1. Introduction
Radiative–convective equilibrium (RCE) is a conceptual model for understanding tropical climates (Manabe and Strickler 1964). In this model, moist convection balances radiative cooling and surface warming to reach an equilibrium climate state with a statically stable thermodynamic structure. When cloud-resolving models (CRMs) are used to simulate RCE, convective self-aggregation (CSA) is observed as a remarkable phenomenon (Nakajima and Matsuno 1988; Held et al. 1993; Tompkins and Craig 1998). CSA is characterized by the spontaneous aggregation of convection into smaller convective regions, which are surrounded by larger, drier subsiding regions (Bretherton et al. 2005; Muller and Held 2012; Wing and Emanuel 2014; Yanase and Takemi 2018). Even though sea surface temperature (SST) is spatially homogeneous, CSA can develop when the domain size is sufficiently large. In 300 K SST simulations, CSA develops over a time scale of about 30 days, corresponding to the subseasonal time scale. Therefore, CSA is regarded as fundamental for understanding cyclogenesis and the Madden–Julian oscillation (Arnold and Randall 2015; Holloway et al. 2017). Furthermore, the sensitivity of CSA to SST provides critical insights into the role of convective clouds in changing climate sensitivity (Mauritsen and Stevens 2015; Wing 2019).
The studies of CSA can be classified based on their perspectives, and we here discuss two major perspectives: 1) the model sensitivity of CSA to SST in the equilibrium state and 2) mechanisms contributing to CSA during the developing stage. The former aims to understand how the cloud and CSA will change with the increased SST by comparing the equilibrium states under different SST conditions. Wing et al. (2018, 2020) organized the RCE Model Intercomparison Project (RCEMIP) to investigate it with various types of models. Large differences in the vertical structures of temperature, humidity, cloudiness, and the degree of CSA are reported across the RCEMIP ensemble. They applied subsidence fraction, moisture variance, and organization index to quantify the sensitivity of CSA to SST in different aspects. The model results do not have consistent sensitivity of CSA to SST based on these metrics. The results suggested that the responses of CSA to warming SST is still unclear, and the contributions of CSA and clouds to climate sensitivity among models requires further investigation. Becker and Wing (2020) found that 70%–80% of the spread in climate sensitivity can be interpreted by the responses of shallow clouds and CSA in each model. Some robust changes in clouds at different levels among models were reported by Stauffer and Wing (2022). Even though consistencies have been found, the contributions of clouds and CSA to climate sensitivity remain uncertain in the RCEMIP. The uncertainty of the responses to SST should be further assessed across the RCEMIP ensemble.
Another group of studies focused on the mechanism for CSA development, which could link to the tropical convective organization, such as tropical cyclones and MJO. Several factors that can influence the development of CSA have been investigated. Coppin and Bony (2015) demonstrated that the mechanism for CSA development changes from cloud-radiative feedback in cold SST conditions to wind–surface flux feedback in warming SST conditions. Holloway and Woolnough (2016) obtained faster development of CSA when turning off rain evaporation. The treatment of subgrid turbulence closure with greater entrainment rates can largely enhance the efficiency of subsidence drying, hence the development of CSA (Tompkins and Semie 2017). The domain size and horizontal resolution can affect whether CSA develops or not (Muller and Held 2012), and Yanase et al. (2020) showed that a critical length for CSA is due to the competition between cold pool propagations and radiative-driven circulation. When the interactive ocean is applied, the presence of air–sea interactions decelerates or halts the development of CSA (Hohenegger and Stevens 2016; Chen and Wu 2019; Tompkins and Semie 2021; Huang and Wu 2022). The above studies examined these mechanisms using specific models, and the sensitivity of these factors might not be exchangeable among different models. It is essential to have a general indicator to assess the sensitivity of physical mechanisms to CSA among cloud-resolving models with quite different physics and numerics.
Hung and Miura (2021) showed that different indexes for defining CSA will capture different physics during CSA development. The organization index (Iorg; Tompkins and Semie 2017), which measures the probability density function of distances between each convective system, grows first because it captures the organization process of convective systems. The spatial moisture variance and large-scale subsidence fraction rise later. These two indices capture the large-scale circulation and moisture gradient. Their results suggest that the organization is important for the subsequent development of moist, dry regions and CSA circulation. From the perspective of tropical convective organization in the real world, convective structures play an essential role in the modulation of large-scale circulation in the real world. Chen et al. (2021) demonstrated that convective systems could be categorized into five groups based on their sizes via the hierarchical clustering method. The category of convective systems with the largest horizontal extent is well coupled with the seasonal cycle of the Asian–Australian monsoon. Many studies have shown that convective systems with large horizontal extents can largely contribute the large-scale circulation change due to their diabatic heating (Yuan and Houze 2010; Hamada et al. 2014; Hoskins et al. 2020). The horizontal extent of convective systems is critical for convection–circulation interactions, and examinations of such variabilities can provide insight into evaluating the mechanism for CSA development. Additionally, the investigation is important for extending the idealized RCE simulations toward real-world convective organization.
Moist convective processes in cloud-resolving models are highly dependent on the generation of buoyancy through model physics and the dynamical responses through the formulation of model dynamics. In particular, Huang and Wu (2022) demonstrated that different treatments of microphysical processes can lead to the model sensitivity to the convective aggregation. They also found that changes in convective structures play an important role in the convective aggregation. Therefore, comparing a momentum-based, fully compressible model with a vector vorticity-based, anelastic model is essential for understanding the model sensitivity in RCE simulations. In contrast to RCEMIP, we carried out the model comparison focusing on the convective variabilities in response to the coupling between dynamics and physics, leading to different mechanisms for CSA development. The two models are chosen because of our familiarity with them allows us to efficiently conduct mechanism-denied simulations and modify code to output advanced diagnostics, which is crucial for our experiments. Section 2 describes the two chosen models and the analysis methods. Section 3 presents the differences in pathways toward CSA, which are caused by the convective variabilities of the two CRMs. Mechanism denial experiments and discussion are provided in section 4. Finally, we summarize this study in section 5.
2. Methodology
a. Model description
1) SCALE
The first atmospheric model used in this study is a regional model constructed with Scalable Computing for Advanced Library and Environment (SCALE, version 5.3.6; Nishizawa et al. 2015; Sato et al. 2015a). The model is governed by the three-dimensional fully compressible nonhydrostatic equations, which predict the three-dimensional momentum (ρu, ρυ, and ρw), total density (ρ), mass-weighted potential temperature (ρθ), and mass concentration of tracers (ρqs). The θ here is the potential temperature for the moist air, considering the effects of vapor and water content. A six‐class single‐moment bulk‐type microphysics scheme is used in this study (Tomita 2008). The subgrid‐scale turbulent process is parameterized through the Smagorinsky–Lilly type first‐order closure scheme (Brown et al. 1994; Scotti et al. 1993), and surface fluxes are calculated by the Monin–Obukhov similarity theory with a nondimensional function (Beljaars and Holtslag 1991; Wilson 2001). The radiative processes are treated with a k-distribution-based broadband radiation transfer model (Sekiguchi and Nakajima, 2008). SCALE has been used in studying the impacts of cloud microphysics on convection (Sato et al. 2018), data assimilation (Honda et al. 2018, 2019), regional climate changes (Adachi et al. 2019), severe weather events (Yoshida et al. 2019), the parameterization of physical processes (Sato et al. 2015b; Iwabuchi and Okamura 2017; Nishizawa and Kitamura 2018), and dynamical downscaling of blowing snow events (Tanji and Inatsu 2019; Inatsu et al. 2020).
2) VVM
The other model used in this study is the vector vorticity equation cloud-resolving model (VVM) developed by Jung and Arakawa (2008). Horizontal components of anelastic vorticity equations are predicted in the VVM, and velocities are diagnosed by solving a three-dimensional elliptic equation. The use of the vorticity equations eliminates pressure gradient force and inherently links the dynamics and the thermodynamics in the governing equations. The direct couple in the equations can better capture circulations associated with strong thermal gradients, such as cold pools. Turbulence processes are treated by a first-order closure (Shutts and Gray 1994), radiative fluxes are calculated by a radiative transfer model using the correlated-k approach (Iacono et al. 2008), surface fluxes are treated by the Monin–Obukhov similarity theory (Chen and Dudhia 2001; Deardorff 1972), microphysical processes are parameterized by the two-moment bulk scheme that predicts properties of ice particles (Morrison and Milbrandt 2015; Huang and Wu 2020), and the effects of the topography are represented by the immersed boundary method in the VVM (Wu and Arakawa 2011; Chien and Wu 2016). VVM has been applied in many studies, such as unified parameterization (Arakawa and Wu 2013; Wu and Arakawa 2014), stratocumulus dynamics (Tsai and Wu 2016), afternoon thunderstorms (Kuo and Wu 2019), impacts of land surface heterogeneity (Wu et al. 2019; Wu and Chen 2021), cloud–aerosol interactions (Chang et al. 2021), coastal convection during summer monsoon onset (Chen et al. 2019), and the aggregated convection (Tsai and Wu 2017; Chen and Wu 2019).
b. Experiment design
Experimental settings in the two models are described in this subsection, and the difference in dynamics and physics between VVM and SCALE are summarized in Table 1. The domain size and horizontal resolution are chosen to be 384 × 384 km2 and 2 km to have the minimal costs for CSA in this study. This is the minimum size for CSA in SCALE, with a horizontal resolution of 2 km (Yanase et al. 2020). We found that CSA develops in VVM with the domain size of 192 × 192 km2, 384 × 384 km2, and 576 × 576 km2 at the 2-km horizontal resolution. Therefore, it is fair to compare different mechanisms for CSA under this domain configuration. We apply 75 vertical levels, which stretch from the surface to 3 km (15 levels) and extend 33 km with 0.5 km resolution (60 levels). An analytically approximated sounding of the moist tropics is spatially homogeneously applied to simulations for initialization (Dunion 2011). We create five ensemble members by adding random thermal noise in the five lowest model levels. The strength of the perturbation is 0.1 K at the lowest level (37 m) and linearly decreases to 0.02 at the fifth level (395 m). All simulations are integrated with a fixed SST of 300 K for 100 days with hourly data outputs. Other model settings, such as solar insolation and greenhouse gas profiles, follow the RCEMIP protocol (Wing et al. 2018).
Summary of difference in model dynamics and physics parameterization for SCALE and VVM.
c. Convective variability analyses
Analysis methods used in this study are introduced to demonstrate their advantages in assessing CSA development and convective variabilities.
1) Spatial autocorrelation length
The development of CSA refers to the process in which moist and dry regions grow as their spatial scale increases (Craig and Mack 2013). To quantify the spatial length scale of CSA, Windmiller and Craig (2019) have proposed using the spatial autocorrelation length. The first step is to create the binary field for calculating the autocorrelation map. The binary field is determined by the criteria of the 20th and 80th percentiles of precipitable water for dry and moist regions, respectively. In the calculation for the dry region, the area where precipitable water is less than the 20th percentile is defined as 1, and the other regions are filled with 0. Conversely, the areas with precipitable water greater than the 80th percentile are set to 1 for the moist region calculation (see online supporting materials for detail, Fig. S1). The spatial autocorrelation function is calculated using convolution on the hourly binary field of precipitable water in spectral space. Then, the spatial scale for the two regions is defined as the root-mean-square radius of the area where the autocorrelation is greater than e−1.
2) Vertically integrated moist static energy variance budget
3) Isentropic analysis
4) Object-based analysis
The object-based analysis method is used to investigate differences in convective variability between SCALE and VVM. This method has been used to study the changes in the convective structure among different environments (Tsai and Wu 2017; Su et al. 2019). The definition of cloud objects in this study follows Wu and Chen (2021). Contiguous cloudy grids where the mixing ratio of the total cloud condensates is greater than 10−5 kg kg−1 are three-dimensionally connected and then identified as a convective cloud object using the six-connected segmentation method. We add two additional criteria that the cloud object base is lower than 2 km and cloud-top height is greater than 6 km to select the deep convection, which can largely influence the environment and circulation. These criteria exclude dissipating anvil clouds and new-born systems.
3. Results
a. General evolution of CSA
We visualize CSA by the spatial precipitable water (PW) distribution of ensemble member 1 (en1) of SCALE (Fig. 1a) and VVM (Fig. 1b) in the equilibrium state, and animations of each simulation can be found in supporting materials (Movies S1 and S2). A clear structure that a moist region surrounded by a dry area can be seen in both models. PW in the moist region reaches 56 mm in VVM, which is significantly greater than that in SCALE (42 mm). PW in both models is similar in the dry areas, but PW in some small regions can be less than 10 mm in SCALE. All members have similar horizontal moisture structures in both SCALE and VVM. The evolutions of domain-averaged PW, liquid water path (LWP), and ice water path (IWP) are compared in Figs. 1c and 1d. The domain-averaged PW declines as the time proceeds in both models, and they reach a quasi-steady state after day 40. LWP similarly evolves in both models throughout the transition toward CSA. IWP in VVM significantly increases before day 20 and then settles to equilibrium, while a smaller temporal variation of IWP is found in SCALE. The difference in IWP suggests that VVM undergoes a drastic transition of cloud structures during the development of CSA. PW, LWP, and IWP in VVM are slightly greater than those in SCALE in the equilibrium state.
Horizontal distribution of daily averaged precipitable water (mm) on day 48 of the first ensemble member for (a) SCALE and (b) VVM. The time evolutions of domain-averaged precipitable water (PW), liquid water path (LWP), and ice water path (IWP) for (c) SCALE and (d) VVM. The time series of the spatial standard deviation of PW across the entire domain (PW_std) and the dry area fraction (DRYFRAC) for (e) SCALE and (f) VVM. The solid lines show the ensemble averages of each variable, and the attenuated lines show each ensemble member.
Citation: Journal of the Atmospheric Sciences 80, 8; 10.1175/JAS-D-22-0250.1
We apply the dry fraction and the standard deviation of PW (PWstd) to identify the differences in the degree of CSA between the two models (Figs. 1e,f). The dry fraction (DRYFRAC) is defined as the fraction of areas where precipitable water is lower than 30 mm under 300 K SST conditions (Yanase et al. 2020). The evolution of DRYFRAC shows that CSA in VVM rapidly grows on days 15–25, while CSA in SCALE develops gradually. The rapid development in VVM coincides with the drastic fluctuation of IWP, and the cloud cover also has similar evolution to IWP (not shown). This indicates that it might be associated with the changes in cloud structures. On the other hand, the growth of PWstd is ahead of the increase of DRYFRAC in both models, and the rapid growth in VVM becomes clearer. PWstd in the equilibrium state show that VVM has greater spatial moisture contrast compared to SCALE. The smaller moisture contrast in SCALE is due to the less PW in the moist region (Fig. 1a). The two metrics show that CSA development is rapid in VVM, and CSA in VVM is more aggregated than that in SCALE. The above results are consistent in each member with small ensemble spreads, which shows the robustness of SCALE and VVM taking different pathways toward CSA.
b. Development of CSA
CSA development accompanies the horizontal expansion of dry and moist regions, which can be identified by the spatial autocorrelation length of the moisture field (Windmiller and Craig 2019; Hung and Miura 2021). We show the evolution of the length for moist and dry regions to investigate the different pathways between the two models (Figs. 2a,b). In SCALE, the length scales for the two regions increase gradually before day 10 (Fig. 2a) with a small spread for each member. On days 10–15, the length of the dry region evolves with different growth rates, while the length of the moist region remains at 30 km consistently in all members. A consistent result across ensemble members is that the length of the dry region always picks up earlier than that of the moist region, suggesting that dry region expansion is evident in SCALE. The linear growth of the dry region length is similar to the evolution of PWstd (Fig. 1e), which also indicates that dry region expansion is critical for CSA development in SCALE.
Time evolutions of the autocorrelation length scale of dry (blue) and moist (red) regions for (a) SCALE and (b) VVM. The spatial autocorrelation length of the two regions is calculated using the criteria of 0.2 and 0.8 quantiles, respectively. The solid lines are the ensemble mean, and the evolutions of dry and moist regions for each member are shown by the attenuated lines paired with the same line style.
Citation: Journal of the Atmospheric Sciences 80, 8; 10.1175/JAS-D-22-0250.1
In VVM, the length of the two regions drastically increases before day 10 (Fig. 2b). In this period, the growth of the dry region length has a large spread among the ensemble members. In contrast, the length of the moist region in all members starts their increase on day 6. The sharp transition of the length on days 6–10 corresponds to the increase in IWP (Fig. 1d), and the increase in PWstd follows the transition of the length with a delay of a few days. The result suggests that CSA development is less sensitive to the dry region in VVM, and changes in convective structures in the moist region could play an important role in CSA development in VVM.
The VI-FMSE variance budget is used to investigate the contributions of each diabatic process from dry to moist regions, which are divided into five regions with an interval of 0.2 quantile PW. The results are consistent in all members of each model, so we only show the evolution of en1 (see supporting material for other members). In the first few days, both models have a large tendency contributed from the advective term because of the spinup from the calm initial state. In SCALE, the total tendency of VI-FMSE decreases with time from day 5 to day 20, and the tendency is mainly contributed by LW and SEF terms (Fig. 3a). The advection term in SCALE becomes negative after day 7, and the SW term remains constant close to zero throughout the simulation. We focus on the two terms positively contributing to CSA development. The decompositions of SEF and LW terms show that the driest and moistest regions have greater contributions to VI-FMSE variance compared to other areas during CSA development in SCALE (Figs. 3c,d).
Time evolutions of each term in vertically integrated moist static energy (VI-FMSE) variance budget for (a) SCALE and (b) VVM. All the terms are normalized by the domain-averaged VI-FMSE variance. The decomposition of SEF term from driest 20% quantile to moistest 20% quantile with an interval of 20% for (c) SCALE and (d) VVM. (e),(f) As in (c) and (d), but for the LW term. Only the first ensemble member is shown here (see supplemental material for other members).
Citation: Journal of the Atmospheric Sciences 80, 8; 10.1175/JAS-D-22-0250.1
In VVM, the contributions come from LW and SEF terms on days 5–10, and the advective term becomes dominant on days 11–20 (Fig. 3b). The decomposition shows that SW and LW in VVM significantly contribute from the moistest 20% areas on days 5–10 (Figs. 3df). The greater SEF term in the moistest region is caused by enhanced surface fluxes via stronger surface wind. The larger LW term is due to more high cloud coverage in the moistest area, which is consistent with the increase in IWP in days 5–10 in VVM (Fig. 1d). Ice clouds can reduce the longwave radiative flux emitting to the space in the moist region, which positively contributes to CSA development (Wing and Emanuel 2014; Holloway and Woolnough 2016). After day 10, these two terms become minor, and the increased advective term indicates that the convective systems can drive circulation to enhance VI-FMSE variance in VVM.
The autocorrelation length analysis and VI-FMSE variance budget provide detailed evolutions of CSA development in SCALE and VVM, especially in the initiation and earlier stage. We briefly summarize the key differences between the two models:
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The autocorrelation length analysis suggests that the dry area initiates CSA development in SCALE. VI-FMSE variance budget shows that the dry and moist regions contribute to the increase in VI-FMSE variance through SEF and LW terms in SCALE. The results indicate that the development of the dry region plays an important role in CSA development in SCALE.
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In VVM, the increase in the length of the moist region corresponds to the increase in domain-averaged IWP and the large LW and SEF terms in the moist region on days 6–10. This suggests that the convective systems in the moist region play a major role in CSA development. Conversely, the growth of the length of the dry region does not correspond to any variables, and both SEF and LW terms in the dry region are smaller. These results indicate that the contribution of the dry region is relatively minor.
c. Evolution of CSA in the isentropic space
The isentropic distributions of initial (days 6–10, Figs. 4a,b), developing (days 21–25 in Figs. 4c,d), and mature stages (days 36–40 in Figs. 4e,f) are presented to discuss differences in CSA development between two models. The differences between the two models are similar in all ensemble members, so we compare the two models using en1 (see supporting materials for other members). On days 6–10, the isentropic distributions are single peak with maximum occurrences around the mean θei profile. The subsiding mass fluxes coinciding with the high occurrences indicate that the subsidence occurs in vast areas (∼95% areas in both SCALE and VVM), and convection develops in limited areas. SCALE has wider isentropic distributions for the altitudes between 1 and 8 km during days 6–10 because dry areas start to expand (Fig. 4a). In VVM, CSA does not develop yet, so isentropic distributions are concentrated and close to the domain-averaged θei profile (Fig. 4b). On days 21–25, both models have a shift of the isentropic distributions toward lower θei values (Figs. 4c,d), which reflects the expansion of dry areas during the CSA development. The isentropic distributions in both models become a bimodal structure between 2 and 6 km, corresponding to the subsiding mass transport. One peak with θei lower than the domain average represents the dry region, and the other peak is located in the region with higher θei, which would be the clear-sky moist region. The subsidence dries the environment when the CSA develops, so the peak of the moist region decreases with an increase in the frequency of the dry region on days 36–40 in both models (Figs. 4e,f).
Isentropic analysis of (left) SCALE and (right) VVM for (a),(b) days 6–10, (c),(d) days 21–25, and (e),(f) days 36–40. The solid black line represents the mean frozen equivalent potential temperature (θei) and the color shading represents the logarithmic probability density function of θei. The contours present the isentropic mass fluxes with the levels of ±0.00151, ±0.003, and ±0.006 kg m−2 K−1. The solid lines represent the positive mass flux, while the dashed lines indicate the negative mass flux. The upper-left inset in each panel is temperature tendency due to radiation in the same sampling period as the isentropic distribution. Only the first ensemble member is shown here (see supplemental material for other members).
Citation: Journal of the Atmospheric Sciences 80, 8; 10.1175/JAS-D-22-0250.1
Notable differences can be found in the evolutions of the isentropic distributions between SCALE and VVM. In the boundary layer, the upward mass flux occurs between 345 and 350 K θei throughout the integration in VVM (Figs. 4b,d,f), while the upward motion in SCALE shifts from 345 to 335 K θei when CSA develops (Figs. 4a,c,e). The difference indicates that the boundary layer moisture in the convective region decreases during the CSA development in SCALE, but this phenomenon does not occur in VVM. This indicates that the boundary layer parcels gain less surface enthalpy flux in the dry region in SCALE.
The subsiding mass flux in both dry and moist regions in SCALE is stronger than that in VVM. In SCALE, the peak of the dry region has significant radiative cooling, especially at the top of the boundary layer in the developing and equilibrium stages (Figs. 4c,e). The peak of the moist region with the subsidence is evident in SCALE, which suggests that, in the physical space, the parcels ascending in the moist region would subside in the adjacent region. These characteristics suggest that the CSA circulation in SCALE is mainly contributed by the subsidence drying due to radiative cooling, and the contribution of convection is limited in the moist region. This feature cannot be observed in VVM, in which both occurrence and downward mass fluxes in the moist region are greatly reduced in the equilibrium stage (Fig. 4f). Weaker radiative cooling in the dry region and less downward transport in the moist region indicates that convective systems are sufficient to drive the circulation between the moist and dry regions. The results show that strong radiative cooling and fewer surface fluxes in the dry region are critical for CSA development in SCALE, while convective systems are able to support CSA development.
We focus on the upward mass flux region in the isentropic diagram to investigate how convective systems are able to drive CSA development. A transition of the vertical structure of upward mass flux can be found in VVM. Even though the upward region in the boundary layer remains in a similar location in the diagram, the vertical tilting structure becomes steeper as time proceeds (Figs. 4b,d). The vertical structure of upward mass flux in SCALE has no significant change, even with a shift of the position in the isentropic diagram (Figs. 4a,c). The θei is conserved in the convective cloud, so the vertical structure of upward mass flux means should not be vertical. The tilting structure means that convective clouds are influenced by the entrainment of environmental dry air. The tilting vertical structure in VVM indicate that the convection on days 6–10 is highly influenced by the entrainment (Fig. 4b). The impacts of the entrainment are reduced when CSA continues developing from days 6–10 to days 21–25 (Fig. 4d). The cloud size can largely influence the effect of dry air entrainment. Large clouds have more inner parts, which is protected from the influence of environment air, so that the effect of entrainment is reduced when the cloud size increases. The negative relationship between entrainment rate and convective system size is validated by large eddy simulations (Hernandez-Deckers and Sherwood 2018) and satellite observation (Takahashi et al. 2017). The change in the isentropic diagram in VVM would be associated with the change in convective cloud sizes, while this feature is not significant in SCALE.
d. Convective variability
The cloud size spectra sampled per five days are presented to demonstrate different transitions of convective clouds between SCALE (Fig. 5a) and VVM (Fig. 5b). The evolution of the size distribution shows that the size of convective clouds tends to be smaller than 10 km in both models. When CSA develops, the size distributions in both models become a bimodal distribution with peaks of smaller and larger sizes, and the bimodal distribution in VVM is more obvious than that in SCALE. The large-size peak splits from the small-size peak and shifts to about 50 km gently on days 6–30 in SCALE, while the large-size peak in VVM leaps to 50 km on days 6–10. The appearance of convective systems on the scale of 50 km in VVM is consistent with the rapid growth of the spatial autocorrelation length in the moist region (Fig. 2b) and the sharp increase of IWP (Fig. 1d). The result indicates that the initiation of CSA in VVM is associated with the upscale process of convective systems, which increases the horizontal extent of ice anvil clouds. In VVM, the large clouds develop more frequently as time evolves. The increased frequency of large clouds is limited in SCALE (Fig. 5a), and the occurrence of the large systems is half that in VVM after day 30.
Time evolutions of the cloud size occurrence frequency for (a) SCALE and (b) VVM are shown by the color shading with 5-day intervals in the upper part of each panel. Only the first ensemble member is shown here (see supplemental material for other members). The lower part of the panels presents the time evolutions of column flux divergence of dry static energy (DSE-div; unit: 106 J m−2 s−1) in the moist region where PW is greater than 30 mm. The black lines are the ensemble average, the gray lines are for each ensemble member, and the red line represents the first ensemble member.
Citation: Journal of the Atmospheric Sciences 80, 8; 10.1175/JAS-D-22-0250.1
The large size of convective clouds is the reason for the ability of VVM to efficiently drive circulation from the moist region to the dry region. With smaller convective clouds in SCALE, the subsidence can occur in the moist region without convective systems, which corresponds to the subsidence nearby the upward motion in the isentropic diagram. This leads to lower efficiency in driving circulation, so radiative cooling dominates the development of CSA in SCALE. The efficiency of convective clouds in driving circulation is quantified by the divergence of the column-integrated dry static energy (DSE-div) in the moist region where PW is larger than 30 mm. The increase of DSE-div accompanies by the gentle shift of the large-size peak in SCALE (Fig. 5a), while the rapid growth of DSE-div follows the appearance of large convective clouds in VVM (Fig. 5b). The growth of DSE-div in VVM is consistent with the period that the advective term dominates in VI-FMSE variance budget (Fig. 3b). After day 30, the exports of DSE in the moist region are greater in VVM, and the greater exports accompany with the frequent occurrence of larger convective clouds. The result suggests that the efficiency in driving circulation between moist and dry regions is associated with the size distribution of convective systems, and large-size systems in VVM largely contribute to the development of CSA compared to SCALE. Based on the isentropic analysis and convective cloud size statistics, we summarize our findings as follows:
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When CSA develops in SCALE, the stronger radiative cooling and less surface enthalpy flux lead to the dry region being drier than that in VVM, and the drier condition further enhances radiative cooling, especially at the top of the boundary layer. The enhanced cooling then drives stronger subsidence and the boundary layer circulation from the dry region to the moist region, which pushes the moist region aggregating. The development associated with radiative cooling and a drier environment is in terms of the dry-radiation pathway.
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In VVM, CSA development initiates from the transition of convective system size in the moist region, which accompanies the increase in high clouds on days 5–10. The high clouds reduce the loss of longwave radiation in the moist region, which leads to a more unstable environment and frequent occurrence of large-size systems. On days 11–20, the circulation is enhanced due to more large-size convective systems, which dominates CSA development. The development controlled by the upscaling of convection is named the convection-upscaling pathway.
4. Mechanism-denial experiment and convective variability
a. Mechanism-denial experiment
We design mechanism-denial experiments in SCALE and VVM to support our analyses of convective variability in CSA. In SCALE, the feedback between radiative cooling, boundary layer circulation, and the supply of surface enthalpy flux in the dry region plays important roles in CSA development. To counteract the two effects, we set the minimum wind speed to 3 m s−1 in surface fluxes calculation to enhance the surface enthalpy flux in the dry region. The experiment is simplified as SCALE_U3. Increasing moisture can reduce the effect of radiative cooling at the boundary layer top, while more sensible heat can make the air buoyant to weaken the radiative-driven circulation. We compare SCALE_U3 with the first ensemble member (SCALE_en1) because the same random noise is applied. The domain-averaged PW only decreases to 37 mm in SCALE_U3, and the value is 15 mm greater than that in SCALE_en1 (Fig. 6a). The result shows that CSA in SCALE becomes less aggregated, and its development is slower than SCALE_en1. The expansion of the dry region becomes slower, which can also be seen in the animation (Movie S3). The evolution of DRYFRAC shows that the dry region in the sensitivity cannot sufficiently expand as SCALE_en1 (Fig. 6a). The autocorrelation length analysis shows that the length of the dry region grows slower (Fig. 7a). The smaller length of the moist region and more frequent occurrence of small-size systems indicate that the upscale process of convective systems is virtually absent without the sufficient dry expansion of the dry area (Figs. 7a,c). These results suggest that SCALE takes the dry-radiation pathway toward CSA, and the convective variability reflects the change in the feedback in the dry region.
(a) Time evolutions of precipitable water for the first ensemble member and mechanism-denied experiments. (b) As in (a), but for DRYFRAC.
Citation: Journal of the Atmospheric Sciences 80, 8; 10.1175/JAS-D-22-0250.1
Time evolution of the spatial autocorrelation length as Fig. 2 for (a) SCALE_U3 and (b) VVM_nohcrad. Evolutions of cloud size occurrence frequency (upper part) and DSE-div (lower part) as Fig. 5 are shown for (c) SCALE_U3 and (d) VVM_nohcrad.
Citation: Journal of the Atmospheric Sciences 80, 8; 10.1175/JAS-D-22-0250.1
CSA development in VVM is controlled by the upscale process of convective clouds, and the radiative effect due to high clouds is the critical factor for the upscale process of convective clouds in VVM. Thus, we eliminate the high-cloud radiative effect by making the clouds above 500 hPa transparent in radiative transfer calculations, which is simplified as VVM_nohcrad. VVM_nohcrad is compared to the first ensemble member (VVM_en1). The decline of the domain-averaged PW is slower and less compared to VVM_en1 (Fig. 6a). DRYFRAC of VVM_nohcrad has a similar growth on days 15–20, but it only grows to 0.5 (Fig. 6b). The evolutions show that CSA becomes less aggregated in VVM_nohcrad. The autocorrelation length of the dry region becomes longer than that of the moist region (Fig. 7b). The occurrence of large-size convective systems is largely reduced, which indicates that the upscale process is less significant (Fig. 7d). The upscale process is the result of interactions between dynamics and physics. The result show that the high-cloud radiative effect is the main factor contributing to the upscale process, so the upscale of convection is largely suppressed when high clouds become transparent. Some features of time evolutions in VVM_nohcrad, such as the timing of DRYFRAC growth, are similar to the VVM_en1. Overall, the results demonstrate that the upscale process is critical for CSA development in VVM.
b. Role of convective variability
The diagnostics of the cloud size spectrum and the spatial autocorrelation length provide a linkage between convective variability and pathways toward CSA. More frequent occurrences of large-size systems can more effectively control CSA development from the moist region, which is consistent with the growth of the length scale of the moist region. VVM_nohcrad shows that the dry region becomes more dominant when the upscale process is insignificant (Fig. 7b), so the ability of the moist region to drive circulation is weaker (Fig. 7d). The convection-upscaling pathway in VVM changes to the dry-radiation pathway due to the weakening of the upscaling process. The result shows that the convective variability is highly related to CSA circulation. This is consistent with the findings from satellite observations that the large-size or organized convective systems can strongly modulate large-scale circulation and environment (Yuan and Houze 2010; Tobin et al. 2012; Hamada et al. 2014; Chen et al. 2021; Tsai and Mapes 2022). From the model simulations, Hung and Miura (2021) pointed out that the organization index responds rapidly in the shorter time scale during CSA development, while the spatial moisture variance and subsidence fraction establish on a longer time scale. Their results hint at the relationship between the convective organization and spatial moisture difference and subsidence. In this study, we demonstrate that the convective variability in the cloud size spectrum can lead to different pathways toward CSA. The evident upscale process due to the high-cloud radiative effect results in the convection-upscale pathway in VVM, while the weaker upscale process makes radiative cooling in the dry region dominant, which leads to the dry-radiation pathway in SCALE.
5. Summary
In this study, RCE simulations are conducted using two CRMs (SCALE and VVM) with five ensemble members to focus on the development of CSA following the RCEMIP protocol (Wing et al. 2020). The minimal setups of the horizontal domain and resolution for CSA development are adopted from Yanase et al. (2020). A series of convective variability analyses are performed to untangle the key mechanism responsible for different pathways to CSA in both models. We apply the autocorrelation length analysis and find that CSA initiates in the dry region in SCALE, while the moist region is more important for CSA in VVM. VI-FMSE variance budget analysis also shows that convective clouds in the moist region have a large contribution to VI-FMSE variance growth in VVM. We further use isentropic analysis and the statistic of convective cloud size to clarify the mechanisms responsible for CSA development in SCALE and VVM. Our results show that the two models have very different mechanisms that drive CSA development. In SCALE, the interactions between radiative cooling, surface fluxes, and boundary layer circulation in the dry region play a critical role in CSA development. In VVM, CSA development is associated with the spatial upscale of convective clouds, which can enhance the circulation between moist and dry regions.
Based on these findings, we perform mechanism denial experiments to support our analyses on the role of convective variability for CSA development in both models. In SCALE, the minimum wind speed is set to 3 m s−1 to counteract the feedback in the dry region. In VVM, the high-cloud radiative effects are turned off by making high clouds transparent in radiation calculation. We obtain a less aggregated state compared to the original settings. The results support our analysis of identifying mechanisms responsible for CSA development in the two models. The mechanism denial experiments changes the convective variability and then suppress CSA development. The results suggest that the convective variability plays an important role in CSA development. The difference in the convective variability between SCALE and VVM results from complicated interactions between quite different treatments of physics and dynamics. Further investigations and sensitivity tests are necessary to identify which physics parameterization is mainly responsible for the difference in convective variability.
This study investigates the mechanism for CSA development in different models under 300 K SST conditions. The different mechanisms can have different sensitivity to SST changes, and the sensitivity of mechanisms to SST could help to understand the large spread in the RCEMIP ensemble (Wing et al. 2020). In the future, we will investigate the sensitivity of mechanisms for CSA with more focus on the equilibrium state. On the other hand, studies of RCE simulations using large-domain CRM showed that the results are also sensitive to domain size when the horizontal scale is large enough (Patrizio and Randall 2019; Matsugishi and Satoh 2022). As the domain size increases, multiple aggregated cells could appear due to the fact that the length of the domain is greater than the spatial scale that a single CSA cell can influence. The spatial scale of CSA cells would be sensitive to different convective variabilities among models. In VVM, convective clouds are larger and can influence a vaster region, so the multicell structure would appear when the domain size increases to a larger area. Such large domain simulations of CSA can be used to link to cyclogenesis and MJO. The different pathways caused by convective variability can help us understand the model sensitivity in simulating cyclones or MJOs.
Acknowledgments.
We thank Prof. Wei-Ting Chen for providing valuable discussions on this study. Jin-De Huang and Chien-Ming Wu were supported by Taiwan’s NSTC through Grant 111-2111-M-002-012 to National Taiwan University and Grant NTU-112L7832. Ching-Shu Hung and Hiroaki Miura were supported by JSPS KAKENHI Grants JP16H04048 and JP20H05729. We thank the National Center for High-Performance Computing (Taiwan) and The University of Tokyo (Japan) for providing computational and storage resources.
Data availability statement.
The two models used in this study can be obtained from https://scale.riken.jp/ (SCALE, version 5.3.6) and https://doi.org/10.6084/m9.figshare.14866260.v1 (VVM, version 1.5.1). The postprocessing data and plotting scripts are available in the online open-access repository (https://doi.org/10.6084/m9.figshare.11933091).
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