We thank the reviewer for important and helpful comments which will allow us to improve our manuscript. Below, we show the reviewers’ comments in italic text, and our responses to all raised concerns are formatted as standard text.

“The goal of this study was to determine how root oxygen loss (ROL) affects wetland soil respiration. This is an important and timely topic because wetland plant ROL clearly affects soil biogeochemical processes, as documented by many of the papers that the authors cite.”

We are glad that the reviewer appreciates the topic of our manuscript, the key role of ROL in the biogeochemistry of wetlands, such as estuarine marshes.

“This study falls short, however, because it is overly simplistic and does not take into account that ROL is spatially or temporally heterogenous.“

Our model represents a highly simplified approach of soil biogeochemical processes, but, in our opinion, this is not necessarily a shortcoming of our study.

Plants are usually represented by average functional types in ecosystem models of estuarine marshes, meaning a uniform base rate of root oxygen loss (ROL). In reality, plant species and individuals may strongly differ in ROL, which likely affects soil heterotrophic respiration rate. In contrast to other aspects of the complex biogeochemistry in estuarine marsh soils, impacts of plant trait diversity have been little considered in modelling approaches so far. Thus, the goal of our study is to assess the potential effect of variation in ROL due to plant trait diversity compared to a uniform ROL for all plants at a given location.

We do not, however, aim to provide an accurate estimate of soil carbon fluxes for a given marsh ecosystem. This would require the inclusion of a multitude of physiological and biogeochemical processes in the model, including the effect of spatial and temporal heterogeneity of O2 concentration, as mentioned by the reviewer. Since these processes are associated with considerable parameter uncertainty, it is not guaranteed that simulating them will substantially improve the assessment of the effect of plant ROL variation, which is the focus of our study.

To make our results more reliable, we carried out additional sensitivity analysis and tested the effect of uncertain parameter values on our main results. Moreover, we will clarify in the next version of our manuscript that we model soils under tidal influence, with fractions of both aerobic and anaerobic conditions, not the permanently water-logged part where aerobic respiration plays little role.

“Moreover it considers oxygen in air rather than the dissolved phase that is typical of wetland rhizospheres.”

We agree with the reviewer; the DAMM model that we use as a basis for our modelling approach indeed only considers diffusion of oxygen in soil air, thereby neglecting the substantially slower diffusion in water. We focus, however, on aerobic respiration that requires the occurrence of aerobic microsites close to the root surface. In a revised manuscript, we will clarify this point and state that we neglect anaerobic processes in our study.

“Root oxygen loss is generally into saturated, anoxic soils where heterotrophic microbes would compete with abiotic oxidative processes. This may be outside of the scope of the study but important to consider because increasing oxygen may not increase heterotrophic respiration linearly.”

We thank the reviewer for this suggestion. The basis for our results (Fig. 3) is the variation in the concentration of oxygen close to the sites of microbial respiration, not the flux of ROL that generates these concentration values. In the next version of the manuscript, we will describe more clearly that we do not mechanistically model the diffusion of oxygen from the root to the site of respiration, but simply assume a range of possible oxygen values at these sites. We will also discuss the important topic of competition for oxygen between microbes and abiotic processes.

“Regardless the models seem to better describe O2 penetration into wetland surface soils (top few mm-cm) during periods of drying than O2 release into the rhizosphere. It lacks the spatial complexity of O2 diffusion in a soil matrix and how the concentration will change with distance from the root and time since release.”

As described above, we do not explicitly consider all aspects of oxygen diffusion in our approach, since we aim at representing a range of possible concentration values caused by plant diversity and their effect on aerobic respiration. We agree with the reviewer that a spatially explicit model of oxygen distribution would be required to accurately estimate all soil carbon fluxes, not only CO2 from aerobic respiration but, in particular, methane fluxes.

“The study assumes that respiration is a function of bulk SOC. This excludes the plant trait of root carbon exudation and differences in bioavailability of recent exudates vs. existing rhizosphere organic matter.”

We are thankful to the reviewer for highlighting the role of root exudates. Indeed, variation in root exudation between plants may, too, have a substantial impact on the carbon balance of estuarine marshes. In our study, however, we focus on ROL since estimates on root exudation rates are not yet available for the locations where the soil samples were collected. We will discuss this aspect in more detail in a revised version of the manuscript.

“Respired CO2 will be released into a saturated matrix where it will become part of the DIC pool and not necessarily contribute to carbon emissions (as described in the title).”

We agree with the reviewer that CO2 produced by respiration may be taken up again by other processes before being emitted from the soil. However, as the concentration of carbon in the DIC pool increases, the disequilibrium to the surface air will become stronger, leading to an ultimate increase in CO2 emissions in the steady state unless DIC is stored in other long-term pools. We will revise the title of the manuscript to be more precise.

“There is not a clear link to plant traits either as the model simulation uses an average plant type (L137).”

In our approach, we represent both an average plant type and a range of individual plants that differ only in their rate of ROL. As described above, the different fluxes of oxygen from root to soil are, however, not mechanistically simulated, but instead a range of oxygen concentration values approximates the effect of variation in plant ROL.

“The authors should see Zhou et al Biogeochemistry (2024) 167:945–963 ’Simulated plant‑mediated oxygen input has strong impacts on fine‑scale porewater biogeochemistry and weak impacts on integrated methane fluxes in coastal wetlands’”.

We thank the reviewer for pointing us to the recently published paper by Zhou et al. We agree that a mechanistic, spatially and temporally explicit modeling approach of pore water biogeochemistry is important for an accurate estimation of methane release from saturated soil. Our study, however, aims at a different process, aerobic respiration close to the root surfaces, and thus makes simplifying assumptions regarding the saturated part of the soil (i.e. we neglect anaerobic processes). We did not find estimates of CO2 release due to aerobic respiration in Zhao et al., but their setup of different oxygen saturation values in the pore water (white boxes in Fig. 4 c1) seems to be conceptually similar to our approach: They test for the effects of variation (spatial heterogeneity) compared to a homogeneous distribution. We thus think that our approach can be seen as complementary.

“L54 and L91 – write out the model names before using the acronym”

We will ensure that all model names are written out in full upon first mentioning, writing "Dual Arrhenius and Michaelis-Menten (DAMM) kinetics model", for example.

“L111. How was the activation energy of the reaction determined (EaSx)? Did this vary as a function of C reactivity? The value is in Table 1 – is there a reference?”

“L115. How were p and Dliq determined? The values are in Table 1 – are there references?”

We thank the reviewer for pointing this out. The reference for these three parameter values is the paper by Davidson et al. (2012). Since we did not examine the temperature response of the respiration rate in our study, we did not recalibrate the value of EaSx. Moreover, we also kept the original values of p and Dliq, since these are constant multipliers of the concentration of soluble substrate as a function of total substrate, and are thus not likely to alter substantially the effect of oxygen on the reaction rate. To test for the effect of uncertain parameters, we ran an additional sensitivity analysis; the results are shown below in Tab. 1 We found that the modelled absolute respiration rate is relatively sensitive to the parameter Ea, while p and Dliq have little effect. However, the parameter variation has no effect on the difference between the average trait approach and the diverse trait approach since the relative response to parameter variation is the same. Moreover, the parameters p and Dliq have the same relative effect since they are constant multipliers of the substrate conversion. We will include this in a revised version of our manuscript.

Table 1: Results of the Sensitivity Analysis. Respiration (in mg C cm^-3h^-1) is calculated at the middle of the range of substrate concentration (0.15 g C cm^-3)

“Equation 4. Why use parameters for oxygen in air? Wetland soils are generally saturated below the top few cm, and gases would be dissolved in a liquid phase.”

We acknowledge the reviewer's concern regarding the use of parameters for oxygen diffusion in air, since this would indeed not be appropriate to describe diffusion of oxygen in water, i.e. in permanently water-logged soil. In our study, however, we focus on soils in estuarine marshes, which are characterized by tidal dynamics and regular fluctuations in water table and soil moisture distribution. In our opinion, the simplified representation of oxygen availability used in the DAMM model is sufficient to account for the variation in oxygen concentration due to alternating water saturation and the effects on aerobic respiration rate. As written above, we consider only respiration at aerobic microsites and how increased oxygen availability by ROL may affect this. Oxygen is emitted along the entire root length in several wetland plant species, such as Phragmites australis and Spartina alterniflora, facilitating aerobic respiration in otherwise anaerobic environments (Armstrong and Armstrong, 2005; Colmer, 2003). We do not consider the process of CO2 production by respiration in entirely anoxic conditions. We agree with the reviewer that in these conditions, the role of ROL for methane and sulphate dynamics is more relevant. We will add these clarifications to a revised version of the manuscript.

“Section 2.1. It is not clear how these experiments mimic conditions with and without ROL.”

We thank the reviewer for this point and we agree that the description should be extended. In a revised version of the manuscript, we will explain more clearly that we use the existing scheme of the DAMM model for oxygen diffusion to approximate the effect of plant aerenchyma on soil oxygen concentration via ROL (see also the paragraph before Sect. 2.1.), rather than explicitly simulating the spatial and temporal heterogeneity of ROL. We assume that negligible ROL corresponds to fully water-saturated soil in the model, while dry soil would correspond to the maximum possible ROL. We will point out that the latter condition is unlikely to occur in nature, but the uncertainty regarding the effects of ROL on soil oxygen availability (e.g. (Colmer, 2003)) would make setting a different upper limit arbitrary.

“L137. What is the average plant type and how is average plant ROL known?”

In our model, the "average plant type" corresponds to the representation of plants that are often used in ecosystem-scale models of estuarine marshes, where inter-and intra-specific functional diversity of plant traits, including ROL, is aggregated into average traits, applied to one or a few plant functional types. The little available data on ROL in marsh soils of the Elbe estuary currently do not allow us to compute an accurate average value of ROL, which is why we assume that a soil water saturation of 30% is representative of the average conditions in the rhizosphere in the part that is not permanently water-logged, including an intermediate value of ROL. We conducted a sensitivity analysis to test the effect of uncertainty in the average value of ROL on our estimates by varying the assumed soil water saturation (Theta) by ±20%. The mean respiration over the range of substrate concentrations changed by -17% and +5% for higher and lower Theta for the average trait approach and by -15% and +1% for the diverse one. The mean impact on the difference between the approaches was larger, ranging from -51% at lower to +42% at higher Theta, which means that ROL becomes less important at drier soil conditions. We will include these results in the revised manuscript.

L146 More details about the experiments that the model was based on are needed. Incubations were under aerobic conditions but was the water flow static or flow-through? If the latter, were conditions monitored to prevent resource limitation – or inhibition by the build-up of metabolites? Were potential microbial metabolites monitored to support the assertion of aerobic conditions (e.g., H2S)?  Were the soils saturated? What was the salinity? Did the DO levels mimic the rhizosphere? What were the SOC levels? The reader is referred to 2 other papers to learn about the methods; including a brief version of that information and the rationale for how the incubations support the present study would be valuable.

We thank the reviewer for raising these points. We agree that the description of the experiment was not self-explanatory. Water was added at the beginning of the incubation, therefore there was no water flow during the experiment. Microbial metabolites were not measured. Soils were not water-saturated but adjusted to 60% water-holding capacity at the beginning of the experiment. Oxygen limitation during the experiment was prevented by flushing the headspace with synthetic air.

We will include the following information in a revised version:

For the soil incubation experiment, 20 g dry mass equivalent of sieved soil samples (2 mm) were adjusted to 60% water holding capacity. The water-adjusted samples were placed in 1000 ml flasks and incubated in the dark at 20 °C for a period of up to 465 days. Headspace samples (1 ml) were collected at regular time intervals for CO₂ measurements by gas chromatography (JAS 6890N, Germany). To maintain a higher pressure within the flasks compared to the surrounding atmosphere and to prevent oxygen deficiency due to excessive CO₂ build-up (> 2.5% in headspace), synthetic air was added when necessary.

Regarding the first part of the modelling approach, we will add: ICBM is a classical and widely used 2-pool model following first-order kinetics of decomposition, with a fast and slow carbon pool. The decomposition rate constants and humification rate constant used in that model were calibrated against the CO2 concentrations measured in the lab incubation study data mentioned above by using a gradient descent optimization method. Methodological details can be found in (Knoblauch et al., 2013) and (Beer et al., 2022)

The incubations and the subsequent ICBM simulations were carried out to estimate characteristic respiration rates for soils in the marshes of the Elbe estuary for a wide range of substrate concentrations. These were then used to calibrate the DAMM model and carry out our analysis of ROL variation effects. We will make this point more clear in a revised version of the manuscript.

References :

Armstrong, J. and Armstrong, W.: Rice: Sulfide-induced barriers to root radial oxygen loss, Fe2+ and water uptake, and lateral root emergence, Ann. Bot., 96, 625–638, https://doi.org/10.1093/aob/mci215, 2005.

Beer, C., Knoblauch, C., Hoyt, A. M., Hugelius, G., Palmtag, J., Mueller, C. W., and Trumbore, S.: Vertical pattern of organic matter decomposability in cryoturbated permafrost-affected soils, Environ. Res. Lett., 17, 104023, https://doi.org/10.1088/1748-9326/ac9198, 2022.

Colmer, T. D.: Long-distance transport of gases in plants: A perspective on internal aeration and radial oxygen loss from roots, https://doi.org/10.1046/j.1365-3040.2003.00846.x, 1 January 2003.

Knoblauch, C., Beer, C., Sosnin, A., Wagner, D., and Pfeiffer, E. M.: Predicting long-term carbon mineralization and trace gas production from thawing permafrost of Northeast Siberia, Glob. Chang. Biol., 19, 1160–1172, https://doi.org/10.1111/gcb.12116, 2013.

We thank Reviewer #2 for their thorough evaluation and constructive feedback, which has helped us significantly enhance the clarity, methodology, and framing of our manuscript. Below, we reproduce each of the reviewer’s comments in italic text, followed by our detailed responses.

General assessment, scope and novelty:

“This study aimed to examine the effects of plant root traits on soil carbon emissions in estuarine marshes using a modeling approach. The authors conducted two model experiments using the DAMM model to simulate microbial respiration: one with constant soil O2 (fixed soil moisture) and another with variable soil O2 (influenced by soil moisture). They observed differing respiration response to soil carbon content under the two conditions.

While soil heterotrophic respiration in estuarine marshes is a critical component of carbon cycling and warrants further investigation, the study employed a relatively simple model based on incubation data. This limits the ability to extrapolate the findings across broader spatial and temporal scales. Additionally, the results are not particularly novel, as the role of O2 in regulating respiration under wetland conditions is well established. The link between the root traits and the model experiments is also unclear. The simulations primarily focused on the effects of soil moisture (and associated O2 availability) on respiration, rather than explicitly root traits. The authors should clarify their methodological framework and more clearly articulate the study’s novelty.”

Response:

We thank the reviewer for these important points and have made explicit clarifications regarding the study’s novelty and methodological framework. The novelty of our study lies specifically in quantifying the aggregation error that arises from spatial variability in rhizosphere oxygen (O₂) levels driven by root oxygen loss (ROL). This factor has not been quantified so far for estuarine marsh ecosystems, but it is key for modelling their carbon fluxes. Below, we further elaborate on these points:

Limited ability for extrapolation:

Our objective was not to directly provide a landscape-scale parameterisation. Instead, we explicitly aimed to assess the ecological relevance of O₂ heterogeneity driven by ROL for heterotrophic respiration in marsh ecosystems. Incubation experiments using real marsh soil samples are thus methodologically appropriate and robust. This intent is explicitly clarified in the manuscript:

“Here, we estimate the effect of plant-induced variation of oxygen levels in soils on heterotrophic respiration in estuarine

marshes using the DAMM model (Davidson et al., 2012). To estimate the aggregation error, we simulate the respiration

response to soil carbon for a range of different oxygen levels and compare this to a model configuration that only considers

one average soil oxygen level.” (p. 3, L 90‑93).

Novelty regarding the role of O₂:

We acknowledge that the general role of O₂ in wetland soil respiration is well-known. However, our study specifically addresses the quantitative implications of O₂ variation on respiration, highlighting the aggregation error introduced when spatial variation is replaced by a single mean O₂ value. This quantification has important implications for improving accuracy in large-scale ecosystem models. We have explicitly articulated this objective in the revised manuscript:

“By comparing the two model configurations (see Fig. 3) we find that the variation of the plant trait root oxygen loss leads to a 10% reduced respiration rate, when averaged over all soil oxygen levels, compared to the model configuration driven only by one average soil oxygen concentration... (p. 7- L 72-74).

“This illustrates the potentially large impacts that may arise from spatial heterogeneity of plant species or changing community composition of plants on the carbon balance of estuarine marshes.” (p. 1- L 26-27).

“Considering only our simple approximation of varied root oxygen loss, and assuming global soil carbon emissions of 31 Tg a⁻¹ via heterotrophic respiration from salt marshes (Alongi, 2020), the estimated reduction by 10% would correspond to roughly 8% of global annual anthropogenic carbon emissions (Intergovernmental Panel on Climate Change (IPCC), 2023).” (p. 9- L 195-198)

A comparison with the detailed pore-scale model by Zhou et al. (2024) has also been included:

Additionally, we include a direct comparison with the detailed pore-scale model by Zhou et al. (2024):

“While Zhou et al. (2024) employed a highly detailed pore-scale model explicitly simulating plant-mediated oxygen transport and fine-scale biogeochemical processes, our approach quantifies aggregation errors resulting from spatial averaging in simpler ecosystem models. Thus, these approaches are complementary, each providing valuable insights into different aspects of oxygen dynamics and carbon cycling in estuarine marshes.”

Unclear link between root traits and experiment:

The experiment was designed explicitly to estimate the effects of O₂ variation on respiration. Root traits serve as the underlying cause of this variation. We acknowledge that we do not explicitly simulate the mechanistic link between specific root traits and soil O₂ levels, but rather we impose observed O₂ variation derived from the literature. This approach allows us to isolate and quantify the aggregation error without introducing speculative parameters. We detailed this approach clearly in the revised manuscript:

“ROL itself is not simulated. Instead, its observed outcome, rhizosphere O₂ concentration, is imposed directly, following the empirical range detailed above. This allows us to quantify the impact of ignoring heterogeneity without speculative parameterisation of the many plant traits that underlie ROL.” (P.6- L 227-229).

Specific comments

1 Abstract:

“Abstract: The background is too long, compared to the methods and results of this study. I recommend the authors to shorten the background information and expand the method part.."

Response:

We thank the reviewer for this suggestion. In the revised Abstract, we shortened the background to two sentences and added one sentence that summarises the two simulation experiments.

Inserted text (p. 1, L 14‑24):

“ Estuarine marshes are crucial components of coastal environments around the world and provide numerous ecosystem services, such as carbon sequestration. Plant-microbe interactions are potential key drivers of organic carbon cycling in these ecosystems. Roots of marsh plants, for instance, leak oxygen into otherwise anoxic sediments, creating a patchy rhizosphere O₂ field that controls heterotrophic respiration. Thereby, traits such as root oxygen loss (ROL) may strongly differ between plant species, leading to strong variation in respiration rates. Ecosystem models that aim to quantify the carbon balance of marshes, however, usually replace this variety with one bulk value, leading to potential biases in carbon flux estimates. We calibrated a Dual Arrhenius–Michaelis–Menten (DAMM) scheme with laboratory incubations and ran two experiments: (i) uniform O₂ versus (ii) the full observed O₂ distribution. Spatial averaging of O₂ reduced the simulated aerobic CO₂ efflux by ≈ 10 %.  This illustrates the potentially large impacts that may arise from spatial heterogeneity of plant species or changing community composition of plants on the carbon balance of estuarine marshes. We thus suggest implementing trait variation in marsh ecosystem models.”

2 L21 – definition of the “root-trait”

“how can the modification of soil O2 concentration be considered as a key plant trait?”

Response: 

We thank the reviewer for raising this important conceptual point. In the revised manuscript, we now clarify that the plant trait in question is the rate of root oxygen loss (ROL) rather than the resulting soil O₂ concentration itself. Following the generic trait definition of Violle et al. (2007), “any phenotypic property that affects ecosystem processes,” ROL qualifies because it is an emergent, plant‑controlled flux governed by root porosity, aerenchyma development, and metabolic demand. Numerous rhizosphere studies show that variation in ROL is the primary proximate control on local O₂ tension and hence on aerobic decomposition rates in marsh sediments (Visser et al., 2000; Armstrong & Armstrong, 2005; Kühl et al., 2021).

Inserted text (p. 3, L 149‑152)

“In the functional‑trait framework (Violle et al., 2007), we treat the flux density of root oxygen loss (ROL) expressed as O₂ flux per root surface area as the focal trait, because ROL directly affects rhizosphere O₂ level and thereby regulates aerobic heterotrophic respiration (Visser et al., 2000; Armstrong & Armstrong, 2005; Kühl et al., 2021). Spatial and temporal variability in ROL therefore propagates to variability in soil O₂ without invoking additional soil‑physical drivers.”

3 L40 – additional literature

“Please provide more references to link the plant roots to root O2 loss.”

Inserted text (p. 6, L 233‑234)

“…intra‑ and inter‑specific variation in ROL has been documented for marsh grasses, rice and sedges (Holmer & Pedersen, 2003; Visser et al., 2000; Armstrong & Armstrong, 2005; Kühl et al., 2021), supporting the empirical O₂ range used here.”

4 L90-91 – choice of the DAMM model

“Why the DAMM model was selected in this study?”

Response:

We thank the reviewer for requesting a more detailed justification. The decisive argument is that DAMM contains an explicit Michaelis–Menten O₂‑limitation term (Davidson et al., 2012). This mechanistic representation is essential for our objective of testing how different prescribed rhizosphere‑O₂ distributions propagate into respiration.

The Dual‑Arrhenius–Michaelis–Menten (DAMM) equation treats oxygen as a true saturating substrate (Ks‑type). Consequently, we can vary [O2] over several orders of magnitude, exactly the range observed around marsh roots while holding all other drivers constant. Most models of carbon cycling at the land‑surface, by contrast, link respiration to soil moisture or redox potential, so O₂ cannot be manipulated independently and the aggregation error we target cannot be isolated. The Michaelis–Menten form also guarantees correct asymptotic behaviour, preventing the non‑physical extremes that can arise from linear moisture scaling.

Inserted text (p. 4, L 163‑170)

“We selected the DAMM model to test the effect of variation in root oxygen loss on soil microbial activity and ecosystem carbon emissions since it includes an additional term for oxygen limitation of heterotrophic respiration (Eq. 1), while most models of soil organic matter decomposition focus only on carbon as a substrate, being developed for well-aerated soils.

DAMM contains an explicit Michaelis–Menten O₂-limitation term (Davidson et al., 2012), allowing us to prescribe the full field-observed rhizosphere O₂ distribution and thereby quantify the resulting aggregation bias. Moreover, it requires only six parameters, which keeps the uncertainty analysis tractable. DAMM has also reproduced hourly CO₂ fluxes in tidal-freshwater marshes (Knox et al., 2021), demonstrating field applicability.”

5 L102 – model simplicity

“Many processed models considered the impacts of temperature, soil moisture (water-filled porosity), O2, and pH. But the model used here is a relatively simple one as showed below (Eq. 1).”

Response:

We thank the reviewer for noting this. We now explain why a simple formulation is adequate for isolating the target bias.

Inserted text (p. 4, L 171‑173):

Addition: “... We deliberately chose a simple modelling approach since the large parameter uncertainty at ecosystem or landscape scales would prevent an accurate estimate based on more complex models. Hence, there would be no reliable additional quantitative information that could be gained from exchanging the simple with a complex model.”

Inserted text (p. 4, L 176‑178):

“Redox‑pH schemes for tidal soils require > 40 marsh‑specific parameters; with so many unknowns, adding complexity would obscure rather than illuminate the aggregation error that we wish to quantify. A six‑parameter DAMM therefore represents a parsimonious tool for the present goal, in our opinion.”

6  L 110 – merge Eqs 1 & 2:

“Merge Eq. 2 into Eq. 1.”

Response

Implemented as requested. The merged equation now integrates temperature, substrate and O₂ limitation; all symbols are listed in Table 1.

R=∝_sx e^(((-E_a)/RT) ) ∗ (S_x/(K_(m_sx)+S_x )) * ([O2]/(K_(m_o2)+[O2] ))

where the three multiplicative terms represent (i) Arrhenius temperature dependence, (ii) Michaelis–Menten limitation by soluble carbon substrate Sx​ derived from ICBM pools, and (iii) Michaelis–Menten limitation by oxygen. Symbols and units are listed in Table 1”

7 L121 – link between O₂ and root traits

“How was O2 related to root trait?”

Response

Methods 2.1 (L 120-149) now describes a two-step procedure:

1. Empirical range.  Direct microsensor studies show steady-state rhizosphere O₂ values well below 0.01 cm³ cm⁻³ in anoxic pores and occasionally above 0.12 cm³ cm⁻³ in narrowly oxygenated ‘hot spots’ next to highly aerenchymatous roots (Armstrong & Armstrong, 2005; Colmer, 2003; Kühl et al., 2021; Visser et al., 2000) We therefore prescribe that empirical interval 0.01–0.12 cm³ O₂ cm⁻³.
2. Trait sampling. The interval is represented by 39 target O₂ values, produced from a soil-moisture grid θ = 0.23 : 0.01 : 0.61. Each O₂ value is interpreted as one plant location combination i.e. a distinct rate of root-oxygen loss (ROL) and hence a separate trait state. Equation (4) converts every target O₂ concentration to the air-filled porosity driver required by DAMM; the conversion is a numerical proxy, not a mechanistic ROL representation.

Inserted text (p. 6, L 230‑233)

“To constrain the oxygen values, we varied soil water content from θ = 0.23 to 0.61 in increments of 0.01, yielding a modelled O₂ range of approximately 0.01 0.12 cm³ O₂ cm⁻³ (air). Each value represents a different trait state of root oxygen loss. This approach allows us to explore heterogeneity in ROL across species and conditions using Eq. (4) as a proxy for rhizosphere oxygen distribution.”

8 L135-140 – moisture versus traits

“It was not clear how the O2 was related to root traits. It seems that the authors simulated O2 related to water content, not root traits.”

Response

As clarified above, soil moisture is employed only as a numeric carrier that maps the preset O₂ values into the porosity variable used by DAMM. The distribution of O₂ values itself spanning ~0.0002 to 0.20 cm³ cm⁻³ is imposed from field observations and literature bounds; θ is not treated as the causal driver of variation.

9 L161 – “visual comparison”

“by visual comparison?”

Response 

We thank the reviewer for asking us to clarify the calibration procedure. The pre-exponential factor (alpha) and the carbon half-saturation constant (KmC) are now fitted by least-squares (MATLAB fminsearch) to the seven median respiration rates derived from the ICBM incubation.

The optimisation yields

alpha = 5.41 × 10¹¹ mg C cm⁻³ h⁻¹

KmC = 4.8 × 10⁻⁶ g C cm⁻³

with RMSE = 2.21 × 10⁻³ mg C cm⁻³ h⁻¹ (Fig. 1).

Inserted text (p. 7, L 282‑290)

“Specifically, we estimated the pre-exponential factor α and the carbon half-saturation constant kMSx by minimizing RMSE between observed and predicted respiration. The best-fit parameters were:

αsx = 5.41 × 10¹¹ mg C cm⁻³ h⁻¹

kMSx = 4.8 × 10⁻⁶ g C cm⁻³

RMSE = 2.21 × 10⁻³ mg C cm⁻³ h⁻¹

Parameter uncertainty was estimated via bootstrap resampling (500 replicates), and Supplementary Table 1 lists each parameter along with its estimate, 95% confidence interval (where applicable), units, and provenance. Fitted values include α and kMSx, while others are adopted from Davidson et al. (2012).”

10 L161-162 – parameter provenance

“how were these model parameters determined?”

Response 

We agree that full provenance and uncertainty ranges should be provided. Supplementary Table S1 now lists each parameter together with its estimate and 95 % bootstrap confidence interval (500 resamples).

11 L171-173 – simulation of ROL

“I’m not sure how the plant root oxygen loss was simulated here.”

Response 

We thank the reviewer for asking us to clarify this point. ROL is not modelled as a physical flux. Instead we prescribe a set of rhizosphere O₂ concentrations that are generated with the diffusion term already built into DAMM (Eq. 4). By letting soil volumetric water content (θ) vary from air‑dry (θ ≈ 0) to full saturation we obtain 70 discrete O₂ levels ranging from 2 × 10⁻⁴ to 2 × 10⁻¹ cm³ O₂ cm⁻³. This span represents in‑situ microsensor measurements for Spartina, Elymus and Phragmites roots (Visser et al., 2000; Colmer, 2003; Armstrong & Armstrong, 2005; Kühl et al., 2021) and therefore serves as a realistic proxy for the outcome of differing ROL rates. Prescribing O₂ in this way allows us to quantify the aggregation bias without introducing poorly constrained anatomical parameters.

Inserted text (p. 6, L 234‑236)

“ROL itself is not simulated. Instead, its observed outcome, rhizosphere O₂ concentration, is imposed directly, following the empirical range detailed above. This allows us to quantify the impact of ignoring heterogeneity without speculative parameterisation of the many plant traits that underlie ROL.

Intra- and inter-specific variation in ROL has been documented for marsh grasses, rice and sedges (Holmer & Pedersen, 2003; Visser et al., 2000; Armstrong & Armstrong, 2005; Kühl et al., 2021), supporting the empirical O₂ range used here.”

12 L172-180 & Fig. 3 – novelty of results

“The results of this study seem to be simple. While the conclusions were clear, the results were not particularly novel. It is understandable that the response of respiration to soil carbon content is influenced by soil O2 concentration.”

Response 

We thank the reviewer for this perspective. Although the qualitative effect of O₂ on respiration is well established, the magnitude of the bias introduced when heterogeneous rhizosphere O₂ fields are replaced by a single bulk value had not been quantified for salt‑marsh soils. Our study provides this missing number and demonstrates its budgetary relevance.

Inserted text (p. 11, L 373‑379)

“Across the full prescribed O₂ distribution, replacing heterogeneity with a single mean concentration underestimates aerobic CO₂ efflux by 10 ± 0.6 %. Even when the O₂ range is restricted to the inter‑quartile span the bias remains 6 % (Fig. S2). Scaling the 10 % correction to the European salt‑marsh sink (30 ± 5 Tg C yr⁻¹; (McLeod et al., 2011)) adds ≈ 3 Tg C yr⁻¹, a flux comparable to the current global net sequestration attributed to seagrass meadows. Hence, the aggregation error is quantitatively significant and should be addressed in regional and global marsh carbon budgets.”

We trust these comprehensive revisions and clarifications fully address the reviewer’s valuable feedback, substantially strengthening the manuscript's methodological transparency and highlighting its novel ecological contributions. We sincerely thank the reviewer for their constructive suggestions, significantly enhancing our work’s potential scientific impact.

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