the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 10 Jun 2025
The Frosty Frontier: Redefining the Tropopause as a transport barrier using the Relative Humidity over Ice
Abstract. The tropopause acts as transport barrier between the troposphere and stratosphere. While common definitions rely on quantities conserved under adiabatic changes, diabatic effects, resulting from radiation, cloud processes or turbulence are also decisive for the tropopause structure. Therefore, we propose a new definition based on the vertical gradient of the relative humidity with respect to ice (RHi). RHi is the key variable for ice cloud formation and incorporates both diabatic and adiabatic processes. Based on high-resolution radio sonde data we can show that our definition reflects the nature of the tropopause as a transport barrier much better than conventional approaches. This is not only evident in individual vertical profiles, but also when looking at statistics of many profiles with a tropopause-relative height axis. Last but not least, the robust and simple calculation of our definition makes it an ideal tool for studies involving the tropopause.
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The requested preprint has a corresponding peer-reviewed final revised paper. You are encouraged to refer to the final revised version.
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- RC1: 'Comment on egusphere-2025-2474', Anonymous Referee #1, 23 Jul 2025
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RC2: 'Comment on egusphere-2025-2474', Anonymous Referee #2, 24 Jul 2025
This paper suggests that relative humidity, or more specifically, the vertical gradient of relative humidity, be used as an alternative definition of the tropopause. Actually this seems to me to be an interesting and potentially useful idea and I have not heard this definition of the tropopause suggested before. So I am certainly in favour of a paper on this topic being published.
However I feel that the current version of the paper has some substantial flaws on which I give comments below. Therefore I recommend that the paper is published only after major revision that addresses my comments (or refutes them in a convincing way).
The major points where I think that the paper could be improved (and it would be a pity if it was not) are the following:
Tropopause vs Extratropical Tropopause:Â
I believe that this new definition applies to the extratropical tropopause. The authors do not show any examples applying it to the tropical tropopause and my guess is that it would not work so well. So I recommend that 'Tropopause' is replaced by 'Extratropical Tropopause' in the title. It certainly isn't necessary to add 'extratropical' to every mention of 'tropopause' in the paper -- but its occasional use would be helpful.Â
Transport barriers:
The abstract states (and there are similar statements at various places in the main text): 'The tropopause acts as a transport barrier between troposphere and stratosphere ...' -- well yes and no. My own view is that the tropopause is should be regarded as air mass boundary -- in particular air below the tropopause (tropospheric air) has experienced a very different recent history to air above the tropopause (stratospheric air). This pattern of transport may arise because of the presence of transport barriers, but these need not coincide with the tropopause it self. For example, one view of the extratropical tropopause (the part poleward of the subtropical jet) is that it results from the fact that on lower isentropes there is free exchange with the subtropics whereas on higher isentropes there is not free exchange because the subtropical jet acts as a barrier to latitudinal transport. The barrier to transport (the jet) and the part of the extratropical tropopause being considered are not co-located. Of course the term 'tropopause as transport barrier' is used in reputable review articles and it would not be appropriate for this referee report to become a kind of independent review article on the nature of the tropopause. But one concrete reason for caution in using this term is that it seems to me to encourage a 1-dimensional view of the extratropical tropopause, with this being an upper limit to strong vertical transport in the troposphere. Most would agree that this is not a satisfactory model for the extratropical tropopause, not least since the relevant transport in the troposphere is not transport in the vertical.
The fact is that what you are proposing is potentially useful definition of the tropopause whether or not one defines it as a transport barrier, or as an air mass boundary, or as any variation on those. So I recommend dropping the very strong emphasis on tropopause as transport barrier.
General comments on the tropopause and related topics:
Some of the general, e.g. review, comments on the tropopause and its structure seem a bit muddled to me. Of course there is room for uncertainty in this general area -- e.g. views of which processes are most important vary across scientists working in this area. But I think that the paper would be more effective if it said less, so that the reader can focus on the interesting idea of using RHi (or its vertical gradient) to identify the tropopause, rather than continually thinking 'my view of how this works is different to that expressed here'.Â
Relation to other tropopause identifiers:
To me the primary explanation for the RHi structure is that in the upper troposphere the water vapour concentrations are primarily determined by relatively local temperature conditions, whereas in the stratosphere they are primarily determined by remote temperature conditions. (The latter was the key insight of the landmark paper by Brewer.) The difference in transport pathways that leads to this difference in RHi is similarly responsible for differences in concentrations of species such as ozone and carbon monooxide. Therefore the RHi approach offers the possibility of identifying this chemical or air mass tropopause using information available from standard radiosonde measurements, rather than requiring in-situ chemical measurements.Â
I am surprised that the authors don't emphasise this point more. (But perhaps they don't agree with me on this point.)Theoretical model:
The current description of this model is not suitable for publication. (See further comments below.)
DETAILED COMMENTS:
Abstract: 'While common definitions rely on quantities conserved under adiabatic changes, diabatic effects ... are also decisive for the tropopause structure' -- this seems to muddle several different points. If we take the use of PV, for example, the advantage of PV (conserved on moderate timescales) over temperature gradient (not conserved on moderate timescales) is that it provides an identification of the tropopause that does change on short time scales through purely reversible dynamics. (Another way of saying this would be that according to the temperature definition an air parcel might be in the troposphere one day, the stratosphere the next, and the troposphere next, and this was recognised many years ago as not consistent with other characteristics of troposphere versus stratosphere.
L24: 'most popular' -- 'most used'? Of course the reason why it is the most used definition is that it was proposed by the WMO and is therefore a natural standard definition for many purposes -- e.g. for researchers who are not particular interested in the tropopause itself, but in some other aspect of the atmosphere which requires a distinction between troposphere and stratosphere.
L26: 'Another definition ...' -- this jumps to the cold point definition but it is essentially irrelevant to the discussion here because it is a tropical definition and, as I have noted above, the emphasis of your paper is on the extratropics.Â
L35: This might be a good point to cite Tinney et al MWR 2022 who specifically discuss the fact that high-vertical resolution causes problems for this definition.Â
L36: 'In reality, several tropopauses can [sometimes] be found in one profile with this type of definition ...' -- but we know this makes physical sense (e.g. filaments of tropospheric air from the subtropics overlying stratospheric air). If you are suggesting here that a useful definition of the tropopause is REQUIRED to identify only one tropopause in a given column then I would say that I do not accept that -- some kind of 'operational' specification of the tropopause should make it clear that sometimes identifying multiple tropopauses is the only sensible outcome.
L47: This very brief description of the dynamical processes contributing to tropopause structure/maintenance is very focused on vertical motion -- upwelling in troposphere/downwelling in stratosphere -- which is a drastic oversimplification (in my view) -- e.g. see reviews such as Gettelman et al (2011), or papers such as Kunkel et al (2016 ACP) which emphasise the three-dimensionality of the dynamics affecting the tropopause. I think that these two or three sentences could straightforwardly be changed to be consistent with that.
L61: 'is assumed to be crucially created by radiative cooling ...' -- I don't see this as a universally held view. The Randel et al (2007) paper focused on high latitudes. Other papers have shown that models can produce a TIL without inclusion of the specific radiative properties of water vapour -- e.g. Son and Polvani (2007 GRL) -- but there are probably more recent papers of this type -- and again see Kunkel et al (2016) who don't specifically emphasise the radiative role of water vapour over other processes.
L97: It seems to be taken as obvious here that standard radiosondes provide water vapour measurements in the tropopause region that are sufficiently accurate to be useful. I had the impression in the past that standard radiosondes were not felt to be sufficiently accurate to provide useful stratospheric water vapour measurements -- but perhaps that applies more to the tropics and to concentrations of 10ppmv or less? Does the fact that it is RHi rather than concentration that is being used help with this potential problem -- if it exists?
L100: 'Vertical Relative Humidity Gradient' would be more precise (and an important aspect of the paper is your emphasis on RELATIVE humidity).
L100: My guess is that the identification of the tropopause is insensitive to the precise choice here. Presumably you tested that? Please confirm. What values would be too high or too low? The same goes for the choice of relative humidity threshold. Please give more explicit information. Having looked at the examples given in Figures 1-3, I am wondering if a criterion of RHi > 20% Â without the gradient criterion would work as well as your chosen criterion. Did you try possibilities of this type?
L106: For clarity it would be best if this 'break' criterion was highlighted in the same way as the other two criteria.
L109: 'We use the same code as ...' -- at first sight this seems unnecessary. But I guess the key point is the requirement for smoothing mentioned a couple of lines later. These two sentences could be combined.
Figure 1: In the 2nd panel temperature and dew point are presumably red/blue respectively.
L127: For reasons given above I don't find it helpful to use 'transport barrier' here -- why not say 'the RHi-GT'.Â
L137: 'the theta' -- delete 'the'
L139: My guess is that these characteristics -- i.e. relatively low static stability in air that is stratospheric from an airmass perspective -- are typical of certain synoptic situations. For example the air in the 8-12 km range could have relatively high PV if cyclonic vorticity was compensating for the low static stability. (But certainly in this example the RHi characterisation appears to capture a clear 'air mass' tropopause.)
L141: replace 'optical' by 'visual'.
L143: 'The WMO thermal tropopause therefore appears somewhat arbitrary at this point.' -- one could say the same about the RHi tropopause. There are multiple relatively moist shallow layers -- presumably filaments penetrating from the subtropics. The RHi approach chooses one of these. Whether this is the best choice, or a better choice than the WMO thermal tropopause, is not very clear. But certainly the RHi approach is no worse than the thermal tropopause.Â
L155: I don't understand 'limited by the dry stratosphere, as the WMO criterion is based on prolonged warming'.
L181: '(and nonphysical)' -- I don't see the justification for 'nonphysical' -- the fact is that both panels are based on the same RHi data -- the difference between them results from the fact that the data has been organised in different ways. There is nothing 'nonphysical' about that. Of course it might be that one panel is more straightforward to explain or provides a simpler conceptual model -- but that is not 'physicality' vs 'non physicality'.
L219: 'more unsteady pattern' -- poorly chosen wording -- there is nothing steady or unsteady about this pattern.Â
L228: 'Thus, we can finally state that a much clearer separation of tropospheric and stratospheric N squared values has been achieved by simply using ...' -- I don't see the justification for 'much clearer'. But certainly there are very interesting differences between the two profiles and further work (beyond the scope of this paper) is needed to understand them.
Section 4:Â
I found this section quite difficult to follow and have made general rather than line-by-line remarks.
You seem to be considering a model in which quantities vary in height (z) and time. Time derivatives seem to be material derivatives -- is that correct? You neglect 'cloud processes' meaning that RHi is a function of T and p, for given q_v, leading to (9). Then there is a jump to vertical gradients rather than rate of change of time in (10) when you conclude that it is vertical gradients of temperature and q_v that primarily determine the vertical gradient of RHi. (I don't think that many would be surprised by that.)
The text L278-284 -- including 'huge benefit of our new definition', 'For definitions it is even worse' -- seems unjustified. Many of the statement are muddled. For example, using PV as a basis for tropopause definition does not 'neglect' diabatic processes. It is a combination of diabatic and dynamical processes that set the overall structure of the PV field and make it suitable as a basis for identifying the tropopause. Then the fact that PV is materially conserved on short timescales is advantageous because it means (as noted above) that a given air parcel does not suddenly change from being tropospheric to stratospheric (or vice versa) through purely reversible dynamics (which is possible according to the lapse-rate approach). Also, to correct a simple factual error -- the (vertical) gradient of potential temperature is NOT, as you state, conserved under adiabatic processes.Â
The toy model is mysterious. You are imposing a positive w in the UT, and a 'typical radiative cooling contribution at the upper part of the humid layer'. No details of the latter are given, but it is clearly playing a crucial role, since, as far as I can tell, it is the sole mechanism for giving any temperature change about 10km. I don't believe that q_v is changing in time (true?), so the whole response in relatively humidity (and its vertical gradient) has to be understood in terms of the temperature dependence of the saturation vapour pressure. You refer to the 'temperature' and 'humidity' terms but because the humidity is kept constant the 'humidity' term changes only through the change in temperature. The main physical effect being demonstrated seems to be that because UT temperatures are decreasing the UT RHi is increasing and therefore the vertical gradient of RHi becomes more negative.
I don't see what this model calculation is supposed to demonstrate. Is it that a strong negative vertical gradient in RHi is somehow self-reinforcing? But the physical ingredients included in the model -- essentially imposed cooling in the troposphere -- don't see a plausible starting point.Â
My overall comment on Section 4 is that the motivation for the model needs to be much clearer -- what is the hypothesis motivating this model? -- and the details needed to be stated more clearly, so that someone else could reproduce the results for themselves if they wished.
Citation: https://doi.org/10.5194/egusphere-2025-2474-RC2 - AC1: 'Comment on egusphere-2025-2474', Philipp Reutter, 24 Sep 2025
Interactive discussion
Status: closed
- RC1: 'Comment on egusphere-2025-2474', Anonymous Referee #1, 23 Jul 2025
-
RC2: 'Comment on egusphere-2025-2474', Anonymous Referee #2, 24 Jul 2025
This paper suggests that relative humidity, or more specifically, the vertical gradient of relative humidity, be used as an alternative definition of the tropopause. Actually this seems to me to be an interesting and potentially useful idea and I have not heard this definition of the tropopause suggested before. So I am certainly in favour of a paper on this topic being published.
However I feel that the current version of the paper has some substantial flaws on which I give comments below. Therefore I recommend that the paper is published only after major revision that addresses my comments (or refutes them in a convincing way).
The major points where I think that the paper could be improved (and it would be a pity if it was not) are the following:
Tropopause vs Extratropical Tropopause:Â
I believe that this new definition applies to the extratropical tropopause. The authors do not show any examples applying it to the tropical tropopause and my guess is that it would not work so well. So I recommend that 'Tropopause' is replaced by 'Extratropical Tropopause' in the title. It certainly isn't necessary to add 'extratropical' to every mention of 'tropopause' in the paper -- but its occasional use would be helpful.Â
Transport barriers:
The abstract states (and there are similar statements at various places in the main text): 'The tropopause acts as a transport barrier between troposphere and stratosphere ...' -- well yes and no. My own view is that the tropopause is should be regarded as air mass boundary -- in particular air below the tropopause (tropospheric air) has experienced a very different recent history to air above the tropopause (stratospheric air). This pattern of transport may arise because of the presence of transport barriers, but these need not coincide with the tropopause it self. For example, one view of the extratropical tropopause (the part poleward of the subtropical jet) is that it results from the fact that on lower isentropes there is free exchange with the subtropics whereas on higher isentropes there is not free exchange because the subtropical jet acts as a barrier to latitudinal transport. The barrier to transport (the jet) and the part of the extratropical tropopause being considered are not co-located. Of course the term 'tropopause as transport barrier' is used in reputable review articles and it would not be appropriate for this referee report to become a kind of independent review article on the nature of the tropopause. But one concrete reason for caution in using this term is that it seems to me to encourage a 1-dimensional view of the extratropical tropopause, with this being an upper limit to strong vertical transport in the troposphere. Most would agree that this is not a satisfactory model for the extratropical tropopause, not least since the relevant transport in the troposphere is not transport in the vertical.
The fact is that what you are proposing is potentially useful definition of the tropopause whether or not one defines it as a transport barrier, or as an air mass boundary, or as any variation on those. So I recommend dropping the very strong emphasis on tropopause as transport barrier.
General comments on the tropopause and related topics:
Some of the general, e.g. review, comments on the tropopause and its structure seem a bit muddled to me. Of course there is room for uncertainty in this general area -- e.g. views of which processes are most important vary across scientists working in this area. But I think that the paper would be more effective if it said less, so that the reader can focus on the interesting idea of using RHi (or its vertical gradient) to identify the tropopause, rather than continually thinking 'my view of how this works is different to that expressed here'.Â
Relation to other tropopause identifiers:
To me the primary explanation for the RHi structure is that in the upper troposphere the water vapour concentrations are primarily determined by relatively local temperature conditions, whereas in the stratosphere they are primarily determined by remote temperature conditions. (The latter was the key insight of the landmark paper by Brewer.) The difference in transport pathways that leads to this difference in RHi is similarly responsible for differences in concentrations of species such as ozone and carbon monooxide. Therefore the RHi approach offers the possibility of identifying this chemical or air mass tropopause using information available from standard radiosonde measurements, rather than requiring in-situ chemical measurements.Â
I am surprised that the authors don't emphasise this point more. (But perhaps they don't agree with me on this point.)Theoretical model:
The current description of this model is not suitable for publication. (See further comments below.)
DETAILED COMMENTS:
Abstract: 'While common definitions rely on quantities conserved under adiabatic changes, diabatic effects ... are also decisive for the tropopause structure' -- this seems to muddle several different points. If we take the use of PV, for example, the advantage of PV (conserved on moderate timescales) over temperature gradient (not conserved on moderate timescales) is that it provides an identification of the tropopause that does change on short time scales through purely reversible dynamics. (Another way of saying this would be that according to the temperature definition an air parcel might be in the troposphere one day, the stratosphere the next, and the troposphere next, and this was recognised many years ago as not consistent with other characteristics of troposphere versus stratosphere.
L24: 'most popular' -- 'most used'? Of course the reason why it is the most used definition is that it was proposed by the WMO and is therefore a natural standard definition for many purposes -- e.g. for researchers who are not particular interested in the tropopause itself, but in some other aspect of the atmosphere which requires a distinction between troposphere and stratosphere.
L26: 'Another definition ...' -- this jumps to the cold point definition but it is essentially irrelevant to the discussion here because it is a tropical definition and, as I have noted above, the emphasis of your paper is on the extratropics.Â
L35: This might be a good point to cite Tinney et al MWR 2022 who specifically discuss the fact that high-vertical resolution causes problems for this definition.Â
L36: 'In reality, several tropopauses can [sometimes] be found in one profile with this type of definition ...' -- but we know this makes physical sense (e.g. filaments of tropospheric air from the subtropics overlying stratospheric air). If you are suggesting here that a useful definition of the tropopause is REQUIRED to identify only one tropopause in a given column then I would say that I do not accept that -- some kind of 'operational' specification of the tropopause should make it clear that sometimes identifying multiple tropopauses is the only sensible outcome.
L47: This very brief description of the dynamical processes contributing to tropopause structure/maintenance is very focused on vertical motion -- upwelling in troposphere/downwelling in stratosphere -- which is a drastic oversimplification (in my view) -- e.g. see reviews such as Gettelman et al (2011), or papers such as Kunkel et al (2016 ACP) which emphasise the three-dimensionality of the dynamics affecting the tropopause. I think that these two or three sentences could straightforwardly be changed to be consistent with that.
L61: 'is assumed to be crucially created by radiative cooling ...' -- I don't see this as a universally held view. The Randel et al (2007) paper focused on high latitudes. Other papers have shown that models can produce a TIL without inclusion of the specific radiative properties of water vapour -- e.g. Son and Polvani (2007 GRL) -- but there are probably more recent papers of this type -- and again see Kunkel et al (2016) who don't specifically emphasise the radiative role of water vapour over other processes.
L97: It seems to be taken as obvious here that standard radiosondes provide water vapour measurements in the tropopause region that are sufficiently accurate to be useful. I had the impression in the past that standard radiosondes were not felt to be sufficiently accurate to provide useful stratospheric water vapour measurements -- but perhaps that applies more to the tropics and to concentrations of 10ppmv or less? Does the fact that it is RHi rather than concentration that is being used help with this potential problem -- if it exists?
L100: 'Vertical Relative Humidity Gradient' would be more precise (and an important aspect of the paper is your emphasis on RELATIVE humidity).
L100: My guess is that the identification of the tropopause is insensitive to the precise choice here. Presumably you tested that? Please confirm. What values would be too high or too low? The same goes for the choice of relative humidity threshold. Please give more explicit information. Having looked at the examples given in Figures 1-3, I am wondering if a criterion of RHi > 20% Â without the gradient criterion would work as well as your chosen criterion. Did you try possibilities of this type?
L106: For clarity it would be best if this 'break' criterion was highlighted in the same way as the other two criteria.
L109: 'We use the same code as ...' -- at first sight this seems unnecessary. But I guess the key point is the requirement for smoothing mentioned a couple of lines later. These two sentences could be combined.
Figure 1: In the 2nd panel temperature and dew point are presumably red/blue respectively.
L127: For reasons given above I don't find it helpful to use 'transport barrier' here -- why not say 'the RHi-GT'.Â
L137: 'the theta' -- delete 'the'
L139: My guess is that these characteristics -- i.e. relatively low static stability in air that is stratospheric from an airmass perspective -- are typical of certain synoptic situations. For example the air in the 8-12 km range could have relatively high PV if cyclonic vorticity was compensating for the low static stability. (But certainly in this example the RHi characterisation appears to capture a clear 'air mass' tropopause.)
L141: replace 'optical' by 'visual'.
L143: 'The WMO thermal tropopause therefore appears somewhat arbitrary at this point.' -- one could say the same about the RHi tropopause. There are multiple relatively moist shallow layers -- presumably filaments penetrating from the subtropics. The RHi approach chooses one of these. Whether this is the best choice, or a better choice than the WMO thermal tropopause, is not very clear. But certainly the RHi approach is no worse than the thermal tropopause.Â
L155: I don't understand 'limited by the dry stratosphere, as the WMO criterion is based on prolonged warming'.
L181: '(and nonphysical)' -- I don't see the justification for 'nonphysical' -- the fact is that both panels are based on the same RHi data -- the difference between them results from the fact that the data has been organised in different ways. There is nothing 'nonphysical' about that. Of course it might be that one panel is more straightforward to explain or provides a simpler conceptual model -- but that is not 'physicality' vs 'non physicality'.
L219: 'more unsteady pattern' -- poorly chosen wording -- there is nothing steady or unsteady about this pattern.Â
L228: 'Thus, we can finally state that a much clearer separation of tropospheric and stratospheric N squared values has been achieved by simply using ...' -- I don't see the justification for 'much clearer'. But certainly there are very interesting differences between the two profiles and further work (beyond the scope of this paper) is needed to understand them.
Section 4:Â
I found this section quite difficult to follow and have made general rather than line-by-line remarks.
You seem to be considering a model in which quantities vary in height (z) and time. Time derivatives seem to be material derivatives -- is that correct? You neglect 'cloud processes' meaning that RHi is a function of T and p, for given q_v, leading to (9). Then there is a jump to vertical gradients rather than rate of change of time in (10) when you conclude that it is vertical gradients of temperature and q_v that primarily determine the vertical gradient of RHi. (I don't think that many would be surprised by that.)
The text L278-284 -- including 'huge benefit of our new definition', 'For definitions it is even worse' -- seems unjustified. Many of the statement are muddled. For example, using PV as a basis for tropopause definition does not 'neglect' diabatic processes. It is a combination of diabatic and dynamical processes that set the overall structure of the PV field and make it suitable as a basis for identifying the tropopause. Then the fact that PV is materially conserved on short timescales is advantageous because it means (as noted above) that a given air parcel does not suddenly change from being tropospheric to stratospheric (or vice versa) through purely reversible dynamics (which is possible according to the lapse-rate approach). Also, to correct a simple factual error -- the (vertical) gradient of potential temperature is NOT, as you state, conserved under adiabatic processes.Â
The toy model is mysterious. You are imposing a positive w in the UT, and a 'typical radiative cooling contribution at the upper part of the humid layer'. No details of the latter are given, but it is clearly playing a crucial role, since, as far as I can tell, it is the sole mechanism for giving any temperature change about 10km. I don't believe that q_v is changing in time (true?), so the whole response in relatively humidity (and its vertical gradient) has to be understood in terms of the temperature dependence of the saturation vapour pressure. You refer to the 'temperature' and 'humidity' terms but because the humidity is kept constant the 'humidity' term changes only through the change in temperature. The main physical effect being demonstrated seems to be that because UT temperatures are decreasing the UT RHi is increasing and therefore the vertical gradient of RHi becomes more negative.
I don't see what this model calculation is supposed to demonstrate. Is it that a strong negative vertical gradient in RHi is somehow self-reinforcing? But the physical ingredients included in the model -- essentially imposed cooling in the troposphere -- don't see a plausible starting point.Â
My overall comment on Section 4 is that the motivation for the model needs to be much clearer -- what is the hypothesis motivating this model? -- and the details needed to be stated more clearly, so that someone else could reproduce the results for themselves if they wished.
Citation: https://doi.org/10.5194/egusphere-2025-2474-RC2 - AC1: 'Comment on egusphere-2025-2474', Philipp Reutter, 24 Sep 2025
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Peter Spichtinger
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