## 2 Experimental Methods  
Two microAeth(r) AE51s were simultaneously tested at indoor environment to eliminate temperature and humidity issues because the indoor office where this test was conducted controlled the temperature and humidity at certain values during day and night. For this reason, no correction for devices was required to display the data. One microAeth(r) AE51 produced in 2014 is denoted by Inst_1 and the other one, purchased in 2012, is denoted by Inst_2. New filter stripes were installed inside both devices before starting comparison test in order to minimize the overloading effect by the filters on the attenuation. The clocks of two devices were synchronized before starting measurement in order to compare data minute by minute based on the standard time. The sampling flow rate was set to 0.1 L/min (lpm) for stable collection of data. It is well known that the \(ATN\) is defined as below based on the Beer-Lambert law. \[ATN=100\ln\left(\frac{I_{0}}{I}\right) \tag{1}\]  
In Equation (1), the number 100 was added for convenience. \(I_{0}\) is the intensity of light transmitted through a reference blank spot, and \(I\) is that through the spot of aerosol deposited on filter. The measurement of \(I_{0}\) and \(I\) at time \(t\) produces \(ATN\) at time \(t\), which is denoted by \(ATN_{t}\). The measurement at the next time step (\(t+\Delta t\)) produces \(ATN_{t+\Delta t}\). Then, the changes in \(ATN\) during the time interval (\(\Delta t\)) is calculated as shown below in Equation (2). \[\Delta ATN=ATN_{t+\Delta t}-ATN_{t} \tag{2}\]  
According to [PERSON] et al. [5], the \(ATN\) is used to estimate BC concentration using the following equation. \[BC=\frac{1}{\sigma_{ATN}}\left(\frac{A\cdot\Delta ATN}{100\cdot Q\cdot\Delta t }\right) \tag{3}\]  
In Equation (3), \(\sigma_{ATN}\) is the mass attenuation cross section, \(A\) is the spot area on filter, and \(Q\) is the sampling flow rate. The mass attenuation cross section used for microAeth(r) AE51 is known to be 12.5 m\({}^{2}\)/g [17; 18]. The spot area is assumed to be constant unless there is a leak. The spot area is reported to be 7.07 mm\({}^{2}\)[18]. The sampling flow rate in the current study is set to 0.1 lpm. The time interval is 60 s. Figure 1 summarizes the procedure of calculating BC concentration from the real-time signals. Uncertainty propagation analysis is performed for the BC concentrations to better understand how many errors are associated with each elements of measurement variables. Combining Equations (1)-(3) produces the following Equation. \[BC=\frac{A}{\sigma_{ATN}\cdot Q\cdot\Delta t}\ln\left(\frac{(I_{0}/I)_{t+ \Delta t}}{(I_{0}/I)_{t}}\right) \tag{4}\]  
Figure 1: Schematic diagram of microAeth® AE51 and flow chart of the procedure for calculating black carbon (BC) concentration from signals. Error propagation can be calculated from Equation (4) as below. See Appendix for more detail. \[\frac{\delta BC}{BC}=\sqrt{ \begin{array}{c}\left[\left(\frac{\delta A_{ATN}}{O_{ ATM}}\right)^{2}+\left(\frac{\delta A}{A}\right)^{2}+\left(\frac{ \delta Q}{Q}\right)^{2}+\left(\frac{\delta A}{\Delta t}\right)^{2}\right]\\ +\left[\left(\left(\frac{\delta A}{I_{0}}\right)_{t+\Delta t}\right)^{2}+ \left(\left(\frac{\delta A}{I_{0}}\right)_{t}\right)^{2}+\left(\left(\frac{ \delta A}{I}\right)_{t+\Delta t}\right)^{2}+\left(\left(\frac{\delta A}{I} \right)_{t}\right)^{2}\right]\end{array} } \tag{5}\]  
In Equation (5) the last term ensues from the sensitivity of detectors. It may be estimated from Equation (5) how sensitive sensors are required in order to satisfy a given uncertainty of the BC concentration. [PERSON] et al. [7] addressed the fact that the uncertainty in BC has more than one component, i.e., the uncertainty in BC is decomposed into a non-drift attenuation term and a drift attenuation term which varies greatly from instrument to instrument. In the present study, however, the reference signal (\(I_{0}\)) and the sensing signal (\(I\)) are considered as noise sources.