General comments

This study focuses on a practical subject needed to quantify the overall accuracy of CO2/H2O measurements from open-path eddy-covariance (OPEC) systems. While I am analyzing my data, I always concern the overall accuracy in CO2 measurements from my infrared gas analyzers in OPEC systems, but the method how to estimate the overall accuracy were unavailable from published literature. Indeed, this manuscript along with Zhou et al (2021) is the completion of systematic study on the overall accuracy of CO₂/H₂O measurements from EC systems.

The OPEC is more popular than CPEC because of, for example, their lower power consumption and maintain demanding, in the flux community. What is estimable is that the authors showed the accuracies of CO₂/H₂O densities based on biologically meaningful data in the field and solid physical principles. Clearly, this study provided valuable results for scientists like me to reference. The analysis methodology based on atmospheric physics and ecosystem background is truly innovative and the equation development is logical in theory and practical in applications. Although the authors only used an old version of OPEC, equations (14) and (22) were easily used to calculate the accuracies of CO₂/H₂O densities for other types of open-path analyzers, e.g., IRGASON and LI-COR 7500 series; and having potentials in applications to analyzers for other gas species like CH₄ and N₂O in the areas of geosciences. Additionally, the structure was well organized and the writing was also easily to understand. Therefore, I would highly recommend this manuscript to be accepted for publication on Geoscientific Instrumentation, Methods and Data Systems after a minor revision.

Major comments

1. I have two open-path analyzers, i.e., EC150 and LI-COR 7500. In practice, when I perform a zero calibration, I always found a positive zero drift about 10 μmol mol^-1 for LI-COR 7500 at ambient temperature, slightly higher in the unit of mg CO₂ m^-3 and much higher than the upper of the values in the manuscript, but a much smaller accuracy due to gain drift when tubing the CO₂ span gas of 500-μmol mol^-1 after a zeroing operation. I speculate that this was caused a non-negligible housing CO₂/H₂O accumulation, although the chemicals in the internal cell needs no replacement of new ones, i.e., after a zero calibration the analyzer works well for months. This is the same for H₂O density. Therefore, in practice, I recommend the author give a short discussion of the possibility of field drift of zero and gain using the big data of analyzer-supplier, for example, that from EC150 in the lab of CSI, in the 6.3 section. These data may be helpful for providing suggestions for new users.

Minor comments

1. Title: “CO₂−H₂O” (and in the text). I understand the authors wanted to identify both gas types using “−” from one of the two gas types using “/”. In my opinion, however, “CO₂/H₂O” may be better, just the same as they are in the profile system. The same for other parts of the manuscript.
2. L24: For a background concentration of atmospheric CO₂?
3. L27-29: I recommend deleting “Under freezing conditions, an H₂O span is both impractical and unnecessary, but the zero procedure becomes imperative to minimize H₂O measurement uncertainty.”, because there was some overlap of this sentence with the next one “In cold/dry conditions, the zero procedure for H₂O, along with CO₂, is an operational and efficient option to ensure and improve H₂O accuracy”.
4. L36: delete “fluctuations”, for consistency with “3-D wind and sonic temperature”.
5. L75: “CO₂/H₂O molar mixing ratio” or “CO₂/H₂O dry molar fraction” is better.
6. L108: “in practice”?
7. L170: Possibly, use “the analyzer often gradually reports that this zero ρCO₂ value, when exposed to a zero gas, is different from zero”.
8. 8. L190: housing CO2/H2O accumulation.
9. L209: housing CO2/H2O accumulation.
10. L224: remove “calibration/”, “span” is clear enough.
11. L233-234: “that is smaller in magnitude by at least two orders” may be more concise.
12. L283: “microbial respiration” is more commonly used.
13. Figure 2: For simplicity, I recommend using only absolute value of accuracy and relative accuracy.
14. Table 2: These numbers are very detailed, and thus are somewhat a repeat of Figures 2 and 3. I recommend only show the temperature points in a coarse resolution, for example, -30, -20, -10, 0, 10, 20, 30, 40, 50 °C.

- General comments:

The manuscript is innovative in trying to quantify the overall uncertainties in the measurements of CO2 and H2O amounts by Open Path Eddy Covariance (OPEC) gas analysers due to their different sources. The aim is pursued by means of a Campbell Scientific IRGASON, and then generalised. A simple model is developed to combine the different sources of errors, and the resulting uncertainties are plotted under different conditions of temperature and gas concentrations. In addition, some applications of the results are reported, together with some suggestions for the users during field calibration. This preprint follows the same approach of a paper published last year by the same main Author relative to the Closed Path Eddy Covariance (CPEC) sensors.

The study has some points of strength and some points of weakness. Among the strenghts it is the fact that the study addresses relevant scientific questions within the scope of GI, using in part novel ideas, and using a proper language. One of the more important strenghts is that it uses the specs of the sensor to define its uncertainties, and it defines the uncertainty in terms of range: the worst case scenario is depicted for each source of error as the limits of the range, and then combined with the others. This is a valid approach to visualising the uncertainty in a straightforward way.

The more important weaknesses are in my opinion: #1. the poor link with the eddy covariance method, despite this is mentioned since the beginning; #2. the generalisation from the IRGASON/EC150 to all the Open Path sensors is not robust enough; #3. Applications and calibration suggestions are only partly relevant; #4. more references are needed, as the most cited are not peer-reviewed papers but sensors manual; #5. the discussion section is more dedicated to other things (recap of what done, applications), but the real discussion is limited; #6. conclusions should be strenghten as well

I'll recall these points in the comments below when relevant

- Specific comments

Suggestion to fix the above:

->1. The EC method includes a very long chain of steps from field measurements to calculation of the fluxes. In this chain, the specs of the sensor are in general considered less important in terms of final uncertainties. Also, the uncertainty are more relevant to the EC method in terms of fluxes (as the result of covariance between sonic and IRGA signals), not concentrations: this is clearly out of the scope of the manuscript, but should be mentioned and maybe discussed a bit. Also, an OPEC system is made of two main sensors: the IRGA and the sonic. But the latter is almost not considered in the study: this could be reconsidered, or at least the reasons for excluding this sensor should be given. A possible alternative could be to reconsider the link with EC: is that really needed? The study may focus on the Open path IRGA (so the EC150, not the IRGASON), just mentioning that it is often used for eddy covariance measurements, but clearly state since the beginning that the study will not focus on EC. (please note this will clearly impact the title as well)

->2. it should be shown that the specs used are all necessary and sufficient, and provide guidance to the reader in case some of them are missing on a different sensor specs (better if also considering additional specs that may be found). In some occasions the authors refer to "OPEC systems" while dealing with the specs of the IRGASON - which may be not the case

->3. the suggestion of calibrating on an "average" temperature (Ta) to basically avoid to be in the worst case scenario (Ta and Tc at the extremes) is not robust as this is what normally happens, also because the range of Ta between two calibrations can be very large. In addition, it is based on the assumption of linear relationship between the difference Ta-Tc and the drift magnitude, which derives from a simplification not so deeply documented. Also the applications proposed are not very impactful: if the EC method is kept (see #1) many more interesting applications could be thought of (but again, probably out of the scope). Even without that, I would use this idea of "applications" to improve the point above: the first and more relevant application should be "how to calcuate the uncertainty for a generic IRGA"

->4. I think the paper from Fratini et al. 2014 (Fratini, G., McDermitt, D. K., and Papale, D.: Eddy-covariance flux errors due to biases in gas concentration measurements: origins, quantification and correction, Biogeosciences, 11, 1037–1051, https://doi.org/10.5194/bg-11-1037-2014, 2014) should definitely be included in the discussion, as it develops a correction of EC fluxes based on the drift of the IRGA as measured during field calibrations. It is different from what presented in this preprint, strongly bounded to the EC method; however it cannot be omitted in a paper dealing with the drift of the IRGA. Some publications on the theory beyond the IRGA working principles, from which the working equations presented are derived, should also be included, in addition (and in support) to the ones in the LICOR manual (not peer-reviewed). Also, publications dealing with uncertainties in EC method should be present, if the link with EC (#1) is maintened

->5. if some more applications are described, I would opt for a separate section of the paper, and for enriching the discussion section with discussion, citing different papers and going more details on what the results suggest. 

->6. with the improvements above, the conclusion section will become more robust

abstract

13-14: as the IRGAs can be used for several scopes, if the link with the EC is maintained it is preferrable to mention "fluxes" (#1)

14: As the focus of the manuscript seems to be only the IRGA, and not the sonic, this should be clearly stated (#1)

20-22: please specify that it refers to IRGASON/EC150 only: it seems to be a generic statement for OPEC systems (#2)

introduction

38-39: If the link with EC is maintained, It may be relevant in my opinion to mention that the exactness of EC measurements depends also on this, but not only. There is a long way to get to the fluxes after the field measurements, and each step sources uncertainty. This should be mentioned in my opinion, also referencing the papers dealing with other sources of uncertainties. (#1)

55-56: this is likely the case. However several publications exist trying to quantifying the uncertainties of EC measurements: this should be mentioned and the difference between this study discussed (here we are dealing with the exacteness of the measurements of the IRGA only, there they are considering the EC flux. In some works the instrumentation uncertainty is included in the overall uncertainty). (#4)

specification implications

91 (tab1): if you want to make it more general, you should specify whether or not this list is sufficient and necessary: what if a different sensor is missing some info? And what if there are more sources of uncertainties listed for a sensor? This should be reported (here and/or in Appendix A) (#2)

Accuracy of CO2 density measurements

148 (eq 5): while I think this equation is general, as it is proposed in a sensor's manual (i.e. not peer-reviewed) in my opinion it is not very robust to include it in a scientific paper without an indepth analysis. As sources are present in LICOR's manual, I would prefer to see it derived from there. Otherwise, in addition to not being scientifically robust, this may also be felt as ambigous in terms of at which sensors can be generalised: its applicability at sensors other than the one the manual is referring to should be shown (IRGASON and beyond). In alternative, if some other publications exist that already "validated" LICOR's equation, they could be referenced here. Then, the parameters in the equation can guide the reader in understanding its applicability, e.g. all the IRGAs using a 5th order polynomial for CO2, etc. (#2, #4)

CO2 zero drift uncertainty

173: ref needed. Indeed, other reasons for the drifts are: dirt contamination, ageing of the IRGA's components, errors in pressure correction (absorptances are normalised to P), and errors in field calibration. If only Ta has to be considered, all of the other sources should be assumed to be zero - which should be at least mentioned. See also Fratini et al. 2014 (#4)

195: For EC150, not for OPEC in general (#2)

203-204: these values are again for the EC150 only. (#2) please also note that "rh" may be misunderstood for relative humidity

CO2 gain drift uncertainty

211: again, if it has to be generic, sentences from LICOR manuals shouldn't be used alone, as 1. they are not peer-reviewed and 2. things could be different for different models (#2, #4)

Evaluation of ΔρCO2

271: Again, it should be noted that these specs, and then the results below, are relative to the EC150, including the operational range: are you sure you can generalise to all the OPEC systems? (e.g. LICOR LI7500DS has a range of -25 to 50°C) (#2)

Δρ H Oz2 (H2O zero drift uncertainty) and Δρ H Og2 (H2O gain drift uncertainty)

323: see the comments in section 4, in particular at line 148 (#2, #4)

335: I think an important point should be taken into consideration here: Tc must be significantly lower than Ta at the moment of field calibration for H2O span to avoid condensation (3-5°C, as reported in the LICOR manual) (#3)

sensitivity-to-CO2 uncertainty

347-348: I understand the logic behind this, however some evidence should be provided that this is the case, against the case, for example, that the lowest cross sensitivity to CO2 unc. is with CO2-free air - or viceversa in the CO2 case, that the lowest cross sensitivity to H2O is with dry air and not with a "stardard" water vapour concentration (somehow related to #4, and to #5 as it could be matter of discussion)

H2O measurement accuracy

360: here could be a good candidate to mention the generalisation point (#2)

ρH2O range

367: please consider rephrasing: this is a plausibility range, and the calibration range of both EC150 and LI7500. It is likely the same for most analysers, but again I think it can't be generalised in absolute terms. (#2)

Discussion

393: in general this section is often more a (even useful) recap of what has been done and an application study (also useful) than a discussion of what done, also against other studies (#5)

Accuracy model

407: here it is a good candidate to discuss the fact that any other uncertainties are lacking in the model (#2)

Formulation of uncertainty terms in Model (2) for accuracy equations

424-426: this is quite a critical point: I agree that such a relationship is not modeled yet, and that considering the maximum range is what the users may want and understand; however, I think assuming a linear scaling of the uncertainty and including it in the computation is a bit risky. At least, how far from the actual uncertainty is that one? Some more discussion needed, also checking Fratini et al. 2014 (#5, #4)

Use of relative accuracy for infrared analyzer specifications

439: applications should probably go in a dedicated section. However, the first two suggested applications of relative accuracy is just a way to define sensors' specs, then in my opinion they should be just mentioned, not reported in such details. (#3, #5)

Application of H2O accuracy in data use

473: As you are considering eddy covariance applications, mentioning only Ta is a bit reductive in my opinion (no user will buy the IRGASON to calculate Ta...). Also, Ta is more related to sonic temperature Ts, and here you are only considering the IRGA uncertainties, not the sonic ones: deltaTs is reported in the sensor's specs, right, as it is deltaCO2 and deltaH2O. Ts is probably less sensitive (e.g. not cross-sensitivity present), but still can drift with temperature for example (see for example Mauder et al. 2007 https://doi.org/10.1007/s10546-006-9139-4). (#1, #3)

Application of accuracy equations in analyzer field maintenance

490-491: this is correct and probably the most relevant part of this section. However, this is strongly related to the drift uncertainty that is rescalded to the difference Tc-Ta, and this is said above to be not exact (@425), and is also based on the assumptions that only the Ta dependency impacts the drits. As no other demonstrations are given, this is also not very robust in my understanding (#5)

500-502: this is also a good place to discuss Fratini paper, which is based on field calibration data (#4, #5)

CO2 zero and span procedures

512-513: it is also true that the widest possible range would apply only if calibrating in extreme conditions far from the daily avarage (#3, #5)

H2O zero and span procedures

524: see comment at line 335: the span procedure with a dew point generator MUST be performed at a much lower temperature than ambient to avoid condensation in the tubes and a bad calibration. This should be mentioned (also, does it worth it to "risk" to perform a bad calibration for correcting this? This is probably out of topic for the manuscript, but a short note could be beneficial to the reader). This risk is also reported in the LICOR manual (a note on "Checking the span" section) (#3, #5)

H2O zero procedure in cold and/or dry environments

568: again, the worst case scenario is also less likely... (#3, #5)

571-572: ref. needed (#4, #5)

conclusions

577: some of the comments above clearly applies to this section as well (all the points)

617-618: this suggestion is mostly for sensors producers (#3, #6)

- technical corrections

abstract

25: "narrow the accuracy" is improving it? Please consider rephrasing

introduction

48-49: such an example at the beginning of the intro is misplaced in my opinion. Also, Ts accuracy is not under discussion. I would keep it for later

64: also CPEC

72: to be more clear: density measurements. It is probably worth it to state that in the manuscript CO2/H2O measurements alway refer to density, not flux (as EC techinque estimates CO2/H2O fluxes)

83: a (typo)

specification implications

88: amount

Accuracy model

128: this is matematically shown in Appendix A: please clearly refer to it (not only later)

133-134: not clear: please consider rephrasing

Accuracy of CO2 density measurements

143 (eq 4): under the assumption that the errors are normally distributed? Please also specify that sigmaCO2 is the std. dev of...

166: please consider expliciting here which parameters of eq. 5 are defined at the factory, and which ones can be corrected by field (or lab) calibration, even if reported in details later. 

CO2 zero drift uncertainty

168: is that part of the experiment? not very clear how it relates to the rest

170-171: bad wording

180-182: I feel it as a "manual-like" text. I suggest avoiding expressions like "must be simple", "indeed", and be more descriptive

197: what do you mean? Almost?

199: respect to...?

CO2 gain drift uncertainty

207: see comment at line 168. I think you are referring here to what is done at the factory during production and/or recalibration. If so, please explain better

214-215: this is correct, this is what is done in 80-90% of the cases. However, there exist the possibility to perform more than one span calibration, e.g. one slighlty below the ambient CO2 concentration and one at a much higher value, to have a better reconstruction of the sensor behaviour: this should be mentioned in my opinion 

216: yes, but you can adjust it twice in the case of two span calibration (in LICOR IRGA, actually this parameter is a linear function relating absorptance to density, and what is set by the software is the offset, as the slope is fix and determined at the factory)

sensitivity-to-H2O uncertainty

255 (eq. 12): please recall to the reader that 44 gH2O m-3 is a threshold for H2O concentration in air based on dew point values

Accuracy of H2O density measurements

318 (eq. 16): where sigmaH2O is the standard deviation of the random errors...

Δρ H Oz2 (H2O zero drift uncertainty) and Δρ H Og2 (H2O gain drift uncertainty)

324 (eq. 17): even if defined earlier in the CO2 section, it is probably worth it to report again what Ac, Aw etc are. Probably a symbols list would help the reader

333: I would also mention the same assumptions as above (i.e., rhoH2O is the closer proxy for true rhoH2O)

sensitivity-to-CO2 uncertainty

348: typo, subscript should be H2O

351: typo

ΔρH2O range

385-386: At which Ta?