Dear authors,

I would like to congratulate you for your work and for completely taking into account the referees' requests. Both referees acknowledge the quality of your manuscript, confirm that the required changes have been made and recommend it for publication.

In their reports, the two referees have also indicated suggestions for very minor corrections, which I would like you to ask to take into account in addition to the remarks that I have listed below. Please check spelling (British vs American) to be consistent throughout the document.

p1 l13 "most relevant" -> "a relevant"

p1 l23 (Crosson 2008). CRDS has been introduced much earlier. Please cite accordingly : O’Keefe and Deacon. “Cavity ring‐down optical spectrometer for absorption measurements using pulsed laser sources.” Rev Sci Instr 59, 2544 (1988).

p2 "recognized" -> "recognised"

p4 l13 "report" - "record"

p4 l18-20 ? description of CRDS principle is misleading. Ring down time is not simply directly proportional to the absorption, but also depends on cavity losses (mirrors). Please rephrase accordingly.

p4 l25 it is not entirely clear what "areal integral" means. An integral corresponds to an area under a curve. Use "integrated absorption" instead.

p5 l12,14 "deionized" -> "deionised"

p6 l 15 "ends to" -> "ends at"

p7 l8 "simultaneously" is misspelled

p10 l24 closing ")" is missing

p11 l6-8. The meaning of the function g is never defined (or only later via Eq 6) and it is called a correction function. But this is likely a misnomer, because g gives the deviation of a measured value from a true value. The correction is only obtained after some algebraic manipulation involving g (see step 6). Please introduce the meaning of g before you use or derive it. For simplification, it would probably make sense to introduce this function as a generalized f_delta(x), namely as f(delta,x) by replacing the parameters a,b,c in eq 4 through their parametric expressions in eq 5.

p11 l13 delta_ref should be called delta or delta_true.

p12 l2 "bootstraping" -> "bootstrapping"

p12 l13 "adressed" -> "addressed"

p12 l14-15 "Note that the fitting functions used here ... While it is possible that physical processes underly the shape ..." Actually, it is hard to imagine other than physical processes that would lead to a deviation, except for artefacts and erroneous data treatment, perhaps. It would therefore probably be better to phrase along the following lines: "Note that the fitting functions used in Eq. (4) and Eq. (5) are purely phenomenological and do not result from a particular physical model. Still, we recommend the proposed parametrization to characterize individual instruments."

p13 l7-8 check singular and plural of subject and verb : "which are" -> "which is", "cluster" -> "clusters"

p14 l20-22 check phrase please. From a grammatical point of view it does not seem to make any sense.

p14 l28 "higher" or "relatively high" instead of "relatively higher"

p16 l2 "O" missing in "H_2^16O"

p16 l12-13 "using wavelength changes rather than cavity length modifications". The actual phrasing is misleading. It seems that keeping the cavity length constant allows to match cavity resonances separated by equidistant frequencies (FSRs). This allows sampling over a well reproducible frequency grid whereas the cavity length changing technique probably adjusts both, the length of the cavity and the laser wavelength to match the maximum of the absorption peak. So there must also be a wavelength change to match the peak of an absorption. It is proposed to replace the above phrase simply by "using a different laser stabilisation scheme" to avoid all ambiguity.

p16 l31 replace both R symbols by ^{18}R

p28 Fig 2e "+-" should be "-", Fig 2a-e check number of significant digits

p31 Fig 5 Explain lower panel in the caption. "O" missing in "H_2^16O". Explain figure legend 0.025 and 0.005 in caption. Does showing the two traces instead of only one of them at the full scale provide additional information ?
Also, the y-label on the upper panel is wrong. The line intensity (cm/molecule) is a constant for each absorption line. It does not make sense to plot it as a continuous function of the wavenumber and it should be the same for the two traces. Anyway, it seems that the figure actually shows an absorption coefficient. This should be indicated on the y axis.

p37 Tables 4+5, check significant figures please

p39 Table caption "ionised"

Dear Authors,

I congratulate you to your paper, which can be published subject to the following technical corrections:

P3 l30: please insert parentheses between equal (=) and times (x) sign for both ratios, 2R and 18R.

P4 l20: please use parantheses around value and uncertainty. Since the pressure unit is non-SI, please give the SI value in parentheses for the Torr reading.

P6 l23: convert to pressure unit within SI (eg 170 hPa).

Fig. 5. y axis label : In accordance with the IUPAC gold book, define absorbance as ln(Io/I) and put the term in parentheses instead of separating by backslash, as the definition of a quantity does not constitute a unit.

Tables 2, 4 and 5: Please report significant figures according to SI and IUPAC recommendations (https://publications.copernicus.org/for_authors/manuscript_preparation.html). While the links on that page may not be specific enough, a more exhaustive source for the reporting of measurement results is the "Guide to the Expression of Uncertainty in Measurement" (https://www.bipm.org/en/publications/guides/gum.html) from which the following paragraph is taken.

7.2.6 The numerical values of the estimate y and its standard uncertainty uc(y) or expanded uncertainty U should not be given with an excessive number of digits. It usually suffices to quote uc(y) and U [as well as the standard uncertainties u(xi) of the input estimates xi] to at most two significant digits, although in some cases it may be necessary to retain additional digits to avoid round-off errors in subsequent calculations.
In reporting final results, it may sometimes be appropriate to round uncertainties up rather than to the nearest digit. For example, uc(y) = 10,47 mΩ might be rounded up to 11 mΩ. However, common sense should prevail and a value such as u(xi) = 28,05 kHz should be rounded down to 28 kHz. Output and input estimates should be rounded to be consistent with their uncertainties; for example, if y = 10,057 62 Ω with uc(y) = 27 mΩ, y should be rounded to 10,058 Ω. Correlation coefficients should be given with three-digit accuracy if their absolute values are near unity.

In Table 2, FARLAB standards are reported accordingly (with uncertainties and values given with the same number of signifcant digits and at most 1 redundant figure). However, deuterium compositions for UI standards are not (with uncertainty having one digit after the decimal point (0.6) as compared to values that have two).

In Tables 4 and 5, you should give -274.95 ± 16.62 as -295 ± 17, -2.60 10^-5 ± 6.23 x 10^-7 as 2.60 x 10^-5 ± 7 x 10^-7, 9511.99 ± 163.45 as 9510 ± 170 etc.