The MS has a range of interesting results on flow and transport in urban terrain. The LES quality is excellent and the LES is used to inform parametrization in a widely used UCM model, the MLUCM. The results thus have the potential to contribute to advancing the field.

The paper is overall well written (some parts could be improved) and can be published with moderate modifications.

Major Comments

1) What models or application besides MLUCM could benefit from the developments of the upgraded closure and how? As is, the paper is presented as simply an effort to improve MLUCM, which misses the chance to reach a broader audience.

2 ) Line 111: LES solves the Navier Stokes equation with the Boussinesq approximation, not the Boussinesq equation. The Boussinesq equation is a different PDE that describe wave propagation.

3) I am a bit confused by the explanation of the terms in eqs. 1 and 2.

(i) The authors write “The fourth term of Eq. 1 represents a term risen from spatially averaging that accounts for momentum sink due to form and skin drag.” This seems to relate to this term

This is quite confusing since this looks like the mean pressure term. For it to be defined as drag, the P here should be defined as the perturbation from an otherwise linearly decreasing pressure in x. Why don’t the authors just call this drag D_i ?

(ii) the last term is the viscous stress which they never explain, and they omit the corresponding molecular flux term in eq. 2. LES at their Re numbers should not be including the viscous term so It is clearer to remove it.

4) In various places the authors write “non-Gaussian dispersive momentum transport”. Not sure why. It seems to distinguish them from a Gaussian turbulent transport, but the turbulent perturbations are not Gaussian either. Nothing here is Gaussian, so why this specification?

5) Equation 12: at steady state in an LES, the driving pressure gradient has to balance the surface drag (and Coriolis if present). So why not scale with the total surface drag instead?

6) related to 5: I suspect the minor influence of the model on the profiles of U and u’w’ is because of the imposed global force balance. At any given height the stress divergence + pressure gradient (driving the flow) must balance building drag (slowing the flow). Since the building drag is imposed in 13a and the pressure gradient is also imposed, the stress divergence is also constrained. This is why the stress profiles in the rightmost column of Fig 9 are identical for all runs. This then also constrains -KdU/dz, and explain the small differences in the U profile.

TKE does not have such constraints and varies more. Maybe more importantly, the heat or scalar flux are also usually not constrained and could vary more with changing closures.

Minor Comments

7) Line 5: l here is a mixing length scale so please define it as such other “length scale” is to generic.

8) Line 32: Usually when one refers to a scheme like the 1.5 order turbulence closure model, the original reference or a textbook is cited. Here the authors cite (Bougeault and Lacarrere, 1989); is that because the MLUCM uses a specific form formulation of the 1.5 order closure that was proposed in (Bougeault and Lacarrere, 1989) ?

9) Line 44: remove “optimally”; this would usually imply a formal optimization, which LES does not do, to balance accuracy and cost. In fact, most LES go for the highest possible resolution so they pay the highest cost they can afford, so that is not an optimization.

10) Line 263 and elsewhere: again avoid using the word optimum. This seems to be an empirical selection, and that is perfectly fine, but it is not the outcome of an optimization.

11) Line 66: some of the citation formats should be corrected. For example, here since the citation is part of the text only the year should be in parentheses.

12) Lines 114 and 116: the authors seem to give a Dirichelet BC on line 114 (value of s) and then a Neumann one on line 116 (flux or gradient of s). Both cannot be imposed at the same time. If I understand correctly, the one on line 116 is the actual one and line 114 is just the surface value of the initial profile but is not imposed. Please clarify.

13) Line 51 and Eq. 7: there should be a minus sign in all these flux models for the flux to be downgradient.

14) Line 159: I think it should be : “The fifth term represents the source of TKE generated..”, right? Maybe then just say D_K to make it clearer.

15) Line 178-179: “due to the resistance difference to the constant pressure gradient between the free atmosphere and urban canopy.” This statement is very confusing and unclear.

16) Line 180: Not sure what the authors mean by “Being first flow moments, the eddy diffusivity…”. The eddy diffusivity is not a statistical moment of the flow field so not sure what is meant here.

17) Caption of Fig 4, the authors use the term “dispersive velocity” but they did not formally define these. Please do.

18) Figure 5 is hard to understand. Is this the PDF rather than the CDF? The integral of the CDF over this plot should be 1, right, so not sure what these contours are. Does it mean you get a CDF of 1 for example if you integrate outside of the contour of CDF=100%?

This manuscript provides a description of improvements to the turbulent-kinetic-energy and dispersive momentum flux terms in the urban canopy parameterisation MLUCM based on LES data. This is an important contribution to urban modelling and the manuscript is overall well written. I have some general comments and specific suggestions on clarifications:

1. I find that there is a bit of a mismatch between what is discussed in the introduction (impact of complex urban geometry) and what is described in section 2 (staggered cubes with different heights). I suggest to better highlight that this study focusses on height differences as the critical variation, not on building geometry or street alignment.
2. I would also like to see a comment on what the authors expect to be the impact of non-cubic buildings on their parameterisations. Maybe a comparison to the work of Blunn et al., 2022 or other relevant studies (if there are any) could be useful.
3. Section 3 is not very clear on which terms (equations) refer to the LES model, mesoscale model or parameterisation. In particular the first part, and I don’t understand the last sentence in Section 3 on what MLUCM does (line 145). Please be more specific.
4. Please ensure all your figures have subfigure labels which are referenced in the main text, and the notation used is properly described either in the caption or main text.

Abstract, line 11: […] we conducted 49 large-eddy simulations … ‘conducted’ suggest that you present the results here for the first time, but they have been presented in another paper, correct? Please be clear on what is the contribution of this manuscript. I suggest to use ‘analysed’.

Line 16: MLUCM v2.0 has not been introduced at this point, please add a sentence where you introduce this particular model.

Introduction, line 76: Related to above. I find it a bit off to talk about the multi-layer model when referring to a specific model, since there are different urban multi-layer models.

Section 3, line 128: “a common approach in this situation…” This sentence is confusing, what situation do you mean? Do you mean a common approach to derive an urban parameterization?

Line 133: the notation of the spatial averaging is not clear, please state what the two decomposed terms on the right-hand side are.

Lines 133-136: I find the justification for using the intrinsic average not very clear. Personally, I think the comprehensive average is more suitable for vertical parameterisations, since it keeps the grid-box volume constant across height and just describes the change of the parameters with height (the buildings are never “physically” in the model). Using the intrinsic average gives you these strange-looking kinks at the canopy top in Fig. 1 and Fig.9. But this is just a comment, I’m not suggesting changing it.

Line 141: “… represents vertical transport events”

Section 3.1, line 197: What do you mean by “that do not break the paramterization in the present study”?

Figure 1: epsilon is not defined. Use a, b, c for 1st, 2nd, 3rd column. Would be even clearer to label each subfigure with a--i and refer to the individual subfigures in the main text.

Line 205: “(note the vertical range of two rows in Fig 1)” I don’t understand what this means. Consider using labels for each subfigure and refer to them specifically.

Paragraph from Line 204: If you are referring to what is shown in Figure 2 here, I believe it would really help to have labels for each subfigure and refer to them explicitly in this paragraph.

Section 3.2, line 247 (equation 8): This equation needs to be embedded in a sentence, e.g.: “The dispersive flux of momentum then reads: …”

Figure 4: Caption contains labels a--d (good!) but the figure does not.

Paragraph from line 254: I don’t think the sampling approach has been explained here, and what do the cut-off values do? Maybe I missed it.

Section 3.3, line 316: ‘mounted’ sounds odd.

Section 4, Table 2: What do you mean by “to K_m” under dispersive momentum flux?

Line 366-368: I would add a sentence saying that you quantify this improvement in the paragraphs below by looking at the RMSE between the LES data and the models.

Line 370; Line 380-382: I t is hard to spot the difference in velocity profiles. Where is the improvement coming from, i.e. at which height levels? Can you say what might be the reason for it?

Line 371: I suggest spelling out ‘MF’.

Line 372: The dispersive flux is not (only) a source of momentum, but also a sink term.

Line 385: Can you speculate on why the turbulent fluxes behave contrary to the TKE (i.e., better in sparse layouts)?

Figure 10: I suggest showing this Figure as the difference to the original scheme (i.e., S1 – original, S2 – original, …) and on the y-axis as percentage of improvement. In this bar chart it is hard to identify the improvements and their significance.

Section 5, line 388: “This [study] refined the characterization …”

Appendix: Figure A1 needs a better caption, explaining what the yellow block is, what the cut-off values are.