Thank you for the opportunity to review this interesting and innovative study. The authors propose an inversion model that allows retrieving the acoustic source of bedload transport during river floods using hydrophone measurements performed at a known distance from that source. This is achieved using constrained transmission-loss functions, which describe the reduction of acoustic energy with distance from the source to the station. Using dedicated bedload flux measurements from two floods (2018 and 2021) in the Griffre River, France, the authors demonstrate that their model can capture the cross-sectional variability of bedload transport. Finally, the authors show that using the inversion model, a former global calibration curve alters, having significant importance for the relationship and interpretation of bedload flux and acoustic energy in rivers.

The relatively simple law of inversion and its good performance in a natural environment is self-evident in its ability to describe the physics underlying the relationship of acoustic wave propagation in rivers. This study hence constitutes a significant contribution to the scientific field of indirect sensing of bedload flux. I also think this study is novel and overall well-executed. With that said, an important issue I would like to see addressed before proceeding with the consideration of the manuscript for publication is a discussion of the various physical models proposed thus far for describing acoustic waves generated by grain impacts in rivers during bedload transport events. Further elaboration is given in the attached comments file.

With additional clarifications, textual changes, and general cleanups, I believe this work is appropriate for publication in ’Earth Surface Dynamics.’ I have separated my comments into overarching suggestions and individual text edits (attached as a separate file).

General comments:

1) This paper presents a method of accounting for propagation effects in the use of SGN to quantify bedload in gravel-bed rivers. Subject to technical revisions, this paper should be published. 

2) There are many instances of mixed tenses throughout the document. For example lines 320, 321, 322 swap between present, past, present 

Specific comments:

1) In section 4.1.1 no comments are made about the data acquisition/recording system used other than referring to another paper. I would like to see at least a brief description of the hardware used and basic parameters such as sampling rate.

2) In section 4.1.1 I would like to see a mention of the uncertainty in position introduced by the moving hydrophone

Technical Comments: 

Line 28: Remove the word 'But' and start the sentence with 'Bedload'

Line 67: 'Second', not 'secondly'

Line 69: add an s after source  'where the inversed sources' 

Line 81: remoive the word 'noise', it's implied in the acronym SGN

Line 90: add a space between 'distance' and 'r', and add 'm' after 1

Line 108: Clarify if 'water level' refers to water depth

Line 156: r(x,y,z) not r(x,y)

Line 200: I believe that the subscript of 'z_hyd,m' or 'z_hyd,n' and again r should be listed as a function of z as well as x and y

Line 220: Should read 'there are more unknowns than equations and ....'

Line 351: I presume that the measured section is under  the bridge not, on it.

Line 361: There is a reference to figure 6a. I believe this is a reference to a figure that has since been removed. 

Line 368: 'window' not 'widow'

Line 370: the negative sign at the very end of the line is very easy to miss. I recommend ensuring that the entire equation is on the same line

Line 377: Remove 'the punctual measuremnets and' 

Line 377: Clarify that the figure shows acoustic power

line 379: 'river' not 'rive'

Figure 5 caption: the caption referes to a), b), a), b) instead of a), b), c), d)

Line 417: Capitalize 'figure' to be consistent with the rest of the document. 

Line 417: The reference is to figure 9; I believe this should be figure 7 (also line 421)

Line 446: Add a space between 'as' and 'predicted'

Line 453: Start the sentance with 'Figure 7', just remove 'on the other hand,'

Line 471: add 'of' between 'attenuation' and 'SGN'

Line 477: again remove 'on the other hand'

Line 480: 'inversed', not 'invesred'

Line 494: 'loss', not 'lost'

Line 499 'as', not 'ss'