Dear referee,

thank you for your fast and helpful review. We will consider revising the structure as suggested to more clearly show why and how we used, for the most part, fixed exchange ratios (ER) as model parameters and their spatial and temporal variability as model output on ecosystem scale. We are aware of the role of N assimilation on ER but decided deliberately to leave this out of the current manuscript to keep a clear focus. We are currently working on a study investigating the N assimilation effect on ER variability. To illustrate the role of possible ER variability, we did a sensitivity analysis by testing a change of ±10% in ER_A, ER_stem, and ER_soil (model parameters) on the variation of O₂ flux. We will move the sensitivity analysis to the methods and results sections to make it more obvious. Besides the impact on O₂ fluxes, we will also test the effect of ER variability on flux partitioning in the sensitivity analysis. We still would expect that the main uncertainty on flux partitioning is caused by the uncertainty of measured O₂ fluxes.

Minor comments:

line 35: Yes, we agree that there are older references. Nevertheless, we prefer these two references cited as they nicely summarize the exchange processes of O₂ and CO₂, both at the land and the ocean interface. But we will also have a look into older references and consider adding these too.

line 49: Following the reference Keeling and Manning (2014), ocean warming of 1 Watt per square meter of ocean area would lead to a correction of the global and ocean sinks by about 0.1 Pg C per year due to the combined N₂ and O₂ solubility effect (section 5.15.4.6 in Keeling and Manning, 2014, citing Manning, 2001). So, the 0.05 Pg C per year uncertainty due to the uncertainty in ER is smaller than the effect of O₂ solubility under 1 Watt per square meter warming, nevertheless still relevant. A better understanding of the ER of land-atmosphere exchange could help to reduce this uncertainty.

line 707: We will add the magnitude of O₂ flux variation and impact on simulated ER_eco and flux partitioning due to the change of ER_A, ER_stem, and ER_soil by ±10%, as mentioned above.

Dear Reviewer, dear Editor,

Thank you very much for your review of the above-mentioned manuscript. We have carefully inspected all reviewer comments. Below, you will find our responses to the comments (in italics) and we describe how we will implement the suggestions made by the reviewers. As suggested by Reviewer #1, we will extend the sensitivity analysis regarding the fixed exchange ratios of gross assimilation, stem and soil respiration. Furthermore, we will discuss the influence of dilution and displacement effects (non-diffusive transport) as suggested by the community comment and Reviewer #2.

We hope that you will find the result satisfying.

Sincerely,

Yuan Yan, Anne Klosterhalfen, Fernando Moyano, Matthias Cuntz, Andrew C. Manning, Alexander Knohl

Reviewer #1

The reviewed manuscript presents an interesting study that models the O₂ and CO₂ fluxes in and above a forest canopy, and aims to determine if the actual measurement of such fluxes will enable the partitioning of the CO₂ fluxes into its components. This is a new and interesting modeling exercise, and the manuscript is generally well-written and clear.

Thank you for the positive feedback.

Major comments:

I find the way the manuscript is structured somewhat confusing. In the method section, the effect of nitrate assimilation on the ER is ignored, and a fixed value for stem and soil ER is assumed, although the introduction mentioned a range found in field studies. That leaves the reader to wonder why these important variations are ignored. Then the results are detailed, based on the simplified assumption of a fixed ER, and only in the discussion, the variability in the sources ER is discussed in detail and a sensitivity test is performed. If the authors want to keep this structure, they should state clearly in the methods and the results sections, that the effect of variability in ER will be discussed and tested later. For me, it seems it will be even better if some of this discussion will be moved to the introduction and the sensitivity analysis will be included in the methods and results.

This issue has also important implications for the conclusions. If chamber studies at a given site show a constant and large difference between the respiration components, there is a much better chance to use the O₂ approach for CO₂ fluxes partitioning. Maybe this could be also demonstrated by a test run of the model.

Authors reply:

We will consider revising the structure as suggested to show more clearly why and how we used, for the most part, fixed exchange ratios (ER) as model parameters and their spatial and temporal variability as model output on ecosystem scale. We are aware of the role of N assimilation on ER but decided deliberately to leave this out of the current manuscript to keep a clear focus. We are currently working on a study investigating the N assimilation effect on ER variability.

As the reviewer suggested, we extended the sensitivity analysis and restructured the manuscript accordingly by adding information in the Methods, Results and Discussions sections. For the sensitivity analysis, we changed each of the ER parameters of gross assimilation, stem and soil respiration (ER_A, ER_stem, and ER_soil) by ±10% and estimated the relative changes in O₂ fluxes, ecosystem ER (ER_eco) and ER of net assimilation (ER_An). Furthermore, we assessed the impact of the model parameters ER_A, ER_stem and ER_soil on the source partitioning results by estimating the relative change in the a posteriori uncertainty of gross assimilation CO₂ flux (σ_FA).

The sum of the O₂ flux (F_O2) for the entire study period (2012-2016) increased or decreased on average by 20.3%, if ER_A was increased or decreased by 10% correspondingly (see also Table below). Similarly, a change by 10% increment on ER_soil and ER_stem caused the sum to decrease or increase by 8.6% and 1.7%, respectively. These results directly followed Eq. (1) where the derivative with respect to a specific ER gives the corresponding flux in percent. Oxygen fluxes are hence most sensitive to the ER of the largest carbon fluxes.

Tab.: Changes in the sum of F_O2 due to 10% variation of ER parameters

In our original simulations, we found a median of the hourly ER_eco throughout the simulation period of 1.08 mol mol^-1, where the annual medians did not differ between years (see Table below). The annual mean ER_eco ranged from 1.06 to 1.12 mol mol^-1 across the five years. By changing ER_A or ER_stem by ±10% the annual median ER_eco only changed by up to 0.02 points. Increasing or decreasing ER_soil had the largest impact, where ER_eco increased or decreased to 1.00 or 1.17 mol mol^-1, respectively. Also here, the interannual difference between years was very small. A similar pattern could be found for the annual mean ER_eco, which varied between 1.04 and 1.15 mol mol^-1 depending on ER_A and ER_stem, and varied even between 1.00 and 1.24 mol mol^-1 due to ER_soil.

In our original simulations, the median and mean of hourly ER_An were 0.99 mol mol^-1 and 0.97 mol mol^-1, respectively, for all growing seasons during the simulation period, and did not vary between years (see Table below). In the sensitivity analysis, ER_An was only slightly impacted by changes in the model parameter of ER_A (ER_stem and ER_soil had no impact).

Tab.: Changes in mean or median annual ER_eco and ER_An due to 10% variation of ER parameters. The range of the five years of the study period are given.

In regard to the source partitioning approach, σ_FA was only slightly impacted by ER_A. σ_FA ranged from 1.42 to 4.83 μmol m^-2 s^-1 for the case of the lower a priori uncertainty, where it ranged from 1.43 to 4.47 μmol m^-2 s^-1 in the original simulation.

Tab.: Variations of σ_FA (μmol m^-2 s^-1) due to 10% variation of ER parameters. Panel (a), (b), and (c) refer to Figure 7 in the manuscript representing the various settings of a priori uncertainties.

In summary, the model simulations showed a small sensitivity towards the model parameter settings, but all model simulations yielded the same tendency and pattern of exchange ratios.

Minor comment 1:

Line 35: I guess there are much older references for this, or this can be just assumed as common knowledge.

Authors reply:

Yes, we agree that there are older references. Nevertheless, we prefer these two references cited as they nicely summarize the exchange processes of O₂ and CO₂, both at the land and the ocean interface. Some older references were also added:

• Krogh A (1919): The composition of the atmosphere. Det Kongelige Danske Videnskabernes Selskab 1, 1-19.
• Keeling RF and Shertz SR (1992): Seasonal and interannual variations in atmospheric oxygen and implications for the global carbon-cycle. Nature 358, 723-727.

Minor comment 2:

Line 49: How important is this 0.05 Pg uncertainty compared to other uncertainties, like the effect of ocean warming on O₂ solubility?

Authors reply:

Following the reference Keeling and Manning (2014), ocean warming of 1 Watt per square meter of ocean area would lead to a correction of the global and ocean sinks by about 0.1 Pg C per year due to the combined N₂ and O₂ solubility effect (section 5.15.4.6 in Keeling and Manning, 2014, citing Manning, 2001). So, the 0.05 Pg C per year uncertainty due to the uncertainty in ER is smaller than the effect of O₂ solubility under 1 Watt per square meter warming, nevertheless still relevant. A better understanding of the ER of land-atmosphere exchange could help to reduce this uncertainty.

Minor comment 3:

Line 707: As in the major comments above – is it worth showing some sensitivity test for this?

Authors reply:

The application and results of the sensitivity analysis by testing a change of ±10% in ER_A, ER_stem, and ER_soil (model parameters) were described in the Methods, Results and Discussion sections. Please refer to the major comment above.

We further added the following to the Conclusions: "The annual mean ER_eco ranged from 1.06 to 1.12 mol mol^-1 during the five years’ study period and depended significantly on our assumptions about the fixed model parameters describing the exchange ratios of the ecosystem components: leaves, stem and soil (ER_A, ER_stem, ER_soil). Especially, changes in ER_soil by ±10% yielded annual mean ER_eco from 1.00 up to 1.24 mol mol^-1."

Dear Andrew Kowalski,

Thank you for your interest in our work and comprehensive comment! And thank you for (virtually) meeting with us and explaining your points in greater detail and searching with us for a suitable solution.

You make a compelling point regarding the non-diffusive transport of O₂ due to a displacement effect caused by evapotranspiration. We agree with you that the description of diffusive and turbulent transport in our version of the CANVEG model is incomplete and disregards the Stefan flow.

As far as we understand these effects, and based on your comments, evapotranspiration has a diluting and a displacement effect on O₂ at the emitting surface (e.g., forest). Due to the dilution, O₂ diffuses downwards, following the gradient. This downward motion can be offset by the displacement effect (Stefan flow). Thus, the vertical gradients are also impacted: during daytime (e.g. sunny, summer’s day), the vertical O₂ gradient would decrease or even switch sign, and during nighttime, it may even increase, but evapotranspiration rates are very small. In our opinion, this impact is relevant when mole fractions regarding moist air are considered. The CANVEG model estimates the mole fractions regarding dry air for O₂, CO₂, and H₂O. Thus, the diluting effect does not play a role here.

The displacement effect/non-diffusive transport of O₂ plays a role in the following parts of our study (as you also described):

- application of flux gradient method (Figs. 5 and 6):

- By assuming all scalars (temperature, water vapor, CO₂, and O₂) are transported similarly (and thus assuming the eddy diffusivities (K’s) are the same), we have added an additional uncertainty.

- The vertical gradients are modified by the non-diffusive transport and so flux estimates based on the flux-gradient method would differ. However, our study considers mostly net ecosystem fluxes in this application. Further, Kowalski et al. (2021) determined that the WPL methodology, based on perturbations in the dry air mass fraction, correctly estimated biogeochemical fluxes (for both H₂O and CO₂) despite incorrectly describing transport mechanisms. Therefore, the WPL methodology predicts that artificially eliminating the effects of H₂O (dilution and displacement) and expressing each gas with reference to dry air will yield the equivalent flux-gradient relationships.

- estimation of ER_conc (Fig. 4b):

- Also due to the change in the vertical gradients, the estimation of ER_conc will be affected, because the displacement by evapotranspiration has a different impact on CO₂ and O₂. However, again for the mole fractions regarding dry air, the effect should be smaller. Also, the estimated ER_conc (and also ER_eco) were reasonable and in line with current process understanding.

In conclusion, we plan to spend more time considering the non-diffusive O₂ transport that you have highlighted in a future work. For this study, however, we would like to refrain from completely rebuilding our model. Thus, we propose the following:

We will add a detailed discussion about the impacts of the non-diffusive O₂ transport including the points made above. We will also follow your example that you gave in your comments about the flux magnitudes of water vapor, CO₂ and O₂, and try to quantify the magnitude of the non-diffusive transport for various temporal scales.

Based on our virtual meeting, we are confident that we will be able to sufficiently address your comment in a revised manuscript. And we very much appreciate your input and help!

Dear Reviewer, dear Editor,

Thank you very much for your review of the above-mentioned manuscript. We have carefully inspected all reviewer comments. Below, you will find our responses to the comments (in italics) and we describe how we will implement the suggestions made by the reviewers. As suggested by Reviewer #1, we will extend the sensitivity analysis regarding the fixed exchange ratios of gross assimilation, stem and soil respiration. Furthermore, we will discuss the influence of dilution and displacement effects (non-diffusive transport) as suggested by the community comment and Reviewer #2.

We hope that you will find the result satisfying.

Sincerely,

Yuan Yan, Anne Klosterhalfen, Fernando Moyano, Matthias Cuntz, Andrew C. Manning, Alexander Knohl

Reviewer #2

Major comments:

This work by Yan et al. is a solid, model-based examination of the ways in which real measurements of atmospheric oxygen (with their limited speed and precision) can be used to assess the exchange ratio of forested ecosystems.  The authors also explore the potential for these measurements to separate net fluxes into the gross fluxes that occur simultaneously.

Overall, I find the reasoning sound, the organization appropriate and the writing generally quite good.

Thank you for the positive feedback.

I have two scientific questions I would like to see addressed before publication:

First, the prose in line 194 led me to wonder if you really can claim that you’re truly predicting the full measure of interannual variability if you’re using static values for leaf phenology and LAI and WAI profiles.  Please clarify this.

Authors reply:

Unfortunately, direct measurements of LAI and WAI were only conducted in 2015, and thus used for all simulation years. The effective LAI was at maximum 4.8 m² m^-2 in the growing season in 2015 (Braden-Behrens et al., 2017). Thus, the interannual variability in our simulations is mainly driven by the meteorological conditions.

However, considering estimates by MODIS (Myneni, R., Knyazikhin, Y., Park, T. (2021). MODIS/Terra+Aqua Leaf Area Index/FPAR 4-Day L4 Global 500m SIN Grid V061. NASA EOSDIS Land Processes DAAC. Accessed 2023-05-04 from https://doi.org/10.5067/MODIS/MCD15A3H.061), the magnitude of LAI did not vary significantly between years from 2012-2016 (see Figure below). The variability of the LAI estimate within one year was larger and the standard deviation is quite large in this data set. Furthermore, the fraction of absorbed photosynthetic active radiation (FPAR) did not differ significantly during growing seasons between years.

In general, the start and end of the season (phenology) can differ between years. Based on the net ecosystem CO₂ flux measurements obtained with the eddy covariance technique, the start of the season varied by up to 18 days within May and the end of the season by only 5 days within November during our study period. Deriving the start and end of season based on canopy photos or satellite data would yield different days.

Implementation of interannual variable leaf phenology in our model simulations would improve the comparison between observations and simulations during the few days of leaf out and leaf fall, but not during the main part of growing seasons. This would mainly decrease the scatter in Figure 2 in the manuscript, but will not have a large impact on the other results, in our opinion. Thus, we like to refrain from changing our model set-up.

Fig.: Leaf area index (LAI) and fraction of absorbed photosynthetically active radiation (FPAR) derived from remote sensing MODIS data (Myneni et al., 2021). All data was included and quality flags were not considered.

Second, I am a little uncomfortable with your choice of “ppm” (i.e. mole fraction) for oxygen values.  Because oxygen is not a trace gas, dilution effects can be significant.  For this reason, the measurement community uses per-meg units when comparing ambient oxygen to reference gases (e.g. Keeling et al, JGR 103, D3, 3381-3397, 1998).  I encourage the authors to switch to per-meg throughout this paper for oxygen.

Authors reply:

Throughout the entire manuscript, we report O₂ and CO₂ concentrations as mole fractions regarding dry air (mixing ratios) in ppm. Thus, diluting effects should be excluded. We prefer to keep it this way, because we applied micrometeorological methods, such as the flux-gradient method and the source partitioning approach, and also like to address the eddy covariance community with our study. Within this community, concentrations are usually reported in ppm and fluxes correspondingly in µmol m^-2 s^-1. Further, we like to be consistent in regard to the calculation of O₂:CO₂ exchange ratios, which are usually presented in mol mol^-1.

However, we can state the equivalent of O₂ mole fractions in per meg in multiple places throughout the manuscript (e.g., when describing the measurement uncertainty) and add the vertical profile of O₂ in per meg in Figure 5.

This question of dilution and units ties in with the thoughtful comments left by Andrew Kowalski.  I am glad to see the authors’ recent reply.  I am far from expert in this area and can’t assess the relative merits of the comments or the reply, but two things come to mind:  First, it is worth emphasizing that that air samples are cryogenically dried before they are analyzed, so water vapor should be disregarded in the model output when characterizing mixing ratios for comparison with observations.  This is unrelated to Stefan flow, but connects to my next point.  Second, as I understand it, Kowalski is essentially comparing the rates of Stefan flow and molecular diffusion.  This might be appropriate when considering the stagnant boundary layer at a leaf’s surface, but I believe it is irrelevant at the branch/canopy/tree scale where air parcels (and their properties) are being rearranged by turbulent eddies.  My instinct (and it’s nothing more than that) is that Stefan flow is much less significant than eddy diffusion.  If a moist, O₂-rich parcel of air in the canopy is ascending through bulk (eddy) transport, while a dry, O₂-poor parcel is descending, there will be a net transport of O₂ upward if molar mixing ratios are calculated for the samples after water is removed.  I recognize that I may be wrong about the relative significance of Stefan flow and turbulent transport, or I may have misunderstood some other aspect of Kowalski’s argument.  Nonetheless, I would like to see my thoughts addressed by the authors.

Authors reply:

We added the information that CANVEG only considers mole fractions regarding dry air in the model simulations to the Methods section. Further, we added the following paragraph in the Discussions section, addressing the diffusive and non-diffusive transports and their meaning for our study:

Minor comment 1:

Throughout the paper: I believe all instances of “a posteriori” and “a priori” should be italicized.  Also, throughout, I am pretty sure that “et al.” should also be italicized.

Yes, done a suggested. All the “a posteriori” and “a priori” are in italic now. Following the author's guide of Biogeosciences, "et al." does not need to be italicized.

Line 13:  Please provide a citation for the 1.10 value of ER

Done. We added the citation: Severinghaus 1995, doi:10.2172/477735.

Line 16 and elsewhere:  Please choose a tense for the manuscript and make it consistent throughout.  I suggest the past tense, so in line 16, change “explore” to “explored”.

Done as suggested. We checked the entire manuscript.

Line 20: Please change to “that the modeled annual mean…” to make it very clear that this is not an observational result.

Done as suggested.

Line 24:  This wording here is confusing.  I think you mean “…could be derived with the flux-gradient method using measured vertical gradients in scalar properties, as well as fluxes of CO₂, sensible heat, and latent energy, all derived from eddy-covariance measurements.”  Please use this, or some other clarifying wording.

Done as suggested.

Lines 38-39:  This should read “ – ranging from hourly to decadal, and from leaf to global, respectively.  Since the relationship of O₂ and CO₂ fluxes…”

Done as suggested.

Line 50:  This should read “…indicating that the ER needs to be…”

Done as suggested.

Line 56:  This should read “over a six-year period with”

Done as suggested.

Line 67:  This should read “…in this study. Very few studies…”

Done as suggested.

Line 76: This should read “(Seibt et al., 2004).  As described by Battle et al. (2019)”

Done as suggested.

Line 119:  This should read “…of ER variations at the ecosystem scale”

Done as suggested.

Line 129:  This should read “…and ER can be plausibly simulated for”

Done as suggested.

Line 152:  Are these properties measured at 44m above the forest canopy (as stated) or 44m above the forest floor?

Thank you for catching this error. The eddy covariance measurements are conducted at 44m above the ground level.

Line 171:  I’m not sure to what fit this R² value refers.

For clarification we rephrased the paragraph as follows: “Atmospheric O₂ mole fraction (O_{2 atm}) as input for the model was deduced from a fixed O₂:CO₂ mole ratio of ‑1.15 mol mol^-1 and continuous CO₂ mole fraction measurements at the site (Table 1). The fixed O₂:CO₂ mole ratio was derived from measurements at the University of Göttingen from November 2017 to January 2018 using a high-precision O₂ measurement system developed by Dr. Penelope Pickers (University of East Anglia, UK) and very similar to the system described in Pickers et al. (2017). For these measurements, the correlation between O₂ and CO₂ mole fractions had an R² = 0.99.”

Line 178/179:  No line break

Done as suggested.

Line 184: This should read “LAI increased and decreased linearly, respectively.”

Done as suggested.

Line 184-186:  The sentence beginning “The maximum LAI…” seems to me like it really belongs in the site description.

Yes, please see lines 147-148: “The canopy height (ht) was 37.5 m and effective leaf area index (LAI) was at maximum 4.8 m² m^-2 in the growing season in 2015 (Braden-Behrens et al., 2017).”

Line 200:  This should read “…2014 to 2016.  To quantify the model…”

Done as suggested.

Line 230:  This should read “For the model simulations, ER can be obtained for the entire ecosystem, the net assimilation at the leaf level, or for only respiratory processes by considering…”

Done as suggested.

Line 275: Is the gradient of O2 best represented by “Δo” or “Δo/Δz”?

In the new manuscript version, we now use ‘Δvariable’ for differences of a variable (CO₂, O₂, temperature, etc.) between two heights, between measurements and simulation, or between fluxes derived by simulations or based on flux-gradient method (see comment below). ‘Δvariable/ Δz’ always refers to a vertical gradient.

Line 315:  I don’t understand the use of the word “even” here.

We deleted now the word ‘even’.

Line 436: Here and afterward, I suggest you use “Δ” instead of “diff”.  I find “diff_xxx” very visually distracting.  With “Fxxx” all as a subscript, there won’t be any confusion with other Δ terms.

Done as suggested throughout the entire manuscript.

Lines 439-445:  This information all really belongs in a table.  Having one to which we can easily refer  (and changing “diff” to “Δ”)  will make this section much, much easier to read.

Done as suggested. We have added the following table to the manuscript:

Table 3. Difference between the F_O2 estimations derived by the flux-gradient method (F^~_O2,(c,T,v), based on F^~_CO2,, H^~ or LE^~ and their respective vertical scalar profile) and by model simulations (F^~_O2,,CANVEG) for above canopy fluxes and for day- and nighttime individually. Results of the two-height approach are shown, where the flux-gradients were derived between z/ht = 2 and each layer below above the canopy. Also results of the three-height approach are shown, where the flux-gradient was derived between three fixed heights.

Line 453: This should read “…the heights with” and “…1.05 were used in”  (“finally” is confusing to me)

We rephrased the sentence as follows: “To guarantee a large gradient, the heights with z/ht = 2 and z/ht = 1.05 were used in inferring F_O2 from vertical CO₂, temperature and water vapor gradients for the following analysis.”

Line 469: Shouldn’t this be “net assimilation” (rather than gross)?

For clarification, we rephrased the sentence as follows: “…, when O₂ mole fractions increased with decreasing height above the canopy due to prevailing gross assimilation over respirations during daytime.”

Figure 5 caption:  The organization of the plots by column (day and night) is good, but please put labels (“day” and “night”) in the individual plots themselves so we can immediately interpret them.  Also, in the legend of panel c, you use ΔC for CO2, when in fact it’s not a difference or anomaly (unlike the O2).  Better to just use “CO2”.  Also, for oxygen, I’d prefer the legend read “O2” or “O2 anomaly”, or at the very least “ΔO2”

We have applied the suggested improvements of the figure and legends.

Figure 6 caption:  The last sentence is ambiguous.  It’s not clear whether it applies to only Plot D, or to all of them.  Again, I would prefer something other than “Δo” for the oxygen anomaly.

The last sentence refers only to panel (d). To clarify, we rephrased the sentence as follows: “In order to include daytime hours with an active canopy for the estimation of  σ_FO2, Δo ≥ 1 ppm was used as a filter, assuming higher oxygen dry air mole fractions close to the canopy than in the top domain layers.”

Line 532:  What is meant by “lower performance”? Are the predicted energies lower, or is there some metric of agreement to which you’re referring? Please clarify.

Yes, we meant the model performance in regard to some metrics. We added this information as follows: “The model performance (in regard to the slope, R² and RMSE) in the energy fluxes was generally lower than for CO₂ flux simulations.”

Line 565: This should read “…2019).  In addition, dry or wet”

Done as suggested.

Line 568:  This should read “…level.  Worrall et al. (2013) also derived”

Done as suggested.

Line 573:  This should read “bulk soil, measured ERsoil varied”

Done as suggested.

Line 575:  This should read “processes strongly suggest that”

Done as suggested.

Line 581:  This should read “change by 10% increments”

Done as suggested.

Lines 587-588:  This should read “…(ERzeco).  The temporal variations in EReco arose from diel and…”

Done as suggested.

Lines 589-590:  As it stands, this is not a sentence (and it’s confusing).  Please correct/clarify.

To clarify, we rephrased the sentence as follows: “Since assimilation and respiration are two individual processes, which are influenced by two differing main drivers - photosynthetic photon flux density and temperature - they usually show shifted diel cycles.“

Line 591:  This should read “fluxes from respiration”

Done as suggested.

Line 595: This should read “information about the turbulent flux exchange, as well as the”

Done as suggested.

Line 600:  I am puzzled by “between our studies”.  I think you mean “between Seibt et al’s work and ours”

Done as suggested.

Line 610:  This should read “by the utilization of varying nitrogen sources”.  Also – haven’t you made an effort to include some of these diverse sources of nitrogen in your model?  Perhaps you’re saying that the balance of nitrogen sources in the model might be wrong, but as written, it reads as if your model has no nitrogen sources at all.

Done as suggested. In the here used model version, we do not consider nitrogen. Another model study about the effects of nitrogen sources on O₂:CO₂ exchange ratio of gross assimilation is under preparation.

Line 613:  This should read “and sinks, and the turbulence”

Done as suggested.

Line 616:  This should read “recently found by Fassen et al. (2022).  We also”

Done as suggested.

Line 619:  This should read “forest over a six-year period”

Done as suggested.

Line 630:  This should read “modeled ERzconc was excessively influenced”

Done as suggested.

Line 632:  This should read “which have become” and “at eddy covariance sites in forests.”

Done as suggested.

Line 641:  This should read “mole fraction gradients, we confirmed that the selected heights should both be above the canopy.”

Done as suggested.

Line 670:  This should read “We also test this three-heights”

Done as suggested.

Line 694:  This should read “due to leaf temperature.  Implementing variable”

Done as suggested.

Line 698:  This should read “derived using the eddy”

Done as suggested.

Line 725:  This should read “based on, for example,  long term chamber measurements, will greatly help”

Done as suggested.

Dear Reviewer, dear Editor,

Thank you very much for your review of the above-mentioned manuscript. We have carefully inspected all reviewer comments. Below, you will find our responses to the comments (in italics) and we describe how we will implement the suggestions made by the reviewers. As suggested by Reviewer #1, we will extend the sensitivity analysis regarding the fixed exchange ratios of gross assimilation, stem and soil respiration. Furthermore, we will discuss the influence of dilution and displacement effects (non-diffusive transport) as suggested by the community comment and Reviewer #2.

We hope that you will find the result satisfying.

Sincerely,

Yuan Yan, Anne Klosterhalfen, Fernando Moyano, Matthias Cuntz, Andrew C. Manning, Alexander Knohl

Reviewer #2

Major comments:

This work by Yan et al. is a solid, model-based examination of the ways in which real measurements of atmospheric oxygen (with their limited speed and precision) can be used to assess the exchange ratio of forested ecosystems.  The authors also explore the potential for these measurements to separate net fluxes into the gross fluxes that occur simultaneously.

Overall, I find the reasoning sound, the organization appropriate and the writing generally quite good.

Thank you for the positive feedback.

I have two scientific questions I would like to see addressed before publication:

First, the prose in line 194 led me to wonder if you really can claim that you’re truly predicting the full measure of interannual variability if you’re using static values for leaf phenology and LAI and WAI profiles.  Please clarify this.

Authors reply:

Unfortunately, direct measurements of LAI and WAI were only conducted in 2015, and thus used for all simulation years. The effective LAI was at maximum 4.8 m² m^-2 in the growing season in 2015 (Braden-Behrens et al., 2017). Thus, the interannual variability in our simulations is mainly driven by the meteorological conditions.

However, considering estimates by MODIS (Myneni, R., Knyazikhin, Y., Park, T. (2021). MODIS/Terra+Aqua Leaf Area Index/FPAR 4-Day L4 Global 500m SIN Grid V061. NASA EOSDIS Land Processes DAAC. Accessed 2023-05-04 from https://doi.org/10.5067/MODIS/MCD15A3H.061), the magnitude of LAI did not vary significantly between years from 2012-2016 (see Figure below). The variability of the LAI estimate within one year was larger and the standard deviation is quite large in this data set. Furthermore, the fraction of absorbed photosynthetic active radiation (FPAR) did not differ significantly during growing seasons between years.

In general, the start and end of the season (phenology) can differ between years. Based on the net ecosystem CO₂ flux measurements obtained with the eddy covariance technique, the start of the season varied by up to 18 days within May and the end of the season by only 5 days within November during our study period. Deriving the start and end of season based on canopy photos or satellite data would yield different days.

Implementation of interannual variable leaf phenology in our model simulations would improve the comparison between observations and simulations during the few days of leaf out and leaf fall, but not during the main part of growing seasons. This would mainly decrease the scatter in Figure 2 in the manuscript, but will not have a large impact on the other results, in our opinion. Thus, we like to refrain from changing our model set-up.

Fig.: Leaf area index (LAI) and fraction of absorbed photosynthetically active radiation (FPAR) derived from remote sensing MODIS data (Myneni et al., 2021). All data was included and quality flags were not considered.

Second, I am a little uncomfortable with your choice of “ppm” (i.e. mole fraction) for oxygen values.  Because oxygen is not a trace gas, dilution effects can be significant.  For this reason, the measurement community uses per-meg units when comparing ambient oxygen to reference gases (e.g. Keeling et al, JGR 103, D3, 3381-3397, 1998).  I encourage the authors to switch to per-meg throughout this paper for oxygen.

Authors reply:

Throughout the entire manuscript, we report O₂ and CO₂ concentrations as mole fractions regarding dry air (mixing ratios) in ppm. Thus, diluting effects should be excluded. We prefer to keep it this way, because we applied micrometeorological methods, such as the flux-gradient method and the source partitioning approach, and also like to address the eddy covariance community with our study. Within this community, concentrations are usually reported in ppm and fluxes correspondingly in µmol m^-2 s^-1. Further, we like to be consistent in regard to the calculation of O₂:CO₂ exchange ratios, which are usually presented in mol mol^-1.

However, we can state the equivalent of O₂ mole fractions in per meg in multiple places throughout the manuscript (e.g., when describing the measurement uncertainty) and add the vertical profile of O₂ in per meg in Figure 5.

This question of dilution and units ties in with the thoughtful comments left by Andrew Kowalski.  I am glad to see the authors’ recent reply.  I am far from expert in this area and can’t assess the relative merits of the comments or the reply, but two things come to mind:  First, it is worth emphasizing that that air samples are cryogenically dried before they are analyzed, so water vapor should be disregarded in the model output when characterizing mixing ratios for comparison with observations.  This is unrelated to Stefan flow, but connects to my next point.  Second, as I understand it, Kowalski is essentially comparing the rates of Stefan flow and molecular diffusion.  This might be appropriate when considering the stagnant boundary layer at a leaf’s surface, but I believe it is irrelevant at the branch/canopy/tree scale where air parcels (and their properties) are being rearranged by turbulent eddies.  My instinct (and it’s nothing more than that) is that Stefan flow is much less significant than eddy diffusion.  If a moist, O₂-rich parcel of air in the canopy is ascending through bulk (eddy) transport, while a dry, O₂-poor parcel is descending, there will be a net transport of O₂ upward if molar mixing ratios are calculated for the samples after water is removed.  I recognize that I may be wrong about the relative significance of Stefan flow and turbulent transport, or I may have misunderstood some other aspect of Kowalski’s argument.  Nonetheless, I would like to see my thoughts addressed by the authors.

Authors reply:

We added the information that CANVEG only considers mole fractions regarding dry air in the model simulations to the Methods section. Further, we added the following paragraph in the Discussions section, addressing the diffusive and non-diffusive transports and their meaning for our study:

Minor comment 1:

Throughout the paper: I believe all instances of “a posteriori” and “a priori” should be italicized.  Also, throughout, I am pretty sure that “et al.” should also be italicized.

Yes, done a suggested. All the “a posteriori” and “a priori” are in italic now. Following the author's guide of Biogeosciences, "et al." does not need to be italicized.

Line 13:  Please provide a citation for the 1.10 value of ER

Done. We added the citation: Severinghaus 1995, doi:10.2172/477735.

Line 16 and elsewhere:  Please choose a tense for the manuscript and make it consistent throughout.  I suggest the past tense, so in line 16, change “explore” to “explored”.

Done as suggested. We checked the entire manuscript.

Line 20: Please change to “that the modeled annual mean…” to make it very clear that this is not an observational result.

Done as suggested.

Line 24:  This wording here is confusing.  I think you mean “…could be derived with the flux-gradient method using measured vertical gradients in scalar properties, as well as fluxes of CO₂, sensible heat, and latent energy, all derived from eddy-covariance measurements.”  Please use this, or some other clarifying wording.

Done as suggested.

Lines 38-39:  This should read “ – ranging from hourly to decadal, and from leaf to global, respectively.  Since the relationship of O₂ and CO₂ fluxes…”

Done as suggested.

Line 50:  This should read “…indicating that the ER needs to be…”

Done as suggested.

Line 56:  This should read “over a six-year period with”

Done as suggested.

Line 67:  This should read “…in this study. Very few studies…”

Done as suggested.

Line 76: This should read “(Seibt et al., 2004).  As described by Battle et al. (2019)”

Done as suggested.

Line 119:  This should read “…of ER variations at the ecosystem scale”

Done as suggested.

Line 129:  This should read “…and ER can be plausibly simulated for”

Done as suggested.

Line 152:  Are these properties measured at 44m above the forest canopy (as stated) or 44m above the forest floor?

Thank you for catching this error. The eddy covariance measurements are conducted at 44m above the ground level.

Line 171:  I’m not sure to what fit this R² value refers.

For clarification we rephrased the paragraph as follows: “Atmospheric O₂ mole fraction (O_{2 atm}) as input for the model was deduced from a fixed O₂:CO₂ mole ratio of ‑1.15 mol mol^-1 and continuous CO₂ mole fraction measurements at the site (Table 1). The fixed O₂:CO₂ mole ratio was derived from measurements at the University of Göttingen from November 2017 to January 2018 using a high-precision O₂ measurement system developed by Dr. Penelope Pickers (University of East Anglia, UK) and very similar to the system described in Pickers et al. (2017). For these measurements, the correlation between O₂ and CO₂ mole fractions had an R² = 0.99.”

Line 178/179:  No line break

Done as suggested.

Line 184: This should read “LAI increased and decreased linearly, respectively.”

Done as suggested.

Line 184-186:  The sentence beginning “The maximum LAI…” seems to me like it really belongs in the site description.

Yes, please see lines 147-148: “The canopy height (ht) was 37.5 m and effective leaf area index (LAI) was at maximum 4.8 m² m^-2 in the growing season in 2015 (Braden-Behrens et al., 2017).”

Line 200:  This should read “…2014 to 2016.  To quantify the model…”

Done as suggested.

Line 230:  This should read “For the model simulations, ER can be obtained for the entire ecosystem, the net assimilation at the leaf level, or for only respiratory processes by considering…”

Done as suggested.

Line 275: Is the gradient of O2 best represented by “Δo” or “Δo/Δz”?

In the new manuscript version, we now use ‘Δvariable’ for differences of a variable (CO₂, O₂, temperature, etc.) between two heights, between measurements and simulation, or between fluxes derived by simulations or based on flux-gradient method (see comment below). ‘Δvariable/ Δz’ always refers to a vertical gradient.

Line 315:  I don’t understand the use of the word “even” here.

We deleted now the word ‘even’.

Line 436: Here and afterward, I suggest you use “Δ” instead of “diff”.  I find “diff_xxx” very visually distracting.  With “Fxxx” all as a subscript, there won’t be any confusion with other Δ terms.

Done as suggested throughout the entire manuscript.

Lines 439-445:  This information all really belongs in a table.  Having one to which we can easily refer  (and changing “diff” to “Δ”)  will make this section much, much easier to read.

Done as suggested. We have added the following table to the manuscript:

Table 3. Difference between the F_O2 estimations derived by the flux-gradient method (F^~_O2,(c,T,v), based on F^~_CO2,, H^~ or LE^~ and their respective vertical scalar profile) and by model simulations (F^~_O2,,CANVEG) for above canopy fluxes and for day- and nighttime individually. Results of the two-height approach are shown, where the flux-gradients were derived between z/ht = 2 and each layer below above the canopy. Also results of the three-height approach are shown, where the flux-gradient was derived between three fixed heights.

Line 453: This should read “…the heights with” and “…1.05 were used in”  (“finally” is confusing to me)

We rephrased the sentence as follows: “To guarantee a large gradient, the heights with z/ht = 2 and z/ht = 1.05 were used in inferring F_O2 from vertical CO₂, temperature and water vapor gradients for the following analysis.”

Line 469: Shouldn’t this be “net assimilation” (rather than gross)?

For clarification, we rephrased the sentence as follows: “…, when O₂ mole fractions increased with decreasing height above the canopy due to prevailing gross assimilation over respirations during daytime.”

Figure 5 caption:  The organization of the plots by column (day and night) is good, but please put labels (“day” and “night”) in the individual plots themselves so we can immediately interpret them.  Also, in the legend of panel c, you use ΔC for CO2, when in fact it’s not a difference or anomaly (unlike the O2).  Better to just use “CO2”.  Also, for oxygen, I’d prefer the legend read “O2” or “O2 anomaly”, or at the very least “ΔO2”

We have applied the suggested improvements of the figure and legends.

Figure 6 caption:  The last sentence is ambiguous.  It’s not clear whether it applies to only Plot D, or to all of them.  Again, I would prefer something other than “Δo” for the oxygen anomaly.

The last sentence refers only to panel (d). To clarify, we rephrased the sentence as follows: “In order to include daytime hours with an active canopy for the estimation of  σ_FO2, Δo ≥ 1 ppm was used as a filter, assuming higher oxygen dry air mole fractions close to the canopy than in the top domain layers.”

Line 532:  What is meant by “lower performance”? Are the predicted energies lower, or is there some metric of agreement to which you’re referring? Please clarify.

Yes, we meant the model performance in regard to some metrics. We added this information as follows: “The model performance (in regard to the slope, R² and RMSE) in the energy fluxes was generally lower than for CO₂ flux simulations.”

Line 565: This should read “…2019).  In addition, dry or wet”

Done as suggested.

Line 568:  This should read “…level.  Worrall et al. (2013) also derived”

Done as suggested.

Line 573:  This should read “bulk soil, measured ERsoil varied”

Done as suggested.

Line 575:  This should read “processes strongly suggest that”

Done as suggested.

Line 581:  This should read “change by 10% increments”

Done as suggested.

Lines 587-588:  This should read “…(ERzeco).  The temporal variations in EReco arose from diel and…”

Done as suggested.

Lines 589-590:  As it stands, this is not a sentence (and it’s confusing).  Please correct/clarify.

To clarify, we rephrased the sentence as follows: “Since assimilation and respiration are two individual processes, which are influenced by two differing main drivers - photosynthetic photon flux density and temperature - they usually show shifted diel cycles.“

Line 591:  This should read “fluxes from respiration”

Done as suggested.

Line 595: This should read “information about the turbulent flux exchange, as well as the”

Done as suggested.

Line 600:  I am puzzled by “between our studies”.  I think you mean “between Seibt et al’s work and ours”

Done as suggested.

Line 610:  This should read “by the utilization of varying nitrogen sources”.  Also – haven’t you made an effort to include some of these diverse sources of nitrogen in your model?  Perhaps you’re saying that the balance of nitrogen sources in the model might be wrong, but as written, it reads as if your model has no nitrogen sources at all.

Done as suggested. In the here used model version, we do not consider nitrogen. Another model study about the effects of nitrogen sources on O₂:CO₂ exchange ratio of gross assimilation is under preparation.

Line 613:  This should read “and sinks, and the turbulence”

Done as suggested.

Line 616:  This should read “recently found by Fassen et al. (2022).  We also”

Done as suggested.

Line 619:  This should read “forest over a six-year period”

Done as suggested.

Line 630:  This should read “modeled ERzconc was excessively influenced”

Done as suggested.

Line 632:  This should read “which have become” and “at eddy covariance sites in forests.”

Done as suggested.

Line 641:  This should read “mole fraction gradients, we confirmed that the selected heights should both be above the canopy.”

Done as suggested.

Line 670:  This should read “We also test this three-heights”

Done as suggested.

Line 694:  This should read “due to leaf temperature.  Implementing variable”

Done as suggested.

Line 698:  This should read “derived using the eddy”

Done as suggested.

Line 725:  This should read “based on, for example,  long term chamber measurements, will greatly help”

Done as suggested.