## 1 Introduction
### AQI for Ambient Air Quality and Individual Health Impact  
Air quality index (AQI) indicates the degree of air pollution and the potential health effects from air pollution. It is a tool designed to help the public understand the local air quality and the adverse health effects of ambient air [3]. AQI is reported as a positive number, and its standard varies across different nations. The U.S. EPA calculates AQI based the concentration of major air pollutants, _i.e._, ground-level O\({}_{3}\), PM\({}_{2.5}\), PM\({}_{10}\), carbon monoxide (CO), nitrogen dioxide (NO\({}_{2}\)), and nitrogen oxide (NO\({}_{\kappa}\)) [4]. AQI is reported following a six-color scheme from green to maroon, corresponding to good air quality to hazardous air quality, respectively (Table 1) [5]. Air pollutants concentrations are measured at many locations, local and nation-wide. Separate AQI is calculated for each pollutant using the standard EPA formula below:  
\[I=\frac{I_{h}-I_{l}}{B_{h}-B_{l}}\left(C-B_{l}\right)+I_{l} \tag{1}\]  
where \(I\) is the AQI value for a pollutant of concern, \(C\) is the air pollutant concentration, \(B_{h}\) is the high break point (\(\geq\)\(C\)) for the concentration of the pollutant, \(B_{l}\) is the low break point (\(\leq\)\(C\)) for the concentration of the same pollutant, \(I_{h}\) is the high AQI limit corresponding to \(B_{h}\), \(I_{l}\) is the low AQI limit \begin{table}
\begin{tabular}{c c c c} \hline AQI & **Health Concern** & **Color** & **Explanation** \\ \hline _7-50_ & Good & Green & Clean air no health risk \\ \hline _51-100_ & Moderate & Yellow & Light air pollution, little health risk \\ _101-150_ & Unhealthy for sensitive groups (USG) & Orange & Only sensitive groups are affected \\ \hline _15-100_ & Unhealthy & Red & Unhealthy air for everyone \\ _201-300_ & Very Unhealthy & Purple & Serious health effects for everyone \\ \hline _101-100_ & Unhealthy & Unhealthy & Severe other health effects, even though \\ \hline \end{tabular}
\end{table} 
Table 1: The U.S. AQI standard (Source: EPA 2009). corresponding to \(B_{i}\). Note that, given an air pollutant, EPA has defined the threshold concentration values of \(B_{h}\), \(B_{i}\), and the corresponding AQI values of \(I_{h}\) and \(I_{l}\) to reflect the health impacts of the pollutant [5]. The highest AQI value during a day is recorded as the AQI of that day. The hourly reports for local and national AQI (such as PM\({}_{2.5}\), O\({}_{3}\), and PM\({}_{2.5}\)-O\({}_{3}\) combined) are updated and published through multiple channels [6,7]. AQI maps show air quality across a mapping area by using the AQI six-color scheme (as Table 1). These maps are usually used for AQI reporting and forecasting. For example, a public web site--WWW.AIRNOW.GOV--provides near real-time hourly AQI maps for the U.S. and AQI readings for major U.S. cities. Figure 1 shows one such map. AQI maps provide a good visualization of air quality and its variation across the mapping area. However, it is very limited for assessing air quality and its adverse health effects for individual human beings. The limitation is related to both the spatial and the temporal resolution of the AQI values. First, most AQI maps show AQIs on a city, township, or county level. To derive directly from these maps the health implication for individuals is subject to ecological fallacy. As [PERSON] [8] pointed out, there is a clear rising need for the assessment of health effects to gear away from deriving environmental effects on the individual level from an aggregated neighborhood level and to move towards assessing the health effects on a personal level. There has emerged in the past few years a number of studies and research projects that piloted the exploration of assessing individual level health effects of air pollution, although most of them are limited in both space and time scales partially due to the technical challenges related  
Figure 1: A U.S. national PM\({}_{2.5}\)-O\({}_{3}\) combined AQI map (Source: AIRNow 2011). to sensors and data collection [9].