the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Thermodynamic model for a pilot balloon
Abstract. In the early part of the 20th century, tracking a pilot balloon from the ground with an optical theodolite was one of the few methods that was able to provide information from the upper air. One of the most significant sources of error with this method, however, was involved in calculating the balloon height as a function of time, a calculation dependent on the ascent rate which was traditionally taken to be constant. This study presents a new thermodynamic model which allows us to compute the thermal jump between the surrounding environment and the lifting gas as a function of different parameters such as the atmospheric temperature lapse rate or the physical characteristics of the balloon. The size of the thermal jump and its effect on the ascent rate is discussed for a 30 g pilot balloon, which was the type used at the Ebro Observatory (EO) between 1952 and 1963. The meridional and zonal components of the wind profile from ground level up to 10 km altitude were computed by applying the model using EO digitized data for a sample of this period. The obtained results correlate very well with those obtained from the ERA5 reanalysis. A very small thermal jump with a weak effect on the computed ascent rate was found. This ascent rate is consistent with the values assigned in that period to the balloons filled with hydrogen used at the Ebro Observatory and to the 30 g balloons filled with helium used by the US National Weather Service.
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RC1: 'Comment on amt2021206', Anonymous Referee #1, 12 Nov 2021
This paper presents a model of the ascent of a sounding balloon. The motivation is the retrieval of horizontal wind information from azimuth and elevation of pilot balloons reported at a time when position information was not directly measured. The topic is of interest to AMT and the paper is clearly written. However, in my opinion, it falls short of new results and more analyses are required before it can be accepted for publication. I detail below a few suggestions to the authors.
Main comments
1) Earlier studies, including those cited by the authors, have already examined the behavior of sounding balloons and it is not clear what is new in the analysis presented in this paper. This should be explicited. The development of the model equations is standard and could be shortened and partly moved to the appendix.
2) The lack of consideration of radiative fluxes is a severe shortcoming in my opinion. This point was also negelected in many previous studies and could be a novel interesting aspect of this paper if treated. Note that even during nighttime the infrared fluxes from the Earth surface might not be negligible compared to heat diffusion.
3) A validation of the numerical model is missing. Even though they do not have access to that information for Ebro launches, the authors could validate their model with ascent rates from present day radiosoundings. The sensitivity of the retrieved horizontal wind to the assumed lapse rate and model parameters should also be presented (currently only this sentence on line 859 ‘correlations obtained between the ERA5 wind profile and the model hardly vary even when using the lapse rate for a standard atmosphere (6.5 K km 1 )’ hints that the authors have carried out such a sensitivity study but the results are not presented).
Other comment :
p5 line 164 : ‘ERA5 pressure levels’: why not use model levels instead ? They have a higher resolution.
Citation: https://doi.org/10.5194/amt2021206RC1 
AC1: 'Reply on RC1', J.J. Curto, 25 Apr 2022
RC1: 'Comment on amt2021206', Anonymous Referee #1, 12 Nov 2021 reply
This paper presents a model of the ascent of a sounding balloon. The motivation is the retrieval of horizontal wind information from azimuth and elevation of pilot balloons reported at a time when position information was not directly measured. The topic is of interest to AMT and the paper is clearly written. However, in my opinion, it falls short of new results and more analyses are required before it can be accepted for publication. I detail below a few suggestions to the authors.
Main comments
1) Earlier studies, including those cited by the authors, have already examined the behavior of sounding balloons and it is not clear what is new in the analysis presented in this paper. This should be explicited. The development of the model equations is standard and could be shortened and partly moved to the appendix.In this paper, we evaluated how the balloon’s ascent rate determines the accuracy of wind calculations. Also, the sensitivity of the ascent rate to variations of some parameters of the model. The last, but not the less, our model, among others items, includes radiative balances. So, we consider it as one of the most complete one to understand the dynamics of a pilot balloon and represents a step forward in their study. Following the referee’s suggestion, we have reduced the number of equations and moved them to the Appendix.
2) The lack of consideration of radiative fluxes is a severe shortcoming in my opinion. This point was also negelected in many previous studies and could be a novel interesting aspect of this paper if treated. Note that even during nighttime the infrared fluxes from the Earth surface might not be negligible compared to heat diffusion.We have included a consideration of radiative fluxes in the model, for both IR and visible fluxes.
3) A validation of the numerical model is missing. Even though they do not have access to that information for Ebro launches, the authors could validate their model with ascent rates from present day radiosoundings. The sensitivity of the retrieved horizontal wind to the assumed lapse rate and model parameters should also be presented (currently only this sentence on line 859 'correlations obtained between the ERA5 wind profile and the model hardly vary even when using the lapse rate for a standard atmosphere (6.5 K km 1 )' hints that the authors have carried out such a sensitivity study but the results are not presented).We have validated the model from radio soundings. We included a section (8.1) for the case of nighttime radio soundings taking into account the radiative balance for IR, and another section (8.2) for daytime soundings which also take into account visible radiation.
We have included a table to show the sensitivity of the ascent rate to variations of some parameters of the model (Table II, part 6).
We have included a complete section (10) to analyze the impact of the assumed ascent rate on the accuracy of the horizontal wind calculation. We believe this question is of the utmost importance and had not previously received the attention it deserves.
Other comment :
p5 line 164 : 'ERA5 pressure levels': why not use model levels instead ? They have a higher resolution.We have interpolated both the ERA5 data and the model data to be able to compare them at a resolution of 500 m. We believe this resolution is sufficient. The 30 g pilot balloon used in the observations has an ascent rate close to 200 m/min and, since the theodolite angles are measured every minute, we only have a little more than two measurements for every 500 m.
Citation: https://doi.org/10.5194/amt2021206AC1

AC1: 'Reply on RC1', J.J. Curto, 25 Apr 2022

RC2: 'Referee comment on amt2021206', Anonymous Referee #2, 25 Nov 2021
After a nice review of the history of piball and theodolite observations for estimating wind, the authors spend 12 or so pages and 30 equations to develop a thermodynamic model for estimating the temperature differences between the environment and the balloon gas, and ,the ascent rate of the balloon, involving flow charts and analog resistance circuits. The hypothesis is that piball observations made in the 1950s could be improved in terms of the altitude profile of the winds if the ascent rate of the balloon was more well characterized than just the assumption of a constant 200 m/min. In the process the authors coin the term thermal jump to indicate the temperature gradient across the skin of the balloon and use Reynolds, Nusselt, and Prandtl numbers in their equations for drag. The authors believe that in particular their model could make a difference if the temperature lapse rate differed from a constant pseudo adiabatic rate and included inversions or isothermal layers. While such features are shown to make a difference in the ascent rate, it is not significant, and the ascent rate model developed was not tested against any observations, which, with modern radiosondes, would not be hard to do.
Instead for a test, the thermodynamical model is applied to wind observations from ten cases of theodolite observations from Ebro observatory in the 1950s and the wind profile derived with the new ascent rates compared with ERA5 reanalysis data. The scatter gram of U and V winds shows a linear correlation between the two, but with no indication of the size of the differences since the graphs are in standard units which are not explained. When the entire Erbo observatory data set using a constant ascent rate is compared against ERA5 the correlations are nearly the same for ascent rates between 195 and 215 m/min.
So it seems all this work, and clearly there was a lot, does not make a significant difference in the historical measurements, and the model is designed for an observation that is no longer made as we have much better systems. Further, if the authors think their model is so precise in calculating ascent rate of balloons, they should compare it to measured lapse rates of real balloons. They could easily control all the parameters going into the test: inflation gas, balloon sizes, weigh off, accounting for a small radiosonde attached. The radiosonde would provide the measured ascent rate directly for comparison with their model. Perhaps all this material could go into a report somewhere, but it certainly does not need to be published in ATM.
Here are just a few editorial comments made on reading the manuscript.
Thermal jump? – What is meant by these words referred to in several places.
169170 … so we carried out an interpolation process with the function of the NCL (The NCAR Command Language) csa1 with 15 knots… Confusing, suggesting an interpolation in altitude but then referring to 15 knots.
185189 redundant.
249253 – previous table? There is no previous table. Tables should be referred to by a number.
262269. This is a poor description, thermal jump is inappropriate. There is a temperature difference between the gas in and outside the balloon, but it should be stated much more simply. Simply put the temperature of the gas in the balloon changes the balloons volume, which changes the volume and hence mass of air displaced and this changes the buoyancy force. This is well known and can be stated quite simply.
273274 more redundant text.
277 How is the radiative and thermal balance determined? And it only takes a few minutes. Thus are not most balloons in near thermal equilibrium with their surroundings after a few minutes?
Section 5 – This is way overdone. The simple calculations of the mass differences described by equations 5, 6, and 7 need a sentence. Then Figure 5 shows that the temperature difference between the balloon and the surroundings is about 2 C after 11 seconds. This then leads to an approximately 1/300 or 0.3% difference from assuming the balloon’s temperature is ambient for a 30 g balloon. I don’t see the need for such detail to be included. Also it appears the authors have not added any new information here, see how closely their measurements reproduce the literature.
326 Do the authors mean figure 5?
451 Earlier the authors assumed, line 359 and showed, figure 5, that Tgas~Tair was within a few K. Now they characterize this difference as a thermal jump.
Figure 9. To assess the importance of the thermal jump each of the cases should be compared to a calculation with no thermal jump. Currently only one example with no thermal jump is included, but it is not even clear if this coincides with the isothermal layer or the inversion.
Figures 11 and 12. Now the results show up to a 3 K thermal jump leading to an overall height difference of about 20 m. Is this significant? And if there is no inversion layer the thermal jump is negligible. Even with an inversion it seems to remain fairly insignificant.
721724 …”The difference is very small, with the former being about 8 m higher than the latter at an altitude of 10 km. This extremely small difference indicates that, at least, for this kind of (30 g) balloon, the heat exchange with the surrounding air has very little effect on the ascent rate and is, therefore, virtually insignificant for calculating wind velocities at height.”
Here the authors essentially agree that all this effort has led to little change in the outcome.
Citation: https://doi.org/10.5194/amt2021206RC2 
AC2: 'Reply on RC2', J.J. Curto, 25 Apr 2022
RC2: 'Referee comment on amt2021206', Anonymous Referee #2, 25 Nov 2021 reply
After a nice review of the history of piball and theodolite observations for estimating wind, the authors spend 12 or so pages and 30 equations to develop a thermodynamic model for estimating the temperature differences between the environment and the balloon gas, and, the ascent rate of the balloon, involving flow charts and analog resistance circuits. The hypothesis is that piball observations made in the 1950s could be improved in terms of the altitude profile of the winds if the ascent rate of the balloon was more well characterized than just the assumption of a constant 200 m/min. In the process the authors coin the term thermal jump to indicate the temperature gradient across the skin of the balloon and use Reynolds, Nusselt, and Prandtl numbers in their equations for drag. The authors believe that in particular their model could make a difference if the temperature lapse rate differed from a constant pseudo adiabatic rate and included inversions or isothermal layers. While such features are shown to make a difference in the ascent rate, it is not significant, and the ascent rate model developed was not tested against any observations, which, with modern radiosondes, would not be hard to do.
Instead for a test, the thermodynamical model is applied to wind observations from ten cases of theodolite observations from Ebro observatory in the 1950s and the wind profile derived with the new ascent rates compared with ERA5 reanalysis data. The scatter gram of U and V winds shows a linear correlation between the two, but with no indication of the size of the differences since the graphs are in standard units which are not explained. When the entire Erbo observatory data set using a constant ascent rate is compared against ERA5 the correlations are nearly the same for ascent rates between 195 and 215 m/min.
So, it seems all this work, and clearly there was a lot, does not make a significant difference in the historical measurements, and the model is designed for an observation that is no longer made as we have much better systems. Further, if the authors think their model is so precise in calculating ascent rate of balloons, they should compare it to measured lapse rates of real balloons. They could easily control all the parameters going into the test: inflation gas, balloon sizes, weigh off, accounting for a small radiosonde attached. The radiosonde would provide the measured ascent rate directly for comparison with their model. Perhaps all this material could go into a report somewhere, but it certainly does not need to be published in ATM.
Here are just a few editorial comments made on reading the manuscript.
Thermal jump? – What is meant by these words referred to in several places.
We have eliminated this term.
169170 … so we carried out an interpolation process with the function of the NCL (The NCAR Command Language) csa1with 15 knots… Confusing, suggesting an interpolation in altitude but then referring to 15 knots.
It refers to an interpolation in altitude. We mention 15 knots in reference to the number of points used in the csa1 function to carry out the interpolation.
185189 redundant.
We have eliminated this part.
249253 – previous table? There is no previous table. Tables should be referred to by a number.
We have expressed it better now. “Previous table” was referring to Table 1.1 from the ‘compendium of lecture notes for training class III’ mentioned beforehand.
262269. This is a poor description, thermal jump is inappropriate. There is a temperature difference between the gas in and outside the balloon, but it should be stated much more simply. Simply put the temperature of the gas in the balloon changes the balloons volume, which changes the volume and hence mass of air displaced and this changes the buoyancy force. This is well known and can be stated quite simply.
Eliminated this part.
273274 more redundant text.
Taken out.
277 How is the radiative and thermal balance determined? And it only takes a few minutes. Thus are not most balloons in near thermal equilibrium with their surroundings after a few minutes?
This part has also been eliminated.
Section 5 – This is way overdone. The simple calculations of the mass differences described by equations 5, 6, and 7 need a sentence. Then Figure 5 shows that the temperature difference between the balloon and the surroundings is about 2 C after 11 seconds. This then leads to an approximately 1/300 or 0.3% difference from assuming the balloon’s temperature is ambient for a 30 g balloon. I don’t see the need for such detail to be included. Also it appears the authors have not added any newinformation here, see how closely their measurements reproduce the literature.
Taken out.
326 Do the authors mean figure 5?
We have taken out this figure.
451 Earlier the authors assumed, line 359 and showed, figure 5, that Tgas~Tair was within a few K. Now they characterize this difference as a thermal jump.
We carried out the approximation T_{gas}/T_{a} =1 in line 395 to be able to resolve more easily equations in an analytical way. This approximation is not necessary if we solve equations numerically, so it has now been taken out.
Figure 9. To assess the importance of the thermal jump each of the cases should be compared to a calculation with no thermal jump. Currently only one example with no thermal jump is included, but it is not even clear if this coincides with the isothermal layer or the inversion.
This figure has been taken out
Figures 11 and 12. Now the results show up to a 3 K thermal jump leading to an overall height difference of about 20 m. Is this significant? And if there is no inversion layer the thermal jump is negligible. Even with an inversion it seems to remain fairly insignificant.
These figures have been taken out
721724 …”The difference is very small, with the former being about 8 m higher than the latter at an altitude of 10 km. This extremely small difference indicates that, at least, for this kind of (30 g) balloon, the heat exchange with the surrounding air has very little effect on the ascent rate and is, therefore, virtually insignificant for calculating wind velocities at height.”
Section eliminated
Here the authors essentially agree that all this effort has led to little change in the outcome.
We agree that this paper has been produced with big effort, but we consider it was worthy. In this paper, we evaluated how the balloon’s ascent rate determines the accuracy of wind calculations. Also, the sensitivity of the ascent rate to variations of some parameters of the model. The last, but not the less, our model, among others items, includes radiative balances. So, we consider it as one of the most complete one to understand the dynamics of a pilot balloon and represents a step forward in their study.
Citation: https://doi.org/10.5194/amt2021206AC2

AC2: 'Reply on RC2', J.J. Curto, 25 Apr 2022
Status: closed

RC1: 'Comment on amt2021206', Anonymous Referee #1, 12 Nov 2021
This paper presents a model of the ascent of a sounding balloon. The motivation is the retrieval of horizontal wind information from azimuth and elevation of pilot balloons reported at a time when position information was not directly measured. The topic is of interest to AMT and the paper is clearly written. However, in my opinion, it falls short of new results and more analyses are required before it can be accepted for publication. I detail below a few suggestions to the authors.
Main comments
1) Earlier studies, including those cited by the authors, have already examined the behavior of sounding balloons and it is not clear what is new in the analysis presented in this paper. This should be explicited. The development of the model equations is standard and could be shortened and partly moved to the appendix.
2) The lack of consideration of radiative fluxes is a severe shortcoming in my opinion. This point was also negelected in many previous studies and could be a novel interesting aspect of this paper if treated. Note that even during nighttime the infrared fluxes from the Earth surface might not be negligible compared to heat diffusion.
3) A validation of the numerical model is missing. Even though they do not have access to that information for Ebro launches, the authors could validate their model with ascent rates from present day radiosoundings. The sensitivity of the retrieved horizontal wind to the assumed lapse rate and model parameters should also be presented (currently only this sentence on line 859 ‘correlations obtained between the ERA5 wind profile and the model hardly vary even when using the lapse rate for a standard atmosphere (6.5 K km 1 )’ hints that the authors have carried out such a sensitivity study but the results are not presented).
Other comment :
p5 line 164 : ‘ERA5 pressure levels’: why not use model levels instead ? They have a higher resolution.
Citation: https://doi.org/10.5194/amt2021206RC1 
AC1: 'Reply on RC1', J.J. Curto, 25 Apr 2022
RC1: 'Comment on amt2021206', Anonymous Referee #1, 12 Nov 2021 reply
This paper presents a model of the ascent of a sounding balloon. The motivation is the retrieval of horizontal wind information from azimuth and elevation of pilot balloons reported at a time when position information was not directly measured. The topic is of interest to AMT and the paper is clearly written. However, in my opinion, it falls short of new results and more analyses are required before it can be accepted for publication. I detail below a few suggestions to the authors.
Main comments
1) Earlier studies, including those cited by the authors, have already examined the behavior of sounding balloons and it is not clear what is new in the analysis presented in this paper. This should be explicited. The development of the model equations is standard and could be shortened and partly moved to the appendix.In this paper, we evaluated how the balloon’s ascent rate determines the accuracy of wind calculations. Also, the sensitivity of the ascent rate to variations of some parameters of the model. The last, but not the less, our model, among others items, includes radiative balances. So, we consider it as one of the most complete one to understand the dynamics of a pilot balloon and represents a step forward in their study. Following the referee’s suggestion, we have reduced the number of equations and moved them to the Appendix.
2) The lack of consideration of radiative fluxes is a severe shortcoming in my opinion. This point was also negelected in many previous studies and could be a novel interesting aspect of this paper if treated. Note that even during nighttime the infrared fluxes from the Earth surface might not be negligible compared to heat diffusion.We have included a consideration of radiative fluxes in the model, for both IR and visible fluxes.
3) A validation of the numerical model is missing. Even though they do not have access to that information for Ebro launches, the authors could validate their model with ascent rates from present day radiosoundings. The sensitivity of the retrieved horizontal wind to the assumed lapse rate and model parameters should also be presented (currently only this sentence on line 859 'correlations obtained between the ERA5 wind profile and the model hardly vary even when using the lapse rate for a standard atmosphere (6.5 K km 1 )' hints that the authors have carried out such a sensitivity study but the results are not presented).We have validated the model from radio soundings. We included a section (8.1) for the case of nighttime radio soundings taking into account the radiative balance for IR, and another section (8.2) for daytime soundings which also take into account visible radiation.
We have included a table to show the sensitivity of the ascent rate to variations of some parameters of the model (Table II, part 6).
We have included a complete section (10) to analyze the impact of the assumed ascent rate on the accuracy of the horizontal wind calculation. We believe this question is of the utmost importance and had not previously received the attention it deserves.
Other comment :
p5 line 164 : 'ERA5 pressure levels': why not use model levels instead ? They have a higher resolution.We have interpolated both the ERA5 data and the model data to be able to compare them at a resolution of 500 m. We believe this resolution is sufficient. The 30 g pilot balloon used in the observations has an ascent rate close to 200 m/min and, since the theodolite angles are measured every minute, we only have a little more than two measurements for every 500 m.
Citation: https://doi.org/10.5194/amt2021206AC1

AC1: 'Reply on RC1', J.J. Curto, 25 Apr 2022

RC2: 'Referee comment on amt2021206', Anonymous Referee #2, 25 Nov 2021
After a nice review of the history of piball and theodolite observations for estimating wind, the authors spend 12 or so pages and 30 equations to develop a thermodynamic model for estimating the temperature differences between the environment and the balloon gas, and ,the ascent rate of the balloon, involving flow charts and analog resistance circuits. The hypothesis is that piball observations made in the 1950s could be improved in terms of the altitude profile of the winds if the ascent rate of the balloon was more well characterized than just the assumption of a constant 200 m/min. In the process the authors coin the term thermal jump to indicate the temperature gradient across the skin of the balloon and use Reynolds, Nusselt, and Prandtl numbers in their equations for drag. The authors believe that in particular their model could make a difference if the temperature lapse rate differed from a constant pseudo adiabatic rate and included inversions or isothermal layers. While such features are shown to make a difference in the ascent rate, it is not significant, and the ascent rate model developed was not tested against any observations, which, with modern radiosondes, would not be hard to do.
Instead for a test, the thermodynamical model is applied to wind observations from ten cases of theodolite observations from Ebro observatory in the 1950s and the wind profile derived with the new ascent rates compared with ERA5 reanalysis data. The scatter gram of U and V winds shows a linear correlation between the two, but with no indication of the size of the differences since the graphs are in standard units which are not explained. When the entire Erbo observatory data set using a constant ascent rate is compared against ERA5 the correlations are nearly the same for ascent rates between 195 and 215 m/min.
So it seems all this work, and clearly there was a lot, does not make a significant difference in the historical measurements, and the model is designed for an observation that is no longer made as we have much better systems. Further, if the authors think their model is so precise in calculating ascent rate of balloons, they should compare it to measured lapse rates of real balloons. They could easily control all the parameters going into the test: inflation gas, balloon sizes, weigh off, accounting for a small radiosonde attached. The radiosonde would provide the measured ascent rate directly for comparison with their model. Perhaps all this material could go into a report somewhere, but it certainly does not need to be published in ATM.
Here are just a few editorial comments made on reading the manuscript.
Thermal jump? – What is meant by these words referred to in several places.
169170 … so we carried out an interpolation process with the function of the NCL (The NCAR Command Language) csa1 with 15 knots… Confusing, suggesting an interpolation in altitude but then referring to 15 knots.
185189 redundant.
249253 – previous table? There is no previous table. Tables should be referred to by a number.
262269. This is a poor description, thermal jump is inappropriate. There is a temperature difference between the gas in and outside the balloon, but it should be stated much more simply. Simply put the temperature of the gas in the balloon changes the balloons volume, which changes the volume and hence mass of air displaced and this changes the buoyancy force. This is well known and can be stated quite simply.
273274 more redundant text.
277 How is the radiative and thermal balance determined? And it only takes a few minutes. Thus are not most balloons in near thermal equilibrium with their surroundings after a few minutes?
Section 5 – This is way overdone. The simple calculations of the mass differences described by equations 5, 6, and 7 need a sentence. Then Figure 5 shows that the temperature difference between the balloon and the surroundings is about 2 C after 11 seconds. This then leads to an approximately 1/300 or 0.3% difference from assuming the balloon’s temperature is ambient for a 30 g balloon. I don’t see the need for such detail to be included. Also it appears the authors have not added any new information here, see how closely their measurements reproduce the literature.
326 Do the authors mean figure 5?
451 Earlier the authors assumed, line 359 and showed, figure 5, that Tgas~Tair was within a few K. Now they characterize this difference as a thermal jump.
Figure 9. To assess the importance of the thermal jump each of the cases should be compared to a calculation with no thermal jump. Currently only one example with no thermal jump is included, but it is not even clear if this coincides with the isothermal layer or the inversion.
Figures 11 and 12. Now the results show up to a 3 K thermal jump leading to an overall height difference of about 20 m. Is this significant? And if there is no inversion layer the thermal jump is negligible. Even with an inversion it seems to remain fairly insignificant.
721724 …”The difference is very small, with the former being about 8 m higher than the latter at an altitude of 10 km. This extremely small difference indicates that, at least, for this kind of (30 g) balloon, the heat exchange with the surrounding air has very little effect on the ascent rate and is, therefore, virtually insignificant for calculating wind velocities at height.”
Here the authors essentially agree that all this effort has led to little change in the outcome.
Citation: https://doi.org/10.5194/amt2021206RC2 
AC2: 'Reply on RC2', J.J. Curto, 25 Apr 2022
RC2: 'Referee comment on amt2021206', Anonymous Referee #2, 25 Nov 2021 reply
After a nice review of the history of piball and theodolite observations for estimating wind, the authors spend 12 or so pages and 30 equations to develop a thermodynamic model for estimating the temperature differences between the environment and the balloon gas, and, the ascent rate of the balloon, involving flow charts and analog resistance circuits. The hypothesis is that piball observations made in the 1950s could be improved in terms of the altitude profile of the winds if the ascent rate of the balloon was more well characterized than just the assumption of a constant 200 m/min. In the process the authors coin the term thermal jump to indicate the temperature gradient across the skin of the balloon and use Reynolds, Nusselt, and Prandtl numbers in their equations for drag. The authors believe that in particular their model could make a difference if the temperature lapse rate differed from a constant pseudo adiabatic rate and included inversions or isothermal layers. While such features are shown to make a difference in the ascent rate, it is not significant, and the ascent rate model developed was not tested against any observations, which, with modern radiosondes, would not be hard to do.
Instead for a test, the thermodynamical model is applied to wind observations from ten cases of theodolite observations from Ebro observatory in the 1950s and the wind profile derived with the new ascent rates compared with ERA5 reanalysis data. The scatter gram of U and V winds shows a linear correlation between the two, but with no indication of the size of the differences since the graphs are in standard units which are not explained. When the entire Erbo observatory data set using a constant ascent rate is compared against ERA5 the correlations are nearly the same for ascent rates between 195 and 215 m/min.
So, it seems all this work, and clearly there was a lot, does not make a significant difference in the historical measurements, and the model is designed for an observation that is no longer made as we have much better systems. Further, if the authors think their model is so precise in calculating ascent rate of balloons, they should compare it to measured lapse rates of real balloons. They could easily control all the parameters going into the test: inflation gas, balloon sizes, weigh off, accounting for a small radiosonde attached. The radiosonde would provide the measured ascent rate directly for comparison with their model. Perhaps all this material could go into a report somewhere, but it certainly does not need to be published in ATM.
Here are just a few editorial comments made on reading the manuscript.
Thermal jump? – What is meant by these words referred to in several places.
We have eliminated this term.
169170 … so we carried out an interpolation process with the function of the NCL (The NCAR Command Language) csa1with 15 knots… Confusing, suggesting an interpolation in altitude but then referring to 15 knots.
It refers to an interpolation in altitude. We mention 15 knots in reference to the number of points used in the csa1 function to carry out the interpolation.
185189 redundant.
We have eliminated this part.
249253 – previous table? There is no previous table. Tables should be referred to by a number.
We have expressed it better now. “Previous table” was referring to Table 1.1 from the ‘compendium of lecture notes for training class III’ mentioned beforehand.
262269. This is a poor description, thermal jump is inappropriate. There is a temperature difference between the gas in and outside the balloon, but it should be stated much more simply. Simply put the temperature of the gas in the balloon changes the balloons volume, which changes the volume and hence mass of air displaced and this changes the buoyancy force. This is well known and can be stated quite simply.
Eliminated this part.
273274 more redundant text.
Taken out.
277 How is the radiative and thermal balance determined? And it only takes a few minutes. Thus are not most balloons in near thermal equilibrium with their surroundings after a few minutes?
This part has also been eliminated.
Section 5 – This is way overdone. The simple calculations of the mass differences described by equations 5, 6, and 7 need a sentence. Then Figure 5 shows that the temperature difference between the balloon and the surroundings is about 2 C after 11 seconds. This then leads to an approximately 1/300 or 0.3% difference from assuming the balloon’s temperature is ambient for a 30 g balloon. I don’t see the need for such detail to be included. Also it appears the authors have not added any newinformation here, see how closely their measurements reproduce the literature.
Taken out.
326 Do the authors mean figure 5?
We have taken out this figure.
451 Earlier the authors assumed, line 359 and showed, figure 5, that Tgas~Tair was within a few K. Now they characterize this difference as a thermal jump.
We carried out the approximation T_{gas}/T_{a} =1 in line 395 to be able to resolve more easily equations in an analytical way. This approximation is not necessary if we solve equations numerically, so it has now been taken out.
Figure 9. To assess the importance of the thermal jump each of the cases should be compared to a calculation with no thermal jump. Currently only one example with no thermal jump is included, but it is not even clear if this coincides with the isothermal layer or the inversion.
This figure has been taken out
Figures 11 and 12. Now the results show up to a 3 K thermal jump leading to an overall height difference of about 20 m. Is this significant? And if there is no inversion layer the thermal jump is negligible. Even with an inversion it seems to remain fairly insignificant.
These figures have been taken out
721724 …”The difference is very small, with the former being about 8 m higher than the latter at an altitude of 10 km. This extremely small difference indicates that, at least, for this kind of (30 g) balloon, the heat exchange with the surrounding air has very little effect on the ascent rate and is, therefore, virtually insignificant for calculating wind velocities at height.”
Section eliminated
Here the authors essentially agree that all this effort has led to little change in the outcome.
We agree that this paper has been produced with big effort, but we consider it was worthy. In this paper, we evaluated how the balloon’s ascent rate determines the accuracy of wind calculations. Also, the sensitivity of the ascent rate to variations of some parameters of the model. The last, but not the less, our model, among others items, includes radiative balances. So, we consider it as one of the most complete one to understand the dynamics of a pilot balloon and represents a step forward in their study.
Citation: https://doi.org/10.5194/amt2021206AC2

AC2: 'Reply on RC2', J.J. Curto, 25 Apr 2022
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