General comments:

The paper “Six years of continuous carbon isotope composition measurements of methane in Heidelberg (Germany) – a study of source contributions and comparison to emission inventories ” is a detailed analysis of observed methane mole fraction and carbon isotope signature in Heidelberg, supported by elaborated discussion of possible origin of observed methane elevation and comparison with existing inventories. The paper focus on observed trend in methane mole fraction and carbon isotopic signature over 6 years and the title clearly reflect the contents of the paper. Also, an abstract provides a concise and complete summary. Overall presentation is well organised and deliberated, and the used language is fluent and precise, making the paper easy to follow and understand. The paper can be treated as case study of methane long-term observation in the urban area. Overall, the paper address relevant scientific questions within the scope of ACP and presents novel data with its interpretation, which are useful to the atmospheric community. The substantial conclusions are reached, showing the long-term trend and similarities and discrepancies with other atmospheric studies and inventories. The scientific method and assumptions are clearly outlined. The specification of measurement site and used instrument (Allan deviation, long-term reproducibility, accuracy based on comparison with MPI-BGC measurements) is well described. However, there is not too much explanation of used Miller-Tans method, especially there is no information about extracted background and its potential impact for determined δ¹³C signature of methane source. More elaborated description of comparison between Keeling and Miller-Tans would be also useful. Also, giving more details about implementation of Miller-Tans method will make results more traceable and reproductive.

Overall, the paper is well balanced, clear and, containing appropriate references and gives important contribution to atmospheric studies of methane. Some questions and comments should be taken into consideration before publishing.

Specific comments:

The more detailed explication of used Miller-Tans method in this study is missing. What was background used in Miller-Tans method? How the background was chosen and how the choice of background could affect obtained values using Miller-Tans method?

Why KuMF results were included in section 3.6 but not in section 3.5? How monthly δ¹³C-CH₄ signatures from inventories were calculated?

Discussion about discrepancies between measurements and inventories in other cities, including comparison with Heidelberg is worth to add.

Line 30-35 Given range of microbial and thermogenic is narrower than in the literature (e.g. Menoud et al, 2022) and not overlapping as it is observed during source signature studies. Please clarify.

Line 42- 45: It would be also worthy to include and cite paper of Rennick et al 21 (https://doi.org/10.1021/acs.analchem.1c01103) as it is another laser spectrometry method for methane isotopes measurements.

Line 121 Could you add short description (e.g., one sentence) to explain principal of CCGCRV?

Line 146 What is frequency of used Mace Head data? What is the height of the inlet in Mace Head? Why Mace Head was used?

Line 177: Why Allan standard deviation was used as uncertainty instead of standard deviation?

Line 182: What tests was made to compare Keeling and Miller-Tans methods? Also, could you elaborate more about the fact you did not observe differences between Keeling and Miller-Tans method? There are studies showing that the differences are observed using these two different methods.

Line 209: Why the method to extend for another hour, up to 12 hours was chosen? Why 12 hours was chosen as criteria to exclude data?

Line 205-214: The one minute step seems quite small, especially that some pollution peaks can last longer. You mentioned you averaged all values directly adjacent in time. Was it done manually? Is it enough valid method to separate individual pollution event? Would wider step (e.g., few minutes) be more adequate?

Line 235-245: First you say there is no significant trend in the monthly mean δ¹³C isotopic signatures, while later you describe visible differences between signatures for individual months. Please clarify.

Line 262-267: Could choosing the wider step than 1 minute could remove possible artefact of averaging and give more reliable values to determine diurnal cycle?

Line 271: First you said it is not possible to get reliable results on diurnal cycle then in line 271 you say, “This indicates that the composition of CH₄ sources in Heidelberg is the same during day and night”. It seems to be contradictory. Please clarify, also regarding impact of the instrument precision for diurnal measurements.

Line 288: Do the monthly approach and moving Miller-Tans approach represent the same catchment area (both bigger than night-time approach? If yes, this hypothesis does not explain differences in results from monthly and moving Miller Tans approaches. Please comment.

In table 1., δ¹³C-CH₄ for road transport comes from Levin et al. 1993. Is it possible this value changed over last 30 years as different cars are used now and then (e.g. diesel versus petrol, better technology etc)? Is it possible the inventories results are biased comparing to atmospheric results due to unaware shift between used δ¹³C-CH₄ from pervious studies and real values?

Line 295-297: “the nearby CH₄ sources are more often natural gas leaks, wastewater, traffic, or emissions from energy for buildings. These CH₄ emissions are on average less depleted.” – it sounds like wastewater is also less depleted, in the same category as other mentioned sources. Based on Tab 1, it is clear they are more depleted, as other microbial sources.

Line 390: What is the difference between value from Widory et al. (2006) and “publications describing ¹³C for CH₄ emitted by waste incineration in the way we needed them to calculate the mean δ¹³C-CH₄ isotopic source signature” What is the “needed way” and how it is different from method presented in Widory et al. (2006)?

Line 415-420: Repeating annual mean results here brings some confusion. I suggest removing it and focus only on annual cycle in this paragraph.

Technical corrections:

Line 30 and further: δ¹³C-CH₄ should be given in order from smaller to bigger, e.g., (-70 ‰ to -55 ‰) instead of (-55 ‰ to -70 ‰).

Figure 9: Remove too at the end of last sentence

The link to access used data does not work.

In this paper, Hoheisel et Schmidt describe new continuous CH4 and δ(13C,CH4) measurements retrieved between 2014 and 2020 In Heidelberg (Germany). After introducing the experimental setup, they analyze the temporal variability of this data and apply the Miller-Tans method to derive estimates of the mean isotopic signature that could cause these variations. These determined estimates are then compared to bottom-up estimates using two different inventories. 

Overall, the paper is well presented and well written. The structure is clear and it is easy to understand where the authors are leading us. Also, the scientific questions addressed in this study are well within the scope of ACP and the analysis conducted to answer these questions is detailed, elaborate and tackles very interesting points, both for experimentalists and atmospheric modelers. Last but not least, this new continuous data is invaluable to better investigate methane sources and will likely be utilized in the future by the rest of the atmospheric community.

Most of my comments only call for additional clarity in the methodology and the presentation of results. Also, a few additional details in the methodology and in the results would be beneficial both for the reproducibility of the study and the comprehensiveness of the analysis. However, these comments are very minor and I can already recommend this paper for a publication in the journal ACP.

You can find my specific and technical comments in the attached supplement.