See attached PDF of my review

The manuscript provides detailed analyses in model and forward operator errors for 94 GHz vertically pointing radar observations, with fog forecast improvement in mind.  The manuscript is generally well written; figures are very clear and effective; and the methodology appears appropriate.  I thought the results are amazing.  The work presented here is necessary for assimilating cloud radar reflectivity, and thus warrants publishing.  However, while the title of the manuscript says exactly what is presented, some wording in the manuscript is confusing and misleading, which must be revised.

1) In the end, the authors have NOT yet assimilated radar reflectivity and demonstrated the improvement in fog forecast.  Therefore, wording like “after selecting the best background profile, a good agreement was found between observations and simulations” in the abstract is really misleading.  What the authors show is the agreement between observations and “selected background profiles”, which is not surprising because the “best background profile” was selected using observations as a reference.  If I somehow misunderstood the manuscript and if new simulations were indeed performed using the best background profiles, then this leads to an even bigger issue.  By definition, the prior is NOT supposed to see the observations beforehand.  Therefore, if new simulations were performed, they must be performed for a different case or time period, and I don’t see any other cases different from those listed in Table 3.  This kind of misleading statements can be found in Section 4.4 and Conclusions as well, which needs to be more precise.  Additionally, I think the use of “Innovations” is too strong and not accurate.  It is an improvement, not an innovation. 

2) Descriptions in Section 3.2 are quite confusing to me, and I am not sure that readers are able to replicate results.  What is “fog profile”?  “Visibility measurements were averaged over 10-min period”, meaning for both observations or simulations or both?  How might a choice of 28 km x 28 km domain relate to the sample size of 15248 in total in Table 4?  Perhaps a figure or flowchart for this part, or more information in Table 3 (e.g., starting time, duration, statistics thickness, etc.) would help readers to understand better the work involved here.   

3) The manuscript will read better if things are defined and clearly stated in a slightly different order.  For example, how to define fog thickness in observations AND simulations?  The term is introduced in 3.1 (page 7) but is not defined/explained until Page 11.  Even so, it is still unclear how exactly it is done and if it is the same for both observations and simulations.  Another example is the information on parameter ranges on Page 15.  It would be nice to mention that earlier, so readers can connect Fig. 4 and the all exercises/results better.

4) Fig.2: Please explain why (c) only has 20 events?  What happened to the other 11 events?  If one wants to improve fog forecast, shouldn’t we worry more about those 11 events?  Can the authors comment if the newly selected background profiles will help improve the forecast for those 11 events?  Additionally, the caption is confusing.  Do you mean “where the event “occurs/dissipates” later in the observations”? If statistics are derived using simulations minus observations, then it is best to be consistent throughout the manuscript (e.g., fig. 2 and fig.3). 

5) Fig. 3:  Do you mean fog thickness can be exchanged with fog top height, since the figure title is fog thickness, not top height? 

The paper presents some preliminary findings to assess the potential of W-band vertically pointing radar observations for improving fog forecast via data assimilation. The authors focus on studying errors associated with the background profiles and  the forward operator. The other reviewers have already commented upon the former (I have similar comments). I will focus on the latter. I find the simulations with the forward operator quite confused. First a Gamma modified PSD is introduced; this has 4 free parameters (the authors do not mention any correlation between parameters). They then introduce other 2 parameters C and X (I do not know really why?). For some reason then they study the variability of a profile with alpha, nu and N_0 but they forget completely Lambda (i.e. the characteristic fog size). Why? 

Fig.4: all units in the y-axis are wrong. Not sure how useful is Fig.4 , particularly the bottom panel. If N_0 changes then there is just an amplification (not sure the figure is actually right, it looks like the maximum of  the blue line is different from the orange one). Similarly simulating reflectivities changing N_0 is trivial and should not be plotted (Fig 5, right panel), doubling N_0 just add 3 dB . On the other hand the change of alpha nu and Lambda should be better investigated accounting for the possible relationship between the different parameters (It is not  enough to change only one parameter at a time).

Line 405-410: I am not convinced that some of the big differences we see in Fig.6 can be attroibuted to non sphericity. Where is the freezing level in this scene? Also instead of ``isotropic particles'' use ``spherical particles''.

Fig8: not sure about the cluster of points bove 500 m. Is that fog? If so why you are cutting the plots at 1km?

Tab1: Range for HATPRO (0 to 10 km) ==> it does not make any sense to specify a range for a radiometer

Fig1, caption: I do not see 11:00 UTC but 10:20 UTC in the plots.