# Developing a Relative Humidity Correction for Low-Cost Sensors Measuring Ambient Particulate Matter

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

_{10}) and 2.5 μm (PM

_{2.5}) [5,6], although some studies also highlight the importance of exposure to smaller particles (e.g., PM

_{1}) [7,8].

_{1}, PM

_{2.5}and PM

_{10}.

_{2.5}measurements for this period, before and after the application of the correction factor proposed in [16], are presented, together with reference data, in Figure 1.

_{2.5}readings relative to the reference measurements associated with high RH periods, although this is not always the case (i.e., period II in Figure 1). Application of the Crilley et al. correction factor [16] improves the Alphasense OPC-N2 derived PM compared to the reference data. Nevertheless, there are multiple periods (e.g., period I in Figure 1) where significant discrepancies remain. Those periods highlight the limitation of the approach presented in [16], when the particle number concentration distribution is relatively unstructured (i.e., period II in Figure 1 and Figure 2). Under such circumstances, a shift toward smaller sizes is broadly equivalent to scaling the number concentration down by a constant factor, as illustrated in Figure 2b, where the Crilley et al. correction produces tolerable agreement with the reference dried particle distribution, so that the reference and corrected PM

_{2.5}values broadly agree. However, when the size distribution shows significant structure (e.g., period I in Figure 1), the approach presented in [16] fails to reproduce the reference dried particle size distribution, and PM values from the corrected OPC particle size spectrum are significantly overestimated.

## 2. Materials and Methods

#### 2.1. Instrumentation

#### 2.1.1. Alphasense OPC-N2

_{1}, PM

_{2.5}and PM

_{10}. Particles passing through the sampling volume scatter incident laser light, which is then detected by a photo detector. Based on the amount of scattered light, particle size and number concentration are both determined. Measured particle size range, dimensions, and operational settings of the instrument are presented in Table 1.

#### 2.1.2. Palas Fidas 200 S

_{1}, PM

_{2.5}and PM

_{10}. However, in this case, a drying system, the Intelligent Aerosol Drying System (IADS), is used to remove water from particles before measurement. Size range, dimensions, and operational settings of Palas Fidas 200 S are presented in Table 2. Unlike the Alphasense OPC-N2, this instrument uses a white LED laser which enables the detection of particles with a diameter as small as 0.18 μm (see Table 2).

#### 2.2. Study Area

#### 2.3. Data Processing

#### 2.3.1. Data Redistribution

#### 2.3.2. Number Concentration to Mass Conversion

_{1}, PM

_{2.5}and PM

_{10}is completed internally to each instrument. Particles are assumed to be spheres with uniform shape and density. In this work, the following equations were therefore used to convert particle concentration values to mass concentration:

^{−3}. Hence, for consistency, we used this value to calculate mass concentration values for both the OPCs and the reference instrument. PM

_{1}, expressed in μg m

^{−3}, was calculated via Equation (5) using bins 1–4. Equally, PM

_{2.5}(μg m

^{−3}) was calculated via Equation (5) using bins 1–7. Penetration curves [20] are normally then used to convert the derived mass spectra to the appropriate PM values. However, for clarity, in the comparison of size and volume spectra for the different instruments, this step has not been applied.

#### 2.3.3. RH Correction Algorithm

#### 2.3.4. RH Correction Statistical Validation

_{1}and PM

_{2.5}data: mean value of measurements, standard deviation (SD), root-mean-square error (RMSE), gradient, and coefficient of determination R

^{2}. The gradient of the scatterplot and coefficient of determination R

^{2}were calculated assuming a linear relationship.

## 3. Results

#### 3.1. Comparision of This Study with Previous Work

_{w}is the water activity, defined as RH/100, and the statistically derived $\kappa $ value for their data is in the 0.38–0.41 range [16]. For clarity, in this paper, we took 0.4 as the $\kappa $ value for the correction presented in [16]. PM

_{2.5}measurements from the Alphasense OPC-N2 between 23 May and 31 May 2017, after the application of the correction factor proposed in [16], and the correction algorithm presented in this study, in comparison with the reference data, are presented in Figure 6. To compare our correction approach to the one presented in [16], Figure 6 also presents our correction applied using two different $\kappa $ values: 0.4, consistent with [16], and 0.61, as discussed in Section 2.3.3. As there is no information regarding the efflorescence point of the compound with $\kappa $ = 0.4, we have assumed it to be the same as Ammonium Sulphate (RH = 35%). Also shown are particle volumes as functions of particle size for two selected periods. As previously mentioned, the size distribution for the Crilley et al. correction factor [16] has been inferred by applying a single correction factor to uncorrected OPC volume concentration data.

_{1}and PM

_{2.5}measurements for corrected Alphasense OPC-N2 and reference data are presented in Figure 7. The figure shows that while the distributions for all three sets of measurements are broadly similar, the Crilley et al. correction overestimates the number of high aerosol events for both PM

_{1}and PM

_{2.5}. This is reflected in the averages in each case (see Table 3).

#### 3.2. Statistical Evaluation of the RH Algorithm

_{1}and PM

_{2.5}in Figure 9 and Figure 10 respectively.

_{1}and PM

_{2.5}between 29 December 2017 and 5 January 2018 (the blue shaded area in Figure 9c and Figure 10c), suggesting that the particles are more hygroscopic (i.e., absorbing more water) during this period. To further investigate this, we ran the Ready Hysplit model developed by NOAA to determine the trajectories of air masses for the December–January period, as shown in Figure 13.

^{2}from 0.42 to 0.73, before and after the application of the correction algorithm, respectively. When sodium chloride was assumed for the 29 December 2017–5 January 2018 period (blue shaded area in Figure 14) with ammonium sulphate elsewhere, the mean value of OPC measurements was improved from a factor of 4.45 before correction to 1.06 after correction, as well as the gradient from a factor of 5.25 to a factor of 1.05 and the R

^{2}from 0.42 to 0.75, before and after the application of the correction algorithm, respectively. Mean values of measurements, SD, RMSE, gradient and coefficient of determination R

^{2}values relative to PM

_{2.5}data are presented in Table 6. As previously observed for PM

_{1}data, values in Table 6 confirm the improvement of the RH algorithm for OPC PM

_{2.5}measurements. Specifically, when ammonium sulphate was taken as the single particle component for the 17 December 2017–16 January 2018 period, the mean value of OPC measurements was improved from a factor of 5.10 before correction to 1.26 after correction, as well as the gradient from a factor of 4.59 to a factor of 1.43 and the R

^{2}from 0.34 to 0.75, before and after the application of the correction algorithm, respectively. Again, when sodium chloride was assumed as sole particle component for the 29 December 2017–5 January 2018 period (blue shaded area in Figure 14) and ammonium sulphate elsewhere, the mean value of OPC measurements was improved from a factor of 5.10 before correction to 1.06 after correction, as well as the gradient from a factor of 4.59 to a factor of 1.01 and the R

^{2}from 0.34 to 0.78, before and after the application of the correction algorithm, respectively.

## 4. Conclusions

_{1}and from a factor of 4.59 to 1.43 for PM

_{2.5}). Nonetheless, there was a period where the corrected PM measurements still consistently overestimated the reference observations to a small degree. We show this event corresponds to a change in air mass origin consistent with a change in particle hygroscopicity. Our analysis showed that the particle hygroscopicity during this overestimation period was consistent with that of sodium chloride (NaCl). By assuming sodium chloride during the overestimation period and ammonium sulphate elsewhere, the corrected Alphasense OPC-N2 measurements improved further when compared to reference data. The results shown in this paper extend those already present in literature on the capacity of low-cost sensors to give reliable ambient PM readings when an appropriate correction is applied. While this work was performed using the instrument characteristics of an Alphasense OPC-N2, this algorithm is independent of sensor type and can be readily adapted to other size speciated particle counters and different environments. Finally, we note that the correction algorithm presented in this work not only is flexible to changes in particle chemical composition but also leads to the possibility of particle chemical speciation using low-cost sensors.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**Time series of Alphasense OPC-N2 PM

_{2.5}measurements compared with reference data: (

**a**) Time series of relative humidity; (

**b**) Time series of Alphasense OPC-N2 PM

_{2.5}measurements, before and after the application of the Crilley et al. correction factor, in comparison with reference data. The two inserts show volume distribution profiles measured by the uncorrected OPC-N2 for periods I and II. The overall measurement period consists of seven consecutive days data between 23 May and 31 May 2017. See text for discussion. (PM: particulate matter).

**Figure 2.**Particle size distributions for (

**a**) period I in Figure 1 and (

**b**) period II in Figure 1. Uncorrected Alphasense OPC-N2 particle size distributions are shown in green. Particle size distributions after application of the Crilley et al. correction factor (assumed to be constant across the size spectrum) are shown in blue, and reference data in red. See text for discussion.

**Figure 4.**Illustration of Palas Fidas 200 S measurements redistributed into the Alphasense OPC-N2 size bins for all bins contributing to PM

_{2.5}for (

**a**) number concentration data and (

**b**) volume concentration data. The black dashed lines represent the average Palas Fidas 200 S measurements in each Alphasense size bin.

**Figure 5.**Growth factor curve as function of relative humidity (RH) for ammonium sulphate. The discontinuity represents the efflorescence point of the compound [27].

**Figure 6.**Figures illustrating Alphasense OPC-N2 measurements in comparison with reference data. (

**a**) Time series of Alphasense OPC-N2 PM

_{2.5}measurements after the application of the correction factor [16] and the correction algorithm (this work) assuming a $\kappa $ value of 0.4 (Cyan) and 0.61 (Black) in comparison with reference data; (

**b**) Size distribution of Alphasense OPC-N2 volume concentration data for all size bins contributing to PM

_{2.5}before and after the application of the correction factor [16] and the correction algorithm (this work) assuming a $\kappa $ value of 0.4 (Cyan) and 0.61 (Black) in comparison with reference data for period I (25 May 03:18:00 UTC–25 May 05:48:00 UTC); (

**c**) as (

**b**) except for period II (28 May 00:31:00 UTC–28 May 03:01:00 UTC).

**Figure 7.**Probability distribution plot of Alphasense OPC-N2 measurement, after the application of the correction factor [16] and the correction algorithm (this work), in comparison with reference data for (

**a**) PM

_{1}and (

**b**) PM

_{2.5}. The dashed lines represent the mean of PM values in each case. The inserts figures show PM probabilities at higher values on expanded scales (see text).

**Figure 8.**Figures illustrating the reproducibility of the two Alphasense OPC-N2. (

**a**) Scatter plot of OPC 1 and OPC 2 PM

_{1}measurement relative to the period between 17 December 2017 and 16 January 2018; (

**b**) OPC 1 and OPC 2 PM

_{2.5}measurement scatter plot of OPC 1 and OPC 2 PM

_{1}measurement relative to the period between 17 December 2017 and 16 January 2018.

**Figure 9.**Time series plots of (

**a**) Relative Humidity, (

**b**) OPC PM

_{1}measurement in comparison with reference data before the application of the correction algorithm, and (

**c**) OPC PM

_{1}measurement in comparison with reference after the application of the correction algorithm. The blue shaded area denotes a period during which the corrected PM values show a systematic overestimation compared to with reference data. More details are given in the text.

**Figure 10.**Time series plots of (

**a**) Relative Humidity, (

**b**) OPC PM

_{2.5}measurement in comparison with reference data before the application of the correction algorithm, and (

**c**) OPC PM

_{2.5}measurement in comparison with reference after the application of the correction algorithm. The blue shaded area denotes a period during which the corrected PM values show a systematic overestimation compared to with reference data. More details are given in the text.

**Figure 11.**Figures illustrating the comparison of OPC measurements with reference data for PM

_{1}values. (

**a**) Scatter plot of reference and uncorrected OPC PM

_{1}measurements relative to the period between 17 December 2017 and 16 January 2018; (

**b**) Scatter plot of reference and OPC RH-corrected PM

_{1}measurements relative to the period between 17 December 2017 and 16 January 2018. The colour scheme reflects the blue and grey shaded areas in Figure 9c.

**Figure 12.**Figures illustrating the comparison of OPC measurements with reference data for PM

_{2.5}values. (

**a**) Scatter plot of reference and uncorrected OPC PM

_{2.5}measurements relative to the period between 17 December 2017 and 16 January 2018; (

**b**) Scatter plot of reference and OPC RH-corrected PM

_{1}measurements relative to the period between 17 December 2017 and 16 January 2018. The colour scheme reflects the blue and grey shaded areas in Figure 10c.

**Figure 13.**Ready Hysplit air mass trajectories plots ending in Cambridge (UK). (

**a**) 27 December 2017; (

**b**) 1 January 2018; (

**c**) 7 January 2018. The blue and red lines correspond to trajectories at 20 m and 50 m above ground level, respectively.

**Figure 14.**Time series plots of OPC PM measurements in comparison with reference data after the application of the correction algorithm assuming Ammonium Sulphate (grey shaded area) and Sodium Chloride (blue shaded area) as unique particle chemical species for: (

**a**) PM

_{1}; (

**b**) PM

_{2.5}.

**Figure 15.**Figures illustrating the comparison of RH corrected PM measurements assuming Ammonium Sulphate (grey points) and Sodium Chloride (blue points) as unique chemical species for PM for the periods discussed above. (

**a**) PM

_{1}; (

**b**) PM

_{2.5}.

**Table 1.**Summary of Alphasense OPC-N2 operational settings [18].

Alphasense OPC-N2 | |
---|---|

Sampling time (s) | 1.4 |

Size range (µm) | 0.38–17.0 |

Number of size bins | 16 |

Flow rate (L/min) | 1.2 |

Data storage (GB) | 16 |

Weight (Kg) | 0.105 |

Dimensions H·W·D (mm) | 63.5 × 75 × 60 |

Temperature range (°C) | −10 to +50 |

**Table 2.**Summary of Palas Fidas 200 operational settings [19].

Palas Fidas 200 S | |
---|---|

Sampling time (s) | 60 (average) |

Size range (µm) | 0.18–18.0 |

Number of size bins | 64 |

Flow rate (L/min) | 4.8 |

Data storage (GB) | 4 |

Weight (Kg) | 60 |

Dimensions H·W·D (mm) | 1810 × 600 × 400 |

Temperature range (°C) | −20 to +50 |

**Table 3.**Average PM values for the corrected OPC and reference measurements in Figure 6.

Reference | Crilley et al. | This Work | |
---|---|---|---|

PM_{1} (μg/m^{3}) | 1.74 | 2.36 | 1.55 |

PM_{2.5} (μg/m^{3}) | 3.64 | 4.25 | 3.03 |

OPC | PM_{1} | PM_{2.5} | ||
---|---|---|---|---|

Gradient | R^{2} | Gradient | R^{2} | |

1 | 1.00 | 1.00 | 1.00 | 1.00 |

2 | 1.03 | 0.99 | 0.99 | 0.99 |

**Table 5.**Statistical parameters for PM

_{1}measurement of reference, uncorrected OPC, and OPC after the application of the RH algorithm.

PM_{1} | Reference | OPC (Uncorrected) | OPC (RH Corrected) | OPC (RH Combined) |
---|---|---|---|---|

Mean (µg/m^{3}) | 3.02 | 13.45 | 3.46 | 3.20 |

SD (µg/m^{3}) | 2.25 | 18.24 | 3.03 | 2.72 |

RMSE (µg/m^{3}) | N.A. | 19.84 | 1.66 | 1.37 |

Gradient | 1.00 | 5.25 | 1.15 | 1.05 |

R^{2} | 1.00 | 0.42 | 0.73 | 0.75 |

Number of points | 43,000 | 43,000 | 43,000 | 43,000 |

**Table 6.**Statistical parameters for PM

_{2.5}measurement of reference, uncorrected OPC, and OPC after the application of the RH algorithm.

PM_{2.5} | Reference | OPC (Uncorrected) | OPC (RH Corrected) | OPC (RH Combined) |
---|---|---|---|---|

Mean (µg/m^{3}) | 5.12 | 26.10 | 6.47 | 5.44 |

SD (µg/m^{3}) | 3.69 | 28.85 | 6.07 | 4.21 |

RMSE (µg/m^{3}) | N.A. | 35.78 | 5.91 | 3.74 |

Gradient | 1.00 | 4.59 | 1.43 | 1.01 |

R^{2} | 1.00 | 0.34 | 0.75 | 0.78 |

Number of points | 43,000 | 43,000 | 43,000 | 43,000 |

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## Share and Cite

**MDPI and ACS Style**

Di Antonio, A.; Popoola, O.A.M.; Ouyang, B.; Saffell, J.; Jones, R.L.
Developing a Relative Humidity Correction for Low-Cost Sensors Measuring Ambient Particulate Matter. *Sensors* **2018**, *18*, 2790.
https://doi.org/10.3390/s18092790

**AMA Style**

Di Antonio A, Popoola OAM, Ouyang B, Saffell J, Jones RL.
Developing a Relative Humidity Correction for Low-Cost Sensors Measuring Ambient Particulate Matter. *Sensors*. 2018; 18(9):2790.
https://doi.org/10.3390/s18092790

**Chicago/Turabian Style**

Di Antonio, Andrea, Olalekan A. M. Popoola, Bin Ouyang, John Saffell, and Roderic L. Jones.
2018. "Developing a Relative Humidity Correction for Low-Cost Sensors Measuring Ambient Particulate Matter" *Sensors* 18, no. 9: 2790.
https://doi.org/10.3390/s18092790