This is an interesting paper, examining a model of the vertical POC flux

in the ocean below the euphotic zone. I found the paper hard to follow in

places, and this was in part because of the choice of English usage: I would

strongly urge the authors to seek out a native English speaker to clean

this up. 

There have been quite a few papers published recently that take a 

similar approach to the problem of modeling particle flux in the 

ocean, and the authors cite all of these (Kriest and Oschlies, 2008;

Omand et al., 2020; DeVries et al., 2014). However, it is unclear what

this manuscript presents that is new when compared with these other

papers. Indeed, as far as I can see, there is no detailed comparison

of results (except to show that one of their analytical solution is

equivalent to that of DeVries et al.). I would like to see an analysis

of what new things we learn from this model. 

The model contains many assumption (as stated by the authors), but there

is little to no analysis of the consequences of these assumptions. For 

example, everything is assumed to be a power-law (the mass-size relationship,

the sinking velocity etc.) and while this makes things analytically

tractable, it is unclear what observational evidence there is for them. 

For example, size distributions are often assumed to be power-law,

but in reality this assumption often holds over a relatively small size range.

The model is a steady state model, and it's unclear if such an assumption 

is a reasonable one. For example. export fluxes out of the euphotic zone can

vary significantly over time periods of days. So whilst I'm not opposed to

the use of the steady state assumption, I do wonder about its validity. 

Line 93, the mass loss is proportional to particle mass, not volume.

The relationship in Equation (4) makes the correspondence between

mass and volume unclear. For example, is the diameter the equivalent

spherical diameter, is the volume the conserved volume or the encased volume?

Line 109: I must be missing something here, because it's unclear to me

that, practically, z-prime can never be larger than the inverse of psi. 

This follows from re-writing equation (10) and realizing that

the constants eta, gamma0, and zeta are all positive. What am I missing?

The authors also need to make their notation more consistent. For example,

in equation (15) we get the definition for C_{p,d}. But in equation (16)

this becomes C_{p,d,i}. Also, in equation (16), n_d becomes n. In equation

(17) we are apparently integrating with respect to a constant (d_0 having

been defined as the initial particle diameter in equation (8)). So, the 

notation needs to be tidied up throughout the paper, not just in these places. 

The paper addresses the depth distribution of particulate organic matter (POM) and its associated flux, introducing analytical solutions and a numerical approach to solve corresponding differential equations.

The equations of the analytical part are based on the assumption that mass and sinking speed of a particle is governed by its diameter, which varies with time due to the degradation processes.

Time-varying solutions of differential equation for POM concentration and flux are given for constant and time-varying degradation rates and are finally converted into corresponding depth-varying solutions.

As a reader who does not juggle with DGL solutions every day, I find the derivation of the formulas difficult to track.

Readers should be able to do so without the need of many calculations on an extra sheet of paper. E.g., you might want to write the integrals that convert sinking speed formulas (9)/(22) into the corresponding depth formulas (10)/(23).

I also would like to see some details about how the depth-varying solutions for sinking speed, particle diameter [and degradation rate] and finally the depth-dependent particle concentration and flux are calculated, i.e., how does (10) applied to (8) and (9) yield (11) and (12) (and finally (14)), and how does (23) applied to (20)-(22) yield (24)-(26) (and finally (28)).

Also, I do not see if formulas (31) (for constant degradation) and (32) (for time-varying degradation), which consider the special case of a constant particle sinking speed, are derived from formulas (14) and (28), respectively.

This would be good to see, because (31) and (32) are used to discuss the differences of solutions with respect to the corresponding assumptions.

The paper also provides a numerical solution algorithm for particle concentration and flux.

The Algorithm is verified w.r.t. the derived analytical solutions (Fig. 1) and applied under the additional assumptions that particle flux is also influenced by (i) temperature and (ii) oxygen concentration.

Results indicate a clear dependence on the temperature profile and on parameters with uncertain range, e.g., the exponent mu which relates particle diameter and sinking speed.

In the corresponding sections 4 and 5 I found some places where S_p was used instead of C_p to refer to POM concentration (Algorithm 3, Figure 5, line 269), please correct.

You may want to place the legend of figures 4-6 (which repeats in every single panel plot) only once to the right of the panels.

I would add the explanation that the three columns of panels in figures 4-6 correspond to the model without dependency of temperature and oxygen (panels a and d), additional temperature dependence (panels b and e), and both additional dependencies (panels c and f) to the figure captions in order to make the figures self-explaining.

In line 280, I interpreted "1/r < 1" and "r > 1" as defining assumptions at first glance (which makes actually no sense without the definition of r). I would define r=1.25 first and then derive p_min and p_max by the ratios 1/r and r, respectively (probably without extra stressing "1/r<1" and "r>1").

This paper presents a combined Eulerian-Lagrangian formulation of the organic particles descent while taking into account their size and age among other things, resulting in a non-trivial relation among them, unlike suggested by previous studies. This is a well-written article with strong positioning regarding motivation, contribution and place among the previous literature. My detailed major and minor comments, mainly refraining to comment on the formulations, are organized below in the order of appearance in the manuscript.

While the contribution is clear around line 45, I would recommend highlighting the novelty by explaining the unique contribution in the context of limitations of previous attempts in the literature.

One major comment I have is that the modeling results section needs to be more specific in terms of presenting the results. The authors are showing and referring to the results but not describing and discussing them.

Same goes for the validations -- I found it hard to follow which parts agree with the measurements more than others. Both of the aspects need to be addressed in the results section for the paper to be strong.

When saying Fig 4-6, as in line 270, I'd recommend being specific when referring to figures and panels to show results.

“As follow” is a typo in line 272

Another major comment is that the paper is missing the significance in terms of closing the loop and relating back the findings back to the implementation in the earth system/biogeochemical models as the authors had described in the introduction section.

Please include significance and follow-up work recommendations before the conclusion. The authors have shown appreciations of the limitations of the work at various places in the text, I'd recommend synthesizing them at the end before conclusions.

In light of my comments above, I’d recommend minor revisions to the manuscript before it is published. Good luck and congratulations on this useful work.