A global analysis of the fractal properties of clouds revealing anisotropy of turbulence across scales

Rees, Karlie N.; Garrett, Timothy J.; DeWitt, Thomas D.; Bois, Corey; Krueger, Steven K.; Riedi, Jérôme C.

doi:https://doi.org/10.5194/npg-31-497-2024

Articles | Volume 31, issue 4

https://doi.org/10.5194/npg-31-497-2024

© Author(s) 2024. This work is distributed under
the Creative Commons Attribution 4.0 License.

https://doi.org/10.5194/npg-31-497-2024

© Author(s) 2024. This work is distributed under
the Creative Commons Attribution 4.0 License.

Articles | Volume 31, issue 4

Research article

| Highlight paper

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21 Oct 2024

Research article | Highlight paper |

| 21 Oct 2024

A global analysis of the fractal properties of clouds revealing anisotropy of turbulence across scales

Karlie N. Rees, Timothy J. Garrett, Thomas D. DeWitt, Corey Bois, Steven K. Krueger, and Jérôme C. Riedi

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Final revised paper (published on 21 Oct 2024)
Preprint (discussion started on 18 Mar 2024)

Interactive discussion

Status: closed

RC1: 'Comment on egusphere-2024-552', Anonymous Referee #1, 17 May 2024

This paper relates theoretically turbulent features and cloud geometry features (mainly perimeter). Then, estimates of the latter on numerous satellite data as well output of numerical simulation enable to confirm previously developed framework to address the issue of anisotropy of turbulence across scales. In general, I found the paper well written and conclusions relevant for the community. I believe that only minor modifications are needed, mainly to improve clarity and help the reader through the numerous equations/approximations and data sets.

General comments:

- Calling “Xi” (Greek letter) the spatial resolution is a bit confusing, because it often called “scale” with resolution being the ratio between outer scale and observation scales. On a similar point, it is not clear to me why either “l” or “xi” are used whereas it seems to me that they both represent the observation scale at which the studied geometrical set/field is studied. Could you please clarify.
- A summary with the main formulas that are first theoretically derived and then validated with data would be helpful for the reader. May be in the form of a figure or table.
- It would be interesting to discuss results of Fig. 4 in light of the scaling relation between perimeter and area which is reminded l. 38.
- For some of the analysed fields, you have 3D data. Why not trying an analysis in 3D directly instead of reconstructing a 2D field before carrying out the analysis ?
- It should be clarified better how a pixel is set to cloudy or not during the coarsening process. Indeed, many of the observed process depends on this. See detailed comments below.

Detailed comments:

- l. 54-55: please clarify what you mean.
- Eq. 2: it assumes no intermittency correction.
- Eq. 8: please provide more explanations on how is obtained.
- l. 171: please explain better the notation D_mu and how it is used.
- l. 177: the issue of the intermittency correction is briefly mentioned here. There could also be one in eq. 2. I believe that this issue and its implications on the various equations used should be clarified.
- l. 187-190: a scheme on how P and A are computed in practice would be helpful, and also how observation scale is changed.
- l. 232-233: what is done once the rounding is implemented ? This approach and its impact should be discussed with regards to a common approach when computing fractal dimension that would be a consider a coarser pixel as cloudy it at least one of the pixels is contains at higher resolution is cloudy.
- Fig. 3: how are side effect due the round shape handled ?
- In general for section 3: a table with a summary of the data used would be helpful for the reader.
- Section 4.1: it is not clear to me why this bifurcation is observed ? How sensitive is it to how a pixel is set to cloudy or not at coarser resolution, which is not very clear for me now ?
- Section 4.2 and Fig. 4.b: Can the range of scales used to perform linear be clarified ? Native scale is excluded but seems inserted in straight lines visible in Fig. 4.b. Points for high values of xi/xi_N also seem to deviate from the straight line. Indicators of the quality of the linear regression should be added and discussed. Again how sensitive are results to the way a coarser pixel is set to cloudy or not ?

Citation: https://doi.org/10.5194/egusphere-2024-552-RC1
RC2: 'Comment on egusphere-2024-552', Anonymous Referee #2, 27 May 2024

The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2024/egusphere-2024-552/egusphere-2024-552-RC2-supplement.pdf

Citation: https://doi.org/10.5194/egusphere-2024-552-RC2
AC1: 'Comment on egusphere-2024-552', Karlie Rees, 16 Jun 2024

The authors thank the reviewers for their constructive comments. The authors' responses and changes to the manuscript are attached.

Citation: https://doi.org/10.5194/egusphere-2024-552-AC1

Peer review completion

AR: Author's response | RR: Referee report | ED: Editor decision | EF: Editorial file upload

AR by Karlie Rees on behalf of the Authors (16 Jun 2024) Author's response Author's tracked changes Manuscript

ED: Publish subject to minor revisions (review by editor) (26 Jun 2024) by Shaun Lovejoy

As a preface, I recognize that I am a invested protagonist in the science reported here, so please take these comments as helpful suggestions, not in the spirit of anonymous referee comments.

This paper is a welcome update on a key question of atmospheric dynamics: over what ranges are they scaling? The key finding is that observations of cloud radiances over a huge range of horizontal scales are indeed scaling. This vindicates Richardson’s wide range scaling hypothesis updated as confirmed by Lovejoy’s 1982 area-perimeter analysis (and numerous spectral and other analyses since). Wide range scaling is incompatible with the still prevalent 2D isotropic/3D isotropic paradigm that necessarily involves a “dimensional transition” somewhere in the mesoscale. The question is which symmetry is dominant: the scale symmetry or the rotational symmetry? Richardson believed it was scaling. Following the isotropic 2D Kraichnan 1968 model, and Charney’s 1971 quasi-geostrophic variant, the atmospheric community has largely considered isotropy to be the dominant symmetry, thus implying an elusive dimensional transition/scale break somewhere near the mesoscale. This paper contradicts the latter hypothesis but supports the former. It would be worth bringing this out in the introduction, it will enhance the significance of the work.

My main issue with the paper is that it is monofractal – both in the theoretical model as well as in the data analysis. This aspect with respect to both area-perimeter relations as well as Korcak laws was considered in some detail in several appendices to [Lovejoy and Schertzer, 1991]:

http://www.physics.mcgill.ca/~gang/eprints/eprintLovejoy/neweprint/NVAGlovejoyall.pdf

The main conclusion relevant to this paper is that the interpretation of the area-perimeter (A-P) exponent, is quite different when monofractal models (such as fractional Brownian motion), or when multifractal models are used. In the former case (assumed here), the cloud regions exceeding a threshold are assumed to be non fractal (they are assumed to be true (2D) areas, with dimension = 2) so that the usual interpretation of the A-P exponent = D/2 is valid. However if clouds are multifractal, then for any exceedance threshold that define “clouds”, the A-P exponent is the ratio D(P)/D(A) of the perimeter dimension D(P) to the fractal dimension of the exceedance set D(A). Since D(P) and D(A) will both decrease with the brightness threshold that defines the sets, the ratio may be quite stable over a range of thresholds, potentially explaining the robustness of the A-P exponent.

The authors may want to reflect and comment on this?

Please see the attachment for more detailed comments.

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AR by Karlie Rees on behalf of the Authors (16 Jul 2024) Author's response Author's tracked changes Manuscript

ED: Publish as is (27 Aug 2024) by Shaun Lovejoy

AR by Karlie Rees on behalf of the Authors (03 Sep 2024)

Short summary

The shapes of clouds viewed from space reflect vertical and horizontal motions in the atmosphere. We theorize that, globally, cloud perimeter complexity is related to the dimension of turbulence also governed by horizontal and vertical motions. We find agreement between theory and observations from various satellites and a numerical model and, remarkably, that the theory applies globally using only basic planetary physical parameters from the smallest scales of turbulence to the planetary scale.