are not widely available for light-duty or heavy-duty vehicles. Thus here we assume that NOx emissions are also indicative of UFP emissions for the purpose of LUR development. To some extent including such a term in the LUR model is a step towards combining features of a sourceoriented dispersion model with a LUR model.

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Several LUR models based on data collected by mobile sampling have been developed in the last few years. Different methods were adopted regarding campaign design and the association of measurements with specific locations. In a study looking at UFP concentrations in Amsterdam and Rotterdam, The Netherlands, Kerckhoffs et al. collected measurements on 2,964 road segments with an electric car, and each segment was visited once or twice. This resulted in an average of 12 seconds of UFP data recorded for each road segment. When developing their final LUR model, the authors kept all road segments in their analysis, even those visited only once, because considering only the segments visited twice (which meant considering only one quarter of the dataset), provided very comparable standard errors of the regression slopes.29 Similarly, Weichenthal et al. choose road segments as their unit of analysis. Authors traveled around the city of Toronto in cars while recording UFP concentrations, and kept only segments with more than 250 seconds of measurement for their final LUR model. It was justified by the fact that this number provided the best compromise between a sufficient number of road segments and a good spatial coverage of the area.22 Sabaliauskas et al. developed a hybrid methodology mixing fixed and mobile monitoring. Their UFP mobile measurements were performed on 10 routes that were visited three times. Each measurement was associated with the closest road segment. In total, 112 segments were covered between 5 and 10 minutes of measurements. All segments were kept for the development of the LUR model.21

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In other studies, measurements were aggregated into points separated by 50, 100, 200, or 300m. In Hong Kong, Shi et al. used a semivariogram function to determine the most appropriate spatial range, choosing 300m, which provided 222 points to use for the LUR model.31 After carrying out a bicycle-based monitoring campaign on three sampling routes and collecting 85 18


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hours of measurements, Hankey and Marshall studied several temporal and spatial aggregation resolutions. They found that modifying the spatial resolution did not have a great impact on the model performance contrary to the time-averaging. Their base-case model was based on a spatial aggregation every 100m, because it was a value close to 120m, the average block length in Minneapolis where they conducted their study, and because it enabled them to have sufficient samples per location (i.e. more than 50). Their model was composed of 1,101 points. The authors also studied spatial aggregations every 50m and 100m.30

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Another way of aggregating mobile measurements into points is to average over time, to get for instance a value for each minute of sampling that is then associated with a specific location. Li et al. sampled NOx and PM2.5 on 210 miles of roads over 20 days, and averaged their measurements into one-minute concentrations.40 Similarly, Smargiassi et al. had measurements every 6 seconds that they averaged over one minute, and took the central point of their 6 seconds-measurements as the location of the sample.41 Larson et al. developed a particular methodology for their mobile monitoring campaign. They had chosen 39 fixed intersection locations prior to the campaign and sampled UFP by doing a cloverleaf around them, therefore ensuring the intersection was crossed four times. They sampled each location only once, but had between 5 and 13 minutes of recording per location.42

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With the rise of mobile monitoring campaigns for air pollution characterized by short-term monitoring and large spatial extents, it is important to investigate the effects of sampling protocols on the resulting LUR models. Our study suggests that caution should be exercised when designing short-term sampling campaigns, as LUR model outcomes are highly sensitive to the locations visited, the number of locations, and the number of visits at each location. In this study, we observe that beyond 150-200 segments and 10-12 visits per segment, our curves begin to show reduced variability indicating more robust LUR models. However, the urban context is important to consider in judging if the optimal number of locations and visits found from our campaign in Montreal is applicable elsewhere. It is difficult to predict whether the actual numbers of segments and visits that we found as optimal in this study would be the same in a different context, but we expect that in similar urban areas with similar intra-urban variability in concentrations of NO2 and UFP, the optimum Nloc and Nvis would not be very different. It is really the variability in repeated measurements that gives rise to these results. This paper is primarily intended to inform the design of data collection campaigns. As we often observe in the recent literature, mobile campaigns are designed in a semi ad-hoc manner (identifying routes and equipping individuals with instruments as they walk, cycle, or in a mobile lab) balancing a range of objectives.

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Our study illustrates that mobile campaigns can be very inefficient especially if large portions of the data will end up being discarded because of low sampling frequency at a large number of locations. Spatial variability is more important than spatial coverage especially in large metropolitan areas where the intuition of the campaign designer would be to maximize coverage by sampling air pollution along hundreds of kilometers of unique roads. Beyond a certain 19



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number of road segments that ensure spatial variability, there is a point of diminishing return and the campaign efforts should be directed towards increasing the number of visits per location. The “optimal” numbers of segments and visits that we have identified in this study may not apply to all types of cities. However, our analysis sheds light on the importance of these parameters in campaign design. Our methodology is applicable to every dataset generated through mobile air pollution monitoring and therefore can be used as a diagnostic tool during LUR model building. Current LUR studies often generate a single model derived from the entire dataset. Yet, our analysis demonstrates that one can arrive at widely different LUR models with portions of the dataset up to a point where models and coefficients become stable. This optimum should be considered when LUR models are developed from mobile sampling.

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Acknowledgements

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This study was conducted thanks to a grant from Environment Canada.

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Supporting Information

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The Supporting Information of this article contains two tables with descriptive statistics for the segments sampled, two figures illustrating the variations in the size of the coefficients for variables in the NO2 and UFP models, two figures illustrating the variation in the coefficient sizes of selected variables while the UFP models are not constrained to the same set of predictors and a search for new predictors is conducted, one figure illustrating the variation in the size of the coefficients for the variables in the UFP models across the different samples with varying numbers of visits Nvis.

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Robustness of Land-Use Regression Models Developed from

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