The dilemma in identifying WMO-defined tropopause height using high-resolution radiosondes

Gou, Yu; Zhang, Jian; Wang, Wuke; Huang, Kaiming; Zhang, Shaodong

doi:https://doi.org/10.5194/egusphere-2024-4198

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https://doi.org/10.5194/egusphere-2024-4198

Preprints

10 Feb 2025

| 10 Feb 2025

The dilemma in identifying WMO-defined tropopause height using high-resolution radiosondes

Yu Gou, Jian Zhang, Wuke Wang, Kaiming Huang, and Shaodong Zhang

Abstract. The tropopause plays a critical role in stratosphere–troposphere exchange and climate change. Its height is conventionally defined based on the World Meteorological Organization (WMO) threshold temperature gradient, yet this gradient is intrinsically linked to vertical resolution. Data with higher vertical resolution inevitably reveal finer gradient structures. While in situ radiosonde temperature measurements are considered the most reliable source for tropopause structure, high-resolution (5–10 m) soundings would be expected to yield more precise height estimates. The near-global coverage of high-resolution radiosondes, accumulated over even decades, promises valuable insights into long-term tropopause variability. However, our analysis demonstrates that the original WMO definition can lead to an underestimation of the tropopause height when using high-resolution soundings, potentially misidentifying the tropopause within thin inversions or temperature gradient discontinuities below tropopause. To address this, we leverage ERA5 tropopause heights as a reference to develop a high-resolution-optimized method. We evaluate three methods: original WMO method, Moving average method, and Coarse–Fine method. The results reveal that the mean differences between the three methods and ERA5 were 800 m, 280 m, and 180 m, respectively. Notably, ERA5 systematically overestimated the tropopause height compared to all methods, with this discrepancy particularly pronounced in the edges of the Hadley circulation. The proposed Coarse–Fine method, by effectively bypassing thin inversions and gradient extrema while preserving the fine–scale structure of the tropopause height, presents a promising tool for future investigations into long-term tropopause trends.

Received: 31 Dec 2024 – Discussion started: 10 Feb 2025

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Yu Gou, Jian Zhang, Wuke Wang, Kaiming Huang, and Shaodong Zhang

Status: final response (author comments only)

RC1:
'Comment on egusphere-2024-4198', Anonymous Referee #1, 28 Feb 2025

Review of 'The dilemma in identifying WMO-defined tropopause height using high-resolution radiosondes' by Yu Gou et al.
General comments
This new study by Gou et al. explores the challenges in identifying the tropopause height using high-resolution radiosonde data based on the World Meteorological Organization (WMO) definition. The study highlights that the original WMO approach tends to underestimate the tropopause height in high-resolution datasets due to the presence of thin temperature inversions and gradient discontinuities. To address this issue, the authors propose two alternative methods, the Moving Average (MV) method and the Coarse-Fine (C-F) method, both of which provide more consistent tropopause height estimates compared to ERA5 reanalysis data. It is found that ERA5 systematically overestimates the tropopause height, particularly near the Hadley circulation edges, while the WMO-defined method underestimates it. The C-F method emerges as the most effective in preserving fine-scale structures while filtering out spurious lower-altitude tropopauses. The study concludes that modifications to the WMO method are necessary when using high-resolution radiosonde data for accurate long-term tropopause trend analysis.
The study addresses a crucial problem with practical implications for climate research and meteorology. The research employs robust statistical techniques, sensitivity analyses, and cross-validation with ERA5, ensuring a high level of scientific rigor. The methodology is well-described, but a deeper discussion on the physical basis of biases and additional validation with independent datasets could enhance transparency. The manuscript is mostly clear and concise. I would like to recommend that the paper be considered for publication, subject to the minor comments listed below.
Specific comments
l40: It is a little unclear to me what you mean by 'constant emitted temperature'?
l106: The dynamical tropopause in the tropics is usually defined by a potential temperature threshold, not by potential vorticity. Please clarify.
l116: Lapse rate is defined as temperature difference over height difference. However, for radiosondes this is probably calculated via pressure differences? Could you please clarify and elaborate?
l119: Reference paper for ERA5 should be cited: Hersbach H, Bell B, Berrisford P, et al. The ERA5 global reanalysis. Q J R Meteorol Soc. 2020; 146: 1999-2049. https://doi.org/10.1002/qj.3803
l136: Please clarify the shape of the moving window. Presumably a boxcar/tophat function was used?
l195: It would be good to know if the high resolution radiosonde data (or a downsampled version of the data) have been assimilated into ERA5? Presumably the data are not independent?
Fig. 6: These maps suggest that the statistical differences are due to a few individual outliers, probably related to inversions, rather than a bias across all profiles.
Technical corrections
l17: below _the_ tropopause
l19: Movering _A_verage method (here and in other places in the manuscript)
l63: 'Instead' -> 'In contrast'
l69: high-resolved radiosonde _data_ can
l69: understanding of __ tropospheric processes
l73: replace 'Hoffmann et al. (2022)' by 'Hoffmann and Spang (2022)' throughout the manuscript
l82: 'directly WMO-defined method' -> 'original WMO method to detect the tropopause' (the term 'WMO direct method', WDM, is defined only later in the manuscript)
l92: regularly __ twice a day
l97: avoid repetition of 'typically'
l132: occurr _at_ higher latitude
l154: _Sensitivity_ analysis
l160 and l172: replace 'enhancement' by 'increase'
l206: revisit/rephrase 'in the austral with equivalent latitude band'
l224: suggest section title 'Discussion and conclusions' (since discussion comes first)
l241: approximately 300 m _in the upper troposphere and lower stratosphere_ (for clarity)
l265: fail to _avoid_ the
Fig. 2: y-axis label 'Hight' -> 'Height'
Fig. 5: Scatter plots would be better visible if they would be shown next to the maps, and not on top of them. Replace 'in the lower side' by 'at the top of the scatter plots' in figure caption.

Citation: https://doi.org/10.5194/egusphere-2024-4198-RC1
- CC1:
  'Reply on RC1', Gou Yu, 19 Mar 2025
  
  We sincerely appreciate your thoughtful and exhaustive comments and
  suggestions, which significantly help us to improve the quality of the manuscript.
  However, I made a big mistake in my understanding of the tropopause as
  defined by the World Meteorological Organization, which made my algorithm
  wrong and on which a large part of the whole article is based. So, we decided to
  withdraw our manuscript.
  Before pulling the manuscript, we would like to express our sincere gratitude
  to the referee for your exceptionally informative, constructive, and detailed
  comments, and we would like to answer some of your questions if my algorithm is
  correct.
  
  Citation: https://doi.org/10.5194/egusphere-2024-4198-CC1
  - RC3: 'Reply on CC1', Anonymous Referee #1, 25 Mar 2025
    
    Dear Authors,
    I’m sorry to hear that you had to withdraw your manuscript. Identifying the tropopause using the WMO criteria is indeed challenging, and difficulties in properly implementing these criteria are common. I carefully examined the temperature profiles presented in your paper, but based on the plots, I was unable to identify any clear contradictions to the WMO definition, I am afraid.
    As the other reviewers have suggested, relying on existing, well-tested codes or algorithms for identifying the tropopause is often a prudent approach.
    I sincerely appreciate the effort you put into addressing my earlier concerns and comments on the paper.
    I hope you will find the time and energy to revisit this study, as I found the topic highly interesting and I believe it has potential.
    Best regards,
    
    Reviewer #1
    
    Citation: https://doi.org/10.5194/egusphere-2024-4198-RC3
    
    AC2: 'Reply on RC3', Jian Zhang, 14 Jul 2025
    
    Dear Reviewer,
    
    We are grateful for your time and constructive feedback. Your comments have strengthened our paper, and we have incorporated your suggestions to improve the manuscript. we adjust the whole article by removing the part of modification to the definition of WMO and adding the long term trend analysis of the tropopause. Hoping the revised version meets your expectations.
    Best regards,
    
    Yu Gou
    
    Citation: https://doi.org/10.5194/egusphere-2024-4198-AC2
RC2:
'Comment on egusphere-2024-4198', Anonymous Referee #2, 14 Mar 2025

The authors leverage a recent year of high-resolution (5-10 m) radiosonde observations and ERA5 reanalysis output to explore application of the conventional World Meteorological Organization (WMO) lapse-rate tropopause definition to these datasets. The authors argue that the WMO definition fails to reliably identify tropopause height using high-resolution data and develop several alternative means of application to improve performance. Finally, they compare their results to those based on ERA5 reanalysis and report upon outcomes. While the study is generally well-structured, the analysis unfortunately is built upon an incorrect implementation of the WMO definition which undermines the fidelity of all analyses presented. Thus, I cannot recommend publication of this study, but encourage the authors to repeat the analysis with correct implementation of the WMO definition (and others) and continue to pursue the comparisons with ERA5 reanalysis, which are a worthwhile effort. I elaborate upon this assessment below.
Incorrect Implementation of the WMO Definition
First, to hopefully put the authors somewhat at ease, I will acknowledge that this is not the first study to incorrectly implement the WMO definition. In fact, many public code packages also have erroneous implementation of the WMO definition, and it is unfortunately easy for such outcomes to occur because the language used in the 1957 WMO publication has resulted in a wide range of interpretations. When I first began to study the tropopause and apply the WMO definition ~20 years ago, I made similar mistakes which were fortunately identified by other scientists in the field and ultimately corrected before publication of my analyses. Rather than write an extensive technical description of the steps required for correct implementation, I will simply point the authors to a recent study which provides such code in multiple programming languages and discusses some important considerations for applying this definition (and the general task of identifying the tropopause for datasets of varying resolution):
Tinney et al., 2022: A Modern Approach to a Stability-Based Definition of the Tropopause, Mon. Wea. Rev., 150, 3151–3174, doi:10.1175/MWR-D-22-0174.1
I will note that the above-referenced study code includes steps for interpolation of coarse-resolution data to a finer vertical grid, which can be omitted for the high-resolution data used in this study.
Omission of Relevant Prior Research
One related and important general point I would like to make at this stage is that I noticed some glaring omissions of relevant prior work. In particular, given the focus on identification of the tropopause and its characteristics using high-resolution radiosonde data, decades of prior work with such a focus was unexplainably absent. This is especially true for the well-recognized series of early foundational studies by Birner:
Birner et al., 2002: How sharp is the tropopause at midlatitudes?, Geophys. Res. Lett., 29, doi:10.1029/2002GL015142
Birner, 2006: Fine-scale structure of the extratropical tropopause, J. Geophys. Res., 111, D04104, doi:10.1029/2005JD006301
These studies and many that follow have demonstrated well that the WMO definition, when applied appropriately, results in reliable definition of the tropopause that is insensitive to profile resolution. There are certainly failure modes of the WMO definition, but resolution is not one of them (except for resolution that is very coarse, which can of course be ameliorated by interpolation).
Another topic that I found to be poorly described and referenced relates to the statement at line 45 of the paper. In particular, the abrupt change in tropopause height near the subtropical jet streams is commonly referred to as the tropopause break. There is vast literature on the subject as well as its relation to Hadley Cell (or lack thereof, as several studies have shown that the tropopause break is not coupled to the HC). A search using the term "tropopause break" should turn up these relevant works. Additional studies that explore numerous tropical edge diagnostics to determine changes in the width of the tropics (a la Davis & Rosenlof, 2012, http://dx.doi.org/10.1175/JCL1-D-11-00127.1 and others that follow) will help resolve the HC link argument.
Specific Comments
The references for the radiosonde data sources appear to be inappropriate. In particular, the University of Wyoming page does not provide access to the full-resolution radiosonde data used in this study, but instead only includes mandatory and significant levels (as in the IGRA archive). The NOAA website referenced appears to only include surface observations and in real-time rather than a historical archive. I believe the most appropriate source of high-resolution radiosonde observations in the United States is https://www.ncei.noaa.gov/access/metadata/landing-page/bin/iso?id=gov.noaa.ncdc:C01500. There are alternative copies of the data in BUFR format from other sites, which the authors may have used. Because the data I can easily grab from U. Wyoming are on mandatory and significant levels and I do not have time to otherwise download the full-resolution BUFR data, I cannot reproduce Figure 1 from the paper to demonstrate my main point above. Nevertheless, the authors should resolve this data citation issue so that the study could be easily replicated by any reader.
Lines 74-75: I am not sure what this sentence means or implies.
Line 85: “retrieve” should be “retrieval”

Citation: https://doi.org/10.5194/egusphere-2024-4198-RC2
- AC1: 'Reply on RC2', Jian Zhang, 14 Jul 2025
  
  Dear Reviewer,
  
  We sincerely appreciate your time and valuable feedback on our manuscript. Your insightful comments have helped us improve the clarity and rigor of the paper. We have carefully addressed all your suggestions, we decided to adjust the whole article by removing the part of modification to the definition of WMO and adding the long term trend analysis of the tropopause. We hope the revised version meets your expectations. Thank you for your constructive critique!
  Best regards,
  
  Yu Gou
  
  Citation: https://doi.org/10.5194/egusphere-2024-4198-AC1
CC2:
'Unsolicited review of egusphere-2024-4198', Juan Antonio Añel, 23 Mar 2025

Review of Guo et al. "The dilemma in identifying WMO-defined tropopause height using high-resolution radiosondes"
I have read this manuscript, and unfortunately, it falls short in terms of quality and presentation. What is worse, it seems to be built on a set of misunderstandings on what tropopause is, apparently, a lack of knowledge of the existing literature and research performed on it. The lack of discussion in the Introduction of the existing work in the field and even the doubtful use of some papers to support some statements (or not citing them) is another issue of concern here. I develop all this below, and because of it, I consider that this manuscript must be rejected for publication, not in this journal, but in any other in its current form. I do not like to be so categorical, but this manuscript presents serious flaws in this case.
First, as evident from the work presented, the title of the manuscript is grandiloquent, overstating, and not representative of the work presented here, which is, at best, a small study on how different statistics give different results. The fact that is applied to the tropopause is a minor detail. It does not exist any dilemma in the scientific community on what it is the tropopause or how to define it, and high-resolution radiosondes, mentioned in the title as if they were a key part of the work, are not compared against other radiosondes, so it is not possible to establish here anything from them. Also, it has been proved that in some cases, the vertical resolution of the radiosonde data compared to IGRA, which they mention here, does not impact the final statistics on tropopause. At least this previous work should be cited in the text: Antuña et al. (2006) https://doi.org/10.5194/angeo-24-2445-2006
The authors try to propose better tropopause "definitions" that accommodate the high-resolution radiosonde data. However, they never study if they are seeing tropospheric and stratospheric air masses, and their reasoning to support their criteria as valid is not backed by anything and obviates all the existing literature on the complex structure of the tropopause, their inversion layer, multiples tropopauses, latitudinal transport of air masses, and regional characteristics. Even their split in different regions does not follow the usual practice in the community, which makes any potential intercomparison hard.
Some parts of the manuscript contain incorrect statements, and the presentation presents flaws in some parts. These problems with the quality of the manuscript submitted undermine confidence in the quality of the work presented here.
Specifically:

------------

Line 32: It is hard to understand the selection of the work by Xian and Homeyer (2019) to establish in a paper what tropopause is in the atmosphere. With all the due respect to their work, their study is one more in a large existing literature about the tropopause, and is cherry-picked here. One would reasonably expect that the first paper to be cited to explain what is the tropopause is a review paper, a seminal work or book, such as the definition in the Encyclopedia of Atmospheric Sciences, or a paper such as Fueglistaler et al. (2009) or Gettelman et al. (2011).

https://doi.org/10.1029/2008RG000267

https://doi.org/10.1029/2011RG000355
Line 45: "defining" the tropopause does not lack a universal approach. The tropopause has a definition given by the WMO. What can be different is the separation between a tropospheric and a stratospheric regime. Obviously, different characteristics of the troposphere and stratosphere produce a transition between both layers that is different from the tropopause thermal definition, but this does not mean that the tropopause does not have a definition.

It is important that the authors make a clear difference here between the characteristics that define the layer that separates the troposphere and the stratosphere regimes and the transition layer itself. This can be done by clarifying that the tropopause has a definition, but many "criteria" can be used to separate the tropospheric and stratospheric characteristics. The dynamic criterion (usually based on Potential Vorticity fields) does not fail at midlatitudes but in the tropics, where potential vorticity isolines get vertical. Actually, the authors make the point correctly in line 107. If they are going to talk about the different criteria in a manuscript that intends to deal with the determination of the tropopause, one would also expect a complete overview of it, mentioning the e90 by Prather et al. and the different PV values tested by Hoinka.
Line 47: It is important to include citations to the different criteria to determine the tropopause for those unfamiliar with the topic. One of the best for the CPT is the paper by Gettelman et al. (2000), which began to make popular the topic. For the dynamical tropopause, the combination of the WMO (1985) technical report and the paper by Hoinka (1998) give the necessary information.

WMO (1985) Atmospheric Ozone, Report No. 16, page 152.

https://doi.org/10.1175/1520-0493(1998)126<3303:SOTGTP>2.0.CO;2
It is also important to note that the WMO definition (as anyone thermal) fails in polar regions, because of the low vertical gradient that exists in those regions during parts of the year, contrary to what the authors state in lines 49-50. And line 49 should read "The tropopause definition (WMO, 1957), which is thermodynamic,..."
Line 51: The upward trend in the tropopause is not recent. The first report on it, already cited by the authors, is from 2003, and the existing data for this trend is from radiosonde data and goes back to 1958 (Seidel and Randel, 2006). I would cite here one of my papers, contemporaneous to the one of Seidel and Randel, Añel et al. (2006).

https://doi.org/10.1007/s00114-006-0147-5
Lines 54-57: It is hard to understand how this manuscript does not include a citation to the paper by Meng et al. (2021) https://doi.org/10.1126/sciadv.abi8065, which is one of the most recent discussing the tropopause rise from radiosondes.
Line 58: You should cite here the papers for IGRA: Durre et al. (2006, 2018), which you already include in the list of references.
Line 63: It is unclear what the authors want to say here. A couple of sentences before, they say that radiosonde data (IGRA) suffers from vertical resolution problems; now, here, they say that radiosonde data have greater vertical resolution. Do you refer now here to "raw" radiosonde data and not the soundings included in IGRA? Please clarify.
Line 70: "tropopause also exits as inversions". It is unclear what you want to say or imply with this sentence fragment. Please clarify.
Line 78: it is unnecessary to clarify that ERA5 is the sucessor to ERA-Interim, please, delete it.
Line 94: quite self-serving, but if you talk about studying the tropopause structure from radiosonde data, you are probably missing the only study that is important to cite (jointly with the Birner et al. (2006) paper on the TIL), the one that studies its global structure until the third tropopause level: Añel et al. (2008) Climatological features of global multiple tropopause events (https://doi.org/10.1029/2007JD009697).
Line 100: Using a previously published paper to cite three different data sources is far from being the best practice. Instead, you should provide the exact data repositories for the datasets that you use. Following the better current standards on data citation, at least they should have a DOI. It would be great if they had it.
Line 105: again, no several methods exist to define the tropopause. Maybe to separate the troposphere from the stratosphere.
Line 106: It is Ertel's Potential Vorticity, not Rossby-Ertel. Rossby's formalism does not contain the features later developed by Ertel (conservation) that make the EPV a tracer that can separate stratosphere and troposphere air masses.
Lines 111 and 114: I am being picky here, but the WMO definition does not contain the quotation marks used by the authors here, but the terms "first tropopause" and "second tropopause" are given in italics. I think that the right way to do it would be to put the full definition between the quotation marks and not only these two terms.
Lines 150-152: I understand the argumentation by the authors; however, the statement "are likely to be more consistent with previous research." what do you mean by this? With what previous research? Why? This sounds like a willingness more than a scientific fact, and no previous research is cited to support such a statement. Then you say, "and understanding of the tropopause." This statement is baseless. Here, in these soundings, the authors do not check what the troposphere or the stratosphere is. For example, in Fig. 1a,b, have you checked if the air mass between the WDM and the MV or C-F is of stratospheric or tropospheric origin? Guessing that the WDM is not a valid tropopause is not enough; if you are stating it, you should prove it, for example, with PV and ozone fields. This station is located around the subtropical jet stream, a region prone to the occurrence of multiple tropopauses (see Añel et al. 2008), and where the tropospheric and stratospheric air masses mix along several km in the vertical. You can not simply state that the WDM is a not valid tropopause when, for January, the tropopause can appear in the region of this sounding at levels so low as 200 hPa (see Añel et al. (2008) again, e.g., Fig.4), and in a latitude where the latitudinal entrainment of mid-latitudes stratospheric air under the tropical tropopause makes hard to define the change between the tropospheric and stratospheric air masses. See Wang and Polvani (2011) and Añel et al. (2012).

https://doi.org/10.1029/2010JD015118

https://doi.org/10.1100/2012/191028
Many references are misplaced in the list, for example, Seidel et al. (2010), Hoffman et al., Houchi et al., Randel et al.
The label in the Y-axis of Fig. 2 is misspelled.

Citation: https://doi.org/10.5194/egusphere-2024-4198-CC2
- AC3: 'Reply on CC2', Jian Zhang, 14 Jul 2025
  
  Dear Reviewer,
  We sincerely appreciate your thoughtful and exhaustive comments and suggestions, which significantly help us to improve the quality of the manuscript.
  However, I made a big mistake in my understanding of the tropopause as defined by the World Meteorological Organization, which made my algorithm wrong and on which a large part of the whole article is based. So, we have adjusted the whole article by removing the part of modification to the definition of WMO and adding the long term trend analysis of the tropopause. We would appreciate it if you could give us your valuable comments for the revised manuscript.
  Best regards,
  
  Yu Gou
  
  Citation: https://doi.org/10.5194/egusphere-2024-4198-AC3
AC4:
'Comment on egusphere-2024-4198', Jian Zhang, 14 Jul 2025
Dear Reviewers,
I sincerely appreciate the time and expertise you have dedicated to evaluating our manuscript. Upon careful re-examination, we recognize that our initial misunderstanding of the WMO tropopause definition constituted a fundamental error that affected key aspects of our study.
I deeply regret this oversight and the additional review burden it may have caused. To rectify this matter, we have:

Completely revised our methodology by removing the incorrect interpretation

Conducted new analyses focusing on long-term tropopause trends

Thoroughly re-evaluated all related conclusions

We are truly grateful for your patience and constructive criticism, which have been invaluable in improving our work. Please accept our sincere apologies for any inconvenience this may have caused during the review process.
Best regards,

Yu Gou
Citation: https://doi.org/10.5194/egusphere-2024-4198-AC4

Yu Gou, Jian Zhang, Wuke Wang, Kaiming Huang, and Shaodong Zhang

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Short summary

The most commonly used tropopause height detection algorithm is based on the World Meteorological Organization (WMO) definition from 1957. However, with the increasing vertical resolution of atmospheric data, this definition has been found to fail in high-resolution radiosonde data. Thus, we propose an improved method to address this issue. This method can effectively bypassing thin inversions while preserving the fine–scale structure of the tropopause.


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