Assimilating Multi-site Eddy-Covariance Data to Calibrate the CH<sub>4</sub> Wetland Emission Module in a Terrestrial Ecosystem Model

Kallingal, Jalisha Theanutti; Scholze, Marko; Miller, Paul Anthony; Lindström, Johan; Rinne, Janne; Aurela, Mika; Vestin, Patrik; Weslien, Per

doi:https://doi.org/10.5194/egusphere-2024-373

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https://doi.org/10.5194/egusphere-2024-373

Preprints

28 Feb 2024

| 28 Feb 2024

Assimilating Multi-site Eddy-Covariance Data to Calibrate the CH₄ Wetland Emission Module in a Terrestrial Ecosystem Model

Jalisha Theanutti Kallingal, Marko Scholze, Paul Anthony Miller, Johan Lindström, Janne Rinne, Mika Aurela, Patrik Vestin, and Per Weslien

Abstract. In this study, we use a data assimilation framework based on the Adaptive Markov Chain Monte Carlo (MCMC) algorithm to constrain process parameters in LPJ-GUESS using CH₄ eddy covariance flux observations from 14 different natural boreal and temperate wetlands. The objective is to derive a single set of calibrated parameter values. These parameters are then used in the model to validate its CH₄ flux output against 5 different types of natural wetlands situated in different locations, assessing their generality for simulating CH₄ fluxes from different boreal and temperate wetlands. The results show that the MCMC framework has substantially reduced the cost function (measuring the misfit between simulated and observed CH₄ fluxes) and facilitated detailed characterisation of the posterior distribution. A reduction of around 95 % in the cost function and approximately 50 % in RMSE were observed. The validation experiment results indicate that four out of 5 sites successfully reduced RMSE, demonstrating the effectiveness of the framework for estimating CH₄ emissions from wetlands not included in the study.

Received: 07 Feb 2024 – Discussion started: 28 Feb 2024

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Jalisha Theanutti Kallingal, Marko Scholze, Paul Anthony Miller, Johan Lindström, Janne Rinne, Mika Aurela, Patrik Vestin, and Per Weslien

Status: closed

RC1:
'Comment on egusphere-2024-373', Anonymous Referee #1, 11 Jun 2024

Overview

The manuscript by Kallingal et al. presents a data assimilation framework and its application to the calibration of model parameters for the wetland methane module in the LPJ-GUESS, a global terrestrial ecosystem model. The data assimilation framework is based on an adaptive Markov Chain Monte Carlo (MCMC) algorithm that is computationally intensive. Such a calibration approach can be very useful to the scientific community in general and wetland methane modellers in particular, because the choice of model parameter values is sometimes done "manually" in a less systematic way than what the authors described in their manuscript.
According to the authors, the objective of the manuscript is to derive a single set of calibrated parameter values for the wetland methane model in LPJ-GUESS (Abstract; Pg 1, Ln 3). Different aims are associated with that objective (Pg 2, Ln 56-59): (1) to investigate the capacity of the data assimilation framework at multiple sites in the northern high-latitudes; (2) to optimise selected model parameters [10 out 11 parameters]; (3) to examine to what extent this optimisation improves the model’s ability to simulate the seasonal cycle of methane from different wetlands over northern latitudes above 40◦ N.
The current version of the manuscript does not convince me with regards to these study aims. In particular, the manuscript falls short with respect to the second and third aims. As a modeller with experience in wetland methane processes, this work sounds incomplete because the authors focus on reducing the RMSE (e.g. Figure 4) but not on improving the simulation of emissions relative to observations (e.g. Figure 6b). Moreover, considering the potential of the LPJ-GUESS as a global model (Pg 2, Ln 40), it is surprising to see that the authors do not show whether/how their calibrated parameters improve the model performance with respect to large-scale methane emissions from northern wetlands (e.g. total methane emissions from wetlands north of 40◦ N) at least. Furthermore, given that their calibration focuses on methane emissions from northern wetlands, it is disappointing to see how poor their posterior-based estimates are for seasonal methane fluxes in general and cold-season methane fluxes in particular.
Considering the above concerns, I find that the current version of the manuscript would need to be revised before it can be considered for publication.
General comments

1) Manuscript structure - Methodology:

The manuscript is quite technical and its current structure makes it hard for readers to digest the presented results (Section 3). You should re-structure the manuscript in order to improve its logical flow. For instance, all formulas, key metrics and other technical aspects should be described prior to the results section (in the methodology section for instance). It would be appropriate to add a new subsection under the methodology section (let's say - Section 2.6: Statistical metrics) in which you would need to include equations 5 and 6 as well as descriptions for the RMSE, the chi-square test, and other statistics in the context of this study.
2) Manuscript structure - Missing discussion:

Although Section 3 is entitled "Results and discussion", I find that there is no authentic discussion in the manuscript. I recommend that you add a discussion (as a section or subsection), in which you should talk about limitations of your study, algorithm, model, etc. by taking into account prior research.
3) Method generalization:

The authors seem to be satisfied with a computationally-intensive algorithm that reduces the so-called cost function and RMSE (Figures 4 and 9) without necessarily improving the ability of the model to simulate wetland methane emissions at the same sites where the algorithm was tested (Figure 6b). So, what's the added value for such an algorithm in terms of model predictions? How would that convince someone interested in applying the algorithm with the end goal of improving their simulations of wetland methane emissions across spatial scales (from the site scale to the global scale)?
4) Method scalability:

Given that LPJ-GUESS is a global model, it would be more convincing to show whether/how the calibrated parameters improve the simulation of wetland methane emissions at large scales. Why not show that for - at least - the magnitude of methane emissions from northern wetlands?
5) Seasonal cycle and cold-season methane emissions:

As your study focuses on northern sites, not capturing cold-season methane flux is a major weakness of your model. In my opinion, this weakness is primarily due to the fact that your methane fluxes are modeled as a function of air temperature but not soil temperature. Various simpler models are able to simulate non-zero methane emissions in winter months (e.g. https://agupubs.onlinelibrary.wiley.com/doi/10.1029/2023GL103037; https://gmd.copernicus.org/articles/14/6215/2021). You should talk about this limitation in your manuscript (results and discussion).
6) Algorithm validation versus Study hypothesis:

You describe your study hypothesis (Pg 2, Ln 53-55) and your plan to do a validation to verify the hypothesis (Pg 2, Ln 64). Does your validation verify the hypothesis? That's not clearly stated in the manuscript.
Also, considering your results on the validation of wetland methane emissions (Figure C1), would you say that your calibration is worth the effort?
Specific comments

Pg 2, Ln 28-29:

Could you be more specific about relevant "stresses"? Alternatively, you can use another word for more clarity.
Pg 3, Ln 59-60:

Please rephrase the part that says "the model process and parameter correlations and uncertainties". It is not clear what correlations you are talking about. Whether there is a link between the words "process" and "uncertainties" in that sentence.
Pg 3, Ln 77:

No comma needed between "including" and "estimation of peat..."
Pg 3, Ln 81:

I suggest you say "...an acrotelm with a thickness of 0.3 m..."
Pg 3, Ln 82:

Not clear what "its " stands for here? Is that the peat composition or the layer composition? Please rephrase for more clarification.
Pg 3, Ln 84:

No need to add "PFT" after "lichen moss".
Pg 4, Ln 86-87:

That's a long sentence. Please break it into two sentences that are easy to digest.
Pg 4, Ln 86:

You write that "The carbon in the soil is transformed to CH4 or CO2 depending on the hydrological conditions". Isn't that supposed to be A PORTION of the soil carbon that gets transformed to CH4 or CO2? The way you say it makes it seem that all soil carbon within LPJ-GUESS is either CH4 or CO2. But I presume that there must be some sort of organic matter that do not get access by microbes for their metabolism (i.e. soil carbon preserved from microbial activity).
Pg 4, Ln 97:

Please describe what w_tiller represents to make it easier for readers who will not check Kallingal et al. (2023).
Pg 5, Ln 110:

Don't you need a dash between measurement and years (i.e. measurement-years) for consistency?
Pg 5, Ln 112:

I suggest you add "for CH4 fluxes" right after "gap-filled data".
Pg 6, Ln 127-128:

I find your description of terms from equation (2) to be confusing. I suggest you talk about M_i and R_i for the i-th site, the same way you did it for Y_i.
Pg 7, Ln 135:

How does P(x) relate to J(x)? In other words, how do you relate the functions in equations (2) and (3)?
Pg 7, Ln 141:

I suggest you insert "CH4 flux" between "actual" and "observations". That is, saying "actual CH4 flux observations".
Pg 8, Ln 155:

What does "model fat" mean?
Pg 9, Ln 185-197:

Please remove the entire paragraph. It has no added value to your Section 3 (which can start right away with Section 3.1).
Pg 10, Ln 220:

Isn't "Rmoist" supposed to be in mathematical typing format similar to "Rmoist_an"?
Pg 15, Ln 311:

You need to use a minor/small "c" letter for "contradiction".
Pg 18, Ln 328:

Please add "of CH4 flux" right after "888 gCm-2" for more clarity.
Pg 20, Ln 359:

The acronyms MAS and MAV are not needed in this sentence. Please remove.
Pg 23, Ln 405:

No need to use "observed" here. Please remove.
Pg 23, Ln 415-416:

What's the point of saying that it takes around 480 computational hours to complete the 100,000 iterations on an AMD Ryzen Threadripper processor here? I suggest you move that whole sentence to the methodology section.
Tables

Table 3:

I suggest that you re-arrange the table columns as follows: Move column 3 to column 5; Move column 4 to column 3; Move column 5 to column 4.
Table 4:

Please add "Posterior" in front of "std" in the third row.
Table 5:

Why do you have totals just under the first 7 sites? Do you need these totals in the first place? Same point for Table B.1
Table 6:

"Hemi-boreal" or "Semi-boreal"?
Table B.1:

Why do you have totals just under the first 7 sites? Do you need these totals in the first place? Same point for Table 5.
Figures

Figure 2:

I suggest that you write "Probability distribution functions (PDFs)", instead of just the acronym.
Figure 5:

The figure caption misses a description of the horizontal green lines. Are these lines representing back-filled values? If so, please describe that in the caption.
Figure 6:

Panel a: Why do you only show time series for four sites out 14?

Panel b: My interpretation of this figure is that only a few sites compare well with observations even with posterior estimates. Isn't that a major conclusion to be drawn from the figure?

Citation: https://doi.org/10.5194/egusphere-2024-373-RC1
- AC1:
  'Reply on RC1', Jalisha Theanutti Kallingal, 18 Sep 2024
  Reply letter to the Referee #1
  We are very thankful to the Referee for the constructive comments. In the following, we have addressed the Referee's comments. The manuscript has also been revised accordingly.
  Note: The reviewer comments are referred to italic font type throughout the texts, and the authors’ responses are referred to as normal font.
  - According to the authors, the objective of the manuscript is to derive a single set of calibrated parameter values for the wetland methane model in LPJ-GUESS (Abstract; Pg 1, Ln 3). Different aims are associated with that objective (Pg 2, Ln 56-59): (1) to investigate the capacity of the data assimilation framework at multiple sites in the northern high-latitudes; (2) to optimise selected model parameters [10 out 11 parameters]; (3) to examine to what extent this optimisation improves the model’s ability to simulate the seasonal cycle of methane from different wetlands over northern latitudes above 40◦ N. The current version of the manuscript does not convince me with regards to these study aims. In particular, the manuscript falls short with respect to the second and third aims.
  Many thanks for these observations and valuable feedback. We understand the concern regarding the parameters not completely converging with a perfect Gaussian structure, and that some mismatch still persists in the model's ability to capture the variability in the flux observations. However, it is not quite true that the parameters are not optimised. This has been showed in the manuscript by the posterior estimates of the parameter structure, parameter correlations and prior and posterior model estimates and uncertainty quantifications. Complete reduction of the misfit is practically not possible. The degree of misfit reduction varies with the model complexity, non-linearity and subsequent model biases compared to the assimilated data. It should be noted that the posterior parameter distribution is expected to be perfectly Gaussian only under the assumption of a linear model. As discussed in the paper, LPJ-GUESS is highly non-linear and complex, which can lead to challenges due to parameter equifinality (likelihood of different parameter combinations yielding similar results) and convergence issues. From experience of our previous study (Kallingal et al. (2023)), we have concluded that some of the equifinality problem might be inherent to the parametrisation in LPJ-GUESS rather than the optimisation algorithm. These challenges were expected in this study too to some extent.
  Beyond the inherent non-linearity of LPJ-GUESS, the suboptimal convergence of parameters suggests that the assimilated fluxes may carry more complex information about the process parameters than initially assumed, or that there are intricate interactions between parameters. This complexity warrants further investigation into both the model structure, temporal correlations within the assimilated data and the structure of the data. Additionally, this indicates that the model could benefit from incorporating non-Gaussian assumptions in GRaB-AM for future studies, which would better capture uncertainties in parameters with high skewness and kurtosis. These details are now included in the discussion section (Sect. 4, Line 377 to 388) in the revised paper. On top of this we also note the observation of reviewer #2 about the Objective 1, in which he says the “first objective is well covered in the manuscript, particularly by the reduction in RMSE as shown nicely ie. in Figure 4. Figure 5 given another comprehensive overview”.
  - As a modeller with experience in wetland methane processes, this work sounds incomplete because the authors focus on reducing the RMSE (e.g. Figure 4) but not on improving the simulation of emissions relative to observations (e.g. Figure 6b).
  Thanks for the observation. It is true that even though there has been a considerable reduction in RMSE and the cost function, the model still fails to fully capture the variability in the assimilated flux observations. RMSE is the best possible measure to assess posterior model improvement against the observations. We use this metric in this study in addition to the cost function reduction since the cost function itself is another version of the model-data misfit. Therefore, we believe that the reduction in RMSE can be considered as an additional measure for the model calibration.
  Addressing the difficulty of the algorithm in capturing the variability in the flux observations, it should be noted that no systematic behaviour is observed in the posterior model residual (see Fig. 1). This indicates that the remaining mismatch is random, not systematic.
  Figure 1. Prior and posterior residuals showing the resulted variability is random.
  It suggests that the model is capturing the essential dynamics correctly, and the mismatch could be due to factors like observation noise, missing processes in the model description, and/or temporal/spatial resolution differences between the model and the observations. The chi-square value indicates the magnitude of this underestimation to a certain extent. This is now explained in detail in the discussion section (Sect. 4.2). Figure 6b in the paper (mentioned above) displays the mean annual sums of CH4 estimated at all 14 sites. It was observed that 9 out of 14 sites showed improvement. It should be noted that the data were assimilated collectively, which was aimed at reducing the overall mismatch. However, this approach may have encountered difficulty in improving all individual sites while balancing the overall variability.
  - Moreover, considering the potential of the LPJ-GUESS as a global model (Pg 2, Ln 40), it is surprising to see that the authors do not show whether/how their calibrated parameters improve the model performance with respect to large-scale methane emissions from northern wetlands (e.g. total methane emissions from wetlands north of 40◦ N) at least.
  We agree that this is a drawback of the paper and reviewer #2 has also commented on this. Initially, we planned to use the posterior parameters derived from this study for a large-scale analysis of methane emissions from northern wetland in a separate manuscript, as mentioned in the conclusion section (see Lines 530 to 533). However, we do acknowledge that this leaves the paper somewhat incomplete. The details of adding such an analysis are given in the reply to the general comment #4.
  - Furthermore, given that their calibration focuses on methane emissions from northern wetlands, it is disappointing to see how poor their posterior-based estimates are for seasonal methane fluxes in general and cold-season methane fluxes in particular.
  Considering that LPJ-GUESS suppresses emissions under sub-zero temperatures and sets a clear temperature threshold for CH4 production, we acknowledge that the poor posterior seasonal estimate is unavoidable. This limitation of LPJ-GUESS could restrict the GRaB-AM framework from adjusting the model's wintertime emissions and capturing the overall variability. Consequently, the algorithm compensates for the winter model-data mismatch by adjusting the summer values. This is now discussed in detail in Sect. 4.2 (Pages 476–494). To address this issue, the model should be modified to incorporate mechanisms that simulate microbial activity under frozen conditions, snowpack insulation, and a more detailed representation of soil temperature dynamics, allowing for CH4 emissions even when surface temperatures drop below zero.
  General comments
  
  1) Manuscript structure - Methodology:
  The manuscript is quite technical and its current structure makes it hard for readers to digest the presented results (Section 3). You should re-structure the manuscript in order to improve its logical flow. For instance, all formulas, key metrics and other technical aspects should be described prior to the results section (in the methodology section for instance). It would be appropriate to add a new subsection under the methodology section (let's say - Section 2.6: Statistical metrics) in which you would need to include equations 5 and 6 as well as descriptions for the RMSE, the chi-square test, and other statistics in the context of this study.
  Many thanks for the suggestion. We agree with the technicality of the paper and have now removed the descriptions of statistical metrics from the rest of the paper. Instead, we have created a new section, 2.6, titled 'Statistical Metrics,' where we have provided detailed descriptions of all the metrics used according to your suggestion.
  2) Manuscript structure - Missing discussion:
  
  Although Section 3 is entitled "Results and discussion", I find that there is no authentic discussion in the manuscript. I recommend that you add a discussion (as a section or subsection), in which you should talk about limitations of your study, algorithm, model, etc. by taking into account prior research.
  We appreciate the suggestion. We have now completely rewritten the results and discussion sections, separating them into distinct sections. A new section (Section 4) has been added for the discussion, while Section 3 now contains only the results. We have expanded the discussion of the results with more detailed explanations and additional literature, as per the suggestion. Additionally, Section 4.4 has been added to discuss the possibilities and limitations of GRaB-AM.
  3) Method generalization:
  
  The authors seem to be satisfied with a computationally-intensive algorithm that reduces the so-called cost function and RMSE (Figures 4 and 9) without necessarily improving the ability of the model to simulate wetland methane emissions at the same sites where the algorithm was tested (Figure 6b). So, what's the added value for such an algorithm in terms of model predictions? How would that convince someone interested in applying the algorithm with the end goal of improving their simulations of wetland methane emissions across spatial scales (from the site scale to the global scale)?
  Thank you for your comment. We realized there was a lack of discussion regarding the points you raised, especially about the possibilities and applications of the algorithm. We have now included a detailed discussion about our various metrics for evaluating the performance of GRaB-AM, its limitations, and potential. Please refer to Sections 4.2, 4.3, and 4.4 for further details.
  4) Method scalability:
  
  Given that LPJ-GUESS is a global model, it would be more convincing to show whether/how the calibrated parameters improve the simulation of wetland methane emissions at large scales. Why not show that for - at least - the magnitude of methane emissions from northern wetlands?
  As mentioned in our response to your overview, this has now been completed, and the results are included in the results and discussion section. We calculated total and mean emissions from above 45°N and compared the results with the output of JSBACH-HIMMELI and other model outputs. Please note that we used 45°N instead of 40°N for easier comparability. We also calculated methane wetlands emissions for the region above 60°N and compared mean values against the GCP’s Global Methane Budget estimates. We also have changed our method section (Sect 2.5) accordingly, and have mentioned the results briefly in our abstract and conclusion. Please refer to Sections 3.5 and 4.3 for further details.
  5) Seasonal cycle and cold-season methane emissions:
  
  As your study focuses on northern sites, not capturing cold-season methane flux is a major weakness of your model. In my opinion, this weakness is primarily due to the fact that your methane fluxes are modeled as a function of air temperature but not soil temperature. Various simpler models are able to simulate non-zero methane emissions in winter months (e.g. https://agupubs.onlinelibrary.wiley.com/doi/10.1029/2023GL103037; https://gmd.copernicus.org/articles/14/6215/2021). You should talk about this limitation in your manuscript (results and discussion).
  Many thanks for the very valuable suggestion. The papers are indeed very interesting and are now included and cited in the revised discussion section (please refer to sections 4.2 and 4.3).
  6) Algorithm validation versus Study hypothesis:
  
  You describe your study hypothesis (Pg 2, Ln 53-55) and your plan to do a validation to verify the hypothesis (Pg 2, Ln 64). Does your validation verify the hypothesis? That's not clearly stated in the manuscript. Also, considering your results on the validation of wetland methane emissions (Figure C1), would you say that your calibration is worth the effort?
  The validation test was conducted to verify the capability of the optimized model to simulate independent observations that were not assimilated in the optimization algorithm. Due to the unavailability of more long-term data, we used all the available data we could gather. This was mentioned in Section 3.5, where it is noted that among the sites used for validation, four out of five sites showed a considerable reduction in RMSE (Table 7). The site Wpt, a temperate marsh in Northern America, exhibited a very minor increase in RMSE.
  One of the major observations from the paper is that different types of wetlands may require different parameterizations, based on a broad spatial classification. Temperate wetlands, in general, were the least optimized. It should also be noted that no marshes were used for optimization, so it is not suprising that the comparison of the optimized model against observations for a marsh resulted in a sligthly increased RMSE. The revised paper discusses this in more detail in the section 4.3.
  Specific comments
  Thanks for pointing out the technical error, they are truly valuable. We have now addressed them in the revised manuscript.
  
  Pg 2, Ln 28-29: Could you be more specific about relevant "stresses"? Alternatively, you can use another word for more clarity
  It has changed to ‘Environmental stresses’ .
  Pg 3, Ln 59-60: Please rephrase the part that says "the model process and parameter correlations and uncertainties". It is not clear what correlations you are talking about. Whether there is a link between the words "process" and "uncertainties" in that sentence.
  It has changed to : We also aim to estimate the posterior process and parameter uncertainties, as well as the posterior parameter correlations
  Pg 3, Ln 77: No comma needed between "including" and "estimation of peat…"
  Corrected
  Pg 3, Ln 81: I suggest you say "...an acrotelm with a thickness of 0.3 m…"
  Corrected
  Pg 3, Ln 82: Not clear what "its " stands for here? Is that the peat composition or the layer composition? Please rephrase for more clarification.
  Thanks. It has changes as: ‘Peat hydrology and peat temperature in this layered structure depend on the composition of each layer and prevailing meteorological conditions.’
  Pg 3, Ln 84: No need to add "PFT" after "lichen moss”.
  Corrected
  Pg 4, Ln 86-87: That's a long sentence. Please break it into two sentences that are easy to digest.
  The sentence is now divided into two: "The basic concept of the CH4 module in LPJ-GUESS is a soil carbon pool distributed in proportion to the root distribution. This ’potential carbon pool’ serves as the substrate for methanogens to produce CH4."
  Pg 4, Ln 86: You write that "The carbon in the soil is transformed to CH4 or CO2 depending on the hydrological conditions". Isn't that supposed to be A PORTION of the soil carbon that gets transformed to CH4 or CO2? The way you say it makes it seem that all soil carbon within LPJ-GUESS is either CH4 or CO2. But I presume that there must be some sort of organic matter that do not get access by microbes for their metabolism (i.e. soil carbon preserved from microbial activity).
  You are right, many thanks for spotting this error! It is indeed just a portion of the carbon. We have corrected this in the paper: "A portion of the soil carbon get transformed to \ce{CH4} and/or \ce{CO2} depending on the hydrological conditions."
  Pg 4, Ln 97: Please describe what w_tiller represents to make it easier for readers who will not check Kallingal et al. (2023).
  Thanks for pointing this. We have now added a brief description.
  Pg 5, Ln 110: Don't you need a dash between measurement and years (i.e. measurement-years) for consistency?
  We agree and inserted a dash.
  Pg 5, Ln 112: I suggest you add "for CH4 fluxes" right after "gap-filled data”.
  Thanks for the suggestion. It is corrected.
  Pg 6, Ln 127-128: I find your description of terms from equation (2) to be confusing. I suggest you talk about M_i and R_i for the i-th site, the same way you did it for Y_i.
  This is reformulate to "where $Y_i$, $M_i(x)$, and $R_i$ are the \ce{CH4} observations, model simulations, and the covariance matrix of the observation errors, respectively, at the $i^\text{th}$ site, and x_p$ are the expected prior parameters and $B$ is the prior parameter error covariance matrix."
  Pg 7, Ln 135: How does P(x) relate to J(x)? In other words, how do you relate the functions in equations (2) and (3)?
  Please see the following:
  
  Pg 7, Ln 141: I suggest you insert "CH4 flux" between "actual" and "observations". That is, saying "actual CH4 flux observations”.
  Corrected
  Pg 8, Ln 155: What does "model fat" mean?
  Sorry that was a typo. Thanks for pointing it out it was ‘at’ at the minimum of the cost function.
  Pg 9, Ln 185-197: Please remove the entire paragraph. It has no added value to your Section 3 (which can start right away with Section 3.1).
  The paragraph has been removed, and a shorter version has now been added to Section 4.
  Pg 10, Ln 220: Isn't "Rmoist" supposed to be in mathematical typing format similar to “Rmoist_an"?
  Yes that is true. Corrected
  Pg 15, Ln 311: You need to use a minor/small "c" letter for “contradiction".
  Corrected
  Pg 18, Ln 328: Please add "of CH4 flux" right after "888 gCm-2" for more clarity.
  Corrected
  Pg 20, Ln 359: The acronyms MAS and MAV are not needed in this sentence. Please remove.
  Removed
  Pg 23, Ln 405: No need to use "observed" here. Please remove.
  It was referred to the observed CH4 fluxes, so corrected as ‘The total estimation of CH4 EC fluxes from..’
  Pg 23, Ln 415-416: What's the point of saying that it takes around 480 computational hours to complete the 100,000 iterations on an AMD Ryzen Threadripper processor here? I suggest you move that whole sentence to the methodology section.
  The sentence is now replaced and added to Section 4.4 (Possibilities and Limitations of GRaB-AM).
  Tables
  
  Table 3: I suggest that you re-arrange the table columns as follows: Move column 3 to column 5; Move column 4 to column 3; Move column 5 to column 4.
  Corrected the table.
  Table 4: Please add "Posterior" in front of "std" in the third row.
  Corrected.
  Table 5: Why do you have totals just under the first 7 sites? Do you need these totals in the first place? Same point for Table B.1
  We have changed the alignment of both, this should make more sense now.
  Table 6: "Hemi-boreal" or “Semi-boreal"?
  It is a Hemi-boreal site. The wetland is situated in a transitional ecological region between the temperate and boreal zones
  Table B.1: Why do you have totals just under the first 7 sites? Do you need these totals in the first place? Same point for Table 5.
  The table is corrected according to the suggestion.
  Figures
  
  Figure 2: I suggest that you write "Probability distribution functions (PDFs)", instead of just the acronym.
  Corrected.
  Figure 5: The figure caption misses a description of the horizontal green lines. Are these lines representing back-filled values? If so, please describe that in the caption.
  They are not the horizontal lines, but the zeros.
  Figure 6: Panel a: Why do you only show time series for four sites out 14? Panel b: My interpretation of this figure is that only a few sites compare well with observations even with posterior estimates. Isn't that a major conclusion to be drawn from the figure?
  Panel a: The remaining sites are in the appendix. We chose to display only four sites because displaying all 14 sites would render the figure unreadable. In the revised paper, their details are included in the result section (Sect. 3.4). Panel b: We disagree, the major conclusion drawn from this figure is that for most of the sites the posterior estimates are closer in line with the observations (9 out of 14).
  Note: Figures 9 and C1 in the appendix have been updated in the revised paper. The total RMSE estimate in Figure 9 was incorrect due to hardcoding; we accidentally divided the total RMSE by 14 when calculating the average. The number 14 corresponds to the number of sites used for assimilation. Similarly, the prior and posterior RMSE values were hardcoded on the plot C1 from a previous experiment.
  
  References:
  Kallingal, J. T., Lindström, J., Miller, P. A., Rinne, J., Raivonen, M., and Scholze, M.: Optimising CH 4 simulations from the LPJ-GUESS model v4. 1 using an adaptive MCMC algorithm, Geoscientific Model Development Discussions, 2023, 1–40, 2023.
  
  Citation: https://doi.org/10.5194/egusphere-2024-373-AC1
RC2:
'Comment on egusphere-2024-373', Anonymous Referee #2, 09 Aug 2024

Kallingal et al. focus in their manuscript on reducing the error introduced by model parameters in larger scale CH4 flux estimates from wetlands. The authors use the wetland methane module in the LPJ-GUESS, a global terrestrial ecosystem model. Based on experience from a previous study – Kallingal et al. 2023 – the authors aim at calibrating model parameters at a wider scale (14 sites instead of 1 and the original “worry” of overparameterization for the single site) across different types of wetlands globally. This approach is logic and can be beneficial to the scientific community to better understand CH4 emissions from wetlands in the Northern latitudes.
The study has three objectives: “The present study’s objective is to investigate the capacity of the GRaB-AM framework developed by Kallingal et al. (2023) for calibrating process model parameters in a more general multi-site framework. We aim to optimise selected model parameters for examining to what extent this optimisation improves the model’s ability to simulate the seasonal cycle of CH4 from different wetlands over northern latitudes above 40◦ N. We also aim to estimate the model process and parameter correlations and uncertainties.
Objective 1 is well covered in the manuscript, particularly by the reduction in RMSE as shown nicely ie. in Figure 4. Figure 5 given another comprehensive overview and I am missing a detailed discussion on the discrepancies between the observations and the posterior estimates for several sites and how these could be explained or addressed. Certainly the overall reduction in the uncertainty of the modelled outputs is already great and the suggested approach seems to work for some sites but not at all for others. Thus, a focus on these would be very beneficial.
In addition I remain puzzled on the shift between CH4 processes between the prior and posterior calibration – Figure 7. What would explain such shifts and how does it reflect the reality (ie observations)?
Last but not least, and I can only agree with Reviewer 1, the implications of the suggested model parameter improvement at larger scale remain unknown, even though I was expecting such based on objective No3.
In summary, I value the approach the authors have taken in this study and still think that this can be a valuable contribution to our scientific understanding of CH4 in the Northern latitudes. However, in the current stage I suggest to reject the manuscript and kindly ask the authors to elaborate either further on objective 3 and the discrepancies in their posterior model estimates or reduce the objectives as currently stated.

Citation: https://doi.org/10.5194/egusphere-2024-373-RC2
- AC2:
  'Reply on RC2', Jalisha Theanutti Kallingal, 18 Sep 2024
  Reply letter to the Referee #2
  We are very thankful to the Referee for the constructive comments. In the following, we have addressed the Referee's comments. The manuscript has also been revised accordingly.
  Note : The reviewer comments are referred to in italic font type throughout the texts, and the authors’ responses are referred to as normal font.
  Kallingal et al. focus in their manuscript on reducing the error introduced by model parameters in larger scale CH4 flux estimates from wetlands. The authors use the wetland methane module in the LPJ-GUESS, a global terrestrial ecosystem model. Based on experience from a previous study – Kallingal et al. 2023 – the authors aim at calibrating model parameters at a wider scale (14 sites instead of 1 and the original “worry” of overparameterization for the single site) across different types of wetlands globally. This approach is logic and can be beneficial to the scientific community to better understand CH4 emissions from wetlands in the Northern latitudes.
  Thanks for your feedback. It is truly valuable.
  The study has three objectives: “The present study’s objective is to investigate the capacity of the GRaB-AM framework developed by Kallingal et al. (2023) for calibrating process model parameters in a more general multi-site framework. We aim to optimise selected model parameters for examining to what extent this optimisation improves the model’s ability to simulate the seasonal cycle of CH4 from different wetlands over northern latitudes above 40◦ N. We also aim to estimate the model process and parameter correlations and uncertainties. Objective 1 is well covered in the manuscript, particularly by the reduction in RMSE as shown nicely ie. in Figure 4. Figure 5 given another comprehensive overview and I am missing a detailed discussion on the discrepancies between the observations and the posterior estimates for several sites and how these could be explained or addressed.
  It is true that the manuscript was missing a detailed discussion of the data-model fitting and the issues the algorithm faced in capturing the variability. Acknowledging this and noting that reviewer #1 raised a similar concern, we have added a separate and detailed discussion section in the revised paper (Please refer to Sect.4). Section 4.2 now discusses individual sites and the possible causes of under- or overestimation and fitting issues. Additionally, Sections 4.2. 4.3 and 4.4 now explore the possibilities of resolving these issues through model modification and improvements to GRaB-AM.
  Certainly the overall reduction in the uncertainty of the modelled outputs is already great and the suggested approach seems to work for some sites but not at all for others. Thus, a focus on these would be very beneficial.
  Thank you for the suggestion. We have analyzed the causes in more detail and describe this in Sect. 4.2. There are three major conclusions:
  A model modification is needed for LPJ-GUESS to include more detailed process descriptions and address its inherent non-linearity.
  
  GRaB-AM should be improved by incorporating non-Gaussian assumptions for the parameter and data space. It should also be enhanced to address temporal correlations, further reducing uncertainty.
  
  Different wetlands behave differently based on their types and locations. Using different sets of parameters for different wetland types or geographical locations will certainly improve the budget estimation. For example, as mentioned in Sect. 4.2, many temperate sites used for optimization exhibited lower performance in terms of the cost function reduction.
  
  See the Sect 4.2, 4.3, 4.4 for a detailed discussion of these aspects. Please also see our reply to the reviewer #1 for more specific details.
  In addition I remain puzzled on the shift between CH4 processes between the prior and posterior calibration – Figure 7. What would explain such shifts and how does it reflect the reality (ie observations)?
  These variations and shifts generally indicate the high sensitivity of the parameters to the emission components and highlight the lack of detailed process descriptions in the model. For example, if the model fails to establish vegetation in a particular wetland due to unfavorable input conditions (such as incorrect hydrological or temperature constraints), the suppression of plant-mediated transport becomes inevitable. This might have occurred in Hue and Att, where there was no significant plant-mediated emission in either the prior or posterior results. It could also happen when the optimisation algorithm attempts to compensate for variability in the observations by adjusting parameter values or compensating for wintertime emissions, which are not well represented in the model. From our experience such structural aspects are difficult to diagnose and even more difficult to explain. However, when assimilating total flux observations (i.e. from measurements that do not separately observer the individual emission pathways) into the model, the optimisation algorithm strives to minimize the overall mismatch given the model structure. To accurately estimate these three pathways, the model requires detailed process descriptions and must be validated against these different components. Unfortunately, no detailed assimilation studies have been conducted in this area due to a lack of data availability, particularly for ebullition, which is typically a highly random process.
  Last but not least, and I can only agree with Reviewer 1, the implications of the suggested model parameter improvement at larger scale remain unknown, even though I was expecting such based on objective No3.
  We acknowledge that this was a limitation raised by both reviewers. As we mentioned in our response to reviewer #1,
  we initially planned to use the posterior parameters derived from this study for a large-scale analysis of methane emissions from northern wetland in a separate manuscript, as mentioned in the conclusion section (please see Sect. 5, Lines 570 to 575). However, we do acknowledge that this leaves the paper somewhat incomplete. This issue has now been addressed, and the results are included in the results and discussion section. We calculated total and mean emissions above 45°N and compared these with the outputs from JSBACH-HIMMELI and other models. For ease of comparability, we used 45°N instead of 40°N. We also calculated methane wetlands emissions for the region above 60°N and compared mean values against the GCP’s Global Methane Budget estimates. We also have changed our method section (Sect 2.5) accordingly, and have mentioned the results briefly in our abstract and conclusion. Please refer to Sections 3.5 and 4.3 for more details.
  In summary, I value the approach the authors have taken in this study and still think that this can be a valuable contribution to our scientific understanding of CH4 in the Northern latitudes. However, in the current stage I suggest to reject the manuscript and kindly ask the authors to elaborate either further on objective 3 and the discrepancies in their posterior model estimates or reduce the objectives as currently stated.
  Many thanks for valuing our approach for optimising the model and providing us the opportunity to revise the manuscript and elaborate in more detail on the outcomes of this study.
  
  Note: Figures 9 and C1 in the appendix have been updated in the revised paper. The total RMSE estimate in Figure 9 was incorrect due to hardcoding; we accidentally divided the total RMSE by 14 when calculating the average. The number 14 corresponds to the number of sites used for assimilation. Similarly, the prior and posterior RMSE values were hardcoded on the plot C1 from a previous experiment.
  
  Citation: https://doi.org/10.5194/egusphere-2024-373-AC2

Status: closed

RC1:
'Comment on egusphere-2024-373', Anonymous Referee #1, 11 Jun 2024

Overview

The manuscript by Kallingal et al. presents a data assimilation framework and its application to the calibration of model parameters for the wetland methane module in the LPJ-GUESS, a global terrestrial ecosystem model. The data assimilation framework is based on an adaptive Markov Chain Monte Carlo (MCMC) algorithm that is computationally intensive. Such a calibration approach can be very useful to the scientific community in general and wetland methane modellers in particular, because the choice of model parameter values is sometimes done "manually" in a less systematic way than what the authors described in their manuscript.
According to the authors, the objective of the manuscript is to derive a single set of calibrated parameter values for the wetland methane model in LPJ-GUESS (Abstract; Pg 1, Ln 3). Different aims are associated with that objective (Pg 2, Ln 56-59): (1) to investigate the capacity of the data assimilation framework at multiple sites in the northern high-latitudes; (2) to optimise selected model parameters [10 out 11 parameters]; (3) to examine to what extent this optimisation improves the model’s ability to simulate the seasonal cycle of methane from different wetlands over northern latitudes above 40◦ N.
The current version of the manuscript does not convince me with regards to these study aims. In particular, the manuscript falls short with respect to the second and third aims. As a modeller with experience in wetland methane processes, this work sounds incomplete because the authors focus on reducing the RMSE (e.g. Figure 4) but not on improving the simulation of emissions relative to observations (e.g. Figure 6b). Moreover, considering the potential of the LPJ-GUESS as a global model (Pg 2, Ln 40), it is surprising to see that the authors do not show whether/how their calibrated parameters improve the model performance with respect to large-scale methane emissions from northern wetlands (e.g. total methane emissions from wetlands north of 40◦ N) at least. Furthermore, given that their calibration focuses on methane emissions from northern wetlands, it is disappointing to see how poor their posterior-based estimates are for seasonal methane fluxes in general and cold-season methane fluxes in particular.
Considering the above concerns, I find that the current version of the manuscript would need to be revised before it can be considered for publication.
General comments

1) Manuscript structure - Methodology:

The manuscript is quite technical and its current structure makes it hard for readers to digest the presented results (Section 3). You should re-structure the manuscript in order to improve its logical flow. For instance, all formulas, key metrics and other technical aspects should be described prior to the results section (in the methodology section for instance). It would be appropriate to add a new subsection under the methodology section (let's say - Section 2.6: Statistical metrics) in which you would need to include equations 5 and 6 as well as descriptions for the RMSE, the chi-square test, and other statistics in the context of this study.
2) Manuscript structure - Missing discussion:

Although Section 3 is entitled "Results and discussion", I find that there is no authentic discussion in the manuscript. I recommend that you add a discussion (as a section or subsection), in which you should talk about limitations of your study, algorithm, model, etc. by taking into account prior research.
3) Method generalization:

The authors seem to be satisfied with a computationally-intensive algorithm that reduces the so-called cost function and RMSE (Figures 4 and 9) without necessarily improving the ability of the model to simulate wetland methane emissions at the same sites where the algorithm was tested (Figure 6b). So, what's the added value for such an algorithm in terms of model predictions? How would that convince someone interested in applying the algorithm with the end goal of improving their simulations of wetland methane emissions across spatial scales (from the site scale to the global scale)?
4) Method scalability:

Given that LPJ-GUESS is a global model, it would be more convincing to show whether/how the calibrated parameters improve the simulation of wetland methane emissions at large scales. Why not show that for - at least - the magnitude of methane emissions from northern wetlands?
5) Seasonal cycle and cold-season methane emissions:

As your study focuses on northern sites, not capturing cold-season methane flux is a major weakness of your model. In my opinion, this weakness is primarily due to the fact that your methane fluxes are modeled as a function of air temperature but not soil temperature. Various simpler models are able to simulate non-zero methane emissions in winter months (e.g. https://agupubs.onlinelibrary.wiley.com/doi/10.1029/2023GL103037; https://gmd.copernicus.org/articles/14/6215/2021). You should talk about this limitation in your manuscript (results and discussion).
6) Algorithm validation versus Study hypothesis:

You describe your study hypothesis (Pg 2, Ln 53-55) and your plan to do a validation to verify the hypothesis (Pg 2, Ln 64). Does your validation verify the hypothesis? That's not clearly stated in the manuscript.
Also, considering your results on the validation of wetland methane emissions (Figure C1), would you say that your calibration is worth the effort?
Specific comments

Pg 2, Ln 28-29:

Could you be more specific about relevant "stresses"? Alternatively, you can use another word for more clarity.
Pg 3, Ln 59-60:

Please rephrase the part that says "the model process and parameter correlations and uncertainties". It is not clear what correlations you are talking about. Whether there is a link between the words "process" and "uncertainties" in that sentence.
Pg 3, Ln 77:

No comma needed between "including" and "estimation of peat..."
Pg 3, Ln 81:

I suggest you say "...an acrotelm with a thickness of 0.3 m..."
Pg 3, Ln 82:

Not clear what "its " stands for here? Is that the peat composition or the layer composition? Please rephrase for more clarification.
Pg 3, Ln 84:

No need to add "PFT" after "lichen moss".
Pg 4, Ln 86-87:

That's a long sentence. Please break it into two sentences that are easy to digest.
Pg 4, Ln 86:

You write that "The carbon in the soil is transformed to CH4 or CO2 depending on the hydrological conditions". Isn't that supposed to be A PORTION of the soil carbon that gets transformed to CH4 or CO2? The way you say it makes it seem that all soil carbon within LPJ-GUESS is either CH4 or CO2. But I presume that there must be some sort of organic matter that do not get access by microbes for their metabolism (i.e. soil carbon preserved from microbial activity).
Pg 4, Ln 97:

Please describe what w_tiller represents to make it easier for readers who will not check Kallingal et al. (2023).
Pg 5, Ln 110:

Don't you need a dash between measurement and years (i.e. measurement-years) for consistency?
Pg 5, Ln 112:

I suggest you add "for CH4 fluxes" right after "gap-filled data".
Pg 6, Ln 127-128:

I find your description of terms from equation (2) to be confusing. I suggest you talk about M_i and R_i for the i-th site, the same way you did it for Y_i.
Pg 7, Ln 135:

How does P(x) relate to J(x)? In other words, how do you relate the functions in equations (2) and (3)?
Pg 7, Ln 141:

I suggest you insert "CH4 flux" between "actual" and "observations". That is, saying "actual CH4 flux observations".
Pg 8, Ln 155:

What does "model fat" mean?
Pg 9, Ln 185-197:

Please remove the entire paragraph. It has no added value to your Section 3 (which can start right away with Section 3.1).
Pg 10, Ln 220:

Isn't "Rmoist" supposed to be in mathematical typing format similar to "Rmoist_an"?
Pg 15, Ln 311:

You need to use a minor/small "c" letter for "contradiction".
Pg 18, Ln 328:

Please add "of CH4 flux" right after "888 gCm-2" for more clarity.
Pg 20, Ln 359:

The acronyms MAS and MAV are not needed in this sentence. Please remove.
Pg 23, Ln 405:

No need to use "observed" here. Please remove.
Pg 23, Ln 415-416:

What's the point of saying that it takes around 480 computational hours to complete the 100,000 iterations on an AMD Ryzen Threadripper processor here? I suggest you move that whole sentence to the methodology section.
Tables

Table 3:

I suggest that you re-arrange the table columns as follows: Move column 3 to column 5; Move column 4 to column 3; Move column 5 to column 4.
Table 4:

Please add "Posterior" in front of "std" in the third row.
Table 5:

Why do you have totals just under the first 7 sites? Do you need these totals in the first place? Same point for Table B.1
Table 6:

"Hemi-boreal" or "Semi-boreal"?
Table B.1:

Why do you have totals just under the first 7 sites? Do you need these totals in the first place? Same point for Table 5.
Figures

Figure 2:

I suggest that you write "Probability distribution functions (PDFs)", instead of just the acronym.
Figure 5:

The figure caption misses a description of the horizontal green lines. Are these lines representing back-filled values? If so, please describe that in the caption.
Figure 6:

Panel a: Why do you only show time series for four sites out 14?

Panel b: My interpretation of this figure is that only a few sites compare well with observations even with posterior estimates. Isn't that a major conclusion to be drawn from the figure?

Citation: https://doi.org/10.5194/egusphere-2024-373-RC1
- AC1:
  'Reply on RC1', Jalisha Theanutti Kallingal, 18 Sep 2024
  Reply letter to the Referee #1
  We are very thankful to the Referee for the constructive comments. In the following, we have addressed the Referee's comments. The manuscript has also been revised accordingly.
  Note: The reviewer comments are referred to italic font type throughout the texts, and the authors’ responses are referred to as normal font.
  - According to the authors, the objective of the manuscript is to derive a single set of calibrated parameter values for the wetland methane model in LPJ-GUESS (Abstract; Pg 1, Ln 3). Different aims are associated with that objective (Pg 2, Ln 56-59): (1) to investigate the capacity of the data assimilation framework at multiple sites in the northern high-latitudes; (2) to optimise selected model parameters [10 out 11 parameters]; (3) to examine to what extent this optimisation improves the model’s ability to simulate the seasonal cycle of methane from different wetlands over northern latitudes above 40◦ N. The current version of the manuscript does not convince me with regards to these study aims. In particular, the manuscript falls short with respect to the second and third aims.
  Many thanks for these observations and valuable feedback. We understand the concern regarding the parameters not completely converging with a perfect Gaussian structure, and that some mismatch still persists in the model's ability to capture the variability in the flux observations. However, it is not quite true that the parameters are not optimised. This has been showed in the manuscript by the posterior estimates of the parameter structure, parameter correlations and prior and posterior model estimates and uncertainty quantifications. Complete reduction of the misfit is practically not possible. The degree of misfit reduction varies with the model complexity, non-linearity and subsequent model biases compared to the assimilated data. It should be noted that the posterior parameter distribution is expected to be perfectly Gaussian only under the assumption of a linear model. As discussed in the paper, LPJ-GUESS is highly non-linear and complex, which can lead to challenges due to parameter equifinality (likelihood of different parameter combinations yielding similar results) and convergence issues. From experience of our previous study (Kallingal et al. (2023)), we have concluded that some of the equifinality problem might be inherent to the parametrisation in LPJ-GUESS rather than the optimisation algorithm. These challenges were expected in this study too to some extent.
  Beyond the inherent non-linearity of LPJ-GUESS, the suboptimal convergence of parameters suggests that the assimilated fluxes may carry more complex information about the process parameters than initially assumed, or that there are intricate interactions between parameters. This complexity warrants further investigation into both the model structure, temporal correlations within the assimilated data and the structure of the data. Additionally, this indicates that the model could benefit from incorporating non-Gaussian assumptions in GRaB-AM for future studies, which would better capture uncertainties in parameters with high skewness and kurtosis. These details are now included in the discussion section (Sect. 4, Line 377 to 388) in the revised paper. On top of this we also note the observation of reviewer #2 about the Objective 1, in which he says the “first objective is well covered in the manuscript, particularly by the reduction in RMSE as shown nicely ie. in Figure 4. Figure 5 given another comprehensive overview”.
  - As a modeller with experience in wetland methane processes, this work sounds incomplete because the authors focus on reducing the RMSE (e.g. Figure 4) but not on improving the simulation of emissions relative to observations (e.g. Figure 6b).
  Thanks for the observation. It is true that even though there has been a considerable reduction in RMSE and the cost function, the model still fails to fully capture the variability in the assimilated flux observations. RMSE is the best possible measure to assess posterior model improvement against the observations. We use this metric in this study in addition to the cost function reduction since the cost function itself is another version of the model-data misfit. Therefore, we believe that the reduction in RMSE can be considered as an additional measure for the model calibration.
  Addressing the difficulty of the algorithm in capturing the variability in the flux observations, it should be noted that no systematic behaviour is observed in the posterior model residual (see Fig. 1). This indicates that the remaining mismatch is random, not systematic.
  Figure 1. Prior and posterior residuals showing the resulted variability is random.
  It suggests that the model is capturing the essential dynamics correctly, and the mismatch could be due to factors like observation noise, missing processes in the model description, and/or temporal/spatial resolution differences between the model and the observations. The chi-square value indicates the magnitude of this underestimation to a certain extent. This is now explained in detail in the discussion section (Sect. 4.2). Figure 6b in the paper (mentioned above) displays the mean annual sums of CH4 estimated at all 14 sites. It was observed that 9 out of 14 sites showed improvement. It should be noted that the data were assimilated collectively, which was aimed at reducing the overall mismatch. However, this approach may have encountered difficulty in improving all individual sites while balancing the overall variability.
  - Moreover, considering the potential of the LPJ-GUESS as a global model (Pg 2, Ln 40), it is surprising to see that the authors do not show whether/how their calibrated parameters improve the model performance with respect to large-scale methane emissions from northern wetlands (e.g. total methane emissions from wetlands north of 40◦ N) at least.
  We agree that this is a drawback of the paper and reviewer #2 has also commented on this. Initially, we planned to use the posterior parameters derived from this study for a large-scale analysis of methane emissions from northern wetland in a separate manuscript, as mentioned in the conclusion section (see Lines 530 to 533). However, we do acknowledge that this leaves the paper somewhat incomplete. The details of adding such an analysis are given in the reply to the general comment #4.
  - Furthermore, given that their calibration focuses on methane emissions from northern wetlands, it is disappointing to see how poor their posterior-based estimates are for seasonal methane fluxes in general and cold-season methane fluxes in particular.
  Considering that LPJ-GUESS suppresses emissions under sub-zero temperatures and sets a clear temperature threshold for CH4 production, we acknowledge that the poor posterior seasonal estimate is unavoidable. This limitation of LPJ-GUESS could restrict the GRaB-AM framework from adjusting the model's wintertime emissions and capturing the overall variability. Consequently, the algorithm compensates for the winter model-data mismatch by adjusting the summer values. This is now discussed in detail in Sect. 4.2 (Pages 476–494). To address this issue, the model should be modified to incorporate mechanisms that simulate microbial activity under frozen conditions, snowpack insulation, and a more detailed representation of soil temperature dynamics, allowing for CH4 emissions even when surface temperatures drop below zero.
  General comments
  
  1) Manuscript structure - Methodology:
  The manuscript is quite technical and its current structure makes it hard for readers to digest the presented results (Section 3). You should re-structure the manuscript in order to improve its logical flow. For instance, all formulas, key metrics and other technical aspects should be described prior to the results section (in the methodology section for instance). It would be appropriate to add a new subsection under the methodology section (let's say - Section 2.6: Statistical metrics) in which you would need to include equations 5 and 6 as well as descriptions for the RMSE, the chi-square test, and other statistics in the context of this study.
  Many thanks for the suggestion. We agree with the technicality of the paper and have now removed the descriptions of statistical metrics from the rest of the paper. Instead, we have created a new section, 2.6, titled 'Statistical Metrics,' where we have provided detailed descriptions of all the metrics used according to your suggestion.
  2) Manuscript structure - Missing discussion:
  
  Although Section 3 is entitled "Results and discussion", I find that there is no authentic discussion in the manuscript. I recommend that you add a discussion (as a section or subsection), in which you should talk about limitations of your study, algorithm, model, etc. by taking into account prior research.
  We appreciate the suggestion. We have now completely rewritten the results and discussion sections, separating them into distinct sections. A new section (Section 4) has been added for the discussion, while Section 3 now contains only the results. We have expanded the discussion of the results with more detailed explanations and additional literature, as per the suggestion. Additionally, Section 4.4 has been added to discuss the possibilities and limitations of GRaB-AM.
  3) Method generalization:
  
  The authors seem to be satisfied with a computationally-intensive algorithm that reduces the so-called cost function and RMSE (Figures 4 and 9) without necessarily improving the ability of the model to simulate wetland methane emissions at the same sites where the algorithm was tested (Figure 6b). So, what's the added value for such an algorithm in terms of model predictions? How would that convince someone interested in applying the algorithm with the end goal of improving their simulations of wetland methane emissions across spatial scales (from the site scale to the global scale)?
  Thank you for your comment. We realized there was a lack of discussion regarding the points you raised, especially about the possibilities and applications of the algorithm. We have now included a detailed discussion about our various metrics for evaluating the performance of GRaB-AM, its limitations, and potential. Please refer to Sections 4.2, 4.3, and 4.4 for further details.
  4) Method scalability:
  
  Given that LPJ-GUESS is a global model, it would be more convincing to show whether/how the calibrated parameters improve the simulation of wetland methane emissions at large scales. Why not show that for - at least - the magnitude of methane emissions from northern wetlands?
  As mentioned in our response to your overview, this has now been completed, and the results are included in the results and discussion section. We calculated total and mean emissions from above 45°N and compared the results with the output of JSBACH-HIMMELI and other model outputs. Please note that we used 45°N instead of 40°N for easier comparability. We also calculated methane wetlands emissions for the region above 60°N and compared mean values against the GCP’s Global Methane Budget estimates. We also have changed our method section (Sect 2.5) accordingly, and have mentioned the results briefly in our abstract and conclusion. Please refer to Sections 3.5 and 4.3 for further details.
  5) Seasonal cycle and cold-season methane emissions:
  
  As your study focuses on northern sites, not capturing cold-season methane flux is a major weakness of your model. In my opinion, this weakness is primarily due to the fact that your methane fluxes are modeled as a function of air temperature but not soil temperature. Various simpler models are able to simulate non-zero methane emissions in winter months (e.g. https://agupubs.onlinelibrary.wiley.com/doi/10.1029/2023GL103037; https://gmd.copernicus.org/articles/14/6215/2021). You should talk about this limitation in your manuscript (results and discussion).
  Many thanks for the very valuable suggestion. The papers are indeed very interesting and are now included and cited in the revised discussion section (please refer to sections 4.2 and 4.3).
  6) Algorithm validation versus Study hypothesis:
  
  You describe your study hypothesis (Pg 2, Ln 53-55) and your plan to do a validation to verify the hypothesis (Pg 2, Ln 64). Does your validation verify the hypothesis? That's not clearly stated in the manuscript. Also, considering your results on the validation of wetland methane emissions (Figure C1), would you say that your calibration is worth the effort?
  The validation test was conducted to verify the capability of the optimized model to simulate independent observations that were not assimilated in the optimization algorithm. Due to the unavailability of more long-term data, we used all the available data we could gather. This was mentioned in Section 3.5, where it is noted that among the sites used for validation, four out of five sites showed a considerable reduction in RMSE (Table 7). The site Wpt, a temperate marsh in Northern America, exhibited a very minor increase in RMSE.
  One of the major observations from the paper is that different types of wetlands may require different parameterizations, based on a broad spatial classification. Temperate wetlands, in general, were the least optimized. It should also be noted that no marshes were used for optimization, so it is not suprising that the comparison of the optimized model against observations for a marsh resulted in a sligthly increased RMSE. The revised paper discusses this in more detail in the section 4.3.
  Specific comments
  Thanks for pointing out the technical error, they are truly valuable. We have now addressed them in the revised manuscript.
  
  Pg 2, Ln 28-29: Could you be more specific about relevant "stresses"? Alternatively, you can use another word for more clarity
  It has changed to ‘Environmental stresses’ .
  Pg 3, Ln 59-60: Please rephrase the part that says "the model process and parameter correlations and uncertainties". It is not clear what correlations you are talking about. Whether there is a link between the words "process" and "uncertainties" in that sentence.
  It has changed to : We also aim to estimate the posterior process and parameter uncertainties, as well as the posterior parameter correlations
  Pg 3, Ln 77: No comma needed between "including" and "estimation of peat…"
  Corrected
  Pg 3, Ln 81: I suggest you say "...an acrotelm with a thickness of 0.3 m…"
  Corrected
  Pg 3, Ln 82: Not clear what "its " stands for here? Is that the peat composition or the layer composition? Please rephrase for more clarification.
  Thanks. It has changes as: ‘Peat hydrology and peat temperature in this layered structure depend on the composition of each layer and prevailing meteorological conditions.’
  Pg 3, Ln 84: No need to add "PFT" after "lichen moss”.
  Corrected
  Pg 4, Ln 86-87: That's a long sentence. Please break it into two sentences that are easy to digest.
  The sentence is now divided into two: "The basic concept of the CH4 module in LPJ-GUESS is a soil carbon pool distributed in proportion to the root distribution. This ’potential carbon pool’ serves as the substrate for methanogens to produce CH4."
  Pg 4, Ln 86: You write that "The carbon in the soil is transformed to CH4 or CO2 depending on the hydrological conditions". Isn't that supposed to be A PORTION of the soil carbon that gets transformed to CH4 or CO2? The way you say it makes it seem that all soil carbon within LPJ-GUESS is either CH4 or CO2. But I presume that there must be some sort of organic matter that do not get access by microbes for their metabolism (i.e. soil carbon preserved from microbial activity).
  You are right, many thanks for spotting this error! It is indeed just a portion of the carbon. We have corrected this in the paper: "A portion of the soil carbon get transformed to \ce{CH4} and/or \ce{CO2} depending on the hydrological conditions."
  Pg 4, Ln 97: Please describe what w_tiller represents to make it easier for readers who will not check Kallingal et al. (2023).
  Thanks for pointing this. We have now added a brief description.
  Pg 5, Ln 110: Don't you need a dash between measurement and years (i.e. measurement-years) for consistency?
  We agree and inserted a dash.
  Pg 5, Ln 112: I suggest you add "for CH4 fluxes" right after "gap-filled data”.
  Thanks for the suggestion. It is corrected.
  Pg 6, Ln 127-128: I find your description of terms from equation (2) to be confusing. I suggest you talk about M_i and R_i for the i-th site, the same way you did it for Y_i.
  This is reformulate to "where $Y_i$, $M_i(x)$, and $R_i$ are the \ce{CH4} observations, model simulations, and the covariance matrix of the observation errors, respectively, at the $i^\text{th}$ site, and x_p$ are the expected prior parameters and $B$ is the prior parameter error covariance matrix."
  Pg 7, Ln 135: How does P(x) relate to J(x)? In other words, how do you relate the functions in equations (2) and (3)?
  Please see the following:
  
  Pg 7, Ln 141: I suggest you insert "CH4 flux" between "actual" and "observations". That is, saying "actual CH4 flux observations”.
  Corrected
  Pg 8, Ln 155: What does "model fat" mean?
  Sorry that was a typo. Thanks for pointing it out it was ‘at’ at the minimum of the cost function.
  Pg 9, Ln 185-197: Please remove the entire paragraph. It has no added value to your Section 3 (which can start right away with Section 3.1).
  The paragraph has been removed, and a shorter version has now been added to Section 4.
  Pg 10, Ln 220: Isn't "Rmoist" supposed to be in mathematical typing format similar to “Rmoist_an"?
  Yes that is true. Corrected
  Pg 15, Ln 311: You need to use a minor/small "c" letter for “contradiction".
  Corrected
  Pg 18, Ln 328: Please add "of CH4 flux" right after "888 gCm-2" for more clarity.
  Corrected
  Pg 20, Ln 359: The acronyms MAS and MAV are not needed in this sentence. Please remove.
  Removed
  Pg 23, Ln 405: No need to use "observed" here. Please remove.
  It was referred to the observed CH4 fluxes, so corrected as ‘The total estimation of CH4 EC fluxes from..’
  Pg 23, Ln 415-416: What's the point of saying that it takes around 480 computational hours to complete the 100,000 iterations on an AMD Ryzen Threadripper processor here? I suggest you move that whole sentence to the methodology section.
  The sentence is now replaced and added to Section 4.4 (Possibilities and Limitations of GRaB-AM).
  Tables
  
  Table 3: I suggest that you re-arrange the table columns as follows: Move column 3 to column 5; Move column 4 to column 3; Move column 5 to column 4.
  Corrected the table.
  Table 4: Please add "Posterior" in front of "std" in the third row.
  Corrected.
  Table 5: Why do you have totals just under the first 7 sites? Do you need these totals in the first place? Same point for Table B.1
  We have changed the alignment of both, this should make more sense now.
  Table 6: "Hemi-boreal" or “Semi-boreal"?
  It is a Hemi-boreal site. The wetland is situated in a transitional ecological region between the temperate and boreal zones
  Table B.1: Why do you have totals just under the first 7 sites? Do you need these totals in the first place? Same point for Table 5.
  The table is corrected according to the suggestion.
  Figures
  
  Figure 2: I suggest that you write "Probability distribution functions (PDFs)", instead of just the acronym.
  Corrected.
  Figure 5: The figure caption misses a description of the horizontal green lines. Are these lines representing back-filled values? If so, please describe that in the caption.
  They are not the horizontal lines, but the zeros.
  Figure 6: Panel a: Why do you only show time series for four sites out 14? Panel b: My interpretation of this figure is that only a few sites compare well with observations even with posterior estimates. Isn't that a major conclusion to be drawn from the figure?
  Panel a: The remaining sites are in the appendix. We chose to display only four sites because displaying all 14 sites would render the figure unreadable. In the revised paper, their details are included in the result section (Sect. 3.4). Panel b: We disagree, the major conclusion drawn from this figure is that for most of the sites the posterior estimates are closer in line with the observations (9 out of 14).
  Note: Figures 9 and C1 in the appendix have been updated in the revised paper. The total RMSE estimate in Figure 9 was incorrect due to hardcoding; we accidentally divided the total RMSE by 14 when calculating the average. The number 14 corresponds to the number of sites used for assimilation. Similarly, the prior and posterior RMSE values were hardcoded on the plot C1 from a previous experiment.
  
  References:
  Kallingal, J. T., Lindström, J., Miller, P. A., Rinne, J., Raivonen, M., and Scholze, M.: Optimising CH 4 simulations from the LPJ-GUESS model v4. 1 using an adaptive MCMC algorithm, Geoscientific Model Development Discussions, 2023, 1–40, 2023.
  
  Citation: https://doi.org/10.5194/egusphere-2024-373-AC1
RC2:
'Comment on egusphere-2024-373', Anonymous Referee #2, 09 Aug 2024

Kallingal et al. focus in their manuscript on reducing the error introduced by model parameters in larger scale CH4 flux estimates from wetlands. The authors use the wetland methane module in the LPJ-GUESS, a global terrestrial ecosystem model. Based on experience from a previous study – Kallingal et al. 2023 – the authors aim at calibrating model parameters at a wider scale (14 sites instead of 1 and the original “worry” of overparameterization for the single site) across different types of wetlands globally. This approach is logic and can be beneficial to the scientific community to better understand CH4 emissions from wetlands in the Northern latitudes.
The study has three objectives: “The present study’s objective is to investigate the capacity of the GRaB-AM framework developed by Kallingal et al. (2023) for calibrating process model parameters in a more general multi-site framework. We aim to optimise selected model parameters for examining to what extent this optimisation improves the model’s ability to simulate the seasonal cycle of CH4 from different wetlands over northern latitudes above 40◦ N. We also aim to estimate the model process and parameter correlations and uncertainties.
Objective 1 is well covered in the manuscript, particularly by the reduction in RMSE as shown nicely ie. in Figure 4. Figure 5 given another comprehensive overview and I am missing a detailed discussion on the discrepancies between the observations and the posterior estimates for several sites and how these could be explained or addressed. Certainly the overall reduction in the uncertainty of the modelled outputs is already great and the suggested approach seems to work for some sites but not at all for others. Thus, a focus on these would be very beneficial.
In addition I remain puzzled on the shift between CH4 processes between the prior and posterior calibration – Figure 7. What would explain such shifts and how does it reflect the reality (ie observations)?
Last but not least, and I can only agree with Reviewer 1, the implications of the suggested model parameter improvement at larger scale remain unknown, even though I was expecting such based on objective No3.
In summary, I value the approach the authors have taken in this study and still think that this can be a valuable contribution to our scientific understanding of CH4 in the Northern latitudes. However, in the current stage I suggest to reject the manuscript and kindly ask the authors to elaborate either further on objective 3 and the discrepancies in their posterior model estimates or reduce the objectives as currently stated.

Citation: https://doi.org/10.5194/egusphere-2024-373-RC2
- AC2:
  'Reply on RC2', Jalisha Theanutti Kallingal, 18 Sep 2024
  Reply letter to the Referee #2
  We are very thankful to the Referee for the constructive comments. In the following, we have addressed the Referee's comments. The manuscript has also been revised accordingly.
  Note : The reviewer comments are referred to in italic font type throughout the texts, and the authors’ responses are referred to as normal font.
  Kallingal et al. focus in their manuscript on reducing the error introduced by model parameters in larger scale CH4 flux estimates from wetlands. The authors use the wetland methane module in the LPJ-GUESS, a global terrestrial ecosystem model. Based on experience from a previous study – Kallingal et al. 2023 – the authors aim at calibrating model parameters at a wider scale (14 sites instead of 1 and the original “worry” of overparameterization for the single site) across different types of wetlands globally. This approach is logic and can be beneficial to the scientific community to better understand CH4 emissions from wetlands in the Northern latitudes.
  Thanks for your feedback. It is truly valuable.
  The study has three objectives: “The present study’s objective is to investigate the capacity of the GRaB-AM framework developed by Kallingal et al. (2023) for calibrating process model parameters in a more general multi-site framework. We aim to optimise selected model parameters for examining to what extent this optimisation improves the model’s ability to simulate the seasonal cycle of CH4 from different wetlands over northern latitudes above 40◦ N. We also aim to estimate the model process and parameter correlations and uncertainties. Objective 1 is well covered in the manuscript, particularly by the reduction in RMSE as shown nicely ie. in Figure 4. Figure 5 given another comprehensive overview and I am missing a detailed discussion on the discrepancies between the observations and the posterior estimates for several sites and how these could be explained or addressed.
  It is true that the manuscript was missing a detailed discussion of the data-model fitting and the issues the algorithm faced in capturing the variability. Acknowledging this and noting that reviewer #1 raised a similar concern, we have added a separate and detailed discussion section in the revised paper (Please refer to Sect.4). Section 4.2 now discusses individual sites and the possible causes of under- or overestimation and fitting issues. Additionally, Sections 4.2. 4.3 and 4.4 now explore the possibilities of resolving these issues through model modification and improvements to GRaB-AM.
  Certainly the overall reduction in the uncertainty of the modelled outputs is already great and the suggested approach seems to work for some sites but not at all for others. Thus, a focus on these would be very beneficial.
  Thank you for the suggestion. We have analyzed the causes in more detail and describe this in Sect. 4.2. There are three major conclusions:
  A model modification is needed for LPJ-GUESS to include more detailed process descriptions and address its inherent non-linearity.
  
  GRaB-AM should be improved by incorporating non-Gaussian assumptions for the parameter and data space. It should also be enhanced to address temporal correlations, further reducing uncertainty.
  
  Different wetlands behave differently based on their types and locations. Using different sets of parameters for different wetland types or geographical locations will certainly improve the budget estimation. For example, as mentioned in Sect. 4.2, many temperate sites used for optimization exhibited lower performance in terms of the cost function reduction.
  
  See the Sect 4.2, 4.3, 4.4 for a detailed discussion of these aspects. Please also see our reply to the reviewer #1 for more specific details.
  In addition I remain puzzled on the shift between CH4 processes between the prior and posterior calibration – Figure 7. What would explain such shifts and how does it reflect the reality (ie observations)?
  These variations and shifts generally indicate the high sensitivity of the parameters to the emission components and highlight the lack of detailed process descriptions in the model. For example, if the model fails to establish vegetation in a particular wetland due to unfavorable input conditions (such as incorrect hydrological or temperature constraints), the suppression of plant-mediated transport becomes inevitable. This might have occurred in Hue and Att, where there was no significant plant-mediated emission in either the prior or posterior results. It could also happen when the optimisation algorithm attempts to compensate for variability in the observations by adjusting parameter values or compensating for wintertime emissions, which are not well represented in the model. From our experience such structural aspects are difficult to diagnose and even more difficult to explain. However, when assimilating total flux observations (i.e. from measurements that do not separately observer the individual emission pathways) into the model, the optimisation algorithm strives to minimize the overall mismatch given the model structure. To accurately estimate these three pathways, the model requires detailed process descriptions and must be validated against these different components. Unfortunately, no detailed assimilation studies have been conducted in this area due to a lack of data availability, particularly for ebullition, which is typically a highly random process.
  Last but not least, and I can only agree with Reviewer 1, the implications of the suggested model parameter improvement at larger scale remain unknown, even though I was expecting such based on objective No3.
  We acknowledge that this was a limitation raised by both reviewers. As we mentioned in our response to reviewer #1,
  we initially planned to use the posterior parameters derived from this study for a large-scale analysis of methane emissions from northern wetland in a separate manuscript, as mentioned in the conclusion section (please see Sect. 5, Lines 570 to 575). However, we do acknowledge that this leaves the paper somewhat incomplete. This issue has now been addressed, and the results are included in the results and discussion section. We calculated total and mean emissions above 45°N and compared these with the outputs from JSBACH-HIMMELI and other models. For ease of comparability, we used 45°N instead of 40°N. We also calculated methane wetlands emissions for the region above 60°N and compared mean values against the GCP’s Global Methane Budget estimates. We also have changed our method section (Sect 2.5) accordingly, and have mentioned the results briefly in our abstract and conclusion. Please refer to Sections 3.5 and 4.3 for more details.
  In summary, I value the approach the authors have taken in this study and still think that this can be a valuable contribution to our scientific understanding of CH4 in the Northern latitudes. However, in the current stage I suggest to reject the manuscript and kindly ask the authors to elaborate either further on objective 3 and the discrepancies in their posterior model estimates or reduce the objectives as currently stated.
  Many thanks for valuing our approach for optimising the model and providing us the opportunity to revise the manuscript and elaborate in more detail on the outcomes of this study.
  
  Note: Figures 9 and C1 in the appendix have been updated in the revised paper. The total RMSE estimate in Figure 9 was incorrect due to hardcoding; we accidentally divided the total RMSE by 14 when calculating the average. The number 14 corresponds to the number of sites used for assimilation. Similarly, the prior and posterior RMSE values were hardcoded on the plot C1 from a previous experiment.
  
  Citation: https://doi.org/10.5194/egusphere-2024-373-AC2

Jalisha Theanutti Kallingal, Marko Scholze, Paul Anthony Miller, Johan Lindström, Janne Rinne, Mika Aurela, Patrik Vestin, and Per Weslien

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Short summary

Our study employs an Adaptive MCMC algorithm (GRaB-AM) to constrain process parameters in the wetlands emission module of the LPJ-GUESS model, using CH₄ EC flux observations from 14 diverse wetlands. We aim to derive a single set of parameters capable of representing the diversity of northern wetlands. By reducing uncertainties in model parameters and improving simulation accuracy, our research contributes to more reliable projections of future wetland CH₄ emissions and their climate impact.


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Assimilating Multi-site Eddy-Covariance Data to Calibrate the CH4 Wetland Emission Module in a Terrestrial Ecosystem Model

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Assimilating Multi-site Eddy-Covariance Data to Calibrate the CH₄ Wetland Emission Module in a Terrestrial Ecosystem Model