The authors are grateful for the thorough and constructive comments. The suggestions have been very helpful and have significantly contributed to improving the quality and clarity of the manuscript.

Specific comments

Line 44: “are designed for coastal scenarios where challenging wet-dry transitions do not occur”. This sentence appears counterintuitive. Generally, on the coast, waves give rise to wet-dry scenarios. Please, specify what you mean.

AUTHORS: The authors appreciate the reviewer’s observation and agree that wet-dry transitions are indeed common in coastal scenarios. The sentence has been revised.

System of equations 9: Please specify that the system of equations (9) represents the discretization of the system of equations (6). Additionally, you could explicitly describe the connection between v_disp in system (6) and the random-walk model in system (9).

AUTHORS: The authors are grateful for the suggestion. A sentence clarifying that system of equations (9) represents the discretization of system (6) has been included.  Moreover, the expressions for the velocity components induced by dispersion have been added to expain the connection between v_disp in system (6) and the random-walk model in system (9).

Lines 188-190: The time step of the particle is not necessarily an exact divisor of the hydrodynamic time step, as shown also in Figure 2b. In Eq. (15), the particle time step is different from the one computed by Eq. (14)? If so, how is the index “m” imposed? And, please check Eq. (15) versus Eq. (16), because they seem inconsistent (if Eq. (15) is correct, the summation of the particle time step is equal to the hydrodynamic time step, so the hydrodynamic time step minus the summation should be equal to zero in Eq. 16)

AUTHORS: The authors appreciate the observation and apologize for the error. Expression (16) has been corrected, and the index "m" has been described in detail in the revised manuscript:

Since particles can travel through at most three cells, the number of subdivisions M satisfies 1 ≤ M ≤ 3. The value of M is determined individually for each particle based on the flow properties in the cells it traverses: M = 1 if the particle remains within the initial cell (Figure 3a), M = 2 if it crosses into a neighboring cell (Figure 3b), and M = 3 if it travels through three cells (Figure 3c), though this case is uncommon as it requires a specific combination of particle location and velocity field characteristics.

Lines 227-228: This restriction appears quite strict. It appears to limit the effect of turbulence. Are the effect of such limitation discussed? Are the Authors planning to remove it in a later version of the code? Furthermore, is it possible for transported objects that reach a dry cell to stop there?

AUTHORS: The authors appreciate the comment. This restriction is implemented for several reasons:

• It is physically inconsistent for a particle with negligible mass to enter a dry cell. The underlying principle is that particles with significant mass could use inertia to traverse dry regions. Therefore, this restriction specifically applies to massless or negligible-mass particles.

• The turbulence term can displace the particle vertically upward relative to its previous position, resulting in an unphysical "jump" in the particle trajectory. This occurs because dispersion terms depend on friction velocity without properly accounting for flow direction constraints.

These explanations have been included in the revised manuscript.

Figure 4: The logical connection between modules is not fully clear. The figure shows a “Lagrangian particle transport” module (LPT), while in the text it is referred to as “Lagrangian model”. Using the same term in the text and in the figure would help the reader, also in Fig. 5. Finally, what do the Authors mean with “Lagrangian model for distributed computations” (lines 249-250)?

AUTHORS: The authors are grateful for the observation. The term "Lagrangian model" has been revised to "LPT model". Additionally, the sentence "Lagrangian model for distributed computations" has been expanded:

The LPT model is currently being implemented to support distributed computations both on multiple CPU-nodes (note that shared memory CPU parallelisation is achieved via OpenMP) and on multi-GPU systems, following the approach used in other SERGHEI modules.

Figure 6 is not clear: are all the three errors normalized by the Euler error? Apparently not (the Euler error should be one), and this is in contrast with both the vertical axis in the figure and the figure caption. The strong dependency on the domain discretization is not clear, either. It appears clear from the MAE and RMSE written in the figures, but not for the graphs. Please, consider to modify this figure.

AUTHORS: The authors appreciate the suggestion and agree that the results were not presented in a sufficiently clear format. Figure 6 has been revised to present the errors in a more standard and readable format. Moreover, a reference line with first-order slope has been added to highlight the expected convergence behavior and to facilitate comparison with the observed error decay.

Figure 8: please consider changing the particles color or zooming in the image to make the particles more visible.

AUTHORS: The authors are grateful for the suggestion. Particle size has been increased, and the image has been zoomed in on the building area.

Caption of Figure 10: 10000 particles are reported. This appears in contrast with line 309, where it is written that the simulation was performed with 1000000. Please, check.

AUTHORS: The authors apologize for the error. The correct number of particles is 100000. This has been corrected in the revised version.

Line 344: Can the Authors clarify what they mean by “areas of stagnant transport”?

AUTHORS: The authors appreciate the comment. The sentence has been revised to describe more precisely that these regions correspond to areas where particles remain stationary for prolonged periods due to low velocities or topographical constraints. The expression “stagnant transport” has been removed to improve clarity:

Furthermore, this stationary time histogram reveals regions where particles tend to accumulate or remain stationary for extended periods, typically due to reduced flow velocities or topographical barriers, which may indicate zones of storage or potential sediment deposition.

Line 348-349: Can the Authors clarify what they mean by “the higher frequency of particles compared to the event 2”?

AUTHORS: The authors have revised the sentence for clarity:

In event 1, the longer travel times observed for most particles in Figure 17a, where particles tend to remain stationary for extended periods, suggest intermittent flow conditions, possibly due to

intermittent rainfall, leading to temporary particle deposition.

Conclusions: Nothing is said about model’s future developments. Are the Authors planning to include a strategy to account for particles deposition? This also depends on the type of particles that they are aiming to model (plastics, seeds. . . ). The work would possibly benefit from a more critical analysis of the potential applications of the model.

AUTHORS: The authors are grateful for the suggestion. The following sentences have been added to the Conclusions section:

Future work will focus on optimizing the model to further reduce computational costs and implementing multi-GPU simulations to leverage the capabilities of the SERGHEI hydrodynamic model. Moreover, several enhancements will be incorporated into the LPT module to increase the realism of particle trajectories. These improvements will enable representation of pollutant transport (e.g., microplastics) and biological dispersal (e.g., seeds). Additionally, incorporating particle mass, volume, and inertia will allow modeling of vertical movement, deposition processes, and macroscopic objects such as wooden logs or urban debris in floods. However, accurate simulation of these transport phenomena requires development and validation of specific physical processes that are currently beyond the scope of the present model.

Typos

Line 175: I guess there is a typo, as “respectively” is repeated twice.

AUTHORS: The word "respectively" has been removed.

Caption of Figure 3: “final position” seems unnecessary.

AUTHORS: The expression "final position" has been removed.

Line 266: It should be “L1 norm”, and not “L1 Norm”. The same for L2 norm at line 270.

AUTHORS: The notation for L1-norm and L2-norm in the text has been uniformed to be consistent in the manuscript.

Line 283: “described” seems unnecessary.

AUTHORS: The word "described" has been removed.

Line 284: “modying” should be “modifying”?

AUTHORS: The correction has been made.

Line 300: another way of presenting the L norm is used. Please be consistent in the terminology (choose between L Norm, L norm or L-norm).

AUTHORS: The notation has been standardized throughout the manuscript.

Line 332: “This” and not “these figure”.

AUTHORS: The correction has been made.

Line 339: Please, use the same term, “travelled distance” or “covered distance” for higher consistency.

AUTHORS: The expression "travel distance" has been used consistently.

Line 347: “the difference between the events is higher”.

AUTHORS: The correction has been made.

The authors sincerely thank the reviewer for the careful reading of the manuscript and for pointing out typographical errors. In addition to the corrections suggested by the reviewer, the authors have thoroughly revised the manuscript and corrected other minor typographical issues present in the original version.