the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 06 May 2024
Dynamic and thermodynamic contribution to the October 2019 exceptional rainfall in West Central Africa
Abstract. Exceptional rainfall hit West Central Africa in October 2019. To understand the underlying mechanisms, we diagnosed the regional moisture and Moist Static Energy (MSE) budgets with a view to highlighting the importance of the dynamic and thermodynamic effects associated with this historic event. Analysis of the moisture budget reveals that the precipitation anomalies in October were mainly controlled by dynamic effects (72.5 % of the sum of dynamic and thermodynamic contributions). Horizontal moisture advection induced by horizontal wind anomalies controls extreme precipitation north of West Central Africa, while vertical moisture advection induced by vertical velocity anomalies controls extreme precipitation south of West Central Africa. Changes in the thermodynamic effect, although not the key factor responsible for the events of October 2019, contribute up to 27.5 % of the total effect. Diagnosis of the MSE balance shows that the anomalous vertical motion is dominated by the dynamic effect, i.e. the wet enthalpy advection induced by the horizontal wind anomalies. The horizontal advection of the MSE induced by the variation of the wet enthalpy and the vertical advection of the MSE induced by the variation of the MSE seem less important. The variations in the MSE balance are linked to its meridional component, in particular the meridional wind anomalies in the dynamic effect and the meridional variations in latent heat in the thermodynamic effect. This is due to the increase in sea surface temperatures in the equatorial Atlantic, associated with the anomalous thermal depression over the Sahara, which has increased rainfall over West Central Africa. Our results suggest that dynamic and thermodynamic effects should be jointly considered for adequately anticipating this kind of extreme event. Understanding the associated mechanisms could help us improve our projections and increase the region's population resilience to these extreme weather events.
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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-2024-1257', Anonymous Referee #1, 03 Jun 2024
This manuscript examines the drivers of the October 2019 extreme rainfall event over western central Africa. I find the overall approach to be novel and useful, but there are some statements in the abstract and conclusions that are not fully supported by the results shown, so I recommend major corrections.
Major points:
- As there appear to be different processes at work over the central and northern parts of the domain, results should in many cases be shown and discussed (including in the abstract and conclusions) for two sub-regions separately, e.g. Fig 4, 6, 7. Statements in the abstract about the dominance of meridional wind anomalies (L39) appear more relevant to the northern rather than the central part of the domain. I also don’t think that ‘Western Equatorial Africa’ (as stated in the caption of Fig. 4) is an accurate description of the current domain, as it includes regions far from the equator.
- L30: There is a large residual term in the moisture budget, so this should be mentioned as a caveat when discussing the partition into dynamic and thermodynamic terms.
- L36 and L366: The MSE budget is diagnostic, so no statements about causality can be made without other supporting evidence. The vertical and horizontal dynamic terms balance one another but there is not enough evidence presented here to say that the vertical term is ‘dominated’ by the horizontal term, as to me that implies causality.
- L41-43: I didn’t see any convincing evidence presented in this study linking the moisture or MSE budget results to Atlantic SSTs or the Saharan heat low. This is the hypothesis of Nicholson et al., 2021, but the authors need to show much more explicitly whether or not their results support this hypothesis.
- L163-164 and L186-187: It can’t just be assumed that the d/dt terms in the moisture and MSE budget are small when applying these budgets to an individual month. This needs to be demonstrated, or at the very least it should be stated that the d/dt term could contribute to the residual in each budget.
- The MSE budget in Fig. 9 doesn’t look to me like it adds up correctly. Is the residual the wrong sign?
Minor points:
- L104: The reference to the greenhouse effect here is confusing. Although an increase in WV would be associated with an enhanced greenhouse effect, I don’t think there is evidence that this process significantly contributes to increasing low-level convergence.
- L105: The convergence feedback mechanism described here is no longer generally accepted. Instead, the large-scale flow and, precipitation and diabatic heating are more generally thought to evolve together under the constraint of convective quasi-equilibrium. However, I do accept that when horizontal moisture gradients exist, as they do between land and ocean, the concept of a feedback might be more appropriate, as increased horizontal flow could increase boundary layer MSE over land, and therefore result in increased precipitation. In any case, this point probably needs a bit more clarification.
- L105-107: Has it really been demonstrated that the reduction in heating has driven the reduction in rainfall, or have both things decreased together?
- L141: When diagnosed from reanalysis, this is more generally referred to as the ‘apparent diabatic heating’.
- Equations: Please improve the image quality of all equations.
- L169: This should say ‘non-linear and transient processes’, as some of the neglected non-linear terms are related to the mean flow.
- 6: This should be Lq, not cvq.
- 6: You need to specify that variations in geopotential height along pressure levels are neglected in this MSE budget formulation.
- L188: I think ‘remaining terms’ would be more precise than ‘remainder’ here.
- L201: The diabatic heating over the continent is associated with moist instability, but I don’t think ‘favouring it’ is the correct way to phrase this.
- L221-223: I can’t see evidence for this in Fig. 1. An anomaly plot might make things clearer.
- L231-232: I don’t think the boundaries of West Central Africa have been defined yet in the manuscript.
- L243: Need to provide evidence or a reference for this statement.
- L256-258: I think this shows that moisture extended further north over West Africa in October 2019, not that there was more moisture in Equatorial West Africa as stated.
- L258-259: Although the moisture source is the Atlantic, it is not necessarily a consequence of warmer SSTs. The northward extension of the meridional winds is the key process here, so perhaps that is more associated with anomalies in the Saharan heat-low?
- L262-263: That result is more relevant to long-term responses to global warming. For regional monthly anomalies, changes in winds will be equally or more important drivers of changes in humidity over land.
- L267: Which heating sources?
- 4 caption: The reference here should be to Fig. 5, not Fig. 2.
- L285-286: I’m not sure how this result about dependence on surface heating is directly relevant to the moisture budget results shown here.
- 5: Need to show the pattern of the residual term as well, because it is large. The pattern might also give some clues as to what is causing the large residual.
- L313: Although the increase in diabatic heating is related to the precipitation change, I don’t think it can be said to be driving it.
- L314-315: From the maps shown here, the increased moisture looks to be mainly associated with winds penetrating further northwards into West Africa, rather than any general increase in moisture associated with increased Atlantic SSTs.
- L318: Why is this the ‘second’ dynamic parameter?
- L320: Grammar doesn’t quite work here.
- 6: Please change the colours used here for the benefit of readers with red-green colour-blindness.
- L339: Minimum, not maximum.
- L340-341: Not necessarily. This depends on the vertical structure of the omega anomalies. This relationship needs to be checked.
- L346: I don’t think it is correct in this context to say that Lq’ approached m’. The vertical gradients of the two terms are very different, and it is the vertical gradients that are crucial here.
- L357-364: This flux term should be investigated further by separating it into surface vs SW and LW radiative fluxes and potentially clear-sky vs cloudy radiative fluxes. From Fig. 8e the flux term seems to be co-located with the rainfall anomaly, so one interpretation is that this is a radiative response to increase in deep convective clouds.
- L360-364: I would have thought that the MSE budget implies that a reduction in energy into the column would be associated with a reduction in ascent and precipitation, not an increase.
- L378: This relationship between the thermodynamic and dynamic terms seems to vary a lot depending on the sub-region.
- L386: By itself it would result in this, but the combination of other budget terms are larger.
- L388: I think ‘interaction’ would be a better word than ‘feedbacks’ here.
- L392: This is clearer for the northern part of the domain than the central part.
- L407-408: I think ‘area-averaged’ would be better than ‘entire’ here, as this result doesn’t hold everywhere in the domain.
- L418: This should say ‘MSE’ instead of ‘moist air’.
- L437-438: Again, I don’t think there is any evidence here to link this directly with enhanced Atlantic SSTs. It is the wind anomalies that are crucial.
- L453-456: This is overstating how much we can learn from this analysis. In order to link the October 2019 rains to global warming a formal detection and attribution study would be needed.
- L457-458: Are there also easterly anomalies over equatorial West Africa? This whole analysis would benefit from separating the central and northern parts of the domain, as different processes appear to be at work. It may be that there is a common driver, but that is not currently demonstrated here.
- L463 and L464: The word ‘controls’ implies causality, which has not been demonstrated here.
- L475: This is true in the northern part of the domain, but not the equatorial part I don’t think.
- L485-487: It’s not clear to me whether the results shown here really are consistent with those of Nicholson et al. (2021). More analysis is needed to demonstrate that.
Citation: https://doi.org/10.5194/egusphere-2024-1257-RC1 - AC1: 'Reply on RC1', Kevin Kenfack, 13 Jul 2024
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RC2: 'Comment on egusphere-2024-1257', Anonymous Referee #2, 20 Jun 2024
The authors seek to explain the anomalously strong 2019 West Central African October rains through a moisture and MSE budget analysis. They find that anomalous meridional transport and anomalous moisture / wet enthalpy export (possibly driven by the combination of a strong Saharan Heat Low and high Atlantic SSTs?) contributed to extreme rainfall in the region.
Overall, this is an important question to study and the authors do a decent job explaining the complex factors making the 2019 rainy season so strong. I have some remaining questions, primarily around the underlying reasons for the anomalies discussed here, in addition to some extra suggested analysis. Contingent on those changes, I recommend publication after Major Revisions.
### Major questions
# SSTs and the Saharan Heat Low
The authors occasionally bring up the role of anomalously high SSTs in the Atlantic Ocean, but that argument could be developed further, especially since it may be linked to the anomalous onshore moisture transport mentioned in the study. Perhaps a figure showing anomalous SSTs (maybe as part of the summary figure I suggest below) could help as well.
The same goes for the Saharan Heat Low, which is mentioned a few times as a driver of the anomalous meridional circulation, but not shown or explained further. It seems like the authors are arguing that these two factors may be the underlying drivers of the anomalies shown in the paper (if I understood correctly!) and it would be great to be more explicit about this, explain the argument better, and show them in a diagnostic figure as well.
# Role of large-scale circulation
The paper could benefit from placing the anomalous circulation / thermodynamics in the context of larger-scale circulation effects happening. 2019 was an El Niño year, are these results typical of El Niño states? (or other major oscillations that affect west central Africa).
# Robustness checks with another reanalysis product
Given the data sparsity over much of equatorial Africa, reanalysis products tend to struggle with aspects of the regional circulation. More generally, they often struggle to close moisture budgets (which may be part of the reason the residual is so high in the budget calculations?). It would be good to see a robustness check of the primary results with another reanalysis product (Hua et al. 2019 suggest MERRA-2, for example).
# The large residual
I would appreciate a more in-depth discussion of the residual, which is the largest single term on the right side of the P-E balance equation. Could it be partially caused by poor moisture budget closure in reanalysis products? Given how large it is – the authors suspect possible influence of the MJO – would rainfall have been substantially lower (or higher, since it seems to counteract precipitation in the balance) if the MJO were in a different phase?
### Figures
It would be very helpful to the reader if the authors could add a new Figure 1 that shows an overview of the study region, with the box over which values are averaged clearly marked. Perhaps the map could show (in addition to lat/lon, borders, and the study area) SST anomalies over ocean, rainfall anomalies over land, and moisture transport (or circulation) as arrows. This would neatly tie together some of the primary arguments of the study and make it easier to geographically place the results (I at least always find it hard to just go off latitude / longitude without a corresponding map).
In Figures 1 and 3, would it be possible to title the subplots? (“1988-2017 avg.” and “2019 avg.” for Figure 1 for example).
In Figure 5 and 8-10, could you specify that the box in panel a is the box over which values are averaged in the analysis? (and could you please replicate the box in every panel?)
### Minor questions / points
Abstract: using « anomalies » instead of “variation” in the abstract when referring to the anomaly terms may be easier to understand.
L72: period missing
L75-76: I would guess the positive SSTs and the increased moisture flux are probably related, right?
L78-L84: Do you think the anomalously strong East African rains were related to the west central African rains? If so, how? (since the two regions seem often dynamically distinct... but I guess they could be indirectly related through the large-scale circulation?)
L150: I think you can drop the 86400 and just specify you’re showing output in K/day.
L163: I assume you meant top of the troposphere? I don’t think Seager et al. 2010 actually makes a statement on this. They actually integrate to the top available level of the model at the time, which is presumably higher than 300hPa.
L164: How true is this? (i.e., how small are changes in q at the monthly level?)
L178 / Eq 6: should be cpT + Lvq. In which case you can use m for this as well.
### References
Hua, Wenjian, Liming Zhou, Sharon E. Nicholson, Haishan Chen, and Minhua Qin. 2019. “Assessing Reanalysis Data for Understanding Rainfall Climatology and Variability over Central Equatorial Africa.” Climate Dynamics 53 (1): 651–69. https://doi.org/10.1007/s00382-018-04604-0.
Seager, Richard, Naomi Naik, and Gabriel A. Vecchi. 2010. “Thermodynamic and Dynamic Mechanisms for Large-Scale Changes in the Hydrological Cycle in Response to Global Warming.” Journal of Climate 23 (17): 4651–68. https://doi.org/10.1175/2010JCLI3655.1.
Citation: https://doi.org/10.5194/egusphere-2024-1257-RC2 - AC2: 'Reply on RC2', Kevin Kenfack, 13 Jul 2024
Interactive discussion
Status: closed
-
RC1: 'Comment on egusphere-2024-1257', Anonymous Referee #1, 03 Jun 2024
This manuscript examines the drivers of the October 2019 extreme rainfall event over western central Africa. I find the overall approach to be novel and useful, but there are some statements in the abstract and conclusions that are not fully supported by the results shown, so I recommend major corrections.
Major points:
- As there appear to be different processes at work over the central and northern parts of the domain, results should in many cases be shown and discussed (including in the abstract and conclusions) for two sub-regions separately, e.g. Fig 4, 6, 7. Statements in the abstract about the dominance of meridional wind anomalies (L39) appear more relevant to the northern rather than the central part of the domain. I also don’t think that ‘Western Equatorial Africa’ (as stated in the caption of Fig. 4) is an accurate description of the current domain, as it includes regions far from the equator.
- L30: There is a large residual term in the moisture budget, so this should be mentioned as a caveat when discussing the partition into dynamic and thermodynamic terms.
- L36 and L366: The MSE budget is diagnostic, so no statements about causality can be made without other supporting evidence. The vertical and horizontal dynamic terms balance one another but there is not enough evidence presented here to say that the vertical term is ‘dominated’ by the horizontal term, as to me that implies causality.
- L41-43: I didn’t see any convincing evidence presented in this study linking the moisture or MSE budget results to Atlantic SSTs or the Saharan heat low. This is the hypothesis of Nicholson et al., 2021, but the authors need to show much more explicitly whether or not their results support this hypothesis.
- L163-164 and L186-187: It can’t just be assumed that the d/dt terms in the moisture and MSE budget are small when applying these budgets to an individual month. This needs to be demonstrated, or at the very least it should be stated that the d/dt term could contribute to the residual in each budget.
- The MSE budget in Fig. 9 doesn’t look to me like it adds up correctly. Is the residual the wrong sign?
Minor points:
- L104: The reference to the greenhouse effect here is confusing. Although an increase in WV would be associated with an enhanced greenhouse effect, I don’t think there is evidence that this process significantly contributes to increasing low-level convergence.
- L105: The convergence feedback mechanism described here is no longer generally accepted. Instead, the large-scale flow and, precipitation and diabatic heating are more generally thought to evolve together under the constraint of convective quasi-equilibrium. However, I do accept that when horizontal moisture gradients exist, as they do between land and ocean, the concept of a feedback might be more appropriate, as increased horizontal flow could increase boundary layer MSE over land, and therefore result in increased precipitation. In any case, this point probably needs a bit more clarification.
- L105-107: Has it really been demonstrated that the reduction in heating has driven the reduction in rainfall, or have both things decreased together?
- L141: When diagnosed from reanalysis, this is more generally referred to as the ‘apparent diabatic heating’.
- Equations: Please improve the image quality of all equations.
- L169: This should say ‘non-linear and transient processes’, as some of the neglected non-linear terms are related to the mean flow.
- 6: This should be Lq, not cvq.
- 6: You need to specify that variations in geopotential height along pressure levels are neglected in this MSE budget formulation.
- L188: I think ‘remaining terms’ would be more precise than ‘remainder’ here.
- L201: The diabatic heating over the continent is associated with moist instability, but I don’t think ‘favouring it’ is the correct way to phrase this.
- L221-223: I can’t see evidence for this in Fig. 1. An anomaly plot might make things clearer.
- L231-232: I don’t think the boundaries of West Central Africa have been defined yet in the manuscript.
- L243: Need to provide evidence or a reference for this statement.
- L256-258: I think this shows that moisture extended further north over West Africa in October 2019, not that there was more moisture in Equatorial West Africa as stated.
- L258-259: Although the moisture source is the Atlantic, it is not necessarily a consequence of warmer SSTs. The northward extension of the meridional winds is the key process here, so perhaps that is more associated with anomalies in the Saharan heat-low?
- L262-263: That result is more relevant to long-term responses to global warming. For regional monthly anomalies, changes in winds will be equally or more important drivers of changes in humidity over land.
- L267: Which heating sources?
- 4 caption: The reference here should be to Fig. 5, not Fig. 2.
- L285-286: I’m not sure how this result about dependence on surface heating is directly relevant to the moisture budget results shown here.
- 5: Need to show the pattern of the residual term as well, because it is large. The pattern might also give some clues as to what is causing the large residual.
- L313: Although the increase in diabatic heating is related to the precipitation change, I don’t think it can be said to be driving it.
- L314-315: From the maps shown here, the increased moisture looks to be mainly associated with winds penetrating further northwards into West Africa, rather than any general increase in moisture associated with increased Atlantic SSTs.
- L318: Why is this the ‘second’ dynamic parameter?
- L320: Grammar doesn’t quite work here.
- 6: Please change the colours used here for the benefit of readers with red-green colour-blindness.
- L339: Minimum, not maximum.
- L340-341: Not necessarily. This depends on the vertical structure of the omega anomalies. This relationship needs to be checked.
- L346: I don’t think it is correct in this context to say that Lq’ approached m’. The vertical gradients of the two terms are very different, and it is the vertical gradients that are crucial here.
- L357-364: This flux term should be investigated further by separating it into surface vs SW and LW radiative fluxes and potentially clear-sky vs cloudy radiative fluxes. From Fig. 8e the flux term seems to be co-located with the rainfall anomaly, so one interpretation is that this is a radiative response to increase in deep convective clouds.
- L360-364: I would have thought that the MSE budget implies that a reduction in energy into the column would be associated with a reduction in ascent and precipitation, not an increase.
- L378: This relationship between the thermodynamic and dynamic terms seems to vary a lot depending on the sub-region.
- L386: By itself it would result in this, but the combination of other budget terms are larger.
- L388: I think ‘interaction’ would be a better word than ‘feedbacks’ here.
- L392: This is clearer for the northern part of the domain than the central part.
- L407-408: I think ‘area-averaged’ would be better than ‘entire’ here, as this result doesn’t hold everywhere in the domain.
- L418: This should say ‘MSE’ instead of ‘moist air’.
- L437-438: Again, I don’t think there is any evidence here to link this directly with enhanced Atlantic SSTs. It is the wind anomalies that are crucial.
- L453-456: This is overstating how much we can learn from this analysis. In order to link the October 2019 rains to global warming a formal detection and attribution study would be needed.
- L457-458: Are there also easterly anomalies over equatorial West Africa? This whole analysis would benefit from separating the central and northern parts of the domain, as different processes appear to be at work. It may be that there is a common driver, but that is not currently demonstrated here.
- L463 and L464: The word ‘controls’ implies causality, which has not been demonstrated here.
- L475: This is true in the northern part of the domain, but not the equatorial part I don’t think.
- L485-487: It’s not clear to me whether the results shown here really are consistent with those of Nicholson et al. (2021). More analysis is needed to demonstrate that.
Citation: https://doi.org/10.5194/egusphere-2024-1257-RC1 - AC1: 'Reply on RC1', Kevin Kenfack, 13 Jul 2024
-
RC2: 'Comment on egusphere-2024-1257', Anonymous Referee #2, 20 Jun 2024
The authors seek to explain the anomalously strong 2019 West Central African October rains through a moisture and MSE budget analysis. They find that anomalous meridional transport and anomalous moisture / wet enthalpy export (possibly driven by the combination of a strong Saharan Heat Low and high Atlantic SSTs?) contributed to extreme rainfall in the region.
Overall, this is an important question to study and the authors do a decent job explaining the complex factors making the 2019 rainy season so strong. I have some remaining questions, primarily around the underlying reasons for the anomalies discussed here, in addition to some extra suggested analysis. Contingent on those changes, I recommend publication after Major Revisions.
### Major questions
# SSTs and the Saharan Heat Low
The authors occasionally bring up the role of anomalously high SSTs in the Atlantic Ocean, but that argument could be developed further, especially since it may be linked to the anomalous onshore moisture transport mentioned in the study. Perhaps a figure showing anomalous SSTs (maybe as part of the summary figure I suggest below) could help as well.
The same goes for the Saharan Heat Low, which is mentioned a few times as a driver of the anomalous meridional circulation, but not shown or explained further. It seems like the authors are arguing that these two factors may be the underlying drivers of the anomalies shown in the paper (if I understood correctly!) and it would be great to be more explicit about this, explain the argument better, and show them in a diagnostic figure as well.
# Role of large-scale circulation
The paper could benefit from placing the anomalous circulation / thermodynamics in the context of larger-scale circulation effects happening. 2019 was an El Niño year, are these results typical of El Niño states? (or other major oscillations that affect west central Africa).
# Robustness checks with another reanalysis product
Given the data sparsity over much of equatorial Africa, reanalysis products tend to struggle with aspects of the regional circulation. More generally, they often struggle to close moisture budgets (which may be part of the reason the residual is so high in the budget calculations?). It would be good to see a robustness check of the primary results with another reanalysis product (Hua et al. 2019 suggest MERRA-2, for example).
# The large residual
I would appreciate a more in-depth discussion of the residual, which is the largest single term on the right side of the P-E balance equation. Could it be partially caused by poor moisture budget closure in reanalysis products? Given how large it is – the authors suspect possible influence of the MJO – would rainfall have been substantially lower (or higher, since it seems to counteract precipitation in the balance) if the MJO were in a different phase?
### Figures
It would be very helpful to the reader if the authors could add a new Figure 1 that shows an overview of the study region, with the box over which values are averaged clearly marked. Perhaps the map could show (in addition to lat/lon, borders, and the study area) SST anomalies over ocean, rainfall anomalies over land, and moisture transport (or circulation) as arrows. This would neatly tie together some of the primary arguments of the study and make it easier to geographically place the results (I at least always find it hard to just go off latitude / longitude without a corresponding map).
In Figures 1 and 3, would it be possible to title the subplots? (“1988-2017 avg.” and “2019 avg.” for Figure 1 for example).
In Figure 5 and 8-10, could you specify that the box in panel a is the box over which values are averaged in the analysis? (and could you please replicate the box in every panel?)
### Minor questions / points
Abstract: using « anomalies » instead of “variation” in the abstract when referring to the anomaly terms may be easier to understand.
L72: period missing
L75-76: I would guess the positive SSTs and the increased moisture flux are probably related, right?
L78-L84: Do you think the anomalously strong East African rains were related to the west central African rains? If so, how? (since the two regions seem often dynamically distinct... but I guess they could be indirectly related through the large-scale circulation?)
L150: I think you can drop the 86400 and just specify you’re showing output in K/day.
L163: I assume you meant top of the troposphere? I don’t think Seager et al. 2010 actually makes a statement on this. They actually integrate to the top available level of the model at the time, which is presumably higher than 300hPa.
L164: How true is this? (i.e., how small are changes in q at the monthly level?)
L178 / Eq 6: should be cpT + Lvq. In which case you can use m for this as well.
### References
Hua, Wenjian, Liming Zhou, Sharon E. Nicholson, Haishan Chen, and Minhua Qin. 2019. “Assessing Reanalysis Data for Understanding Rainfall Climatology and Variability over Central Equatorial Africa.” Climate Dynamics 53 (1): 651–69. https://doi.org/10.1007/s00382-018-04604-0.
Seager, Richard, Naomi Naik, and Gabriel A. Vecchi. 2010. “Thermodynamic and Dynamic Mechanisms for Large-Scale Changes in the Hydrological Cycle in Response to Global Warming.” Journal of Climate 23 (17): 4651–68. https://doi.org/10.1175/2010JCLI3655.1.
Citation: https://doi.org/10.5194/egusphere-2024-1257-RC2 - AC2: 'Reply on RC2', Kevin Kenfack, 13 Jul 2024
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Kevin Kenfack
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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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