To study the contributions of various physical and chemical processes to the formation of PM2.5, we employ a simple approach by using the Hybrid Single Particle Lagrangian Integrated Trajectory model (HYSPLIT version 4.7, http://www.arl.noaa.gov/ready/hysplit4.html [Draxler, 2003]) to determine a back trajectory, linking a downwind receptor to upwind source areas and then applying process analysis (PA) to the CMAQ grid cells along the trajectory of the air mass transport path. This can provide quantitative information about the relative importance of each process in changing the PM2.5 concentrations along the trajectory. This enables us to determine the relationship between sources and receptors with respect to PM2.5 formation within the moving air mass. In the CMAQ output, the results of PA provide the hourly time series of vertical advection/diffusion (ZADV/VDIF), horizontal advection/diffusion (HADV/HDIF), dry deposition (DDEP), cloud process (CLD), aerosol process (AERO) and emission (EMIS) at each grid cell. In the CMAQ, aerosol process (AERO) refers to the effects of aerosol module, which includes processes of nucleation, condensation and coagulation, and equilibrium thermodynamics. Note that wet deposition is included in the cloud process and the effects of aerosol gaseous precursors, such as H2SO4 and HNO3, generated by the gas-phase chemistry on the formation of aerosol particles are included in the aerosol process.
 For the back trajectory analysis, the same meteorology applied in the Eta-CMAQ simulation was used to generate input data sets for use in the HYSPLIT back trajectory calculation. By using an ensemble approach to estimate uncertainty in HYSPLIT back trajectory calculation, Draxler  found that the trajectory ensemble approach accounted for about 41% to 47% of the variance in the measurement data although a cumulative distribution of the ensemble probabilities compared favorably with the measurement data. This uncertainty needs be kept in mind when HYSPLIT back trajectories are calculated and used. Figure 9 shows the 24-h backward trajectories ending at 1100 UTC 17 August 2004 at the South Allegheny High School (SAHS) and John sites in Pennsylvania, and ending at 1100 UTC 19 August 2004, at the South Dekalb (SD), McDonough (MD) and Newnan (NN) sites in Georgia. These sites and times were chosen because their PM2.5 concentrations were high (>40 μg m−3) relative to other sites as shown in Figures 9a and 9b. Another reason for these choices is to illustrate two different scenarios in Northeast and Southeast for how the high PM2.5 concentrations were formed. The mean primary emissions of PM2.5 and SO2 over the domain during the period of 6 to 18 August 2004, are shown in Figure 10. Additionally, since during the daytime pollutants are well mixed vertically through the PBL, we examine vertically integrated process tendencies; we choose 2 km as being representative of the mean daytime PBL height for this analysis. Yu et al. [2007a] indicated that average daytime PBL heights during the ICARTT period in the Eta model at Concord, NH, can be ∼2 km. In a study of the summertime atmospheric boundary layer over the eastern United States, Rao et al.  found that the PBL heights can vary from <200 m (nighttime) to ∼2.5 km (the afternoon). Additionally, since efficient long-range transport occurs above the nocturnal PBL, we use a height of 2 km to integrate the process tendencies along the back trajectories. Also, since dispersion is irreversible, the 2 km layer should be maintained for the full duration of the trajectory. Figures 11 and 12 show the accumulated contributions of each process to PM2.5 formation along the 24-h back trajectories at the SAHS and John sites, Pennsylvania, and South Dekalb and Newnan sites, Georgia. Table 5 summarizes the total accumulated contributions of each process to the PM2.5 formation along the 24-h back trajectories (see Figure 9) at the five sites. As can be seen, the dominant processes for PM2.5 formation and sink vary from the site to site.
 There are noticeable differences for the PM2.5 formation at the Pennsylvania and Georgia sites. For example, horizontal advection (i.e., transport) process contributes to the loss of PM2.5 at most of sites except the SAHS site where it increases PM2.5 significantly (see Figure 11 and Table 5). In most of cases, vertical diffusion and vertical advection processes make small contributions to the loss of PM2.5, and the effects of horizontal diffusion on the PM2.5 formation are negligible as shown in Table 5. Aerosol process is one of major sources for the PM2.5 formation for all sites as expected. Table 5 shows that the total changes in PM2.5 concentration along the 24-h trajectory due to aerosol process are 4.58, 2.90, 3.10, 3.12 and 2.49 μg m−3 for NN, SD, MD, SAHS and John sites, respectively, contributing to 53, 70, 68, 20 and 24% of total sources of the PM2.5 formation, respectively. Emissions are another significant source contributing to PM2.5 burden. The total changes in PM2.5 concentration along the 24-h trajectory due to emissions are 4.04, 1.25, 1.47, 1.21 and 0.71 μg m−3 for NN, SD, MD, SAHS and John sites, respectively, contributing to 47, 30, 32, 8 and 7% of total sources of the PM2.5 formation, respectively. The aerosol process and primary emissions are major sources for the PM2.5 formation at the Georgia locations. On the other hand, it is of interest to note that the integrated process budgets along the trajectories at the Pennsylvania sites in Table 5 indicate large contributions from cloud processing to PM2.5. In contrast, the trajectories reaching the sites in Georgia are characterized by negligible contributions by the cloud process to PM2.5 formation inn this case. The total changes in PM2.5 concentration along the 24-h trajectory due to cloud process are 6.48 and 7.28 μg m−3 for SAHS and John sites of Pennsylvania, respectively, contributing to 42 and 69% of total sources of the PM2.5 formation, respectively. At the SAHS site of Pennsylvania, SO42−, NH4+ and OCM comprise 80, 6 and 4% of PM2.5, respectively, on average, whereas at the NN site of Georgia, they comprise 58, 13 and 13% of PM2.5, respectively (also see Figures 11c and 11d). This suggests relatively large contribution of SO42− from the cloud process to PM2.5 in these air masses reaching the Pennsylvania sites.