General comments

 The paper describes the improvement and validation  of an operational model set that allow fast Lagrangian computation of pollutant dispersion in  urban area. The paper is clear well structured and well written. Only a few clarification are needed.

The model and the validations are openly available as indicated.

My main regret is that the validation with analytical solutions is performed only with Eulerian solutions. For me it is therfore incomplete and this needs to be done in further work

Specific comments

l33 examples of Eulerian models given are large scale. Examples of micro scale obstacle resolving Eulerian models should be given

l55: the unstable modes are in the numerical solution not the equations. Also they are not really "modes »

idem l 108

l 111: the top boundary conditions is mentioned here but not really discussed in the rest of the paper

Table 1: anisotropy is taken into account for different terrain type ( renal, urban, forest...) but there is no discussion of the impact of atmospheric stability. Why? Please give some argument and some dis

L 185 : the non local background mixing coefficient is based on wind tunnel. How can we justify it for low wind speed strongly stratified real cases?

L 223: a well mixed test is mentioned but without details. Was it performed with obstacles ? as it is more difficult for the scheme ? can you comment on this?

Equation 20:  this analytical solution chosen for the validation is a purely Eulerian solution. Therefore we do not expect a good agreement with a Lagrangian solution near the source. Did you compare the near source behavior? What is the Lagrangian time scale (and associated distance from the source?

Eg. 21-26 ; because we are in a uniform flow there is no turbulence production by shear. Can you comment on how this the bulent flow is maintained?

Eq. 27 : this is again an Eulerian solution for which we do not expect a perfect agreement. Why did you not use Taylor's solution which is well suited to Lagrangian validation ?

Figure 5: The concentration gradient at the ground is shaving a stange behavior and is very differen in the model and the analytical solution. A non zero concentration gradient is  associated with a deposition flux. Can you check an explain this behavior ?

Figure 8: the modd concentration profiles are more noisy than the measurements. This is unusual and can probably be related to the strong shear discussed en the appendix and linked to the flow wake contruction by the diagnostic wind field. Same of the discussion in the appendix should therefore be moved here. As this is en issue , is there a possibility that the flou es smoothed before computing the  derivatives  for the turbulence?

L 429: is is mentionned a near source and for source behavior as expected in ce La gran qu'on model. Is it ponible to make this more clear by discussing the La grangian time in the model and experiment?

L 427:"complied" : compiled

Figue 9: ts there an explanation for the points outside the factor of 10?

L464: importance of non local  mixing : this is for the wind tunnel what about the real atmosphere ?

This manuscript presents the QES-Plume model, a lagrangian dispersion model that can be used to quickly estimate particles concentration in fields or in urban areas. The model use the Generalized Langevin Equations with an implicit time-integration method from Bailey (2017) to alleviate the stiffness problem from the GLEs and eliminate “rogue” trajectories such as described in Yee and Wilson, 2007. The context, need for such model and state-of-the art are very complete and well adressed. The description of the model is very detailed and most of the choices made are well motivated and documented. The model is validated step by step using analytical solutions of simple problems and then compared to data obtained from wind tunnel experiments using arrays of cubes.

The performances are quite good and there is no "rogue" effect observed when applying the model to the arrays of cubes. Most of my comments are minor remarks and propositions to make clearer parts of the article. A single negative comment is that I could not use QES due to computer limitation. It seems that it is necessary to have a NDVIA GPU to use the software for the moment. Hopefully the feature for non GPU calculation will come soon.

Two main comments:

• that the average concentration error could be added on the spatial representation of the plume on Figure 7 to more easily compare results from the model and observations.
• I would expect having the mean or median RMSE in Table 6 for each class of "Factor X" error in order to illustrate that the error can be relatively important but is probably really low in terms of absolute value.

More detail about these two points and all comments can be found in the following extracted annotations:

• « However, the performance of Gaussian models in complex environments is limited » (Margairaz et al., 2022, p. 2)

-> would be nice to detail further this point (illustrate the "performance limited" and maybe the context and reason when it is limited)

• « non-local turbulence mixing coefficient Cnlm » (Margairaz et al., 2022, p. 8)

-> how is set this coefficient outside the experiment presented in the article ?

• « Tfinal » (Margairaz et al., 2022, p. 9) on the figure 2 (t < Tfinal condition)
  
  

-> I suppose this is Tfinal but I only have "T in l" in my pdf reader.

• « n+1 » (Margairaz et al., 2022, p. 9)

-> Is n the iterations process ? Is that possible to say that somewhere ? And maybe to try to add that to the Figure 2 ?

• « C∗ » (Margairaz et al., 2022, p. 12)

-> not defined  (normalized concentration I suppose)

• « flow velocit » (Margairaz et al., 2022, p. 13)

-> at zs = 70 m ? -> Uniform horizontally and vertically ?

• (Margairaz et al., 2022, p. 16) On bottom figures (e, f, etc.),

-> x/H values should be added ?

• « y/H = 0 » (Margairaz et al., 2022, p. 16)

-> y/H = 12.5 ?

• (Margairaz et al., 2022, p. 19) Concentration maps
  
  

It would be nice if such map would be used to also illustrate the spatial variability of the error, for example averaging the concentration measured within different zones and comparing them to the model. In my opinion, it would be easier to read and interpret for the reader.

• « 0.068 » (Margairaz et al., 2022, p. 21)

-> might be interesting to add the relative value for all RMSE given

• « RMSEs » (Margairaz et al., 2022, p. 22)

-> might it be relevant to also have the relative error ?

• Table 6

-> It could be interesting to add the mean (or median) RMSE for each class since the RMSE is probably much lower for factor 10 than factor 2 classes