2.2.2. Analysis of Water-Soluble Ions

Water-soluble ions obtained from half of the quartz fiber filters were analyzed by an ion chromatography (IC, DIONEX Corporation, Model ICS-90, Sunnyvale, CA, USA). The IC was periodically checked with standard reference materials. The relative standard deviation for each measurement (repeated twice) was within 3%. The method detection limit (MDL) was provided by the ion chromatography manufacturer. Determination of inorganic cations and ammonium in environmental waters was performed by ion chromatography with a high-capacity cation-exchange column. The MDLs of cations were 22, 20, 5, 48, 6, and 48 ng/mL for Na+, NH4 +, K+, Mg2 +, Ca2 +, and (CH3)2 NH2 +, respectively. The MDLs of anions were 2, 4, 11, 9, 66, 7, and 15 ng/mL for F−, Cl−, NO3 <sup>−</sup>, SO4 <sup>2</sup>−, CH3COO−, HCOO−, and C2O4 <sup>2</sup>−, respectively.

#### 2.2.3. Analysis of Carbonaceous Materials

Carbonaceous materials (OC and EC) obtained from another half of the quartz fiber filters were analyzed by a thermal/optical carbon analyzer (DRI, Model 2001, Desert Research Institute, Reno, NV, USA) with the thermal/optical reflectance (TOR) method [37,38]. A circle piece of 0.53 cm2 was cut off from the filters and was sent into the thermal optical carbon analyzer. A blank sample was analyzed for blank subtraction. Quality control and quality assurance procedures were routinely applied for all the elemental, ion, and carbonaceous analyses.

## *2.3. CMB Model*

The chemical mass balance (CMB) receptor model was used in this study to apportion the source contributions to the size-fractionated PM at different heights. The EPA CMB 8.2 version (US EPA, 2004) with the effective variance weighted least-squares fitting method was applied. CMB is a widely used method for source apportionment of particulate matter. It consists of a solution to a set of linear equations that expresses each receptor chemical concentration as a linear sum of products of source profile abundances and source contributions. Source samples were collected and analyzed, and then profiles were determined for local representative emissions [18,26]. The chemical abundances are normalized to values between 0% and 100%.

$$\mathbf{C}\_{\rm if} = \sum\_{i=1}^{N} F\_{\rm in} S\_{\rm nt} + E\_{\rm it} \tag{1}$$

In Equation (1), *Cit* represents the ambient concentration of the *i*-th chemical species measured at time t. It is equal to the sum of the contributions from *N* sources, in theory. *Fin* is the fractional abundance (source profile) of the *i*-th species in the *n*-th source type. *Snt* is the mass contribution of *n*-th source at time *t*. *Eit* represents the difference between the measured and estimated ambient concentration [25].
