Fine Particulate Matter (PM 2.5 , aerodynamic diameter <2.5 μm) is one of the six criteria pollutants that are routinely monitored across the United States by the Environmental Protection Agency (EPA). These particles can penetrate deep into the lungs and even enter the bloodstream, leading to premature death in individuals with heart or lung disease, aggravated asthma, and decreased lung function. 1 PM 2.5 monitoring in the U.S. began between 1999 and 2001 as part of the EPA's efforts to establish consistent operational and quality assurance procedures for air quality monitoring. 2 The EPA's Federal Reference Methods (FRMs) and Federal Equivalent Methods (FEMs) are used by all states and monitoring organizations to measure outdoor air pollutants accurately and reliably, ensuring compliance with National Ambient Air Quality Standards (NAAQS). However, these regulatory monitoring devices are often expensive and sparsely distributed, making community-scale PM 2.5 exposure assessment challenging. 3 The advent of low-cost air quality sensors has transformed environmental monitoring, allowing communities to assess air quality with high spatial and temporal precision. PurpleAir (PA) sensors are especially popular due to their affordability, ease of use, and reliable data. 4,5 Traditional networks, like those managed by the U.S. EPA, rely on expensive, stationary instruments with limited coverage, often missing small-scale pollution variations. 6 PA sensors provide real-time PM 2.5 data at a fraction of the cost of regulatory-grade monitors. After appropriate correction, their measurements have shown strong correlation with reference monitors (r > 0.9) and annual average errors below 1 μg/m 3 in colocated studies. 7,8 The widespread use of PA sensors has created dense networks, enriching air quality data and empowering communities to make informed decisions on pollution exposure. PA's integration into EPA's AirNow Fire and Smoke Map highlights their value in providing localized, accessible air quality information, fostering greater public awareness and engagement in environmental health. 9 As of 2024, PA sensors form an extensive global network with approximately 9000 indoor and 29,000 outdoor devices worldwide. In the United States alone, around 6000 indoor and 17,000 outdoor sensors are actively transmitting data, covering all states and significantly enhancing air quality monitoring capabilities. In California, hyperlocal PA sensor networks have revealed persistent air quality challenges in disadvantaged neighborhoods, leading to targeted interventions under programs like California's AB617, 10 which shows the critical role that low-cost, community-based air quality monitoring plays in advancing environmental justice and public health initiatives.
The PA PM 2.5 sensing platform uses two Plantower PMS 5003 laser particulate sensors to measure PM 1 , PM 2.5 , and PM 10 concentrations by detecting the scattering of ∼680 nm light at ∼90°. 11 Each device costs approximately $250, which is about one one-hundredth the price of a regulatory-grade instrument. Correction procedures are often necessary for optical PM sensors due to the varying optical properties of aerosols, influenced by their physical and chemical characteristics, and the impact of meteorological conditions such as temperature (T) and relative humidity (RH). 8 A PA sensor uses a laser to detect particles drawn through a fan. At low temperatures, condensation and ice can form on the laser and photodetector, reducing detection efficiency. The fan's reduced performance in cold conditions further lowers particle detection rates. High humidity levels above 75%, can cause PM 2.5 readings to spike by up to 80% due to particle hygroscopic growth. 12 Temperature fluctuations necessitate corrections to improve accuracy by up to 10%. 13 Placement near roadways can elevate PM 2.5 readings by 25% compared to rooftop locations. 14 Regular maintenance is vital, as dust and debris can degrade performance by 20%. 5 Rigorous correction is essential to adjust low-cost sensor measurements to more accurately reflect reference-grade data, reducing discrepancies and improving their reliability for scientific use. 7 Monitoring PM 2.5 in cold climates is crucial due to elevated pollution from increased heating requirements, which significantly impacts air quality. 8 During winter, PM 2.5 levels often exceed health standards, posing serious respiratory and cardiovascular risks. In Fairbanks, Alaska, wood smoke contributes up to 80% of PM 2.5 , with secondary pollutants like sulfate and ammonium nitrate adding 8-20% and 3-11%, respectively. 15 Accurate data, essential for public health measures, require robust monitoring and calibration. Developing location-specific correction factors is necessary to improve the accuracy of low-cost sensors in cold environments, ensuring effective public health interventions and regulatory policies. 16 In Alaska, there are currently only 26 indoor and 154 outdoor PA sensors publicly reporting data. Despite the wide availability of correction factors for PA sensors, none are specifically tailored to perform accurately in Alaskan temperatures, which may limit their deployment and effectiveness in this region. To expand the use of PA sensors across Alaska, a new correction factor optimized for the state's unique, cold climate conditions is essential. Existing correction factors are primarily developed for temperate regions, failing to address issues like condensation, ice formation, and reduced fan efficiency at low temperatures. 17 These factors significantly distort PM 2.5 readings, compromising data accuracy. Furthermore, high humidity exacerbates particle detection inaccuracies. This study aims to fill this gap by developing a correction equation for PA sensors based on data from a Beta Attenuation Monitoring (BAM) reference sensor and testing its effectiveness on nearby PA sensors. Addressing this gap is crucial for enhancing the reliability of air quality assessments in cold environments.
Although machine learning methods have been applied to low-cost sensor correction, this study focuses on linear regression models due to their transparency and ease of interpretation. Previous research has shown that linear models incorporating meteorological variables such as temperature and relative humidity can achieve performance comparable to more complex approaches. 7,8,18,19 This study builds on those findings to develop cold-climate correction models that are both statistically robust and practical for implementation in Arctic and sub-Arctic environments like Alaska.
2.1. Data Collection. Data was collected from four PA sensors and a BAM (model 1020X, MetOne) located in North Pole, Alaska. The BAM sampler is part of the Alaska DEC Air Quality Monitoring station at Hurst Road Fire Station and is installed at a height of approximately 10 feet. The nearest PA sensor is approximately 0.25 miles from the Hurst Road Fire Station. Hourly PM 2.5 measurements were obtained from the BAM sensor, while PA sensor data was collected at 2 min intervals from SD cards and 10 min intervals from the data cloud. The data from the nearest PA sensor (PA1) was used to develop the correction model. The remaining three PA sensors (PA2, PA3, PA4) located at varying distances (0.4-0.7 miles) from the Alaska DEC Monitoring site, were used for model testing and validation. All PA sensors are installed at approximately 7 to 10 feet in height within the residential area where wood heating is the dominant emission source during winter. There is minimal influence from other local sources such as traffic or cooking, and none of the PA sensors were positioned immediately next to chimneys or directly beside roads. This placement ensures similar exposure conditions and supports meaningful comparison between the PA and BAM data. Statistical analysis and data processing were conducted using R version 4.3.2, and plots were created using OriginPro 2025.
Processing. The study focused on developing a correction factor for PA sensors during colder periods. Therefore, data from October 2022 to March 2023 were used, when temperatures ranged from 14.8 °C to -42.1 °C. The uncorrected PM 2.5 data (PA cf1 ), referred to as raw PM 2.5 , was calculated by averaging the outputs of two Plantower sensor channels (A and B) in the PA sampler. Outliers were identified by examining hour-by-hour PA data and excluding values outside three standard deviations within any given hour. For both 2 min and 10 min data sets from PA, it was ensured that approximately 70% of data points per hour were available (i.e., 21 data points for 2 min and 4 data points for 10 min data) for calculating hourly averaged raw PM 2.5 ; if this criterion was not met, the data were not averaged for that hour and was labeled as "NA". T and dew point (DP) values measured by sensors in PA were used for analysis to make the model self-sufficient.
After applying data cleaning procedures, 99.2% of data (4333 out of 4368 hourly data points collected over six months) was retained for further analysis. To ensure model robustness, raw PM 2.5 collected at temperatures below -25 °C and raw PM 2.5 concentrations above 100 μg/m 3 were excluded.
These thresholds were chosen to minimize the impact of potential biases caused by extreme cold temperatures. Additionally, heteroscedasticity was observed in the residuals of the models for PM 2.5 concentrations above 100 μg/m 3 . Heteroscedasticity occurs when the variance of the residuals is not constant across different levels of the independent variable. In this case, the variance of the residuals increased as PM 2.5 concentrations rose above 100 μg/m 3 . To address heteroscedasticity and improve model performance, models were constrained to operate within the -25 to 10 °C temperature range and 0 to 100 μg/m 3 PM 2.5 concentration range. This filtering process retained approximately 91.6% of the data (4002 points), allowing the development of more accurate and reliable models.
A literature review was conducted to identify existing correction models for PA sensors, which are summarized in Table 1. The applicability of these correction models for PA sensors located in North Pole, Alaska, was assessed. Raw PM 2.5 data were applied to the available correction equations, and the results were compared to the BAM sensor readings. The performance of each model was evaluated by calculating the Root Mean Square Error (RMSE) and the coefficient of determination (R 2 ) between the corrected PM 2.5 concentrations and the BAM sensor data. This analysis aimed to determine if any existing correction models could provide suitable correction to the PA sensor data for the specific conditions in North Pole, Alaska.
To develop the correction equations, raw PM 2.5 data, RH, DP, and T from the nearest PA (PA1) sensor were used as predictors, with BAM sensor readings as the response variable. Various combinations and interactions of these predictors, detailed in Table 2, were considered. Nonlinear relationships for RH, previously identified in studies on Plantower sensors and other lightscattering measurements, 8,24 were included in model 13 (M13).
Seventeen models were developed for Ordinary Least Squares (OLS), Lasso, Ridge, and Elastic Net regression techniques. These models were trained on the collected data, and their performance was evaluated using R 2 and RMSE values. Subsequently, the models were validated using three test data sets, with distances of 0.7 miles (PA2, Test Sensor 1), 0.5 miles (PA3, Test Sensor 2), and 0.4 miles (PA4, Test Sensor 3) from the BAM. RMSE and R 2 values were calculated for each test data set.
A heuristic multicriteria scoring system was developed to thoroughly assess each model's predictive accuracy, generalization capability, and complexity. This scoring system incorporated a dynamic approach, utilizing multiple weighting configurations to examine the impact of prioritizing different evaluation criteria rather than relying on a single, fixed set of criteria. To quantify complexity, each model was assigned a score based on its regression technique and the number of predictor variables. Lasso regression, which shrinks the number
of coefficients and selects a sparse set of predictors, was given a base complexity score of 1 due to its simplicity. 25 Ridge regression, which regularizes without eliminating predictors, was given a base complexity score of 1.5. 26 Elastic Net, combining the strengths of both Lasso and Ridge, received a base score of 1.75, reflecting its intermediate complexity. 27 To further refine the complexity score, the base score was adjusted by adding the number of coefficients divided by 10. This adjustment penalizes models with multiple predictor variables, ensuring that excessively complex models are not favored, while allowing models with predictors that genuinely enhance performance to be considered favorable.
To evaluate predictive accuracy and generalization, the average differences in RMSE (mRMSE) and R 2 (mR 2 ) between training and testing data sets were prioritized as key metrics. Lower mRMSE and mR 2 values indicate greater consistency in model performance when applied to data from a different sensor than the one used for training, reflecting stronger generalization. These metrics were weighted more heavily to favor models with consistent performance across data sets. Training RMSE and R 2 were also included but assigned lower weights to reduce the risk of overfitting. Model complexity was penalized to deprioritize models with unnecessary predictors. The scoring system balanced performance, generalization, and simplicity calculated as Score = w1
To ensure robustness in model selection and avoid reliance on a single set of weights or assumptions, seven distinct weighting configurations (WC) were applied. These configurations explored various trade-offs between key metrics, mRMSE, mR 2 , training performance, and complexity under different conditions. Each configuration represented a unique evaluation perspective, ensuring models performed well across multiple scenarios. The weighting framework was developed in this study to support flexible and comparative evaluation across a range of model priorities.
The weights for each configuration were assigned based on model evaluation priorities, such as minimizing test error, ensuring generalizability, controlling model complexity, or achieving a balance among these goals. The values were selected through iterative testing to produce meaningful differences in model rankings across configurations. Rather than optimizing for a single objective, this approach evaluates models from multiple perspectives, allowing flexible comparison across evaluation criteria. The structure of this approach makes it adaptable to other modeling contexts where similar trade-offs are present.
•
Each model (M1-M17) combines the raw PA reading (PA cf1 ) with different environmental variables, including temperature (T), relative humidity (RH), and dew point (DP), and interaction terms.
•WC3 (R 2 -Heavy Configuration): In this configuration, mR 2 and training RMSE are given the highest weights of 5. Lower weights were assigned to mRMSE (4) and training R 2 (3), while model complexity was weighted minimally at 2. This configuration emphasizes models with stronger explanatory power, even if they exhibit slightly higher prediction errors.
•WC4 (Complexity-Heavy Configuration): This configuration assigns the highest weight (5) to model complexity. Moderate weights of 4 were given to mRMSE, training RMSE, and mR 2 . This approach favors models that balance performance and simplicity while maintaining higher complexity to capture nuances in the data. The models consistently ranked in the top five across multiple configurations were identified. Models that appeared in the top five rankings in more than three configurations were considered robust and selected for further analysis. This approach ensured that the final models were accurate, generalizable, and balanced in performance and complexity, making them suitable for practical application.
The coefficients for each top-performing model were computed and tested at different levels of decimal precision to assess the impact on performance. Based on this analysis, coefficients were rounded to the lowest level that maintained model stability, ensuring a balance between simplicity and predictive accuracy for practical application. These coefficients were then used to generate predictions of PA readings based on the raw testing PM 2.5 data (PA1). For each model, the predicted values were compared against the reference BAM sensor data. Key performance metrics, which include Mean Absolute Error (MAE), RMSE, and R 2 , are calculated. In this study, a lower RMSE and MAE indicate better performance, reflecting minimal error between the corrected PA sensor predictions and the BAM sensor readings. Higher R 2 values suggest a better fit, meaning the model captures a larger proportion of the variance in the BAM sensor data. In addition, paired t tests were performed to assess the statistical significance of differences between BAM sensor values and corrected PA sensor predictions.
To further assess the robustness of the selected models, the Diebold-Mariano (DM) test was conducted to compare the residuals (errors) of the competing models. This test evaluates whether there is a statistically significant difference in their predictive accuracy. The DM test was performed in a twosided manner, comparing models pairwise to identify which one provided the most accurate predictions based on the raw PM 2.5 data. A positive DM statistic indicates that the first model outperformed the second, while a negative DM statistic suggests the opposite. A significant p-value (<0.05) indicates that the difference in predictive performance between the two models is statistically significant.
By balancing multiple evaluation criteria, including low RMSE, low MAE, high R 2 , statistical significance from the t tests, and predictive performance through the DM test, the methodology ensured that the final selected model not only provided the most accurate predictions but also demonstrated generalizability across different testing data sets.
Literature review, summarized in Table 1, identified several existing correction factors for PA sensors. These models were evaluated for their applicability to PA sensors in the North Pole, Alaska. Raw PA PM 2.5 data were corrected using these equations, and the results were compared to BAM sensor readings. The performance of each model was assessed by calculating the RMSE and the R 2 .
Figure 1 presents a scatter plot comparing the corrected PA concentrations from various existing models to the BAM sensor readings. Significant variability is evident, particularly at higher PM 2.5 levels, indicating inconsistencies in model performance. The data points are dispersed around the 1:1 line, highlighting deviations in correction accuracy. Figure 1 summarizes the RMSE and R 2 values for the existing correction models. Model IV exhibited the highest RMSE (32.6 μg/m 3 ) and a negative R Pole, Alaska. Significant variability in PA correction factors with temperature and humidity has also been noted in studies. 8,28 Studies have shown that under high humidity, PA sensors tend to overestimate PM 2.5 concentrations due to the hygroscopic growth of particulate matter, which increases light scattering within the sensor. 7 Similarly, temperature fluctuations can affect sensor performance, leading to variations in output that necessitate the application of site-specific correction factors. Jaffe et al. (2023) evaluated the U.S. EPA's correction equation for PA sensors found that the correction factor's effectiveness varied with temperature and humidity, highlighting the need for tailored adjustments to improve data accuracy. 29 Regional calibration has been emphasized as critical for improving the accuracy of low-cost sensors in diverse conditions. 20,30 The critical role of local climate in sensor accuracy is reinforced, supporting the need for tailored corrections. 7,28 Small variations in environmental conditions can significantly impact sensor readings, highlighting the limitations of existing models. 30 The significant differences in RMSE and R 2 values among the evaluated models underscore the necessity for a tailored correction approach. While moderate R 2 values (∼0.5-0.6) indicate some level of correlation, existing models do not fully account for the specific environmental factors in the North Pole, Alaska. The substantial deviations between corrected PA data and BAM sensor readings highlight the limitations of existing models and reinforce the need for a location-specific correction approach.
To evaluate the performance of PA sensors in comparison to BAM in cold climates, the PM 2.5 concentrations and temperature readings recorded by both sensors were analyzed. Figure 1
levels, particularly during peak pollution periods in winter. The extremely low p-value of 1.2 × 10 -130 from the t-test confirms that the differences are statistically significant.
Figure 3E displays a linear regression of temperature readings between the PA sensor and the ambient temperature reported by the Alaska DEC site. The regression analysis yielded an interception of 4.3 and a slope of 0.93, indicating a strong linear relationship between the two data sets. The maximum and minimum temperatures recorded by the PA sensor were 18.23 °C and -34.41 °C, respectively, while the Alaska DEC site recorded 14.8 °C and -42.1 °C. The results suggest that the PA sensor consistently reads temperatures approximately 4.3 °C higher than ambient conditions, likely due to internal heat generated by the device's electronics. While this offset exists, the high correlation and linearity indicates that the PA temperature values are still reliable for relative comparisons and modeling applications, and a separate correction for temperature was not deemed necessary in this study.
Field evaluations have shown that low-cost sensors like the PA tend to overestimate PM 2.5 levels under cold conditions, particularly when temperatures fall below -10 °C. 28 This overestimation can lead to inaccurate air quality assessments, emphasizing the need for calibration models that account for local temperature variations. Incorporating local temperature data into these models can significantly improve the accuracy of PM 2.5 measurements, reducing errors by up to 20%. 31 Regular calibration against reference-grade instruments, such as the BAM sensor, is essential for maintaining data reliability. Studies have demonstrated that frequent calibration can reduce discrepancies in PM 2.5 readings by up to 15%, thereby enhancing the accuracy of low-cost sensors. 5 This approach aligns with findings that without proper calibration, low-cost sensors can misrepresent air quality data, potentially leading to incorrect public health advisories. 13,32 Therefore, developing tailored correction models and incorporating regular calibration practices are critical steps to ensure accurate air quality assessments and effective public health interventions. 86.8% of the filtered data. This range represents typical environmental conditions in North Pole, Alaska, during the monitoring period. Additional discussions on data availability, averaging methods, and quality assurance steps are provided in Supporting Information (Section S1).
Figure 3 presents the temperature-dependent comparison of PM 2.5 concentrations between BAM and PA sensors, illustrating the impact of temperature on sensor performance. The fitted line for the unfiltered data set (Figure 2D) has a slope of 1.08, an R 2 of 0.62, and an RMSE of 19.66, indicating a moderate correlation and a general trend of overestimation in raw PA sensor readings relative to BAM. Figure 2E focuses on data filtered for temperatures between 10 °C and -25 °C, with raw PM 2.5 between 0 and 100 μg/m 3 . The slope of 1.12 from this data set highlights the need for temperature-specific calibration models.
When breaking down the data into narrower temperature ranges, as shown in Figure 3A-D, it becomes evident that the overestimation by PA sensors becomes less pronounced as temperatures drop. The slopes decrease from 1.68 in the 10 to 0 °C range to 0.82 in the -20 °C to -25 °C range, indicating that PA readings increasingly converge toward BAM values at lower temperatures. Although the agreement between PA and BAM improves at lower temperatures, sensor performance may still be affected by physical limitations such as condensation on electrical components and changes in light scattering efficiency. 12 Further discussion of sensor limitations in extreme cold is provided in Section S1 of the Supporting Information.
The monthly comparisons presented in the Supporting Information (Figure S1A-F showing how each winter month remained well below freezing. The slopes decrease from 1.52 in October to 1.07 in February, suggesting that agreement between PA and BAM improves at lower temperatures. Zheng et al. (2018) noted that prolonged exposure to cold can significantly impact the accuracy of lowcost sensors. 13 This temperature dependence underscores the importance of localized calibration models that incorporate temperature adjustments to minimize measurement errors.
To identify the most accurate correction models for PA sensor data, various regression techniques were employed, including OLS, Lasso, Ridge, and Elastic Net. These models were trained using raw PA data, T, RH, and DP as predictors, with BAM sensor readings as the response variable. For the Lasso, Ridge, and Elastic Net models, the regularization parameter (λ) was selected using cross-validation, with the minimum λ value being chosen by default for analysis to ensure optimal model performance. The models considered are detailed in Table 2.
Seventeen different model equations (M1 to M17) were based on RMSE and R 2 . The training phase revealed that the model incorporating nonlinear relationships (M13) and interactions between predictors demonstrated improved performance, highlighting the significance of capturing complex environmental influences on PM 2.5 measurements. The Lasso regression technique was particularly effective, indicating its strength in managing multicollinearity and selecting relevant features. 25 The R 2 and RMSE values for the training and testing data sets are shown in Figures S2-S5 While comparing the different models, it was observed that OLS did not handle multicollinearity or feature selection as effectively as regularized models. Lasso regression is notable for its feature selection capability and improved performance, and it managed multicollinearity by shrinking some coefficients to zero. Ridge and Elastic regression demonstrate consistent performance with relatively low RMSE and high R 2 values across different data sets.
To find the best correction equation, a rank-based evaluation system was applied to 68 models (17 OLS, 17 Lasso, 17 Ridge, and 17 Elastic Net-based models), providing a structured way to assess their performance across multiple weight configurations (WC1 to WC7). These configurations emphasized different criteria, such as testing RMSE, training R 2 , and model complexity, allowing for a comprehensive comparison. Figure 4 highlights the best-performing models among the 68, showing those that ranked within the top 5 across different WCs. Lower-ranked models, represented, indicate better performance across multiple weight configurations.
Models M17 (Lasso), M10 (Ridge), M14 (Lasso), M4 (Lasso), M5 (Rigid), M12 (Lasso), and M15 (Lasso), ranked in the top 5 in at least one weight configurations but did not consistently perform well across all criteria. The inconsistency in performance emphasizes the need for a multicriteria approach rather than relying on a single metric. Models that ranked in the top 5 across more than three weight configurations were selected for further analysis to ensure robustness. This step avoids bias toward any specific criteria and ensures adaptability, especially when developing correction equations for PA sensors in cold environments (-25 to 10 °C).
Only three models (M13 (Lasso), M10 (Lasso) and M6 (Lasso)) consistently ranked in the top five across more than three WCs and were selected for further consideration. M13 (Lasso), having the highest average ranking, showed consistent performance across configurations, with testing RMSE ranging from 8.4 to 9.85 and R 2 between 0.57 and 0.65, reflecting a strong balance between complexity and accuracy. M10 (Lasso) performed well in training-heavy configurations (WC6) but struggled under WC7, which focused on generalization, with testing RMSE rising to 10.36 and R 2 dropping to 0.57, which
could be due to overfitting. M6 (Lasso) showed good generalization across most configurations, but its performance dropped under WC6, which prioritized training data. Testing RMSE values ranged from 9.31 to 10.02, and testing R 2 from 0.59 to 0.64, indicating it is better suited for generalization than for purely training-focused tasks.
The selection process avoids bias from a single weight configuration and ensures that the chosen models, M6 (Lasso), M10 (Lasso), and M13 (Lasso), are versatile and capable of adapting to multiple conditions. The complexity score adjustment used in this study assigns a base score based on the regression method and adds a penalty based on the number of predictors, favoring simpler models to reduce the risk of overfitting. This method aligns with the principle of parsimony in model selection. 33 These models will be analyzed in more detail to develop a robust correction equation for PA sensors in low-temperature environments.
The rank-based evaluation system successfully identified models that performed consistently across different weight configurations, ensuring that the chosen models M6 (Lasso), M10 (Lasso), and M13 (Lasso), are suitable for further analysis. By applying the rank based multicriteria selection method, the models chosen for further analysis were both accurate and adaptable to varying performance priorities. Subsequent analysis discussed below will focus on absolute RMSE and R 2 values to finalize the models that will be used for developing correction equations for PA sensors in cold environments.
The selected models reduce the overestimation observed in uncorrected PA sensor data, as evidenced by improved RMSE and R 2 values compared to existing correction models (Figure 1) and summarized in Table 3. The Lasso models' ability to manage feature selection and regularization proved advantageous. The incorporation of nonlinear relationships in M13 further enhanced correction accuracy. Studies have shown that incorporating interactions between predictors such as temperature and relative humidity can significantly improve the accuracy of PM 2.5 measurements. 7,13 The selected models were evaluated to determine which provided the most accurate correction for PA sensor data under cold temperature conditions in the city of North Pole, Alaska: M6 (which includes raw PM 2.5 , T, and RH), M10 (which relies on PM 2.5 and RH), and M13 (a nonlinear model incorporating RH 2 ). The performance of each model was assessed based on a range of criteria, including MAE, RMSE, R 2 , and p-values from paired t tests comparing corrected PA values to BAM sensor data. The results, presented in Table 3, provide a comprehensive view of each model's effectiveness.
The impact of decimal precision on model performance was evaluated by testing each selected model across multiple levels of decimal precision. Models M6 and M10 showed stable RMSE and R 2 values down to two decimal places. M13 was more sensitive to rounding beyond three decimal places, but this behavior was not consistent across models. To ensure consistency and maintain overall model accuracy, all final coefficients were rounded to two decimal places.
Model M13, which included the squared relative humidity term (RH 2 ), performed poorly with an RMSE of 16.65 and a negative R 2 (-0.199), indicating it introduced more error than it resolved. The underperformance was largely due to rounding coefficients to three decimal places for practical application.
For terms like ( )
RH 1 RH 2 and ( ) PA RH 1 RH 2 • , which had small magnitudes, rounding effectively nullified their influence, reducing the model's ability to capture important patterns. A paired t-test confirmed M13's limitations, yielding a statistically significant p-value, indicating that its corrected PM 2.5 values differed significantly from BAM reference readings. The added complexity from RH 2 terms did not improve accuracy, and rounding the small coefficients for practical use further diminished their effect. In contrast, model M10 (Lasso) demonstrated the highest R 2 (0.695) and lowest RMSE (8.411) among the tested models, suggesting strong predictive potential. However, a paired t-test produced a p-value of 0.036, indicating a statistically significant difference between M10s corrected PM 2.5 values and BAM readings. This misalignment raises concerns about its reliability as a correction model despite favorable metrics. Model M6 (Lasso), with an RMSE of 8.71 and an R 2 of 0.67, emerged as the most reliable correction model. Its paired t-test yielded a p-value of 0.360, indicating no statistically significant difference between the corrected PM 2.5 values and BAM readings. This lack of deviation suggests M6's corrections closely align with BAM measurements, making it the most practical and robust model for real-world applications. To further validate these findings, DM test was conducted to compare M6 and M10. The DM statistics of 3.965 and p-value <0.05 strongly rejected the null hypothesis of equal performance, confirming that M6 outperformed M10 in terms of correction reliability. The final correction equation derived from the M6 (Lasso) model is T T PM 0.48 PA 1.31 0.07 RH 0.02 RH 3.83 2.5 = • • • + • • +
This equation is specifically tailored for cold climates ranging from -25 to 10 °C and demonstrates up to a 35% reduction in RMSE compared to existing models (Figure 1), representing a clear improvement in the accuracy and reliability of low-cost air quality sensors. The R 2 value of 0.676 indicates that 67.6% of the variance in PA sensor data is explained by the model. The remaining variance is likely due to localized wood-burning emissions, as all sensors were situated in a residential area. This specific emission source introduces variability that affects the overall correlation between PA sensor readings and BAM measurements. By balancing simplicity and performance, the developed correction model provides a practical and accurate solution for real-world applications, particularly in cold climate conditions. Despite these promising results, the model has limitations. It was developed and validated using data from North Pole, Alaska, where the average winter (October to March) temperature is -15 °C and relative humidity frequently exceeds 80%. Future studies should focus on validating and recalibrating the model for diverse environments to ensure its generalizability and robustness across different conditions. While the model incorporates key environmental factors like temperature and humidity, it does not account for other potential sources of error such as sensor aging, aerosol composition variations, and maintenance issues. Future research should aim to integrate these factors, potentially through advanced machine learning techniques, to enhance the model's comprehensiveness and accuracy. Additionally, the effects of prolonged exposure to low temperatures and sudden temperature fluctuations on sensor performance were not addressed in this study and should be investigated in future research. These conditions can also introduce significant measurement errors, as sensors may respond differently under sustained cold stress or abrupt thermal changes. Investigating these effects further in a laboratory setting will help refine the correction model and improve its accuracy in real-world applications.
The heuristic approach used for model ranking, involving RMSE and R 2 , proved effective in this study. However, more sophisticated methods, such as ensemble learning or neural networks, could offer improved predictive capabilities.
In conclusion, the developed correction model improved accuracy by reducing RMSE by approximately 35% compared to existing correction models and achieved an R 2 of 0.67, demonstrating reliable performance for low-cost air quality monitoring in cold climates. In addition to the correction model development, a flexible multicriteria model selection framework was introduced to enable balanced evaluation of accuracy, generalization, and complexity, offering a transferable approach for future model selection across diverse applications. Addressing the identified limitations, such as validating the model in diverse climatic conditions and incorporating additional sources of error, will be crucial for its broader applicability. Continuous monitoring and periodic recalibration will ensure sustained accuracy and reliability of the model over time. This advancement ultimately contributes to better public health outcomes and more informed policy decisions, particularly in regions facing extreme weather conditions. The model's success in North Pole, Alaska, with its unique climate challenges, sets a precedent for future adaptations and implementations in other regions.
The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acsestair.5c00018.
Additional details about the data cleaning processes and sensor performance, including plots showing monthly variation in PA performance at the North Pole, Alaska (October 2022-March 2023; Figure S1), and comparisons between various correction models when applied to training and testing data sets (Figures S2-S5) (PDF) ■ AUTHOR INFORMATION Corresponding Authors Raghu Betha -Department of Civil and Environmental Engineering, Texas Tech University, Lubbock, Texas 79409, United States; orcid.org/0000-0002-7556-9141; Phone: 806-834-4038; Email: raghu.betha@ttu.edu Srijan Aggarwal -Department of Civil, Geological, and Environmental Engineering, University of Alaska Fairbanks, Fairbanks, Alaska 99775, United States; orcid.org/0000-0002-9141-9936; Phone: 907-474-6120; Email: saggarwal@alaska.edu
https://doi.org/10.1021/acsestair.5c00018 ACS EST Air 2025, 2, 1191-1201
ACS ES&T Air