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Estimating PM2.5 Concentrations in the Conterminous United States Using the Random Forest Approach Xuefei Hu, Jessica Hartmann Belle, Xia Meng, Avani Wildani, Lance Waller, Matthew Strickland, and Yang Liu Environ. Sci. Technol., Just Accepted Manuscript • Publication Date (Web): 23 May 2017 Downloaded from http://pubs.acs.org on May 25, 2017

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Environmental Science & Technology

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Estimating PM2.5 Concentrations in the Conterminous United States Using the Random

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Forest Approach

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Xuefei Hu1, Jessica H. Belle1, Xia Meng1, Avani Wildani2, Lance A. Waller3, Matthew J.

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Strickland4, Yang Liu1*

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Atlanta, GA 30322, USA

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USA

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Department of Environmental Health, Rollins School of Public Health, Emory University,

Department of Mathematics and Computer Science, Emory University, Atlanta, GA 30322,

Department of Biostatistics & Bioinformatics, Rollins School of Public Health, Emory

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University, Atlanta, GA 30322, USA

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School of Community Health Sciences, University of Nevada Reno, Reno, NV 89557, USA

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KEYWORDS: PM2.5, AOD, National, and Random Forests

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* Corresponding Author:

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Yang Liu

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Tel: +1-404-727-2131, Fax: +1-404-727-8744

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E-mail: [email protected]

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1 ACS Paragon Plus Environment


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Abstract: To estimate PM2.5 concentrations, many parametric regression models have been

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developed, while non-parametric machine learning algorithms are used less often and national-

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scale models are rare. In this paper, we develop a random forest model incorporating Aerosol

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Optical Depth (AOD) data, meteorological fields, and land use variables to estimate daily 24-

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hour averaged ground level PM2.5 concentrations over the conterminous United States in 2011.

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Random forests are an ensemble learning method that provides predictions with high accuracy

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and interpretability. Our results achieve an overall cross validation (CV) R2 value of 0.80. Mean

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prediction error (MPE) and root mean squared prediction error (RMSPE) for daily predictions

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are 1.78 and 2.83 µg/m3, respectively, indicating a good agreement between CV predictions and

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observations. The prediction accuracy of our model is similar to those reported in previous

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studies using neural networks or regression models on both national and regional scales. In

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addition, the incorporation of convolutional layers for land use terms and nearby PM2.5

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measurements increase CV R2 by ~0.02 and~0.06, respectively, indicating their significant

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contributions to prediction accuracy. Two different variable importance measures both indicate

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that the convolutional layer for nearby PM2.5 measurements and AOD values are among the most

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important predictor variables for the training process.

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1. Introduction

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PM2.5 refers to airborne particles less than 2.5 µm in the aerodynamic diameter and has been

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linked to many adverse health outcomes including cardiovascular and respiratory morbidity and

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mortality 1-4. Hence, obtaining accurate local PM2.5 concentrations plays a crucial role in

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addressing many environmental public health concerns. However, measurements from central-

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site monitors often lack adequate spatiotemporal resolution to capture variability in the study

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population exposures, thus resulting in exposure error and biased health effect estimates, while

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using remote sensing and air quality models can improve spatiotemporal variability of ambient

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pollutant concentrations and related exposures5.

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Satellite-derived aerosol optical depth (AOD) data with comprehensive spatiotemporal coverage

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have the capability to expand PM2.5 predictions beyond those provided by ground monitoring

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networks alone and such data have been increasingly used for PM2.5 concentration estimation in

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areas where ground measurements are not available. AOD products used in previous studies

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include those derived from the Moderate Resolution Imaging Spectroradiometer (MODIS) 6-8,

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Multiangle Imaging SpectroRadiometer (MISR) 7, 8, Geostationary Operational Environmental

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Satellite Aerosol/Smoke Product (GASP) 9, 10, Multi-Angle Implementation of Atmospheric

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Correction (MAIAC) 11-13, and Visible Infrared Imaging Radiometer Suite (VIIRS) 14. To

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establish the relationship between PM2.5 and AOD, previous efforts tend to focus on the

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development of various regression models 9, 11, 15. Those models have evolved from the use of

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AOD as the only predictor 16-18 to the incorporation of multiple additional predictors including

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meteorological and land use variables 6, 7, 9, 13, 19, 20 and from one-stage 6, 18, 19 to multi-stage

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models 9, 11, 15, 20, 21.



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Although parametric regression models can sometimes reach a high level of prediction accuracy

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with cross-validated R2 values above 0.8 22, they become increasingly complicated and encounter

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difficulties when datasets have a large number of predictors and many data records. Compared to

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traditional parametric regression models, non-parametric machine learning algorithms have

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several strengths. First, they typically involve fewer and less restrictive assumptions regarding

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independence of observations and distributions of outcomes and these assumptions are refined as

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new data are added. Second, modelers do not need to define as strict of a set of relationships

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among variables before implementing non-parametric machine learning algorithms as they do for

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traditional parametric regression approaches. Examples of the use of non-parametric machine

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learning algorithms for PM2.5 concentration estimation include Gupta and Christopher 23, who

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used an artificial neural network (ANN) to estimate surface level PM2.5 from MODIS AOD data

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in the southeastern United States. Zou, et al. 24 proposed a radial basis function (RBF) neural

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network method to estimate PM2.5 concentrations in the state of Texas, USA. Reid, et al. 25used

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the generalized boosting model (GBM) with 29 predictor variables to estimate PM2.5

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concentrations during the 2008 northern California wildfires. Di, et al. 26 used a backward

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propagation neural network to calibrate GEOS-Chem simulations and predicted PM2.5

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concentrations in 1 km x 1 km grid cells in the Northeastern United States.

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These studies demonstrate the potential of using non-parametric machine learning algorithms for

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PM2.5 concentration estimation on the regional scale. Nevertheless, such efforts made on a

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national scale (e.g., over the conterminous United States) are still very limited to date. Zhan, et

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al. 27 developed a geographically-weighted gradient boosting machine (GW-GBM) to predict

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daily PM2.5 concentrations across China. Di, et al. 28 incorporated convolutional layers into a

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neural network to account for spatial and temporal autocorrelation and PM2.5 concentrations were


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estimated with high accuracy (e.g., cross-validated R2 above 0.8) over the continental United

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States from 2000 to 2012. Although neural networks tend to produce high prediction accuracy,

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their results are difficult to interpret. Neural networks lack variable importance measures in the

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classification, which can help estimate the strength of relationships between PM2.5 and various

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predictors (e.g., meteorological and land use variables). Additional families of machine learning

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algorithms provide such variable importance measures, and when building a national model for

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PM2.5 concentration estimation, we examined random forest algorithm in this light. Like neural

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networks, random forests provide multi-variate, non-parametric, non-linear regression and

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classification based on a training dataset. Because random forests are an ensemble method, the

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training time can be reliably tuned based on desired accuracy and available computing resources.

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More importantly, the random forest approach also provides variable importance measures to

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measure the prediction strength of each variable 29, thereby yielding more interpretable results

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than those typically generated from neural networks.

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In this paper, we develop a multi-variate random forest model incorporating AOD data (e.g.,

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satellite AOD and model simulated AOD), meteorological fields, and land use variables to

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estimate daily 24-hour averaged ground-level PM2.5 concentrations over the conterminous United

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States for the year 2011. Prediction accuracy is evaluated by 10-fold cross validation (CV)

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statistics, and two variable importance measures are implemented to examine the impact of each

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predictor on PM2.5 concentration estimation on a national scale.

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2. Materials and Methods

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We define our study area as the conterminous United States consisting of 48 adjoining U.S.

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states and Washington D.C. (Figure 1). The entire area is divided into nine climate regions,



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including Northwest, West North Central, Northeast, East North Central, Central, West,

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Southwest, South, and Southeast. These climate regions were identified by National Oceanic and

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Atmospheric Administration’s (NOAA’s) National Centers for Environmental Information

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scientists (https://www.ncdc.noaa.gov/monitoring-references/maps/us-climate-regions.php). [Insert Figure 1 about here]

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2.1 PM2.5 measurements

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The 24-hour averaged PM2.5 concentrations for 2011 collected from 1248 U.S. Environmental

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Protection Agency (EPA) federal reference method samplers were downloaded from the EPA’s

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Air Quality System Technology Transfer Network (http://www.epa.gov/ttn/airs/airsaqs/).

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2.2 AOD data

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We use satellite-derived AOD from MODIS as our primary predictor and GEOS-Chem AOD

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simulations when satellite AOD is missing.

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2.2.1 MODIS AOD

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Collection 6 level 2 Aqua MODIS retrievals at 550 nm wavelength, specifically MYD04_L2

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files, at a nominal resolution of 10 km were regridded to the 12 x 12 km2 grid used in the

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Community Multi-Scale Air Quality (CMAQ) modeling system 30. Regridding to a static grid is

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necessary when modeling with Level 2 MODIS data since the pixels shift in location and size

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with each satellite overpass. We used a regridding approach based on the full area of individual

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MODIS pixels, using pixel boundaries reconstructed from neighboring midpoints using a

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Voronoi tessellation algorithm31. The daily average AOD value within each CMAQ grid cell was

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calculated by averaging any MODIS pixels that fell at least partially within that cell. AOD

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averages were calculated using only high confidence AOD retrievals from the combined deep-

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blue and dark-target parameter (DB-DT) introduced in Collection 6 32. Our approach combines

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the best elements of two distinct AOD retrieval algorithms, effectively creating an AOD 6 ACS Paragon Plus Environment

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parameter that combines the accuracy users have come to expect from the dark-target algorithm

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with the increased coverage that the deep-blue algorithm provides33. Lee, et al. 18 used Aqua

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AOD to predict missing Terra values to increase the spatiotemporal coverage of AOD. However,

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predicted AOD values inevitably contain additional errors that may reduce model performance.

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Thus, we only used Aqua AOD in this study.

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2.2.2 GEOS-Chem AOD

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The GEOS-Chem model is a global three-dimensional model of tropospheric chemistry driven

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by assimilated meteorological observations from the Goddard Earth Observing System (GEOS)

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of the NASA Global Modeling Assimilation Office (GMAO)

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(http://acmg.seas.harvard.edu/geos/doc/man/index.html). We use GEOS-Chem v10.1 in the

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current analysis, driven by meteorological data of GEOS-5 for year 2011. The nested grid

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simulations in North America with 0.5° x 0.666°spatial resolution produces compositional

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AODs, including sulfate-nitrate-ammonium AOD, black carbon AOD, organic carbon AOD,

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accumulation mode sea salt AOD, coarse mode sea salt AOD and total dust AOD at 3-h

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intervals. We calculate total column AOD by summing all 6 AOD parameters over 37 vertical

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layers (up to ~20 km from the surface) 34.

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2.3 Meteorological fields

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We obtained meteorological fields from two separate datasets. The first is the North American

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Regional Reanalysis (NARR) (http://www.emc.ncep.noaa.gov/mmb/rreanl/) with a spatial

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resolution of ~32 km and a temporal resolution of three hours. The second is the North American

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Land Data Assimilation System Phase 2 (NLDAS-2) (http://ldas.gsfc.nasa.gov/nldas/) with a

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spatial resolution of ~13 km and a temporal resolution of one hour. The meteorological fields



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used in this analysis include air temperature, dew point temperature, visibility, pressure, potential

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evaporation, downward longwave radiation flux, downward shortwave radiation flux, relative

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humidity, u-wind (east-west component of the wind vector) and v-wind (north-south component

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of the wind vector). All meteorological measurements for the period from 10 am to 4 pm local

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standard time were averaged to generate daytime meteorological fields. The averaged

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meteorological fields represent the average weather condition at the Aqua overpass time (~1:30

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pm local time) and reduce the adverse impact of possible extreme weather occurred at the

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satellite overpass time on the relationship between PM2.5 and meteorological variables.

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2.4 Land use variables

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We downloaded elevation data at a spatial resolution of ~30 m from the National Elevation

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Dataset (NED) (http://ned.usgs.gov). We extracted road network data, including limited access

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highway, highway, and local roads, from ESRI StreetMap USA (Environmental System

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Research Institute, Inc., Redland, CA). We obtained forest cover and impervious surface, both at

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the spatial resolution of ~30 m, from the 2011 Landsat-derived land cover map and impervious

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surface map downloaded from the National Land Cover Database (NLCD)

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(http://www.mrlc.gov). We obtained primary PM2.5 and PM10 emissions data (tons/year) from the

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2011 EPA National Emissions Inventory (NEI) facility emissions report

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(https://www.epa.gov/air-emissions-inventories/2011-national-emissions-inventory-nei-data).

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Finally, we obtained 2010 population density data at the census tract level from the U.S. Census

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Bureau (https://www2.census.gov/geo/tiger/).

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2.5 Regional and temporal dummy variables


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The PM2.5-AOD relationship has been shown to exhibit some regional variation due to

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meteorological conditions 35, and there are also daily variations in this relationship 18. Hence, we

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include a dummy climate region variable to account for regional variations and monthly and

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daily dummy variables to account for daily variations.

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2.6 Data integration

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All data were re-projected to the USA Contiguous Albers Equal Area Conic coordinate system.

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For the model training dataset, we assigned meteorological fields and AOD data to each PM2.5

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monitoring site using the nearest neighbor approach. We averaged forest cover, impervious

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surface, and elevation values and summed road length and point emission values over a 1 km x 1

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km square buffer centered on each PM2.5 monitoring site. We assigned each monitoring site a

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population density value of the census tract containing its location. For prediction dataset, the

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same procedure was applied to each MODIS grid cell.

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2.7 Methods

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2.7.1 Convolutional layer

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To account for spatial and temporal autocorrelations , we adopt the distance-inversed weighted

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average function proposed by Di, et al. 28 to create convolutional layers for nearby PM2.5

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measurements and all land use terms and use these layers as ordinary input predictor variables in

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our model. For each monitoring site and MODIS grid cell, distance-inversed weighted averages

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of nearby PM2.5 measurements and land use terms were calculated for that site and grid cell.

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Although it is optimal to use monitoring sites within a certain distance, due to the difficulties in

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identifying such a distance, we used all monitoring sites in the conterminous U.S. to create the



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convolutional layers, and this also helps to reduce possible missing values in convolutional

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layers. The kernel function can be expressed in general terms as n

zj

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∑ = ∑

i =1 n

wij z i

(1)

w i =1 ij

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where zj is the value of convolutional layer at monitoring site or grid cell j, zi is the PM2.5 and

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land use terms at monitoring site i, and wij ∝

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monitoring site i). When creating convolutional layers for monitoring site j, the PM2.5 and land

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use terms at monitoring site j were not included in the calculation.

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2.7.2 Model structure and validation

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Random forests are a set of decision trees, and each tree is constructed using the best split for

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each node among a subset of predictors randomly chosen at that node. In the end, a simple

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majority vote is taken for prediction. Random forests are user-friendly and have only two

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parameters, including mtry (the number of predictors sampled for splitting at each node) and ntree

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(the number of trees grown). The random forest algorithm first draws ntree bootstrap samples

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from the original data, and then for each sample, grows an unpruned classification or regression

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tree with mtry of predictors randomly sampled and the best split chosen at each node. Finally,

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predictions are made by aggregating the predictions of ntree trees (e.g., majority vote for

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classification and average for regression). The error rate can be calculated using predictions of

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out-of-bag samples (the data not in the bootstrap sample) 36, 37. In this study, by comparing

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results of different settings of mtry and ntree, we set mtry as 12 and ntree as 1000 to achieve the best

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prediction accuracy.

1 ( d ij is the distance between grid cell j and d ij2


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We developed a random forest model incorporating AOD data, meteorological fields, land use

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variables, and their convolutional layers to estimate ground-level PM2.5 concentrations over the

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conterminous United States in 2011. The predictor variables include

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(1) daily 24-hour averaged ground level PM2.5 measurements (µg/m3) ; (2) the x-y coordinates of

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monitoring sites or MODIS grid cell centroids in the Albers projection used for this analysis; (3)

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dummy variables: month, day, and climate regions; (4) meteorological fields: NARR variables

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(dew point temperature (K), visibility (m), 2-m pressure (pa), 10-m pressure (pa), 30-m pressure

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(pa), 30-m temperature (K), 180-150mb temperature (K)), NLDAS variables (potential

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evaporation (kg/m2), downward longwave radiation flux (W/m2), downward shortwave radiation

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flux (W/m2), connective available potential energy (J/kg), pressure (pa), 2-m temperature (K), 2-

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m relative humidity (%),east-west component of the wind vector (m/sec) at 10 m, north-south

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component of the wind vector (m/sec) at 10 m); (5) land use terms: elevation (m), local road (m),

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forest cover (unitless), primary PM2.5 point emissions (tons/year), impervious surface (%), and

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population density (persons/km2); (6) convolutional layers for elevation (m), local road (m),

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forest cover (unitless), primary PM2.5 point emissions (tons/year), impervious surface (%),

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population density (population/km2), highway (m), limited access highway (m), primary PM10

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point emissions (tons/year), nearby PM2.5 measurements (µg/m3); (7) MODIS AOD (unitless)

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and GEOS-Chem simulated AOD (unitless) used when MODIS AOD was missing.

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We applied a 10-fold cross validation (CV) technique to establish and validate our prediction

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results. The entire training dataset was randomly split into 10 subsets with each subset containing

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approximately 10% of the training data. In each round of cross validation, we use nine subsets

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for model training and make predictions for the held-out test subset. The process was repeated 10

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times until every subset was tested. In addition, we also conducted a spatial CV and a temporal



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CV, based on partitioning the training dataset by monitoring site and day of year, respectively.

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We calculated statistical indicators such as R2, Mean Prediction Error (MPE), and Root Mean

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Squared Prediction Error (RMSPE) between CV predictions and observations to assess the

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prediction accuracy of the proposed model for the entire study area and study period. We also

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ran the model and conducted CV for each season and each climate region separately. We

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calculate two importance values for each predictor variable to examine what variables provide

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the largest impact on our predictions. The first measure is the increase of mean square errors

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(MSE) of predictions which are estimated using out-of-bag samples as a result of each predictor

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variable being permuted. The higher the number, the more important the predictor variable. The

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second one is the increase in node purities from splitting on the predictor variable. Node purity

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measures the similarity of responses at a node across regression trees in the runs of the random

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forest model. More useful variables achieve higher increases in node purities 37. All modeling

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was done using R statistical software version 3.3.2 38.

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3. Results

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3.1 Descriptive statistics

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The mean, standard deviation, maximum, and minimum for all variables over 2011 are presented

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(Table S1). The annual mean PM2.5 concentrations is 9.69 µg/m3 for the continental U.S. in

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2011, and the overall mean of MODIS AOD is 0.14. The percentage of missing MODIS AOD is

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~68% in the conterminous U.S. during 2011. A Pearson’s correlation was conducted for all

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variables (Table S2) to avoid potential multicollinearity problems. The results show that the

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correlation coefficients between most of the variables are relatively low. It should be noted that

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random forests are applicable even with highly correlated variables 39.

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3.2 Results of model validation


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Table 1 and Figure 2 presents the overall, spatial, and temporal CV validation results for the

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entire study area and study period, including the values of R2, MPE, and RMSPE between CV

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predicted values and observations. The results show that the overall R2 reached a relatively high

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value of 0.80. MPE and RMSPE for daily predictions are 1.78 and 2.83 µg/m3, respectively,

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indicating a good agreement between CV estimates and observations over the conterminous

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United States in 2011. In addition, using GEOS-Chem simulated AOD to replace MODIS AOD

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reduced CV R2 by ~0.01 to 0.79, indicating the feasibility of using simulated AOD when

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MODIS AOD is not available. Nevertheless, mirroring previous studies, we find prediction

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accuracy varies by season and climate region (Tables 2 and 3). For instance, model performance

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is the best in summer, followed by winter and fall, and the worst in spring in terms of CV R2.

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For different climate regions, prediction accuracy is relatively high in west, northeast, central,

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and east north central regions, and low in northwest and west north central regions. The model

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has intermediate performance in southeast, south, and southwest regions.

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[Insert Tables 1-3 about here]

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[Insert Figure 2 about here]

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3.3 Variable importance assessment

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Figure 3 illustrates the results of variable importance assessment for predictor variables in the

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final model. The results show that the convolutional layer for nearby PM2.5 measurements and

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AOD are among the top five most important predictor variables for both importance measures.

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[Insert Figure 3 about here]

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3.4 Contribution of convolutional layers

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We compared the CV R2 values between models with and without convolutional layers (Table

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S3). The results show that incorporation of convolutional layers for land use terms could increase 13 ACS Paragon Plus Environment


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CV R2 by ~0.02, and inclusion of the convolution layer for nearby PM2.5 measurements increases

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CV R2 by ~0.06, indicating a strong contribution of these convolutional layers to prediction

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accuracy. We also compared CV R2 between models using our convolutional layers and surfaces

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yielded using universal kriging (Table S4). The results show that CV R2 of the model using

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surfaces generated using universal kriging is ~0.04 lower than that of our model, indicating that

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geostatistical interpolation methods such as universal kriging can also be used to generate

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convolutional layers.

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3.5 Estimation of PM2.5 concentrations

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Due to the use of GEOS-Chem simulated AOD when MODIS AOD is missing, the coverage of

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our predictions extends from ~32% to full coverage. Our annual mean PM2.5 surface on the

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CMAQ grid (12 x 12 km2) over the continental U.S. in 2011 appears in Figure 4. The results

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show that PM2.5 predictions (Figure 4a) and observations (Figure 4b) share a similar spatial

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pattern. PM2.5 concentrations are generally higher in the eastern U.S. (e.g., the southeast and

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central regions) than in the western part. There are also areas with high predicted and observed

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PM2.5 levels in the western U.S. (e.g., the San Joaquin Valley in California). High concentrations

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also occur in large urban centers such as Indianapolis, IN, Houston, TX, Columbus, OH,

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Chicago, IL, and Los Angeles, CA. Figure 4c illustrates the difference between annual mean

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PM2.5 predictions and ground measurements at each ground monitor and difference

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interpolations over the continental U.S. generated using the inverse distance weighted (IDW)

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interpolation. Figure 4c shows that underestimation mostly occurs in areas with high

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concentrations which are mainly in the eastern U.S., while overestimation appears primarily in

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the western U.S. where PM2.5 concentrations are generally low. The observed differences at


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~95% of ground monitors are within ±4 µg/m3. Seasonal PM2.5 maps (Figure S1) show that air

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pollution is more severe in summer, particularly in the eastern U.S. [Insert Figures 4 about here]

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4. Discussion

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Our approach has several strengths. First, we used random forests to build a PM2.5 predictive

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model on a national scale and demonstrated that such an approach can achieve high prediction

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accuracy, even across so broad a geographic area. For instance, on the regional scale, our model

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yields a similar CV R2 to previous studies conducted in the northeastern U.S. 22 and the southeast

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40

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region. On the national scale, the prediction accuracy of our model is comparable to that of a

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neural network approach proposed by Di, et al. 28. Both their model and ours used many similar

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predictor variables such as AOD, land use terms, and meteorological data. However, our final

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model did not include those variables with low importance such as additional GEOS-Chem

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outputs, Normalized Difference Vegetation Index (NDVI), absorbing aerosol index (AAI),

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boundary layer height, and albedo. In fact, including them reduced prediction accuracy. We also

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tested interactions between climate regions and meteorological variables, between day and

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meteorological variables, between climate regions and AOD, and between day and AOD. These

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interaction terms did not help improve prediction accuracy and thus were not included in the

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final model. In addition, we included some variables not included in Di, et al. 28 such as forest

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cover and percent impervious surface, both of which show high importance in our model.

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Compared to their neural network approach based on more than 50 predictors, our random forest

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approach has fewer predictors (~40). In addition, the neural network approach involves a more

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complex, two-stage structure, while our random forest approach is based on a simpler, one-stage

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structure.

in 2011, even though we optimize our model for the continental U.S. instead of within each



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Another strength of our random forest approach is that it provides an importance estimate for

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each predictor variable. Variable importance measures can help pinpoint what variables are most

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important in the reduction of prediction errors and thus make variable selection more efficient

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than neural networks. Our random forest approach provided two types of variable importance

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measures during the training process, including the increase in MSE and the increase in node

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purities, both of which provided additional insight into the set of predictor variables yielding the

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greatest improvements in prediction accuracy. In our implementation, when we chose variables,

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we tried to avoid highly correlated variables that may severely affect original importance

346

measures 39. To make importance values directly comparable, we first added all potential

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predictor variables into the random forest model and calculated importance values (e.g., the

348

increase in MSE) for all variables, and then compared the prediction accuracy of models

349

incorporating different combinations of variables to identify the best set of predictors among

350

those under consideration. Díaz-Uriarte and Alvarez de Andrés 41 suggested a backward

351

elimination strategy and iteratively fitted random forests, at each iteration building a new forest

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after discarding variables with the smallest variable importance values. We adopted a similar

353

strategy and iteratively fitted random forests with each time discarding the variable with the

354

smallest importance value. Finally, we identified a threshold where the incorporation of variables

355

with importance values above the threshold generally increased prediction accuracy, while the

356

inclusion of those with importance values below the threshold tended to decrease prediction

357

accuracy. The variables with importance values below the threshold were discarded, and those

358

with importance values above the threshold were further considered. This variable selection step

359

dramatically simplified the process of identifying useful predictor variables. For example, we

360

tested NDVI as a predictor in our model. We found that the importance value of NDVI fell


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below our threshold, and the inclusion of NDVI in the model slightly reduced the prediction

362

accuracy, probably due to the incorporation of other predictors with stronger individual

363

associations with the outcome (e.g., forest cover and impervious surface). In contrast, for neural

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networks, variables need to be toggled on and off individually to compare model performance in

365

order to determine whether the variable is useful or not. This can be time-consuming, especially

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when large training and testing datasets are involved.

367

One potential limitation of this study is our use of MODIS AOD data with 10 km spatial

368

resolution, instead of a new AOD product with 1 km spatial resolution derived using the Multi-

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Angle Implementation of Atmospheric Correction (MAIAC) algorithm. Lee, et al. 40

370

demonstrated that the 1-km MAIAC AOD can outperform the existing 10-km data in predicting

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PM2.5. An advantage of 10-km data over 1-km data is considerable reduction in computing time.

372

However, incorporating 1-km MAIAC AOD data into our model not only can predict PM2.5

373

concentrations at a higher spatial resolution, but may further improve the prediction accuracy,

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and we plan to extend our approach to this setting. Another limitation is regarding the temporal

375

mismatch among PM2.5 measurements, MODIS AOD, and meteorological fields. In this study,

376

PM2.5 measurements are 24-hour averaged, while MODIS AOD is a single value obtained at the

377

Aqua overpass time and meteorological variables are averaged from 10 am to 4 pm. It is optimal

378

to use both 24-hour averaged AOD and meteorological variables in the model. For

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meteorological fields, we tested the 24-hour averaged meteorological values in the model and did

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not find a substantial difference in prediction accuracy between models using meteorological

381

fields averaged within two different time periods. For AOD, other AOD products should be

382

considered. GASP AOD retrievals are attempted every half hour during daylight and thus can

383

help with the temporal mismatch between PM2.5 and AOD. Although Green, et al. 42 found that



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384

PM2.5 predicted from MODIS AOD is more accurate than those generated from GASP AOD at

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Bondville, Illinois, It is still worthwhile to examine its performance on a national scale, we will

386

address this issue in future research. Furthermore, the results of spatial and temporal CV indicate

387

that the model is more capable of explaining temporal variation in the relationship between PM2.5

388

and predictor variables than accounting for spatial variation. Thus, more work needs to be done

389

in the future to address this issue. Finally, although our model reached a relatively high

390

prediction accuracy, the results depict overestimation and underestimation of PM2.5

391

concentrations across the continental U.S. If these outputs were used in an epidemiologic study,

392

then these regional differences in accuracy could produce (or obfuscate) regional heterogeneity

393

in health associations.

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405


Table 1. Cross validation results for the entire study area and study period. Overall Spatial Temporal

R2 0.80 0.70 0.79

RMSPE (µg/m3) 2.83 3.43 2.88

MPE (µg/m3) 1.78 2.24 1.81

Slope 1.00 1.00 1.01

MPE (µg/m3) 1.62 1.71 1.75 2.20

Slope 1.00 1.00 1.01 1.01

MPE (µg/m3) 1.19 1.72 1.86 1.77 1.98 2.14 1.66 1.73 1.68

Slope 1.01 1.00 1.00 0.98 1.00 1.01 1.01 1.01 1.00

406 407

Table 2. Cross validation results for each season. Spring Summer Fall Winter

R2 0.78 0.81 0.79 0.80

RMSPE (µg/m3) 2.54 2.78 2.67 3.55

408 409

Table 3. Cross validation results for each climate region. Northwest West North Central Northeast East North Central Central West Southwest South Southeast

R2 0.68 0.64 0.79 0.82 0.80 0.83 0.74 0.74 0.74

RMSPE (µg/m3) 2.37 2.61 2.84 2.50 2.86 3.32 2.85 2.66 2.71

410 411 412 413 414 415 416 417 418 419 420 421 19 ACS Paragon Plus Environment


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422 423

Figure 1. Study area.

424 425 426 427 428 429 430 431 432 433 434 435


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436 437

Figure 2. 10-fold cross validation. (a) Overall; (b) Spatial; (c) Temporal.

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Figure 3. Variable importance. (a) Increase in mean square errors (%IncMSE); (b) Increase in

442

node purities (IncNodePurity). 22 ACS Paragon Plus Environment

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443 444

Figure 4. Annual mean predictions. (a) Annual mean PM2.5 predictions over the continental U.S.

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for 2011; (b) Annual mean PM2.5 measurements at ground monitors; (c) Difference between

446

annual mean predictions and observations at ground monitors and difference interpolations over

447

the continental U.S.

448 449 450 451 452 453 454 455 456 457 23 ACS Paragon Plus Environment


458

AUTHOR INFORMATION

459

Corresponding Author

460

* (Y.L.) Phone: +1-404-727-2131; fax: +1-404-727-8744; e-mail: [email protected].

461

Present Addresses

462

1

463

Atlanta, GA 30322, USA

464

Author Contributions

465

The manuscript was written by Xuefei Hu and edited by all authors. All authors have given

466

approval to the final version of the manuscript.

467

Notes

468

The authors declare no competing financial interest.

469

ACKNOWLEDGMENT

470

This work was partially supported by the NASA Applied Sciences Program (grant No.

471

NNX16AQ28G, PI: Liu).

472

SUPPORTING INFORMATION AVAILABLE

473

Tables S1-S4 and Figure S1. This information is available free of charge via the Internet at

474

http://pubs.acs.org.

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Department of Environmental Health, Rollins School of Public Health, Emory University,

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