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the Creative Commons Attribution 4.0 License.
| 20 Aug 2024
Distance of flight of cosmic-ray muons to study dynamics of the upper muosphere
Abstract. The Earth can be divided by main layers, including the atmosphere, geosphere (solid Earth), and biosphere, depending on its predominant component. In this work, the layer of the Earth which constantly contains a high concentration of muons (~8 × 1012 muons) and its upper border are respectively defined as the muosphere and muopause. The altitude of the muosphere spans from the lower stratosphere to the upper crust of the Earth. In order to study its dynamics, the muopause height was spatiotemporally studied with a new kind of technique called the distance of flight (DoF) which utilizes variations in the muon’s decay length. In this work, (A) numerical modeling was performed, and it was clarified that seasonal variations in the cosmic muon flux are predominantly ruled by muopause dynamics, (B) the muon data were compared with the balloon-based measurement results, and it was confirmed that muopause dynamics is closely related with lower-stratospheric height variations. Since the muopause is the region spanning between the upper troposphere and the lower stratosphere, the potential of the current DoF approach needs to be further investigated by cross-comparing related case studies and other atmospheric climate datasets.
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RC1: 'Comment on gi-2024-4', Anonymous Referee #1, 09 Sep 2024
Dear,
Editorial support team
Copernicus Publications
Referee report of the manuscript gi-2024-4 (Distance of flight of cosmic-ray
muons to study dynamics of the upper muosphere).
The paper presents the concept of muosphere as the region where a high concen-
tration of muons and its limit respectively. It describes muosphere/muopause
dynamics depending on crustal density (millennia time order) or isobaric surface
height variations. The author introduces the DoF (Distance of Flight) technique
for characterizing the muosphere based on measured data of the muon flux. The
paper describes in detail the modeling process and compares it with measured
data.
The technique is interesting but its application in a concrete problem isn’t ob-
vious. It’s important to extend this technique in a real scenario and contrast it
conceptually with techniques (like LIDAR) that can perform the same work. I
recommend publishing the paper after adding the modifications listed below.
line 49. The muosphere is defined from +10 km to -10 km, however in the
equation at line 55 the muosphere thickness is 3.5×104 m.
line 54. Typo in 1.6 × 102m−2s−1.
line 53. The estimated muon abundance is ∼ 8 × 1012 muons, however solving
the equation is ∼ 9.3 × 1012 muons. I recommend to put the equation out from
the text.
line 53. In the muon abundance equation a constant integral muon flux is used,
this flux is the one measured at sea level, but not the same underground where
the muon flux significantly decreases. Does it affect the abundance calculation?
line 72. The author establishes that study of muopause dynamics contribute to
the research field and mention some cases. Could you describe, in more detail,
how the parameterization of the muosphere/muopause can contribute?
line 95. Some reports on the study of barometric and temperature effects in
the muon flux are mentioned. The Pierre Auger Observatory has made stud-
ies on the influence of atmospheric pressure/temperature (using meteorological
balloons) in cosmic ray flux, it’s important to cite them. J. Blumer et al. Atmo-
spheric Profiles at the Southern Pierre Auger Observatory and their Relevance
to Air Shower Measurement. 2005.
line 102. The author set three major identified characteristics, but only A and
B are described, is there a C?
Figure 2. The scale of the muon flux variation is not clear in the panel A. Was
equation 1 obtained form panel-B plot on Figure 2?Figure 3. It’s important to add error bars to the plots A and B due to they
are based on data.
Figure 4. The number label on the left of the blue line is missing.
Figure 5. It’s valuable to add the line legend to both plots. The plot description
is split into two different pages and it makes the figure reading difficult.
Figure 5. Why does the curve behave different at 90◦ zenith? isn’t expected
to follow the same trend than for the other zenith angles?
line 246. If the zenith angle is close to zero the equation diverges, so ”the
spherical curvature of the Earth has to be considered (for θ = 90◦)”. Does it
mean that the angle dependence is taken into account only for θ = 90◦?
Figure 6. Add error bars to plots contained in Figure 6.
line 270. The zenith-angle integration range was set to be 50◦ − 80◦. Why?
line 294. Typo, a dot is missing. (. Three PSDs ...)
line 295. In the apparatus description, the author says that between detection
layers two absorbing layers are set (10-cm thick lead block and a 3-cm thick
stainless-steel), if you have 10 cm of lead, is it necessary to have 3 cm of stainless-
steel? why?
line 296. Typo. ”10-cm thick lead block and a 3-cm thick stainless-steel with
a thickness of 3 cm”.
line 240. Write properly equation 2-2. It’s confusing.
Equation 2-2. What is the meaning of the constant 660? where does it come
from?
Equation 1. The relationship between atmospheric pressure and muon flux is
inverse, in that way, isn’t the slope of equation 1 negative? - RC2: 'Comment on gi-2024-4', Anonymous Referee #2, 11 Sep 2024
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RC3: 'Comment on gi-2024-4', Anonymous Referee #3, 13 Sep 2024
The paper proposes an original link between sea-level muon flux measurements and assessment on the atmosphere state's equation in a whole. It introduces a neologism "muosphere" defined as the part of the atmosphere + geosphere where muon flux is relevant, in a way which still not completely clear after the reading of the article, especially on the lower border (the geosphere one) since muons penetrate the Earth over distances depending on their incident energy. The article focuses on the "muopause" but I do not see much considerations on the underground probing of the geosphere. Please develop more on both borders of your "muosphere".
The main weakness of this article is that, apart from the invention of the term "muosphere", it does not propose innovative approaches on the use of muons fluxes o derive properties of the atmosphere. It has been published in the past that muons flux is correlated to barometric observables, stratospheric temperatures etc and be used to detect transient phenomena of abrupt changes in those parameters (e.g. SSW as mentionned but not cited in the article) or to anticipate violent phenomena such as storms.TOF methods are also well documented and I would not focus the title of the article on this item.
The real originality of the paper is the use of cyclones for the calibration of the method. I would suggest to focus more on that point and try to implement a concept close to the one of "standard candles" used is cosmology with the supernovae for instance. Please try to elaborate on this item and provide more details on the analysis tools, goodness-of-fit, likelihood analysis to assess whether the results of this method may be reproducible.Best regards.
Citation: https://doi.org/10.5194/gi-2024-4-RC3 -
CC1: 'Comment on gi-2024-4', Pasquale Noli, 19 Sep 2024
The article is well-written and structured, once again demonstrating the effectiveness of studying cosmic muons for indirect measurements of related phenomena. Measurements of muon flux at the Earth's surface have consistently shown a close relationship with the thermodynamic characteristics of the atmosphere. Therefore, the technique presented does not seem innovative but rather an alternative to existing ground-based atmospheric measurement techniques. Although the results are still far from those obtainable with conventional techniques, with improvements to the apparatus in terms of effective area to increase acquisition statistics, this technique could prove effective for studies on seasonal time scales.
Despite the meticulous writing, there are some numerical errors:
- Line 53: The result of the equation should be 9.3×1012 , not 8×1012 .
- Line 57: The muon flux multiplied by the Earth's surface area is 1.6×102 muons/m2s × 5×1014 m2=8×1016 muons/s not 5×1016muons/s.
I would ask the author to be more specific in explaining how the values between lines 172 and 179 were calculated. Furthermore, although the article includes comparisons between the variation in the number of muons observed at sea level and the theoretical model, it is not shown how the theoretical model can be used to extrapolate the altitude or variation in the altitude of the muonsphere.
Citation: https://doi.org/10.5194/gi-2024-4-CC1 -
CC2: 'RC on gi-2024-4', Pasquale Noli, 19 Sep 2024
The article is well-written and structured, once again demonstrating the effectiveness of studying cosmic muons for indirect measurements of related phenomena. Measurements of muon flux at the Earth's surface have consistently shown a close relationship with the thermodynamic characteristics of the atmosphere. Therefore, the technique presented does not seem innovative but rather an alternative to existing ground-based atmospheric measurement techniques. Although the results are still far from those obtainable with conventional techniques, with improvements to the apparatus in terms of effective area to increase acquisition statistics, this technique could prove effective for studies on seasonal time scales.
Despite the meticulous writing, there are some numerical errors:
- Line 53: The result of the equation should be 9.3×1012 , not 8×1012.
- Line 57: The muon flux multiplied by the Earth's surface area is 1.6×102muons/m2s ×5×1014 m2=8×1016 muons/s , not 5×1016 muons/s.
I would ask the author to be more specific in explaining how the values between lines 172 and 179 were calculated. Furthermore, although the article includes comparisons between the variation in the number of muons observed at sea level and the theoretical model, it is not shown how the theoretical model can be used to extrapolate the altitude or variation in the altitude of the muonsphere.
Citation: https://doi.org/10.5194/gi-2024-4-CC2 - AC1: 'Comment on gi-2024-4', Hiroyuki Tanaka, 10 Oct 2024
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