# Direct Measurement of Aerosol Liquid Water Content: A Case Study in Summer in Nanjing, China
## 3 Results and Discussion  
### Improvement of ALWC Measurement  
First, to ensure the consistency of the acquired data between the two PDRs, we compared the measured PM\({}_{2.5}\) concentrations at an RH \(<\) 50% for the two PDRs, as shown in Figure 2. The correlation between them is very tight, with a Pearson's r\({}^{2}\) of 0.98; the slope of the linear fit is 1.3, denoted as \(c\) in Equation (1). This value represents the instrumental deviation of these two monitors and is therefore used as a calibration factor to derive the real ambient wet PM\({}_{2.5}\) mass concentration (PDR_wet), as shown in Equation (2). The reason that we used data at an RH \(<\) 50% rather than a smaller RH threshold (for example, 20%) is due to the fact that the RH during the measurement period was mostly higher than 40% (as shown in Figure 3a). Moreover, the regression of the very few data with an RH \(<\) 40% yielded a slope of 1.28 and r\({}^{2}\) of 0.96, which are almost similar to those obtained under an RH \(<\) 50%; therefore, we used the calibration factor obtained at an RH \(<\) 50% for consistency with our previous work [34] as well as for a broader coverage of the measurement data and thus robustness of the regression. Note that this systematic difference is instrument-dependent; we thus recommend that users perform this calibration for each pair of PDRs that are used in users' specific ALWC measurements. If there are enough data, we also recommend obtaining the calibration factor by comparing data at a  
Figure 1: Location and surroundings of the sampling site.  
smaller RH (such as 20% or 30%) to reduce the influence of possible absorbed water on the PDR_wet_original.  
\[c=\frac{\text{PDR\_wet\_original}}{\text{PDR\_dry}} \tag{1}\]  
\[\text{PDR\_wet}=\frac{\text{PDR\_wet\_original}}{c} \tag{2}\]  
Figure 3: (a) Relative humidity (RH) and air temperature (T); (b) wind speed (WS) and wind direction (WD); mass concentrations of gaseous pollutants of NO\({}_{2}\), CO (c), SO\({}_{2}\) and O\({}_{3}\) (d); (e) PM\({}_{2.5}\) mass concentration measured by the 5030i and the calibration factor (CF = PDR_dry/5030i_PM); (f) derived ALWC values and measured visibility.  
Figure 2: (a) Correlation of the PM\({}_{2.5}\) mass concentrations (PDR_wet_original vs. PDR_dry) between the two PDRs at RH \(<\) 50%. (b) Simple schematic of the ALWC measurement method.  
In our previous work [34], we used an Aerodyne high-resolution time-of-flight aerosol mass spectrometer (AMS) as a reference instrument to correct the readings of the PDR_dry to reflect the true fine PM concentrations. However, in practical terms, an AMS is a highly expensive and sophisticated instrument, requiring well-trained personnel to operate it [40; 41], and it is not an instrument conventionally employed for atmospheric environmental monitoring. Moreover, an AMS typically measures submicro-meter particles (30-1200 nm) rather than PM\({}_{2.5}\) due to the transmission efficiency of its inlet system [42], unless the PM\({}_{2.5}\) lens system is adopted [43; 44]. Therefore, instead of an AMS, we used the 5030i, which is broadly equipped as the routine PM\({}_{2.5}\) mass monitor worldwide, as the reference instrument in this work. Similarly, we introduced the calibration factor (CF) (calculated as CF = PDR_dry/5030i_PM) to correct the PDR_dry and then to calculate the PM\({}_{2.5}\) mass concentration under real ambient conditions (PDR_wet_ct) using Equation (3).  
\[\text{PDR\_wet}_{\text{ct}}=\frac{\text{PDR\_wet}}{\text{CF}} \tag{3}\]  
Next, the ALWC is simply the difference between the PDR_wet_ct and 5030i_PM, as shown in Equation (4). The flow chart of the improved ALWC measurement method is shown in Figure 2b.  
\[\text{ALWC}=\text{PDR\_wet}_{\text{ct}}-5030\text{i\_PM} \tag{4}\]