# Scale-Dependence of Tropical Oceanic Deep Convective Systems' Cloud Shield Morphology to Environmental Conditions

Rémy Roca, Thomas Fiolleau, Louis Netz

► To cite this version:

Rémy Roca, Thomas Fiolleau, Louis Netz. Scale-Dependence of Tropical Oceanic Deep Convective Systems' Cloud Shield Morphology to Environmental Conditions. Journal of Geophysical Research: Atmospheres, 2025, 130 (9), pp.e2024JD042494. 10.1029/2024jd042494. hal-05294734

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# JGR Atmospheres

## RESEARCH ARTICLE

10.1029/2024JD042494

**Key Points:**

* Observational data set reveals robust scale dependence between deep convective cloud shield morphology and initial environmental conditions

* Scale dependence of the system's shield growth rate is strongly related to the wind shear over a deep tropospheric layer

* Scale dependence of the depth of the systems is also related to deep shear with additional contribution from precipitable water

**Supporting Information:**

Supporting Information may be found in the online version of this article.

**Correspondence to:**

R. Roca,
remy.roca@cnrs.fr

**Citation:**

Roca, R., Fiolleau, T., & Netz, L. (2025). Scale-dependence of tropical oceanic deep convective systems' cloud shield morphology to environmental conditions. *Journal of Geophysical Research: Atmospheres, 130*, e2024JD042494.
https://doi.org/10.1029/2024JD042494

Received 17 SEP 2024
Accepted 14 APR 2025

**Author Contributions:**

**Conceptualization:** Rémy Roca

**Data curation:** Thomas Fiolleau, Louis Netz

**Funding acquisition:** Rémy Roca

**Methodology:** Rémy Roca, Thomas Fiolleau, Louis Netz

**Project administration:** Rémy Roca

**Software:** Rémy Roca, Thomas Fiolleau, Louis Netz

**Visualization:** Rémy Roca

**Writing – original draft:** Rémy Roca

**Writing – review & editing:** Rémy Roca

<figure><img src="image_2.png" /></figure>

## Scale-Dependence of Tropical Oceanic Deep Convective Systems' Cloud Shield Morphology to Environmental Conditions

Rémy Roca¹ ID, Thomas Fiolleau¹ ID, and Louis Netz¹ ID

¹Laboratoire d'Etudes en Géophysique et Océanographie Spatiales (CNRS/CNES/IRD/UPS), Université de Toulouse, Toulouse, France

**Abstract** Deep convective systems are ubiquitous over the tropical oceans and are central to the Earth radiation budget due to their upper-level cloud shields. Possible evolution of the morphology of these cloud shields with climate change remain poorly understood. In this study, the sensitivity of the cloud shield to environmental conditions is therefore investigated using a large data set of atmospheric profiles from reanalysis and satellite observations. The initial environmental conditions in stability, thermodynamics, and dynamics are explored. Multilinear regression between morphology and environment is used in a 2D phase space linked to the life cycle of the systems, namely the time to reach the maximum area and the associated maximum area. Dynamical drivers show stronger morphological control than the thermodynamic factors. The result reveals an overwhelming role for wind shear over a deep tropospheric layer in explaining the scale dependence of cloud shield morphology. In particular, the variability of the shield growth rate is very well explained by deep layer shear ($R^2 > 0.8$). The depth of the systems is also strongly related to dynamics and secondly to water vapor loading. These results feed the debate on the relative role of deep- versus low-level shear in influencing deep convection and extend previous precipitation-centric considerations to the cloud shield of the systems. Possible underlying mechanisms are discussed, and the need to extend previous theoretical considerations on idealized convective geometry toward the whole spectrum of deep convective systems populating the tropical oceans is emphasized.

**Plain Language Summary** In the tropics, large decks of ice-topped convective cloud systems are frequently observed. These clouds play an important role in the climate-change energetics, yet how they will evolve and influence climate change remains a challenge. In this observational study, we analyze the sensitivity of these individual cloud systems to the atmospheric environment in which they develop as a prerequisite to better assess their role in climate change. Based on a very large data set of satellite measurements and atmospheric analysis, the results indicate dominating factors in the main characteristics of these cloud decks. The wind shear, the change of magnitude between the surface and an elevated layer at roughly 8 km in the atmosphere, is shown to strongly influence the morphology of the cloud shields. This study calls for a more elaborate theory than the existing one to clarify the response of the systems to climate change.

### 1. Introduction

In the tropics, deep convection does not occur only in isolation. A large fraction of tropical precipitation arises from deep convective systems (DCS) (e.g., Roca et al., 2014), which consist of deep convective cells organized in space and time. The associated upper-level cloud shield is composed of high-level ice-topped clouds forming a consistent object in space and time (Redelsperger, 1997) easily spotted on satellite imagery (Kidder & Vonder Haar, 1995). These clouds span a wide range of space and timescales from a few dozen to millions of square kilometers and can last from a few hours to multiple days (Houze, 2004). Due to their ubiquity over tropical oceans, these cloud shields have an important role in the Earth's radiation budget and in related climatic feedbacks (Bony et al., 2020). Anticipating the fate of these systems requires establishing how changes in the environment will eventually affect deep convection (Tomassini, 2021) and associated upper cloud decks. The evolution of these anvil cloud with global warming remains much discussed (Hartmann, 2016; Ito & Masunaga, 2022; Lindzen & Choi, 2021; McKim et al., 2023; Wing and Coauthors, 2020).

At first order, neglecting other potentially influential factors such as aerosol loading, deep convection over tropical ocean interacts with the environment through thermodynamics (instability and humidity), and dynamics

<footnote>© 2025. The Author(s).
This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.</footnote>
(vertical shear of the horizontal wind) (e.g., Galarneau et al., 2023). However, the environment-deep convection relationship is an ill-posed problem owing to the ambiguity of the activation versus control paradigms (Mapes, 1997). In fact, the environment can influence both the occurrence and intensity of deep convection. The first question can be folded, under the “ingredients-based” approach, for which the favorable environment for deep convection is elaborated and aims mainly to establish the sensitivity of the *occurrence of DCS* to the change in the environment. The latter question, the environmental control view, aims at elucidating the sensitivity of an *intensity* metric of DCS to change of the environment. A similar dichotomy exists for the hurricane-climate change question, where the occurrence of hurricanes still lacks a theory (Sobel et al., 2021) whereas the hurricane intensity appears to increase with global warming in observations, as per theoretical expectation (Emanuel, 2020). Here, we explore the second aspect of the problem and restrict ourselves to the nonhurricane DCS over tropical ocean.

The typical life cycle of DCS cloud shield exhibits a simple growth and decay pattern (Roca et al., 2017 and references therein). The precipitation structure of the cloud shield is slightly more complicated with an early phase where convective precipitation dominates followed by the lagged growth of the stratiform precipitation and of the nonprecipitating part of the shield. When the convective precipitation vanishes, the whole cloud shield starts shrinking, and the nonprecipitating fraction of the cloud increases before the system dissipates (Elsaesser et al., 2022; Houze, 2004). This recalls the nontrivial relationship between the precipitation features and the cloud shield of convective systems. Many previous investigations focused on precipitation characteristics, for instance, convective precipitation intensity (Bretherton et al., 2004; Schiro et al., 2020a, 2020b; Abramian et al., 2023; Mulholland et al., 2021a; Maybee et al., 2024 submitted) or lighting activity (Bang & Zipser, 2019; Stolz et al., 2017). Most were restricted to the longest and largest systems, the mesoscale convective systems (MCS) (e.g., X. Chen et al., 2023; Galarneau et al., 2023). Here, we opt to (a) focus on the less understood cloud shield morphological intensity metrics (duration, area, growth rate, eccentricity, depth, and propagation speed) and (b) consider the full spectrum of DCS not only MCS. Morphology characteristics are often strongly correlated together, such as duration and maximum area, assuming that the sustainability concept is at work (Houze, 2004). However, the large geographic variability observed in the duration-size relationship in the DCS spectrum of the tropical oceanic is not compatible with this interpretation (Roca et al., 2017). Indeed, maximum extent for a given duration can vary by up to two-to-three orders of magnitude (Fiolleau & Roca, 2024). Moreover, field campaigns analysis indeed tends to suggest that although shear influences the spatial organization of convection, thermodynamics influences the convection depth and longevity of the systems (LeMone et al., 1998). This led us to explore environmental thermodynamics and dynamics sensitivity on both the duration and spatial area scales and to attempt to reconcile space and time with the addition of the growth rate as a key morphological parameter of the system cloud shield.

The mesoscale nature of organized deep convection adds to the complexity of its sensitivity to the environment, sometimes yielding seemingly contradictory results. For instance, a dry midtroposphere can be detrimental to isolated deep convection, following entrainment arguments under the parcel model (e.g., Sherwood & Wahlich, 1999). On the other hand, it is a key element for the longevity of already triggered squall lines with a rear-to-front inflow structure (Redelsperger & Lafore, 1988; Roca et al., 2005). The morphology of MCSs from the Maritime continent and, in particular, the lifetime of MCSs exhibit no discernible sensitivity to either its dynamical or thermodynamic environment in the case of realistic high-resolution simulations (Hagos et al., 2013a). Satellite observations show that only a weakly explained variance in MCS duration by the environment on tropical continents (Chakraborty et al., 2016) and that the morphology of the systems overall exhibits weak sensitivity to CAPE (Igel & Heever, 2015). However, recent analysis emphasizes the role of low-level moisture in controlling MCS area (X. Chen et al., 2023) consistent with precipitation characteristic size sensitivity to low-level humidity (B. Chen et al., 2017). The influence of the wind shear and its location in the vertical, either in the low levels or over a deep atmospheric layer, has also received a lot of attention and is still much debated (Mulholland et al., 2021a; Weisman & Rotunno, 2004). The width of mature oceanic MCS anvils seems to increase with low-level shear (Igel & Heever, 2015) and so does the size of precipitation features (Bang & Zipser, 2016). According to Chen et al. (2023), nevertheless both MCS lifetime and maximum area do not correlate with deep layer shear. Using radiative-convective equilibrium (RCE) high-resolution simulations, Robe and Emanuel (2001) investigated the sensitivity of convective organization and intensity to vertical shear. They showed that adding upper-level shear to optimal low-level shear can intensify the updrafts and possibly the precipitating area when the proper relative angles between the layers is considered; that is, when deep shear is
maximized. More recently, still under idealized setting for tropical oceanic deep convection, that is, RCE but including a coupling with the circulation, Anber et al. (2016) showed that in their deep shear case, a larger anvil cloud fraction is produced than in the low-level shear case.

These apparent inconsistencies led us to use a large data set of 9 years over the entire tropical ocean of satellite observations of the DCS cloud shield and the recent European Center for Medium range Weather Forecast reanalysis to build robust statistics of the morphology-environment relationship. We show that CAPE and humidity play less of a role than shear in explaining the variability of the morphological characteristics of the DCS and that shear over a deep layer (0–8 km), followed by very low-level shear (0–1 km), are strong controlling factors of the morphology of the system shield. For that purpose, the sensitivity of the cloud shield morphology, across the time and space scale, to both its thermodynamics and dynamics environment is revisited. In the latter case, all shear layers from 0-1to 0–8 km by steps of 1 km are explored to attempt to clarify the role of the layer depth. In Section 2, satellite observations of tropical ocean DCS are introduced and their salient features are discussed. Atmospheric analysis along with the rationale for computing environmental conditions for a reduced set of environmental variables is also presented. The results are presented in Section 3 and discussed in Section 4. A conclusion section ends the paper.

## 2. Data

### 2.1. Deep Convective Systems

#### 2.1.1. The TOOCAN Data Set

The morphology of the DCS is obtained thanks to the TOOCAN algorithm (Fiolleau & Roca, 2013a) that has been applied to a homogenized archive of geostationary infrared observations spanning the period 2012–2020 and covering the intertropical belt (Fiolleau et al., 2020). Data for 25 S–25 N are used here and only systems initiated and terminated over ocean are selected. The TOOCAN algorithm processes time series of infrared images using a multistep multithreshold protocol. It first detects the coldest part of the cloud cluster and grows these initial regions with classic image processing operators (dilatation, erosion) using the 10-connectivity operator (8 in space and 2 in time dimensions). Constraints on the spatial gradient of brightness temperature (BT) are further imposed in this growing step. This is repeated until the 235K threshold is reached. The latter threshold is commonly used as a limit for the edge of anvil cloudiness and was recently confirmed for tropical systems using active sensors (Bouniol et al., 2016). The TOOCAN method permits fixing the split/merge artifacts that can plague some alternative tracking approaches (Prein and Coauthors, 2024). The result consists in a suite of DCS or objects for which a number of characteristics are computed such as the duration, the maximum area of the cloud shield during its lifecycle ($S_{max}$), the eccentricity of the shield, the BT of 10% of the coldest pixels of the cloud shield, and a proxy for the system depth (Roca & Ramanathan, 2000). The mean growth rate during the growth phase (Roca et al., 2017) is calculated as the maximum area divided by the time it takes to reach it, assuming the initial shield area is zero. Using the actual area does not change significantly the computation given the ability of the TOOCAN algorithm to track back to very small initial shields (Fiolleau & Roca, 2013a). The mean propagation speed of the system is also estimated by dividing the overall propagation distance from initiation to dissipation by the duration. The TOOCAN data have been extensively used for various scientific investigations (Djakouré et al., 2024; Elsaesser et al., 2022; Roca et al., 2017). Hurricane affected convective systems are filtered out of our statistics by removing systems that are closer than 250 km from a tropical cyclone based on IbTRacs data (Knapp et al., 2010) that has been collocated with TOOCAN in the most recent version of the product (Fiolleau & Roca, 2024).

#### 2.1.2. The DCS Over the Tropical Ocean

Following earlier classification effort, only the cloud systems lasting more than 5h and exhibiting a well-defined life cycle are considered here (class 2 of Roca et al., 2017). We further filtered out systems with propagation speeds greater than 20 m/s to insure that the remaining objects are indeed tropical convective systems and not frontal or jet related cloud structures or extratropical systems entering the area (Feng and Coauthors, 2021). We also restrict our analysis to the systems for which the BT of the 10% of the coldest pixels at maximum area are colder than 210K (Roca et al., 2002) to focus only on the very DCS. Over the period and considering ocean over the 25°S–25°N belt, more than 685388 DCS have been identified. Figure 1 shows how these systems are distributed in terms of time to reach maximum area ($h$) and maximum area ($km^2$) in a phase space diagram. The
<figure><img src="image_3.png" /><figcaption>**Figure 1.** Phase space distribution of the (a) deep convective systems (DCS) and (b) the fraction of the latter that fit the mesoscale convective systems definition. Only area with at least 10 DCS is shown and a 2 × 2 smoothing operator is applied. Horizontal dotted lines are plotted at 500 and 50,000 km2. Vertical dotted lines at 6, 12, and 18 hr.</figcaption></figure>

DCS are mostly found in the range up to 10 hr and 5,000–50000 km² but spans a wide range of space and time scales. Figure 1b shows the fraction of the DCS that can be labeled as MCS using the cloud shield based MCS definition (Feng et al., 2012; Galarneau et al., 2023; Jirak et al., 2003). The corresponding 23716 MCS are mainly distributed in the upper right part of the phase space where most of the DCS indeed qualify as MCS.

Figure 1 further indicates that for a given duration, area of DCS can vary up to 2–3 orders of magnitude. Conversely, for a given maximum area, time to maximum can vary for 1 hr up to 20 hr. This variance is encapsulated in the computation of the systems growth rate defined as the maximum area divided by the time it took to reach it and is conveniently estimated in km² min⁻¹. Figure 2a shows the mean growth rate in the phase space diagram. The growth rate is strongly influenced by the maximum area. For the larger and longer to grow systems, corresponding to the MCS category, the growth rate dependency on time is becoming smaller. The other morphological parameters are summarized in Figures 2b–2d. On average, the eccentricity is larger than 0.5 indicating circular shaped cloud shield and exhibits not much variance. The short-grown systems have the minimum value of eccentricity whereas the longest grows are more circular. The 90th percentile of the coldest BT gets cooler with both increasing area and time, the MCS being the deepest systems of the DCS. Finally, the propagation speed of the systems exhibits strong sensitivity to maximum areas and only a weak to no dependency of speed to time to S_max for a given area range.

## 2.2. Environment

### 2.2.1. Rationale for the Definition of Environment

#### 2.2.1.1. Meso-Alpha Environment From ERA-5

It can be convenient to discriminate between the environment on the meso-alpha scale (>200 km; >6 hr) and the near environment of deep convection (immediate environment or even underneath convective cells) the meso-gamma scale (2–20 km; <30 min). Indeed, such separation, if not the only possible one, can help focus of the processes and the variables expected to be at play in these contrasted environments (Minamide & Posselt, 2022). Although field campaigns provide useful near-environment data sources (Alexander & Young, 1992; Rodenkirch & Rowe, 2024), sampling remains limited and one cannot rule out that regional dependence might limit the applicability to the diversity of situations and systems encountered over the tropics. Although it is tempting to look at hourly ERA-5 data at full 0.25° resolution (Hersbach & Co-authors, 2020) to explore the near environment of deep convection over the tropical oceans, it would require ERA-5 to well represent the timing and the location of the DCS and their evolution there where fewer observations are assimilated compared to land-based data rich area, which is not yet in reach (Chan et al., 2022; B. Chen et al., 2017). Regional high-resolution reanalysis would be a useful alternative (Coniglio et al., 2010) but are not yet readily available over the tropical ocean. Promising quasitropical efforts are only emerging and are, for now, very limited in time span (Chan et al., 2022). On the other hand, using ERA-5 to characterize the “far” environment of DCS (the meso-alpha scale), both dynamically and thermodynamically, seems to be to be better suited and has been successfully carried out by many studies (Liu et al., 2022; Chen et al., 2017, 2023; Stolz et al., 2017). One argument in favor of its use also lies in the Sea Surface Temperature being used in the reanalysis that filter out high frequency variance (<3 days, <150 km) and may contribute to enhance the analysis relevance at these scales in assimilated data-scarce areas such as the tropical ocean (e.g., De Meyer & Roca, 2021).

Instability can be diagnosed thanks to various more or less elaborated CAPE computations (Alfaro, 2017; Groenemeijer et al., 2019; Schiro et al., 2018) to account for thermodynamics details or for the depth of layer actually providing instable air to the organized deep convective system. However, Most Unstable Convective Available Potential Energy is readily available from the reanalysis and will be used here pragmatically in place of more complicated instability index computations. In the near environment, low-level humidity sets the level of
<figure><img src="image_4.png" /><figcaption>**Figure 2.** The DCS morphological parameters in the phase space. (a) Growth rate (b) 90th Percentile of brightness temperature (c) Eccentricity at time of maximum area and (d) mean propagation speed. Only area with at least 10 DCS is shown and a 2 × 2 smoothing operator is applied. Horizontal dotted lines are plotted at 500 and 50,000 km2. Vertical dotted lines at 6, 12, and 18 hr.</figcaption></figure>

condensation and influences the width of the convective cores and the depth of deep convection (Mulholland et al., 2021b; Takahashi et al., 2023), but at the meso-alpha scale, the full vertical distribution of relative humidity in the free troposphere is also to be accounted for (Del Genio et al., 2012; Lafore & Coauthors, 2016; Roca et al., 2005). Recent investigation underscores the importance of vertically integrated moisture flux convergence in complement to midlevel relative humidity and total column water vapor (TCWV) in driving MCS occurrence over global land regions (Muetzelfeldt et al., 2025) The details of the humidity profiles near convection remain hard to reach (Stevens et al., 2017) and here the effect of humidity on deep convection is primarily estimated, in bulk, using TCWV content or precipitable water, a moisture measure successfully replicated in reanalysis (Schröder et al., 2016).

In the near environment of deep convection, mechanical forcing of convection, for instance via cold pool collision and associated enhanced low-level vertical velocity, is thought of as a dynamical process of importance to trigger deep convection over tropical ocean (Feng et al., 2015). Lemone et al. (1998) nevertheless recall that in the tropics self-organization of deep convection happens without mesoscale-alpha dynamical forcing unlike in midlatitudes where frontal structures with vertical velocity are often invoked to organize deep convection into systems so that for our meso-alpha analysis vertical velocity is not used to characterize the dynamical environment notwithstanding the difficulty for reanalysis to diagnose such parameters. Instead, we focus on the magnitude of the shear of the horizontal wind between a given level and surface. In complement to the shallow shear, rooted in the Rotunno-Klemp-Weisman (RKW) theory (Rotunno et al., 1988), deep layer shear appears as a more prevalent feature for instance with the African Easterly Jet in West Africa (Redelsperger et al., 2002) or the midtropospheric wave trough in the central plains of the US (Yang et al., 2017). The shear is thus computed on roughly every kilometer considering all layers from 900 hPa to 400 hPa per 100 hPa steps.
In summary, here, we focus on the far or meso-alpha environment of deep convection using daily 3° × 3° degrees average from ERA-5 using CAPE, shear (SHEAR) and TCWV to explore the sensitivity of both the occurrence and the intensity of DCS to instability, dynamics, and thermodynamics, respectively. A limited subset of 3 parameters is used, out of the large array of possible candidate parameters mentioned in the above references in order to ease the statistical analysis and to focus on representative variables of the three well-established ingredients for tropical convection. In addition to these 3 key parameters, relative humidity at 700 hPa, specific humidity at 800 hPa, and convective inhibition are also diagnosed as important secondary environmental factors.

### 2.2.1.2. Same Day Environment

The environment variables are computed on the daily 3° × 3° degree scale centered on the genesis location of the DCS of the genesis day ("same day environment"). It is assumed that in the course of the DCS subsequent evolution, the system evolution will happen faster than changes in this meso-alpha environment. As a result, our baseline computations are the daily average of the day from the start time. The correlation analysis indicates some imprints on the MCS environment up to 24 hr before initiation (X. Chen et al., 2023; Galarneau et al., 2023). Recall that the environment affects the properties of the cloud shield through its interaction with deep convection that is mainly active in the first half of the life of the system (Elsaesser et al., 2022; Fiolleau & Roca, 2013b), so the effect is likely to be felt even for the longest-lasting systems, even though the longest-lived systems are more likely to be influenced not only by initial but also by boundary conditions as well (Coniglio et al., 2010). The sensitivity of this definition and the memory effect of the initial conditions is further characterized by exploring the impact of a lag at 1 and 2 days on the results (Section 4).

## 3. Results

### 3.1. Averaged Statistics

The averaged distributions for CAPE, TCWV, and SHEAR, which help to identify the dependency of one to the other, are shown in Figure 3.

CAPE decreases with time to $S_{max}$ up to 8 hr, after which it remains almost constant, showing only slight variation with $S_{max}$. However, when considering the combination of these two factors through the growth rate, CAPE steadily increases as the growth rate increases. On average, the small variability in TCWV (<4%) becomes even more apparent, revealing no significant sensitivity to time to maximum, maximum extent, or growth rate. Wind shear across any layer is independent of the time to maximum shows a slight increase with $S_{max}$. For the deepest layer (400 hPa-surface), the relationship is characterized by an increase with growth rate from 5 to 9 m/s across the growth rate observed range.

### 3.2. Distribution of Thermodynamics and Dynamics Environmental Variables

The distribution of the variables in the phase space allows to characterize their scale dependence. CAPE varies significantly across scales (Figure 4a). Overall, CAPE increases with maximum area and decreases with the time to $S_{max}$. Systems growing in more than 6h show less sensitivity of CAPE to time, and its variability is driven primarily by maximum area. These two regimes highlight the limitations of the sustainability concept. In particular, the weakly sensitive regime suggests that a similarly unstable environment can support DCS events that vary widely in duration or time to reach their maximum area. However, for a given duration, a higher CAPE corresponds to a larger maximum area. Similarly, CIN increases with maximum area and decreases with time to maximum, though this trend is consistent across all scales of interest (Figure 4b).

Water vapor, whether in terms of TCWV (Figure 4c) or specific humidity at 800 hPa (Figure 4d), is generally high and shows little variability across the spectrum (less than 5 mm or less than 1 g/kg). It peaks for the MCS portion of the phase space. This lack of significant scale dependence for environmental water vapor along with its narrow range suggests that water vapor loading is not a key driver of DCS morphology but rather a necessary condition for DCS formation, aligning with the threshold perspective on tropical convection (Bretherton et al., 2004). This minimal impact on DCS morphological characteristics contrasts sharply with precipitation-based metrics (Schiro et al., 2020a, 2020b) but is consistent with previous analysis (Hagos et al., 2013b).

The distribution of wind shear in the phase space is illustrated in Figure 5. The deepest layer (400 hPa to the surface) demonstrates sensitivity to both the time to maximum and the maximum extent across all scales with
<figure><img src="image_5.png" /><figcaption>**Figure 3.** The averaged statistics for CAPE (left), total column water vapor (TCWV) (middle) and SHEAR (right). As a function of Time to maximum area (top), maximum area (middle), and growth rate (bottom). For shear, the various layers have an individual color. Black: 400 hPa-surface; Green 500 hPa Blue 600 hPa, Purple 700 hPa Orange 800 hPa, and Yellow 900 hPa.</figcaption></figure>

values ranging from approximately 4 to 10 m/s. This gradient remains noticeable when considering the 500 hPa to surface layer but diminishes as the layer is confined to the lower atmospheric levels. However, the lowest levels still exhibit a significant gradient though over a smaller range of magnitude. The covariability of these environmental distributions and that of the DCS morphological properties is investigated in the next two sections.

### 3.3. Scale-Resolved Statistics

The covariability between these environmental distributions and the DCS morphological properties is quantitatively assessed using linear correlation analysis of the 250 nonzero values available in the phase space. Results are summarized in Table 1. A more detailed version of this table is available in the Table S1 in Supporting Information S1. Given the similarity in the 400 and 500 hPa correlations (Table S1 in Supporting Information S1), the former is kept in the analysis as a representative of deep shear. The low-level shear is well characterized by the 900 hPa layer. Variability in growth rate across scales shows a strong correlation with shear in both the deepest and the lowest layers. Thermodynamic correlations are weaker with CAPE being more correlated than TCWV. The 90th percentile of cluster BT exhibits similar sensitivities, although CAPE appears uncorrelated with the depth of the convective system. Eccentricity shows weak correlations with all environmental variables and is notably uncorrelated with shear. However, a strong positive correlation is observed with specific humidity at 800 hPa (Table S1 in Supporting Information S1). The propagation speed is weakly correlated with all variables with no notable connections emerging.
<figure><img src="image_6.png" /><figcaption>**Figure 4.** Distribution of the mean environment in the phase space. (a) CAPE (b) CIN (c) TCWV and (d) q at 800 hPa. Only area with at least 10 DCS is shown and a 2 × 2 smoothing operator is applied. Horizontal dotted lines are plotted at 500 and 50,000 km2. Vertical dotted lines at 6, 12, and 18 hr.</figcaption></figure>

A simple multiple linear regression approach is employed to determine the relative contribution of each envi-
ronmental variable in explaining the variability of morphological characteristics across the phase space (e.g.,
Stolz et al., 2017 and references therein). A forward selection method is used to build explanatory models by
sequentially adding the most correlated individual variables to the regression (e.g., Vera et al., 2024). The
resulting correlation serves as an indicator of the relative importance of each variable. Based on the results from
the previous section, the models are constructed with a limited set of predictors: TCWV, CAPE, deep shear (400–
1,000 hPa), and low shear (900–1,000 hPa). The results are summarized in Table 2.

The variability in growth rate is well captured by the multipredictor model with an R² value greater than 0.85. This strong correlation is primarily attributed to the deep shear variable, as adding low shear to the regression only marginally improves the R². The system depth, estimated using the 90th percentile BT proxy, is also well represented by the model with deep shear and TCWV being the main contributors. However, eccentricity and speed are not reproduced as accurately by the regression, suggesting a less direct relationship with the environment as described by the selected predictors. The fact that adding low-level shear to the predictor set hardly changes the overall performance of the regressions does not necessarily suggest that low-level shear has no influence on DCS morphology. Instead, it emphasizes the strong correlation between low- and deep-shear variabilities across scales (R² = 0.67).

**3.4. Sensitivity to the Lag**

The “memory” effect of initial conditions is examined by introducing lag in the computations. At a 1-day lag, the variability in growth rate is still well characterized by the first two predictors, achieving an R² of 0.77 (Table S2 in Supporting Information S1). When the lag is extended to 2 days, the 4-predictor model continues to perform well with an R² of 0.75 (Table S3 in Supporting Information S1). However, for other morphological characteristics, the statistical fit decreases strongly for lags of 1 day or more compared to the baseline of 0-day lag.
<figure><img src="image_7.png" /><figcaption>**Figure 5.** Distribution of the mean environment in the phase space. Shear between surface and 400 hPa (a) 500 hPa (b) 600 hPa (c) 700 hPa (d) 800 hPa (e) 900 hPa (f). Only area with at least 10 DCS is shown and a 2 × 2 smoothing operator is applied. Horizontal dotted lines are plotted at 500 and 50,000 km2. Vertical dotted lines at 6, 12, and 18 hr.</figcaption></figure>

**4. Discussion**

The analysis reveals a number of features. First, eccentricity and propagation speed are only weakly related to the system's environment as described by the limited set of predictors used here. The eccentricity of the cloud shield is
<table><caption>**Table 1**
The Pearson Correlation Coefficient (R²) Between Morphological Parameters (Lines) and a Subset of Key Environmental Variable (Column)</caption><thead><tr><th>Lag = 0 days</th><th>CAPE</th><th>TCWV</th><th>Shear 400 hPa</th><th>Shear 900 hPa</th></tr></thead><tbody><tr><td>Growth rate</td><td>0.32</td><td>0.22</td><td>0.82</td><td>0.71</td></tr><tr><td>90th BT</td><td>0.06</td><td>0.53</td><td>0.65</td><td>0.34</td></tr><tr><td>Eccentricity</td><td>0.22</td><td>0.23</td><td>0.00</td><td>0.06</td></tr><tr><td>Speed</td><td>0.07</td><td>0.13</td><td>0.33</td><td>0.22</td></tr></tbody></table>

mainly circular ($e > 0.7$) but never strongly linear in agreement with previous classification efforts (Jirak et al., 2003). The orientation of the upper wind field with the cloud shield could provide more information on these morphological variables. Similarly, propagation environmental control should be further assessed using orientated steering level identification and is left for future work. The analysis also reveals the lack of a simple relationship between time to maximum (or duration) and the system initial environment especially for the longest-lived systems. This can be attributed to the limited influence of initial conditions on long-lasting systems for which boundary conditions are important too (Coniglio et al., 2010). This confirms and provides context for the previously very weak correlation between MCS morphology and initial environmental conditions (Hagos et al., 2013b).

The maximum shield area expresses slightly more sensitivity, but it is the growth rate that encapsulates both size and duration that revealed a strong correlation to its environment. The growth rate distribution in the phase space shows regular gradients indicating similar physics for rapidly growing small systems to that for slow to grow larger systems. The dependence of the system growth rate scale is very well explained by the variabilities of the horizontal wind shear over a deep layer (400 hPa-surface) with $R^2$ greater than 0.8. The depth of the system is also well explained by the variabilities of the horizontal wind shear over a deep layer (400 hPa-surface) and of TCWV mainly. The deeper systems show larger shear and moister conditions. In contrast with previous analysis, our result favors control by dynamical environment rather than by stability or moisture. This situation can be explained due to two main reasons. First, here the entire spectrum of DCS is considered and second, the focus is on the cloud shield morphology of the system not on the morphology and intensity metrics of precipitation features.

Many previous studies have focused primarily on MCSs rather than considering the entire spectrum of DCSs (DCS). When we replicated our analysis focusing solely on MCSs, defined here by their cloud shield signature, the results presented in Tables S1 and S2 in Supporting Information S1 showed significantly weaker correlation coefficients between initial environmental conditions and MCS shield morphology (Tables S4 and S5 in Supporting Information S1). This aligns with previous findings that reported a very weak relationship between the MCS properties and their environment (X. Chen et al., 2023; Igel & Heever, 2015). We attribute this to the limited number of DCSs that fit the MCS definition, which restricts the environmental diversity required to reveal potential relationships. This highlights the importance of population selection in such statistical analysis. Additionally, within this regime of weak correlations, although deep shear remains the dominant factor, the influence of various predictors on the morphology of the MCS becomes more balanced compared to that for the full spectrum of DCSs. For DCSs, dynamical drivers are shown to be more critical, whereas for MCSs, low-level humidity accounts for slightly more variance in scale dependence than low-level shear only (Table S2 in Supporting Information S1) as also found by Chen et al. (2023).

As mentioned in the Introduction, the life cycle of the system connects its precipitation features to the shield morphology. By accounting for such a life cycle in the present study, we have clarified the drivers of the cloud shield. Precipitation-related metrics, either morphology or intensity, have been shown to relate more to the thermodynamics (buoyancy, water vapor) than to dynamical factors (e.g., Feng et al., 2025; Schiro et al., 2020a; Schiro et al., 2020b). A number of investigations on the MCS is using the AMS definition of MCS that includes a threshold in precipitation area and intensity as discussed by Houze (2004). By linking the definition of MCS to precipitation feature morphology, the analysis tends to emphasize environmental controls driven by thermodynamics rather than dynamics, which helps explain the differences in relative environmental contributions between DCS and MCS.

At this stage, we can only speculate on the underlying mechanisms and processes that could be supported by our observations. Focusing on squall line geometry, Coniglio et al. (2006, C06 hereafter) suggested a process by which enhanced lifting is associated with deep shear (compared to the case without deep shear case). C06 shows that in their simulations an overturning circulation caused by shear over the deep layer and the lower level cold pool, further raises the air parcels from ~2 km to above, enhancing the parcel lifting in contrast to no deep shear case for which the elevating parcel are deflected to the rear of the cold pool and reach lower depth of the troposphere. C06 also suggests that this overturning has consequence on the size of the system thanks to two contemporaneous mechanisms: the associated slowing down the cold pool propagation and by augmented
<table><caption>**Table 2**
The Multilinear Pearson Correlation Coefficient (R²) Between Morphological Parameters (Lines) and a Combination of Multiple Environmental Variable (Column)</caption><thead><tr><th>Lag = 0 day</th><th>2 predictors</th><th>3 predictors</th><th>4 predictors</th></tr></thead><tbody><tr><td>Growth rate</td><td>0.85</td><td>0.85</td><td>0.86</td></tr><tr><td>90th BT</td><td>0.80</td><td>0.80</td><td>0.83</td></tr><tr><td>Eccentricity</td><td>0.62</td><td>0.64</td><td>0.64</td></tr><tr><td>Speed</td><td>0.33</td><td>0.34</td><td>0.34</td></tr></tbody></table>

likelihood of convective initiation along the flanks of the cold pool. Our results show that the depth of the deep convection is also influenced by the deep shear and would further support the deepening process of C06. C06 contrasts the spatial distribution and intensity of convection from various simulations at after the same elapsed time, indicating that their conclusions about the precipitating area are indeed worth for growth rate as well. As shown by Elsaesser et al. (2022) following a simple detrainment perspective, the DCS shield growth rate can be written as

$$ \frac{dA}{dt} = \frac{dA_c}{dt} - \frac{1}{\rho} \frac{dM}{dz} - \frac{A}{\tau} $$

where A is the DCS cloud shield area, $A_c$ the area of deep convection, M is the mass flux, respectively, and $\tau$ is a removal timescale; z is the altitude. When assessed with satellite observations, such a form function is shown to fit a wide range of tropical DCS and performs equally well over the full size and duration spectrum of the DCS (Elsaesser et al., 2022). The observed sensitivity of the growth rate to deep shear through convective area production, detrainment, and removal rates is consistent with the C06 model. However, the relevance of such geometry and model for the entire tropical DCS is difficult to assess. Houze (2004) argues that the squall line conceptual model is fit for understanding other geometry insofar a cold pool and a mesoscale circulation are present in the system. Several convective features over the tropical ocean indeed show linear organization (Bang & Zipser, 2016; Liu & Zipser, 2013). These factors form a strong incentive to analyze this in more detail in future work.

## 5. Conclusion

The cloud shields of tropical DCS are an important element of the Earth radiation budget. However, their role in climate feedbacks remains poorly understood. A carefully curated satellite database of convective systems is therefore utilized along with ERA-5 data to investigate the scale dependence of the cloud shield morphological properties of the convective system and its relationship to the meso-beta scale thermodynamic and dynamic environment. The analysis covers a wide spectrum of DCS size and duration and is not restricted to MCS. A phase space is used to document the morphological and environmental scale dependences. The analysis is based on a large number of DCS over the tropical ocean and thus provides statistically sound results. In this work, we focus on the pathways through which the thermodynamic and dynamic environment of the system influence their morphology. Our study extends previous works by considering the entire spectrum of the DCS and not only the MCS and by specifically addressing the cloud aspect of the convective systems and not only the underlying precipitation features morphology. A discussion on the consequence of using considering MCS versus DCS permits one to reconcile our findings with previous works.

The main result highlights the important role of the wind shear over a deep tropospheric layer as a key driver of the cloud shield's morphology over a wide spectrum of convective systems. The role of shear in the influence of the duration, extent, and intensity of convective systems, particularly deep layer shear versus low-level shear, remains a topic of much debate. Our observational study offers a fresh perspective on this issue specifically for DCS over tropical oceans, highlighting the strong correlation between deep shear magnitude and the growth rate of the DCS cloud shield. C06 proposed a mechanism that could relate the morphology of the systems to the deep layer wind shear, yet, in the case of an idealized, midlatitude, intense, and linearly organized system. The relevance of such a mechanism for the spectrum of DCS discussed here remains to be assessed. Our results suggest that in complement to thermodynamics, deep shear could be a useful diagnostic to help characterize the recently revealed morphological biases in km-scale climate simulations (Feng et al., 2025; Prein and Coauthors, 2024).

One limitation of the present investigation lies in the use of ERA-5 reanalysis, which prevents a closer inspection of the near environment of the DCS initiation and evolution. Using a long span of high-resolution reanalysis (Chan et al., 2022) when available would be a straightforward way to complete and enhance the present study. Similarly, the use of precomputed CIN for instance does not allow the sensitivity of the reported scale dependence to the formulation of CIN to be readily assessed and requires further investigations. Also, it would be interesting
Acknowledgments

We thank S. Cloché for her support with the handling of these various data sets. This study benefited from the IPSL mesocenter ESPRI facility, which is supported by CNRS, UPMC, Labex L-IPSL, CNES, and Ecole Polytechnique. The authors acknowledge the CNES and CNRS support under the Megha-Tropiques program. The authors are grateful for insightful comments from the reviewers that improved the clarity of the paper.

to explore our phase-space approach at more regional scale to assess their relevance for specific regional features (e.g., Mejía et al., 2021).

Data Availability Statement

The TOOCAN data are available from http://toocan.ipsl.fr with the DOI https://doi.org/10.14768/1be7fd53-8b81-416e-90d5-002b36b30cf8. ERA-5 data set can be accessed through Copernicus Climate Data Store https://cds-beta.climate.copernicus.eu/.

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