### 1. Introduction

_{2.5}

*β*-attenuation monitor (BAM-1020, MetOne) during continuous operation at a regulatory monitoring site in California. This co-location calibration method is usually time consuming. A similar co-location test method was employed to calibrate a low-cost PM sensor in the ambient environment over several winters by Kelly et al. [4]. For laboratory calibrations of low-cost sensors, two types of test methods are known, i.e., a chamber method [7, 8, 12, 14, 15, 20, 21] and a low-speed wind tunnel test [4, 13]. In these studies, the low-cost sensors were mostly tested in an environment with uniform and consistent concentration or under a stepwise concentration change. The test method using a constant particle concentration can provide information on the accuracy of the sensor reading at a given particle concentration; however, this method usually requires considerable time to obtain several data points and provides little information about how well the sensor responds to concentration changes. In addition, because most low-cost sensors adopt a moving time average technique for data processing in order to eliminate noise, sensor performance in an environment with rapidly changing concentration is uncertain and needs to be evaluated.

### 2. Methods

### 2.1. Aerosol Generation and Test Duct Systems

### 2.2. Mass Balance in the Particle Mixing Chamber

*V*is the chamber volume,

*C*

*is the initial particle concentration,*

_{i,0}*Q*

*is the incoming clean air flow rate,*

_{i}*C*

*is the particle concentration in the incoming air,*

_{0}*Q*

*is the exiting aerosol flow rate, and*

_{e}*C*

*is the particle concentration of the exiting aerosols at time*

_{i}*t*.

*R*represents the rate of particle loss caused by particle deposition on chamber walls. With these notations, the rate equation for the particle concentration in the mixing chamber is

*C*

*= 0 owing to the particle-free clean air, and*

_{0}*R*= 0 under the assumption of negligible particle loss in the chamber. Therefore, the particle concentration in the mixing chamber at time

*t*can be expressed as follows:

*τ = V/Q*

*, Eq. (2) becomes*

_{i}*C*

*on a logarithmic scale as a function of time*

_{i}*t*on a linear scale, the plot is a straight line with a slope of −1/

*τ*, and the slope of the decaying particle concentration can be altered by changing the incoming clean air flow rate

*Q*

*.*

_{i}### 2.3. Validation of the Test Duct System

^{3}, without exceeding ±5% of the mean value, as shown in Fig. S1 in the Supplementary Materials (SM). Each data point is the average value for 1-min measurements.

_{2.5}concentrations measured using the reference instrument for 10 min under the decaying particle concentration from approximately 100 to 10 μg/m

^{3}. The regression line for the measurements shows excellent exponential decay with a correlation coefficient,

*R*

*, of more than 0.97. The test system performance can be easily evaluated by obtaining results similar to those in Fig. 2(b). If the aerosol generation system or the reference instrument does not function appropriately, the regression data for the measurements shown in Fig. 2(b) do not form a straight line on the semi-log graph.*

^{2}### 3. Results and Discussion

### 3.1. Performance of Low-cost Sensors

_{2.5}mass concentrations. AirBeam2 measured PM

_{1}, PM

_{2.5}, and PM

_{10}mass concentrations, and the DC1100 measured particle number concentrations in two size ranges: > 1 and > 5 μm.

^{3}. Two decay times were used because some of the low-cost sensors require a long averaging time to handle data internally, and this long averaging time may not ensure accurate measurements of rapidly changing concentrations in the real world. Therefore, with this test, the response characteristics of the sensors to concentrations with different decay rates could be ensured.

_{2.5}concentration measurement data obtained by unit #1 of the AirBeam2 with a 3-min decay time. The blue solid regression line is from the reference instrument data, i.e., the Grimm monitor. The correlation coefficient and slope of AirBeam2 #1 are 0.9443 and −0.0076, respectively. Table S2 in the SM summarizes the results of units #2 and #3 of AirBeam2. The correlation coefficient values for all three units have excellent linearity on the semi-log graph, and the variability between the units is also stable. However, near the low particle concentration region, after an elapsed time of approximately 2 min, the measured concentration starts to deviate from the regression line. The tests were repeated once more, and the results are summarized in Tables S2–S4 in the SM. Furthermore, at a high particle concentration of approximately 100 μg/m

^{3}, the concentration obtained by AirBeam2 is approximately 40 μg/m

^{3}, i.e., 40% of the reference data value. At a lower concentration of approximately 10 μg/m

^{3}, the sensor reading is approximately 7 μg/m

^{3}. The tests demonstrate that the overall reading of the AirBeam2 sensors is approximately 40% lower than that of the reference instrument.

*Q*

*, supplied to the particle mixing chamber, and the test results of AirBeam2 are shown in Fig. 3(b) and Table S2 in the SM. In general, the sensor readings are quite similar to the 3-min decay case. However, the slope of the regression line is relatively well aligned compared with the faster-decay case. This implies that the sensor response is affected by the rate of concentration change. The ratio of the slope estimated by each low-cost sensor to the slope of the reference data (Table S2 in the SM) was also obtained. A low-cost sensor with a ratio close to 1 indicates that the sensor performs better in terms of the response characteristics. The average ratio for the 6-min decay tests on AirBeam2 was estimated to be approximately 0.7 or more, and this decreased to approximately 0.6 for the 3-min decay tests, i.e., for the faster-decaying concentration.*

_{i}^{3}and approximately three times higher at a low concentration of approximately 10 μg/m

^{3}. More importantly, the slope of the regression line obtained by the DC1100 under the 3-min decay time is between −0.0102 and −0.0092, and the ratios between the slopes obtained by the DC1100 and reference instrument are more than 0.7.

*R*

*, for DC1100 is generally higher than that for AirBeam2. However, a direct comparison of these values might result in a misleading measure of the model fit. The number of data points can affect the value of the correlation coefficient. A detailed explanation of the correct use of*

^{2}*R*

*is well documented in a study by Alexander et al. [27]. Therefore, the values of the obtained coefficients shown in Figs. 3–5 should be considered as the criteria for indicating the relative goodness of model fit, e.g., a good model fit is considered when*

^{2}*R*

*> 0.9.*

^{2}### 3.2. Calibration of AirBeam2 and DC1100 Low-cost Sensors

*C*

*is the concentration reading before the correction. The regression coefficients are listed in Table S5 in the SM.*

_{CLS_raw}*C*

*). Using these results, linear regression models were obtained, and a summary of the models is shown in Table S6 in the SM. When applying the quadratic correction models, the corrected values of the low-cost sensors under 3- and 6-min concentration decay conditions agree well with reference data, exhibiting a linear relationship with small values of mean absolute error (MAE) and root mean square error (RMSE), which were obtained as follows [28]:*

_{ref}##### (6)

$$\text{RMSE}=\sqrt{{\scriptstyle \frac{\mathrm{\Sigma}{({C}_{ref}-{C}_{LCS\_corrected})}^{2}}{n}}}.$$^{3}and 155 #/L, respectively. For the 6-min decay case, the estimated maximum MAEs are 2.84 μg/m

^{3}and 229 #/L for these sensors. Moreover, the maximum difference in the slope against the identity line is obtained for unit #3 of the AirBeam2 sensor under the 6-min concentration decay condition (slope: 0.978).