This study proposes an alternative equation to describe and predict the degradation of organic matter in marine sediments. A log-normal function is fitted to 123 depth profiles of TOC, demonstrating that this function better characterizes organic matter decay over time and depth. Moreover, the function is extrapolated to a global map of surface reactivities, based on 5600 TOC concentration measurements.

This initiative to improve the characterization and understanding of long-term organic matter behaviour is very welcome, as previous models have not fully resolved the complexity of the problem. This study clearly is an important contribution to the field. I only propose to consider a few aspects which could make this work even more universal and help to address a broader audience.

The mathematics is rather complex to understand, including terms as “gamma”-function and “lognormal”-function. According to Wikipedia: “In probability theory, a log-normal (or lognormal) distribution is a continuous probability distribution of a random variable whose logarithm is normally distributed. Thus, if the random variable X is log-normally distributed, then Y = ln(X) has a normal distribution”. It should be thought through what physical meaning this has, i.e., what in the nature of a mix of organic matter gives rise to this function?

One general finding from ocean drilling is the observation of general power law decrease in activity with depth. This was already recognized during some of the early studies in deep biosphere research (Jørgensen, 1978), and a power law trend has been repeatedly confirmed, not only for organic matter decay but also for prokaryotic cell numbers (D’Hondt et al., 2004; Kallmeyer et al., 2012) and metabolic rates measured using the radiotracer method (Parkes et al., 2005).

It is understandable that microbial activity and abundance is ultimately controlled by the rate of decay of larger molecules via hydrolysis, then giving rise to a cascade of fermentation processes. While a single compound reacts with an exponential decay function (Berner, 1964), it has been the common tenet that a complex mixture of compounds results in an approximate power law decay function (see Tarutis, 1993). We can therefore ask the heretical question why it matters, whether a gamma function or a lognormal function is used, if the physical meaning is anyway the one of a power-law function.

Minor comments:

Line 31: The results show that …

Lines 45-49: I suggest to modify the sentence as follows, thereby specify the references with respect to the listed phenomena:

“In particular, the reactivity of benthic OM imposes a substantial control on the magnitude of benthic carbon export and burial (… sequestration happens in the photic zone!) over geological timescales due to the recycling of inorganic carbon by dissimilatory microbial activity in the deep biosphere (Boudreau, 1992), the dissolution and precipitation of carbonates (Meister et al., 2022), and the production of methane (Dickens et al., 2004).

Line 60: Here it would be good to refer to the power law function (see comments above).

Line 92: “Boudreau and Ruddick” is duplicated

Line 98: “Middelburg” is duplicated

Line 127: Consider re-organizing the methods description to start with explaining what was simulated.

Line 142: Title 2.3 should be rephrased: not the sedimentation rate is upscaled, the model is.

Line 154: Eq. 5 defines the sedimentation rate as a function of waterdepth z. However, sedimentation rate has also been observed to vary with depth due to compaction. This has an effect also on the organic matter decay with depth.

Line 170: Why is a multi-G method used if the log-normal method would be better?

Line 185: on the shelf

Line 194: Also, Meister et al. (2013) evaluated the effects of a and nü in the reactive continuum model on the sulphate and methane concentration profile. Presumably, the log-normal model has similar effects?

Line 198: WHAT is divergent?

Line 237: This matches the observations by Kallmeyer et al. (2012) that also microbial cell numbers are shifted by magnitudes between the regions.

Line 242: In the reactive continuum model, the parameter a has actual meaning, as the “initial age”. Which parameter would represent this property in the lognormal model?

Line 262: Perhaps also refer to the South Pacific Gyre, as the region that is most depleted in organic carbon (see also Kallmeyer et al., 2012).

Line 287: But often the OMZ is in shallower depth, on the shelf or shelf slope, and also affects anoxic shelf basins.

References:

Berner R. A. (1964) An idealized model of dissolved sulfate distribution in recent sediments. Geochim. Cosmochim. Acta 28, 1497–1503.

D’Hondt S., et al. (2004) Distributions of microbial activities in deep subseafloor sediments. Science 306, 2216–2221.

Jørgensen B. B. (1978) A comparison of methods for the quantification of bacterial sulfate reduction in coastal marine sediments. Geomicrobiology 1, 11–64.

Kallmeyer, J. et al. (2012) Global distribution of microbial abundance and biomass in subseafloor sediment. PNAS 109, 16213–16216.

Meister, P., Herda, G., Petrishcheva, E., Gier, S., Dickens, J., Liu, B. (2022) Microbial alkalinity production and silicate alteration in methane charged marine sediments: implications for porewater chemistry and diagenetic carbonate formation. Frontiers in Earth Science 9, 756591, 1–18. https://doi.org/10.3389/feart.2021.756591

Meister, P., Liu, B., Ferdelman, T.G., Jørgensen, B.B., and Khalili, A. (2013b) Control of sulphate and methane distributions in marine sediments by organic matter reactivity. Geochim. Cosmochim. Acta. 104, 183–193. https://doi.org/10.1016/j.gca.2012.11.011

Parkes, R. J., Webster, G., Cragg, B. A., Weightman, A. J., Newberry, C. J., Ferdelman, T.G., et al. (2005). Deep Sub-seafloor Prokaryotes Stimulated at Interfaces over Geological Time. Nature 436, 390–394. doi:10.1038/nature03796

Tarutis, Jr., W. J. (1993) On the equivalence of the power and reactive continuum models of organic matter diagenesis. Geochim. Cosmochim. Acta 57, 1349–1350.

This manuscript is based on the premise that a lognormal reactive continuum model for sediment organic matter reactivity is “better” than the multi-G model or other continuum models for fitting and explaining sediment OM depth profiles and data from OM degradation experiments.  From there these workers apply this model to OM data from a wide range of sedimentary environments to develop two relationships between the average rate constant for OM degradation and sediment accumulation rates (ω).  With this they then generate a global map of sediment OM reactivity.

In general, I like such big data compilations. While one might quibble about what it really means to have a better fit to a sediment OM profile (given the complexity of the process itself across all marine sediments globally, let alone the complexity of the OM being degraded), the approach here is at least internally consistent (more or less) across a broad range of OM reactivities (although do see specific comment 7 below).  I support the eventual publication of this manuscript, although I also think the manuscript needs extensive revisions before being accepted.

“Big picture” comments

1.  When all is said and done, the main take home point of this work seems to be Fig. 3 and its subsequent discussion.  Perhaps I’m being unduly harsh, but I’m not really sure I see a lot here that is really that new, as is indicated by the discussion toward the latter part of section 3.2. In some senses though, this consistency between the model results here and wide range of diverse observations regarding organic matter reactivity and composition is re-assuring, and in some ways this work does act to help “unify” these observations.  On the other hand, in other places (lines 339 and 359), the authors note that “the l-RCM can be further used to calculate the budget of OM degradation at regional or global scales and assess the significance of the sedimentary carbon cycle on the hydrosphere and atmosphere.”  To me at least, adding such a calculation to this manuscript would be as (if not more) important and interesting as is Fig. 3.  It could then be compared to other regional and global estimates of such quantities cited on lines 328-330, or reported more recently in Jørgensen et al. (2021, Earth-Sci. Rev. 228:103987).  These estimates might also be a way of somewhat independently verifying how “good” this lognormal approach is, as compared to other models of sediment OM reactivity.

2.  The overall manuscript is chopped up in such a way that makes it very hard for the reader (or at least me) to follow.  Specifically, things discussed in the Supplementary Material section are not well-referenced in the text, and I was very confused when I first started reading the main text, until I realized I had better go through the Supplementary Material section first.  In revising the manuscript I would work to restructure the work as a whole so that it flows better, i.e., better link the main text and the Supplementary Materials sections and also minimize repetition in places.

3. The math in the supplementary section is very dense and confusing in places (also see point 5 below).

4.  Maybe I’m missing something, but there seem to be two definitions of  (eqn. 4 and eqn. 7, which is the same as eqn. S3) and in plots like Figs. 2 and 3 it’s not clear which is being used.  This confusion needs to be cleared up in the revisions.

5.  The quantity ρ(ln(k)) or ρ(k) is plotted in several places (Figs.1C, S4, S5, S12, S13).  This parameter is not clearly defined in the text (maybe I missed it), and it is also not clear how it relates to other parameters being looked at here (this comment may actually be a specific example of the general concern noted in point 3 above).

6.  The referencing in the early part of the manuscript needs to be cleaned up.  You don’t write “… Washington and Jefferson (Washington and Jefferson, 1776) said …” but rather “… Washington and Jefferson (1776) said …”.  Also references with 2 authors do not use et al. (e.g., see lines 138 and 179), and again remove the author names from inside the parenthetical statement.

Other more specific comments (line numbers in parentheses).

1. (82) – I’m not sure where this R² comes from.

2.  (127-9) – I think I know what is meant here, but it could be worded better, and a reference or two might be useful.  Also you can see the tail that is referred to here in Fig. S13 (vs. Fig. S4) – perhaps this point could somehow be included here?

3.  (128) – I think is better referred to as the mean rate constant for bulk OM degradation.

4.  (145) – Does ω vary with depth at any of these sites, and if so, is this a problem?

5.  (160) – I’m having a hard time understanding how F­_i(k,0) is defined, both here and in sections S4 and S5. For example, here it seems like the i subscript in eqn. (6) refers to each 1°x1° grid cell and that this is then used to calculate the values for each grid cell plotted in Fig. 3.  On the other hand, eqn. (S2) is almost identical to eqn. (6) but this equation refers to this (line 99, SM) as the “distribution of OM reactivity at the regional to global scale”.  What am I missing here?

6.  (179) – The 8 data sets plotted in Fig. S3 do not come from the Westrich and Berner (1984) paper.

7.  (292-299) – Separating out certain regions (e.g., EWEP, SWAF, NWAM, and ARBS) in Fig. 2B based on the discussion here of R² values from different modeling efforts seems a bit suspect.  It might also be interpreted as applying a “2-G” approach to the l-RCM (i.e., different types of OM produced in different parts of the oceans show different trends in reactivity). In the end though if all of the data in Fig. 2B were fit to a single straight line and then used to recalculate Fig. 3 I wonder if the results would be that much different.  I don't want to make a big deal about this, but this is something to consider.

8.  (297) – The phase “is less quality” needs revision.

9.  (109-10) – How exactly are the curves shown in Fig. S12 obtained? Is each curve used in each of the 30 regions to generate the distribution of values shown in Fig. 3?  If so, does this then mean that the observed variation in within each region is driven solely by differences in water depth and sedimentation rate?  Please clarify this in the revisions.

9.  (139, SM) – What is an “irregular distribution”?

10.  (142-148) – I think the authors are simply saying here that eqn. (S4) is a trapezoidal approximation used to numerically integrate eqn. (S3). If so, I would say it as such (here and in the main text near line 172).  As written, it sounds odd to talk about dividing the OM into 1000 fractions (which isn’t really being done), especially after reading the Introduction where the authors talk about problems with multi-G models.  I realize the components of a multi-G model are not conceptually the same as the components (or fractions) being discussed here in this calculation.  At the same time, since there is no need to use terminology that even hints at these similarities, I would modify this text to avoid any unnecessary confusion.