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 ?