Review: A method for characterizing the spatial organization of deep convective cores in deep convective systems’ cloud shield

This paper introduces a novel method to classify and study the spatial organization and geometry of convective systems as well as their distribution of convective cores. Four key metrics are introduced based on infrared brightness temperatures in geostationary satellite observations and outgoing longwave radiation in km-scale numerical simulations (with a delta x of 3km) of idealized cloud scenes. The metrics give a more holistic description of convective organization, including the size and relative fraction of convective cores as well as their spatial arrangement  and randomness. The metrics are discussed well in the context of already existing metrics for convective organization and the authors make an argument that convective organization cannot be well described when relying on one single parameter instead of combining different aspects of the spatial structure. Overall, the paper is well-structured, well-written and is a valuable contribution to allow for a more sophisticated analysis of convective processes. While I do not think that any additional analyses are needed, I think there are still a few parts in the paper that need clarifications, in particular because the main point of the paper is to introduce a new technique that should be straightforward to reproduce. I recommend the paper for minor revisions. 

General comments 

Physical processes

Acknowledging that this paper focuses on the introduction and development of a new method, it is not expected that the conclusions center around new findings about convective organization. However, I think the paper would benefit from explaining how the introduced metrics and the classes that are based upon these four metrics, could be used to identify certain processes. Right now, the differences in the distributions (e.g. in Fig. 13-14) are not really discussed in the context of which underlying weather systems and processes would produce the different signatures in convective organization. In addition, it would be useful to name a few examples of how this method can be applied in weather and climate research. 

Decomposition into elementary structure

It appears to me that the decomposition into the elementary structures that is based on the square-like nature of the convective core has implications for the characteristic length L. Can you explain in more detail if this assumption is a limitation for the range of L values that you get? 

Differences between observations and model simulations

In the very beginning of the paper, the definition of “convective” vs. “stratiform” is introduced for models and observations. I am wondering how much of the differences that you find between the datasets actually go back to how you define “convective” in the model dataset. It makes sense to base this definition on physical processes such as updrafts, but I am afraid that, as you mention yourself, this would lead to significantly different regions than the purely radar-based signature in the satellite observations. In addition to that, I think that the paper would benefit from a more thorough discussion of differences between models and observations, as an example for how to apply the introduced method (i.,e. that it can help to validate models that partly resolve convective processes). 

Figure labels

The font size in all figures need to be increased. In some figures, such as, Fig. 3, the labels are barely readable. 

Detailed comments 

1. 21: Variables -> metrics ? (variables sounds more like specific atmospheric fields whereas metrics specifies that you introduce and suggest a measure) 

1. 27: Idealized kilo-meterscale numerical simulation

1. 54 - 67: When reviewing the existing literature on convective organization indices, could you go a bit more into detail on what variables these indices are usually based on? 

1. 104:  remove “…”

L,. 134 ff: When introducing the radar collocations, could you clarify which variables you are working with - is it only the retrieved rain rates or other retrieved quantities? Do you leverage the radar reflectivity values at all? 

1. 144, 146: colocation -> collocation 

1. 179: Is this classification based on radar reflectivity thresholds? 

1. 236: It makes sense that a grid cell can be classified as convective either when it contains heavy convective rainfall or when there are updrafts that indicate strong vertical motion (which may happen prior to and in a different grid cell than the heavy precipitation). However, it is not clear to me why a grid cell below the downdraft threshold would also be classified as convective. While strong downdrafts are part of the convective system as a whole, the processes are quite different than in updraft regions, so I would like to better understand what we gain from having strong updrafts and strong downdrafts in the same category. Would it make sense to leverage the information of hydrometeors in the model? 

1. 286: Can you explain the “high-resolution precipitation ground based core and updrafts/downdrafts joint occurrence analysis”? 

1. 282- 284: I understand the assumption that the hydrometeor distribution is the result of small-scale convective dynamics and cloud microphysics, and that, in other words, we can see convective cores as aggregates of these small-scale processes. But where does the assumption of a square-like geometry come from? Could it not be that these small-scale aggregates are, for instance, elongated like in squall lines, or is there evidence that convective cores have a circle- or square-like geometry with the same distance to all its surroundings? 

Fig. 4: Is the core size given in the number of pixels? 

Fig. 5: Add in the figure caption that this is for the satellite data. Are those the composites over all tracked DCSs? 

1. 657: A new method for what? 

1. 727: Please check the DOI of your dataset. I could not access it. 

1. 344: What is meant by this sentence: “As a consequence, unlike regular gridded data, the method is required to be shield-specific.” I am confused by the statement that the method cannot work for regular gridded data. 

1. 371: It is not clear what the difference is between the "distribution of convection across the scene” and its “spatial arrangement”. As I understand it the first two metrics describe the area and amount of convection (“how much?”) and the last two methods focus more on the geometry and where within the cloud shield convection is present? 

Fig. 11: The difference in the maximal area between the satellite data and the model simulation appears to be quite significant. Is this a consequence of the effective resolution of the datasets, and does this indicate that the model physics cannot reproduce the large cloud shields that we can observe? In addition, the duration of the DCs seems similar, which is interesting because the spatial and temporal scales should also be linked or not?  I think it would be useful to discuss this point in more detail. 

1. 544: I think it would be helpful to remind the reader what the four key variables are in the figure caption? 

L. 546: If I understood it correctly, K-means clustering is used to produce the four classes in Fig. 13 and these classes are based on the multivariate coherence of the four metrics. It is, however, not explained in detail how the PDFs of each metric relate to the respective class (from random to organized). For instance, Fig. 13 a) shows quite distinct distributions for F between class 0 and 1 although these are the classes closer related to each other. I do not expect to go into the details of all possible combinations of the four metrics, but it would be decent to describe a little bit more how convective systems with substantially different distributions for F and P can still be more alike each other when they are similar in terms of L and S. 

The manuscript entitled “A method for characterizing the spatial organization of deep convective cores in deep convective systems’ cloud shield” presents a comprehensive methodology for analyzing the spatial organization of deep convective cores (DCCs) within Mesoscale Convective Systems (MCSs). Recognizing the limitations of existing organization indices when used in isolation, the authors propose a multidimensional approach based on four variables: (1) the convective fraction, (2) the total area of deep convective cores, (3) a characteristic length scale of aggregation among the cores, and (4) a metric quantifying deviation from a uniform spatial distribution.

A notable innovation of the study lies in the representation of DCCs as filled squares within the deep convective region, which enables the characterization of the spatial organization of the most elemental deep convective structures, although this identification relies on strong assumptions. Applying this framework to both observational and model datasets, the authors identify four distinct modes of DCC organization. They conclude by emphasizing the method’s effectiveness, robustness, and adaptability, and suggest several promising avenues for future application.

Overall, this manuscript is of good scientific quality and aligns well with the scope of Atmospheric Measurement Techniques (AMT). The scientific content is clearly presented and well written. However, I have a few minor comments that should be addressed prior to publication. My main concern pertains to the robustness of the proposed method, as the sensitivity analyses provided are, in my view, somewhat insufficient (see detailed comments below).

Detailed comments

Figures:

The labels are sometimes too small. Besides, adding letters to identify each panel could help.

L. 138-140:

There are some words missing in this sentence.

L188-197:

The motivation for using SAM with this configuration could be added.

L. 203: “73.9 W/m2”

It is not clear how this value was chosen.

L. 279-284: elementary convective structures

Could the authors clarify whether there is a physical justification for defining, for example, a 4×4 square as a single elementary convective structure rather than interpreting it as four 2×2 structures grouped together? In particular, how does this assumption impact the calculation of the spatial organization metric (variable P)? It would be helpful to discuss whether this structural definition influences the interpretability of P.

Additionally, would one expect such regularly shaped (e.g., circular or square) deep convective cores in environments with strong vertical wind shear? In such cases, convective elements may be elongated or tilted, which may not align with the chosen geometric representation. A short comment on the sensitivity of the method to these physical variations would be valuable.

Figure 4: “larger structures are associated with stronger and deeper convection”

It might be useful to mention that this relationship is consistent with observations. For instance, Moseley et al. (2019) show that larger convective cells tend to exhibit more intense precipitation.

Moseley, C., Haerter, J. O., Berg, P., & Hohenegger, C. (2019). A Statistical Model for Isolated Convective Precipitation Events. Journal of the Atmospheric Sciences, 76(10), 3049–3064. https://doi.org/10.1175/JAS-D-18-0337.1

L. 354 355: “characteristics of the scene”

Consider referring to the “Scene characterization” section below to precise the variables that are retained for it.

Figure 6:

“length” → “length”

Some text are in bold font or in italics without obvious reason to me.

Consider adding a yellow and an orange line for step 5 as these processes are also applied to the random grids.

L 367: Scene area

Could the authors clarify how the scene area is precisely defined in the analysis? From Figure 3, it does not appear to correspond to the minimal rectangular bounding box enclosing the cloud shield. Since the scene area directly affects both the computed convective fraction and the generation of the reference random distribution for the spatial organization metric (P), its definition is critical.

In particular, I am concerned about potential biases introduced by the shape of the cloud shield. For instance, in the case of an elongated DCS, the encompassing scene area may include large regions outside the actual cloud shield — areas that do not contain any DCCs. This could lead to an artificially low convective fraction and/or a misleadingly high organization score (e.g., P close to 1), depending if the DCS itself is densely populated with DCCs.

Conversely, for more rectangular DCSs, the scene area might better reflect the actual cloud shield, resulting in more representative values of these metrics.

The DCS shown in Figure 14d is a good example of the limitations of the current definition of convective fraction based on the rectangular scene area. Although this system appears to have a high proportion of convective precipitation pixels relative to stratiform ones (possibly >50%), its computed convective fraction is only 7%. In contrast, the DCS in Figure 14c has a visibly lower ratio of convective to stratiform pixels, yet its convective fraction is twice as high. This discrepancy appears to stem from differences in cloud shield shape — with case c being more rectangular and thus more tightly filling the bounding box used as the scene area.

This illustrates that the current definition of F is highly sensitive to cloud shield geometry, particularly for elongated or irregular systems, and may not reflect the true convective content of the DCS. I suggest that the authors more explicitly discuss this limitation and consider whether an alternative scene definition — e.g., based on the actual cloud shield contour, the area of precipitation, or a convex hull — might reduce this bias.

L. 394: “convex”

The use of a "convex" contour to define the central region of the autocorrelation field is somewhat unclear. In Figure 7, the contour shown does not appear strictly convex or minimal. Could the authors clarify how this contour is derived and to what extent its geometry affects the estimation of the typical aggregation distance?

I am concerned that applying a convex hull to potentially irregular or elongated shapes may artificially increase the value of L. Since L is defined as the maximum internal distance within the convex hull — rather than within the original (possibly non-convex) shape — the metric may become sensitive to shape distortions, particularly for highly anisotropic or fragmented patterns. This could introduce a systematic overestimation of L for some systems but not others, depending on the complexity of the spectral power field.

I suggest that the authors clarify how often such distortions occur in practice, and whether they have assessed the sensitivity of L to the convex hull approximation.

Fig. 7:

Consider representing the metric L on this figure.

L. 408: “anisotropy”

The mention of anisotropy feels somewhat out of place, given that it is not used in the method. That said, it raises an interesting point. One could imagine that a variable quantifying the anisotropy of the DCC distribution might complement the current set of metrics used to characterize spatial organization. While I understand the motivation to limit the number of variables for clarity and robustness, this example illustrates that additional descriptors could be considered in future work for a more refined or context-specific characterization of convective organization.

L. 415-416:“spatial morphology” vs. “condensed structural information”

I find the distinction between “spatial morphology of the raw field” and “condensed structural information captured” somewhat unclear. Could the authors clarify what is meant by this difference?

L. 420:

What is “C”?

L. 424, 427, 459, and elsewhere: Use of “probability” to describe P

In several places, P is referred to as the “probability of the scene being randomly organized” or “probability of deviation from a random distribution.” However, as I understand it, P is more precisely defined as the percentile rank of the scene’s characteristic length (L) within a reference distribution derived from randomly generated (uniform) DCC patterns. It does not represent a statistical probability in the formal sense.

For clarity and consistency, I suggest revising the terminology throughout the manuscript to reflect this. Referring to P as e.g. a percentile-based measure of deviation from randomness would more accurately describe its meaning and avoid potential confusion with probabilistic frameworks.

L. 431 and elsewhere: “bootstrapping”

As I understand it, the authors generate randomized spatial patterns of DCCs by redistributing a fixed number of DCCs uniformly within the scene. Since this process does not involve resampling from the observed data with replacement, it does not correspond to a formal “bootstrapping” procedure. Rather, it is more accurately described as a Monte Carlo approach for generating a reference distribution under spatial randomness.

I recommend updating the terminology accordingly to avoid confusion with statistical bootstrapping methods.

L. 443: “500”

I wonder whether 500 samples are sufficient to robustly estimate the distribution of L under the assumption of a uniform DCC distribution. While some sensitivity analysis is provided in the appendix, the figures are somewhat limited in really showing the accuracy or convergence of the Monte Carlo approximation in each case.

Since P is a percentile rank estimated from a finite sample, its uncertainty can be approximated as √(P(1–P)/n), which implies a standard error of about ±1–2% for n = 500. This level of uncertainty is likely acceptable for the broad classification presented in this manuscript. However, it may become problematic if users wish to compare two scenes with similar P values. I suggest the authors consider including a more detailed justification of this sample size or provide confidence bounds on P where relevant.

L. 447: “spatial organization” → “spatial aggregation”?

L. 465: “such a specific spatial arrangement (or its equivalent) almost never occurs in the randomly generated scenes”

This statement could be made more precise. A scene being rare under the assumption of randomness does not, in itself, indicate whether the spatial distribution is clustered or regular. Since the main goal is to assess clustering or aggregation of DCCs, I suggest rephrasing this to highlight that P captures deviation from randomness, and that high P values specifically indicate increased clustering, rather than rarity alone.

L. 472-473: “… the generation of the ensemble of scenes with a given convective fraction (F) is constrained by a few parameters of the stochastic model …”

I would like to point out that the scene area is also a critical parameter influencing the metrics (see my comment above on scene area).

L. 475-477: “sensitivity of F”

The current analysis of the sensitivity of the L distribution to the convective fraction F (Figure 10, B1, B2) is informative but could be presented in a more visual or intuitive way. For example, plotting histograms or kernel density estimates of L across several discrete values of F could help the reader more clearly understand how F shapes the reference distribution and, by extension, the behavior of P. This might be more accessible than the current presentation.

L. 484: “challenging to compute a meaningful probability”

The phrase “meaningful probability” is somewhat vague, and it’s not clear from Figure 10 what specifically supports this statement. If the issue is uncertainty in L and P for extreme values of F, it would strengthen the analysis to move beyond the empirical filtering approach (e.g., excluding scenes with F < 8% or F > 25%).

Instead, I suggest a more quantitative uncertainty-based filtering method. For instance, the authors could:

1. Estimate or infer the uncertainty in L,

2. Combine this with the Monte Carlo sampling error (as discussed above) to deduce a total uncertainty in P,

3. And exclude scenes for which the total uncertainty in P exceeds a given threshold (e.g., ±5%).

This would provide a clearer and more defensible basis for filtering scenes, and would strengthen the methodological transparency of the approach.

Figure 10, B1, B2:

Please indicate what the shaded area represents.

L. 499: “grid size” → “scene size”?

L. 518: “consistent with the unfiltered distribution”

Please indicate whether this is shown in the paper or not.

L. 534:

See comment for line 465.

L. 535: “distribution” → “distributions”

L. 549: “Empircal metrics … show”

The wording here is slightly misleading. The metrics are quantitative and not empirical in nature. It is rather the interpretation of these metrics that involves empirical reasoning or subjectivity.

L. 551: “Figure 12” → “Figure 13”?

L. 559: “more randomly distributed” → “less aggregated”

L. 562: “This indicates that F alone is not a discriminating variable …”

I do not find that the last two sentences indicate that F is not a discriminating variable (but maybe more the end of this sentence), please reformulate.

L. 563: “very unlikely to be randomly spatially distributed”

This could also be the case of regular patterns in the other end of the distribution. Please specify.

L. 564: “do not necessarily have high F values”

The statement that “highly organized scenes do not necessarily have high F values” is phrased as if it were surprising. If this is indeed counterintuitive or contrasts with previous assumptions, it would be helpful for the authors to provide citations or context to support why this is the case. Otherwise, I suggest rephrasing the sentence to avoid implying that this decoupling is unexpected.

L. 566: “(Figure 12)” →”(Figure 13)”?

L. 578: “Figure 11” → “Figure 13”?

L. 546-585:

I find it difficult to form a synthetic view of the organizational classes after reading this paragraph, as the presentation feels somewhat interwoven and comparative from the start. I suggest restructuring the paragraph to improve clarity: the authors could first systematically describe the main characteristics of each class individually, and only after that proceed to comparisons across classes. This would help readers better understand and differentiate the classes before being asked to contrast them.

L. 621-631:

I think it is also important and interesting that the authors compare their percentile-based organization metric (P) to the organization index Lorg introduced by Biagioli and Tompkins (2023). While Lorg is based on nearest-neighbor distances and does not require scene-level resampling, P is derived from the maximum spatial extent of the autocorrelation field and relies on Monte Carlo sampling.

It would be helpful if the authors could briefly discuss how these differing foundations may affect the quantification of the spatial aggregation of DCC and under what conditions one metric might outperform or complement the other.

L. 642: “However, the fact that ABCOP distinguishes the classes more effectively than ROME suggests that while organization is more influenced by the total convective area (S), it cannot be fully captured by this single variable or its combination with F”.

I may be misunderstanding the logic here, but the sentence seems to suggest that because ABCOP outperforms ROME, this implies that spatial organization cannot be fully captured by S combined with F. It would be helpful for the authors to clarify the reasoning behind it.

L. 657: “In this study, a new method is introduced”

This sentence would benefit from a clearer link to the utility or purpose of the method, as it currently appears disconnected from the previous discussion. I suggest rephrasing to briefly restate what the method is intended to achieve.

L. 663: “establishing a probabilistic distance from a random spatial organization”

Not really (see previous comments). Please also note that the Lorg index (Biagioli and Tomkins, 2023) is also a measure of the deviation from a random spatial organization.

L. 700:

Missing closing parenthesis.

Conclusion:

As I understand it, the TOOCAN algorithm defines Deep Convective Systems (DCSs) such that only one convective seed is permitted within each cloud shield. Given that deep convective cores (DCCs) typically coincide with the coldest cloud-top temperatures, this definition could influence the resulting spatial organization of DCCs within individual DCSs. In particular, constraining the number of convective seeds may limit the diversity of spatial arrangements that the method can capture.

While this does not undermine the value of the proposed approach, I suggest briefly discussing this methodological dependency in the conclusions—especially regarding the sensitivity of the characterization framework to the specific MCS tracking algorithm used.

L. 888-889: “a sensitivity analysis revealed that this non-uniqueness has no significant effect on the subsequent methodology”

Please indicate that this is not shown in this paper.

L. 905: “Figure B2” → “Figure B1”?

L. 909-912: “the most suitable”,”reasonable”

The use of terms like “most suitable” and “reasonable” in reference to scene selection feels vague, especially when based solely on empirical observation. As mentioned earlier, it would strengthen the methodological rigor of the study to define selection criteria based on a quantitative threshold — for instance, by estimating the uncertainty on P for each scene and excluding those with uncertainty above a predefined limit. This would provide a more transparent and reproducible basis for filtering.

L. 914: “We prove (not shown) that it would be interesting …”

Please reformulate.

L. 924: “histograms” Figure B1 and B2 do not show histograms (... although it would be helpful to see histograms here, see comment on L. 475–477).

Figures B1, B2: “Same as figure 9 ...” → “Same as figure 10”