A ternary diagram is a triangular graph used to visualize the proportions of three components in a mixture, where each corner of the triangle represents 100 % of one component and any point inside represents the relative contributions of all three, which must sum to 100 %. In this study, the three components are the percentages of cloudy pixels in three τc classes: thin (τc<7), intermediate (7≤τc<12), and thick (τc≥12). The partitioning of τc among the three components was done by counting the pixels in each 2°×2° scene whose retrieved τc falls into each of the three classes, then normalizing by the total number of pixels with a valid τc in the entire scene. Each scene can therefore be represented as a single point in the ternary diagram corresponding to a unique fractional composition of τc, which exhibits a unique morphology (see examples in Fig. ).

The ternary space was discretized into evenly sized bins, each representing a unique τc morphology. 2°×2° scenes were assigned to a corresponding morphology bin within the ternary space, and microphysical statistical properties were computed for each bin. Bins containing fewer than 25 scenes were excluded from the analysis and are shown as NaN.

The τc class thresholds are defined on physical grounds, based on fundamental radiative transfer considerations: at τc≈7, Ac transitions from an approximately linear to a more logarithmic dependence on τc, and beyond τc≈12, any further increase in τc produces only minimal additional brightening of Ac. We also tested τc thresholds of 5 and 10 to align with the common definition of thin clouds as those having τc<5 . The results did not change the key findings, and the main difference was a shift in the distribution of scenes within the ternary space.

The ternary framework allows us to estimate cloud susceptibilities to Nd, conditioned on τc morphology. It should be emphasized that the ternary binning does not fix τc or other cloud properties within each morphology bin, as each bin retains natural variability in Nd, LWP, τc, Ac, and CF. This is evident, for example, in the difference between the LWP of cloud cores and that of the entire scene (Fig. c and d). Sensitivity tests in which the bin size was increased to allow greater variability in cloud properties within each bin did not affect the results. Transitions between morphology bins could have a stronger albedo response, such as in the case of transitions between closed and open cells , however these are temporally dependent and not considered here.

A commonly used approach to estimate SLWP from satellite observations is to regress dln⁡LWP on dln⁡Nd. However, when LWP and Nd are calculated under the adiabatic assumption using the satellite retrieved τc and re , changes in re are expected to produce a linear sensitivity of -0.4 between dln⁡LWP and dln⁡Nd, assuming constant τc . This effect was found to dominate SLWP in our analysis (Fig. ) because the variability in τc within each ternary bin is relatively small, as each bin is constrained by a τc class composition. To avoid this bias, SLWP was calculated by subtracting the theoretical approximation of SAc from the satellite derived Snet. The residual is assumed to be primarily attributable to SLWP, as shown below.

Snet (the in-cloud albedo susceptibility) can be written using the chain rule as: 2Snet≡dln⁡Acdln⁡Nd=∂ln⁡Ac∂ln⁡NdLWP+∂ln⁡Ac∂ln⁡LWPNddln⁡LWPdln⁡Nd.

Here, Snet is defined as the susceptibility of in-cloud albedo to Nd, and therefore does not include adjustments in CF. This differs from formulations based on scene-mean albedo , where CF changes contribute an additional term. The first term on the right hand side represents the cloud albedo response to Nd, SAc . Using the cloud albedo theoretical approximation , 3SAc≡∂ln⁡Ac∂ln⁡NdLWP=13(1-Ac), where Ac is the in-cloud albedo of each 2°×2° scene. SAc is then averaged to obtain the mean SAc within each morphology bin, S‾Ac.

∂ln⁡Ac∂ln⁡LWPNd in Eq. () represents how changes in LWP modify Ac. Because Ac depends primarily on τc, and τc∝LWP5/6Nd1/3 , we can write: 4γ≡∂ln⁡Ac∂ln⁡LWPNd=56∂ln⁡Ac∂ln⁡τcNd=56(1-Ac) so that Eq. () becomes: 5Snet≡dln⁡Acdln⁡Nd=SAc+γdln⁡LWPdln⁡Nd.

For each morphology bin, we estimate Snet by regressing the observed ln⁡Ac on ln⁡Nd using all scenes within that bin. For consistency with SAc, we use the bin mean in-cloud albedo, Ac‾ in γ, so that γ‾=56(1-Ac‾). Evaluating Eq. () at each morphology bin gives: 6Snet=S‾Ac+γ‾dln⁡LWPdln⁡Nd.

Solving for SLWP yields SLWP per morphology bin: 7SLWP≡dln⁡LWPdln⁡Nd=Snet-S‾Acγ‾.

SLWP may implicitly include the influence of CF adjustments on the sampled in-cloud LWP, consistent with previous LWP adjustment studies .

SCF, defined as the CF susceptibility to Nd, was calculated by regressing the observed ln⁡(CF) on ln⁡(Nd) for each ternary bin. Explicitly disentangling SLWP from SCF is challenging, as it is not uniquely defined how spatially heterogeneous changes in LWP should be attributed to variations in CF .

Figure a shows the 2015 distribution of scenes within the ternary morphology space. The most frequent morphologies are composed of a mixture of homogeneous optically thick and homogeneous optically thin clouds, with a relatively small contribution from the intermediate τc class. This implies that most of the variability in scene morphology arises from changes in the relative contributions of the thick and thin τc classes, whereas the fractional contribution of the intermediate τc class is relatively low. Such a mixtures of τc classes characterize active convective cores that coexist with thin clouds diverging from the cloud tops . The example in Fig. c and d shows this morphological type, consisting primarily of open cells and disorganized mesoscale cellular convection . Similar spatial variability in LWP has been used to distinguish disorganized mesoscale cellular convection from closed and open cells, and from stratus cloud layers with no cellular structure .

The least frequent morphologies correspond to homogeneous scenes with intermediate τc. Interestingly, the scene-mean τc of all sampled scenes falls within this τc class, with an average value of approximately 9. This means that scene means often reflect a mixture of thick and thin clouds and are therefore not representative of the underlying τc distribution. Indeed, showed that relying on the scene-mean τc, rather than accounting for its spatial variability, can lead to a substantial bias in SAc. Another less frequent morphology appears near the very left side of the ternary, where scenes are dominated by a mixture of thick and thin clouds, with minimal contribution from the intermediate τc class.

Figure b shows the median CF per ternary bin, revealing a clear separation between overcast and broken scenes. This indicates that overcast and broken scenes are associated with different τc morphologies. The highest scene occurrence (Fig. a) is found for broken cloud morphologies, consistent with previous studies. These scenes are attributed to the high occurrence of disorganized mesoscale cellular convection . The analysis therefore mainly represents stratocumulus clouds, primarily closed and open cells, disorganized mesoscale cellular convection, and stratus layers with no cellular pattern.

Figure c and d show the morphology evolution of simulated clouds obtained from a Lagrangian LES of closed cells transitioning to open cells . The simulated clouds evolve along a morphology trajectory that closely matches the region of highest occurrence in the observations (Fig. a). This suggests that most observed scenes lie within the stratocumulus morphology evolution space that the analysis is designed to represent.

The simulated evolution of the cloud morphology also provides insight into key cloud processes. One example is cloud thickening during nighttime at the beginning of the simulation, driven by cloud top radiative cooling . Another is the diurnal cycle in cloud morphology, evident from the daytime loop feature in Fig. c and d. The loop feature shows an increased contribution from the intermediate τc class at the expense of the high τc class during the daytime morphology evolution (Fig. c), implying cloud thinning. It is driven by the daytime increase in solar radiation, which leads to cloud thinning and CF reduction (Fig. d) through warming and evaporation . Interestingly, the afternoon cloud thickening follows the same morphological trajectory as the cloud thickening during the previous night, suggesting a preferred evolutionary path. This can explain why the observed cloud morphologies do not span the entire ternary space but instead are concentrated along a preferred region within the morphology space (Fig. a). It remains an open question for future study whether a given morphological state can be reached through different paths.

The ternary representation also captures the rapid cloud breakup, indicated by the downward-pointing arrows in Fig. c and d. Because cloud breakup occurs concurrently with the development of substantial precipitation , scenes occupying this morphology space are presumably associated with collision and coalescence processes .

The above demonstrates that the distribution of scenes within the ternary space encodes information about underlying cloud processes, such as cloud thickening, thinning, and collision–coalescence. Satellite observations projected onto the ternary space can therefore provide information about the state of the cloud field, as different regions of the diagram correspond to distinct cloud processes.

Figure a shows that SLWP is negative across the entire ternary space. This contrasts with previous studies that reported both positive and negative SLWP, with the positive values attributed to precipitation suppression . The negative SLWP indicates that entrainment-related evaporation processes dominate across all morphologies, leading to a reduction in LWP as droplet size decreases with increasing Nd . The strongest SLWP of nearly -1 is found in morphology bins where the intermediate τc class is dominant. In these scenes the horizontal cell sizes are relatively small (Fig. a), consistent with , who found similarly strong SLWP in nonprecipitating small closed cells.

SLWP weakens (becomes less negative) as the contribution from the intermediate τc class decreases and is replaced by increasing contributions from the lowest and highest τc classes. This partly coincides with an increase in re to values close to 15 µm (Fig. b), indicating the presence of precipitation , and suggests that precipitation suppression contributes to the weakened SLWP, but not sufficiently to reverse its sign. Additionally, the dominance of thin cloud layers in these morphologies tends to be associated with more quiescent turbulent conditions , limiting their ability to entrain free-tropospheric air and thus constraining SLWP. Our findings are consistent with , who showed that the positive SLWP reported for precipitating scenes in many inverted-V studies does not necessarily reflect precipitation suppression, but can instead arise as an artifact of aggregated sampling across different cloud morphologies.

The weakest SLWP is found in morphologies composed of a mixture of thick and thin τc classes, with minimal contribution from the intermediate τc class. These morphologies are characterized by relatively large cell sizes (Fig. c) and re close to or exceeding 15 µm (Fig. ), indicating mature closed cells approaching breakup . This is consistent with , who reported weak SLWP for the largest cell sizes. In addition to delayed cloud breakup due to the delayed onset of precipitation, the weak SLWP in these morphologies may also arise from differences in entrainment efficiency between thick cloud cores and the surrounding thin clouds . Additionally, the non-negligible contribution of the highest τc class indicates the presence of thick, dynamically active cores, as evidenced by the large core-LWP (Fig. d). These cores likely supply cloud water to the diverging thinner clouds at their tops, which could partially offset LWP losses due to entrainment-driven evaporation, thereby further weakening the negative LWP response.

Figure b shows that the strongest SAc occurs in the lowest τc class and extends toward the top corner, towards the highest τc class, with the largest gradient along the left side of the ternary diagram. This is consistent with the theoretical approximation of SAc , which predicts the largest susceptibility for scenes with the lowest Ac (see Fig.  for the distribution of Ac across the ternary space).

Figure c shows a strong dependence of Snet on cloud morphology. Snet is negative in scenes dominated by intermediate τc classes and shifts toward positive values as the morphology becomes dominated by a mixture of thick and thin τc classes. The similarity between the morphological dependence of Snet and SLWP (Fig. a) arises because SAc (Fig. b) exhibits relatively little variability compared to SLWP. This indicates that Snet is primarily controlled by SLWP. The strong influence of LWP adjustments on the net albedo response can also be shown theoretically .

The strongest negative Snet is found in scenes dominated by the intermediate τc class, where SLWP outweighs the relatively strong in-cloud albedo response associated with the Twomey effect, SAc (Fig. b). This is consistent with , who found that thicker non-precipitating clouds, which likely correspond to the intermediate τc class here, exhibit cloud darkening. The strongest positive Snet, on the other hand, occurs where SLWP is weakest, that is, least negative (Fig. a), allowing the Twomey brightening (SAc) to enhance Ac without being substantially offset by the LWP adjustments.

Both the strongest negative and the strongest positive Snet are associated with the least frequent morphologies (Fig. a), whereas for the most frequent morphologies, SLWP and SAc approximately balance each other, resulting in Snet near zero. As a result, the global mean Snet is relatively small, with a value of approximately 0.015±0.007. The uncertainty of the weighted mean slope was estimated from the variability across bin-specific slopes, accounting for the effective sample size. A substantial offset of the Twomey induced brightening by LWP adjustments has also been reported in previous studies . It should be noted that the global mean Snet reflects the morphological occurrence of the year analyzed here. A future study will explore whether there are interannual differences in morphological occurrence, for example during El Nino years, as well as across seasons and regions.

The LWP and Ac susceptibility analysis focused on in-cloud changes, without considering changes in CF. Here, we further examine SCF (Fig. d). Positive SCF is found in precipitating scenes, as indicated by re>15µm (Fig. b), consistent with studies reporting a positive relationship between CF and Nd . Since stratocumulus breakup is driven by the formation of precipitation , the positive SCF reflects the effect of increased Nd in slowing precipitation formation, which slows down the reduction of CF.

Negative values of SCF, by contrast, are found in non-precipitating scenes (re<15µm). These scenes are composed primarily of the intermediate τc class, where SLWP is strong and negative (Fig. a). This suggests that the negative strong SLWP drives the negative SCF. The scene-mean LWP in these morphology bins is relatively low (Fig. c), such that evaporation of cloud water associated with the strong SLWP presumably leads to cloud dissipation and, consequently, a reduction in CF. We assume that the reduction in CF is associated with the thinner clouds at the edges of the cells (see examples in Fig. e), consistent with the assumptions in . The daytime cloud thinning and the associated small reduction in CF shown in Fig. c and d correspond to the negative SCF shown in in Fig. d, consistent with the reported daytime decrease in CF . Weak negative SCF are found where scenes are dominated by the thickest τc class. In these scenes, clouds are thick and have high LWP, so changes in LWP do not substantially affect scene CF.