Measuring the

The observational separation of the fossil fuel CO

Therefore, more frequently measured gases, like carbon monoxide (CO), which is typically co-emitted with ffCO

Continuously measured

The basic idea of using

We have collected almost 350 hourly integrated

We further compare the flask-based

We calculate representative

At both stations, CO is continuously measured with a cavity ring-down spectroscopy (CRDS) gas analyzer (for OPE data, see Conil et al., 2019). Furthermore, hourly air samples are collected at both stations with an automated ICOS flask sampler (see Levin et al., 2020); the airflow into the flasks is regulated by mass flow controllers, so that the final air sample in the flasks approximates 1 h average concentrations of ambient air. In Heidelberg, we sampled very different atmospheric situations, i.e., during well-mixed conditions in the afternoon, during the morning and evening rush hours, and at night, with almost 350 flasks during the 2 years period from 2019 to 2020. At OPE, the flask sampler was programmed to fill one flask every third noon between September 2020 and March 2021, so that there are

We construct a continuous

Obviously, MHD is a less representative background station for situations with non-western air masses (e.g., for continental air masses from the east). For this, Maier et al. (2023a) conducted a model study and estimated a background representativeness bias and uncertainty of 0.09

To calculate the

Table 1 shows a compilation of all components of Eq. (2) with short explanations. In general, we used the same procedure as described by Maier et al. (2023a) to estimate the correction terms in Eq. (2). Note that we only use the flask results with a modeled nuclear contamination below 2 ‰, to avoid nuclear corrections whose uncertainty exceeds the typical uncertainty in the

Description of the components in Eq. (2).

We then use the weighted total least-squares algorithm from Wurm (2022) to calculate regression lines to the

To compare the

Map of the European WRF-STILT model domain (framed in blue). The Heidelberg (HEI) and OPE observation sites as well as the Mace Head (MHD) background site are indicated. The red rectangle shows the Rhine Valley domain.

Figure 2 shows the

The slope of this regression yields an average ratio of 8.44

Because of the small daily and seasonal differences in the

In the following, we want to establish the sources of this increased uncertainty. Thus, we assess if it is mainly caused by the measurement and background representativeness uncertainties in the

We also compared our flask

WRF-STILT simulation of the TNO

This comparison with the flask observations highlights two complementary findings. First, the Heidelberg observation site is rarely influenced by events with strong point source contributions larger than 50 % because hardly any of the observed ratio scatters around the red regression line in Fig. 4a and thus shows a point-source-dominated ratio (that lies around 2 ppb ppm

We now want to investigate if the flask observations from a more remote site can be used for estimating a continuous

Again, we want to use this estimated ratio from the collected flasks to calculate, with Eq. (1), an hourly

Finally, Fig. 5b shows the simulated

Vogel et al. (2010) estimated

In Heidelberg, almost 350

Thus, we must emphasize the difficulty involved in estimating reliable ratios for the summer period and even question the meaning of such an approach. If, for example, only the flasks from the three main summer months, June, July, and August, are considered, the correlation between

The comparison of the

At OPE, afternoon

We use the STILT forward runs to assess the representativeness of the collected flask samples for the entire period covered by the

After having shown that the flask pools from both observation sites seem to be quite representative, we investigate how many flasks are needed to determine a robust average ratio to construct the

Results of the bootstrapping experiment. We used an increasing number of random flasks from the Heidelberg (in red) and OPE (in blue) flask pools to deduce an average

Overall, this experiment shows that the number of flasks needed to determine a robust average

Flask-based

At the urban site Heidelberg, the model-based estimations face two issues. First, the model predicts events with pure point source emissions which have very low

Indeed, the emission ratios of the heating sector come along with large uncertainties. In particular, the share of wood combustion has a major impact on the

At the more remote site OPE, the model results show no distinct point source events. This is expected, as the ICOS atmosphere stations are typically located at distances of more than 40 km from large point sources (ICOS RI, 2020). The average simulated

To investigate the potential contribution from non-fossil CO sources, we calculate the linear regression through the flask

Overall, these results show that only observation-based ratios should be used for constructing a continuous

In the present study, we investigated if

At the rural site OPE, about 50 afternoon flasks were collected from September 2020 to March 2021. Compared with Heidelberg, these flasks showed a slightly smaller correlation but still allowed the determination of a (constant) ratio to construct the

Overall, this study highlights a number of challenges and limitations in estimating

Finally, we also compared the flask-based ratios with simulated ratios using the TNO inventory and the STILT transport model. At both sites, there are significant differences between the observed and the modeled ratios, which might be caused by inconsistencies in the TNO emission ratios and deficits in the STILT transport model. Consequently, inventory-based ratios can lead to systematic biases in the

Here, we show why one should use a weighted total least-squares regression to calculate average

For a comparison, we now can calculate the arithmetic mean, the error-weighted mean, and the median of the synthetic error-prone ratios as well as the slope of a weighted total least-squares regression line from Wurm (2022) using the synthetic error-prone

arithmetic mean of the ratios of 9.42

error-weighted mean of the ratios of 8.24

median of the ratios of 8.39

slope of regression line of 8.44

This indicates that only the slope of a regression line, which considers the uncertainty of the

This synthetic-data experiment simulates the situation at an urban site like Heidelberg with a large range of

In Sect. 3.1.2, we wanted to estimate the contribution of the observational uncertainties (i.e., the measurement and background representativeness uncertainty) to the RMSD between the

Scatterplot of the measured

Simulated

The flask results from Heidelberg and OPE as well as the corresponding STILT simulations can be found in Maier et al. (2023b).

FM designed the study with contributions from IL, SH, and MG. SH and SC provided the observations from Heidelberg and OPE, respectively. HDvdG was responsible for the TNO emission inventory. FM evaluated the data and conducted the modeling. FM wrote the manuscript with contributions from all co-authors.

The contact author has declared that none of the authors has any competing interests.

Publisher’s note: Copernicus Publications remains neutral with regard to jurisdictional claims made in the text, published maps, institutional affiliations, or any other geographical representation in this paper. While Copernicus Publications makes every effort to include appropriate place names, the final responsibility lies with the authors.

We thank Julian Della Coletta, Sabine Kühr, Eva Gier, and the staff of the ICOS Central Radiocarbon Laboratory (CRL) for conducting the continuous measurements in Heidelberg and preparing the

This research has been supported by the German Weather Service (DWD), the ICOS Research Infrastructure, and VERIFY (grant no. 776810, European Union's Horizon 2020 framework). The ICOS Central Radiocarbon Laboratory is funded by the German Federal Ministry of Transport and Digital Infrastructure.

This paper was edited by Eliza Harris and reviewed by John Miller and one anonymous referee.