The Beromünster tall tower (47∘11′23′′ N, 8∘10′32′′ E) is located near the southern border of the Swiss Plateau, the comparatively flat part of Switzerland between the Alps in the south and the Jura Mountains in the northwest, which is characterized by intense agriculture and a high population density. The tower was built in 1937 for medium-wave radio transmission and has a height of 217 m. The site is located on a gentle hill with an elevation of 797 m a.s.l. between the small towns of Sursee (6 km to the southwest) and Beromünster (2 km to the northeast), with an estimated population of 9100 and 4800, respectively (Fig. 1). Further details about the site, the local environment, wind conditions, and the concentration footprint (area of sensitivity to regional sources) are presented in Oney et al. (2015).

Figure 3 shows the raw instrument readings of CO, CO2, and CH4 for the target gas together with the calibrated measurements obtained applying Eq. (1). Apparently, the variability in the raw readings was similar for the three aluminum cylinders used for the HS, LS, and target gas measurements, so that the target values were rather stable after span calibration. However, this might give a false impression of accuracy because the variations in the raw values of HS and LS concentrations are driven by instrumental biases and temperature changes as discussed below. Instrumental biases associated with long-term instrumental drifts shall be easily accounted for by applying a simple span calibration. However, the span-calibrated working gas measurements shown in Fig. 4 clearly depict that, despite this calibration procedure, a strong variability is still present in the measured mixing ratios. While CH4 measurements of the WG are stable after span calibration, CO and CO2 measurements show significant variation with time. Hence, the standard approach of using WG measurements to correct for instrumental drifts in between the span calibrations (see Sect. 2.2.4) may be problematic and require an additional correction. As shown in the bottom panel of Fig. 4, despite the stable analyzer's cavity temperature during the measurement period, the Picarro data acquisition system (DAS) box temperature (the nominal instrument-temperature measured within the analyzer) fluctuated significantly between 30 and 60 ∘C, due to a combination of diurnal and seasonal variability of the outside air temperature (as the measurement system is not kept in an air-conditioned room), and heat produced by the Picarro instrument and its peripherals. As mentioned in Sect. 2.2.4, a problem with the fan of the Picarro CPU in October 2013 might have led to additional warming of the analyzer around this period. Even after span calibration, the WG measurements of CO and CO2 closely trace the DAS temperature variations, suggesting a strong temperature effect. This strong correlation between the measured mixing ratios and the DAS temperature is further illustrated in Fig. 5. This is most likely associated with a temperature-dependent adsorption–desorption effect which was found to be stronger for steel cylinders (i.e., WG) than for aluminum cylinders (target gas) (Leuenberger et al., 2014). According to their study, approximately 10 times more CO2 may be desorbed from steel cylinders than from aluminum cylinders, and a strong linear temperature dependence was observed for steel cylinders (0.0014 to 0.0184 ppm ∘C-1), while aluminum cylinders showed only a weak sensitivity (-0.0002 to -0.0003 ppm ∘C-1). In addition to the abovementioned temperature effect, drifts or shifts in the instrument's sensitivity were also observed, which can be seen from the layered structure of the raw WG measurements of CH4 (Fig. 5, left panel). As a consequence of the strong temperature effect present in the steel cylinder used for the WG measurements, and of the instrumental biases, a simple drift correction using the WG measurements (as described in Sect. 2.2.4) could not be applied, so a different approach had to be introduced. In addition, correction for the temperature effect present in aluminum cylinders needed to be applied.

This new approach is based on a multiple linear regression model correcting for temperature effects and instrumental biases. For each of the four different standards (HS, LS, T, and WG) a separate regression model was estimated since it is assumed that the temperature effect is dependent on the specific calibration gas cylinder (Leuenberger et al., 2014). The instrument bias term accounts for all the systematic variations in the raw readings not related with temperature; it is estimated based on the WG measurement of CH4 (CH4,WG) since it is expected to be insensitive to the temperature-driven adsorption–desorption effect (Leuenberger et al., 2014). This regression model can be expressed mathematically as χmeasi=χ‾+ai⋅T+bi⋅CH4,WG+ε, where χmeasi and χ‾ denote the raw and the mean of the raw dry mole fractions of the measured species (CO, CO2, and CH4), respectively, and i corresponds to any one of the measured gas cylinders, i.e., WG, T, HS, and LS. The ε term in this equation describes the residuals of the fit. Equation (3) can also be rewritten as deviations from a mean value as χmeasi′≈ai⋅T′+bi⋅CH4,WG′, where the prime denotes the deviation from the mean (e.g., χmeasi′=χmeasi-χ‾).

The derived slopes ai and bi in Eq. (4) as well as r2 values are provided in Table S1 of the Supplement. The model can explain most of the variations observed around the mean mixing ratio measurements; however, only a small fraction of the variance in the CO measurements in HS and LS is explained by the model, expressed by very low r2 values. This is most probably associated with the less frequent HS and LS measurements (i.e., once a week) in contrast to WG and target gas.

The corrected mixing ratios were calculated as the difference between measured raw mixing ratios (χmeasi) and the fitted offset values (χmeasi′) of each cylinder (Eq. 4), which can be written as χcorri=χmeasi-χmeasi′. Then, the corrected CO, CO2, and CH4 mixing ratios were calibrated using the corrected HS and LS calibration values.

Figure 6 shows the time series of CO, CO2, and CH4 mixing ratios of the target gas after the multiple regression correction and span calibration procedures mentioned above. The variability in the target gas measurements are reduced when compared to simple span-calibrated mixing ratio measurements, which can also be seen from the calculated precisions in Table 2.

In the case of ambient air measurements, temperature fluctuations may still have an effect on the measured mixing ratios through adsorption–desorption on the gas manifold system which is made of stainless steel or fractionations induced by splitting of high-pressure sample flow into two pathways (Manning et al., 1999). However, the contributions from these effects are significantly lower when compared to deviations from the mean mixing ratio measurements of the ambient air which are strongly dominated by natural variability. Hence, a multiple linear regression fit using Eqs. (4)–(5) could not be applied. Instead, we have used the fitted values (χmeasi′) obtained from the target gas measurement to correct for these possible effects. The choice of the target gas for correcting ambient air measurements is twofold: (i) it accounts for the adsorption–desorption effect in the gas manifold unit, and (ii) the adsorption–desorption effect is minimal as it is an aluminum cylinder in contrast to the WG, which may introduce larger errors in the ambient air measurements due to the stronger temperature effect (mainly for CO and CO2).

In order to verify if the multiple linear regression correction and calibration for CO, CO2, and CH4 had a significant effect on the target gas and ambient air measurements, we have calculated the differences between the calibrated values based on the new approach and the values obtained by a simple span calibration approach. Figure 7 shows the absolute difference in the measured mixing ratios of the target gas obtained from these two approaches as well as the analyzer's DAS temperature. A minor difference was observed between the CO2 and CH4 mixing ratios, and most of the differences are within the WMO measurement compatibility target, shown by the grey shaded region. However, a considerable difference was observed in CO mixing ratios, probably associated with a stronger temperature effect in CO than CO2 and CH4. The figure further illustrates that these instances of larger differences (outside the WMO compatibility target values) mostly coincide with periods of higher DAS temperature records (usually greater than 45 ∘C) such as July till August 2013 and June 2014. However, these differences are relatively small when compared to the variations in the CO, CO2, and CH4 mixing ratios of ambient air, implying only a minor influence on the ambient air measurements by following either of the two approaches.

Table 2 summarizes the long-term reproducibility of the target gas measurements during the entire measurement period. The calculated precisions for CO2 and CH4 are within the WMO compatibility target for greenhouse gas measurements. However, the precision calculated for CO was slightly outside this target, which might be associated with the temperature effect discussed in Sect. 3.1, but it is certainly also due to the lower precision of the CO measurement.

The accuracy for the target gas measurements determined using Eq. (2) and the multiple linear regression correction and calibration on the raw measurements is dominated by the measurement precision.

Figure 8 shows the measured mixing ratios of CO, CO2, and CH4 for the ambient air at the 12.5, 71.5, and 212.5 m height levels. The lowest CO mixing ratios were recorded during summer, associated with the seasonality of the OH radical, which is the major scavenger of CO in the troposphere (Logan et al., 1981), and the seasonality of atmospheric transport and mixing. Elevated levels of CO reaching up to 600 ppb were recorded from winter to early spring (mainly January to April) due to low OH levels; enhanced anthropogenic emissions, e.g., from residential heating with fossil fuels and biofuels; and reduced vertical mixing leading to accumulation of air pollutants in the planetary boundary layer.

The CO2 time series shows a seasonal cycle with maximum mixing ratios in wintertime, and a minimum in summertime. In contrast to CO, the summertime minimum of CO2 is mainly caused by uptake by plants for photosynthesis. The highest CO2 mole fractions (∼ 460 ppm) were observed in winter, and the lowest (∼ 380 ppm) in summer.

In contrast to CO and CO2, CH4 showed almost no seasonal trend, but events of high methane peaks occurred in all seasons, which might be associated with local emissions from agriculture and ruminants.

Based on Fig. 8, it is difficult to discern a gradient of these species with height. For all species, especially CO2 and CH4, a stronger variability can be observed in the measurements at 12.5 m compared to higher levels, which is likely associated with the influence of local sources and sinks at the surface.

Figure 9 shows the monthly mean diurnal cycles of the CO, CO2, and CH4 mixing ratios at Beromünster in June 2013. The x axis represents time of the day between 00:00 and 24:00 GMT, where midnight corresponds to 23:00 LT. Each data point represents an hourly average mixing ratio where the highest and lowest 5 % of the data were trimmed to minimize the influence of extreme values. CO mixing ratios exhibit only a weak diurnal trend with two peaks in the morning and evening hours around 9:00 and 18:00 GMT, respectively, possibly associated with regional accumulation of CO emissions from traffic. Note that, in the vicinity of the tower, traffic is very low. A distinct vertical gradient is present in CO mixing ratios among the three height levels, with higher mixing ratios at the lowest level throughout the day. This is associated with local to regional ground-based sources and hence higher CO mixing ratios close to the ground, which is subsequently vertically mixed to higher levels. The vertical gradient is reduced to only a few parts per billion during the day (mainly in the early afternoon) due to strong vertical mixing. The time lag of about an hour between the morning peaks at the highest and lowest level is a result of the evolution of the planetary boundary layer in the morning and the time required for locally emitted CO to reach the highest level.

In the case of CO2, clear distinctions exist between daytime and nighttime mixing ratios as well as among the three heights due to the combined effects of photosynthesis, respiration, and vertical mixing. During nighttime, CO2 mixing ratios accumulate near the ground level due to plant respiration and probably due to anthropogenic emissions. Vertical mixing is weak, driven by radiative cooling of the surface favoring the formation of a stable boundary layer, and correspondingly a strong gradient at the three height levels. However, the highest level is not completely disconnected from the nocturnal boundary layer, which can be seen from the increase in CO2 mixing ratios at 212 m during nighttime. As soon as the sun rises in the morning, the stratified nighttime boundary layer starts dissipating, and the CO2 mixing ratios begin to decrease with the onset of photosynthesis by plants. Between noon and late afternoon, the distinct vertical gradients from the previous night completely disappear due to strong surface warming and convective mixing, with nearly the same CO2 mixing ratio at all levels, though with slightly lower values near the surface due to proximity to the vegetation sink.

The CH4 mixing ratios showed a pattern in between those of CO and CO2. Similar to CO2, they showed an increasing trend during the night from its daytime minimum, reaching its maximum early in the morning. At the lowest level, this maximum occurs about 3 h earlier than the maximum of CO, suggesting that CH4 sources are closer to the tower than those of CO. During the day, a sharp decrease from this maximum CH4 mixing ratio takes place due to the effect of vertical mixing.

In this section we provide a short update about an air-conditioning system (AC hereafter) that was recently (on 18 May 2015) installed at the measurement cabin in order to investigate the improvements on the quality of the calibration gas measurements. Since then, better stability of the measurement cabin and the instruments DAS temperature (between 39 and 46 ∘C) has been achieved, instead of the 30 to 60 ∘C range recorded before installation of the AC system.

When comparing the simple span-calibrated target gas measurements after installation of the AC with the measurements from the previous period calibrated with the multiple regression approach, no significant improvement was observed in the target gas measurements. This is due to the very low sensitivity of the aluminum cylinders to the temperature-dependent adsorption–desorption effects. However, the steel cylinder working gas showed less improvement in the CO measurement precision after installation of the AC when compared to the previous period. The CO2 mixing ratios of the working gas were also already stable with the simple span calibration, which was not the case before installing the AC system. Additionally, the correlation coefficients for the multiple regression model of the working gas became lower after installation of the AC system, implying a reduced temperature effect on the working gas as well. In general, after installation of the AC system, applying a multiple regression approach has no significant effect on the calibration results of the aluminum cylinder calibration gases since it is unable to explain the observed offsets in terms of instrumental drift and temperature instability.