Review of “Diurnal variability of atmospheric O₂, CO₂ and their exchange ratio above a boreal forest in southern Finland” by Faassen et al.

In this paper, the authors present diurnal variations in δ(O₂/N₂) and CO₂ observed at two heights above the boreal forest. They calculated ER_forest and ER_atmos based on flux and concentration measurements, respectively, and found ER_forest and ER_atmos cannot be used interchangeably. The authors also applied the observed ER_forest to separate the NEE into GPP and TER, and they found comparable results to the commonly used eddy covariance approach. These findings supported and refined the discussion by Seibt et al. (2004) and Ishidoya et al. (2013, 2015) who reported differences between ER_forest and ER_atmos and its application to forest carbon cycle. There are only a few data sets of continuous measurements of both δ(O₂/N₂) and CO₂ over forests, and accurate estimate of ER_forest at various forests is highly important for not only forest but also global carbon cycle. This paper makes a valuable contribution in this respect. However, I find some issues in the observed variations in δ(O₂/N₂) which should be addressed before publication.

Main Points

The authors ascribed the temporal decreases of O₂ and CO₂ between 13:00-20:00 (P3b) in Figure 4 to a remaining artefact that could not be corrected for with the pressure correction associated with the instability of the MKS pressure regulator in 2019. If so, I think the artefact also superimposed on the O₂ data during the other periods (P1, P2, and P3a), and I am concerned about the unrealistic values of ER_atmos of 2.28±0.01 and 2.05±0.03 found in Fig. 5 are also attributed to the artefact. In my experience, larger ER_atmos than 2.0 has never been observed in a diurnal cycle at a forest in a growing season. I recommend the authors to create the aggregate day based on the periods other than 7-13 July, 2019, and calculate the ER_atmos for the average diurnal cycles. Especially, the ER_atmos in 2018, when the pressure correction was not applied, will be useful for comparison. If larger ER_atmos than 2.0 is also found in the average diurnal cycles in 2018, then the value will be reliable. However, if larger ER_atmos than 2.0 is found only in the diurnal cycles in 2019, then it may be due to the artefact and the ER_forest may also be affected by the artefact. To discuss differences between ER_forest and ER_atmos properly, it is important to rule out the possibility of the significant effect of the artefact.

Other Specific Points

1) Line 175-178 and Table 1: What does “our own calibration” mean? Did the authors calibrate the target cylinder using the primary Scripps cylinders by themselves? I think the declared value with calibration in Groningen is based on SIO scale. Therefore, the values of target cylinder based on “our own calibration” should also be on SIO scale to calculate the mean of the difference.

2) Line 190-192: Related to the main points, the period of 7 through 12 July 2019 to create the aggregate day is shorter than that by Ishidoya et al. (2015). I am concerned about the artefact during this period considering the very high ER_atmos found in Fig. 5.

3) Line 223-226: The authors calculated the ER_forest from means of the O₂ and CO₂ flux during night, day, and entire day. I think it can also be calculated by applying a linear regression between O₂ and CO₂ flux (or ΔO₂ and ΔCO₂) on the points as Ishidoya et al. (2015, 2020) did. Wouldn’t this method reduce the uncertainty on ER_forest?

4) Figure 4: Do the error bars indicate standard error? Please specify.

5) Figure 7: The ER_forest is negative value in this figure, although it is defined as positive value throughout the paper. Please be consistent with the terms you use.

6) I think it would be better to add the references and/or brief description of the EC method and temperature-based function used in this study, since comparison of EC method and O₂ method in Fig. 8 is an important topic.

7 )The words “Eddy Covariance (EC)” appears repeatedly at line 30, 131, 227, and “Eddy Covariance fluxes” and “eddy-covariance CO₂ flux” also appear at line 429 and 634, respectively. I think it’s better to use “EC” throughout the paper after the definition at line 30.  

Diurnal variability of atmospheric O₂, CO₂ and their exchange ratio above a boreal forest in southern Finland

Faassen et al. present a highly novel dataset of O₂ and CO₂ measurement in the surface layer over a boreal forest. Such measurements are technically very challenging making this study one of the very few so far that have succeeded to apply O₂ in micrometeorological land surface flux measurements. Typically, the signal to noise ratio in O₂ gradient above forests is very small which limits the application of the flux gradient methods. Here the authors make use of a 125 m tall tower to increase the O₂ gradient.

A major challenge in this study is that the measurement uncertainty of the O₂ system is below comparable systems. This limits the interpretation of the data. Nevertheless, in my view the authors found a suitable way forward by aggregating the data to a “representative day”.

While the experimental design and analysis is well done, there are several aspects that need to be addressed before publication.

Major comments

• Footprints: A major question regarding the study is that the ERatmos values are much higher than in previous studies. Some potential reasons are discussed in lines 481 to 490. What I am, however, missing is a proper treatment of the concentration footprints. Firstly, they differ between heights, particularly if the height difference is 100 m. This could lead to situations where the bottom height sees the local land surface whereas the top height sees air influenced at a regional level. Secondly, right next to the towers (roughly 200 m) is a large lake. Given that lakes have different O₂:CO₂ exchange ratios, I am wondering how this would influence the observed signal. Some of the co-autors have published articles on eddy covariance flux measurements over that lake. For the manuscript it would be help to add a footprint analysis and evaluate and discuss the influence of these two aspects on ERatmos and ERforest.
• Flux partitioning: It I understood correctly, the exchange ratio of assimilation (ERa) is calculated based on equation 8 assuming a constant ERr and ICOS data of NEE, GPP and TER (line 276). Once ERa and ERr are retrieved for one representative day, these values are used to calculate GPP and TER on other days. For me it is not clear what we learn from this exercise as GPP is used to constrain ERa and then ERa used to constrain GPP. Other studies such as Wehr et al. 2016 Nature have shown that NEE partitioning with an independent method using 13C in CO₂ resulted in lower TER and lower GPP compared to the temperature-based function following Reichstein et al. 2005 possibly indicating a Kok effect. If now the temperature-based GPP is used to calculate ERa, the O₂ based method does not provide additional and independent information. While I understand that the authors have no independent measurements of ERa at hand, I still miss a more careful discussion including Wehr et al. 2016 and addressing the limits of this approach.

Minor comments

Line 23: better “net uptake” than “uptake”

Line 23 and 24: better be consistent using ether land biosphere or terrestrial biosphere

Line 27: Add a citation for last sentence in first paragraph.

Line 30-32: here I am missing a mentioning of Wehr R et al. 2016 Nature where they showed that fluxes partitioning using 13C differ from fluxes partitioning following Reichstein et al. 2005.

Line 36/7: fluxes of O₂ and CO₂ are opposite. Here a positive ER is used. It might be helpful to indicate this by saying  “indicates the amount of moles O2 consumed per mole of CO2 produced (or vice versa)“.

Figure 1: in the text of the introduction the term GPP and TER are used and in figure 1 respiration and assimilation. Please use consistent terms.

Line 90 to 94: personally, I prefer if the given objectives are presented with the term “objectives” for allowing speed-reading. Maybe a matter of taste

Line 113: what is the influence of the nearby lake on the exchange ratio. The footprints at 23 m and at 125 m are very different. How does this influence the results?

Line 129/130: It seems that the sampling lines are alternatingly flushed with 120 ml/min and 2 l/min. Has it been evaluated whether these changes in flow rate lead to any effects on the O₂ signal? Or are all these effects removed by discarding the first 4 minutes after switching.

Line 210: I find it confusing that in equation 5, eddy covariance terms for the turbulent fluxes are presented, but the turbulent fluxes are obtained from flux gradient measurement. Why are not equation 5 and  6 combined?

Line 218: In my view it is not the stability that characterised if in a period respiration or assimilation dominate, but it is the radiation regime. Why was here stability used and not nighttime vs. daytime?

Line 255: unit is missing. Should be “0.4 m s-1”.

Line 271: here it is referred to ICOS NEE and GPP from EC measurements. It would be good to say how ICOS partitions NEE into GPP.

Line 304: why was a fixed calibration time during the day selected (20:00 - 22:00). An alternative could be using a moving calibration time.

Line 307: 0.70 ± 0.65: the unit is missing.

Fig. 4a: for the height 23 m, the CO₂ concentration varies with a range of 15 ppm, whereas the O₂ concentration varies with a range of 35 ppmEq. Wouldn’t we expect to see a similar range of variation? What is the role of the nearby lake?

Fig. 4b: at night we see a vertical gradient in O₂ concentration (roughly 10 ppmEq) that exceed instrument precision (roughly 4 ppmEq), but during daytime the gradient is – even averaged over multiple days – lower than instrument precision. To me it is unclear how the uncertainty of the measurements is propagated to the final fluxes and ERforest.

Line 318: in P3b: O₂ and CO₂ concentration changes show the same sign, instead of the expected opposite sign. This is related to an instability of the MKS pressure regulator. It is unclear why this effect should only affect P3b and no other times of the day. How was this evaluated?

Fig. 5: Which regression type was used to calculate the regression?

Line 339: Given that the measurement uncertainty is so high compared to the variation during P3a, I am wondering how the uncertainty could be included via error propagation when calculated the slope and its uncertainty.

Fig. 6: The units of the fluxes are given in ppm m m-1. This is very unusual for the flux community. Typically, the fluxes are reported in µmol m-2 s-1. Also, I find it confusing that the y-axis label is the covariance, but the fluxes are calculated from a flux-gradient approach and not from eddy covariance.

Fig. 6b: Could please describe in the caption what are the error bars. Could just be moved from the main text (line 380). Also here, it is unclear to me if an error propagation incl. measurement uncertainty was carried out.

Fig. 7 : It is surprising to see ERforest values at -2 to -2.5. This is much more negative that other reported data and it is unclear what this could mean physiologically. It is also surprising that the fluxes with the most negative values are also the largest fluxes, where we would expect to see large gradients and thus robust flux calculations.

Appendix: Personally, I prefer that the units are shown as well.

Overall, this is very nice paper presenting important results.  The authors conduct challenging measurements, analyze the data intelligently and combine their own data with ancillary datasets in a clever way to extract interesting values.  They focus on the O2/CO2 exchange ratio for a boreal forest (unprecedented) and then extend their work to seperately assess the exchange ratios associated with respiration and assimilation.  The work is valuable, the paper is generally well organized and it definitely deserves publication.

That said, I do have some concerns that need to be addressed prior to full acceptance:

1. The authors use α_b, ER and OR somewhat interchangeably in the introductory part of the paper.  Each of these symbols really does have a distinct and specific meaning.  Although the use of these terms in the literature has been somewhat sloppy, as our field matures it becomes more important to use the right word in the right context.
2. The authors assume ERr is constant day and night.  This may well be true, but it's possible it isn't true.  Since this assumption is central to the subsequent analysis, there should be more discussion of this assumption and its validity.
3. The data were compromised at times by the failure of some MKS pressure/flow controllers.  The authors apply a correction to the data, but there are a few points with (apparently) anomalous values where we're told that the correction simply wasn't adequate.  Since we aren't told any of the details of the correction, I'd like to see evidence that the other (non-anomalous and corrected) data are valid, and not just because their values are close to what we expect.
4. The authors attribute differences between ER_atm and ER_forest to "boundary layer dynamics and entrainment" or the unique nature of boreal ecosystems.  I think the first explanation misses the point and the second if very likely wrong.  Whenever you see O2 and CO2 changing with time with a slope more negative than -1.2, this indicates the influence of fossil fuel combustion.
5. There appears to be circularlity in some of the analysis.  For example, the EC data are used to set a value of the free parameter K (a transport coefficient) for getting fluxes from O2 gradients.  Then the O2-based fluxes are assessed by comparing them to the EC data.  Similarly, NEE is split into GPP and TER using the O2 and CO2 data.  Then the O2 and CO2 data are further interpereted by taking GPP and TER as if they were known a priori. 

It's quite possible (particularly for #5) that the authors have done nothing wrong and I have simply failed to understand their work.  If that's the case, then my comments should be taken as a plea for clarification and explanation in the text.

All of these concerns, along suggestions/corrections on word choice, punctuation, sentence structure and grammar, and covered in the attached "marked up" PDF.  The markings are in three colors:  Red - add/delete/move text, to be taken verbatim   Green - questions/directives for the authors  Yellow - highlighting text for which I have typed a "sticky note".  Be sure to open the note and read to the end.  Scrolling may be required.

Finally, I would like to acknowledge that the writing quality is very high.  Even though I have made numerous editorial markings, as a native English speaker (with a modest proficiency in German) I am in awe of the authors' ability to write so well in a second language.  Well done!