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\newcommand{\nox}{NO$_{\mbox{x}}$ }   % NOx
\newcommand{\noxns}{NO$_{\mbox{x}}$} % NOx No Space
\newcommand{\etal}{\emph{et al., }}
\newcommand{\pmt}{PM$_{2.5}$ }              % PM2.5
\newcommand{\pmtns}{PM$_{2.5}$}           % PM2.5 No Space
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\newcommand{\mgm}{$\mu g/m^3$ }           % microgram per meter cube
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%{\large\textbf {Predicting traffic-related pollutant concentrations in near-road environments using a Bayesian spatio-temporal model}}\\~\\
\received{00 Month 2018}
\revised{00 Month 2018}
\accepted{00 Month 2018}

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\runninghead{O. Gilani, V.J.~Berrocal, and S. A. Batterman}{Non-stationary Spatiotemporal Bayesian Data Fusion - Supplementary Material}

\begin{document}

\title{Non-stationary Spatiotemporal Bayesian Data Fusion for Pollutants in the Near-road Environment}

\author{O. Gilani\affil{a}\corrauth, V. J. Berrocal\affil{b}, and S. A. Batterman\affil{c}}

\corraddr{Owais Gilani, Department of Mathematics, Bucknell University, Lewisburg, PA 17837, USA.
Email: owais.gilani@bucknell.edu}

\address{\affilnum{a} Bucknell University, Department of Mathematics, Lewisburg, PA, USA
\affilnum{b} University of Michigan, Department of Biostatistics, School of Public Health, Ann Arbor, MI, USA
\affilnum{c} University of Michigan, Department of Environmental Health Sciences, School of Public Health, Ann Arbor, MI, USA}



\textbf{Supplementary Material}


\setcounter{figure}{0} 
% Histogram of NRIs
\begin{figure}[!ht]
	\centering
	\begin{tabular}{c c}
	\subf{\includegraphics[width=70mm]{Figures/histogram_nox.png}} {(a)} & \subf{\includegraphics[width=70mm]{Figures/histogram_pm25.png}} {(b)} \\
	\end{tabular}	
	\caption{Histogram of the near-road increment (NRI) in concentrations of (a) \nox and (b) \pmtns, as observed between Friday, December 14, 2012 and Thursday, December 20, 2012 at monitoring sites located in nine transect areas across major highways in Detroit, Michigan. }
	\label{fig:hist}
\end{figure} 

\newpage


% Boxplots comparing upwind vs. downwind; morning vs. evening; weekday vs. weekend on log scale
\begin{figure}[!ht]
	\centering
		\includegraphics[width=\textwidth]{Figures/boxplots.png}
	\caption{Box plots of log(NRI) in (a) \nox concentration (in log ppb) and (b) \pmt concentration (in log $\mu g/m^3$) for downwind and upwind sites, respectively; (c)  \nox concentration (in log ppb) and (d) \pmt concentration (in log $\mu g/m^3$) for mornings and evenings, respectively; and  (e) \nox concentration (in log ppb) and (f) \pmt concentration (in log $\mu g/m^3$) for weekdays and weekends, respectively.}
	\label{fig:boxplots}
\end{figure} 

\newpage




% Plot of Semivariogram for upwind and downwind sites - NOx and PM2.5
\begin{figure}[!ht]
	\centering
		\begin{tabular}{c c}
		\subf{\includegraphics[width=70mm]{Figures/NOxPlots/semivar_nox_up_down_resid.png}} {(a)} & \subf{\includegraphics[width=70mm]{Figures/PM25Plots/semivar_pm25_up_down_resid.png}} {(b)} \\
		\end{tabular}	
	\caption{Empirical and fitted (WLS) semivariogram for log(NRI) in (a) \nox concentrations and (b) \pmt concentrations for upwind and downwind sites. \newline \newline Fig. \ref{fig:semivar} shows the empirical semivariogram for log(NRI) in (a) \nox concentrations and (b) \pmt concentrations, along with the fitted exponential variogram (using weighted least squares (WLS)) for downwind and upwind sites.  For \noxns, the fitted variogram model for downwind sites is given by $0.51 + 0.45 ~ \mbox{exp} \{-\frac{d}{1240}\}$, with an effective range of 3.7 km, and for upwind sites is given by $0.85 + 6.13~ \mbox{exp}\{-\frac{d}{295487}\}$, with an effective range of 885 km. For \pmtns, the fitted variogram model for downwind sites is given by $0.58 + 0.21~ \mbox{exp} \{-\frac{d}{4000}\}$, with an estimated effective range of 11.98 km, and for upwind sites is given by $0.85 + 0.37~ \mbox{exp}\{-\frac{d}{7000}\}$, with an effective range of 20.97 km. }
	\label{fig:semivar}
\end{figure} 





\end{document}