Automatic Baseline Correction (ABC) is a CO₂ signal processing feature available as part of the NDIR CO₂ sensors employed in this study. Initially, the sensor manufacturer recommended enabling this function, as it is intended to correct for baseline drift over time. The ABC algorithm is activated when the measured CO₂ baseline falls below the background mixing ratio, typically set by default at 400 ppm. The system periodically assesses whether this condition has been met over a predefined interval, usually 10 d, although this period may vary. If the sensor records CO₂ mixing ratios below 400 ppm for the majority of that interval, the algorithm calculates the deviation and applies an automatic correction to the baseline.

Step correction was required only for the rural AirGradient (AG) LC device. No evidence of step changes was observed in the AG S8 deployed at the urban site, nor was step correction required for the Magic K33 or AirGradient Sunrise devices, both of which had automatic baseline correction (ABC) deactivated (Table 1).

As major step changes occurred infrequently in the LC AirGradient S8 sensors used in this study, they were identified through manual inspection of scatter plots of the co-located measurements. Periods during which the ABC was triggered were identified by examining the co-location data in short batches (approximately 2 weeks) against measurements from the reference instruments. A batch was considered indicative of an ABC trigger when the coefficient of determination (R2) was low (< 0.6) and two distinct clusters were evident in the scatter plot (Fig. 2b). The associated step change was then identified as an abrupt shift in the measured CO₂ mixing ratio (around 11:00 UTC on 13 August, Fig. 2a). For each step change, its position in the time series and magnitude were determined. The magnitude was estimated as the difference between the CO₂ mixing ratio at the occurrence of the step and the subsequent CO₂ measurement. Two corresponding lists were then constructed: the positions of the identified steps (posco2i) and their respective magnitudes (stepco2i).

To illustrate the correction procedure, consider a list of raw CO₂ records. Suppose that step changes are identified at positions posco2i = {100, 121, 335},

with corresponding magnitudes

stepco2i = {10, -13, 8} ppm.

A cumulative offset is calculated to account for the persistence of each step change. The correction is implemented as follows:

A δ CO2 array of length is initialised with zeros.

The resulting δ CO2 time series is subtracted from the raw CO2 measurements to obtain the step-corrected CO₂ mixing ratios. Thus, rather than correcting each step independently, the procedure accounts for the cumulative effect of successive changes in the instrument baseline.

Step changes were observed only to a limited extent and occurred in one device (AirGradient LC-S8) deployed at the rural site. Figure 2 shows an example of the step-correction procedure for this instrument.

Whilst we did not observe baseline drift in our study when the ABC was deactivated, long-term drift is expected to introduce error into the measurements. Users should therefore characterise this drift by detrending the data prior to applying the environmental correction framework presented in this work (Sect. 3.3).

For devices deployed as part of a network, users can correct for baseline drift using the approach described by Müller et al. (2020). This method exploits periods of minimal horizontal CO₂ gradients and a well-mixed boundary layer to derive time-dependent offset corrections relative to the nearest reference CO₂ measurement within the network. In the absence of a reference instrument, a modified version of this approach can be used, whereby an LC NDIR device is deployed away from local emission sources and at an elevated location (> 20 m), with the remaining network devices referenced to this sensor. Any gradual intrinsic drift in the reference LC device can then be corrected by comparing monthly mean CO₂ mixing ratios with hemispheric background CO₂ measurements (from Mauna Loa for the Northern Hemisphere and American Samoa for the Southern Hemisphere) over the corresponding study period (Pétron et al., 2026).

Previous studies have demonstrated that LC used for the measurement of other atmospheric species are influenced by environmental parameters, particularly temperature (Crilley et al., 2018; Di Antonio et al., 2018; Mead et al., 2013; Spinelle et al., 2017). These effects are often attributable to inherent trade-offs between portability and cost on the one hand, and instrument sensitivity and measurement resolution on the other. Another factor that suggests the possible effect of external environmental parameters on the performance of LC under real world application is the fact that they are often calibrated under controlled environmental conditions in the lab. NDIR is a spectroscopic technique, and any external factors that might affect its optics and detectors will impact sensor performance. The extreme temperature diurnal variabilities characteristic of summertime might affect the optics and invariably sensor performance. On an extended timescale, we postulate that pressure could additionally affect the performance of the CO₂ sensor. The provenance of this effect can be related to the fact that the sensors OEM are calibrated at a fixed pressure and report the signal in mixing ratios (parts per million, ppm).

Previous studies have demonstrated that variations in pressure can affect the observed mixing ratios if not adequately accounted for (Müller et al., 2020; Gaynullin et al., 2023). In addition, pressure-induced spectral broadening can affect the accuracy of LC NDIR devices. However, this effect is generally smaller than that associated with pressure-dependent changes in number density. For most applications, correcting for the latter is therefore considered sufficient (Gaynullin et al., 2023).

In the absence of a controlled laboratory experiment similar to that reported by Gaynullin et al. (2023), we leveraged the co-location measurements to derive corrections for the effects of two major environmental factors, pressure and temperature, on the LC NDIR CO₂ measurements. The LC AG-S8 device deployed at the urban site was used to derive the pressure-correction parameters. To minimise the confounding influence of high temperatures on the LC CO₂ response, only measurements from the winter period (15 January–15 February 2025) were used to develop the pressure-correction algorithm.

The ratio of the offset-corrected LC CO₂ measurement to the reference CO₂ measurement was calculated and related to the normalised pressure, P/P0 where P0= 1012 mbar and P uses the hourly pressure data described in Sect. 2.2. The CO₂ offset was determined from the mean difference between a subset of the LC AG-S8 and reference measurements obtained under conditions close to the selected standard conditions (pressure = 1012 ± 2 mbar and temperature = 20 ± 1 °C). For applications where co-located reference measurements are unavailable, an approximate offset may instead be estimated, where a significant factory bias is evident, from the difference between the lowest observed raw LC NDIR CO₂ value and the Northern Hemisphere background CO₂ mixing ratios during the corresponding study period (Pétron et al., 2026).

A linear relationship was observed between the LC-to-reference CO₂ ratio and P/P0, with the regression describing the pressure-dependent correction factor. Figure 3a shows the relationship between the LC / reference CO₂ ratio, P/P0, and ambient temperature. The fitted expression (slope and intercept in Fig. 3a) is analogous to the compensation coefficient described by Gaynullin et al. (2023). The pressure-corrected CO₂ mixing ratios, χCO2reference is therefore defined as 1χCO2reference=χCO2offsetcorrK+offset(atP0) where 2K=1.05⋅PP0-0.08 and offset(atP0) is expected to be zero for an ideal calibrated device, in the case of the device used in this study, offset(atP0)=-0.02-0.031⋅χCO2offsetcorr, with P0= 1012 mbar (Fig. S5 in the Supplement).

The offset (at P0) is obtained by fitting a linear model to the difference between χCO2reference and χCO2offsetcorrK at P=P0= 1012 mbar where K= 0.97 for a range of χCO2offsetcorr spanning low to high mixing ratios. The correction is formulated such that, at the ambient pressure (P=P0), the pressure-corrected LC measurement approaches the reference CO₂ measurement i.e., χCO2Pcorr=χCO2reference. An optimised version of Eqs. (1) and (2) was used to generate the pressure corrected CO₂ mixing ratios as formulated in Eq. (3). 3χCO2Pcorr=11.05⋅PP0-0.08⋅χCO2offsetcorr+-0.02-0.031⋅χCO2offsetcorr

Figure 3b shows the comparison of the input CO₂ and pressure-corrected CO₂. As the temperature remained relatively low (< 10 °C), with limited diurnal variability, pressure was identified as the environmental parameter most strongly associated with the observed the LC / reference CO₂ ratio variability, as indicated by the strong correlation in Fig. 3a. The correction approach yields a compensation expression that depends on both pressure and CO₂ mixing ratios, as it is derived empirically from real-world measurements in which the CO₂ mixing ratio varies with pressure. Applying the pressure correction substantially improved the agreement, with R2 increasing from 0.69 to 0.97 and the RMSE decreasing from 7.3 to 3.6 ppm, Fig. 3b. Analysis of the residual dependence of the uncorrected CO₂ reading with the pressure for the analysis shows the error associated to be approximately 0.5 ppm mbar⁻¹ about five times that reported by Müller et al., 2020.

Two sets of correction parameters were derived for the two variants of the low-cost (LC) AirGradient CO₂ sensor used in this study: the AG-S8 and AG-Sunrise.

For the long-term co-location deployments at the rural and urban sites, measurements from the urban co-location were used to derive a generic temperature correction, which was subsequently applied to the LC AG-S8 devices at both locations. To minimise overfitting whilst adequately representing the two temperature extremes, subsets of the summer (17–24 August 2023) and winter (29 November–6 December 2023) measurements from the urban co-location site were used to derive the temperature correction.

The first step involved calculating the ratio of the pressure-corrected LC CO₂ measurement to the corresponding reference CO₂ measurement and examining its dependence on the absolute sensor temperature (K). Figure 4a–b shows that the relationship between these variables is non-linear. A power-exponential function provided the best representation of the temperature dependence of the CO₂ sensor sensitivity, resulting in the correction described by Eq. (4): 4χCO2PcorrχCO2Tcorr=AS8+BS8⋅CS8sensorT Here, χCO2Pcorr and χCO2Tcorr represent the pressure-corrected and temperature-corrected CO₂ mixing ratios, respectively, and sensorT is the sensor temperature expressed in kelvin. The optimal fit parameters for the LC AG-S8 sensor used in this study were AS8= 0.95, BS8= 4.40 × 10⁻⁵ and CS8= 1.03 (Fig. 4c).

The LC AG-Sunrise nodes used in the network deployment were corrected using the same functional form given in Eq. (4), with parameters derived specifically for this sensor variant. The temperature-correction results for the four nodes during their laboratory co-location (12–20 June 2024) are presented in Fig. S6 and Table S1 in the Supplement. The daytime temperature-dependent biases observed in the LC AG-Sunrise measurements, which were particularly evident between 18 and 20 June 2024 (Fig. S6a), were substantially reduced after accounting for the temperature dependence (Fig. S6b). Across the four nodes, the RMSE decreased from approximately 7.5–12 ppm for the pressure-corrected measurements to 2.7–3.9 ppm following combined pressure and temperature correction (Fig. S6c).

The approximately 10 ppm bias evident during the warmer summer period was largely removed following temperature correction (Fig. 4d). Consequently, the RMSE decreased from 7.3 ppm for the pressure-corrected measurements to 2.2 ppm following combined pressure and temperature correction (Fig. 4e). Based on this analysis, the magnitude of the temperature effect, estimated from the residual difference between the pressure-corrected and pressure-temperature-corrected data, was 0.6 ppm K⁻¹.

An NDIR sensor measures CO₂ mixing ratios by comparing two infrared (IR) signals from the same IR source at two distinct wavelengths (IR-high and IR-low), detected using a dual-bandpass filter after transmission through the air sample within an optical cavity. For CO₂ measurements, the IR-high channel is centred at approximately 3.9–4.0 µm, where CO₂ exhibits negligible absorption (reference band), while the IR-low channel is centred around 4.26 µm, corresponding to a strong CO₂ absorption band. In the presence of CO₂, the IR-low signal is attenuated, resulting in a reduced signal magnitude relative to the IR-high channel.

The presence of water vapour can influence the IR-low channel, as H₂O exhibits weak but non-zero absorption within the 3–5 µm region, potentially leading to an overestimation of CO₂ mixing ratios in NDIR measurements. Under conditions of extremely high relative humidity, condensation may occur on the optical cavity mirrors, causing additional signal attenuation and resulting in spurious CO₂ readings. The effect of RH and water condensation on the performance of NDIR is a well-known phenomenon (Cai et al., 2025; Martin et al., 2017; Pereira and Ramos, 2022; Ren et al., 2025; Wu et al., 2023; Xu et al., 2024). Most LC devices have the CO₂ sensing unit housed in a weatherproof unit and tend to rely on passive sampling to minimise power demand. In the absence of an internal heating system that helps reduce water condensation, in combination with a preference for passive sampling in LC (to reduce power demand), there is an increased likelihood that high RH episodes would affect the CO₂ measurement. Such environmental conditions are more common in rural applications than in urban settings, where average temperatures are relatively higher (Si et al., 2024; Weng et al., 2004). We investigated the effect of RH by deploying the same pair of Magic boxes initially in the urban (December 2022) and subsequently in the rural environment (January 2023).

To assess the potential deployment of LC Airgradient S8 CO₂ monitoring in rural environments, we compared measurements from corrected LC units with those obtained from reference-grade instruments at two locations, as outlined in Sect. 2. Although simple linear scaling produced similar trends to the reference data in both day-of-week diurnal and monthly plots, the LC measurements consistently underestimated CO₂ mixing ratios, particularly during the winter months by approximately 10 and 20 ppm at both urban and rural sites respectively. However, as illustrated in Fig. 10b–d, the LC Airgradient S8 data corrected for pressure and temperature effects from the rural site show very good agreement with the reference measurements, both in terms of absolute values (see statistics in Sect. 3.3) and temporal trends.

Based on the pressure-corrected measurements, the LC AirGradient S8 and AirGradient Sunrise sensors (Sects. 3.2 and 2.4.2) are capable of measuring ambient CO₂ mixing ratios with an accuracy of approximately 5 ppm. This performance suggests that the sensors can reliably resolve changes in CO₂ mixing ratios exceeding 15 ppm, representing an improvement over the 30 ppm resolution reported by Müller et al. (2020). The performance of the LC AirGradient S8 therefore supports its application in both urban and rural environments, including locations where CO₂ mixing ratios may periodically reach substantially higher values than those typically observed in urban environments.

To facilitate a direct comparison with Gaynullin et al. (2023), we also evaluated the performance of our correction method using the mean absolute percentage error (MAPE) for the LC AirGradient S8 deployments. This metric expresses the measurement error relative to the observed CO₂ mixing ratio. The MAPE ranged from 0.86 % for the urban deployment, where CO₂ mixing ratios were approximately 410–550 ppm, to 1.5 % at the rural site, where CO₂ increased from background levels to approximately 1000 ppm. These errors are lower than those reported by Gaynullin et al. (2023) for their one-dimensional compensation method. However, they are higher than the -0.02 % error reported for the two-dimensional compensation method at 800 ppm, while the lower MAPE obtained for our urban deployment (0.86 %) is comparable to the 0.83 % error reported at a CO₂ mixing ratio of 3000 ppm.

A direct statistical comparison with the reference measurements was not performed because the reference instrument was not collocated with any of the sensors within the network (Fig. S7). However, because the reference instrument was deployed within the same land-use environment and at a distance of less than 1 km from each sensor, the slowly varying background CO₂ signal is expected to influence both the LC network and the reference instrument in a similar manner. Deviations from this background signal observed by individual devices can therefore be attributed primarily to local sources and sinks in the immediate vicinity of each measurement location. This rural deployment consequently provides a valuable opportunity to assess the performance of LC devices under rural environmental conditions.

The observed CO₂ mixing ratios were strongly influenced by local emissions associated with crop respiration, particularly during the night, when photosynthesis ceased and the planetary boundary layer was shallower (with above background CO₂ ranging periodically in excess of 200 ppm for a 5 min averaged data). Notably, daytime errors of approximately 15–30 ppm (27–28 August 2024), present in the uncorrected dataset (Fig. 11a and d) were substantially reduced by applying the pressure-temperature correction approach, as demonstrated in the comparison with the reference measurement (Fig. 11b and e). In this case, the correction was primarily driven by temperature, which exhibited marked diurnal variability (Fig. 11c and f), whereas pressure changes over the one-month deployment period were comparatively minor (Fig. 11c). Figure 11e shows that the corrected measurements exhibit a background level comparable to that of the reference data, with intermittent departures from this background. These departures, observed as short-duration enhancements (for example the enhancement of approximately 180 ppm observed at P11 shortly after midnight on 27 August 2024, shown in Fig. 11e), indicate a stronger influence from nearby emission sources (respiration from the crop) at this location compared with other sites within the network.