the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 29 Apr 2024
Global scale gravity wave analysis methodology for the ESA Earth Explorer 11 candidate CAIRT
Abstract. In the past, satellite climatologies of gravity waves (GWs) have initiated progress in their representation in global models. However, these could not provide the phase speed and direction distributions needed for a better understanding of the interaction between GWs and the large-scale winds directly. The ESA Earth Explorer 11 candidate CAIRT could provide such observations. CAIRT would use a limb imaging Michelson interferometer resolving a wide spectral range allowing temperature and trace gas mixing ratios measurements. With the proposed instrument design, a vertical resolution of 1 km, an along-track sampling of 50 km, and an across-track sampling of 25 km in a 400 km wide swath will be achieved. In particular, this allows for the observation of 3-dimensional, GW-resolving temperature fields throughout the middle atmosphere.
In this work, we present the methodology for the GW analysis of CAIRT observations using a limited-volume 3D sinusoidal fit (S3D) wave analysis technique. We assess the capability of CAIRT to provide high-quality GW fields by generating synthetic satellite observations from high-resolution model data and comparing the synthetic observations to the original model fields. For the assessment, wavelength spectra, phase speed spectra, horizontal distributions, and zonal means of GW momentum flux (GWMF) are considered. The atmospheric events we use to exemplify the capabilities of CAIRT are the 2006 sudden stratospheric warming (SSW) event, the QBO in the tropics, and the mesospheric pre-conditioning phase of the 2019 SSW event.
Our findings indicate that CAIRT would provide highly reliable observations of global scale GW distributions and drag patterns but also of specific wave events and their associated wave parameters. Even under worse-than-expected noise levels of the instrument, the resulting GW measurements are highly consistent with the original model data. Furthermore, we demonstrate that the estimated GW parameters can be used for ray tracing, which physically extends the horizontal coverage of the observations beyond the orbit tracks.
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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-2024-1084', Anonymous Referee #1, 12 Jun 2024
Review of: "Global scale gravity wave analysis methodology for the ESA Earth Explorer 11 candidate CAIRT" by S. Rhode et al.
In this manuscript, the motivation for and the methodology of the atmospheric gravity wave research using The ESA Earth Explorer 11 candidate CAIRT is outlined and demonstrated. The prospective CAIRT mission would have an enormous impact on the atmospheric dynamics and transport research and for research of the middle atmosphere in general. Here, a group of world leading experts presents a cutting edge methodology that documents the ability of CAIRT to derive unprecedented information on the GW field and wave-mean flow interaction. The paper is clearly structured and very well written and I can recommend it for publication after the authors revise some technical issues and typos that I list below.
However, I feel that besides being just published, the paper has a potential to become a highlight paper and to have a really big impact on the community. But, sadly, I feel that in the current form the paper falls short of that, esp. in terms of readability of the text. Hence, I also give below some editorial comments/suggestions that should not prevent publication but if the authors pick them, they can possibly help improving the paper in this regard.
Minor and technical comments (chronological):
L25 - On breaking...
L30 ..GWs are of small horizontal scales compared to climate model resolutions and are, hence, not well taken into account for long-term projections..This is a low quality sentence. I think that the issue of underrepresentation of parts of GW spectra in climate and global weather prediction models deserves a more thorough discussion. Also, there should be a paragraph on how the unresolved effects are included (parameterizations). Clearly distinguishing between orography and non-orography GWs and highlighting how important the parameterizations are for climate models (for orography GWs - e.g. impact on SSW frequency Sigmond et al. (2023, GMD), Fig. 18); impact on stratospheric dynamics in general (Hajkova and Sacha, 2024, CliDyn) and for non-oro GW schemes e.g. Choi et al. (2018, Asia-Pacific J Atmos Sci)
L43..costly infrastructure.. the people working with ground based measurements on the other side argue that the ground based measurements are very cost effective compared to satellite obs. Can you substantiate your claim here?
L84 ..intermittency - Here, again would be useful to distinguish between non-orographic and orographic parameterizations, where the issue of intermittency has been also discussed (e.g. Kuchar et al. (2020, WCD))
L89 ...propagate..here your discussion is inaccurate. GWs in the parameterizations (outside MS-GWaM) do not propagate at all. Only the saturation criterion is evaluated in a vertical column. Again, I argue that a paragraph devoited to importance and limitations of GW parameterizations is needed.
L93..a major part...I would say that for current GCMs it would be more accurate to say some part of the GW spectrum (their effective resolutions are much worse than simply their horizontal resolution).
L99 the whole spectrum of GWs - again for accuraccy I would say almost the whole spectrum
L135 .. and that it is possible from the aircraft - please rewrite
L150 depends its
L159 .. , from where the SSW propagates downward.- This is certainly not true for the SSWs in general.
L161 For agreeing results - rewrite.
L165 GCM model data - rewrite
L169 - here you say that you use NWP not GCM data..
L173 Sec .6
L176 an estimate of an actual observation - an estimate of a potential observation?
L179 comparison to model data is based on model data - rephrase
around L229 Is interpolation really the correct way and should not the spatial averaging be used to mimic what the coarse resolution instrument would see?
Tab. 1 - I would prefer additional column showing the meaning of the numbers (e.g. band, range or something). As it is now, you do not need a table.
L255 vertical flux of horizontal pseudomomentum - please state clearly that you are computing only a simplified version of the vertical flux of horizontal pseudomomentum valid under certain assumptions
L277 We all know that the Earth is not a sphere
L277 ..comprises always a multiple of full wavelengths of any wave in zonal direction...I do not understand this, certainly not all wavelengths satisfy this.
L278 Fx, is a true reference ...I do not understand the meaning of this statement.
L280 is not a true reference...the same as above.
L281 ..For the closure of the momentum budget, the pseudo-momentum flux needs to be calculated.. - The momentum budget can certainly be closed without pseudo-momentum, only it takes a less elegant form. Also, you should be aware that you compute only a very simplified form of a pseudo-momentum (homogenous background winds..).
L297.. linked to the temperature amplitude (Ern et al., 2004) - again, include assumptions of this link (mid-frequency range etc.)
L347 Chí squared was not defined before?
L349-L356 and the whole subsection - There is so much of text and too few formulas or visuallization. It is really hard to follow the rationale behind the penalty in particular..
L367 ..local phenomena cancel in the zonal mean... for the zonal mean, GWDxx averages out by definition, but not the components connected with local meridional propagation
L396 ..local events..->local peaks?
Figure 4..panel a)... panel b)...
Paragraphs around L445 and 450 - Please rewrite this section of results in a more consistent manner and do not jump between Fig. 5 and Fig. 6
L489 In general, the good resemblance of the reference phase speed spectrum gives confidence that CAIRT would see a representative sample to estimate the full GW phase speed spectrum even in the case of higher-than-expected noise...Based on the figure, I am afraid that this is true only for the slow, likely orographic GWs. It seems like the non-orographic part (modes with large phase speeds) will be increasingly plagued by artificial signals. This can influence reliability of the ray tracing. Generally I think that it would be good to separate a little bit more between OGWs and non-OGWs in description of your results (I know that it is impossible to distinguish clearly between them).
L504 - From Fig. 2, by eye, it seems that the biggest GWMF values are seen above Japan, but in Fig. 8 this is not that clear. Is it only due to subjective perception or is it likely a result of filtering of shorter waves?
L531 ..GWs assume long vertical wavelengths..please rephrase
L576.. As a rule of thumb...rephrase and rather state the assumptions behind this estimate
L609.. panel a) ...panel b)
Figure 15.... Zonal mean zonal GWMF (a, b) and zonal mean zonal drag (c, d, e) deduced from JAGUAR model wind fluctuations (a, c), from CAIRT-sampled data (e), and from end-to-end simulations including radiative transfer, instrument noise and retrieval (b, d)...It is so difficult to understand this caption, please rewrite..
around L653 .... The comparison to the S3D analysis directly applied to the JAGUAR data (Fig. 17b and d) confirms the strong bias to the orbit tracks at 25 km. This bias is alleviated to some extent at 45 km altitude and the most prominent large-scale structures are resembled within the ray-tracing simulation. Also note that the ray tracing results are better at resembling larger scale structures simply due to more and stronger GWs being present in these regions (e.g., southern subtropics, Himalaya, and Scandinavia)....The discussed features are really hard to see and follow. It would be better to find a way of presenting this to get more quantitative.
Figure 18 and general - Opposed to tracing GWs to sources, I am not convinced about the utility of ray tracing for deriving GWD estimates. Are you not working outside of the underlying ray tracing assumptions? On the other side, I acknowledge that the resulting zonal mean drag in Fig. 18 indeed looks more „realistic“.
L666... deviated as the vertical derivative...
L680... (e.g. ??))...
L689.. They inspired the development of global atmospheric models. -> I think that you want to say.. They inspired the development of GW parameterizations in global atmospheric models.
L710 ...(also, without penalty, the target range of wavelengths isnot reliable; not shown)..maybe this should be shown at a relevant place of the manuscript, because I have found the penalty discussion hard to follow earlier in the text.
Outside of the chronological ordering:
Figs. 8, 9, 15, 16..Instead of subjectively interpreting the information seen in the swaths, can you come with some more quantitative way of presenting these results? (less prone to subjective perception).
Footnotes - I do not consider it necessary that the footnotes are included
In addition to the analysis presented I would like to see it addressed in the manuscript, whether the CAIRT observations can contribute with information on short-term variability of GWD (hours, days?) and also long-term trends (Is the projected accuracy and stability of the measurements sufficient for this?)
Citation: https://doi.org/10.5194/egusphere-2024-1084-RC1 - AC1: 'Reply on RC1', Sebastian Rhode, 08 Aug 2024
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RC2: 'Comment on egusphere-2024-1084', Anonymous Referee #2, 08 Jul 2024
Review of manuscript egusphere-2024-1084: Global scale gravity waves analysis methodology for the ESA Earth Explorer 11 candidate CAIRT, by S. Rhose, P. Preusse, J. Ungermann, I. Polichtchouk, K. Sato, S. Watanabe, M. Ern, K. Nogai, B.-M. Sinnhuber, and M. Riese.
This paper constitutes a proof of concept for the ESA Earth Explorer 11 candidate CAIRT in terms of ability to provide valuable global information on gravity wave characteristics, including dissipation, throughout the middle atmosphere. Two high resolutions models are sampled to generate synthetical observations, mimicking the observational design of an the instrument on board (an limb imaging Michelson interferometer). The results show the great potential of the instrument.
The manuscript is clearly written, I only have a few minor comments, as listed below.
- Line 23-25. Although there exists a wave-induced flux of momentum, strictly speaking waves in fluids do not have momentum (McIntyre 1981). So (gravity) waves do not gain or release momentum. Perhaps it would be more precise to say that gravity waves transport (or redistribute?) momentum/energy within different layers of the atmosphere.
McIntyre ME. On the ‘wave momentum’ myth. Journal of Fluid Mechanics. 1981;106:331-347. doi:10.1017/S0022112081001626 .
- Lines 29-30. Radiative cooling is a very important driver of the vortex recovery after SSWs. Are GWs really the main driving force?
- Line 45. This sentence is not well written, needs to be rephrased.
- Lines 60-65. To my knowledge, the first successful implementation of a GW drag parameterization in a climate model (actually a NWP model) was reported by Palmer et al. (1986), not by Lindzen (1981). Lindzen’s study was indeed one of the first to show that a parametrization based on linear saturation theory (convective instability) of a monochromatic wave could provide a dynamical forcing in the mesosphere able to explain the warm mesopause in winter and the cold in summer, but no GCM was used.
Palmer, T.N., Shutts, G.J. and Swinbank, R. (1986), Alleviation of a systematic westerly bias in general circulation and numerical weather prediction models through an orographic gravity wave drag parametrization. Q.J.R. Meteorol. Soc., 112: 1001-1039. https://doi.org/10.1002/qj.49711247406
- Line 187. At what altitude does the sponge layer start?
- Lines 360, 363. Vertical gradient of the GWMF → vertical derivative (or divergence of the momentum vertical flux).
- Line 368. They should cancel out also in the time mean, which may be more relevant if the process we are dealing with is wave propagation imprint on the EP flux divergence.
- Line 371. What is the meaning of “potential drag”?
- Line 576-577. It would seem that those numbers have been calculated using the mid-frequency approximation of the wave dispersion relation. Please specify.
- Line 695. Many scientific articles that present results on observations of gravity waves, both from a global perspective or based on case studies, use the argument that GW parameterizations are poorly constrained by observations, and hence the need for those kind of studies. The argument is valid, but it is not straightforward how to use the information provided by observations to improve the calibration of the parameterizations. Perhaps the main reason for this is that the tunable parameters have to do with GW characteristics (e.g. momentum flux, phase speed spectrum, etc.) at the source level. But the propagation and dissipation of the waves are not easily tunable.
One of the strengths of CAIRT in this respect is to be able to provide information on the dissipation of waves (phase speeds, drag, range of altitudes, etc.). This would be extremely valuable to assess the output of current parameterizations, study and refine their performance, and evaluate whether their level of complexity (WKB solutions, columnar approach, etc.) is good enough to emulate the observations.
Citation: https://doi.org/10.5194/egusphere-2024-1084-RC2 - AC2: 'Reply on RC2', Sebastian Rhode, 08 Aug 2024
Interactive discussion
Status: closed
-
RC1: 'Comment on egusphere-2024-1084', Anonymous Referee #1, 12 Jun 2024
Review of: "Global scale gravity wave analysis methodology for the ESA Earth Explorer 11 candidate CAIRT" by S. Rhode et al.
In this manuscript, the motivation for and the methodology of the atmospheric gravity wave research using The ESA Earth Explorer 11 candidate CAIRT is outlined and demonstrated. The prospective CAIRT mission would have an enormous impact on the atmospheric dynamics and transport research and for research of the middle atmosphere in general. Here, a group of world leading experts presents a cutting edge methodology that documents the ability of CAIRT to derive unprecedented information on the GW field and wave-mean flow interaction. The paper is clearly structured and very well written and I can recommend it for publication after the authors revise some technical issues and typos that I list below.
However, I feel that besides being just published, the paper has a potential to become a highlight paper and to have a really big impact on the community. But, sadly, I feel that in the current form the paper falls short of that, esp. in terms of readability of the text. Hence, I also give below some editorial comments/suggestions that should not prevent publication but if the authors pick them, they can possibly help improving the paper in this regard.
Minor and technical comments (chronological):
L25 - On breaking...
L30 ..GWs are of small horizontal scales compared to climate model resolutions and are, hence, not well taken into account for long-term projections..This is a low quality sentence. I think that the issue of underrepresentation of parts of GW spectra in climate and global weather prediction models deserves a more thorough discussion. Also, there should be a paragraph on how the unresolved effects are included (parameterizations). Clearly distinguishing between orography and non-orography GWs and highlighting how important the parameterizations are for climate models (for orography GWs - e.g. impact on SSW frequency Sigmond et al. (2023, GMD), Fig. 18); impact on stratospheric dynamics in general (Hajkova and Sacha, 2024, CliDyn) and for non-oro GW schemes e.g. Choi et al. (2018, Asia-Pacific J Atmos Sci)
L43..costly infrastructure.. the people working with ground based measurements on the other side argue that the ground based measurements are very cost effective compared to satellite obs. Can you substantiate your claim here?
L84 ..intermittency - Here, again would be useful to distinguish between non-orographic and orographic parameterizations, where the issue of intermittency has been also discussed (e.g. Kuchar et al. (2020, WCD))
L89 ...propagate..here your discussion is inaccurate. GWs in the parameterizations (outside MS-GWaM) do not propagate at all. Only the saturation criterion is evaluated in a vertical column. Again, I argue that a paragraph devoited to importance and limitations of GW parameterizations is needed.
L93..a major part...I would say that for current GCMs it would be more accurate to say some part of the GW spectrum (their effective resolutions are much worse than simply their horizontal resolution).
L99 the whole spectrum of GWs - again for accuraccy I would say almost the whole spectrum
L135 .. and that it is possible from the aircraft - please rewrite
L150 depends its
L159 .. , from where the SSW propagates downward.- This is certainly not true for the SSWs in general.
L161 For agreeing results - rewrite.
L165 GCM model data - rewrite
L169 - here you say that you use NWP not GCM data..
L173 Sec .6
L176 an estimate of an actual observation - an estimate of a potential observation?
L179 comparison to model data is based on model data - rephrase
around L229 Is interpolation really the correct way and should not the spatial averaging be used to mimic what the coarse resolution instrument would see?
Tab. 1 - I would prefer additional column showing the meaning of the numbers (e.g. band, range or something). As it is now, you do not need a table.
L255 vertical flux of horizontal pseudomomentum - please state clearly that you are computing only a simplified version of the vertical flux of horizontal pseudomomentum valid under certain assumptions
L277 We all know that the Earth is not a sphere
L277 ..comprises always a multiple of full wavelengths of any wave in zonal direction...I do not understand this, certainly not all wavelengths satisfy this.
L278 Fx, is a true reference ...I do not understand the meaning of this statement.
L280 is not a true reference...the same as above.
L281 ..For the closure of the momentum budget, the pseudo-momentum flux needs to be calculated.. - The momentum budget can certainly be closed without pseudo-momentum, only it takes a less elegant form. Also, you should be aware that you compute only a very simplified form of a pseudo-momentum (homogenous background winds..).
L297.. linked to the temperature amplitude (Ern et al., 2004) - again, include assumptions of this link (mid-frequency range etc.)
L347 Chí squared was not defined before?
L349-L356 and the whole subsection - There is so much of text and too few formulas or visuallization. It is really hard to follow the rationale behind the penalty in particular..
L367 ..local phenomena cancel in the zonal mean... for the zonal mean, GWDxx averages out by definition, but not the components connected with local meridional propagation
L396 ..local events..->local peaks?
Figure 4..panel a)... panel b)...
Paragraphs around L445 and 450 - Please rewrite this section of results in a more consistent manner and do not jump between Fig. 5 and Fig. 6
L489 In general, the good resemblance of the reference phase speed spectrum gives confidence that CAIRT would see a representative sample to estimate the full GW phase speed spectrum even in the case of higher-than-expected noise...Based on the figure, I am afraid that this is true only for the slow, likely orographic GWs. It seems like the non-orographic part (modes with large phase speeds) will be increasingly plagued by artificial signals. This can influence reliability of the ray tracing. Generally I think that it would be good to separate a little bit more between OGWs and non-OGWs in description of your results (I know that it is impossible to distinguish clearly between them).
L504 - From Fig. 2, by eye, it seems that the biggest GWMF values are seen above Japan, but in Fig. 8 this is not that clear. Is it only due to subjective perception or is it likely a result of filtering of shorter waves?
L531 ..GWs assume long vertical wavelengths..please rephrase
L576.. As a rule of thumb...rephrase and rather state the assumptions behind this estimate
L609.. panel a) ...panel b)
Figure 15.... Zonal mean zonal GWMF (a, b) and zonal mean zonal drag (c, d, e) deduced from JAGUAR model wind fluctuations (a, c), from CAIRT-sampled data (e), and from end-to-end simulations including radiative transfer, instrument noise and retrieval (b, d)...It is so difficult to understand this caption, please rewrite..
around L653 .... The comparison to the S3D analysis directly applied to the JAGUAR data (Fig. 17b and d) confirms the strong bias to the orbit tracks at 25 km. This bias is alleviated to some extent at 45 km altitude and the most prominent large-scale structures are resembled within the ray-tracing simulation. Also note that the ray tracing results are better at resembling larger scale structures simply due to more and stronger GWs being present in these regions (e.g., southern subtropics, Himalaya, and Scandinavia)....The discussed features are really hard to see and follow. It would be better to find a way of presenting this to get more quantitative.
Figure 18 and general - Opposed to tracing GWs to sources, I am not convinced about the utility of ray tracing for deriving GWD estimates. Are you not working outside of the underlying ray tracing assumptions? On the other side, I acknowledge that the resulting zonal mean drag in Fig. 18 indeed looks more „realistic“.
L666... deviated as the vertical derivative...
L680... (e.g. ??))...
L689.. They inspired the development of global atmospheric models. -> I think that you want to say.. They inspired the development of GW parameterizations in global atmospheric models.
L710 ...(also, without penalty, the target range of wavelengths isnot reliable; not shown)..maybe this should be shown at a relevant place of the manuscript, because I have found the penalty discussion hard to follow earlier in the text.
Outside of the chronological ordering:
Figs. 8, 9, 15, 16..Instead of subjectively interpreting the information seen in the swaths, can you come with some more quantitative way of presenting these results? (less prone to subjective perception).
Footnotes - I do not consider it necessary that the footnotes are included
In addition to the analysis presented I would like to see it addressed in the manuscript, whether the CAIRT observations can contribute with information on short-term variability of GWD (hours, days?) and also long-term trends (Is the projected accuracy and stability of the measurements sufficient for this?)
Citation: https://doi.org/10.5194/egusphere-2024-1084-RC1 - AC1: 'Reply on RC1', Sebastian Rhode, 08 Aug 2024
-
RC2: 'Comment on egusphere-2024-1084', Anonymous Referee #2, 08 Jul 2024
Review of manuscript egusphere-2024-1084: Global scale gravity waves analysis methodology for the ESA Earth Explorer 11 candidate CAIRT, by S. Rhose, P. Preusse, J. Ungermann, I. Polichtchouk, K. Sato, S. Watanabe, M. Ern, K. Nogai, B.-M. Sinnhuber, and M. Riese.
This paper constitutes a proof of concept for the ESA Earth Explorer 11 candidate CAIRT in terms of ability to provide valuable global information on gravity wave characteristics, including dissipation, throughout the middle atmosphere. Two high resolutions models are sampled to generate synthetical observations, mimicking the observational design of an the instrument on board (an limb imaging Michelson interferometer). The results show the great potential of the instrument.
The manuscript is clearly written, I only have a few minor comments, as listed below.
- Line 23-25. Although there exists a wave-induced flux of momentum, strictly speaking waves in fluids do not have momentum (McIntyre 1981). So (gravity) waves do not gain or release momentum. Perhaps it would be more precise to say that gravity waves transport (or redistribute?) momentum/energy within different layers of the atmosphere.
McIntyre ME. On the ‘wave momentum’ myth. Journal of Fluid Mechanics. 1981;106:331-347. doi:10.1017/S0022112081001626 .
- Lines 29-30. Radiative cooling is a very important driver of the vortex recovery after SSWs. Are GWs really the main driving force?
- Line 45. This sentence is not well written, needs to be rephrased.
- Lines 60-65. To my knowledge, the first successful implementation of a GW drag parameterization in a climate model (actually a NWP model) was reported by Palmer et al. (1986), not by Lindzen (1981). Lindzen’s study was indeed one of the first to show that a parametrization based on linear saturation theory (convective instability) of a monochromatic wave could provide a dynamical forcing in the mesosphere able to explain the warm mesopause in winter and the cold in summer, but no GCM was used.
Palmer, T.N., Shutts, G.J. and Swinbank, R. (1986), Alleviation of a systematic westerly bias in general circulation and numerical weather prediction models through an orographic gravity wave drag parametrization. Q.J.R. Meteorol. Soc., 112: 1001-1039. https://doi.org/10.1002/qj.49711247406
- Line 187. At what altitude does the sponge layer start?
- Lines 360, 363. Vertical gradient of the GWMF → vertical derivative (or divergence of the momentum vertical flux).
- Line 368. They should cancel out also in the time mean, which may be more relevant if the process we are dealing with is wave propagation imprint on the EP flux divergence.
- Line 371. What is the meaning of “potential drag”?
- Line 576-577. It would seem that those numbers have been calculated using the mid-frequency approximation of the wave dispersion relation. Please specify.
- Line 695. Many scientific articles that present results on observations of gravity waves, both from a global perspective or based on case studies, use the argument that GW parameterizations are poorly constrained by observations, and hence the need for those kind of studies. The argument is valid, but it is not straightforward how to use the information provided by observations to improve the calibration of the parameterizations. Perhaps the main reason for this is that the tunable parameters have to do with GW characteristics (e.g. momentum flux, phase speed spectrum, etc.) at the source level. But the propagation and dissipation of the waves are not easily tunable.
One of the strengths of CAIRT in this respect is to be able to provide information on the dissipation of waves (phase speeds, drag, range of altitudes, etc.). This would be extremely valuable to assess the output of current parameterizations, study and refine their performance, and evaluate whether their level of complexity (WKB solutions, columnar approach, etc.) is good enough to emulate the observations.
Citation: https://doi.org/10.5194/egusphere-2024-1084-RC2 - AC2: 'Reply on RC2', Sebastian Rhode, 08 Aug 2024
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Peter Preusse
Jörn Ungermann
Inna Polichtchouk
Kaoru Sato
Shingo Watanabe
Manfred Ern
Karlheinz Nogai
Björn-Martin Sinnhuber
Martin Riese
The requested preprint has a corresponding peer-reviewed final revised paper. You are encouraged to refer to the final revised version.
- Preprint
(19542 KB) - Metadata XML