Field measurements were carried out at the Toolik wet sedge site (TWE; 68∘37′27.62′′ N, 149∘36′08.10′′ W; 728.14 m elevation, WGS 84 datum) where seasonal eddy covariance flux measurements were carried out during the summer seasons of 2010–2015 and partially during winters starting in 2014 until 15 June 2016, with the continuation as a meteorological station until present. The site is a wetland that is a local source of CH4 with a flux rate that is roughly 1 order of magnitude stronger than adjacent Toolik Lake, where the study was performed. The site is a wet graminoid tundra dominated by sedge species, namely cotton grass (Eriophorum angustifolium) and Carex aquatilis .

Two Figaro TGS 2600 sensors that were already deployed over Toolik Lake (TOL) during the ice-free season in 2011 were installed at the TWE site in late June 2012 (Fig. ). Sensor 1 is the primary sensor used in this study, whereas sensor 2 was only used as a replicate to simplify assessing potential problems with sensor 1. Because no such problems occurred, we will focus only on the results obtained with sensor 1 except in Sect. , where we used both sensors to assess their performance at weekly time resolution. The TGS 2600 is a high-sensitivity solid-state sensor for the detection of air contaminants . It is sensitive to methane at low mole fractions but also to hydrogen, carbon monoxide, isobutane, and ethanol. It is the only low-cost solid-state sensor that we are aware of for which the manufacturer indicates a sensitivity to methane even under ambient (≈2 µmolmol-1) methane mole fractions, whereas most other sensors are only sensitive at mole fractions that exceed ambient levels by at least 1 or 2 orders of magnitude. This high sensitivity to low-methane mole fractions comes at the expense that no specific molecular filter prevents the other components from reaching the sensor surface. Thus, our considerations made here assume that deployment is made in an area like the Arctic, where levels of carbon monoxide, isobutane, ethanol, and hydrogen are rather constant and do not vary as strongly as methane so that the sensor signal can be interpreted as a first approximation of a methane mole fraction signal. For additional details on the TGS 2600 sensor the reader is referred to .

The TWE site receives line power from the Toolik Field Station (TFS) power generator. During the snow- and ice-free summer season (typically late June to mid-August) measurements are almost interruption-free, but during the cold season (typically September to late May) longer power interruptions limit the winter data coverage. Nevertheless, this is the first study that provides low-cost sensor methane mole fraction measurements over a temperature range from Arctic winter temperatures of -41 ∘C to a relatively balmy 27 ∘C during short periods of the Arctic summer. Reference CH4 dry mole fractions were measured by a Fast Methane Analyzer (FMA, Los Gatos Research, Inc., San Jose, CA, USA; years 2012–2016), which was replaced by a Fast Greenhouse Gas Analyzer (FGGA, Los Gatos Research, Inc., San Jose, CA, USA; since 2016) for combined CH4, CO2, and H2O dry mole fraction measurements. Until 18 June 2016 the CH4 mole fractions were calculated as 1 min averages from the raw eddy covariance flux data files. We report all gas mole fractions in micromoles per mole or nanomoles per mole. The FMA and FGGA sampling rate was set to 20 Hz, and the flow rate of sample air was ca. 20 Lmin-1. After the termination of eddy covariance flux measurements, the FGGA measurements were continued with the instrument's internal pump (flow rate ca. 0.65 Lmin-1) with 1 Hz raw data sampling. In addition to digital recording, the CH4 signal was converted to an analog voltage that was recorded on a CR23X data logger (Campbell Scientific Inc., CSI, Logan, UT, USA). The same data logger also recorded air temperature, relative humidity (HMP45AC, CSI), wind speed, and wind direction (034B Windset, MetOne, Grants Pass, OR, USA) as well as ancillary meteorological and soil variables not used in this study. The factory-calibrated HMP45AC sensor head was exchanged for a newly calibrated one ca. every 3 years to minimize long-term drift effects in temperature and relative humidity measurements (James Laundre, personal communication, 2020). Sensors were measured every 5 s, and 1 min averages were stored on the logger. These data were then screened for outliers and instrumental errors and failures, and 30 min averages were calculated for the present analysis.

Both FMA and the later FGGA analyzers were used for eddy covariance applications, and thus the instruments were not calibrated as frequently as is done in applications for the Global Atmosphere Watch network . Both sensors were more accurate than the available calibration CH4 gases at TFS. In 2015 it was possible for the first time to use an NOAA (National Oceanographic and Atmospheric Administration, Boulder, CO, USA) reference gas cylinder (no. CB09837) to fine-tune the FGGA. This was typically done in the early summer season, when field personnel arrived at TFS (late May).

Because the TGS 2600 sensors only show a weak response to CH4 but are highly sensitive to temperature and humidity, a LinPicco A05 Basic sensor (IST Innovative Sensor Technology, Wattwil, Switzerland) was added next to the TGS 2600 (see Fig. ). The A05 is a capacitive humidity module that also has a Pt1000 platinum 1 kΩ thermistor on board to measure ambient temperature. The relative humidity output by the A05 is a linearized voltage in the range of 0–5 V, and the Pt1000 thermistor was measured in three-wire half-bridge mode using an excitation voltage of 4.897 V.

Before analyses the data were processed in the following way: (1) outliers were removed (2) relative humidities greater than 105 % (accuracy of capacitive humidity sensors) were deleted, and (3) reference CH4 mole fractions obtained from the FGGA (since 2016) were filtered based on hard boundaries of housekeeping variables available for quality control. For the latter we used the following hard boundaries for filtering: (a) sample cell pressure had to be in the range of 130–143 Torr and (b) the instrument-specific ringdown time of the laser for CH4 measurements had to be in the range of 13–17 ms. The accepted reference CH4 mole fractions were thus all measured in the narrow range of cell pressures between 139.7 and 140.3 Torr and laser ringdown times between 14.02 and 14.94 ms, which indicates best performance of the analyzer. Before 2016 (FMA instrument) these housekeeping variables were not recorded.

The basic principle of operation of the TGS 2600 sensor was described in detail by . The methane sensing mechanisms of different active materials used in solid-state sensors were described by . The TGS 2600 uses an SnO2 microcrystal surface . Whereas the manufacturer defines the sensor signal as Rs/R0, the ratio of the electrical resistance Rs of the heated sensor material surface normalized over its resistance R0 in the air under absence of CH4, define the sensor signal as the ratio between Rs and Rg, the resistance of the surface in the pure gas of interest (here CH4). In all cases, considerations of technical sensor information are made for high mole fractions of CH4 (e.g., 200 µmolmol-1) for an SnO2 surface according to , not for ambient mole fractions in the typical range of 1.7–4 µmolmol-1 (or less). Hence, some adaptations are always necessary because present-day sensors are not yet designed for such low mole fractions. In order to simplify calculations compared to what we presented in – which closely followed the technical information provided by the manufacturer – we define the sensor signal as Sc=Rs/R0 but with R0 arbitrarily set to the resistance observed when the sensor delivers V0=0.8 V output at Vc=5.0 V supply voltage. The highest voltages measured at TWE were 0.7501 and 0.7683 V from sensors 1 and 2, respectively (which theoretically corresponds to the lowest CH4 mole fractions). With these assumptions the sensor signal Sc can easily be approximated as a function of the inverse of the measured TGS signal voltage Vs, 1Sc=RsR0≈0.952381⋅1Vs-0.1904762. The full derivation is RsR0=Vc⋅RLVs-RLVc⋅RLV0-RL=Vc⋅RL-Vs⋅RLVsVc⋅RL-Vs⋅RLV0==V0Vc-VsRLVsVc-V0RL=V0Vc-VsVsVc-V0==V0Vc-V0VcVs-1=1Vs⋅Vc⋅V0Vc-V0-V0Vc-V0. Here RL is the load resistor over which Vs is measured (see , or , for more details) but which can be eliminated in this algebraic simplification.

To compute absolute humidity, we used the Magnus equation to estimate saturation vapor pressure esat (in hPa) at ambient temperature Ta (in ∘C), esat=6.107×10a⋅Ta/(b+Ta), with coefficients a=7.5 and b=235.0 for Ta≥0 ∘C and a=9.5 and b=265.5 for Ta<0 ∘C.

Actual vapor pressure e (hPa) was then determined as e=esat⋅RH100%, with relative humidity RH in percent and converted to absolute humidity ρv (kgm-3) with ρv=eTa+273.15⋅pp-e⋅100Rv≈0.217⋅eTa+273.15, with p being atmospheric pressure (hPa) and Rv the gas constant for water vapor (461.53 Jkg-1K-1).

Statistical analyses were performed with R version 3.5.2 . Trend analyses were performed for both trend in CH4 mole fraction and drift of TGS 2600 measurements using the Mann–Kendall trend test implemented in the rkt package that is based on . The annual linear trend (or drift) was calculated using the robust Theil–Sen estimator using weekly median values, and the significance of the trend (or drift) was assessed using Kendall's τ parameter. All trend and drift estimates were significant at p<0.05. The highest two-sided p value of the presented results was p=0.000054, and thus no detailed information on p values is given when statistical significance of trends or drift is mentioned in the following.

For assessing the quality of the proposed calculation of CH4 mole fractions from TGS 2600 sensors we inspected weekly aggregated data using four key indicators:

Bias. This is the mean of the difference of each 30 min averaged pair of CH4 mole fractions in micromoles per mole, CH4,TGS – CH4,ref.

Stability. This is the bias expressed as a percent deviation from the reference CH4 mole fraction, (CH4,TGS-CH4,ref)/CH4,ref⋅100%.

Variability. This is the mean relative deviation of the 95 % confidence interval (CI) observed with the TGS 2600 sensor from the corresponding 95 % CI of the CH4 reference measurements (in percent), (CI95%,TGS/CI95%,ref-1)⋅100%.

Correlation of median diel cycles. Pearson's product-moment correlation coefficient between hourly aggregated median diel cycles of CH4 measured by the TGS 2600 and reference instruments.

In addition to conventional linear model fits (least square method) we used an ANN approach. This was performed in Python 3.7.1 using MLPRegressor from sklearn.neural_network version 0.20.2 . We used a network with four hidden layers of sizes 500, 100, 50, and 5, respectively, and an adaptive learning rate. Learning was done with the data obtained during the calibration period 2014–2016, whereas the remaining years 2012–2013 and 2017–2018 were used for validation.

Using Eq. () yields satisfying agreement with 30 min averaged data under both typical low-Arctic summer and winter conditions (Fig. ) with an overall R2 of 0.424 (Table ). When testing the linear model approach (Eq. ) more rigorously by splitting the available data into a calibration period (years 2014–2016) and a validation period (years 2012–2013 and 2017–2018), some limitations can be seen, in particular under cold conditions, where none of the approaches performed very well in the validation period. The ANN had a more balanced performance between the calibration and validation periods, although it performed slightly less well under warm conditions (Ta≥0 ∘C).

A detailed inspection of four representative 7-week time periods at full 30 min resolution is shown in Figs. –. Typical summer conditions at the beginning of this study (Fig. ) and towards the end of the analyzed period (Fig. ) indicate that the short-term agreement (R2=0.653; Fig. ) was better when the TGS sensor was still relatively new than when it was 7 years old (R2=0.381; Fig. ), but the variability decreased (improved) from -42 % to -9 % with no relevant difference in bias and stability (0.01 µmolmol-1 and 0.4 % vs. 0.00 µmolmol-1 and 0.0 %, respectively). In winter the timing of most events is correctly captured (Fig. ) with an R2 of 0.445, but the dynamics are not satisfactorily captured by the TGS sensor, indicated by a 59 % underestimation of the 95 % CI during this midwinter period. The transition from warm to cold season (Fig. ) shows a mixture of days when the regular diel cycle, which is typical for the warm season, is still adequately captured, but the dynamics of periods with an air temperature below 0 ∘C (see Fig. ), when CH4 mole fractions tend to be highest as in winter (Fig. ), are not adequately captured. Still, with an R2 of 0.512 (Fig. ) more than 50 % of the variance observed in the 30 min averaged CH4 reference measurements is captured by the low-cost TGS 2600 sensor.

Because of the absence of local sources of carbon monoxide and other air pollutants to which the TGS 2600 sensor is also sensitive (besides CH4), we investigated a special case when smoke and haze from wildfires south of the Books Range polluted the air in the TFS area on 26 June 2015 and compared the performance of both TGS sensors during that day with conditions 3 d before that event and on the same date in the following 3 years. The net effect of increased air pollutants was an apparent small decrease in the CH4 mole fractions calculated via Eq. () by approximately -0.03 µmolmol-1. At the same time the variability of the residuals increased from typically ±0.014 to ±0.027 µmolmol-1 (24 h averages). Thus, the influence of the wildfire smoke was of the same order of magnitude as the difference between TGS-derived CH4 mole fractions and the reference instrument on most other days of the year (see Figs. –).

The TGS 2600 is not expected to provide short-term accuracy comparable to high-quality instrumentation see also. However, argued that such measurements may still provide additional insights as compared to the passive samplers described by by integrating over longer time frames. Thus, here we inspected the performance of weekly aggregated estimates derived from the TGS 2600 in order to inspect drift of the two sensors and their performance over the 7-year deployment period. Note that in Eq. () we did not include a drift correction. Figure  shows weekly medians of sensor signals, the agreement with the reference signal, and the difference between the CH4 mole fractions obtained from both TGS 2600 sensors mounted at the same position (Fig. ). The two TGS 2600 sensors (1 and 2) showed a trend in their signals of -18.8 and -15.5 mVyr-1, respectively (Fig. a). Thus, with typical signals on the order of 200–700 mV (Fig. a) the lowest (winter) readings may no longer be measurable after 10–13 years of continuous operation, indicating the end of life of a TGS 2600.

Figure  shows the weekly median bias, variability, and the correlation between the weekly aggregated median diel cycle of CH4 at hourly resolution between the TGS 1 measurements and the reference. Despite the trend of the sensor signal shown in Fig. a and b, both the bias and variability primarily show a seasonal pattern with a slightly negative bias (around -0.02 µmolmol-1) during peak growing season and a corresponding positive deviation in midwinter when temperatures can be well below -30 ∘C (Fig. a). The variability (Fig. b) shows the inverse pattern of the bias. If bias is expressed as the relative bias (i.e., stability), the stability vs. variability plot (Fig. ) shows points lying uniformly around the line of a -1:1 relationship (R2=0.67). This indicates that both variability and stability can be improved at the same time because there is no tradeoff visible in Fig. .

All linear trend estimates were statistically significant (see Sect. ). However, our measurements started with warm-season measurements only (2012–2014) that were successively expanded to include cold-season measurements. Thus, all interpretation of the trends and drifts presented here should be considered with caution given the long gaps in data due to the technical challenges of operating such equipment under adverse winter conditions. The CH4 mole fraction trend observed with the high-quality reference measurements was 10.1 nmolmol-1yr-1. This is 2.5 times the trend observed from 2005 to 2011 by NOAA (28.6±0.9 nmolmol-1 or 4.09 nmolmol-1yr-1; Table 2.1 in ) but of the same order of magnitude reported by for 2013 (last year covered by that study) for latitudes north of the Tropic of Cancer. Thus, this trend may be real, and hence all trends seen in low-cost sensor signals are not necessarily solely an artifact of such sensors. However, it remains a challenge to deduce the true trend in CH4 mole fractions over longer time periods using such a low-cost sensor because of drifting signals. Thus, we inspected the drift of the TGS 2600-derived mole fraction with respect to the (true) CH4 trend observed with the high-quality reference instrument. These drifts appear to be smaller than the true trend but are still considerable: the bias of TGS-derived CH4 mole fractions drifted by 4–6 nmolmol-1yr-1 (40 %–60 % of actual trend), and variability drifted by -0.24 % yr-1. They provide encouraging results suggesting that with occasional (infrequent) calibration with a high-quality standard, e.g., using a traveling standard operating during a few good days with adequate coverage of the near-surface diel cycle of CH4, TGS 2600 measurements might be suitable for the monitoring of CH4 mole fractions in other areas as well. As shown in Fig. c the correlation of median diel cycles between TGS estimates and CH4 reference measurements is one of the weak points in the current performance of the TGS 2600 sensors. Furthermore, we observed a significant negative trend of the correlation coefficient of -0.051 yr-1 (Fig. c). However, the key finding is that the typical diel cycle during the warm season (air temperature >0 ∘C) disappears during winter conditions (Figs. , ), and thus separate transfer functions for warm and cold temperatures might be a solution for future studies (Table 1). Our Eq. () is thus intentionally derived from the entire dataset to provide a starting point for more elaborate fine-tuning in projects where this is desired.

found that artificial neural networks (ANNs) outperformed linear models in mitigating curvature and linear trends in trace gas measurements when used with the same set of input variables during a 3-month comparison period. To inspect the potential of ANNs at our Arctic long-term dataset, we added the ANN results to Figs. –. In summer (Figs. , ) we did not find a substantial difference between an ANN and the linear approach of Eq. () in terms of root mean square error (RMSE) or R2 between predicted and measured CH4 mole fractions (Table 1). In winter, with temperatures below freezing, the ANN performed clearly better in the validation than the linear approach, but both approaches remained unsatisfactory (R2<0.1) despite the fact that both approaches were similar in the calibration period (R2≈0.3, Table 1).

During the warm period we found cases where the ANN was much better in capturing a specific daily feature, as for example on 11 July 2012 (Fig. a), when the daily minimum was nicely captured by the ANN, but the linear model was much too low. Contrastingly, in 2017 (Fig. a) periods could be found when the daily dynamics were correctly captured by the ANN but at too low of mixing ratios (e.g., 10–18 July 2017; Fig. a). It should be noted that at this latitude the sun does not set between 24 May and 20 July; thus nocturnal conditions are clearly different from conditions at lower latitudes such as the ones investigated by . Similarly, the transition from warm to cold season (Fig. ) was challenging with both the linear model and ANN approach. We have only used two variables, Ta and humidity, that according to manufacturer specifications influence the TGS 2600 sensor signal. In reality, the same two variables also influence the CH4 production in water-logged ecosystems and thus contribute to the true CH4 signal in addition to the cross-sensitivity, which we try to correct with Eq. ().

An ANN that can separate the effect of ambient variations of CH4 mole fractions from the artifact of cross-sensitivity of the TGS 2600 to Ta and humidity may however outperform a linear model approach in future studies if more potentially important driving variables are included than only those specified by the manufacturer .

The interquartile ranges and 95 % confidence intervals of each air temperature (Fig. a) or absolute humidity bin (Fig. b) are very similar over a wide range of temperatures and humidity levels but tend to become more variable in bins with few data (i.e., lowest and highest temperatures and highest absolute humidities in Fig. ). Deviations are generally constrained within ±0.1 µmolmol-1 or better but with higher variability at both temperature ends, where data coverage is poor (gray bars at bottom of Fig. a) as temperatures below -30 ∘C were not frequently covered due to technical problems with the measurement station and summer temperatures above 20 ∘C are still rather rare at this low-Arctic latitude . A slightly different picture emerges for low absolute humidity: 56 % of measurements are at lower humidities than the saturation humidity at 0 ∘C (0.0049 kgm-3); thus the rather homogenous variances at low humidity (Fig. b) indicate that humidity is not of concern at low temperatures, and future attempts for improvements should rather focus on humidity above 0.01 kgm-3 and temperatures above 20 ∘C that are not normally found in the Arctic.

Based on physical considerations one might expect that specific humidity or water vapor mixing ratio instead of absolute humidity could lead to further improvements because absolute humidity still depends on temperature. However, our tests have not indicated a relevant gain of information or accuracy of prediction, but future work should also try to find a better physical correction model than the purely empirical one used here based on manufacturer information.

Another approach was taken by , who performed an in-depth laboratory calibration of the very similar but less sensitive Figaro TGS 2611-E00 sensor (the manufacturer only specifies a response above 300 µmolmol-1 CH4; ) at different temperatures and levels of relative humidity over a CH4 calibration range starting at ≈2 µmolmol-1 ambient mole fraction up to 10 µmolmol-1 CH4. Despite the effort, the residual mole fractions remained large (range of ca. -1.5 µmolmol-1 to +1.1 µmolmol-1) – too large for the application we present here. Our efforts to calibrate our TGS 2600 sensors in a laboratory climate chamber in a similar way were not satisfactory (Eugster, unpublished), hence our approach presented here to determine the sensor behavior from long-term outdoor measurements under real-world conditions. Contrastingly, are convinced that “to be of use for advanced applications metal-oxide gas sensors need to be carefully prepared and characterized in laboratory environments prior to deployment”. While this is theoretically correct, it remains difficult to carry out laboratory treatments from -41 to 27 ∘C as would be required for our Arctic site. The data we present indicate that it is most likely absolute humidity (or specific humidity or mixing ratio), not relative humidity, that should be used for such calibrations, which in principle should provide the best quality results if the relevant factors are known and can be included in the calibration setup. Ideally, manufacturers should carry out both laboratory tests and field trials and provide the necessary correction functions together with sensors. However, due to the expense and time it takes to carry out long tests, be it in the laboratory or in the field, the present development goes in the direction of collocation studies en route to certification of sensors (Nick Martin, NPL, UK, personal communication, 2020), similar to what we have done in the Arctic.

The TGS 2600 sensor's best performance is in applications where passive samplers would be another option see also. Contrastingly, using the TGS 2600 for short-term measurements (resolution of seconds to minutes) has not yet led to satisfactory results . In our dataset we found that adding wind speed to the empirical linear model slightly improved the model fit during the warm season, but because no reliable continuous winter wind speed measurements were possible at the TWE site we did not include wind speed in our Eq. (). However, this may be a key component for understanding the variability of TGS 2600 measurements when flying an unmanned aerial vehicle (UAV) where turbulent conditions may change within seconds to minutes. To address this additional factor, we used the heat loss model given in Eq. (). However, although this approach is more mechanistic than Eq. (), it was much less able to predict CH4 mole fraction from TGS 2600 measurements than the empirical linear model and ANN approaches (Table 1). But in order to make further progress on improving the transfer function from TGS 2600 signals to defensible CH4 mole fractions it will be essential to increase our understanding of the physical processes that influence such measurements. This is not an easy task since there is substantial proprietary knowledge that the manufacturer has not revealed. Newer, promising developments are underway that work with a mixed-potential sensor using tin-doped indium oxide and platinum electrodes in combination with yttria-stabilized zirconia electrolytes that show a logarithmic signal range of 0–10 mV for the 1–3 µmolmol-1 CH4 range of interest for ambient air studies . The basic principle that the active metal oxide is charged with O2 (or O2-), which then oxidizes CH4, seems to be similar to the SnO2-based TGS 2600; thus there is a good chance that our findings for the TGS 2600 are also useful for assessing the performance of newer solid-state sensors with different active materials.