Comments to 

"The extratropical tropopause inversion layer and its correlation with relative humidity"

by D. Köhler et al. 

The paper deals with the correlation between TIL properties and relative humidity in a few kilometres thick layer around the tropopause. The authors mention two theories or hypotheses that explain the strong stability maximum that is found in high-resolution profiles at the tropopause, namely a dynamic and a radiative mechanism. Their results seem to support both theories, but not always simultaneously at the same location and season. 

It is not clear to me whether supporting one or both of these theories was the motivation of the study; this is not clearly stated. And it seems to have been not so clear to the authors as well, as it is never clear what the correlations actually mean. Sometimes the text seems to indicate that high relative humidity CAUSES a strong (but thin) TIL, but a corresponding mechanism is not mentioned. Furthemore, if the radiation mechanism is in focus, it should be the radiation extinction and emission by the water molecules that is important, that is, it is the absolute rather than the relative humidity one should look at. If, however, the dynamical mechanism is in focus, consideration of the relative humidty is probably the correct choice, since vertical motions lead to increasing relative humidity.

In any case, I miss the description of mechanisms, that explain or at least suggest how water molecules, either in absolute number or as relative humidity, are involved in the formation of the TIL by either radiation or dynamics. 

The paper thus needs a major revision before it can be accepted for publication. Below I give some further suggestions for improvements.

Major points:

Section 3.1.1: Why do you use the simple differences E(x)-R(x)? This may average out to quite small values and you think everything is ok, where in reality you might have large local differences. Usually, therefore, other measures are used that avoid such cancellation effects, e.g. RMSE, mean ABSOLUTE difference etc. I think, to convince the reader, it is necessary that these traditional standard measures are used instead of the simple average distance. This will certainly broaden your histograms in figures 4 and 5, and perhaps modify or change your conclusions.

Lines 218 ff: another difficulty arises from averaging over the profiles: In this paragraph a shift to higher values of RHi in ERA5 is explained with details of the humidity gradient at the TP. While this is a plausible explanation, it cannot be seen from averaged profiles. Here it would help to split the data into data below the TIL and above the TIL.

Finally, please think whether the quoted values are actually as precise as given (e.g. 10.318). 

  

Section 3.2.1: I see that the mean T-difference at the TP between strong and weak TIL cases is about 10K, and this difference is almost constant throughout the 3 km below the TP. If a strong TIL has a higher TP, one can estimate a height difference of 1-1.5 km (according to usual lapse rates). This means, the T-difference applies in the whole profile at least 1.5 km down from the TP. Your argument in line 257, that there should be a stronger T-gradient, is weak, because it seems that the T-gradient (on average) is the same in all TIL-classes.

A similar observation can be made for the RHi profiles. The higher RHi in the strong TIL case is already present at least 1.5 km below the TP. So the question here is, why and how the TIL is affected by profile characteristics that begin at least 1.5 km below the TP.  

You should also consider the absolute humidity, q. From what I see, I expect that a strong TIL is correlated to the lowest values of q and vice versa. This might be important for the question how radiation can affect the TIL.

The argument, that high RHi at the TP may result from vertical motion, is reasonable, but it weakens your statement from above that radiation might cause the sharpness of the TIL. I suggest to go back and to downplay this argument. This would also strenghten the justification to focus on relative than on specific humidity (which does not change in vertical motions).

Minor points:

Line 67: Why explains the latitude of Idar Oberstein that the geopotential height is close to the geographic height?

L 70: Why are profiles discarded when they end before 20 km? The tropopause in Idar Oberstein probably never reaches such an altitude.

L 77-78: Are the Miloshevich corrections applicable for the RS92 and RS41? And how large are the corrections on average?

L 80ff: This sentence is a bit misleading. It is not "past model forecast" but rather recalculation (hindcast) of the past weather with a recent version of the forecast model. Further, the vertical dimension is represented by rather than calculated on sigma coordinates. 

L 106 ff: see above. If it is cloud formation, then RHi is the natural variable to choose. However, if it is radiation, it should be the absolute water vapour concentration that regulates the optics.

Section 2.2.1: I am not sure whether this section is actually needed. The equations are textbook knowledge, and it probably suffices to write a few sentences instead of a subsection. The approach for the numerical treatment of the derivation should, however, be retained, as this is essential for the paper. The other details are not actually needed here (they might be important elsewhere, though). The lead away from the topic of the paper.

L 153 ff: This remark should be removed. First, the reader cannot see what in the WMO definition requires to look "broadly" or at large scale at the system, and second, the potential effects of this "tacit" assumption are then ignored, for whatever reason. This puzzles the reader and leads away from the central topic.  

L 165 ff: For WHICH averaging process? It comes out of the nothing. I have no clue what happens here.

L 168 ff: and it does not get clearer. It seems that you average your 10000 or so profiles, but that is not so clear to me. Here is the place to provide more details.

L 236 ff: Please reformulate. I think, one should not write that the LS is "more unstable" ... or "too unstable". The word "unstable" should be avoided when it is about the LS.

L 301 ff: If you write "a moist upper troposphere is sharpening the TIL", I think you must at least have a mechanism for the very process in mind and you must tell the reader how it works. But if you only find a coincidence (that is, by the way, a better word describing what you have than correlation, which has a mathematical definition), you should only write that there is a coincidence and avoid the impression that there is a certain process causing high relative humidity to sharpen the TIL.

L 324/325: Again, please reformulate. You found a coincidence, but nothing shows that the humidity has an influence on the TIL. 

L 327-329: Check the sentence. It sounds ugly. And it again indicates the RH somehow acts physically on the TIL.

L 347-348: If water vapour has this cooling effect, shouldn't then the absolute humidity be high? Can you show this?

L 365/366: "The winter/summer similarity further support the idea that radiative and baroclinic forcing can have similar amplifying effects." Please explain this statement.

L 413: the word "confirm" is too strong. I would say your data do not contradict these hypotheses and would be expected in one or both of the scenarios.

L 415 and L 417: "this is supporting...", again I think, this is too strong and should be reformulated.

Miscellaneous:

Line 26: hypotheses

L 27: analyses, a stronger

L 59: radiosonde soundings

L 69: focusses

L 72: replace "unscientific" with "unrealistic". The threshold values still appear quit high. Would 400 K be more realistic, or 200% RH?

L 86: radiosonde (twice)

L 88: What is the difference between PHI_g and PHI_p?

Section 2.1.3: The words consistent and inconsistent are slightly out of place. What is a "consistent spcacing"? I assume you mean that the two data sets are interpolated on the same grid, isn't it. Later: "inconsistent with respect to time"? Here I am lost. Please reformulate.

L 98: set (not sets)

L 123: Insert a paragraph break before "Potential temperature".

L 141: radiosonde

L 172: is the TIL indeed a measure? I suggest to simply delete this unneccessary sentence. Start with the second sentence.

L 175: I would agree that the importance of the TIL is that it is a tranport barrier. But what has it to do with any kind of diagostics? Please reformulate.

L 181: diagnostics

L 190: is quite robust DUE TO small scale variations? What do you mean?

L 194: delete "measured"

L 229: criterion

L 346: season is

L 355: the word "perfomed" does not fit here

L 401: Like above: avoid the word "unstable" when speaking about the stratosphere

L 415: its

See comments in the attached file