## 2 Time Geography and Individual Space-Time Behavior Analysis
With the development in GIS and visualization technologies in the 21 st century, important progresses were made to profile individual space-time behavior using GIS-based 3D modeling and visualization. For example, [PERSON] [22] explored the activity-travel behavior of more than 10,000 individuals in Portland, Oregon. The space-time behaviors of these individuals were mapped using a GIS-based 3D geovisualization where individual space-time paths was integrated with the base map. [PERSON] and [PERSON] [23] believe that individual's daily activity and travel behavior are highly influenced by modern Information and Communication Technologies (ICT), and therefore the virtual space makes a significant component for an individual's living space. They developed individual space-time path maps that integrate individual's virtual activities (such as teleconference and mobile phone calls) with his/her physical activities (such as working, commuting trips, and meeting). [PERSON] _et al._[24] developed an ArcGIS space-time extension--Activity Pattern Analyst (APA) to visualize and analyze individual space-time behavior aiming at exploring the hidden aggregate patterns in large spatiotemporal datasets. In the last ten years or so, development in hand-held Global Position System (GPS) and that in ICT (especially mobile and wireless communication technologies) have greatly enhanced the advancement in pervasive location acquisition [25]. This made the data collection for individual level space-time trajectory more practical and benefited the space-time analysis of individual behavior. [PERSON]'s space-time cube was implemented by recent studies for both visualization (e.g., [26]) and analysis (e.g., [27,28]) of individual's space-time trajectories. [PERSON] _et al._[29] analyzed the travel patterns of 19 parolees and mapped their 3D space-time paths using GeoTime software; their individual space-time trajectory data were collected by portable GPS units. However, these studies examined individual-level space-time behavior by focusing mostly on an individual's space-time trajectory while considering away the dynamics of individual-environment interaction and environmental exposure. A trajectory is described as a collection of tri-tuples, \(I\left(x_{i},y_{i},t_{i}\right)\). The environment impacts along the trajectory are either overlooked or treated as constant. This approach is limited for modeling the dynamic nature of the interaction between an individual and the environment, which is critical for understanding individual-level environment exposure and the related health effects. The dynamics of an individual's exposure to air  
Figure 2: A space-time path in a time geography space-time cube. pollution as one moves along a spatiotemporal trajectory must be properly accounted for in order to accurately assess the health effects of air pollution on an individual. There is a lack in literature to connect an individual's spatiotemporal trajectory (_i.e._, space-time path in [PERSON]'s space-time cube) with the changing nature of his/her environment exposure in general and air pollution exposure in particular. To the authors' knowledge, the only study that has explicitly developed the traditional time geography space-time cube to include a description of the environment dynamics was [PERSON] and [PERSON] [30]. [PERSON]'s space-time cube was extended to an air pollution cube of space-time in this study where the base 2D map shows the air pollution concentration and variation across space and the third-dimension shows the progress of time along which the spatial distribution of air pollution concentration changes. Following [PERSON] and [PERSON] [30], we propose that an individual's interaction with environment along a particular space-time path through a space-time cube can be modeled as a collection of qua-tuples, \(I\left(x_{i},y_{i},t_{i},\,E_{i}\right)\), where \(E_{i}\) represents the environmental exposure of an individual at \(i\), a particular space-time position.