Calibration of Low-cost Sensors for Measurement of Indoor Particulate Matter Concentrations via Laboratory/Field Evaluation

Received: April 28, 2023
Revised: April 28, 2023
Accepted: May 16, 2023

 Copyright The Author(s). This is an open access article distributed under the terms of the Creative Commons Attribution License (CC BY 4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are cited.

Cite this article:

Kim, D., Shin, D., Hwang, J. (2023). Calibration of Low-cost Sensors for Measurement of Indoor Particulate Matter Concentrations via Laboratory/Field Evaluation. Aerosol Air Qual. Res. 23, 230097. https://doi.org/10.4209/aaqr.230097

HIGHLIGHTS

• This study evaluates the accuracy of LCSs in comparison to a reference PM monitor.
• LCSs show higher PM concentrations than the reference monitor, with variations.
• This study conducted regression analysis to identify the causes of varied trends.
• Identifying causes of varied trends, calibrating models to enhance LCS accuracy.

Keywords: Indoor air quality, Particulate matter, Regression analysis, PM2.5, PM10

1 INTRODUCTION

Recently, the use of low-cost particulate matter (PM) sensors that measure total light scattering intensity by particles has enabled wide-ranging and high-density spatiotemporal measurements to be conducted (Giordano et al., 2021; Zheng et al., 2018). As light scattering-based low-cost PM sensors (LCSs) can provide almost instantaneous feedback on changes in air quality, users can immediately check and respond to high air pollution levels (Bhattacharya et al., 2012; Kim et al., 2010; Zheng et al., 2018). The light scattering-based LCS generally comprises a laser (650 nm), a phototransistor, and a focusing lens (Fig. 1).

Fig. 1. (a) Schematic diagram of light scattering-based LCS (PMS3003, PMS7003); (b) Light scattering when PM₁₀/PM_2.5 ratio is low; and (c) Light scattering when PM₁₀/PM_2.5 ratio is high.

A major limitation of LCS is that they are not as accurate as expensive reference PM monitors (Gao et al., 2015; Kelly et al., 2017; Zheng et al., 2018). An LCS can be affected by operating conditions (relative humidity, temperature, PM mass concentration) and aerosol characteristics (aerosol composition, size distribution). These disturbance factors can cause an LCS to produce output data showing different trends (Gao et al., 2015; Kelly et al., 2017). To minimize the different trends triggered by the disturbance factors, LCS output should be compared with output from a reference PM monitor. In this study, GRIMM 11-D, one of the portable research-grade PM monitors widely used for indoor PM measurement was selected as a reference PM monitor. The GRIMM 11-D is an advanced optical particle counter (OPC) with the ability to divide particles from 0.253 to 35.15 µm by optical size into 31 channels and to count individual particles with a diode laser (30 mW, 655 nm).

In general, air quality regulations stipulate 'dry' PM when the relative humidity is less than 40%. In higher relative humidity environments, a hygroscopic effect may overestimate the LCS output value. Magi et al. (2020) reported that the hygroscopic effect started to affect Plantower PMS5003 when the relative humidity exceeded 65–70%. Jayaratne et al. (2018) showed that relative humidity has a significant effect on LCSs Sharp GP2Y and Shinyei PPD42NS, even when the relative humidity is over 50%. In Badura et al. (2019), linear regression models for relative humidity showed equal or better performance than nonlinear regression models. Zheng et al. (2018) suggested that applying a nonlinear empirical calibration model for relative humidity could improve the PM mass concentrations of Plantower PMS3003 to close to the dry state, even in a high humidity environment. Gao et al. (2015) and Malings et al. (2020) reported that nonlinear empirical calibration models can obtain lower mean absolute errors (MAE) and higher correlation coefficients than theoretical approaches can. Ultimately, the choice between linear/nonlinear and theoretical/empirical models to calibrate for relative humidity will depend on end-user preferences and requirements.

In contrast, temperature has less effect on LCSs than relative humidity. The literature generally reported that low error values (–5 to 5 µg m^–3) were shown even at low temperatures (–5 to 5°C). In the linear/quadratic calibration model for temperature, the error term appears larger than the coefficient; thus, the effect of temperature can be neglected in normal environments but not in extreme environments, such as deserts (Magi et al., 2020).

In this study, laboratory and field (indoor) evaluations were conducted to construct an effective calibration model for LCSs. The GRIMM 11-D and LCSs were placed at the same location to measure PM_1.0, PM_2.5, and PM₁₀. The room temperature and relative humidity were also measured using a temperature/humidity sensor module. The LCSs and the sensor module were controlled by Arduino and integrated into a wireless network type sensor box using Wi-Fi module. Simultaneously, real-time open API (Application Programming Interface) data (outdoor PM_2.5 and PM₁₀) were collected by Air Korea (www.airkorea.or.kr). Among the collected data, the outdoor PM₁₀/PM_2.5 ratio (written as (PM₁₀/PM_2.5)_API) and relative humidity were selected as independent variables. The purpose of our study was to suggest an effective calibration model for LCSs to be used in indoor spaces using various regression analyses.

2 METHODS

 
2.1 Specifications of Sensor Modules

In this study, we evaluated Plantower PMS3003 and Plantower PMS7003 (PMS3003 and PMS7003, respectively). The shape and structure of each LCS are shown in Fig. 2, and the specifications of the LCSs are shown in Table 1. Each LCS simultaneously displays particle mass concentrations (µg m^–3) for PM_1.0, PM_2.5, and PM₁₀.

Fig. 2. Shape and structure of LCS: (a) Plantower PMS3003; (b) Plantower PMS7003.

A guiding principle for LCSs is that particle mass concentrations are calculated by measuring scattered light intensity, which are obtained from a phototransistor, as shown in Fig. 1 (Sayahi et al., 2019; Kelly et al., 2017; Zheng et al., 2018; Badura et al., 2018, 2019). However, the results may differ depending on the unique expertise of each manufacturer. A DHT 22 sensor module was used to obtain temperature and humidity information.

 
2.2 Structure of Wireless Network Type PM Evaluation Sensor Box

First, the measured values of PM and temperature/humidity were determined by Arduino (Fig. 3). Second, Arduino converted the data into byte format and transmitted the converted data to a NodeMCU module by I2C (Inter-Integrated Circuit) communication method with 4 bytes for each measured value. Finally, the data transmitted to the NodeMCU module were converted back to string format, with the converted data being transmitted every 4.5 seconds and stored in a Google datasheet (data cloud) using wireless communication.

 Fig. 3. Schematic diagram of wireless network type PM evaluation sensor box.

The NodeMCU module has an operating voltage of 3.3 V, a power consumption of less than 1.0 mW, and an indoor transmission range of approximately 40 m and an approximately 100 m range outdoors, with an operating radio frequency of 2.4 GHz.

 
2.3 Light Scattering-based PM Measurement and Correction Factor

The GRIMM 11-D PM monitor and LCSs calculate particle number concentration by measuring scattered light intensity from particles entering each device. Assuming that the total light intensity and the particle number concentration have a proportional relationship, the total scattered light intensity (I_total) is a summation of each light intensity scattered by a single particle (i(d_p)) (Friedlander, 2000), as follows:

where d_p is the particle diameter, and n(d_p) is the number concentration of particles of size d_p. The total mass concentration (m_total) can then be calculated from n(d_p) as follows:

where ρ_p is the particle density that is set in each device (usually 1 g cm^–3). Therefore, based on Eq. (1) and Eq. (2), m_total is calculated through I_total measurement.

The GRIMM 11-D, a research-grade reference PM monitor, displays the total mass concentration (m_total,Ref) by measuring the total light scattering intensity (I_total,Ref) with a diode laser (30 mW, 655 nm). The GRIMM 11-D measures particles in the range of 0.253–35.15 µm (optical diameter) with 31 channels. The GRIMM 11-D measures the particles every 6 seconds with a sampling flow rate of 1.2 lpm.

PMS3003 and PMS7003, the LCSs, display the total mass concentration (m_total,LCS) by measuring the total light scattering intensity (I_total,LCS) obtained from a phototransistor. Each LCS displays mass concentrations of PM_1.0, PM_2.5, and PM₁₀ with three channels.

As m_total is calculated through I_total measurement, the following equations are obtained:

where η_Ref and η_LCS represent the response coefficients of GRIMM 11-D and LCS, respectively.

From Eq. (3a) and Eq. (3b), the following equation is obtained:

where α is a target correction factor between GRIMM 11-D and LCS and is expressed in Eq. (5):

Other factors may affect the light scattering intensity: temperature (T), relative humidity (RH), and particle shape (S). However, the effect of temperature was neglected in this study because the temperature barely changed in an indoor space. In addition, the effect of particle shape was ignored, as reported in previous studies (Badura et al., 2019; Barkjohn et al., 2020; Crilley et al., 2020; Magi et al., 2020).

The light scattering intensity of GRIMM 11-D, according to time resolution (∆t_n), is written in Eq. (6a):

For LCS, the concentration section (∆[PM]) and the outdoor PM₁₀/PM_2.5 ratio ((PM₁₀/PM_2.5)_API) are considered as factors that additionally affect the light scattering intensity. Therefore, the light scattering intensity of LCS according to time resolution can be expressed by Eq. (6b):

2.4 Laboratory Evaluation

The laboratory evaluation was performed in a 83 × 83 × 158 cm chamber (Fig. 4). To prevent particle leakage from the chamber, the edges were siliconized. In addition, four fans were mounted at the corners (mid-height of the chamber, 80 cm) to create a uniform particle distribution. To minimize the effects of temperature and humidity on the measurements, they were maintained at 20°C and 20%, respectively. Generated particles flowed into the chamber through a stainless-steel tube located at the top center of the chamber. While the GRIMM 11-D was located outside the chamber, two LCSs were located on the inside. The distance between the inlets of the LCSs was approximately 5 cm (narrow gap ratio, 0.06, to total chamber width, 83 cm). The distance between each LCS inlet and the sampling port inlet of the GRIMM 11-D was also approximately 5 cm. Therefore, GRIMM 11-D and LCS measure particles are assumed to exist in the same space (Li and Biswas, 2017).

Fig. 4. Schematic diagram of laboratory evaluation (chamber test).

Laboratory evaluation was conducted with two size distributions of polystyrene latex (PSL) particles: mono-disperse PSL (0.56 µm, corresponding to the peak of a typical atmospheric aerosol size distribution) and poly-disperse PSL (1.3, 1.5, 1.8, and 2.0 µm, realizing a PM_2.5 size distribution) (Table 2). The PSL particles were generated by an atomizer (TSI, Jet Atomizer 9302) and passed through a diffusion dryer (TSI, Diffusion Dryer 3076) to remove moisture. The aerosolized PSL particles flowed into the chamber to increase the particle concentration. The particle generation was stopped when the particle concentration did not increase further. Consequently, after stopping, the particle concentration started decreasing. The measurement was complete when the particle concentration could no longer be detected by the LCSs. Fig. 5 shows the size distributions of PSL aerosols immediately before the particle generation was stopped.

 Fig. 5. Size distribution of PSL aerosols measured by GRIMM 11-D: (a) Mono-disperse PSL (0.56 µm); (b) Poly-disperse PSL (1.3, 1.5, 1.8, 2.0 µm).

 
2.5 Field Evaluation

Fig. 6(a) shows the field experimental setting, which was conducted in the Engineering Building at Yonsei University (37.5618°N, 126.9366°E) located in Sinchon, Seoul, South Korea. In this study, for accurate evaluation and calibration, all inlets of LCSs and GRIMM 11-D were proximately positioned at a height of approximately 0.8 m to reduce noise caused by re-dispersion of fine dust (Giordano et al., 2021). Fig. 6(b) shows the PM evaluation sensor box comprising PMS3003, PMS7003, and DHT22. Each sensor was operated by Arduino, and the measured data were transmitted wirelessly through the Wi-Fi module (NodeMCU).

Fig. 6. (a) Field evaluation; (b) PM evaluation sensor box; (c) Cross-section schematic diagram of lab-made heat-based dehumidifier.

Using GRIMM 11-D, operating conditions for temperature and relative humidity (RH) were 0–40°C and 0–40%, respectively. Therefore, dehumidification was required when the relative humidity exceeded 40%. For dehumidification, we fabricated a heat-based dehumidifier capable of increasing the temperature up to 60°C, with a total length of 30 cm (heating part: 10 cm from the front end, Fig. 6(c)). The heat-based dehumidifier was connected to the inlet of GRIMM 11-D and was used when the indoor RH exceeded 40%. Therefore, the RH term in Eq. (6a) can be neglected and can be expressed as Eq. (7):

In the field evaluation, we collected open API PM data (atmospheric PM_2.5 and PM₁₀) as well as output values from the PM evaluation sensor box (T, RH and PM_1.0, PM_2.5, PM₁₀ mass concentrations) together with the GRIMM 11-D (PM_1.0, PM_2.5, PM₁₀ mass concentrations). The open API PM data were collected hourly from a measurement station available near the field test site. In this study, two stations were selected; 0.75 km distance from the site and 3.8 km away from the site. After collecting data from the two stations, average values were used for (PM₁₀/PM_2.5)_API. The PM mass concentrations measured from GRIMM 11-D and LCS were averaged per 1-hour and are represented as PM^Ref (PM mass concentration measured with GRIMM 11-D) and PM^LCS (PM mass concentration measured with LCS), respectively. The field test was conducted from 12 February to 31 March 2022.

 
2.6 Calibration Model

In this study, to create a calibration model based on regression analysis, the following three steps were used: 1) select useful independent variables through the regression analysis of collected data; 2) derive the correction factor (CF) corresponding to α of Eq. (5); and 3) construct a calibration model by applying the derived CF.

We constructed four calibration models, and the detailed description of each model is as follows (a description of each calibration model is also summarized in Table 3):

 
2.6.1 Simple calibration model

After plotting the data of PM^LCS and PM^Ref in an X-Y graph, the slope and intercept were obtained by assuming a linear relationship between PM^LCS and PM^Ref. Subsequently, the newly obtained PM^LCS (PM^Cal.LCS) was calculated using the following equation:

where CF1 represents the correction factor 1, and CF1_Slope and CF1_Intercept are the slope and intercept, respectively. Therefore, PM^Cal.LCS implies a CF applied to PM^LCS. To evaluate the calibration performance of PM^Cal.LCS, a comparison is made with PM^Ref.

 
2.6.2 Calibration model with (PM₁₀/PM_2.5)_API

CF2 is a correction factor that applies (PM₁₀/PM_2.5)_API as an independent variable. Therefore, CF2 applied to PM^LCS results in PM^Cal.LCS. The PM^Cal.LCS is calculated using the following equations:

In the above equations, the constants a, b, and c represent regression coefficients. The target correction value of CF2 is the reference correction factor (CF^ref) defined by Eq. (11):

where, the CF^ref is same as α of Eq. (5). To evaluate the calibration performance of PM^Cal.LCS (Eq. (9)), a comparison is made with PM^Ref.

 
2.6.3 Calibration model with (PM₁₀/PM_2.5)_API by dividing concentration sections

As the sensitivity of LCS decreases at low concentrations owing to the limit of detection (LOD), low and high PM concentrations should be considered prior to applying the regression analysis. The criterion for dividing the PM concentration section was PM_1.0 of LCS (PM_1.0^LCS). CF3 is a correction factor that applies (PM₁₀/PM_2.5)_API as an independent variable after dividing PM concentration sections. Therefore, CF3 applied to PM^LCS results in PM^Cal.LCS. The PM^Cal.LCS is calculated using the following equation:

here,

where the constants a, b, and c represent regression coefficients. CF3_Low and CF3_High are CF3 in the low and high concentration sections, respectively. The target correction value of CF3 is the reference correction factor (CF^ref) of Eq. (11). To evaluate the calibration performance of PM^Cal.LCS (Eq. (12)), a comparison is made with PM^Ref.

 
2.6.4 Calibration model with (PM₁₀/PM_2.5)_API and RH by dividing concentration sections

CF4 is a correction factor that applies (PM₁₀/PM_2.5)_API and RH as independent variables after dividing PM concentration sections. Therefore, CF4 applied to PM^LCS results in PM^Cal.LCS. The PM^Cal.LCS is calculated using the following equation:

here,

In the above equation, the constants a, b, c, and d represent regression coefficients. CF4_Low and CF4_High represent CF4 in the low and high concentration sections, respectively. The target correction value of CF4 is the reference correction factor (CF^ref) of Eq. (11). To evaluate the calibration performance of PM^Cal.LCS (Eq. (13)), a comparison is made with PM^Ref.

 
2.7 Evaluation of Calibration Models Performance

In this study, we used three indicators to evaluate the performance of calibration models: correlation coefficient (R²), root mean square error (RMSE), and match rate (MR). The R², RMSE, and MR are represented by Eqs. (14), (15), and (16), respectively:

here, n is the amount of data; y_i denotes a data point of PM^Ref; ŷ_i denotes a data point of PM^Cal.LCS (PM^LCS to which a CF is applied); y̅ represents the average of all data points of PM^LCS; MR has different implications depending on the configuration of variables a and b. When a = ŷ_i and b = y_i, Eq. (16) represents the MR of PM^LCS for PM^Ref. When a = ŷ_1i and b = ŷ_2i, Eq. (16) represents the MR between the two LCSs (subscript 1 = Plantower PMS3003, subscript 2 = Plantower PMS7003). The performance of the model is better when R² is closer to 1, RMSE is closer to 0, and the MR is closer to 100%.

3 RESULTS AND DISCUSSION

 
3.1 Laboratory Evaluation

To determine the performance of LCSs, laboratory evaluation was conducted with two size distributions of PSL: mono-disperse (0.56 µm) and poly-disperse (1.3, 1.5, 1.8, and 2.0 µm). Fig. 7 shows the results of this evaluation.

Fig. 7. Results of the laboratory evaluation: (a) Time series graph in mono-disperse PSL test; (b) Correlation analysis graph for PM_2.5 in mono-disperse PSL test; (c) Time series graph in poly-disperse PSL test; (d) Correlation analysis graph for PM_2.5 in poly-disperse PSL test.

First, mono-disperse PSL particles were sprayed into the chamber using an atomizer until the concentration did not increase further (based on GRIMM 11-D, 279.52 µg m⁻³). Thereafter, the gradually falling concentration was measured until each LCS showed zero (based on GRIMM 11-D, 2 µg m⁻³) (Fig. 7(a)). As a result, the correlation (R²) between each LCS and GRIMM 11-D was over 0.99 (PMS3003: 0.9968 and PMS7003: 0.9986). The ratios (= LCS/GRIMM 11-D) were 1.0772 (± 0.2055) and 1.2686 (± 0.1572), respectively, for PMS3003 and PMS7003 (Fig. 7(b)). Therefore, the results showed high correlation and low deviation.

Second, poly-disperse PSL particles were sprayed into the chamber using the atomizer until the concentration did not increase further (based on GRIMM 11-D, 60.26 µg m⁻³). Thereafter, the gradually falling concentration was measured until each LCS showed zero (based on GRIMM 11-D, 10 µg m⁻³) (Fig. 7(c)). As a result, the correlation (R²) between each LCS and GRIMM 11-D was over 0.98 (PMS3003: 0.9815 and PMS7003: 0.9876). The ratios (= LCS/GRIMM 11-D) were 0.2462 (± 0.1091) and 0.3129 (± 0.1439), respectively, for PMS3003 and PMS7003.

Therefore, each LCS was significantly lower than GRIMM 11-D and showed higher deviations than in the case of mono-disperse PSL particles (Fig. 7(d)). To explain these trends, we hypothesized two possible causes: 1) owing to the internal structure of LCSs, larger particles may not fully reach the measurement part of the LCS (Fig. 2); 2) as larger particles can block smaller particles, the light scattering caused by smaller particles remains undetected, resulting in underestimation or noise generation (Figs. 1(b) and 1(c)).

 
3.2 Field Evaluation

The measured data are shown in Fig. 8. The average room temperature was 15.91°C (± 2.16) while the average indoor relative humidity was 34.83% (± 11.32), showing a large variation. The ranges of PM_2.5^Ref and PM₁₀^Ref were 1.33–72.92 µg m⁻³ (20.45 ± 12.55 µg m⁻³) and 1.65–119.27 µg m⁻³ (29.07 ± 17.52 µg m⁻³), respectively. Likewise, in the case of PMS3003, the ranges of PM_2.5^LCS and PM₁₀^LCS were 1.00–137.54 µg m⁻³ (39.28 ± 28.46 µg m⁻³) and 1.04–153.03 µg m⁻³ (42.88 ± 31.02 µg m⁻³), respectively. In the case of PMS7003, the ranges of PM_2.5^LCS and PM₁₀^LCS were 1.29–129.72 µg m⁻³ (38.40 ± 26.71 µg m⁻³) and 1.65–172.33 µg m⁻³ (50.71 ± 34.95 µg m⁻³), respectively. The PM^LCS generally showed higher mass concentrations than PM^Ref.

Fig. 8. Results of the field evaluation: (a) Time series graph of temperature/humidity and PM_2.5 output data of GRIMM 11-D, PMS3003, PMS7003; (b) Time series graph of temperature/humidity and PM₁₀ output data of GRIMM 11-D, PMS3003, PMS7003.

Prior to constructing the calibration model, the ability of each LCS needed to be evaluated to discriminate between PM_2.5 and PM₁₀ as PM₁₀^LCS had a significantly lower correlation than PM_2.5^LCS. Fig. 9 shows the correlation between PM₁₀/PM_2.5 of GRIMM 11-D (PM₁₀/PM_2.5)_Ref and that of LCS, (PM₁₀/PM_2.5)_LCS. As (PM₁₀/PM_2.5)_Ref increased, (PM₁₀/PM_2.5)_LCS tended to increase, and PM₁₀^LCS had a non-linear relationship with PM_2.5^LCS. Therefore, PM₁₀^LCS was determined as reliable data.

 Fig. 9. Correlation analysis between (PM₁₀/PM_2.5)_Ref and (PM₁₀/PM_2.5)_LCS.
 

3.2.1 Simple calibration model

Fig. 10(a) shows the relationship between PM_1.0^LCS and PM_1.0^Ref. The slope for PMS3003 was higher and closer to unity than the slope for PMS7003. However, no difference in slope was observed in Fig. 10(b), which shows the relationship between PM_1.0^Cal.LCS and PM_1.0^Ref. PM_1.0^Cal.LCS was a result of applying CF1 to PM_1.0^LCS. As a result, even if the simple calibration model was applied, PM_1.0^Cal.LCS was close to PM_1.0^Ref. In cases of PM_2.5 and PM₁₀, some PM^LCS were different from PM^Ref (black and red circles of Figs. 10(c) and 10(d)). Fig. 10(e) shows the relationship between PM_2.5^Cal.LCS (obtained with CF1) and PM_2.5^Ref. Fig. 10(f) shows the relationship between PM₁₀^Cal.LCS (obtained with CF1) and PM₁₀^Ref.

Fig. 10. Processes and results of deriving a calibration model using CF1: (a) CF1 for PM_1.0; (b) PM_1.0^Cal.LCS; (c) CF1 for PM_2.5; (d) CF1 for PM₁₀; (e) PM_2.5^Cal.LCS; and (f) PM₁₀^Cal.LCS. ** In the figure, PM^Cal.LCS = CF1_Slope∙PM^LCS + CF1_Intercept **

Table 4 shows R², RMSE, and MR values obtained with CF1 for PM_2.5^LCS and PM₁₀^LCS. The results are shown for both PMS3003 and PMS7003. For PMS3003, the RMSE and MR values of PM_2.5^Cal.LCS were significantly lower and higher than those of PM_2.5^LCS, respectively, implying performance improvement after calibration. In contrast, the RMSE and MR values of PM₁₀^Cal.LCS were not that different from those of PM₁₀^LCS, implying that the calibration with CF1 did not significantly improve performance.

When RMSE and MR were used as indicators for calibration performance, the performance seemed to improve with the use of CF1 for PM_2.5^LCS. However, when R² was used as an indicator, no performance improvement was observed for both PM_2.5^LCS and PM₁₀^LCS (Table 4 shows almost the same R² values of PM^LCS and PM^Cal.LCS for both PM_2.5 and PM₁₀). We surmise that this lack of improvement was due to the data shown in the black and red circles (Figs. 10(c) and 10(d)).

In addition, the use of CF1 for PMS3003 caused the minimum detectable concentration (in other words, LOD) to increase from 1.33 to 3.98 µg m⁻³ for PM_2.5 and from 1.65 to 10.48 µg m⁻³ for PM₁₀ (Figs. 10(e) and 10(f)). For PMS7003, similar trends were obtained.

 
3.2.2 Calibration model with (PM₁₀/PM_2.5)_API

For PMS3003 and PMS7003, CF^Ref (= PM^Ref/PM^LCS) values for PM_2.5 and PM₁₀ were calculated from the results of Fig. 8 and plotted, respectively, in Fig. 11(a) and Fig. 11(b), which also show the (PM₁₀/PM_2.5)_API variation with time. For both PM_2.5 and PM₁₀, CF^Ref increased with (PM₁₀/PM_2.5)_API.

Fig. 11. Processes and results of deriving a calibration model using CF2: (a) Time series graph of (PM₁₀/PM_2.5)_API and CF^Ref for PM_2.5; (b) Time series graph of (PM₁₀/PM_2.5)_API and CF^Ref for PM₁₀; (c) CF2 for PM_2.5; (d) CF2 for PM₁₀; (e) PM_2.5^Cal.LCS; and (f) PM₁₀^Cal.LCS. ** In the figure, PM^Cal.LCS = CF2∙PM^LCS **

To better understand the relationship between CF^Ref and (PM₁₀/PM_2.5)_API, the results were re-plotted in Figs. 11(c) and 11(d). Fig. 11(c) shows a linear correlation between CF^Ref for PM_2.5 and (PM₁₀/PM_2.5)_API, whereas Fig. 11(d) shows a second-order polynomial correlation between CF^Ref for PM₁₀ and (PM₁₀/PM_2.5)_API. Using these correlations, CF2 in Eq. (10) was determined and then PM₁₀^Cal.LCS values were obtained for each case (Eq. (9)). Finally, Fig. 11(e) shows the relationship between PM_2.5^Cal.LCS (obtained with CF2) and PM_2.5^Ref for both LCSs. Similarly, Fig. 11(f) shows the relationship between PM₁₀^Cal.LCS (obtained with CF2) and PM₁₀^Ref for both LCSs.

Table 4 shows R², RMSE, and MR values obtained with CF2 for PM_2.5^LCS and PM₁₀^LCS for both PMS3003 and PMS7003. The RMSE values of PM_2.5^Cal.LCS were significantly lower than these of PM_2.5^LCS, whereas the R² and MR of PM_2.5^Cal.LCS values were significantly higher than those of PM_2.5^LCS. This finding indicated that the performance improved with the use of CF2 for PM_2.5^LCS. Similarly, the performance significantly improved for PM₁₀^LCS.

Moreover, the use of CF2 showed higher performance than the use of CF1 (Table 4). In particular, the data shown in the black and red circles were corrected for PM_2.5 and PM₁₀ (Figs. 10(c) and 10(d)). In addition, the use of CF2 did not increase the minimum detectable concentration. However, some data points of PM_2.5^Cal.LCS and PM₁₀^Cal.LCS still deviated from the trend-line in the concentration range of 30–90 µg m⁻³ (Figs. 10(e) and 10(f)).

 
3.2.3 Calibration model with (PM₁₀/PM_2.5)_API by dividing concentration sections

For both PMS3003 and PMS7003, the data shown in Fig. 10(a) were re-plotted to show the relationship between CF_1.0^Ref (= PM_1.0^Ref/PM_1.0^LCS) and PM_1.0^LCS. As a result, the following relationships were derived:

where x and y denote PM_1.0^LCS and CF_1.0^Ref, respectively. The y value rapidly decreased as the x value increased until x was approximately 6–7, and then converged after x = 6–7. This rapid decrease suggests that the LCS is less sensitive than GRIMM 11-D at concentrations below x = 6–7, likely due to the difference in LOD between LCS and GRIMM 11-D. This changing point value (x = 6–7) became the threshold point in Eqs. (12a) and (12b). If the changing point was defined as the x-value when the y′′ is equal to the y̅′′ (an average of y′′; y̅′′ = 0.0036 for PMS3003, y̅′′ = 0.0026 for PMS7003), the changing points were 7.3355 µg m⁻³ and 6.8852 µg m⁻³, respectively, for PMS3003 and PMS7003.

Fig. 12. Processes and results of deriving a calibration model using CF3: (a) Correlation with CF^Ref according to PM_1.0^LCS; (b) CF3 in PM_2.5 low conc. section; (c) CF3 in PM_2.5 high conc. section; (d) CF3 in PM₁₀ low conc. section; (e) CF3 in PM₁₀ high conc. section; (f) PM_2.5^Cal.LCS; and (g) PM₁₀^Cal.LCS. ** In the figure, PM^Cal.LCS = CF3·PM^LCS **

For PM_2.5, Figs. 12(b) and 12(c) show linear correlations between CF^Ref and (PM₁₀/PM_2.5)_API in low and high concentration sections, respectively. For PM₁₀, Figs. 12(d) and 12(e) show second-order polynomial correlations between CF^Ref and (PM₁₀/PM_2.5)_API in low and high concentration sections, respectively. Using these correlations, CF3 in Eqs. (12a) and (12b) were determined, after which PM^Cal.LCS values were obtained (Eq. (12)). Finally, Fig. 12(f) shows the relationship between PM_2.5^Ref and PM_2.5^Cal.LCS (obtained with CF3). Fig. 12(g) shows the relationship between PM₁₀^Ref and PM₁₀^Cal.LCS (obtained with CF3).

Table 4 shows R², RMSE, and MR values obtained with CF3 for PM_2.5^LCS and PM₁₀^LCS. The results are shown for both PMS3003 and PMS7003. Considering the decrease in LCS sensitivity at low concentrations, the use of CF3 showed improved performance compared with the use of CF2.

 
3.2.4 Calibration model with (PM₁₀/PM_2.5)_API and RH by dividing concentration sections

Figs. 13(a) and 13(b) show the correlations between CF^Ref (= PM^Ref/PM^LCS) and RH for PM_2.5 and PM₁₀, respectively. When the RH was higher than 40%, CF^Ref slightly decreased with increasing RH, indicating that the hygroscopic effect was not significant. However, when the RH was lower than 40%, no correlation and data points showed significant deviation from the trend-line (y = ax + b). Nonetheless, using these correlations, CF4 in Eq. (13a) and (13b) were determined (Table 5), and then PM^Cal.LCS values were obtained (Eq. (13)). Consequently, Figs. 13(c) and 13(d) show that PM^Ref values were well correlated with those of PM^Cal.LCS (obtained with CF4), respectively, for PM_2.5 and PM₁₀. Considering that the red and black circle data shown in Figs. 10(c) and 10(d) were obtained at a RH lower than 40%, we expected that the challenge of data point deviation was solved by using calibration models, including (PM₁₀/PM_2.5)_API.

Fig. 13. Processes and results of deriving a calibration model using CF4: (a) Correlation between RH and CF^Ref for PM_2.5; (b) Correlation between RH and CF^Ref for PM₁₀; (c) PM_2.5^Cal.LCS; and (d) PM₁₀^Cal.LCS. ** In the figure, PM^Cal.LCS = CF4·PM^LCS **

Table 4 shows R², RMSE, and MR values obtained with CF4 for PM_2.5^LCS and PM₁₀^LCS. The results are shown for both PMS3003 and PMS7003. The use of CF4 showed practically insignificant improvement compared with the use of CF3. However, if the RH was higher than 70%, the effect of RH could not be neglected (Magi et al., 2020; Jayaratne et al., 2018; Badura et al., 2019; Zheng et al., 2018).

Fig. 14 shows the time series graph of PM^Ref and PM^Cal.LCS (obtained with CF4). Therefore, compared with the time series graph before calibration in Fig. 8, a remarkable performance improvement was observed. Considering the performance evaluation using CF4 and lower susceptibility to hygroscopic effects, we determined that the PMS7003 showed a higher performance than the PMS3003 did (Table 4).

 Fig. 14. Time series graphs of PM^Ref and PM^Cal.LCS (CF4 calibration model): (a) PM_2.5 case; (b) PM₁₀ case.

Fig. 15 shows the MR between PMS3003 and PMS7003 before and after calibration (Raw, CF1, CF2, CF3, and CF4), and the MR of PM^Cal.LCS between PMS3003 and PMS7003 was higher than those of PM^LCS between PMS3003 and PMS7003. While using CF4, the MR was highest for both PM_2.5^Cal.LCS (96.1%) and PM₁₀^Cal.LCS (96.1%).

Fig. 15. Match rate between PMS3003 and PMS7003 before and after calibration.

 
4 CONCLUSIONS

In the field evaluation, LCSs (PMS3003 and PMS7003) show generally higher PM mass concentrations than GRIMM 11-D; however, some data points of LCSs show different trends. Outdoor PM₁₀/PM_2.5 and relative humidity have notable impacts on the LCSs data. In addition, LCS sensitivity depends on the quantity of PM concentrations. Based on these observations, regression-based calibration models were constructed using the selected independent variables (outdoor PM₁₀/PM_2.5 and relative humidity) after dividing the PM concentration into low and high sections. As a result, PMS7003 show better performance than PMS3003 (RMSE: 2.03 µg m⁻³, 4.89 µg m⁻³ for PM_2.5 and PM₁₀, respectively; MR: 91.43%, 86.39% for PM_2.5 and PM₁₀, respectively).

 
ACKNOWLEDGMENTS

This work was supported by the Korea Institute of Energy Technology Evaluation and Planning (KETEP) and the Ministry of Trade, Industry & Energy (MOTIE) of the Republic of Korea (No. 20181110200170).