the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 07 Oct 2024
Cairns-Tsallis distribution applied to differences of magnetic field intensity in solar wind
Abstract. Relevance of the Cairns-Tsallis probability distribution in its application to time series of spatial magnetic field differences is shown. In particular, we explore its ability to explain the data obtained by the Ulysses mission during solar cycles 23 and 24. Our findings reveal that the Cairns-Tsallis density function provides an optimal fit to the data, showing a sensitivity to the small time scale of magnetic field changes. Fit parameters obtained with this model were analyzed, as well as some multifractal indices obtained through corresponding time series analysis. Furthermore, significant discrepancies have been identified between our results and those obtained by other authors, highlighting the appropriateness of the Cairns-Tsallis distribution in capturing the underlying complexity in the data.
- Preprint
(1220 KB) - Metadata XML
- BibTeX
- EndNote
Status: final response (author comments only)
-
RC1: 'Comment on npg-2024-20', Anonymous Referee #1, 18 Nov 2024
In this work the Authors apply the Cairns-Tsallis (CT) probability distribution to time series of spatial magnetic field differences. The work discusses a best approximation of the observed distribution function of magnetic field increments using the CT distribution in respect to the very preliminary work by other authors on a similar topic. Anyway, in spite of the best fitting results I do not see any significant cultural/scientific advancement to justify the publication of this work in NPG. Furthermore, the Authors do not discuss other similar studies, as for instance those by M. Leubner and co-Authors, who apply the Tsallis statistics to solar wind study. Another critical issue that I have fond is that the analysis done by the Authors is related to solar wind feature during solar activity maximums and minimums. To me this is not the best appropriate way how to do this study. Indeed, the solar wind has a duplex character, i.e. fast and slow solar wind, whose physical properties (Alfvénic nature, presence of coherent structures, etc.) are different. A best approach would be to distinguish between fast and solar wind periods. The previous study, to which the Authors refer, is indeed a very long-standing period of slow solar wind. Following these general comments I cannot recommend this work for publication in NPG.
Citation: https://doi.org/10.5194/npg-2024-20-RC1 -
AC1: 'Reply on RC1', Ewin Sánchez, 12 Jan 2025
We agree that the scientific advancement has not been sufficiently emphasized in the manuscript, and it appears that its importance is not clear upon a first reading. We have addressed this critical point by proposing a new section in the manuscript, where a more thorough analysis reveals the clear advantages of the proposed PDF. These new results highlight the model's ability, via its parameter \(\beta\) (originally conceived to measure "non-thermality"), to distinguish data from both maximum and minimum solar activity periods, and its compatibility with intermittency. The significant potential of the CT PDF to describe short timescales, with \(\tau\) on the order of just a few seconds, is also demonstrated, underscoring this as a strength of the model (which is a weakness in many other Tsallis-type distributions). Furthermore, the model's ability to identify recorded data during each solar maximum/minimum activity period is emphasized, despite the extraordinary underlying complexity generated by the mixing of fast and slow wind flows, as well as other additional features.
About the other similar studies analyses. The insufficient bibliographic review regarding different aspects of Tsallis statistics in the study of the solar wind is an issue we have now addressed with greater dedication, improving the manuscript’s introduction and adequately complementing the content accordingly. We have included additional references that discuss solar wind, various models based on Tsallis statistics, and the results of their application across different scenarios, distances, and temporal lags, among other related aspects. From this extended review, it is evident that some studies are based on data analysis without distinguishing between fast and slow solar wind. While we acknowledge the relevance of segregating data according to wind type, we believe that analyzing data without such segregation represents an equally valid alternative approach, presenting an even greater challenge due to complexity of the data.
On the other hand, regarding the Consolini (2009) study that we have referenced, in relation to the time period in which the data were selected. This point appears to have been misunderstood. We had clarified that the data were taken without filters and that the data from that study (Consolini) were part of our dataset. To avoid confusion, we have revised the corresponding section of the text to enhance clarity on this matter.
Citation: https://doi.org/10.5194/npg-2024-20-AC1
-
AC1: 'Reply on RC1', Ewin Sánchez, 12 Jan 2025
-
RC2: 'Comment on npg-2024-20', Anonymous Referee #2, 03 Dec 2024
The presente manuscript utilizes the Cairns-Tsallis (CT) probability distribution to analyze time series of spatial Interplanetary magnetic field differences. The paper explores the optimal approximation of the observed distribution function of magnetic field increments using the CT distribution, in comparison to the preliminary work by other researchers on a similar topic using different PDFs. Their work shows that the CT fits better the IMF fluctuations than other previous work. Anyway, the discussion section is very poor, and the work lacks in possible comparison with previous studies (e.g. Leubner et al., 2005). In addition, the authors did not made any different analysis between fast and slow solar wind which, as the authors should know, presents different Alfvénicity proprieties and are characerized by different coherent structures.
So, I recommend to reject the paper in the present form and suggest the authors to repeat their analysis for fast and solar wind, before trying to submit the paper again.Leubner, Manfred P., and Z. Vörös. "A nonextensive entropy approach to solar wind intermittency." The Astrophysical Journal 618.1 (2005): 547.
Citation: https://doi.org/10.5194/npg-2024-20-RC2 -
AC2: 'Reply on RC2', Ewin Sánchez, 12 Jan 2025
Regarding the lack of references to previous studies, as well as analyses and/or comparisons based on these (also indicated by another reviewer), we have now significantly improved this aspect. This issue has been incorporated into the introduction of the manuscript and has been taken into account in various discussions and analyses throughout the text.
About the issue of both fast and slow solar wind, we do not deny the differing properties of data taken for each case. We recognize the importance of conducting studies under such considerations. However, we believe that analyzing data coming from a mixture of flows is equally valid and relevant, as evidenced by other studies (some of which are cited in the revised manuscript). A study of this type (without distinguishing between fast and slow wind) provides a valuable description of the system by accounting for its real behavior. From this perspective, the data inherently contain a high degree of complexity, making our approach an alternative that is both more comprehensive and consistent with other models.
Below we show some responses to the other reviewer, which complement this response:
We agree that the scientific advancement has not been sufficiently emphasized in the manuscript, and it appears that its importance is not clear upon a first reading. We have addressed this critical point by proposing a new section in the manuscript, where a more thorough analysis reveals the clear advantages of the proposed PDF. These new results highlight the model's ability, via its parameter \(\beta\) (originally conceived to measure "non-thermality"), to distinguish data from both maximum and minimum solar activity periods, and its compatibility with intermittency. The significant potential of the CT PDF to describe short timescales, with \(\tau\) on the order of just a few seconds, is also demonstrated, underscoring this as a strength of the model (which is a weakness in many other Tsallis-type distributions). Furthermore, the model's ability to identify recorded data during each solar maximum/minimum activity period is emphasized, despite the extraordinary underlying complexity generated by the mixing of fast and slow wind flows, as well as other additional features.
About the other similar studies analyses. The insufficient bibliographic review regarding different aspects of Tsallis statistics in the study of the solar wind is an issue we have now addressed with greater dedication, improving the manuscript’s introduction and adequately complementing the content accordingly. We have included additional references that discuss solar wind, various models based on Tsallis statistics, and the results of their application across different scenarios, distances, and temporal lags, among other related aspects. From this extended review, it is evident that some studies are based on data analysis without distinguishing between fast and slow solar wind. While we acknowledge the relevance of segregating data according to wind type, we believe that analyzing data without such segregation represents an equally valid alternative approach, presenting an even greater challenge due to complexity of the data.
Citation: https://doi.org/10.5194/npg-2024-20-AC2
-
AC2: 'Reply on RC2', Ewin Sánchez, 12 Jan 2025
Viewed
| HTML | XML | Total | BibTeX | EndNote | |
|---|---|---|---|---|---|
| 196 | 36 | 121 | 353 | 9 | 8 |
- HTML: 196
- PDF: 36
- XML: 121
- Total: 353
- BibTeX: 9
- EndNote: 8
Viewed (geographical distribution)
| Country | # | Views | % |
|---|
| Total: | 0 |
| HTML: | 0 |
| PDF: | 0 |
| XML: | 0 |
- 1