The Role of Interactive SST in the Cloud‐Resolving Simulations of Aggregated Convection

This study investigates the role of interactive sea surface temperature (SST) in the early development of aggregated convection using a vector vorticity equation cloud‐resolving model coupled to a slab ocean. The simulations are initialized by a mock Walker circulation driven by initial SST gradient in the elongated x axis, with an average of 300 K and sinusoidal variation of amplitude ranging from 1.5 to 3 K. According to large‐scale perturbation strength, which is caused by SST variation, the results can be divided into two groups. Under weak perturbation, convection‐SST feedback efficiently eliminates SST gradient and moisture anomaly. The large‐scale environment is homogenized within 2 days. Even though SST in the group with stronger perturbation undergoes a similar process, significant moist static energy (MSE) advection in the boundary produces enough moisture difference to introduce virtual temperature effect and aggregation is triggered. Once dry zone starts to expand, radiative and convective effects regenerate SST gradient, which intensifies circulation and accelerates the process. We further show that the evolution of aggregation or not is captured by the trend of MSE‐EIS (estimated inversion strength) variance. The results highlight the boundary layer processes on the formation of aggregated convection in the tropics.


Introduction
Moist convection is often viewed as an adjustment toward statistical equilibrium with the environment, suggesting that convection consumes external forcing with time scale much less than the large-scale motion (Arakawa & Schubert, 1974). This concept has been applied to radiative-convective equilibrium (RCE), in which convective processes balance radiative disturbances vertically, a simplified but useful approach to tropical atmosphere modeling. Despite one feature of RCE state is vertical energy adjustment without lateral transport, large-scale circulations are allowed to develop within a large horizontal domain.
In RCE simulations, the presence of convective aggregation is a conceptual breakthrough. It also provides insights to understand convective phenomena including cyclogenesis, Madden-Julian Oscillation, and even climate sensitivity . Held et al. (1993; see also Nakajima & Matsuno, 1988) found that individual convective cumulus can aggregate to an organized convective system surrounded by extremely dry region despite uniform bottom boundary conditions, such as time-invariant sea surface temperature (SST) in a certain range (e.g., 301-307 K in . The process, now referred as convective self-aggregation, has been studied with a hierarchy of numerical simulations, wide span of climate domain geometry and grid resolution (Bretherton et al., 2005;Coppin & Bony, 2015;Holloway & Woolnough, 2016;Jeevanjee & Romps, 2013;Muller & Bony, 2015;Muller & Held, 2012;Tompkins, 2001;Tompkins & Craig, 1998;Su et al., 2000;Wing & Cronin, 2016;Yang, 2018). Mutual findings include that longwave radiation and water vapor (or clouds) interactions are essential for aggregation. With the development of self-aggregation, the convection occurs only within the wet patch occupying roughly 25% of the domain, leaving 75% of the area dry. Convective aggregation also reshapes domain-mean climate, including overall drying that reduces the greenhouse effect and therefore enhances longwave cooling (Bretherton et al., 2005;Khairoutdinov & Emanuel, 2010;Wing & Cronin, 2016).
As an aggregated state is associated with excess longwave cooling that lowers energy of the atmosphere, several recent studies interpreted the inhomogeneity of convective patches as one of the equilibrium states possessed by radiative-convective coupling (Beucler & Cronin, 2016;Beucler et al., 2018;Emanuel et al., 2014). When column water vapor exceeds a certain threshold that allows radiative cooling to decrease with enhanced column water vapor, either positive or negative moisture perturbation would be amplified via interaction between radiative cooling and latent heat energy transport, namely, moisture-radiative cooling instability.
On the other hand, with fixed SST, some crucial feedbacks are prohibited. For example, a wind perturbation will bring moisture flux into the atmosphere. At the same time, the extraction of the surface fluxes can cool down the surface temperature, producing a negative feedback for convection. To include SST effects with optimized computer resource, a remedy is to add a slab ocean in which only thermodynamic effects are considered. Using a global model with superparameterized convection, Grabowski (2006) found that when coupled to a shallow slab ocean, negative convection-SST feedback impedes large-scale convective organization since shortwave radiative effect of convection damps local SST perturbation. Interactive SST in RCE also brings additional surface energetic balance consideration, and thus, it is not surprising that several global model simulations used convective parameterizations exhibit different equilibrium characteristics with atmosphere-ocean coupling by a dynamically passive slab ocean (Popke et al., 2013;Reed et al., 2015).
The studies of aggregation coupled to a slab ocean can produce different results compared with fixed SST simulations. The general point is that SST response to surface energy imbalance would probably delay or even prevent the onset of aggregation, especially in simulations with less ocean heat capacity. In Bretherton et al. (2005), a cloud-resolving model simulation with a thin slab ocean could still aggregate but more slowly, and the authors suggested that this is caused by the cloud shading effect that cools convective region over warm SST. Hohenegger and Stevens (2016) further showed that when slab ocean is thin enough (less than 1 m in their study), aggregation would not occur since the SST gradient, which becomes colder (warmer) in convective (nonconvective) zone, generates a thermally direct shallow circulation that counteracts dry zone expansion. Both studies pointed out that the reduced water vapor longwave absorption (Nakajima et al., 1992) associated with aggregation cools the climate system significantly, preventing runaway greenhouse climate, and implied that aggregation is an efficient regulator of radiative energy budget.
In this study, we focus on the development of aggregated convection with slab ocean coupling. Instead of equilibrium states, we aim to elucidate processes in the transient stage of aggregation under large-scale SST perturbation, which would generate a mock Walker cell associated with a large-scale ascent region over the warm SST in a few hours. It is known that a large-scale circulation brings tropopause air with limited vapor amount down to the midlevels. Thus, a stronger circulation causes more drying in subsidence region via entrainment and mixing, which is known as moisture-convection feedback (Grabowski & Moncrieff, 2004) that consumes positive buoyancy in the originally drier zone and suppresses further convection development there. On the other hand, with interactive SST, convection-SST feedback suggests that convection may hinder itself by blocking solar insolation and enhancing surface heat fluxes that both cool local SST, and convection would therefore emerge at the originally nonconvective zone with relatively high SST (Grabowski, 2006). Competing interactions between free-tropospheric moisture and boundary processes posit a question on whether convective zone would spread, remain concentrated, or even get more aggregated, and this is what we are going to investigate in this study.
The outline of the content is organized as follows. Section 2 describes the model setup and experiment design. Section 3 demonstrates an overview of simulation results, including large-scale behavior and MSE variance feedback analysis, and section 4 shows boundary structure that is crucial for the buildup of moisture gradient. Summary and discussion are presented in section 5. The spatial SST budget evolution and feedback mechanisms with interactive SST are briefly shown in the appendix.

The Model
The cloud-resolving model used in this study was developed by Jung and Arakawa (2008) based on the three-dimensional anelastic vector vorticity equation (VVM). A unique aspect of the model is that it predicts the horizontal components of vorticity and diagnoses vertical velocity using a three-dimensional elliptic equation. Instead of the use of momentum equations, vorticity equations are advantageous for simplification of cumulus momentum transport and more intuitively description on circulation. A bulk three-phase cloud microphysics parameterization including cloud droplets, ice crystals, rain, snow, and graupel is used in this model (Krueger et al., 1995), accompanied by RRTMG radiation scheme (Iacono et al., 2008). The model has also been used to study topography effect through immersed boundary method (Chien & Wu, 2016;Wu & Arakawa, 2011;Wu et al., 2019), stratocumulus dynamics with perturbed free atmospheric moisture (Tsai & Wu, 2016), convective aggregation with heterogeneous land surface fluxes (Wu et al., 2015), and wind shear (Tsai & Wu, 2017).

Experiment Setup
The experiments are conducted with a cloud-resolving model, VVM, coupled to a slab ocean mixed layer, and the setup is largely similar to previous convective aggregation studies (cf. Bretherton et al., 2005;Muller & Held, 2012) with uniform boundary condition except that triggered by difference initial conditions. The SST is predicted by an energy budget equation: where is mixed layer density (1,024 kg/m 3 ), C is water heat capacity (4,218 J·kg −1 ·K −1 ), and H is set to be uniform 2 m, which is thin but contains almost equal heat content as in the troposphere, and is sufficient to demonstrate the impact of an interactive SST (cf. Bretherton et al., 2005;Hohenegger & Stevens, 2016). SW sfc and LW sfc are surface net shortwave and surface net longwave radiative fluxes, LH is the latent heat flux, SH is the sensible heat flux, and Qflux is set invariant with time, which is set as homogeneous −50 W/m 2 . Qflux is a simplified approach to mimic thermal effects of oceanic physical processes like mixing and ocean circulation. Otherwise, a mere add of slab ocean in tropical study will easily lead to rapid greenhouse warming (Pierrehumbert, 2010) since in reality there are energy sinks not presented in a relative small and simple system, for instance, heat transport to midlatitude. Similar effect can also be achieved by reducing solar insolation (Hohenegger & Stevens, 2016).
The simulations are triggered by a thermally direct circulation generated by initial SST distribution, which is given as where L is the length of elongated dimension, 1,024 km. Initial SST varies sinusoidally along the elongated x axis with the warmest locates at the center, with an domain mean SST 0 set to 300 K. The strength of circulations are adjusted by SST amplitude, ranging from 1.5 to 3 K, as shown in Figure 1. After the first time step, SST is predicted by equation (1) and varies freely to respond to energy imbalances in the mixed layer. All experiment settings have no y-direction dependence, and initial conditions are integrated over 20 days with hourly output. This integration length is shorter than the the estimated internal variability time scale suggested by Coppin and Bony (2017), which is approximately 1.  The domain-mean SST is 300 K for all simulations with sinusoidal variation ranging from 1.5 to 3 K. See context for more details.
domain-mean wind nudging. Similar approach has been implemented in several studies, like Kuang (2012), Muller and Held (2012) and Patrizio and Randall (2019)

Overall Evolution
Results from the sensitivity experiments can be visualized by snapshots of column relative humidity (CRH) and outgoing longwave radiation at Days 1 and 20 in Figures 2 and 3. In the first 24 hr, convection occurs at high SST region with the large-scale ascent. With stronger initial circulation induced by larger spatial SST gradient, the 3-K simulation is slightly drier compared with the 1.5-K simulation, particularly in the subsidence region. The convective zone is slightly concentrated under stronger circulation while the quantitative distinction is less than 2% in terms of domain mean CRH. Despite similarity in the beginning, the moisture distribution and deep convection show huge disparity at Day 20. The convective zone in 1.5-and 1.75-K simulations is homogenized and scattering deep convection occurs spontaneously in a warm and moist atmosphere. On the contrary, in 2.25-and 3-K experiments, the convection aggregates into a moist patch, surrounded by an extremely dry environment. The moist patch is stationary since the domain-average wind field is nudged to zero, and convection propagates within the moist patch. Although the integration length is only 20 days, the evolution of aggregation or not is qualitative similar if the simulations are extended to 100 days: the 1.5-K simulation keeps random deep convection over the domain, and the 3-K simulation develops a more aggregated convection. Since the variation in the x direction is more significant than that in the y direction, the analyses are expressed in two-dimension (X-Z) with a meridional average applied in advance unless specified.
The vertical structure of the convection at the end of simulations is demonstrated by moist static energy, streamfunction, and SST in Figure 4. Since the initial SST perturbation is symmetric in the x direct, the evolution can be visualized by half of the domain. In the nonaggregated case, the initial SST perturbation is homogenized and deep convection grows spontaneously over the warm ocean, leading to chaotic streamfunction. On the contrary, when aggregation occurs, a large-scale circulation extending from surface to top of the troposphere can be visualized. A low-level circulation occupying beneath 850 hPa is evident in the simulation, which is identified as an important process for aggregation since it transports MSE up-gradient to the convective zone (Bretherton et al., 2005;Muller & Bony, 2015;Muller & Held, 2012) and generates a low-level moisture contrast, which further introduces radiative feedbacks. In addition, the low-level wind is associated with underlying SST distribution, with strong wind stress collocates with the maximum SST gradient. It is noteworthy that even for aggregated cases, the SST gradient is not sustained all the time: It vanishes first as an immediate response of convection-SST feedback, and it reappears along with the aggregation. The spatial SST budget evolution is presented in the appendix.
Previous literature has reported that aggregated convection changes domain-mean climate, especially for evident drying and cooling. Similar results could be found in Figure 5, which shows the time evolution of the domain-average CRH, SST, precipitation, and column cloud condensates. The CRH (Figure 5a) displays streamfunction (kg/s); the contour interval is 2e + 9 for the 1.5-K simulation and 1.5e + 10 for the 3-K simulation. Solid is positive value, representing clockwise motion and dash is for negative value, representing counterclockwise motion; white contour: water vapor mixing ratio (g/kg), with the contour interval 5 g/kg starts starting at 1 g/kg. Bottom portion of each panel: Gray: initial SST (K); blue: SST (K) at Day 20.
two paths of response to initial perturbation: One keeps a humid state and the other dries significantly. In 1.5-, 1.75-, and 2-K simulations, the nonaggregated environment restores a humid state with CRH around 80%. Despite discernible drying caused by initial weak circulation in first several days, a steady CRH at final stage suggests that the nonaggregated scenario approaches RCE. Oppositely, in 2.25-and 3-K simulations, the drying of troposphere continues for more than 20 days. In the 3-K simulation, CRH even reduces from 90% to roughly 50% at Day20. The contrasting CRH evolution allows us to easily identify the existence of convective aggregation. The evolution of SST ( Figure 5b) in all simulations undergoes continuous heating with a similar trend before day 10. After that, the heating in 2.25-and 3-K simulations slows down, and the 3-K simulation even starts to cool around Day 11. It is noteworthy that humidity evolution spreads among experiments prior to SST, which indicates that the mean SST state is a response of convective aggregation. With identical Qflux dissipation in all simulations, SST variation comes from the energy imbalance in the ocean mixed layer. Within the first 5 days, the precipitation rate ( Figure 5c) in all simulations is much alike despite high-frequency variabilities of the convective activities are a bit stronger in the 3-K simulation. The results show that aggregated convection exhibits higher precipitation even though the surrounding environment is drier, with no significant change on column cloud hydrometeor (Figure 5d).

The Role of Interactive SST
With a slab ocean, the change of SST represents an additional part of energy source or sink. Also, from Figure 5b we see that SST apparently responses to the state of aggregation. Although the increase rate of SST is not monotonically connected to CRH value, the cooling role associated with aggregation is revealing.
The SST tendency is decomposed by the mixed layer energy budget in Figure 6. The sensible heat flux and Qflux are not drawn individually since they are relatively small and time invariant, respectively, and they are included in the net flux instead. The unit is converted from W/m 2 to K/day by dividing the heat capacity of the slab ocean per unit column. The surface net shortwave heating (Figure 6a) shows that after 7 days, an aggregated state (in 2.25-and 3-K simulations) evolves to possess an additional heating rate of 0.1 K/day, possibly due to less cloud shading effect, which allows more incoming solar insolation, as in Hohenegger and Stevens (2016). The prevailing effect of aggregated convection is the enhanced surface net longwave cooling (Figure 6b), which generates a difference of cooling rate at 0.2 K/day among experiments. The efficient cooling effect is consistent with the radiative fin mechanism proposed in Pierrehumbert (1995), which emphasized that the excess longwave cooling in the dry zone can reduce the greenhouse effect locally. In all simulations, the latent heat flux (Figure 6c), which is the main component of surface enthalpy fluxes, experiences a significant increase from 0.9 K/day to around 1.2 K/day, though in the end the simulations with aggregated convection the cooling rate is around 0.1 K/day higher than without. For each simulation, the net effect of surface fluxes ( Figure 6d) reaches roughly the same value after 10 days, suggesting an equilibrium of mixed layer energy, although the nonaggregated simulations retain an extra heating rate around 0.1 K/day.
The composition of the net surface fluxes suggests two schemes of energy regulation in either aggregated or nonaggregated scenerio. In an aggregated environment, a large-scale circulation is maintained with distinct convective and subsidence regions. The surface net shortwave heating is mainly balanced by strengthened net longwave cooling in the dry zone and latent heat flux by surface wind stress associated with the large-scale circulation. Even though the latent heat flux could transport water vapor to the low-level and moisten the dry area, the moisture is immediately advected to the convective zone through the low-level circulation. Oppositely, in the nonaggregated environments (1.5 and 1.75 K), even though the widespread cumulus convection blocks part of the surface net shortwave insolation, the longwave cooling is largely hindered due to the strong greenhouse effect of water vapor. The heating in the mixed layer is alternatively offset by the latent heat flux, which is bolstered by strong deep convection under rising SST. Compared with aggregated simulations, it is suggested in Figure 6d that the energetic adjustment by transient convective systems, which leaves the heating around 10 W/m 2 more, is not as efficient as the large-scale circulation. As the prescribed energy sink (Qflux) is identical in all experiments, the coupling of SST highlights the impact of aggregation to climate regulation.

Moist Static Energy Variance Feedback
To identify the key mechanism that controls the initiation of aggregation and subsequent evolution, we follow the analytic framework based on the spatial variance of column integrated MSE introduced in Wing and . This method quantifies feedback of each physical processes. For MSE, we include cloud condensate effect by using frozen moist static energy defined in Bretherton et al. (2005): where c p is specific heat of dry air at constant pressure, L v is latent heat of vaporization, L f is latent heat of fusion, q v is water vapor mixing ratio, and q ice is ice condensates mixing ratio. With the density-weighted vertical integration, the source and sink terms occur only at the surface and top of atmosphere. The vertical convergence term is also eliminated since the vertical velocity is restricted to vanish at the upper and lower boundary. The budget equation for column MSE is then For an arbitrary quantity X,X denotes density-weighted vertical integral, SW and LW refer to column shortwave and longwave radiative fluxes convergence, SEF is surface enthalpy fluxes consisting of latent heat flux and sensible heat flux, u is vector wind that is reduced to y averaged zonal wind in this study, and ∇ h ·ûh is horizontal divergence of column MSE flux. By defining X ′ as anomaly from horizontal mean and multiplying equation (4) withĥ ′2 , budget equation for MSE spatial variance can be written as In equation (5), terms with positive correlation implies that the certain process increases MSE variation and thus contributes to aggregation. The calculation is based on daily mean model output, and the MSE divergence term is taken as a residual from the budget equation and diabatic fluxes. The time evolution of domain-mean MSE variance composition is presented in Figure 7. The magnitudes are not normalized byĥ ′ as done in many aggregation studies since we focus on the early stage of variance growth, and the magnitude of the MSE variance is quite small during this period. For the 1.5-K simulation, which evolves to nonaggregation, the diabatic terms, consisting of radiation and surface enthalpy fluxes, contribute to the MSE variance development in first 8 days, and this effect diminishes afterward. Although the MSE convergence term slightly increases the MSE variance in the very beginning, from Day 3 it becomes the dominant negative term that opposes the MSE variance growth and eventually smooths the inhomogeneity of MSE. While the moisture contrast is eliminated, associated diabatic contributions are therefore suppressed and individual contributions to the MSE variance no longer exist. The domain becomes humid everywhere, and the convection distribution is in a random pattern. In the early stage of the 3-K simulation, diabatic terms share qualitatively similarities with the 1.5 K one for they are also positive contributions. These terms are then gradually amplified and are associated with enhanced MSE convergence contribution. Although the MSE convergence term later becomes negative around Day 17, the diabatic terms prevail, suggesting the aggregated convection could be sustained by the radiative and the surface fluxes effects.
Among these two simulations, the resemblance in the beginning suggests that horizontal moisture difference generated by initial Walker circulation brings about a direct diabatic response, which is stronger in the aggregated simulation (3 K) because of the stronger initial SST gradient. The MSE variance is dominated by water vapor distribution, and water vapor brings out radiative effects on aggregation. The longwave feedbacks that include the greenhouse heating effect in convective zone and the cooling effect in dry zone always

10.1029/2019MS001762
increase the MSE variance and have been proposed as an essential mechanism for aggregation for simulations without rotational effect (Bretherton et al., 2005;Holloway & Woolnough, 2016;Muller & Held, 2012). The shortwave term also contributes to MSE variance steadily, as reported in Wing and Emanuel (2014), Holloway and Woolnough (2016), and Wing and Cronin (2016). As water vapor is the main absorber of solar heating in the troposphere, the shortwave feedback is directly connected to moisture distribution that enlarges MSE variance. The surface enthalpy fluxes largely account for initial growth Wing & Cronin, 2016), and their predominate role of aggregation is similar to several other aggregation studies (Bretherton et al., 2005;Holloway & Woolnough, 2016;Muller & Held, 2012;Tompkins & Craig, 1998). Although the surface enthalpy fluxes start to hinder aggregation since Day 8, the MSE convergence term becomes large enough that propels the MSE variance to grow, and it agrees with previous works that the MSE convergence by advective process would contribute to aggregation (Bretherton et al., 2005;Muller & Bony, 2015;Muller & Held, 2012). Even though this term acts against aggregation after Day 18, it has been proposed as a local low-level up-gradient effect unrepresented in this column-integrated metric (Coppin & Bony, 2015). For instance, when the large-scale overturning circulation is strong enough, the upper branches of the large-scale ascending region would pump out ample MSE, and the column MSE could decline there without sufficient MSE supply by the low-level advective process. Under this circumstance, the low-level moisture gradient could potentially support other diabatic effects toward aggregation. A more detailed discussion on spatial MSE variance feedback in moisture space is presented in the appendix.
The dominant distinction between aggregated and nonaggregated scenario is the MSE convergence term, which exhibits an opposite effect and suggests that the horizontal moisture advection is decisive for triggering the convective aggregation. Under weak perturbation experiments (Figure 7a) in which the convection disaggregates, the mechanisms listed in equation (5) do not establish significant MSE variance. The wind convergence term gets fragile and even imposes negative effect after 3 days, largely homogenizing MSE distribution. Although all other diabatic terms slightly act to enhance the MSE variance, they turn out to be impotent as the spatial moisture contrast is annihilated. In spite of some qualitative similarities between 1.5-K simulations, 3-K simulations, and previous aggregation studies (e.g.,  in terms of domain-mean MSE variance budget in the beginning, the convection is not necessary to aggregate, and this leads us to investigate the initiation of aggregated convection.

Initiation of Aggregated Convection
The convective aggregation can be considered as the process of convection to gradually get localized. Thus, we synthesis the large-scale environment in the early stage to assess the initiation of aggregation. For local thermodynamic condition, we adopt the estimated inversion strength (EIS) following Wood and Bretherton (2006). The EIS is a modification of lower-troposphere stability (LTS; Klein & Hartmann, 1993) to be more responsive to moderate tropospheric subsidence and applicable to a wider span of climatological conditions, which can be useful in diagnosing the stabilizing effects by deep convection. The EIS is defined as The LTS is potential temperature difference between 700 hPa and the surface. Γ 850 m is the moist adiabatic lapse rate at 850 hPa, z 700 is the height of 700 hPa surface, and the LCL is lifting condensation level.
Due to the weak temperature gradient approximation (Sobel et al., 2001), 700 shows little spatial variance, and therefore, the EIS is mainly determined by the low-level moisture and surface temperature, which incorporates the net effect of interactive surface fluxes and SST. In addition, we use virtual temperature T v as an indicator for horizontal buoyancy gradient in the boundary layer, which is defined as where r is the water vapor mixing ratio. Figures 8 and 9 demonstrate snapshots of the boundary structure of first several days. Driven by initial SST perturbation, the large-scale circulation generates a convective zone locates at the warm region and the subsidence with higher EIS elsewhere. It also creates a virtual temperature gradient and associated low-level circulation. Despite similarity in the very beginning, several qualitative differences emerge since Day 3. In the 1.5-K simulation (Figures 8b-8d), the horizontal virtual temperature gradient and the SST gradient are flattened, with weakened low-level horizontal circulation, and EIS in the nonconvective zone is reduced. On Day 5, the virtual temperature and SST gradient in the 1.5-K simulation become reversed, indicating a buoyancy gradient that directs the low-level wind toward the nonconvective zone. This reversed flow advects MSE down-gradient, and the large-scale MSE horizontal gradient gets weakened compared to Day 3. Till Day 7, along with the SST distribution, the reversed virtual temperature gradient further forces the reversed low-level circulation, transporting MSE down-gradient, homogenizing the horizontal MSE and the EIS difference. As there is a net MSE convergence in the nonconvective zone, the distinction between the convective and nonconvective zone generated by the initial mock Walker circulation is then eliminated. This MSE down-gradient transport is consistent with the negative sign of MSE convergence in Figure 7 around Days 4 to 8.
On the contrary, for the 3-K simulation, the horizontal virtual temperature gradient, SST gradient, and EIS gradient are still apparent at Day 3, maintaining the low-level circulation. Even though the SST is flattened around Day 5, which is similar to SST evolution in the 1.5-K simulation, the structures in the boundary layer still holds (Figure 9c). Consequently, the low-level circulation is maintained by the virtual temperature gradient in the boundary layer, enhancing the spatial MSE variance. The boundary layer profile is in agreement with Figure 7, which quantitatively shows that the net MSE convergence effect on the buildup of MSE variance is the dominant role that dictates the development of aggregated convection.
We interpret the localization of convection from the lower tropospheric stability perspective, which is quantified by the EIS. In the beginning of simulations, initial circulation constitutes a larger EIS (more stable) in the subsidence zone, where the magnitude is controlled by the large-scale circulation strength and the SST, and the EIS in subsidence region decides the subsequent buoyancy distribution. Subsidence region with weaker stability (smaller EIS) tends to develop more convection (1.5-K simulation; Figures 8b-8d), which moistens and lightens the boundary layer and further reverses buoyancy anomaly along with warmer air. On the other hand, subsidence region with larger stability (larger EIS) inhibits convection and maintains the moisture distribution (3-K simulation; Figures 9b-9d). After the large-scale moisture contrast is established, the longwave cooling in subsidence region is the main component to generate temperature anomaly while the surface fluxes cooling difference is not as significant between the dry and the moist region. Thus, the EIS provides an indication to evaluate the large-scale environment resulting from counteracting role between moisture and SST on convective aggregation.
The MSE and EIS variation evolutions, expressed in terms of standard deviation, are depicted in Figure 10 for all simulations. The MSE variance can be used to identify the degree of aggregation (cf. Wing et al., 2017), and the EIS variance can be used to assess the local thermal stability of convection development. The increase of EIS horizontal variance can be interpreted as the increase of suppressed region or the increase of bottom boundary SST gradient. The simulations with aggregated convection (2.5 and 3 K) are characterized by the monotonically growth of MSE variance, in the same way as previous aggregation studies. The EIS variances also increase but slowly in the beginning, and they are amplified faster when the large-scale circulation is getting steady. As to nonaggregated simulations (1.5 and 2 K), the MSE variance peaks around Day 5 and decreases thereafter, evidencing the destruction of contrasts between convective and nonconvective zones, while the EIS variance does not increase accordingly in the first 5 days. The EIS variance roughly keeps a stable but smaller value than aggregated simulations during this period; afterward, the EIS variance decreases to nearly zero, revealing the absence of spatial boundary layer variation. The large-scale circulation also vanishes. During the evolution, especially in the beginning, the MSE variation increases, but the EIS variation does not necessary follow the increase, suggesting that the boundary layer buildup is not simply subjected to the free troposphere. Since a spatial boundary structure variation favors inhomogeneous convective patches, we add the EIS variation as a precursor of aggregated convection to address the importance of boundary layer processes.
The spatial MSE and EIS standard deviation evolution are further shown jointly in Figure 11. Each marker represents the standard deviation calculated over the whole domain based on daily average data. The different strength of large-scale perturbation creates a spread of the EIS variance while the MSE variance difference is relatively small. Although all the simulations experience a stage that both MSE and EIS variance grow, the trend is divided into two groups. For aggregated simulations, the MSE and EIS variance continue to expand altogether. On the contrary, with smaller EIS variance growth, the trend encounters a turning point around Day 6 that both the EIS and MSE variance start to shrink and result in disaggregation, suggesting that there is a threshold of the EIS variance (with standard deviation around 0.7 K in this study) for the development of aggregation. This figure not only shows the relationship between the degree of convective aggregation and corresponding large-scale environment but also demonstrates the notable differentiation in the boundary layer during aggregation process, which further highlights the role of boundary layer process on the development of aggregated convection, especially with an interactive SST.

Summary and Discussion
In this study, we examine the role of interactive SST on the initiation of convective aggregation with an idealized cloud-resolving model (VVM). The simulations are conducted over a uniform thin slab ocean with a range of SST sinusoidal perturbation strength without Coriolis effect. Although all of these perturbations immediately produce a Walker-like thermally direct circulation associated with a large-scale ascent region full of deep convection over warm SST and a subsidence region with suppressed convection, the results show contrasting evolution in around 5 days. For simulations with weak SST perturbation, the deep convection randomly spreads to the whole domain, whereas for simulations with stronger SST perturbation, the convection aggregates to a single moist patch that is surrounded by extremely dry atmosphere. Our analyses show that the MSE transport by the low-level circulation that maintains the establishment of horizontal moisture contrast is crucial to the bifurcation. This low-level circulation first comes from the horizontal moisture and buoyancy gradient created by initial mock Walker circulation and then strengthened by the interaction between convection, SST, water vapor and radiative effects. The overall effect is summarized by the EIS.
A schematic of the bifurcated development of aggregated convection is described in Figure 12. The initial circulation resulting from SST perturbation generates the spatial moisture gradient and accompanied radiative effect on SST, which leads to the EIS variance. In the first few days, temperature and water vapor play opposite effect in terms of large-scale buoyancy contribution. Compared with the convective region, Figure 11. Joint standard deviation evolution of daily averaged moist static energy (MSE) and estimated inversion strength (EIS) for all simulations. Each simulation is denoted by individual marker, and the time interval for each marker is based on daily averaged data. The evolution during first 6 days are marked with gray, with the first day thickened. The black (red) markers represent evolution for nonaggregated (aggregated) simulations after Day 7.
the buoyancy over the subsidence region of mock-Walker cell is reduced by subsidence drying while also increased by subsidence and shortwave warming. The overall buoyancy is larger in the convection region and forms a low-level circulation that transports MSE into convective region. The longwave cools the subsidence region, but it is not efficient to compensate the warming. This scenario is the qualitatively same for both aggregated and nonaggregated experiments.
Under stronger perturbation that creates a more stable subsidence zone, the EIS variance is larger, indicating that the moisture contrast between convective and nonconvective region is more likely to be maintained. The longwave radiative feedback cools the subsidence zone and amplifies virtual temperature gradient as well as the low-level circulation. The MSE up-gradient transport supports the positive feedback loop and promotes convective aggregation. Contrarily, with a weak EIS variance, the subsidence region is prone to develop convection that moisten and lighten the air. With weaker longwave cooling in the subsidence zone, the convection-SST feedback reverses the virtual temperature gradient. The resulting reversed low-level circulation then down-transport the MSE. Without a particular moist patch, the convection disaggregates,  spreading randomly over the whole domain and the SST rises everywhere. We show that the MSE transport is responsible for the transition between two sorts of equilibrium states, and it can be predicted by the large-scale EIS variance.
With interactive SST by coupling to a slab ocean, the convection-SST feedback could destroy the virtual temperature gradient and aggregation feedback loop, while Coppin and Bony (2017, hereafter CB17) suggested that convection-SST feedback could drive internal variability of aggregation movement, with estimated time scale of 1.5 months for 2-m-thick slab ocean. The results might not be able to directly compare with CB17. In our study, the convection is explicitly simulated while it is parameterized in CB17. In both works, SST is increased in the dry region and in CB17 warm SST draws the whole aggregated convection toward the previously drier clear-sky region while dry region remains no convection in our study. We speculate that the convective parametrization in CB17 is less sensitive to the environment moisture so that the convective instability builds up with warm SST and therefore the aggregated convection moves toward dry region. In our study, however, the low-level stability builds up over the dry region shown by the increase of EIS. Decreased CRH in the dry region further prohibits the development of deep convection. The detailed evolution is SST budget is presented in the appendix, while we focused on how the SST gradient is maintained in our study.

Journal of Advances in Modeling Earth Systems
There are remaining issues worth further investigation. In a RCE environment, the convection occurs where there is a external forcing. Yang (2018) proposed a framework based on available potential energy, which mainly originates from the boundary layer processes with prescribed SST, and it would be worthwhile to examine to what degree would the SST coupling influence this framework. Also, it has been proposed that the low cloud radiative effect is a key component for aggregation with a fixed SST (Muller & Held, 2012). In our study, however, the low-level cloud barely exists, and thus, we cannot identify its role. In several RCE simulations, the initiation of aggregation has been attributed to low-level cloud radiative feedbacks, which provides an inhomogeneous boundary stability over fixed bottom boundary, while it may not be necessary for freely evolved SST simulations.

A. Spatial Evolution of SST Budget
The spatial evolution of SST and its budget analyses are shown in Figures 13 and 14, and only half of the domain is presented. Initially, the mock Walker circulation creates a drying in edges (Figure 13a), which lasts about 7 days. The dry region receives more heating that generates a warm dry region and relatively cool convective region (Figure 13bc) prior to the moistening of dry region around Day 7. From the SST budget analysis in Figures 13e-13h, the vanishing stage is dominated by convection-SST feedbacks, consisting of warming (by solar heating) in colder nonconvective region and cooling (by deep clouds shadowing and latent heat flux) in warmer convective region. The latent heat flux also tend to eliminate SST gradient, but this term is more dependent on wind variance and surface humidity contrast instead of CRH. Due to large-scale humidity contrast, there is spatial longwave cooling difference that cools the nonconvective region more than convective one, but its role is inferior to shortwave and surface fluxes. After Day 8 that the large-scale

Journal of Advances in Modeling Earth Systems
10.1029/2019MS001762 humidity, SST, surface fluxes contrast vanish, the SST heats everywhere. The aggregated convection patch does not emerge again if the simulation is extended to 100 days.
Under strong SST perturbation (Figure 14), the large-scale humidity contrast, or more precisely, the EIS contrast, is larger; the boundary buoyancy anomaly and low-level circulation are maintained in spite of negative convection-SST feedbacks. It is noteworthy that even for the aggregated simulation, the SST gradient is not sustained all the while (Figure 14b) and its evolution can be divided into two stages: vanishing (Days 1-7) and reestablishing (after Day 8). The vanishing SST gradient is an immediate response of convection-SST feedback as in the 1.5-K simulation. After that, the SST gradient reappears along with aggregation. The longwave cooling in the dry region is significantly amplified and thus mainly controls the reestablishment of SST gradient. The surface fluxes turn to support SST gradient while the cooling maximum does not locate in the driest region caused by the surface wind stress.

B. Spatial MSE Variance Feedback
To investigate feedback terms of MSE variance with SST coupling, the 3-K experiment is further integrated to Day 50 to reach a stable aggregated state. The covariance is normalized by domain-meanĥ ′2 with units of per day. Evolution of individual terms of MSE variance contribution in equation (5) in moisture space is shown in Figure 15, ranked from the driest to wettest by CRH. Despite the figure is shown in moisture space, it can be understood as the left half part of physical space since in this study the aggregated convection locates at the center of domain with dry zone on both edges.
For net effect, the strongest positive feedback occurs in the dry zone at early stage, which emphasizes the essential role of dry zone expansion that leads to the onset of aggregation. As the convective zone starts to shrink, the feedback at driest patch weakens and even evolves to be slightly negative around Day 20. The receding of moist zone is then led by convection itself, where positive correlation is maintained. For individual processes, the results share some qualitative similarities with Wing and Emanuel (2014), which discusses aggregation in uniform fixed SST simulations. For instance, the shortwave flux convergence contributes to aggregation everywhere throughout the simulation, and the longwave flux convergence is strongest in the dry zone in the first 10 days. Then the longwave flux mainly supports aggregation via convective zone during equilibrium state. Also, advection process becomes opposed to aggregation after Day 25 since the strong upper branches of the large-scale flow pump out abundant MSE from moist region to dry region. The growth of dry zone is then stagnated, suggesting an equilibrium reached by MSE convergence and diabatic effects.
The main difference is surface enthalpy fluxes term, which is the main positive correlation term during initiation stage and is slightly positive in the dry zone most of time. In Wing and Emanuel (2014), surface enthalpy fluxes term is important during early stage of dry zone establishment as well, while it turns to significantly undermine aggregation in intermediate stage. As surface enthalpy fluxes is the medium between ocean and the atmosphere, we need to consider the role of SST. Components of surface enthalpy fluxes are latent heat flux (LHF) and sensible heat flux (SHF), and they are given by bulk formulae: = c H c p U ΔT.
Here is surface air density, c E and c H are heat exchange coefficient for latent heat and sensible heat, U is surface wind speed, q vs is saturation water vapor mixing at the surface temperature, SST is sea surface temperature, and q v and T a are water vapor mixing ratio and temperature at the lowest level, respectively.