This paper provides a thorough analysis  of water vapour correction and calibration strategies for measurements of delta-13C in CH4 using a Picarro G2201-i CRDS analyser in humid- and dried-air field measurements. The paper is very clearly written and well structured, and comprehensive in its treatment. There are few typos or cases of unclear language. The biases between the two calibration methods (isotopologue- vs delta-based) are clearly documented and assessed. It is clearly suitable for publication in AMT and I recommend publication with only minor technical corrections and clarifications listed below.

General comments:

L118 et seq.      It isn’t clear at this point if the Picarro water corrections on d13CH4 are applied automatically, or replaced by new ones from this work. Are the water-corrected and un-corrected raw data available from the Picarro logs, and if so which have you used to define your own water vapour correction coefficients?

Sections 3.2-3.4 compare calibration strategies and identify systematic CH4-dependent inter-method bias, and discuss the linear and inverse CH4 dependence.  As a comment here, perhaps useful for future work, if the analyser can be calibrated for the delta method with a set of at least 3 reference gases covering a reasonable CH4 range, and  the simple linear delta-based calibration equation (6) is replaced with a 3-parameter equation of the form of Eq 15 in Griffith 2018,

Del13CH4(cal) = alpha*del13CCH4(meas) + (alpha-1)  + beta/CH4 + gamma*CH4  

(alpha ~ 1, gamma ~ 0, see also section 3.4) the concentration dependence is automatically taken into account in the delta calibration.  No spread in del13C values across the reference gases is required.

Technical comments:

L 21       introduce not introduces

L28        Site not stie

L31        In the abstract, better to avoid terms that you have not yet defined, here Dd¹³CH₄. Better here to say “difference in d¹³CH₄ between the calibration methods” and define Dd¹³CH₄ at first use in the main text.

L33        if there is a strong correlation with 1/CH4, do you mean non-linear effects at LOW concentrations, where the 1/CH4 term is largest?

L 150 et seq – This section is unclear - there has been no reference to Ref1 and Ref 3 yet in the text and it is not clear if the calibrations referred to are for CH4 or for isotopic quantities. Firstly, please cross reference Table 1. Further, Ref1 and Ref 3 cover a wide CH4 span but only a narrow del13CH4 span. I assume that this “correction” refers to CH4 not del13CH4. At line 152-153 specify that that ref4 and ref5 have similar CH4 composition

Fig 1      The multiport valve is labelled solenoid valve in one diagram and Valco in the other – is this correct? A solenoid would not normally be an 8-port valve.

L 167     Perhaps, in context, move the sentence “A detailed description of all reference gases is given in Table 1.” up before first reference to ref gases at line 150

Eq 1 and 2 – subscript  on LHS should be true not ture

Eq 1-7   I believe the IUPAC preferred, safest and least ambiguous way to include delta values in equations is to NOT include the factor 1000‰ explicitly. Thus Eq 3 for example would be

del13CH4 = (13r/13rref-1).

If the delta value is say 0.001 it can be referred to in text as d = 0.001 or more commonly d = 1‰. This is the same way % is normally treated. 1000‰ simply says “multiply by 1000 then divide by 1000” .

L218 and/or caption to Table 1, the quantity Rsum (introduced in Griffith 2018) may not de widely recognised. Although Griffith 2018 is widely cited elsewhere (perhaps even repetitively so), it would be useful to cite it directly here for practitioners following the calculations.

L220      It would be helpful to calculate and quote the error in del13C caused by an error in the assumed value of delD and hence Rsum for atmospheric air, to confirm that this is a minor error over reasonable range of values of delD in air.

L240      Just to clarify, please confirm that all measurements were made with the same Picarro G2201 analyser, but several years apart? The correction factors may vary slightly from one instrument to another. This could also be done in section 2.2.

Review of “Evaluation of Calibration Strategies for Accurate δ¹³CH₄ Measurements in Dry and Humid Air” by Li et al., for publication in AMT

General Comments

This manuscript addresses an important and practical problem in atmospheric trace gas measurements: the accurate calibration of methane isotopic composition (δ¹³CH₄) using cavity ring-down spectroscopy under variable conditions. The motivation is clear and relevant: isotopic measurements of CH₄ are a key tool for source attribution, but current calibration strategies can be biased by water vapor interference and instrument drift, particularly in moist air. The authors conduct laboratory and field evaluations of two calibration strategies, a typical delta-based calibration and an isotopologue-specific calibration, and apply empirical humidity corrections to quantify performance differences. While humid air can generally be dried, the study is particularly interesting because it reveals a CH₄-dependent bias in the delta-based calibration.

The study is well structured, with a logically ordered presentation of methods, calibration experiments, and field application. The topic fits the requirements of AMT, as it focuses on methodological improvements in high-precision trace gas analysis. The results, particularly the finding that δ¹³CH₄ can be biased under humid conditions and under varying methane concentrations, can be significant for the community. However, there are several important points that require clarification and justification. Some of these may constitute major issues before the manuscript is ready for publication. These are described below.

Major Comments

• The manuscript does not clearly define how accurately δ¹³CH₄ is intended to be measured and for which scientific purpose. Please clarify the target precision and accuracy (e.g. WMO compatibility goals) and how these relate to the different measurement environments. In particular, requirements may differ substantially between a background site and sites with strong variability and source influence such as Jurong.
• The manuscript lacks a sufficiently detailed description of how the values of the reference gases were obtained. How were their CH₄ concentrations and δ¹³CH₄ values calibrated relative to the working standard linked to INSTAAR? Were the reference gases calibrated using a delta-based or isotopologue-specific approach, and could this choice influence the comparison of calibration strategies later in the manuscript? This point is particularly important to avoid potential circular reasoning when evaluating the performance of the calibration strategies.
• The manuscript does not sufficiently address whether the derived humidity and calibration correction functions are stable over time. Were humidity tests performed only once or repeated multiple times and averaged (as, for example, required in the ICOS ATC MLab initial tests)? Over what time period were the laboratory experiments conducted? A discussion of temporal stability and the need for periodic repetition of these tests is essential for assessing the long-term applicability of the proposed calibration approach.
• Figure 7 shows that the δ¹³CH₄ values have a cross sensitivity to the CH₄ concentration and the H₂O content of the sample, but does not clearly distinguish between the effects of humidity and CH₄ A clear CH₄ dependency in δ¹³CH₄ was already reported in other studies (e.g. Miles et al., 2018 https://doi.org/10.5194/amt-11-1273-2018 and Rella et al., 2015). Additional laboratory tests under dry and wet conditions (e.g. a dilution series with reference gases) are essential to isolate the effects of δ¹³CH₄ dependency on CH₄ and to enable a robust scientific interpretation of the results.

Specific Comments

• L. 107: It is not completely clear whether the same instrument was used for both lab and field measurements, or if different instruments of the same model were employed. Instrument-specific behavior (e.g., detector response, CH₄ dependency and water vapor sensitivity) can affect instrument performance (see Miles et al., 2018). Moreover, even if the same instrument was used for both lab and field measurements, its characteristics may change over time, which could also influence the results. The authors should clarify how many instruments were used and how any instrument-to-instrument variability was assessed.
• L. 118: The description of the internal water correction applied by the instrument is unclear. Please specify what type of correction is implemented by the manufacturer (e.g., linear, quadratic, or higher-order empirical function) and whether this correction is instrument-specific or identical for all analyzers of the same model.
• L. 165: A 5-minute averaging time is relatively short for high-precision isotopic measurements. Please justify this choice with respect to measurement precision and stability, e.g. provide Allan variance analysis and to typical atmospheric variability at the two sites. Previous studies (e.g. Hoheisel et al., 2019) suggest that longer averaging times are often necessary to achieve optimal δ¹³CH₄ precision before drift becomes dominant.
• L. 178: “The calibration and correction methods applied to these datasets are described in Section 2.3.” Section 2.3 describes two different calibration strategies. Which one was used to calibrate the reference gases (δ¹³CH₄) against the working standards linked to INSTAAR?
• Table 1: It is unclear how the reported true vales for ¹²CH₄ and ¹³CH₄ were obtained. Please clarify whether these values were measured directly, derived from total CH₄ and δ¹³CH₄, or taken from assigned reference-gas specifications. Since they are required for isotopologue-specific calibration, their origin should be clearly stated. Furthermore, uncertainties are missing in Table 1.
• Under section 2.3.1, Eq. 1 and Eq. 2: It should be made explicit whether the instrument’s own humidity/water correction (e.g., internal manufacturer algorithms) was applied to the raw data, or whether all corrections are entirely based on the empirical functions developed here. If both corrected and uncorrected raw data exist, indicate which one was used to derive the humidity correction functions and how this choice affects the calibration.
• L. 221-222: “An assumed δD value of -100‰ for atmospheric CH₄ was adopted from Quay et al. (1999).” It is unclear whether this value was applied generally for atmospheric CH₄ or whether the actual δD values of the reference gases used for calibration were known and applied.
• L. 365: The delta-based calibration after water correction is almost identical to the calibration before water correction. However, the isotopologue-specific calibration shows a substantial change. Could you please explain why the delta-based approach is largely insensitive to the applied water correction here? Could this be due to cancellation effects, the amount of water vapor in the target gas or the specific form of the correction function? Could you also provide the water concentration in the humidified target gas?
• L. 415: The statement should be emphasized, as Fig. 7b shows a clearly stronger correlation between CH₄ mole fraction and δ¹³CH₄ than between H₂O and δ¹³CH₄. This could be underlined more explicitly in the text and, if possible, supported by correlation coefficients.
• L. 413-420: The manuscript shows a significant difference between calibration strategies at the humid site, including a clear correlation of Δδ¹³CH₄ with 1/CH₄. The authors correctly note that part of the observed Δδ¹³CH₄-H₂O relationship may arise from covariance between humidity and CH₄ during high-emission episodes at the Jurong site, rather than from a direct spectroscopic effect of water vapor alone. However, it would be useful to further clarify whether the remaining concentration dependence primarily reflects intrinsic CH₄ non-linearity of the instrument (as reported in previous studies), residual spectral interferences (e.g. pressure or temperature effects), or limitations of the empirical correction approach. A clearer separation between true humidity-driven effects and concentration-related dependency would strengthen the interpretation of the field results and their implications for source attribution.
• L. 480: Please clarify whether an offset of 0.29 ‰ is considered “minor” in the context of δ¹³CH₄ measurement goals and typical instrumental uncertainty. A brief justification would help readers assess the practical significance of this bias.
• L. 470-500 (Discussion): The authors should discuss limitations of their calibration approach regarding different instruments. Are the empirical correction functions transferable, or would they require recalibration for each instrument and site?

Technical Corrections/ Suggestions

• In the abstract and early text, avoid introducing symbols before definitions (e.g., Δδ¹³CH₄ should be defined at first mention).
• The symbol for methane isotopologues appears incorrectly spaced/formatted in some places. Ensure that isotopologue labels such as ¹²CH₄ and ¹³CH₄ are formatted consistently throughout (i.e. L. 279 and L. 473). Same with δ¹³C-CH₄ and δ¹³CH₄, please decide for one notation style.
• In 2.1, the manuscript should explicitly state whether all measurements were made with one instrument (Picarro G2201‑i) or if multiple analyzers (same model but different instruments) were used (field vs. lab). A reviewer comment already highlights this as missing.
• L. 28: Correct to “SORPES site”.
• L. 29: Clarify sentence structure: “site, where”.
• L. 135: “¹²CH₄” instead of “²CH₄”.
• L. 144: Complete location information with height a.s.l. also for SORPES site.
• L. 158: “Ref4-Ref5” instead of “Ref5-Ref6”
• L. 162: Update Figure reference to Fig. 1b-c, as no Fig. 1d is available.
• L. 179: Subscripts in Table 1 are not properly formatted (low/high positioning is incorrect).
• L. 182: set “CH3D” to “CH₃D”
• Eq. 1 and Eq.2: I think subscript should be "true” instead of “ture”
• L. 295: Correct “vapor correction” for consistent terminology

Recommendation



Overall, this manuscript makes a meaningful contribution to the further development of calibration strategies for δ¹³CH₄ measurements under variable ambient conditions. With clarifications to the calibration methodology and expanded uncertainty characterization, as well as clearer justification of functional corrections and discussion of temporal stability and transferability, as well as conducting and reporting additional laboratory tests the manuscript would be suitable for publication in AMT. I recommend publication in AMT after major revisions addressing the points outlined above.