the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 24 Aug 2026
Environmental controls on methanotrophic oxidation capacity in the southeastern North Sea
Abstract. Shallow coastal seas contribute disproportionately to marine methane (CH₄) emissions, yet the efficiency of the microbial sink that attenuates them remains poorly constrained. Under first-order kinetics, aerobic methane oxidation (MOx) is the product of ambient CH₄ concentration and the fractional turnover rate k′, the latter representing the oxidation capacity of the methanotrophic community. Here we test whether k′ can be predicted from routinely measured environmental variables, drawing on water samples collected during repeated campaigns between 2010 and 2014 across riverine, estuarine, and marine waters of the Elbe and the adjacent southeastern North Sea. In the estuary and adjacent marine waters, a second-order polynomial model based on temperature, salinity, and nitrate reproduced 80 % of the observed spatiotemporal variability in k′ under five-fold cross-validation, indicating that these predictors captured the main environmental controls on k′ and that nonlinear interaction terms cannot be omitted. Neither ambient CH₄ concentration nor phosphate improved model performance, indicating that k′ is not directly controlled by substrate availability or phosphorus limitation. In riverine waters, by contrast, the same approach systematically underpredicted k′ with large uncertainty, suggesting a distinct regional response regime that is likely linked to river-specific environmental controls. Overall, our results highlight that k′ can be parameterized as a dynamic, environmentally dependent term, opening a route to estimating MOx in coastal systems.
Competing interests: At least one of the (co-)authors is a member of the editorial board of Biogeosciences.
Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims made in the text, published maps, institutional affiliations, or any other geographical representation in this paper. While Copernicus Publications makes every effort to include appropriate place names, the final responsibility lies with the authors. Views expressed in the text are those of the authors and do not necessarily reflect the views of the publisher.- Preprint
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Status: final response (author comments only)
- RC1: 'Comment on egusphere-2026-4822', Anonymous Referee #1, 22 Sep 2026
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RC2: 'Comment on egusphere-2026-4822', Anonymous Referee #2, 11 Oct 2026
This manuscript presents a valuable investigation into parameterizing the fractional turnover rate (k') of aerobic methane oxidation using routinely measured environmental variables across a land-sea gradient. This work addresses an important knowledge gap within coastal carbon budgets, by seeking to replace static fixed‑rate constants with a dynamic formulation dependent on ambient environmental conditions. The statistical analysis is methodologically rigorous, deploying polynomial regression, repeated five‑fold cross‑validation, out‑of‑fold prediction metrics, and variance inflation factor diagnostics to mitigate overfitting and assess multicollinearity. Nevertheless, multiple conceptual and region‑specific points require further elaboration and clarification prior to publication.
Major comments:
1. While the second-order polynomial model (T+S+NO3-) successfully reproduces approximately 80% of the spatiotemporal variability in the estuarine and marine regions, it completely fails in the riverine Elbe where k' is highest and most variable. The authors attribute this failure to a distinct regional response regime or uncaptured abiotic variables. However, this limits the applicability of the proposed framework across the entire coastal continuum. The manuscript would be strengthened by a more thorough discussion or secondary analysis exploring why standard abiotic predictors break down entirely in the riverine zone, and whether factors such as high turbidity, short water residence times, or specific organic matter inputs dominate the Elbe region.
2. The selected predictors (T, S, and NO3-) perform exceptionally well in terms of predictive metrics (R2 = 0.82 for validation), but they largely act as macro-environmental proxies for seasonality and water-mass mixing rather than direct physiological controls on methanotrophs. Given that k' is inherently an integrated outcome of active methanotroph abundance, community composition, and cell-specific activity, the authors correctly point out in the conclusion that future work must incorporate microbial data. The discussion should more explicitly address how these statistical proxies link to underlying microbial community shifts, especially since community composition can change rapidly across salinity and nutrient gradients. Additionally, please address whether high collinearity among nutrient variables within the riverine subset could impair model‑selection outcomes, even though multicollinearity was evaluated using VIF metrics computed over the full dataset.
3. The finding that ambient methane concentration contributes no predictive information for k' runs counter to classical enzyme kinetics (such as Michaelis-Menten frameworks). While the authors attribute this to oxidation capacity being driven by broader environmental conditions rather than substrate supply, the authors should clarify whether the narrow concentration ranges sampled in certain sub-regions or analytical limitations could have masked a kinetic response.
4. Nitrate improves model performance primarily via the temperature‑nitrate interaction term (T×NO3-). The text hypothesizes that warm, high‑nitrate conditions support higher methanotroph biomass. However, the present dataset cannot disentangle whether nitrate functions as a direct nutritional resource supporting methanotroph growth, or merely acts as a passive tracer for river‑derived water masses and associated co‑varying unmeasured variables. This critical ambiguity should be explicitly acknowledged within the Discussion, and overinterpretation of nitrate’s direct causal biological effects should be avoided
Minor comments:
Table 2: Please standardise the formatting of ion chemical symbols throughout the table.
Figure 2： This figure uses non‑linear y‑axes for visualization. While this is reasonable, please add explicit annotation within each panel to alert readers about non‑linear scaling, to avoid visual misinterpretation of box‑plot magnitudes.
Line 57: Seasonal differences in the fractional contribution of MOx to total methane loss are attributed primarily to variability in k'. However, the environmental drivers modulating k' also simultaneously alter other relevant variables (e.g. dissolved methane concentrations, nutrient availability). This confounding co‑variation renders the original statement overly simplistic and requires revision.
Line 128: High statistical goodness‑of‑fit does not equate to established causal mechanisms. Some predictors incorporated in the optimal model may represent confounding covariates that correlate spatiotemporally with true underlying drivers of k', rather than exerting direct biological control.
Line 132: Correlation cannot establish causation. Please clarify how the authors rule out the possibility that predictors retained within the final optimal model are confounders rather than mechanistic drivers shaping k'?
Line 224: Is nitrate a direct causal driver of k', or a confounding variable whose spatiotemporal pattern merely coincides with that of the genuine underlying driver?
Line 278: Note that temperature and salinity act as proxies for water-mass mixing processes.
Line 297: Please add brief consideration that ammonium may exert inhibitory effects upon MOx activity.
Line 267: How do these environmental factors modulate k'? Do these factors exert consistent directional effects (uniformly positive or uniformly negative) upon k'?
Line 305: Please expand discussion regarding the potential role of ammonium?
Line 351: Ambient methane concentration contributed no predictive information, suggesting that oxidation capacity is determined by the environmental conditions experienced by the methanotrophic community rather than by substrate supply?
Lines 393, Line 390: Formatting inconsistencies appear across the reference list (including inconsistent journal‑abbreviation conventions). The reference section should be carefully proof‑read to enforce uniform formatting.
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- 1
The authors present a study reconstructing k′, the water-column first-order rate constant usually prescribed as a fixed value in methane oxidation, from routinely measured environmental variables. To do so, the authors compile existing campaign data from the Elbe-estuary-German Bight continuum (which is actually pretty rich for this radiotracer measurement), select a proper statistical approach, and interpret the results in a careful way. In general, the manuscript is clear and well written, and I recommend that after a revision, it can be considered for publication in Biogeosciences. Below I outline the points that would improve the manuscript.
Specific comments:
p1 l19 "not directly controlled by substrate availability or phosphorus limitation". I would say this statement is too strong: the absence of an improvement in model performance does not by itself support a causal conclusion.
p7 l123 "As a subset of GAMs, polynomial regression therefore provides a simple parametric framework...". Did you benchmark against a more flexible model, e.g. a tree-based model or neural network, to quantify how much predictive performance the parametric framework costs?
p10 l166 Please verify the salinity reported for station 8.57, as its standard deviation looks suspicious.
p12 l192 Please state in the Methods that both surface and bottom data were used for model development.
p14 l204-205 Can N:P ratios play a role here and give a better estimation compared to the individual nutrient?
p17 l245 Please clarify the model-selection criterion used to select the final model when several candidate models showed similar predictive performance.
p20 l301-307 The discussion of NH₄⁺ is missing, though it was included in the correlation matrix.
p20 l308 A recent study on methane oxidation by Borges et al. (2026) would strengthen the discussion of the riverine part.
p21 l326-331 The cited study was conducted in a lake and therefore may not be directly comparable.
Supplement p5 l77 How do the observation vs. predicted plots look for these two regimes? Show them either here or elsewhere, as appropriate.
Technical corrections:
p8 l156 "reported by (Kappenberg and Grabemann, 2001)": remove the parentheses.
p11 l167 Replace "correlations analysis" with "correlation analysis".
p14 l204-205 Some correlation values are hard to read. Please improve the readability of these two figures.
p16 l231 The Abstract gives 80 %, whereas here it is 0.82 (Figure 4a also shows 0.82). Please make these consistent.
p28 l506-511 Osudar et al. 2017a and 2017b are the same reference.
Supplement p2 l40 Replace “H2SO4” with H₂SO₄.
Supplement, p3 l53 The detection limit 0.010 ± 0.009 is missing the unit, and the second “< 10 nM” should be “> 10 nM”. Also, nM should be replaced with nmol L⁻¹ here and elsewhere.