In the manuscript "Intercomparison of methods to estimate GPP based on CO2 and COS flux measurements", the authors compare 4 different models for calculating GPP on ecosystem level. Two of them are based on CO2 and environmental measurements, whereas the other 2 include a dependence on carbonyl sulfide fluxes. The GPP, based on a neural network, agreed very well with classic flux partitioning. The GPP based on the LRU of chamber measurements from the top of the canopy also agreed well with the classic approach, but tended to overestimate GPP during periods of high incoming photosynthetic radiation. The second COS based approach, using a stomatal optimization model, agreed much better with classic flux partitioning and, although its implementation to other field sites might be promising, still needs to be tested.

I generally agree, that this manuscript deserves to be published, but I have some questions and suggestions to improve the document.

General comments:

• I suggest using an ANOVA and post-hoc tests to compare the results of 4 different models, daytimes and timescales instead of doing t-tests between only 2 of them. This could also end up in a nice table/plot for the reader. It's sometimes hard to grasp the differences within the text, which model results in a higher/lower GPP at different timescales and daytimes.
• (Also, if a pairwise t-test is used to compare so many samples, the p-values need to be adjusted - see Bonferroni Holm).
• I also think the publication would profit if you put plots showing the modeled versus the measured daytime NEE (for all approaches) for interested readers into the supplement (to compare over/underestimation of the models).
• Where do the differences between the daily and monthly GPPs averages come from?
• I suggest having an English native speaker proofread the manuscript since some sentences feel off.

Specific comments:

38-40 The daytime approach of Lasslop et al. does not assume, that the respiratory processes are the same during day and nighttime, at least the base respiration is based on daytime data!

60 The carbonic anhydrase is also located within the cytoplasm. I would add this information. (see: Polishchuk, O. V. (2021). "Stress-Related Changes in the Expression and Activity of Plant Carbonic Anhydrases.")

99 Was the friction velocity threshold applied during both day and nighttime?

105 For the sake of completeness, it would also be nice to have the company/origin of pt100 sensor stated here.

112 Why did you use 50% as a threshold?

168 I think the 4^th method should get a separate section including a title like the other 3.

186 Why did you use these exact values? Is there a reference for them? In which way will this influence the resulting LRU during the season regarding over and underestimation. It would be nice to see a sentence or two about this.

193 I am not sure the data is presented in a form, that will help the reader understand the data. Maybe it would be better to sort the sentences chronologically from 2013 to 2017 or group them by the environmental variables following Fig 1.

202 What does slightly higher mean? Can you give a percentage or absolute values?

209 Was the half-hourly data also statistically different?

210 How can GPPnlr be negative? Shouldn’t the equation make it positive in any case, and set it to 0 when the air temperature is below 0?

215-216 The GPP difference in 4d is not for daily but for 30 min data, “e” shows daily values.

232 LRUcap might be higher than LRU from chamber measurements. The LRU chamber measurements might not be best in representing the whole canopy. The higher LRU of GPPcap might even be closer to the true LRU value of the canopy, depending on the position of the chamber measurements. A higher LRU indicates more COS uptake per CO2 uptake, which might happen in the lower part of the canopy since there is less PAR, but the COS uptake should continue unhindered. I would refrain from concluding that LRUcap was overestimated during times of high radiation, but discuss the difference (and possible reasons) between the two COS based GPP.

234 I feel like introducing 2 new “parameters” in the result section is the wrong place, introduce them in the methods section.

239 Instead of writing “not large” can you tell if they are statistically different, and which one was higher/lower.

250-253 I don't think the comparison to a full season is needed, only state, that these cumulative measurements account for 13 weeks around the peak growing season.

274 How did you find the saturation point. Which algorithm did you use?

279 You could put a reference for Figure B2 here, showing the higher LRU at higher PAR for LRUcap

283 Usually, an increase in VPD should decrease the stomatal conductance/GPP. (see page 480-481 Körner, C. (1995). Leaf Diffusive Conductances in the Major Vegetation Types of the Globe. Ecophysiology of Photosynthesis. E.-D. Schulze and M. M. Caldwell. Berlin, Heidelberg, Springer Berlin Heidelberg: 463-490.

and Lasslop, G., et al. (2010). "Separation of net ecosystem exchange into assimilation and respiration using a light response curve approach: critical issues and global evaluation." Global Change Biology 16(1): 187-208.

The correlation between VPD and GPP in spring might only be caused by the correlation of the air temperature with VPD.

286-289 Since you have not observed a drought or heatwave, these sentences feel unnecessary.

303 State the difference here, "similar" feels unclear.

316 I actually dislike the term measured LRU, as LRU is a product of GPP and COS fluxes, so it can't be measured. I suggest replacing measured LRU with “LRU derived from chamber measurements” or a wording that is more representative for the LRUs calculation.

318 Why was it not comparable to the chamber measured LRU?

322 It would be nice to have the information about the position of the leaf chambers in the methods section, so that the reader knows what the basis for the LRUpar is.

336 I am not sure that you should conclude that the LRUcap model underestimates GPP during midday compared to GPPpar. Due to the aforementioned issue of only having a chamber at the top of the canopy, the GPPpar might be overestimated and GPPcap could actually better. (The LRU at the top of the canopy might be lower compared to areas within the canopy). I propose, just writing that the GPP is lower instead of underestimated, since “underestimated” gives the impression that GPPpar is correct.

Fig 3 Is this figure based on half-hourly data points? Are these really average or median differences like in Fig 2?

Fig 5 Do you mean cumulative daily fluxes when you write daily flux data points? You mention, that all medians have been calculated using the same number of data points. Were these also the same data points, or could there be a bias from different days?

Fig 7 Why did you use 700 par as the threshold?

Fig B2 If measured means “chamber -measured” LRU please state so.

Technical corrections:

91 “Consisted of a Gill HS”

112 I feel like some words are missing in this sentence. The second part about monthly averages feels disconnected. Are you trying to say, that the monthly averages were also only calculated from daily means, when 50% of the half-hourly data was available?

218 To investigate further the causes for the …

253 remove brackets from (on average 25%)

332 Do you mean noisy (scattered)?

The study by Kohonen et al. compares gross primary productivity (GPP) estimates at a boreal forest derived from two CO₂-based flux partitioning methods and two COS-based methods. One of the COS approaches to GPP, developed in previous studies, relies on an empirical light response of the COS vs CO₂ leaf relative uptake (LRU) ratio. The other COS approach, developed in this study, considers stomatal optimization as represented by the CAP model (Dewar et al., 2018) in simulating LRU responses to environmental conditions. The authors show that GPP estimates derived from the LRU_CAP approach agree with those from the two CO₂-based approaches in terms of diurnal and seasonal cycles, cumulative GPP in the growing season, and environmental responses. By contrast, the COS approach based on the light dependence of LRU alone shows considerably higher GPP estimates than those from other methods, especially at high radiation. The authors conclude that their new approach is an improvement over previous empirical LRU fits for obtaining accurate COS-based GPP estimates.

Overall, the study marks a valuable methodological advance in estimating GPP at the ecosystem scale and is worthy of publication. While the authors succeed in deriving COS-based GPP estimates consistent with those from CO₂-based methods, they have not presented a strong case for the robustness and generalizability of the new method they developed. In other words, do we know that the LRU_CAP approach produces the right results for the right reason, or is it so malleable that one can tune the parameters to get any desirable responses? To ensure the robustness of the method, the authors may need to clarify the physiological underpinnings of the method, the assumptions it makes, and its limitations. I have a few questions on this aspect.

1. There are many optimization-based stomatal models, and CAP is not the simplest one. What is the motivation for choosing this specific model over, say, the Medlyn model (Medlyn et al., 2011), which has only two parameters to fit?
2. The "carboxylation conductance", g_c, seems to be a pure model construct to linearize the nonlinear response of the assimilation rate (A) to the chloroplast CO₂ concentration (c_c). The assumption that g_c is constant is inconsistent with the Farquhar et al. (1980) model because the transition from Rubisco carboxylation limitation to electron transport limitation necessarily changes the slope of the A–c_c curve. What is the rationale behind this treatment? What bias does it introduce?
3. Several parameters assumed constant in fitting the model may vary across the season, for example, CO₂ compensation point and photosynthetic quantum yield. Where do those fixed values come from? Are they representative of the Scots pine species at the site?
4. The impact of mesophyll conductance (g_m) on LRU is an intriguing but understated point. It seems that infinite g_m works best for explaining LRU variability at low light but overestimates LRU at high light. By contrast, a finite g_m works well at high light but predicts too low LRU values at low light (Fig. B2). Is there a physiological explanation for this? A discussion on this point would be desirable.

Specific comments

L21–22: "removes approximately 30% of the annual anthropogenic carbon dioxide (CO₂) emissions from the atmosphere". This is a misinterpretation. Global GPP far outweighs the anthropogenic carbon emissions (~120 PgC vs ~10 PgC). The 30% fraction refers to net biome productivity, which is the net balance of GPP, ecosystem respiration, and emissions from land use changes and disturbances. See Chapin et al. (2006) for standard definitions of carbon flux terms.

L25: It is the net balance not the ratio that dictates the magnitude and direction of the terrestrial carbon budget.

L33: The origin of the partitioning method based on nighttime respiration predates Reichstein et al. (2005). The idea goes back at least as early as in Wofsy et al. (1993), though not in the exact form of relationship between R_eco and temperature. It is likely that this method has an earlier origin in the eddy covariance community. Therefore, better change "a method introduced by Reichstein et al. (2005)" to "a method in Reichstein et al. (2005)".

L35: And storage change fluxes, if not constrained by concentration profile measurements, also introduce bias to nighttime fluxes.

L40: "These limitations lead to uncertainties in the derivation of mechanistically sound descriptions of respiration and its drivers, especially when contributions of different biomass compartments to total CO₂ efflux vary across ecosystems and seasonally even within one ecosystem." The point of this sentence is unclear.

L48–55: It would be helpful to add a sentence on how this neural network approach tackles the problem of the inhibition of daytime respiration.

L66: "recent studies have shown that LRU is a function of solar radiation because CO₂ uptake is highly radiation dependent while COS uptake is not" - This notion that LRU depends on PAR goes back as early as Stimler et al. (2010).

L123: Specify the value of T₀.

Section 2.3.2: Did you create a hold-out data set for validation as in Tramontana et al. (2020), or perform cross-validation?

L161: "atmospheric concentrations of CO₂ and COS" - Specify at which height these concentrations were measured.

L164: Kooijmans et al. (2019) presented data from two chambers. Was this relationship derived from measurements from both chambers?

L193–200: I share the other referee's concern that this paragraph is not helpful for readers to grasp the year-to-year variability of environmental conditions. Try to present the anomaly features in chronological order.

Table 1: List the source of each parameter value in a column instead of in the caption. Specify which values are from the literature and which are fitted to data presented in this study.

L203–204: "... when comparing GPP_ANN to standard FLUXNET partitioning during summer months for multiple sites." - What about the subset of evergreen needleleaf forest (ENF) sites?

L209–L210: "However, at 30 min time scale the GPP_ANN was on average 15 % lower than GPP_NLR." - Could you compare GPP_ANN and GPP_NLR at half-hourly timescales with negative values filtered?

L211–L212: "while GPP_NLR may have even negative values due to random noise in the NEE measurements." - GPP should not be negative. Even if we consider random noise, the uncertainty range of GPP estimates should not encompass negative values because this is physically impossible. In your calculation of cumulative fluxes, the negative values may need to be capped at zero.

L231: Given that GPP is higher at high radiation, shouldn't the parameter fitting prioritize reducing LRU bias at high radiation?

L242: "The agreement of this method was better than assuming infinite mesophyll conductance at high PAR, but worse at low PAR" - Could you elaborate on why this is the case? Have you tried temperature-dependent g_m as in Wehr et al. (2017)?

L245–246: "We thus concluded that the assumption of infinite gm is more valid." - It would be more appropriate to say that given the uncertainty in LRU, minimizing LRU errors by itself does not offer a robust constraint on g_m. This fact does not necessarily mean that an infinite g_m is valid in the real world.

L249: It is worth noting that g_m becomes more limiting relative to g_s. We do not know how g_m varies during the day. It could be that g_s increases to a point such that g_m becomes more limiting.

L267–L269: If the fraction of leaf respiration in total ecosystem respiration is small, I would not expect a clear break point to be found in the light response of NEE. Do you see any evidence for the Kok effect in leaf chamber measurements?

L274: "in summer a saturation point was found at PAR>500" - This apparent saturation point could be partly caused by VPD limitation on stomatal conductance around midday.

L359: What purpose does rewriting the equation in terms of c_a – Γ^* serve? In the Farquhar et al. (1980) model, Γ^* appears in c_c – Γ^*, because it is used to represent the difference between carboxylation and oxygenation. But c_a – Γ^* does not seem to carry a physiological meaning.

Technical comments

L24: "increased" -> "increasing"

L30: "widely" and "globally", superfluous

L61: "triggered" -> "catalyzed"

L69: "ecosystem scale" -> "ecosystem-scale"

L71–72: This sentence seems to be the topic sentence of the paragraph.

L84: "where first flux measurements started in 1996 ..." - This information does not seem relevant since only the flux measurements between 2013 and 2017 are presented.

L86: "50 ha" - Better use SI units, for example, 0.5 km².

L139: "ecosystem level" -> "ecosystem-level"

L146: "assure" -> "ensure"

L193: "higher average" -> "higher than average"

L195: The units of PAR are incorrect in this line.

L214: "Fig. 2,3" -> "Figs. 2 and 3"

References cited

• Chapin, F. S., Woodwell, G. M., Randerson, J. T., Rastetter, E. B., Lovett, G. M., Baldocchi, D. D., Clark, D. A., Harmon, M. E., Schimel, D. S., Valentini, R., Wirth, C., Aber, J. D., Cole, J. J., Goulden, M. L., Harden, J. W., Heimann, M., Howarth, R. W., Matson, P. A., McGuire, A. D., … Schulze, E.-D. (2006). Reconciling Carbon-cycle Concepts, Terminology, and Methods. Ecosystems, 9(7), 1041–1050. https://doi.org/10.1007/s10021-005-0105-7
• Dewar, R., Mauranen, A., Mäkelä, A., Hölttä, T., Medlyn, B., & Vesala, T. (2018). New insights into the covariation of stomatal, mesophyll and hydraulic conductances from optimization models incorporating nonstomatal limitations to photosynthesis. New Phytologist, 217(2), 571–585. https://doi.org/10.1111/nph.14848
• Farquhar, G. D., von Caemmerer, S., & Berry, J. A. (1980). A biochemical model of photosynthetic CO2 assimilation in leaves of C3 species. Planta, 149(1), 78–90. https://doi.org/10.1007/BF00386231
• Kooijmans, L. M. J., Sun, W., Aalto, J., Erkkilä, K.-M., Maseyk, K., Seibt, U., Vesala, T., Mammarella, I., & Chen, H. (2019). Influences of light and humidity on carbonyl sulfide-based estimates of photosynthesis. Proceedings of the National Academy of Sciences, 116(7), 2470–2475. https://doi.org/10.1073/pnas.1807600116
• Medlyn, B. E., Duursma, R. A., Eamus, D., Ellsworth, D. S., Prentice, I. C., Barton, C. V. M., Crous, K. Y., De Angelis, P., Freeman, M., & Wingate, L. (2011). Reconciling the optimal and empirical approaches to modelling stomatal conductance. Global Change Biology, 17(6), 2134–2144. https://doi.org/10.1111/j.1365-2486.2010.02375.x
• Reichstein, M., Falge, E., Baldocchi, D., Papale, D., Aubinet, M., Berbigier, P., Bernhofer, C., Buchmann, N., Gilmanov, T., Granier, A., Grunwald, T., Havrankova, K., Ilvesniemi, H., Janous, D., Knohl, A., Laurila, T., Lohila, A., Loustau, D., Matteucci, G., … Valentini, R. (2005). On the separation of net ecosystem exchange into assimilation and ecosystem respiration: Review and improved algorithm. Global Change Biology, 11(9), 1424–1439. https://doi.org/10.1111/j.1365-2486.2005.001002.x
• Stimler, K., Montzka, S. A., Berry, J. A., Rudich, Y., & Yakir, D. (2010). Relationships between carbonyl sulfide (COS) and CO2 during leaf gas exchange. New Phytologist, 186(4), 869–878. https://doi.org/10.1111/j.1469-8137.2010.03218.x
• Tramontana, G., Migliavacca, M., Jung, M., Reichstein, M., Keenan, T. F., Camps‐Valls, G., Ogee, J., Verrelst, J., & Papale, D. (2020). Partitioning net carbon dioxide fluxes into photosynthesis and respiration using neural networks. Global Change Biology, 26(9), 5235–5253. https://doi.org/10.1111/gcb.15203
• Wehr, R., Commane, R., Munger, J. W., McManus, J. B., Nelson, D. D., Zahniser, M. S., Saleska, S. R., & Wofsy, S. C. (2017). Dynamics of canopy stomatal conductance, transpiration, and evaporation in a temperate deciduous forest, validated by carbonyl sulfide uptake. Biogeosciences, 14(2), 389–401. https://doi.org/10.5194/bg-14-389-2017
• Wofsy, S. C., Goulden, M. L., Munger, J. W., Fan, S.-M., Bakwin, P. S., Daube, B. C., Bassow, S. L., & Bazzaz, F. A. (1993). Net Exchange of CO 2 in a Mid-Latitude Forest. Science, 260(5112), 1314–1317. https://doi.org/10.1126/science.260.5112.1314