The new version of the manuscript looks better; however, I still see that the quality of the study needs to be improved. I have a serious problem with understanding your definition and use of the Richardson number. If your explanation is true (which I believe you confirmed in the responses), then I think your methodology is used incorrectly, which may invalid your investigation.
I strongly recommend that ALL the authors read the paper very carefully again. Please be very critical about every sentence you wrote, and ask yourselves if each of those sentence makes sense. It would also be good to check the final version of the text for errors and confusing formulations. Please see my specific comments below showing how difficult it was for me to understand some parts of the text.
Title: “Comparisons” - I would suggest to change it to a more standard ‘Comparison’ as your study is a comparison of different approaches to estimating PBLH.
There is no need to use ‘stable atmospheric boundary layer conditions’ or ‘unstable atmospheric boundary layer conditions’ so many times in one paragraph. Once you introduced it, a shorter version (‘stable conditions’ or ‘unstable conditions’) can be used.
L29: Still confusing because PBLHT as a parameter doesn’t have any impact on air quality or climate. No parameter has any impact on those elements of the Earth system. I am not sure what the authors are trying to say here. Please consider reformulating it and think about the reader that may not understand everything.
Tropics -> tropics
L54: ‘Under the SBL condition, turbulence tends to be suppressed by the statically stable air above it and occurs only sporadically’ - What do you mean by ‘above it’? Above the boundary layer? But then it doesn’t make much sense. This sentence is confusing and needs some clarification. Do you want to involve everything that happens above the PBL?
L62: ‘The PBLHT in atmospheric models is usually calculated by using either diagnostic equations that take surface fluxes and the initial temperature profile as inputs ‘ – This is a very confusing sentence. It wrongly suggests that most of the models (I'm sure you know that atmospheric models include large-eddy simulation, regional, and global circulation models) calculate PBLHT this way, but this is not true. Why only initial conditions? How can PBLHT vary if you use initial conditions? PBLHT may be calculated in many ways, not necessarily by using surface fluxes. In one of the next sentences, you suggest that those methods are only applicable to observational data, which is questionable (once you have some data, you can apply any method you want). Please reformulate this paragraph. You may need to do some research on those methods before you update it.
L73: ‘Observing atmospheric boundary layer transitions with high temporal-spatial resolutions is required to investigate atmospheric thermodynamic processes (Fritz et al., 2021).’ – Another confusing sentence. What thermodynamic processes do you have in mind? That sentence suggests all of them. I think the message from the Fritz et al paper is different as they show that there are many important details that cannot be measured when using instruments with coarser resolution than their DTS, in addition to the fact that their method of determining PBLH based on the temperature gradient is quite reliable.
L115: ‘limited cases’ suggests a problem with those cases. Did you mean limited number of cases?
L155: found from -> found in (or found from … to… )
L162: Each ARM observatory generally launches four times a day (except twice daily at NSA and OLI) the balloon-borne sounding system (SONDE) at roughly 5:30, 11:30, 17:30, and 23:30 Universal Time Coordinate (UTC) (5:30 and 17:30 UTC at NSA 165 and 17:30 and 23:30 UTC at OLI). – This sentence is confusing. First you say ‘each’, then you say not each. Please be as precise as possible. You can say something like ‘The balloon-borne sounding system is launched four times a day (at 5:30, 11:30, 17:30, and 23:30 UTC) at most of the sites, except twice a day at NSA (5:30 and 17:30 UTC) and OLI (17:30 and 23:30 UTC).
Are different UTC times chosen to match similar local times and facilitate morning and afternoon observations of PBL? If yes, please mention that.
L167: “atmospheric dynamic environment” – justify why dynamic or simplify to atmospheric environment
L191: “boundary layer structure regimes “ – boundary layer regimes (or structures);
L209: I raised that point before as to me you are calculating Ri in the layer from 0 to z. In your response, you said that you calculate Ri in a thin layer only, although in the text you now say that Ri is calculated at given altitude (not in a layer?). Then you show Eq. 1 and say that theta_vz and theta_v0 are the virtual potential temperatures at the surface and height z, which means that you actually calculate the temperature gradient in the entire layer between 0 and z, contrary to what you said. The same applies to wind: you can only use the values of wind at z knowing that they diminish at 0, otherwise their difference should be used.
I strongly suggest that the authors review their approach carefully. The gradient Richardson number formulation includes dz, which in your case is replaced by z, meaning that your layer always has the thickness of z: https://glossary.ametsoc.org/wiki/Gradient_richardson_number
L420: If you hypothesize that PBLHT CEIL is greater than PBLHT Liu-Liang because of aerosols, explain what exactly you mean. Are you suggesting that free-tropospheric aerosol may cause some overestimation? If yes then be very specific in your explanation. What do you mean by ‘transported aerosol layers’?
L423: “As being pointed by many previous studies” – this formulation seems grammatically incorrect
L427: “The diurnal evolution of PBLHT is important to better understand boundary layer processes.” – This sentence is confusing. Diurnal evolution of PBLH is the result of boundary layer processes, but I don’t quite see what you want to say here. In the current form, this sentence says that without the diurnal evolution of PBLHT (i.e., for non-evolving PBL) you cannot understand PBL processes, which probably is not the authors intention.
L483: “Ceilometer provides continuous measurements of aerosol backscatter profiles, which have been widely used to estimate the planetary boundary layer height (PBLHT). Good agreements between ceilometer- and radiosonde-estimated PBLHTs have been reported using limited data from a single location or a short-term campaign. To test the robustness of ceilometer-estimated PBLHT under different atmospheric conditions, we compared ceilometer- and radiosonde-estimated PBLHTs using multiple years of U.S. DOE ARM measurements at six ARM observatories located around the world.” – This paragraph needs some polishing (as many others), and I want to show the authors what I mean by that. Please see if my version makes more sense:
Ceilometer observations facilitate continuous measurements of aerosol backscatter profiles, which have been widely used to estimate the planetary boundary layer height (PBLHT). Good agreements between the ceilometer and radiosonde estimations have previously been reported for short-term campaigns at single locations. In this study, we extend that comparison to multi-year time series for nine different DOE ARM sites located over land and ocean in different climate zones.
L487: “at six ARM observatories located around the world” – This is confusing. Once you say nine (Tab. 1, Fig. 1), then you say six. Again, I strongly encourage the authors to read their paper very carefully and check every single sentence for consistency.
Figs. 6, 8, 10 – what are the values corresponding to the colors (from red to blue)? Is that scale linear?