General comments

This model seems to have a lot of potential to improve predictions and upscaling of lake methane emissions, which is a global need. However, a few overarching concerns need addressing:

1. The data currently presented for model testing do not show improved model performance compared to existing models. For instance, how does this model compare to the other processed-based models mentioned in the introduction, including Lake 2.0, bLake4Me, ALBM, and the Canadian Small Lake Model? Why was this model an expansion of CSLM rather than using the other models? It would be useful to run these models and show how FLaMe improves estimates. It needs to be better than the others to become most useful.
2. The lakes selected for testing and comparison should report every value that is used in the model and should fit within the size limits specified by the model. This was attempted with the four lakes chosen, but two of the four testing lakes seem inappropriate for model testing.
   • Lake Erssjon has a surface area that is too small to fit within the smallest size bin specified by the model
   • Lake Villasjon lacks a reported mean depth, and the model states that maximum depth must be >2x mean depth.
3. Recent papers have highlighted that laterally transported methane may better explain surface CH4 concentrations in lakes, yet this is not accounted for or discussed as a shortcoming. This needs to be mentioned.

Specific comments

• Line 31: add minimum size
• Line 37: is this due to ice blocking emissions (mention role of ice)?
• Lines 49-52: wetlands are not included as inland waters for the Global Methane Budget; they are estimated to be bigger emitters than inland waters (see Saunois recent budget).
• Lines 102 - 103: The wording tripped me up here…there may be a typo “However, including an explicit description of these processes is challenging, because it requires to account for a…”
• Line 113: Explain why you’re building from the CSLM model instead of one of the newer models
• Lines 145 -146: Explain why these size bins were selected. The upper and lower bounds will exclude the very smallest and largest systems
• Fig 1. Line 160: Consider changing the arrow size to represent the magnitude of flux from each size class; this would likely have more impact.
• Line 166: Please define thermocline depth and photic depth as they are used in this study
• Lines 186-188: What are the impacts of the maximum depth needing to be >2x mean depth? I assume there are lakes that don’t fit this relationship—what are the effects on modeled CH4 if the lake does not meet the assumption?
• What is the minimum depth for the model?
• Lines 194-195: provide citations for 5 m depth
• Line 198: Explain the rationale for ignoring horizontal material and gas exchanges
• Lines 228 – 229 and throughout: Are European lakes largely P limited? To what extent has this been explored? Please address and provide citations.
• Lines 252-255: If allochthonous / stained DOC is not considered in the model, how does Kd account for light attenuation from cDOM?
• Lines 270-272: What is the range/ variability in C burial and mineralization rates? Assuming that burial is half of mineralization seems problematic. Could it be modeled based on DO and OM source?
• Lines 278-281: What about transport of littoral methane? (e.g., DelSontro et al 2018, Khatun et al. 2024, Doda et al. 2024)
• Figures: consider changing lines / line types to print black/white friendly
• Figure 3: please define i and j in the caption
• Lines 305-306: Describe fmm range and calculations from the Hanson and Bastviken papers
• Section 2.2.2.2: Bring the table of parameters up earlier and begin referencing them. There is a lot to keep track of, and referencing that table early in this section would be helpful.
• Lines 396-397: Turnover often happens at much warmer temps than 4C. How does this affect the model?
• Lines 395 - 406: Please address how the balance between emissions and oxidation is addressed during storage release events
• Table 1: I suggest merging with Table 3 to reduce repetition and show the ranges for these parameters. Ranges for all parameters should be shown, and the variables used in the sensitivity analysis could be bold or starred.
• Table 1: I think the units for mineralization and C burial are incomplete – should then be g C / m2 / day?
• Lines 546-548: What is the area of the theoretical lakes?
• Table 2: What is the mean depth for Villasjon? Is max depth > 2x mean depth as needed for the model?
• Table 2: Erssjon is 0.062 km2, which is below the size range that FLaMe can model. This seems problematic. It seems like two of the four modeled lakes do not meet model assumptions based on depth or area.
• Section 3.1: Is the shallow, eutrophic lake polymictic? If it is large, a 10 m (zmax) and 5 m (zmean) system may mix in summer. Can the model handle polymixis? Similarly, is Villasjon polymictic? Is that what could explain the wide margins of error for Villasjon (Fig 6)? Similarly, Erssjon may be polymictic.
• Fig 5. Please increase and equalize axis font sizes to match the aesthetics of boxes g and h. Ebullitive fluxes are not visible in box g, though I believe there is a faint line at the bottom of the figure…please extend the y-axis below zero to show ebullitive fluxes more visibly. Apply unique labels to the y-axis of boxes g and h (as with the rows above) to make the scale of h more apparent and move the location of the “x10-4” to the axis label so it’s more obvious.
• Lines 693-695: What if lake depth was decreased from 15 m to 5 m? How shallow can the model go? What is the distribution of lake depths in Europe?
• Lines 795-796: The dataset of 47 European lakes was not described in the Methods; please provide more details on this dataset and analysis. For instance, what environmental variables were measured that could be incorporated into the models?
• Lines 799-803: Provide average values or percent differences between observed and estimated in the text or a table
• Line 832: provide lower bound number as well as upper bound
• Line 838-840: How much of this is also due to ice cover (i.e., reduced fraction of year with emissions)?
• Line 846: continuous makes it seem like fluxing through the ice. Clarify.
• Lines 880-882: suggests whether lake is N or P limited is important to consider. How much would N-limitation change model outputs? To what extent are lakes N or P limited in Europe?
• Table 4: Add more description to the caption. How was this done and what are the mean values representing? I suggest adding % change to the estimates.
• Sensitivity analysis did not look at diffusion rates; are these uncertain? How important can that be?
• Lines 1020-1021: add lower bound to lake size

This manuscript presents a process-based model for methane emissions from European lakes, and uses the model to estimate methane emissions from European lakes <1000km2 via a gridded approach.  The authors compare their model results to a regional dataset of summer point-in-time methane emissions (Rinta et al. 2017) and time series methane data from 4 European lakes (Natchimuthu et al. 2016, Sollberger et al. 2017, Varadharjan et al. 2009, and multiple studies on Villasjön as cited in Tan et al. 2024). The authors note generally good agreement, but also some interesting differences between the model estimates and the time series data. They call for more time series and ancillary data to help refine models. Overall, this paper represents an important advance in our ability to model regional-scale methane emissions from lentic waterbodies.

I would like to see a bit more discussion of the strengths and weaknesses of the underlying comparison datasets the authors did use.  For example, the fact that the FLaME model estimates higher ebullitive emissions than were reported in Rinta is not surprising to me given that the Rinta et al. 2017 study used floating chambers over a relatively short duration (6hr) and did not employ bubble traps, but rather estimated ebullition based on k600 of methane (which could be estimated high if every chamber on a given lake had some amount of ebullition, but not enough to generate “unreasonable” k600).  In general, the ability of the studies on these 4 lakes to differentiate the relative role of diffusion and ebullition (and to capture turnover, weather & water level-related hot moments) could be discussed.

The sensitivity analysis is very helpful for understanding the importance of various model parameters (which are informed by literature values).  The importance of f_mm (fraction of mineralization that results in methane production) is interesting & the authors could discuss some literature finding very different sediment methane production potential in different lentic sediment types (Bodmer et al. 2025 L&O). On a related note, did this upscaling include reservoirs? The authors mention using the Messager et al. 2016 dataset, but don’t describe whether they filtered out reservoirs.  Finally, I was surprised at the relatively limited effect of methane oxidation rate and Q10.  At least mentioning that the model requires oxygen for methane oxidation (but that anaerobic methane oxidation can also be important) would help better represent some uncertainty here I think.

Finally, the authors present a range of estimated European lake methane emissions in the introduction, but they do not revisit the range of estimates in their discussion.  How does the emission they estimate with a process-based model compare?  Can the authors separate the effect of lakes >1000km2 on the existing estimates to do a direct comparison?

Line By Line

Title:  I think the acronym FLaMe is fine, but I did want to make sure the authors were aware that there is already a method for “high speed limnology” that has been used to study methane dynamics in rivers called FLAMe, see original description: https://pubs.acs.org/doi/epdf/10.1021/es504773x?ref=article_openPDF, and example of application to methane: Large Spatial and Temporal Variability of Carbon Dioxide and Methane in a Eutrophic Lake - Loken - 2019 - Journal of Geophysical Research: Biogeosciences - Wiley Online Library

Line 24: I don’t love the term “CH4 cycling” since I think of elements cycling (e.g. ch4 is part of carbon cycling)

Line 25: maybe add that these are theoretical lakes (not lakes with data to verify against)

Line 26: I think by a “trophic” lake, you mean “eutrophic”

Line 76: You might also mention that our appreciation for emergent vegetation (aerenchyma transport) has also lagged… I see you mention this in the discussion

Line 109: remove “with” and just say “to tackle these challenges”

Line 120: define ESM

Line 127: add “the” between real and world

Line 147: how do you know the arithmetic mean lake depth?

Line 181: “are” to “is”

Figure 2: describe the colors in your legend. I think purple is the water column and orange is the “sediment column”?

218: You might consider a “but see” statement about the Grasset et al. 2018 paper, they did find degradation of fresh allocthonous OC to stimulate methane production, but they found that autochthonous organic carbon generally decomposed faster https://aslopubs.onlinelibrary.wiley.com/doi/full/10.1002/lno.10786

480:  It won’t change the Schmidt numbers much at all, but there is a more updated paper by Wanninkhof with small adjustments to the coefficients: Wanninkhof 2014 L&O Methods

505:  fix typo: should be “anaerobic”

512: See comments in general summary above.  The Rinta dataset is not the most robust

553: contrast to “contrasting”

562: citation for lake methane data?

578:  Did you just use natural lakes (type 1) or did you include type 2 and type 3 (reservoirs)?

617: “to” should be “with”

Table 3: It is difficult to tell how the range of methane oxidation Q10s compare to the Q10 of methanogenesis since the methanogenesis is tied directly to the Q10 of overall mineralization.  Did your scenarios include cases where the Q10 of methane oxidation is higher than for methanogenesis (as was seen in rivers in Shelley et al. 2015 Freshwater Biology)?

Figure 5:  Is this just showing modeled estimates without data?

Line 675: I suggest reporting in mg m-2 d-1. Also, this is a very low rate… There are only 4 lake/reservoirs in Rosentreter et al. 2021 dataset that are below 0.24 mg CH4 m-2 d-1 (and they are all reservoirs as it happens): Solina (Gruca-Rokosz et al. 2010), St. Aniol (Gómez-Gener et al. 2015), CB2 and CB3 (Teodoru et al. 2015).

690: again, I think you mean “eutrophic” not “trophic” here

695: would be nice to quantify how much lower the emissions are when the lake is modeled as deeper instead of just saying that emissions were “lower”

Figure 6: The y axes are labelled mg CH4 m-2 d-1, but the text is discussing very high emissions in panel A in units of g CH4 m-2 d-1.  Check for accuracy? I agree that 18.76 g CH4 m-2 d-1 (line 712) would be a very very high lake-wide flux.

728-730: Figure 3 depicts hydrostatic pressure…is the model input incorporating barometric pressure (such that it is not sensitive to weather events)?  Also unclear if this model is setup to estimate ebullition events associated with water level fluctuation

749: “will require assembling”—Also, you could cite some examples of nice time series here (either that are outside the European domain or are reservoirs instead of lakes). Rodriguez-Velasco et al. 2024 Limnology and Oceanography Letters is an example (but for a reservoir) https://aslopubs.onlinelibrary.wiley.com/doi/full/10.1002/lol2.10409   It also took a bit of hunting for me to figure out where the data for the 4 verification lakes came from (and its spatial temporal resolution). Right now the authors cite Tan et al. 2024 in their data availability statement, but I think these studies (and a description of the types of data) should be integrated in the text.

Figure 8- consider plotting y axis on a log scale so it is easier to see the comparison for the boreal systems

859: What data source are you using to estimate the depth distribution of European lakes? Or is this based on the assumed shape?  Clarify.

867:  Not sure what you mean by “dashed colors” maybe “colors with transparency”?

913-914: grammar: change to: “suggesting that it can capture the relationship between… well”

916-917: maybe remind readers again here that this estimate excludes the largest lakes?  Possibly present a back of the envelope range for the relative possible contribution from the largest lakes?

Table 4: provide some explanation of the numbers presented in the table… I think these are fractional percentages of the estimate generated by the baseline model run?

944: change from “large scale” to “regional scale” and possibly clarify lakes <1000km2

966: you mean aerenchyma flux?