Calibration models that perform well with colocation data may still produce large error in field predictions if the model is not transferable to the environmental and sensor conditions at field sites. For instance, showed how sensor drift reduces the accuracy of calibration models when applied to field data collected long after the colocation period. Others have demonstrated how calibration models can overfit to the environmental conditions, source mixtures, and pollutant concentrations present at the colocation site, making the model less reliable when transferred to field sites . These impacts are especially important to consider for VOCs, which exhibit higher spatial variability than other pollutants and are composed of a complex mixture of chemicals, further complicating model transferability .

To ensure a calibration model is transferable to field data, colocations must capture the range of environmental conditions expected during field deployment, though many colocations occur only before and/or after field deployment, potentially during different seasons . In contrast, a two-step colocation occurs simultaneously with field deployment, making it possible to capture data under the same seasonal conditions. In a two-step colocation, a single LCS system, referred to here as the secondary standard, is colocated with a reference-grade monitor while the remaining LCS systems collect data at field sites . The field sensors are then colocated with the secondary standard for a shorter period, referred to as the harmonization step, to address inter-sensor variability. A two-step colocation can improve calibration transferability, especially when the colocation with the reference monitor occurs close to the field deployment sites, as this increases the likelihood of capturing similar environmental conditions within the same seasonal timeframe. Two-step colocations also allow for more extensive colocation periods without decreasing the amount of field data that can be collected, which is advantageous for complex machine learning models that require extensive data to prevent overfitting. In this study, we improve upon the two-step colocation process developed by and to further address sensor drift and model transferability.

Machine learning algorithms can improve calibration models by accounting for the non-linear signal response of LCSs . Due to their complexity, machine learning models require more extensive colocation data to prevent model overfitting to the colocation data, as this can make the model less reliable under changing field conditions . The optimal machine learning model varies by dataset and is typically selected by comparing calibration model performance metrics, such as root mean squared error (RMSE) and mean bias error (MBE), for a portion of colocation data excluded from model training . Evaluating the excluded data, called testing data, helps prevent overfitting to the training data.

Studies comparing the performance of various machine learning calibration models, such as random forest, artificial neural networks, support vector machine regressions, and gradient boosting, have relied on PM_2.5, CO, NO₂, CO₂, and O₃ datasets . Compared to these pollutants, TVOC and BTEX data are often much more imbalanced, with the majority of measurements clustered near low parts-per-billion baseline levels and occasional episodic spikes multiple orders of magnitude higher . Imbalanced datasets make it more difficult to assess calibration model performance, as models that poorly fit elevated concentrations may still achieve strong overall performance metrics if they accurately predict baseline concentrations . In these cases, partitioning the performance metrics by data percentile can reveal significantly underestimated peak concentrations . Additionally, certain machine learning models, especially gradient boosting, are generally better suited to address data imbalance , but calibrations for low-cost TVOC and BTEX sensors have been limited to linear regression, random forest, and neural network models . Thus, our study provides the first comparison to our knowledge of a comprehensive suite of machine learning models for TVOC and BTEX sensor calibration, including random forest, gradient boosting, support vector regression, artificial neural network, ridge, and lasso algorithms. We also evaluate model performance for NO₂ calibration to compare how these models perform on a more balanced dataset.

HAQ-Pods were developed in the Hannigan Air Quality (HAQ) Lab and have previously been used to capture local pollution events . HAQ-Pods use interchangeable, commercial sensors to quantify various pollutants. The metal oxide and electrochemical sensors used in this study are listed in Table . We also used a Bosch BME 680 sensor for temperature and humidity measurements. The sensors are housed in a weather-proof case (10.7′′×9.8′′×4.8′′) outfitted with fans to draw air across the sensor surfaces. HAQ-Pods feature updated circuitry compared to Y-Pod air monitors, which have been described elsewhere .

For the TVOC calibration, the secondary standard HAQ-Pod was colocated with an Extractive Fourier Transform Infrared Spectrometer operated and maintained by the South Coast Air Quality Management District (South Coast AQMD) using methods similar to those described in . Ambient air is continuously drawn through heated Teflon inlet (1-inch ID) mounted on the roof of the station into a 25-liter cell at ∼25 L min⁻¹. Infrared light is generated with a glow-bar and directed into the cell with a series of mirrors. The light beam is passed through the cell multiple times via a series of curved mirrors to achieve a total path length of ∼100 m before exiting the cell and being directed into the infrared spectrometer (Bruker, Type: Matrix-M). Light is detected with an Indium/Antimonide detector in the 1800–4000 cm⁻¹ region and the spectrometer has a spectral resolution of 0.5 cm⁻¹.

Gas concentrations are calculated using synthetic spectra generated by fitting calibration spectra taken from the HITRAN and PNNL databases to the raw spectra collected by the spectrometer in a linear least squares type fitting algorithm within the spectral evaluation window of 2725 to 3007 cm⁻¹ . The spectral fit includes calibration spectra for H₂O, CH₄, HDO, Propane, Butane, and Octane with TVOC reported as the sum of Propane, Butane, and Octane.

For the BTEX calibration, the secondary standard HAQ-Pod was collocated with an automated gas chromatograph (auto-GC) instrument (Tricorntech; MiTAP P320 Series) operated and maintained by South Coast AQMD. The auto-GC operates continuously with a distinct sampling and analysis phase that span 40 and 20 min, respectively. During the sampling phase, the auto-GC continuously draws ambient air at 5 cm³ min⁻¹ through a roof mounted inlet into a pre-concentrator for 40 min, totaling 200 cm³ of gas. During the analysis phase, the sample passes through a series of heated GC columns by way of pressurized inert carrier gas (N₂), where compounds are separated by polarity and subsequently detected with a series of photoionization detectors. Digital chromatograms are recorded and used to calculate ambient gas concentration via reference to a set of previously determined calibration chromatograms. Calibration chromatograms are determined by routinely (twice weekly) directing gas from a concentration-certified compressed cylinder into the auto-GC. The method is capable of an accuracy of 0.1 parts per billion by volume (ppbv).

For the NO₂ calibration, the secondary standard HAQ-Pod was colocated with a Teledyne T200 instrument maintained by the South Coast AQMD. The reference instrument was calibrated by the South Coast AQMD every six months and underwent weekly zero and span checks, in addition to nightly PC checks to ensure correct values.

The secondary standard HAQ-Pod was colocated with the South Coast AQMD instruments while all other HAQ-Pods were deployed at field sites in South Los Angeles from 10 October 2023 to 18 March 2024. The field HAQ-Pods were harmonized with the secondary standard HAQ-Pod from 4 to 9 October 2023 and from 18 to 28 March 2024. The physical set-up of the harmonization is shown in Fig. . Unlike previous two-step colocations, the HAQ-Pods were harmonized with the secondary standard both before and after field deployment to better account for sensor drift across the entire study period, as suggested by .

and demonstrated different approaches for propogating the calibration model to the field LCSs in a two-step colocation (Fig. ). developed a primary calibration model between the secondary standard and reference instrument. In the harmonization step, the field LCS systems were then calibrated via a secondary calibration model to the concentration timeseries predicted by the calibrated secondary standard. This method is better suited for projects where the colocation and harmonization steps are similar in length, since each step requires equally complex calibration models.

Conversely, first developed a multi-linear regression model for each sensor signal corrected to the secondary standard's corresponding sensor signal. The multi-linear regression models for the pollutant sensors included temperature and humidity in addition to the pollutant sensor signal. The primary calibration model between the secondary standard and reference monitor could then be applied directly to the corrected field LCS systems. Since this method uses only a linear regression in the harmonization step, it is well-suited for projects where the harmonization is much shorter than the colocation. However, including temperature and humidity in the pollutant sensor regression model may introduce dependencies on environmental conditions that then require the harmonization step to span the full range of conditions expected in the field – thereby reducing the method’s usefulness for short harmonizations. To avoid this, we included only the pollutant sensor signal and a time elapsed variable in our linear regressions for harmonization, so that the regression corrects only for inter-sensor linear baseline shifts and drift (Eq. ). 1yi=β0+β1xi+β2Ti+ϵi Where βs represent the model coefficients, xi is the sensor signal for the ith observation, Ti is the time elapsed from the start of data collection for the ith observation, and ϵi represents the error term for the ith observation.

Inputs into the TVOC and BTEX colocation calibration models included the signals from the metal oxide sensors, as well as temperature, humidity, and a time elapsed feature to account for sensor drift. The NO₂ calibration model used inputs from the electrochemical NO₂ sensor along with temperature, humidity, and time-elapsed data.

To evaluate model performance, we split the colocation data into training and testing datasets, allocating 80 % for training and 20 % for testing. While this train/test split is typically performed once, we repeated the calibration process 20 times to assess model robustness. For each run, we used a different split of the data. Specifically, for each iteration, we randomly selected a starting point in the time series and designated the next 10 % of data as testing data. A second 10 % segment was selected from a point halfway through the dataset relative to the first chunk, wrapping around if necessary. Figure  shows an example test/train split for each pollutant with reference and predicted concentrations (using a linear regression model) to demonstrate how this test/train approach allows the testing data to span different times of the year. This approach ensures the model is not overfit to a specific environmental state or season, while minimizing information leakage from autocorrelation between training and testing datasets .

The sensor signals are time averaged to 60-minute intervals prior to model training to reduce noise . Signals were then z-scored to a mean zero and standard deviation equal to one based on the training data. During model training, we use k-fold cross-validation (k=5) to tune hyper-parameters to values that minimize the loss function, or mean squared error (MSE), shown in Eq. (). We used the Scikit-learn Python module for all models except the artificial neural network, which used Tensorflow, and extreme gradient boosting, which used the Xgboost package. 2MSE=1n∑i=1n(yi-y^i)2 Where yi is the reference concentration for the ith observation and yi^ is the predicted concentration for the ith observation, and n is the number of observations.

We evaluated the overall fit of the calibration models using three performance metrics: root mean squared error (RMSE) (Eq. ), mean bias error (MBE) (Eq. ), and coefficient of determination (R2) (Eq. ). We also evaluated RMSE and MBE by percentile groups to assess model fits across the entire range of data. For the percentile-based assessment, the data were partitioned into 0–5th percentile, 5–25th percentile, 25–75th percentile, 75–95th percentile, and 95–100th percentile groups. 6RMSE=1n∑i=1n(yi-y^i)27MBE=1n∑i=1n(yi-y^i)8R2=1-∑i=1n(yi-y^i)2∑i=1n(yi-y¯)2 Where yi is the reference concentration for the ith observation and yi^ is the predicted concentration for the ith observation, and n is the number of observations.

Lastly, we applied the calibration models to sensor data collected from three field sites within the Los Angeles study area. We compare the predictions of each model to understand how they vary when applied to field conditions.

As observed during harmonization, colocated HAQ-Pod raw sensor signals are generally well correlated, with correlation coefficients between the secondary standard HAQ-Pod raw signals and corresponding raw signals in the other HAQ-Pods ranging from 0.87 to 1 (Supplement). However, some shifted baselines and amplitudes are still visible in the left column of Fig. , especially for the metal oxide sensors, demonstrating the importance of correcting individual sensor signals rather than relying on a universal or general calibration. After applying the linear correction developed during harmonization (coefficients listed in Tables S2–S7), the signals are visually more aligned (right column of Fig.  and have correlation coefficients with the colocation HAQ-Pod signal ranging from 0.96–1 (Supplement).

The left column of Fig.  also reveals why performing both pre- and post-harmonization is essential for some sensors, especially Figaro TGS 2600 and 2611 in this case. These sensors show different behavior compared to the secondary standard HAQ-Pod signal in the pre- and post- harmonization, indicating sensor drift. We addressed this drift by including a time-elapsed feature in the harmonization correction, which approximates the drift as a linear function. It is likely the sensor drift is not perfectly linear, but the approximation appears to be sufficient here based on performance at both the start and end of harmonization. Conducting both pre- and post- harmonizations was essential for checking the drift approximation, as otherwise the model may extrapolate drift beyond what is reasonably possible.

The temperature and humidity ranges recorded during the field deployment show strong overlap with the temperature and humidity ranges recorded at the HAQ-Pod colocation site (Fig. , note that measurements are uncalibrated sensor temperature and humidity). This overlap, which is important for colocation model transferability to field data, is possible because the two-step colocation allows for simultaneous colocation and field data collection. If colocation had occurred only before and after field deployment, as is typical for many low-cost sensor deployments, the overlap would look more like that of the field and harmonization phases in Fig. . Conditions during the harmonization phase trended towards higher temperature and humidity because the harmonizations occurred in fall and spring, while the field deployment was mainly in winter. This seasonal difference could lead to poor transferability if temperature and humidity impacts on the sensors were corrected in the harmonization phases because the model would have to extrapolate the impacts at low temperature and humidity ranges. Instead, our two-step colocation strategy corrects for sensor cross-sensitivity to temperature and humidity in the colocation phase only, where there is sufficient overlap of environmental conditions.

Figure  highlights how the distribution of TVOC and BTEX concentrations measured by the reference instruments during colocation are more skewed than NO₂, as 75 % and 78 % of the total concentration range falls within the 95–100th percentile group for TVOC and BTEX, respectively, compared with just 31 % for NO₂. Thus, the inclusion of NO₂ in our analysis provides a useful comparison of machine learning calibration performance on a more balanced dataset.

In the following sections, we show the calibration model performance for each pollutant across all 20 calibration repetitions (Figs. , , ). R2 values for these models are available in Fig. S1. To better visualize how these models actually predict testing and field data concentrations, we show predicted data from one calibration run in Figs. , , , , , and . The calibration run we selected to visualize in these plots is one that was close to the median overall performance, based on RMSE and MBE, for each pollutant.

Across the three pollutants, the calibration models generally underestimated peak concentrations and overestimated baseline levels, though the extent of this bias varied with the distribution of the reference data. For TVOC and BTEX, which had more imbalanced distributions, peak underestimation was more pronounced, likely due to the wider range of high concentrations. These results highlight the importance of evaluating model performance across the full concentration distribution, rather than relying solely on overall metrics. In many cases, biases at the extremes were masked in the overall statistics because the baseline overestimation and peak underestimation often offset each other around the median, resulting in overall MBE values near zero.

While there was broad variability in model performance across pollutants, some patterns still emerged. For example, our results also showed nearly identical performance for linear regression (LR) and ridge regression (R) across the three pollutants, suggesting that L2 regularization was not beneficial for these datasets. Lasso regression also did not lead to improved predictive performance for linear regression, especially for BTEX and NO₂, where removing features through L1 regularization actually worsened model performance. To better understand the importance of each feature in response to the lasso performance, we plot the feature importances from the ensemble decision tree-based models (RF, GB, and XGB) in Fig. . The feature importances were calculated using the Mean Decrease in Impurity using the Scikit-learn Python module. Based on Fig. , it is clear that the target pollutant sensor features were more important than the temperature, humidity, and time elapsed features across all pollutants. However, given the reduced performance of lasso regression for BTEX and NO₂, it appears that even “less important” features can still play an essential role in model training. The increased importance of TGS 2602 for BTEX compared to TVOC aligns with previous work, which found TGS 2602 to be more sensitive to BTEX than TGS 2600 .

Boosting methods, which are known for their improved ability to handle imbalanced data, reduced the underestimation of peak concentrations for TVOC. However, for BTEX, linear-based models (LR and R) actually outperformed boosting methods and other complex machine learning models for both peak concentrations and overall performance. For NO₂, the linear models performed the worst, especially at baseline concentrations, highlighting that no single model consistently performs best across all colocation datasets. When applied to field data, the models predicted similar mean concentrations for each site but had more variability in baseline and peak concentration predictions. Generally, the variability followed patterns evident in the testing data performance.

We built each calibration model multiple times, with differing test/train splits, to assess the robustness of each model. The performance metrics showed some variability, especially in the 95–100th percentile for BTEX and TVOC, based on the test/train split. This was not surprising, given that the range of concentrations in the 95–100th percentile for the BTEX and TVOC testing data could vary dramatically depending on the test/train split. These results motivate further study into how data should be split into testing and training sets to ensure transferability and robustness. At a minimum, we suggest ensuring that the testing data encompass the full range of concentrations measured during colocation.