see attached pdf

I have reviewed the manuscript titled “A profile-based estimated inversion strength” submitted by Wang et al. to the Atmospheric Chemistry and Physics (ACP). The authors analyzed the radiosondes data at the Southern Great Plains (SGP) station and found the Inversion Strength estimation deviation in the current two variables, the Lower-Troposphere Stability (LTS) and Estimated Inversion Strength (EIS). Two sources of errors are identified, a systematic deviation from the dry adiabat below the lifting condensation level (LCL) and error from the spread of the actual potential temperature around the moist adiabat above the LCL. Based on the findings, the authors proposed a new measure/variable, profiled based inversion strength estimate (EIS_p) to estimate the inversion strength from the profiles in the reanalysis data. This new measure is defined as the potential temperature difference between the top and bottom of a layer with the maximum potential temperature gradient and with a subtraction of potential temperature changes due to the moist adiabat in this layer. Further analysis shows the EIS_p explains the low-level cloud significantly better in term of both spatial and temporal variations than the existing variables. The research presented in this manuscript is within the scope of ACP, and appears to significantly improve the understanding of low-level cloud changes by the proposed new measure. The new measure of the inversion strength is likely to be well accepted by the research community and extensively used in future studies. The manuscript is well written and easy to follow. Thus, I recommend the manuscript be accepted with minor revisions.

My major comments are:

1. It appears the removal of the moist adiabat above the LCL does not benefit a better estimation of inversion strength in EIS based on the radiosonde analysis. Of course, this might be attributed to the spread of the inversion layer. It would be interesting to see if the EIS_p would actually perform better without the subtraction of the removal of the moist adiabat contribution, i.e. EIS_p as the potential temperature difference between the top and bottom of a layer with the maximum potential temperature gradient
2. It appears there are some limitations of the newly proposed variable. Firstly, it is for reanalysis data. For radiosondes with high vertical resolution, it seems the inversion strength can be directly calculated and might perform better than EIS_p. (Just curious, would the authors suggest the new variable for weather forecasting? It seems the LTS is commonly used in weather forecasting when only reanalysis data are available.). Secondly, all the test data sets are over extratropical regions and it is not clear how the controlling of low-level cloud compare over tropics with over extratropical regions, e.g. Figure 9. As the authors stated in the manuscript, this new variable may have limitations in the polar regions. The author could consider including the limitations this in the abstract.
3. The structure of the manuscript seems fine. The EIS_p definition can appear earlier in the manuscript. The authors could consider either moving section 3.1 to section 2, or making section 3.1 a separate section.

Minor comments:

1. Please spell out SGP (Southern Great Plains)
2. L178, change “or” to “and”?
3. L215, this sentence only considers land case, please add the part for ocean case.
4. L222, can you add explantion why the heigh difference can be used to differentiate the coupled and decoupled PBLs?
5. L257, by eye check, it appears it is as sensitive as LTS.
6. L261, I was just wondering whether the strong IS is the result of the cloud formation and then maintain the low level cloud?
7. L288-L292, this part is really confusing and hard to understand.
8. L293, this paragraph is confusing and hard to understand.
9. L312, for extreme case, e.g. radiosonde with very high vertical resolution, the EISp is the Inversion Strength? If this is the case, the authors might want to state this in the manuscript.
10. Fig 9, why these is negative values for R-square? This figure shows correlation rather than R-square?
11. Fig 9, The quality of text in this figure seems low compared to other figures.
12. L448, please explain how you calculate the values for different time scales, in section 2?
13. L454, it appears the values are negative over tropical oceans.
14. Figure 10, curious why use for example “Californian” than “California” or “Californian region”?
15. L482, should be explained variance rather than “variance”? also L516.