Editorial Type:
Article
Article Type:
Research Article

The Role of Cloud–Cloud Interactions in the Life Cycle of Shallow Cumulus Clouds

Jingyi Chen aPacific Northwest National Laboratory, Richland, Washington

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https://orcid.org/0000-0001-6347-5677
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Samson Hagos aPacific Northwest National Laboratory, Richland, Washington

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Zhe Feng aPacific Northwest National Laboratory, Richland, Washington

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Jerome D. Fast aPacific Northwest National Laboratory, Richland, Washington

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Heng Xiao aPacific Northwest National Laboratory, Richland, Washington

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Online Publication:
10 Feb 2023
Print Publication:
01 Mar 2023
DOI:
https://doi.org/10.1175/JAS-D-22-0004.1
Page(s):
671–686
Free access

Abstract

Some of the climate research puzzles relate to a limited understanding of the critical factors governing the life cycle of cumulus clouds. These factors force the initiation and the various mixing processes during cloud life cycles. To shed some light into these processes, we tracked the life cycle of thousands of individual shallow cumulus clouds in a large-eddy simulation during the Holistic Interactions of Shallow Clouds, Aerosols, and Land-Ecosystems field campaign in the U.S. southern Great Plains. Concurrent evolution of clouds is tracked and their respective neighboring clouds are examined. Results show that the clouds initially smaller than neighboring clouds can grow larger than the neighboring clouds by a factor of 2 within 20% of their lifetime. Two groups of the tracked clouds with growing and decaying neighboring clouds, respectively, show distinct characteristics in their life cycles. Clouds with growing neighboring clouds form above regions with larger surface heterogeneity, whereas clouds with decaying neighboring clouds are associated with less heterogeneous surfaces. Also, those with decaying neighboring clouds experience larger instability and a more humid boundary layer, indicating evaporation below the cloud base is likely occurring before those clouds are formed. Larger instability leads to higher vertical velocity and convergence within the cloud, which causes stronger surrounding downdrafts and water vapor removal in the surrounding area. The latter appears to be the reason for the decaying neighboring clouds. Understanding those processes provide insights into how cloud–cloud interactions modulate the evolution of cloud population and into how this evolution can be represented in future cumulus parameterizations.

© 2023 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Jingyi Chen, jingyi.chen@pnnl.gov

Abstract

Some of the climate research puzzles relate to a limited understanding of the critical factors governing the life cycle of cumulus clouds. These factors force the initiation and the various mixing processes during cloud life cycles. To shed some light into these processes, we tracked the life cycle of thousands of individual shallow cumulus clouds in a large-eddy simulation during the Holistic Interactions of Shallow Clouds, Aerosols, and Land-Ecosystems field campaign in the U.S. southern Great Plains. Concurrent evolution of clouds is tracked and their respective neighboring clouds are examined. Results show that the clouds initially smaller than neighboring clouds can grow larger than the neighboring clouds by a factor of 2 within 20% of their lifetime. Two groups of the tracked clouds with growing and decaying neighboring clouds, respectively, show distinct characteristics in their life cycles. Clouds with growing neighboring clouds form above regions with larger surface heterogeneity, whereas clouds with decaying neighboring clouds are associated with less heterogeneous surfaces. Also, those with decaying neighboring clouds experience larger instability and a more humid boundary layer, indicating evaporation below the cloud base is likely occurring before those clouds are formed. Larger instability leads to higher vertical velocity and convergence within the cloud, which causes stronger surrounding downdrafts and water vapor removal in the surrounding area. The latter appears to be the reason for the decaying neighboring clouds. Understanding those processes provide insights into how cloud–cloud interactions modulate the evolution of cloud population and into how this evolution can be represented in future cumulus parameterizations.

© 2023 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Jingyi Chen, jingyi.chen@pnnl.gov
Keywords: Boundary layer; Clouds; Convective clouds

1. Introduction

Warm convective clouds play an essential role in the energy and moisture redistribution in the boundary layer and serve as the seed for deep convection. However, representation of these clouds in large-scale models is affected by the discrepancy between coarse model grid size and small cloud size, and large uncertainty in cloud modeling. Many traditional cumulus parameterization schemes focus on “relating the statistical properties of a cumulus cloud ensemble to the large-scale variables, and thereby to obtain a closed system of prognostic equations for the large-scale variables” (Arakawa and Schubert 1974). When the spatial resolution of the climate model increases, the parameterized convection goes from smoothly behaving from a fully sampled population to a more discrete behavior for a significantly subsampled population and eventually to a binary behavior of every single cloud (i.e., growth or decay). Hence, understanding how cloud–cloud interactions could be represented in future cumulus parameterizations is an important topic to explore.

Observations indicate that thermodynamic instability influences the spatial distribution and temporal evolution of shallow convective clouds via cloud-base forcings (Dagan et al. 2018). The cloud-base forcing is critical to the evolution of the convective clouds. Cloud-base mass flux for the ensemble of subgrid clouds is a commonly used variable in describing the net effect of the forcing in many plume models (Arakawa and Schubert 1974; Grell 1993; Krishnamurti et al. 1983; Hagos et al. 2018). Sakradzija and Hohenegger (2017) found that the partitioning of the surface turbulent fluxes into sensible and latent heating controls the shape of cloud-base mass flux distribution, which shows similarity with the shape of cloud size distribution. Cloud-base vertical velocity (w) is another factor because it accounts for the subgrid-scale horizontal variability, which has a direct connection to cloud droplet size distribution and aerosol–cloud interactions (Donner et al. 2016). Fletcher and Bretherton (2010) and Zheng et al. (2021) showed the dependence of cloud-base w on the mixing-layer turbulent kinetic energy (TKE) via numerical simulations and observations, respectively. Fletcher and Bretherton (2010) showed that the simulation that incorporates the relationships between cloud-base w and mixing-layer TKE outperformed other convective schemes.

Entrainment is the primary process through which environmental and cloudy air are mixed. It is a first-order mechanism that governs the depth to which clouds penetrate and affects the vertical profile of heat, humidity, and momentum (Bretherton et al. 2004; Brast et al. 2016). Since Stommel (1947) presented the fundamental framework of cumulus convection with updraft air that entrains environmental air, lateral entrainment mixing has been recognized as another critical process in the interactions between cumulus clouds and their environment (de Rooy et al. 2013). Heus et al. (2008) studied shallow clouds using large-eddy simulations (LES) and particle trajectories and found that virtually all mixing occurs laterally with little cloud-top mixing. Morrison et al. (2020) and Peters et al. (2020) suggested that thermal chain structures in cumulus updrafts is strongly influenced by lateral entrainment mixing below the level of maximum w. Moreover, progress has been made on estimating the properties of entrained air and entrainment rate (Lu et al. 2012; Jensen and Del Genio 2006; Romps 2010; Dawe and Austin 2011; Gregory 2001; Kirshbaum and Larmer 2021; Eissner et al. 2021; Stevens 2002; Becker et al. 2018). An important question is, as framed by Romps and Kuang (2010), what affects the state of cloud updraft? Are the initial conditions at cloud base more important than lateral entrainment? This question is referred to as “nature versus nurture” in subsequent studies. Romps and Kuang (2010) found that the correlations of in-cloud properties with cloud-base state go to zero a few hundred meters above cloud base where the correlations with entrainment are large. Dawe and Austin (2012) used a tracking algorithm in the shallow cloud field and found that thermodynamic properties of clouds are primarily influenced by entrainment and detrainment processes while cloud area and height are primarily influenced by cloud-base properties.

Above discussed studies emphasize the importance of lateral processes in the development of convection and most of these studies focus on one of the following two questions: 1) How do clouds impact the environment, and 2) how does the cloud environmental field (i.e., below cloud-base instability and environmental entrained air) impact the evolution of clouds? Few studies have examined the two questions together to understand how clouds impact the evolution of other cloud nearby. In other words, assuming clouds form in the same environmental fields, do all the clouds grow and dissipate at the same rate (i.e., no cloud–cloud interactions)? Does the presence or absence of other clouds affect the life cycle of a given cloud? Does the existing shallow cloud inhibit the growth of other clouds or favor that (i.e., with a certain pattern of cloud–cloud interactions)? These questions are important to understand how the evolution of shallow cloud depends on existing clouds, which has not been addressed yet.

Existing convection parameterizations typically assume an ensemble of steady-state plumes (e.g., Squires and Turner 1962). However, there has been a longstanding debate over whether the nature of moist convection in the atmosphere is plume-like or bubble-like (e.g., Yano 2014; Romps et al. 2021). The traditional assumptions related to the plume framework for convection parameterizations have been shown to contribute to the uncertainty in estimating the entrainment mixing (e.g., Romps 2010; Hannah 2017). Many previous studies showed that individual bubbles (i.e., thermals), each with distinctive toroidal circulations and local w maxima near their centers, rise in succession within clouds (e.g., Raymond and Blyth 1989; Damiani and Vali 2007; Moser and Lasher-Trapp 2017). Those bubbles within the same clouds interact and form a “thermal chain” structure (Morrison et al. 2020; Peters et al. 2020). In those studies, only bubbles in the same clouds defined by the same cluster of liquid or solid phase water mixing ratio were discussed. Adjacent bubbles in separate clouds could also interact to form separate clouds, but these interactions have not been studied.

In this paper, we track thousands of clouds throughout their lifetime and statistically examine their spatial interactions with surrounding clouds. Section 2 provides an overview of the case study, model configurations, and the postprocessing tracking algorithm. Section 3 illustrates the role of cloud-base fluxes and neighboring clouds on the evolution of the cloud life cycle. Section 4 presents the conclusions and discussion.

2. Method

a. Case description and model settings

The Holistic Interactions of Shallow Clouds, Aerosols, and Land-Ecosystems (HI-SCALE) field campaign (Fast et al. 2019a) was designed to provide measurements for understanding the life cycle of shallow clouds by coupling measurements of cloud macrophysical and microphysical properties to land surface properties, ecosystems, and aerosols. Among the days with shallow clouds within the two 4-week intensive observational periods, this study focuses on 30 August 2016. On that day, clouds associated with a trough of low pressure propagated from New Mexico to western Kansas, but clear-sky conditions prevailed over most of eastern Oklahoma and southeastern Kansas in the early morning. Shallow cumulus clouds formed in the late morning. Some of those shallow cumuli transitioned to cumulus congestus and deep convection during the afternoon. Fast et al. (2019b) conducted LES with the Weather Research and Forecasting (WRF) Model with interactive land surface parameterization to simulate the complex population of shallow clouds on this day. They found that the size distribution of the observed shallow cloud population was reproduced only with the realistic variations in soil properties and land use. In this study, we focus on the concurrent evolution of the clouds and their environmental clouds to study the cloud–cloud interactions by using the inner domain simulation with 100 m grid spacing with the realistic variations in soil properties and land use in Fast et al. (2019b).

The simulation includes a 297-km-wide outer domain over central Oklahoma and southern Kansas using a 300 m horizontal grid spacing and a 120-km-wide inner nested domain with a 100 m horizontal grid spacing that encompasses the Atmospheric Radiation Measurement (ARM) Southern Great Plains (SGP) Central Facility sites during the field campaign. Both domains have 304 vertical grid levels extending up to 16.2 km above mean sea level (MSL) with a constant 24 m vertical grid spacing from near the surface up to 6.2 km MSL, and gradually increases above that level. Four soil layers are used by the Interactive Noah land surface parameterization (Chen and Dudhia 2001). The simulation period was between 1200 UTC 30 August (0600 local time) and 0000 UTC 31 August (1800 local time). The default WRF settings are refined by modifying the soil moisture, soil temperature, and land use type. Both ARM and Oklahoma Mesonet stations and Global Land Evaporation Amsterdam Model (GLEAM) satellite data are used to construct the spatial variations of soil moisture. Final Operational Model Global Tropospheric Analyses of the National Centers for Environmental Prediction (NCEP FNL) was imposed on the outer domain to represent the initial and boundary meteorological conditions (National Centers for Environmental Prediction 2000). In this study, we focus on the inner domain to study the interactions among clouds and the influences of the boundary layer conditions on cloud–cloud interactions.

b. Tracking algorithm

To study the life cycle of shallow clouds while they are being advected by the background wind, we take a Lagrangian perspective. Lagrangian tracking algorithms have been used in many previous studies to track the life cycle of individual clouds (Zhao and Austin 2005a,b; Heus et al. 2008; Heus and Seifert 2013; Dawe and Austin 2012; Plant 2009). We use the Flexible object Tracker (FLEXTRKR) algorithm (Feng et al. 2018) to identify 26 617 cloud tracks from 1610 UTC 30 August (0940 LST) to 0000 UTC 31 August (1730 LST). Same as the method used in Fast et al. (2019b), tracking is based on overlapping of cloud masks between two consecutive time steps (i.e., 1 min) to determine whether they represent the movement of the same cloud or not. The cloud masks are defined by liquid water path (LWP) larger than 0.1 kg m−3. Merging and splitting are taken into account to explain the rapid cloud area gain/loss (appendix A). Because we are interested in the clouds that last long enough to form cloud cluster, we only focus on 3179 of the 26 617 cloud tracks to include those clouds larger than 1 km2 (i.e., maximum area in their lifetime), lasting longer than 10 min, and 10 km away from the inner domain boundary.

To illustrate the size and lifetime of our tracked clouds, Fig. 1 shows the joint PDF of the lifetime and the ranges of cloud characteristic length of those 3179 tracks. Here the characteristic length L adopts the convention that L=A where A is the projection area (defined by LWP) of cloud over a horizontal surface. Most clouds have a lifetime shorter than 1 h and a characteristic length between 300 m and 3 km, which means the mesoscale organization and clustering are not considered in this study.

Fig. 1.
Fig. 1.

Joint probability density function of the lifetime (T) and maximum (minimum) cloud characteristic length (L).

Citation: Journal of the Atmospheric Sciences 80, 3; 10.1175/JAS-D-22-0004.1

To better show the life cycle of those tracked clouds, Fig. 2 provides two different examples. The top row shows a short-lived cloud lasting 13 min without rain on the surface. Figure 2c shows the liquid water path when the cloud reaches its maximum size (marked by a green cross in Fig. 2a). Most of the tracked clouds have their lifetime between 10 and 20 min with one peak in size similar to Figs. 2a–c. The bottom row shows a long-lived cloud lasting 124 min with surface rain. It extends up to 6 km and experiences two peaks in the time series of cloud area. Such cloud track with a long lifetime is rare. Our analysis below will focus on the first growing (i.e., G0) and decaying period (i.e., D0) so that the history will not complicate the analysis. Both kinds of cloud tracks are shallow and do not involve ice phase hydrometeor.

Fig. 2.
Fig. 2.

Two examples of the cloud track with the lifetime as (a)–(c) 13 and (d)–(f) 124 min. (a),(d) Time series of cloud area and merging and splitting area. (b),(e) Profiles of cloud-averaged hydrometer mixing ratio at the maximum area. (c),(f) The spatial distribution of LWP at the maximum area. Dotted blue lines donate the phases in their lifetime (see text for details).

Citation: Journal of the Atmospheric Sciences 80, 3; 10.1175/JAS-D-22-0004.1

One common issue related to tracking by horizontal cloud mask (i.e., 2D tracking) is that overlapping untouched clouds are considered to have connectivity, but tracking by considering the vertical morphology of clouds (i.e., 3D tracking) is more expensive from the computational point of view. To clarify how much 2D tracking will bias the cloud identification, we investigate whether this case experiences heavy overlapping at high altitudes. The sensitivities of cloud vertical extent to the assigned gap height between cloud layers is shown in Fig. 3, where the gap height means the height used to separate different untouched cloud layers. When the gap height reaches 1 km, the bottom of the second cloud layer starts to separate from the top of the first layer, so we think 1 km is a reasonably estimated gap height to define the overlapping cloud layers. When the gap height is 1 km and larger, less than half of the tracks contain a second layer (Fig. 3c), and the horizontal cloudy area of the second layer is less than 20% of the bottom main cloud layer (Fig. 3d). Therefore, overlapping is not very common in this case on 30 August. The cloud growth and decaying are assumed to be mainly driven by cloud-base and lateral forcings.

Fig. 3.
Fig. 3.

(a) Cloud-base and cloud-top height of each layer. (b) Depth of each cloud layer. (c) Fraction of overlapping high cloud layers. (d) Averaged fraction of the area of overlapping high cloud layers.

Citation: Journal of the Atmospheric Sciences 80, 3; 10.1175/JAS-D-22-0004.1

3. Results

a. Impacts of cloud-base fluxes

Previous studies of the 30 August case showed that cumulus clouds are driven by the diurnal cycle above heterogeneous surface (Chen et al. 2020). The tracked clouds have lifetimes ranging from 10 min to more than 2 h with the median and 98th percentile of the lifetime at 16 and 45 min (Fig. B1a in appendix B). Figure 4 summarizes the overall evolution of the cloud area growth, mass flux, and length scale as a function of time, normalized by the cloud life cycle duration. Figure 4a shows the time series of cloud area growth rate (i.e., dA/dt), indicating an area growth in the first half of the life cycle and decaying in the second half. Figure 4b shows positive cloud-base mass flux in the first ∼70% of the life cycle. Figure 4c shows an almost symmetric temporal distribution of the length scale. The white dots mark the maximum density after using 2000 bins between 200 and 5000 m. The red line is the fitting curve by using 1050 × sin[απ + (1 − 2α)πx], where x is the relative time ranging from 0 to 1 and α is 0.15. Romps et al. (2021) showed that shallow cumulus (ShCu) could be fit with sin(πx) without a plateau in the middle, indicating those clouds are the bubble-like clouds, which are not plume-like clouds with a steady state. This study confirms their findings that the sine function can be an excellent fitting function for the characteristic length scale. The coefficients are presented here only because we use the actual length scale instead of the normalized length. The value of α is informative; it can measure the selected period of cloud are more bubble-like or plume-like. If α is 0, then it can be assumed to be a bubble-like cloud, and if α is close to 0.5, the times series will be a flat line where the steady-plume hypothesis can be assumed to be valid. Thus, a fitting to the middle of the life cycle will lead to α close to 0.5, indicating plume-like clouds.

Fig. 4.
Fig. 4.

Time series of (a) area growth rate, (b) mass flux, (c) length scale L.

Citation: Journal of the Atmospheric Sciences 80, 3; 10.1175/JAS-D-22-0004.1

The vertical extent of the clouds is shown in Fig. 5. Figure 5a shows an elevated averaged cloud-base height. This elevation is not due to the elevation of the planetary boundary layer (PBL) height because the PBL height does not significantly change in the life cycle of clouds compared to cloud-base height. The slightly decrease of PBL height comes from the disturbances of cold pool on the calculation of PBL height using potential temperature (θ) (Sakaguchi et al. 2021). Studies about the “thermal chain” suggest that upward moving of the thermals leads to more entrainment mixing in the bottom of the thermals, which leads to an elevated cloud-base height (Morrison et al. 2020; Peters et al. 2020). Figure 5a confirms a bubble-like cloud in this case, especially for the clouds with a lifetime shorter than 45 min. Note that the cloud-base height is expected unchanged under the steady-state “plume” assumption. The time series of the cloud vertical extent also follows a nearly sine function. It indicates that the “bubble” expands both horizontally and vertically. The clouds with a lifetime longer than 45 min have a plateau in the time series of their vertical depth and cloud-base height, suggesting that longer-lived cumulus clouds can behave like “plume” during their mature stage.

Fig. 5.
Fig. 5.

Time series of cloud base and cloud depth of the lowest layer. The x axis is the time normalized by the lifetime of each cloud track.

Citation: Journal of the Atmospheric Sciences 80, 3; 10.1175/JAS-D-22-0004.1

Those longer-lived clouds usually have several peaks (Fig. 2d) and involve more complex processes than the short-lived clouds which typically have a single peak. We now examine the in-cloud properties in the first growing stage (i.e., G0) and the first decaying stage (i.e., D0). After applying a first-order low-pass filter with frequency as 0.1 to dA/dt, 2702 of the total 3179 tracks show one growing stage and subsequent decaying stage (Table B1) before disappearing (i.e., G0 + D0 pattern). The lifetime of those tracks with G0 + D0 patterns is shorter than 1 h, and most of the G0 and D0 stages are less than half an hour (Fig. B1). There are more time snapshots falling into G0 in the first half of the cloud life cycle, while more time snapshots into D0 in the second half of cloud cycle (red and blue lines in Fig. B2). Considering that ShCu are affected by the diurnal boundary layer cycle, the longer-lived clouds occur at a slightly later time than the short-lived clouds, but the standard deviation in G0 and D0 with all the lifetime groups are large (Fig. B3). Therefore, we believe the dataset in the subgroups with different lifetime and growth states are not showing the impacts from diurnal cycle in the analysis below.

Figures 6 and 7 show the correlations between cloud-base properties and the area growth rate during the G0 and D0 stage. Those correlations indicate the relative importance of cloud-base forcings. The Spearman rank-order correlation coefficient is used to represent a nonparametric measure of the monotonicity of the relationship between two datasets. For shorter-lived clouds, including lifetimes between 10–16 and 16–45 min, correlations between cloud-base mass flux and dA/dt become negative after 3 and 5 min, respectively. Those tracks with a 10–16 min lifetime show negative correlations between A and dA/dt, while those tracks with 16–45 min lifetime and longer than 45 min lifetime show negative correlations after 2 and 7 min, respectively. The correlations between cloud-base averaged ρw and dA/dt are mostly positive (Fig. 6c). The response time of dA/dt to ρw for a lifetime of 10–16, 16–45, and >45 min is largest at 2, 5, and >10 min, respectively. Overall, during the cloud growth stage, the impact of cloud-base mass flux on dA/dt is the net effect of two relationships: the relatively stronger positive correlations of dA/dt with ρw, and the relatively weaker positive correlations with cloud area. Long-lived clouds are usually associated with a larger area, stronger positive relationships between A and dA/dt, and a stronger positive correlation with cloud-base mass flux than the short-lived clouds. The latter correlation in those long-lived clouds is associated with the plume-like behavior of those clouds compared with short-lived clouds. The dashed lines are the same as the solid lines, except that the first 10 min of dA/dt and the last 10 min of factors (i.e., ρwA, ρw, A) on each trajectory are removed so that all the points on the same dashed line has the same sample size. Slight differences between solid lines and dashed lines indicating different data sampling do not influence the results in G0 stage. Correlations between dA/dt and equivalent potential temperature (θe) (and water vapor mixing ratio qυ) are very similar to that with cloud-base ρw (Figs. 7a,c), which indicates the moisture and energy transported by mass flux are the reason for the cloud area growth. Cloud-base θ has slightly negative correlation with dA/dt during the G0 stage (Fig. 7b) when the lifetime is <45 min, most likely because of less instability from the higher θ anomalies at within subcloud layer.

Fig. 6.
Fig. 6.

Correlation between area growth rate excluding merging and splitting with (a),(d) cloud-base mass flux. (b),(e) cloud area, and (c),(f) cloud mean ρw for (a)–(c) G0 stage and (d)–(f) D0 stage. Dashed lines are the same as solid lines except applying to the same datasets when dealing with lagging. Dots and crosses mark the points with the p values larger than 0.01, indicating statistical insignificance.

Citation: Journal of the Atmospheric Sciences 80, 3; 10.1175/JAS-D-22-0004.1

Fig. 7.
Fig. 7.

Correlation between area growth rate excluding merging and splitting with (a),(d) θe anomalies (b),(e) θ anomalies, and (c),(f) qυ anomalies for (a)–(c) G0 and (d)–(f) D0 stage. Dashed lines are the same as solid except applying to the same datasets when dealing with lagging. Dots and crosses mark the points with the p values larger than 0.01, indicating statistical insignificance.

Citation: Journal of the Atmospheric Sciences 80, 3; 10.1175/JAS-D-22-0004.1

Comparing to the G0 stage, correlations between dA/dt and A are entirely negative during the D0 stage, indicating that larger cloud horizontal area leads to smaller dA/dt (i.e., dissipating faster because dA/dt is mostly negative during the D0 stage) (Fig. 6d). Different sampling by removing the first 10 min of dA/dt and the last 10 min of factors (i.e., ρwA, ρw, A) on each trajectory influences the results in Figs. 6e and 6f, especially for the shorter-lived clouds, which indicates the correlations between cloud-base mass flux and dA/dt are not robust in D0, which might relate to less linkage between cloud-base mass flux and area change during the dissipation phase. In this phase, cloud entrainment mixing and other processes might be more influential than the cloud-base forcings.

b. Impacts of neighboring clouds

When clouds merge, the cloud area experiences a sudden growth, which is one of the important processes affecting cloud development. Splitting is opposite to merging and possibly plays an important role in cloud dissipation. FLEXTRKR takes into account merging and splitting, and the overall frequency of merging and splitting as a function of time is shown in Figs. 8a and 8b. The peak merging frequency occurs around the middle of the life cycle, where clouds have the largest cloud size. A larger merging frequency is associated more with the longer-lived clouds than shorter-lived clouds. This finding is possibly due to long-lived clouds usually having a larger perimeter and/or the long-lived clouds occur at a slightly later time with more clouds in the surrounding area, which increase the chance of coming into contact with other clouds. The splitting frequency is larger toward the end of the cloud life cycle when the clouds are in the dissipating stage. The larger splitting frequency is likely related to weakening of the cloud-base updraft and evaporation of the low LWP region within the cloud. Figure 8c shows the cloud area growth rate due to the net effects from merging and splitting (i.e., Rmer/spl, merged area growth rate–split area growth rate). Merging dominates during the first half of the life cycle, while splitting dominates the rest. Although the merging frequency is the highest in the middle of the cloud life cycle (Figs. 8a,b), the net effects from merging and splitting are minimum during that stage (Fig. 8c). The quasi-steady state during this mature stage is also reflected in the relatively flat temporal trend of L in Fig. 4c. Those tracks with a lifetime > 45 min show large variations in the temporal trends of the Rmer/spl. Still, the overall values are positive, indicating that merging plays positive roles in sustaining those long-lived clouds. The above analysis indicates the frequency of merging and splitting is related to the cloud life cycle stage. Figure 8d shows how the merging and splitting frequency is related to cloud fraction. To gauge the density of cloudy mask around, we define cloud fraction in the rectangles with the size length 8 km larger than the rectangles fitting to the projected cloud masks. Positive Rmer/spl corresponds to the largest cloud fraction and largest variations, while Rmer/spl = 0 corresponds to the smallest cloud fraction and smallest variations. This is possibly related to larger cloud fraction increases the probability for clouds to merge. Splitting often occurs during the dissipation phase of the clouds so that evaporation removes the clouds from the fields and leads to lower cloud fraction.

Fig. 8.
Fig. 8.

(a) Merging frequency with the relative time. (b) Splitting frequency with the relative time. (c) Cloudy-area growth rate due to merging and splitting. (d) Cloud fraction in a box with side length 8 km larger than the box fitting to the projected cloud mask.

Citation: Journal of the Atmospheric Sciences 80, 3; 10.1175/JAS-D-22-0004.1

Besides merging and splitting, shallow clouds are also hypothesized to influence each other by modifying or competing for the resources (i.e., water vapor and buoyancy). Here we examine the relationships between the area growth rate of tracked clouds and their neighboring clouds to test if competition exists. We assume that in the absence of competition the environmental clouds would develop similarly (Fig. C1), due to similar cloud-base forcings. Figure 9 shows the normalized averaged neighboring cloudy area divided by the tracked cloudy area. Datasets are grouped by their lifetime, cloud stage (i.e., G0 vs D0), and neighboring cloud growth status (i.e., growing or decaying). Here neighboring cloud represents those clouds within 2000 m to the edge of the tracked clouds, including both clouds existing in other tracks and those untracked clouds. Only the time with a sample size larger than 20% of the maximum sample size along the time are shown. Thus, the clouds during the G0 period mostly appear in the first half of the life cycle, and those during the D0 appear in the second half. Solid or dashed lines correspond to the subgroups as expanding or shrinking neighboring clouds, respectively. In the first half of the life cycle, Ae,i¯/Ac decreases with time, indicating that the tracked clouds grow quicker than the neighboring clouds, where Ae,i donates the area of each individual neighboring cloud, and Ac is the tracked cloudy area. In contrast, the increasing Ae,i¯/Ac with time during the second half of the life cycle indicates the neighboring clouds dissipate slower than the tracked clouds. This competing effect is apparent regardless of the cloud lifetime, indicating there are several mechanisms responsible for cloud growth at the expense of neighboring clouds. The solid and dash lines correspond to the neighboring cloud state. The competition is weaker when the tracked clouds behave in the same direction as the neighboring clouds (i.e., they both grow or dissipate together), especially when the lifetime is shorter than 16 min. During the mature phase of the clouds (i.e., when the relative time is around 0.5), Ae,i¯/Ac stays flat, indicating that clouds and their neighboring clouds are in a quasi-steady state with weak competition. Longer-lived clouds have more time with the flat Ae,i¯/Ac reflecting sufficient resources (i.e., cloud-base forcings), which is consistent with Fig. 6 that longest-lived clouds have a strong correlation between cloud-base mass flux and dA/dt. The role of the small untracked clouds is discussed in appendix C.

Fig. 9.
Fig. 9.

Normalized environmental cloud size by the tracked cloud size with different lifetime of the tracked clouds.

Citation: Journal of the Atmospheric Sciences 80, 3; 10.1175/JAS-D-22-0004.1

c. Cloud–cloud interactions during cloud growth

In this subsection, we will reveal the processes involved in the coevolution of the ShCu and their neighboring clouds by examining two possible competing mechanisms between a cloud and other clouds that surround it:

  1. The downdrafts surrounding the clouds with convective updrafts might suppress the development of neighboring clouds.

  2. Stronger convergence and convective updrafts within clouds are possibly leading to less water vapor for the overall surrounding environment.

All the time snapshots in all ∼3000 tracks are divided into four groups depending on the growing state (i.e., growth or decay) of the tracked clouds and their neighboring clouds. The group with both tracked clouds and their neighboring clouds growing is thought to have the cloud-mass flux strong enough to maintain the growth of both. The group with both tracked clouds and their neighboring clouds decay is thought to have weak cloud-base mass flux. Two other groups are thought to experience stronger competition with the strength of cloud-base mass flux in the middle: 1) the tracked cloud grows (G0), and the neighboring cloud decays, and 2) the tracked cloud decays (D0) and their neighboring cloud grows.

To reveal the two mechanisms during the G0 stage, we show the vertical profiles of variables compared to a reference state (Fig. 10). Here we define the reference state as the averaged values 5 km away from the cloud edge. We choose 5 km to make sure that the reference state includes neglectable information of the cloud–cloud interactions so that it can represent a typical environmental state during the day with the PBL height at 1.9 km. The surface solar heating leads to large values of buoyancy (Btv) and TKE (Figs. 10a,h) in the PBL. The negative Btv values above the PBL height come from the virtual temperature negative anomalies in the clear region due to the latent heating in the cloud. The values of w and convergence are close to 0 at all altitudes (Figs. 10b,g). The values of qυ, θe, and θ are well mixed in the boundary layer and liquid water mixing ratio (ql) is close to 0.

Fig. 10.
Fig. 10.

Profiles of (a) buoyancy, (b) w, (c) θe, (d) θ, (e) ql, (f) qυ, (g) convergence rate, and (h) TKE at the reference state. The reference state is defined at 5 km away from cloud edge.

Citation: Journal of the Atmospheric Sciences 80, 3; 10.1175/JAS-D-22-0004.1

To understand the first mechanism, we consider Fig. 11, which shows the profiles of w, convergence, and the water vapor mixing ratio of the clouds with growing surrounding clouds in the top row, and the differences between the clouds with growing surrounding clouds and decaying surrounding clouds in the bottom row. The growing or decaying surrounding clouds are defined by whether the cloudy area surrounding the tracked clouds increases or decreases, where the surrounding area is defined to be 2 km away from the tracked cloud edge. We focus on the clouds with a short lifetime (10–16 min) because of the closer linkage between clouds and the boundary layer properties below the cloud base. Only the data in the first 20% and last 20% of the cloud life cycle are used here because those two periods are not steady state and have bubble-like convection. Figures 11a and 11d demonstrate the first mechanism. Figure 11a shows the w anomalies from the subgroups with G0 and growing neighboring clouds. Below cloud base (∼1.3 km), the area directly underneath the cloud mask has the largest w, and the surrounding w decreases with the distance from the cloudy mask. Above cloud base, large in-cloud w leads to downdrafts in the surrounding area with the strongest downdraft in the nearest region to the cloud. Figure 11d shows the differences of w between decaying neighboring clouds and growing neighboring clouds. Those clouds with decaying neighboring clouds have stronger updrafts within the cloud and stronger downdrafts (or weaker updrafts) in the surrounding area at the altitude close to cloud top. That stronger downdraft plays a role in suppressing the growth of the neighboring clouds because the stronger downdrafts (or weaker updrafts) gradually vanish when farther away from the tracked clouds. Figures 11b, 11c, 11e, and 11f examine the second mechanism. In the cloud, convergence occurs in the lower cloudy region and below the cloud base (i.e., below 2 km), while divergence occurs in the upper levels of the cloud. The surrounding column experiences convergence to divergence in lower height from the surface up to ∼3 km altitude. Those clouds with decaying neighboring clouds experience stronger convergence mostly between ∼1500 m and ∼2 km and stronger divergence above (black line in Fig. 11e). The surrounding regions experience less convergence or more divergence below ∼2 km. Those clouds with decaying neighboring clouds have more qυ in the boundary layer but less within the cloudy layer, probably due to weaker convergence. Above analysis based on Fig. 11 supports the two mechanisms.

Fig. 11.
Fig. 11.

Profiles of the anomalies of (a) w, (b) convergence rate, and (c) water vapor mixing ratio (qυ). Profiles of the differences of (d) w, (e) convergence rate, and (f) qυ between the clouds with decaying neighboring clouds and with growing neighboring clouds. Here we only include the datasets in G0 stage with lifetime between 10 and 16 min. The shading in (a)–(c) represents the standard error. The subscript “Denv” donates to the group with decaying neighboring clouds.

Citation: Journal of the Atmospheric Sciences 80, 3; 10.1175/JAS-D-22-0004.1

There are still two questions about the two groups with different neighboring cloud growth states: 1) Why do some regions experience larger w and stronger convergence but others do not? 2) Does more water vapor in the boundary layer only coincide with larger w and stronger convergence? Are the differences between those two groups related to the surface heterogeneity and cold pools (or “ghost” cold pools, which forms from droplet evaporation and rainfall draft but recovering through surface heat and moisture fluxes)? Figure 12 provides explanations to the first question. Those clouds with decaying neighboring clouds are associated with colder air below cloud base than those with growing neighboring clouds (Fig. 12f), which leads to lower boundary layer Btv and TKE (Figs. 12e–g). Those clouds with decaying neighboring clouds are also associated with larger instabilities (Fig. 12f) in the boundary layer, which leads to the more vigorous convection, higher in-cloud w, in-cloud and subcloud TKE, in-cloud ql and in-cloud and subcloud Btv. Those air parcels starting from a relatively cold and humid boundary layer (i.e., with decaying neighboring clouds) have the same surface θ as those from warm and dry boundary layer (i.e., with growing neighboring clouds). Thus, higher absolute values of θ gradient lead to more vigorous convection and larger convergence above ∼1500 m, leading to the stronger downdrafts for neighboring clouds and removing water vapor from the surrounding area.

Fig. 12.
Fig. 12.

Profiles of the anomalies of (a) buoyancy, (b) θ, (c) TKE, and (d) ql. Profiles of the differences of (e) buoyancy, (f) θ, (g) TKE, and (h) ql between the clouds with decaying neighboring clouds and with growing neighboring clouds. The shading in (a)–(c) represents the standard error. Here only includes the datasets in G0 stage with lifetime between 10 and 16 min.

Citation: Journal of the Atmospheric Sciences 80, 3; 10.1175/JAS-D-22-0004.1

Figure 13 provides hints to the second question. The Bowen ratio (i.e., the ratio of surface sensible heat flux to the surface latent heat flux) below clouds are averaged in the same way as Figs. 11 and 12. The group with growing tracked clouds and neighboring clouds has a larger Bowen ratio in the region directly below and near the tracked clouds than the region farther away, although all the clouds are above the surface with the Bowen ratio similar or larger than the domain-mean values (i.e., ∼1). Another group with decaying neighboring clouds does not show heterogeneity in the surface Bowen ratio conditions. Air over the higher Bowen ratio region is generally warm and dry, while that area with lower Bowen ratios is generally cold and humid. The contrast in atmospheric conditions generates a secondary circulation, which lifts air parcels over the high Bowen ratio region with water vapor convergence and forms clouds. Such secondary circulation provides plenty of cloud-base mass flux (i.e., “nature”) to maintain the growth of both tracked clouds (i.e., close to the center of updraft in secondary circulation) and their neighboring clouds (i.e., close to the boundary of the updraft in secondary circulation). Those clouds without surface heterogeneity form in different processes with the stronger competition that the tracked clouds grow by suppressing the updraft of their neighboring clouds and obtaining water vapor in the subcloud and lower in-cloud layers through stronger convergence. Besides the surface heterogeneity driven convection, Fast et al. (2019b) also mentioned that the light precipitation forms cold pools near the surface, which also triggers convection in their vicinity. However, Fig. 12h does not show any precipitation below the cloud base, suggesting cold pools from evaporating precipitation is not the main factor for suppressing neighboring clouds. Rapid evaporation is likely responsible for the large qυ and the low θ within subcloud layers, which is usually excluded from cold-pool identification (Schlemmer and Hohenegger 2014). Enhanced downdraft along with evaporation is also consistent with weaker updrafts in the boundary layer below the clouds (∼1.3 km) with decaying neighboring clouds than growing neighboring clouds. Another potential process might also occur indicating the neighboring clouds impact the tracked clouds. Those cold and wet air within the subcloud might lead to the lifting in the growing tracked clouds with decaying neighboring clouds due to the dynamic lifting from warm-air advection because stronger updraft and convergence (Figs. 11d,e) are right above those maximum θ differences in Fig. 12f. When the lifetime is larger than 16 min, the above analysis is the same except that the group with a lifetime longer than 45 min has a large standard error (not shown). Clouds with a longer lifetime have higher cloud altitude and higher boundary layer θ. Still, the differences between decaying neighboring clouds and growing neighboring clouds are the same as lifetime between 10 and 16 min.

Fig. 13.
Fig. 13.

Bowen ratio below the cloudy mask and neighboring air surrounding the clouds.

Citation: Journal of the Atmospheric Sciences 80, 3; 10.1175/JAS-D-22-0004.1

4. Conclusions

In this study we examine the interactions among continental shallow cumulus clouds to reveal how the clouds impact their neighboring clouds. The shallow clouds observed during the HI-SCALE field campaign near the ARM Southern Great Plains site in north-central Oklahoma on 30 August 2016 are selected as a case study. We use Weather Research and Forecasting Model to conduct a large-eddy simulation of those shallow cumulus clouds with interactive surface parameterization. A Lagrangian cloud tracking algorithm is applied to track the life cycle of the shallow cumulus clouds in the LES. We explore the statistical characteristics of the tracked clouds during their life cycle. We also reveal various processes through which the behaviors of the surrounding clouds influence their growth and dissipation.

The tracked clouds with lifetime of 10–45 min are found to be bubble-like in that the cloud-base height and depth evolve continuously. Those clouds with a lifetime longer than 45 min (i.e., only at the highest 2% of the lifetime) have a plateau in their vertical extent and horizontal area and show constant cloud-base height during the middle of their life cycle, indicating a plume-like structure. When the lifetime of clouds is shorter than 45 min, our results are consistent with previous studies supporting bubble-like clouds (Romps et al. 2021). The area growth rate of the bubble-like clouds has a strong positive correlation with the averaged cloud-base ρw but negative correlations with cloudy horizontal area in their growing period. The plume-like clouds have strong positive correlations between area and area growth rate. It suggests that the sign of the correlation between area and area growth rate can indicate the convection type (i.e., bubble vs plume). In the dissipation stage, the correlation between area growth rate and cloud-base properties is not robust.

When initially separated neighboring clouds merge in the cloud area experiences sudden growth. We show that merging occurs mostly in the middle of the life cycle, perhaps because merging is most likely when clouds are at their largest size (by virtue of probability). In contrast, splitting occurs most frequently toward the end of the life cycle due to the lack of cloud-base forcings. For the clouds with a lifetime between 10 and 45 min, the net effects from merging and splitting on cloud area growth rate are dominated by merging in the first half of the life cycle and by splitting in the second half of the life cycle. In the middle of the life cycle, merging and splitting have comparable frequency and reach a quasi-steady state. Those clouds with a lifetime longer than 45 min do not show significant temporal trends of net effects from merging and splitting in their life cycles. We also show that merging-dominated steps are associated with larger cloud fractions than other steps as expected from the higher probability. These results suggest an important role of merging and splitting in the cloud growth and dissipation.

By examining the concurrent evolution of the tracked clouds and their surrounding clouds, we found that generally the clouds in the growing stage start from a size smaller than neighboring clouds and their size can be larger than the neighboring clouds by a factor of 2 within 20% of lifetime. We conclude that a growing cloud experiences higher vertical velocity when they are surrounded by decaying neighboring clouds than by growing neighboring clouds, which suggests competition through two processes: 1) downdraft surrounding the clouds from the convective updrafts suppresses the development of the surrounding clouds; 2) stronger convergence in the clouds with stronger convective updrafts leads to less water vapor in the neighboring area. We also found that the clouds surrounded by growing clouds are above the heterogeneous land region with higher Bowen ratios beneath the cloud than the surrounding area. Clouds with dissipating surrounding clouds occur over more uniform land surfaces and the colder and moister air in the upper boundary layer below clouds suggests that those clouds also experience evaporation below the cloud base. The cooling in the subcloud layer increases the thermodynamic instability in the boundary layer and leads to more vigorous updrafts and then surrounding area experiences more downdrafts for compensating. The latter one leads to the dissipation of the surrounding clouds. Evaporation below those clouds, which are associated with dissipating surrounding clouds, might not originate from evaporated precipitation. While Fast et al. (2019b) showed that cold pools form after 1300 CST at the surface and suppress turbulence and cloud formation, all the subgroups in this study do not show evidence of precipitation to the surface and the potential temperature from the two subgroups with different surrounding cloud behaviors are the same. The difference with Fast et al. (2019b) is likely due to the focus of this paper on the initial growing and dissipation stage of the inner domain simulation such that precipitation is not widespread in our analysis. The evaporation might be due to an entrainment–evaporation mechanism (Xue and Feingold 2006). Circulation of the thermals leads to the detrainment at the thermal top and entrainment at the thermal bottom. The subgroup with dissipated surrounding clouds has larger TKE indicating stronger entrainment. Then the stronger entrainment is thought to cause more evaporation below the cloud base.

This study shows a negative effect of the shallow cumulus clouds on their surrounding clouds. The rough estimate of the effective distance is 2–5 km from the edge of the clouds. The processes related to those effects are revealed in this case, but additional studies are needed to generalize how these processes interact under different surface forcings and synoptic conditions. These results have implications for parameterization of shallow clouds especially in high-resolution models where smaller grid spacing implies multiple shallow clouds in a grid box are likely to interact in a way that affects the evolution of the statistics of clouds and the feedback to the environment. Systematic utilization of these results in the development of simple models of evolution of shallow cloud statistics is the subject of our future work.

Acknowledgments.

This study was supported by the U.S. Department of Energy Office of Science Biological and Environmental Research as part of the Atmospheric Systems Research (ASR) program. The Pacific Northwest National Laboratory is operated by Battelle for the U.S. Department of Energy under Contract DE-AC05-76RLO1830. Computing resources for the simulations were provided by the National Energy Research Scientific Computing Center (NERSC), a DOE Office of Science user facility supported under Contract DE-AC02-05CH11231; the facilities of the PNNL institutional computing center (PIC); and the Environmental Molecular Science Laboratory’s (EMSL) on its computational cluster Cascade. We thank Koichi Sakaguchi for the discussions about the calculation of boundary layer height. We also would like to thank David Romps and Adam Varble for their feedback to this work.

Data availability statement.

WRF Model output generated by the simulations in this study is saved on PNNL’s long-term storage system, Aurora (rc-support@pnnl.gov). The postprocessed data by Lagrangian tracker are available from Zenodo (https://doi.org/10.5281/zenodo.6792889).

APPENDIX A

The Detailed Description about Merging–Splitting in the Tracking Algorithm

The merging and splitting are similar to the algorithm described in Feng et al. (2012). Shallow cloud masks are defined as LWP larger than 0.1 kg m−2 with the cloud core as LWP > 0.75 kg m−2. Cloud masks are considered in the same track if the overlapping area fraction between two consecutive time snapshots is larger than 0.5. The overlapping fraction is decided based on an estimation of boundary layer mean wind (averaged horizontal wind speed = 2.65 m s−1 at ∼1 km above the surface) and advection distance of clouds within the output time resolution (i.e., less than 159 m within 1 min) given that we focus on the clouds with a minimum characteristic length (L) larger than 300 m. By using this overlapping method, we assume the cloudy area change is generally smaller than the distance among clouds. Otherwise, uncertainty exists between merging and disappearing due to decay. Merging occurs when two or more cloud masks overlap with one cloud mask in the next time step, and the largest overlapped mask is treated as a continuation of the same track, and the smaller overlapped clouds are terminated and flagged as merging. Similarly, when one cloud splits into several clouds, the largest overlapped fragment continues to be tracked and the smaller overlapped fragments are labeled as split clouds. The merging and splitting processes are recorded for each time step; thus, the tracks that experience merging or splitting during their life cycles can be identified in further analysis.

APPENDIX B

The Basic Features of the Subgroups

Histogram of the lifetime of all the tracks is shown in Fig. B1a as the blue color. Some tracks experience more than one maximum in their life cycle with the 50th and 98th percentile as 16 and 45 min, respectively. Those tracks with only one maximum are shown in orange colors. The differences tell that longer tracks have larger probability to have more than one maximum horizontal area in their life cycle. Table B1 shows the total number of the tracks with same pattern. “G” donates to growth period and “D” donates to the decay period. Number after “G” or “D” donates the order of the growth or decay period. The duration of the first growth period and the first decay period is shown in Fig. B1b as G0 and D0. The growth period and decay period is defined after smoothing the area growth rate by low-pass filter. Most duration of G0 or D0 is shorter than half an hour for those ShCu. G0 and D0 are not strictly in the first and second half of life cycle (Fig. B2). When the lifetime is smaller than 45 min, G0 has larger sample size than D0 in the first half of the life cycle and D0 has larger sample size than G0 in the second half of the life cycle. More time steps have the neighboring clouds grow or decay with the tracked clouds together. The local time of those subgroups slightly depends on the lifetime but the standard deviation of each group much larger than the differences of mean values caused by the lifetime (Fig. B3).

Fig. B1.
Fig. B1.

(a) PDF of the lifetime of all tracks and those tracks with G0 + D0 pattern. The median and 95% of the values correspond the 16 and 45 min. (b) PDF of the duration of G0 and D0 stage.

Citation: Journal of the Atmospheric Sciences 80, 3; 10.1175/JAS-D-22-0004.1

Fig. B2.
Fig. B2.

Time series of the sample size along relative time.

Citation: Journal of the Atmospheric Sciences 80, 3; 10.1175/JAS-D-22-0004.1

Fig. B3.
Fig. B3.

Local time of each group by lifetime and cloud growth state.

Citation: Journal of the Atmospheric Sciences 80, 3; 10.1175/JAS-D-22-0004.1

Table B1

Counts of the patters of the selected 3179 tracks.
Table B1

APPENDIX C

The Cloud–Cloud Interactions between Tracked Clouds

We assume that in the absence of competition, the environmental clouds would develop similarly, due to similar cloud-base forcings. We test it by examining the distribution of environmental cloud area growth rate in Fig. C1. For the tracked clouds in the growth state (G0), the environmental area growth rate has a larger tail on the positive side than those with the tracked clouds in the decaying state (D0). Therefore, we think statistically environmental clouds would develop similarly with the tracked clouds without competition.

Fig. C1.
Fig. C1.

Distribution of environmental area growth rate.

Citation: Journal of the Atmospheric Sciences 80, 3; 10.1175/JAS-D-22-0004.1

Neighboring clouds in Fig. 9 include the cloud masks both existing in other identified ∼3000 tracks or not to be identified (i.e., too short and/or too small and/or too close to the domain boundary). The number of those “untracked” clouds is larger than the “tracked” clouds because the cloud size distribution usually approximately follows a power law distribution. To further show the interactions between tracked clouds, we show the comparisons when considering both tracked and untracked neighboring clouds in Fig. C2a and only tracked neighboring clouds in Fig. C2b. The decreases in the ratio in the first half of the life cycle and increases in the ratio in the second half of the life cycle exist in both figures. Figure C2a shows a larger sample size than Fig. C2b by a factor of 2. Also, the lowest point in the “sine behavior” has smaller values in Fig. C2a than in Fig. C2b because of the consideration of small “untracked” clouds.

Fig. C2.
Fig. C2.

(a) The ratio of neighboring clouds to the tracked clouds, where neighboring clouds include both clouds in other tracks and untracked clouds. (b) As in (a), but only considering clouds in other tracks in the neighboring clouds.

Citation: Journal of the Atmospheric Sciences 80, 3; 10.1175/JAS-D-22-0004.1

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  • Plant, R. S., 2009: Statistical properties of cloud lifecycles in cloud-resolving models. Atmos. Chem. Phys., 9, 2195–2205, https://doi.org/10.5194/acp-9-2195-2009.

    • Search Google Scholar
    • Export Citation

  • Raymond, D. J., and A. M. Blyth, 1989: Precipitation development in a New Mexico thunderstorm. Quart. J. Roy. Meteor. Soc., 115, 1397–1423, https://doi.org/10.1002/qj.49711549011.

    • Search Google Scholar
    • Export Citation

  • Romps, D. M., 2010: A direct measure of entrainment. J. Atmos. Sci., 67, 1908–1927, https://doi.org/10.1175/2010JAS3371.1.

  • Romps, D. M., and Z. Kuang, 2010: Nature versus nurture in shallow convection. J. Atmos. Sci., 67, 1655–1666, https://doi.org/10.1175/2009JAS3307.1.

    • Search Google Scholar
    • Export Citation

  • Romps, D. M., R. R. Rusenöktem, S. Endo, and A. M. Vogelmann, 2021: On the life cycle of a shallow cumulus cloud: Is it a bubble or plume, active or forced? J. Atmos. Sci., 78, 2823–2833, https://doi.org/10.1175/JAS-D-20-0361.1.

    • Search Google Scholar
    • Export Citation

  • Sakaguchi, K., and Coauthors, 2021: Determining spatial scales of soil moisture—Cloud coupling pathways using semi-idealized simulations. J. Geophys. Res. Atmos., 127, e2021JD035282, https://doi.org/10.1029/2021JD035282.

    • Search Google Scholar
    • Export Citation

  • Sakradzija, M., and C. Hohenegger, 2017: What determines the distribution of shallow convective mass flux through a cloud base? J. Atmos. Sci., 74, 2615–2632, https://doi.org/10.1175/JAS-D-16-0326.1.

    • Search Google Scholar
    • Export Citation

  • Schlemmer, L., and C. Hohenegger, 2014: The formation of wider and deeper clouds as a result of cold-pool dynamics. J. Atmos. Sci., 71, 2842–2858, https://doi.org/10.1175/JAS-D-13-0170.1.

    • Search Google Scholar
    • Export Citation

  • Squires, P., and J. S. Turner, 1962: An entraining jet model for cumulo-nimbus updraughts. Tellus, 14, 422–434, https://doi.org/10.3402/tellusa.v14i4.9569.

    • Search Google Scholar
    • Export Citation

  • Stevens, B., 2002: Entrainment in stratocumulus-topped mixed layers. Quart. J. Roy. Meteor. Soc., 128, 2663–2690, https://doi.org/10.1256/qj.01.202.

    • Search Google Scholar
    • Export Citation

  • Stommel, H., 1947: Entrainment of air into a cumulus cloud. J. Atmos. Sci., 4, 91–94, https://doi.org/10.1175/1520-0469(1947)004<0091:EOAIAC>2.0.CO;2.

    • Search Google Scholar
    • Export Citation

  • Xue, H., and G. Feingold, 2006: Large-eddy simulations of trade wind cumuli: Investigation of aerosol indirect effects. J. Atmos. Sci., 63, 1605–1622, https://doi.org/10.1175/JAS3706.1.

    • Search Google Scholar
    • Export Citation

  • Yano, J. I., 2014: Basic convective element: Bubble or plume? A historical review. Atmos. Chem. Phys., 14, 7019–7030, https://doi.org/10.5194/acp-14-7019-2014.

    • Search Google Scholar
    • Export Citation

  • Zhao, M., and P. H. Austin, 2005a: Life cycle of numerically simulated shallow cumulus clouds. Part I: Transport. J. Atmos. Sci., 62, 1269–1290, https://doi.org/10.1175/JAS3414.1.

    • Search Google Scholar
    • Export Citation

  • Zhao, M., and P. H. Austin, 2005b: Life cycle of numerically simulated shallow cumulus clouds. Part II: Mixing dynamics. J. Atmos. Sci., 62, 1291–1310, https://doi.org/10.1175/JAS3415.1.

    • Search Google Scholar
    • Export Citation

  • Zheng, Y., D. Rosenfeld, and Z. Li, 2021: Sub-cloud turbulence explains cloud-base updrafts for shallow cumulus ensembles: First observational evidence. Geophys. Res. Lett., 48, e2020GL091881, https://doi.org/10.1029/2020GL091881.

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  • Plant, R. S., 2009: Statistical properties of cloud lifecycles in cloud-resolving models. Atmos. Chem. Phys., 9, 2195–2205, https://doi.org/10.5194/acp-9-2195-2009.

    • Search Google Scholar
    • Export Citation

  • Raymond, D. J., and A. M. Blyth, 1989: Precipitation development in a New Mexico thunderstorm. Quart. J. Roy. Meteor. Soc., 115, 1397–1423, https://doi.org/10.1002/qj.49711549011.

    • Search Google Scholar
    • Export Citation

  • Romps, D. M., 2010: A direct measure of entrainment. J. Atmos. Sci., 67, 1908–1927, https://doi.org/10.1175/2010JAS3371.1.

  • Romps, D. M., and Z. Kuang, 2010: Nature versus nurture in shallow convection. J. Atmos. Sci., 67, 1655–1666, https://doi.org/10.1175/2009JAS3307.1.

    • Search Google Scholar
    • Export Citation

  • Romps, D. M., R. R. Rusenöktem, S. Endo, and A. M. Vogelmann, 2021: On the life cycle of a shallow cumulus cloud: Is it a bubble or plume, active or forced? J. Atmos. Sci., 78, 2823–2833, https://doi.org/10.1175/JAS-D-20-0361.1.

    • Search Google Scholar
    • Export Citation

  • Sakaguchi, K., and Coauthors, 2021: Determining spatial scales of soil moisture—Cloud coupling pathways using semi-idealized simulations. J. Geophys. Res. Atmos., 127, e2021JD035282, https://doi.org/10.1029/2021JD035282.

    • Search Google Scholar
    • Export Citation

  • Sakradzija, M., and C. Hohenegger, 2017: What determines the distribution of shallow convective mass flux through a cloud base? J. Atmos. Sci., 74, 2615–2632, https://doi.org/10.1175/JAS-D-16-0326.1.

    • Search Google Scholar
    • Export Citation

  • Schlemmer, L., and C. Hohenegger, 2014: The formation of wider and deeper clouds as a result of cold-pool dynamics. J. Atmos. Sci., 71, 2842–2858, https://doi.org/10.1175/JAS-D-13-0170.1.

    • Search Google Scholar
    • Export Citation

  • Squires, P., and J. S. Turner, 1962: An entraining jet model for cumulo-nimbus updraughts. Tellus, 14, 422–434, https://doi.org/10.3402/tellusa.v14i4.9569.

    • Search Google Scholar
    • Export Citation

  • Stevens, B., 2002: Entrainment in stratocumulus-topped mixed layers. Quart. J. Roy. Meteor. Soc., 128, 2663–2690, https://doi.org/10.1256/qj.01.202.

    • Search Google Scholar
    • Export Citation

  • Stommel, H., 1947: Entrainment of air into a cumulus cloud. J. Atmos. Sci., 4, 91–94, https://doi.org/10.1175/1520-0469(1947)004<0091:EOAIAC>2.0.CO;2.

    • Search Google Scholar
    • Export Citation

  • Xue, H., and G. Feingold, 2006: Large-eddy simulations of trade wind cumuli: Investigation of aerosol indirect effects. J. Atmos. Sci., 63, 1605–1622, https://doi.org/10.1175/JAS3706.1.

    • Search Google Scholar
    • Export Citation

  • Yano, J. I., 2014: Basic convective element: Bubble or plume? A historical review. Atmos. Chem. Phys., 14, 7019–7030, https://doi.org/10.5194/acp-14-7019-2014.

    • Search Google Scholar
    • Export Citation

  • Zhao, M., and P. H. Austin, 2005a: Life cycle of numerically simulated shallow cumulus clouds. Part I: Transport. J. Atmos. Sci., 62, 1269–1290, https://doi.org/10.1175/JAS3414.1.

    • Search Google Scholar
    • Export Citation

  • Zhao, M., and P. H. Austin, 2005b: Life cycle of numerically simulated shallow cumulus clouds. Part II: Mixing dynamics. J. Atmos. Sci., 62, 1291–1310, https://doi.org/10.1175/JAS3415.1.

    • Search Google Scholar
    • Export Citation

  • Zheng, Y., D. Rosenfeld, and Z. Li, 2021: Sub-cloud turbulence explains cloud-base updrafts for shallow cumulus ensembles: First observational evidence. Geophys. Res. Lett., 48, e2020GL091881, https://doi.org/10.1029/2020GL091881.

    • Search Google Scholar
    • Export Citation
  • <sc>Fig</sc>. 1.
    View in gallery
    Fig. 1.

    Joint probability density function of the lifetime (T) and maximum (minimum) cloud characteristic length (L).

  • <sc>Fig</sc>. 2.
    View in gallery
    Fig. 2.

    Two examples of the cloud track with the lifetime as (a)–(c) 13 and (d)–(f) 124 min. (a),(d) Time series of cloud area and merging and splitting area. (b),(e) Profiles of cloud-averaged hydrometer mixing ratio at the maximum area. (c),(f) The spatial distribution of LWP at the maximum area. Dotted blue lines donate the phases in their lifetime (see text for details).

  • <sc>Fig</sc>. 3.
    View in gallery
    Fig. 3.

    (a) Cloud-base and cloud-top height of each layer. (b) Depth of each cloud layer. (c) Fraction of overlapping high cloud layers. (d) Averaged fraction of the area of overlapping high cloud layers.

  • <sc>Fig</sc>. 4.
    View in gallery
    Fig. 4.

    Time series of (a) area growth rate, (b) mass flux, (c) length scale L.

  • <sc>Fig</sc>. 5.
    View in gallery
    Fig. 5.

    Time series of cloud base and cloud depth of the lowest layer. The x axis is the time normalized by the lifetime of each cloud track.

  • <sc>Fig</sc>. 6.
    View in gallery
    Fig. 6.

    Correlation between area growth rate excluding merging and splitting with (a),(d) cloud-base mass flux. (b),(e) cloud area, and (c),(f) cloud mean ρw for (a)–(c) G0 stage and (d)–(f) D0 stage. Dashed lines are the same as solid lines except applying to the same datasets when dealing with lagging. Dots and crosses mark the points with the p values larger than 0.01, indicating statistical insignificance.

  • <sc>Fig</sc>. 7.
    View in gallery
    Fig. 7.

    Correlation between area growth rate excluding merging and splitting with (a),(d) θe anomalies (b),(e) θ anomalies, and (c),(f) qυ anomalies for (a)–(c) G0 and (d)–(f) D0 stage. Dashed lines are the same as solid except applying to the same datasets when dealing with lagging. Dots and crosses mark the points with the p values larger than 0.01, indicating statistical insignificance.

  • <sc>Fig</sc>. 8.
    View in gallery
    Fig. 8.

    (a) Merging frequency with the relative time. (b) Splitting frequency with the relative time. (c) Cloudy-area growth rate due to merging and splitting. (d) Cloud fraction in a box with side length 8 km larger than the box fitting to the projected cloud mask.

  • <sc>Fig</sc>. 9.
    View in gallery
    Fig. 9.

    Normalized environmental cloud size by the tracked cloud size with different lifetime of the tracked clouds.

  • <sc>Fig</sc>. 10.
    View in gallery
    Fig. 10.

    Profiles of (a) buoyancy, (b) w, (c) θe, (d) θ, (e) ql, (f) qυ, (g) convergence rate, and (h) TKE at the reference state. The reference state is defined at 5 km away from cloud edge.

  • <sc>Fig</sc>. 11.
    View in gallery
    Fig. 11.

    Profiles of the anomalies of (a) w, (b) convergence rate, and (c) water vapor mixing ratio (qυ). Profiles of the differences of (d) w, (e) convergence rate, and (f) qυ between the clouds with decaying neighboring clouds and with growing neighboring clouds. Here we only include the datasets in G0 stage with lifetime between 10 and 16 min. The shading in (a)–(c) represents the standard error. The subscript “Denv” donates to the group with decaying neighboring clouds.

  • <sc>Fig</sc>. 12.
    View in gallery
    Fig. 12.

    Profiles of the anomalies of (a) buoyancy, (b) θ, (c) TKE, and (d) ql. Profiles of the differences of (e) buoyancy, (f) θ, (g) TKE, and (h) ql between the clouds with decaying neighboring clouds and with growing neighboring clouds. The shading in (a)–(c) represents the standard error. Here only includes the datasets in G0 stage with lifetime between 10 and 16 min.

  • <sc>Fig</sc>. 13.
    View in gallery
    Fig. 13.

    Bowen ratio below the cloudy mask and neighboring air surrounding the clouds.

  • <sc>Fig</sc>. B1.
    View in gallery
    Fig. B1.

    (a) PDF of the lifetime of all tracks and those tracks with G0 + D0 pattern. The median and 95% of the values correspond the 16 and 45 min. (b) PDF of the duration of G0 and D0 stage.

  • <sc>Fig</sc>. B2.
    View in gallery
    Fig. B2.

    Time series of the sample size along relative time.

  • <sc>Fig</sc>. B3.
    View in gallery
    Fig. B3.

    Local time of each group by lifetime and cloud growth state.

  • <sc>Fig</sc>. C1.
    View in gallery
    Fig. C1.

    Distribution of environmental area growth rate.

  • <sc>Fig</sc>. C2.
    View in gallery
    Fig. C2.

    (a) The ratio of neighboring clouds to the tracked clouds, where neighboring clouds include both clouds in other tracks and untracked clouds. (b) As in (a), but only considering clouds in other tracks in the neighboring clouds.

Fig. 1.

Joint probability density function of the lifetime (T) and maximum (minimum) cloud characteristic length (L).
Fig. 2.

Two examples of the cloud track with the lifetime as (a)–(c) 13 and (d)–(f) 124 min. (a),(d) Time series of cloud area and merging and splitting area. (b),(e) Profiles of cloud-averaged hydrometer mixing ratio at the maximum area. (c),(f) The spatial distribution of LWP at the maximum area. Dotted blue lines donate the phases in their lifetime (see text for details).
Fig. 3.

(a) Cloud-base and cloud-top height of each layer. (b) Depth of each cloud layer. (c) Fraction of overlapping high cloud layers. (d) Averaged fraction of the area of overlapping high cloud layers.
Fig. 4.

Time series of (a) area growth rate, (b) mass flux, (c) length scale L.
Fig. 5.

Time series of cloud base and cloud depth of the lowest layer. The x axis is the time normalized by the lifetime of each cloud track.
Fig. 6.

Correlation between area growth rate excluding merging and splitting with (a),(d) cloud-base mass flux. (b),(e) cloud area, and (c),(f) cloud mean ρw for (a)–(c) G0 stage and (d)–(f) D0 stage. Dashed lines are the same as solid lines except applying to the same datasets when dealing with lagging. Dots and crosses mark the points with the p values larger than 0.01, indicating statistical insignificance.
Fig. 7.

Correlation between area growth rate excluding merging and splitting with (a),(d) θe anomalies (b),(e) θ anomalies, and (c),(f) qυ anomalies for (a)–(c) G0 and (d)–(f) D0 stage. Dashed lines are the same as solid except applying to the same datasets when dealing with lagging. Dots and crosses mark the points with the p values larger than 0.01, indicating statistical insignificance.
Fig. 8.

(a) Merging frequency with the relative time. (b) Splitting frequency with the relative time. (c) Cloudy-area growth rate due to merging and splitting. (d) Cloud fraction in a box with side length 8 km larger than the box fitting to the projected cloud mask.
Fig. 9.

Normalized environmental cloud size by the tracked cloud size with different lifetime of the tracked clouds.
Fig. 10.

Profiles of (a) buoyancy, (b) w, (c) θe, (d) θ, (e) ql, (f) qυ, (g) convergence rate, and (h) TKE at the reference state. The reference state is defined at 5 km away from cloud edge.
Fig. 11.

Profiles of the anomalies of (a) w, (b) convergence rate, and (c) water vapor mixing ratio (qυ). Profiles of the differences of (d) w, (e) convergence rate, and (f) qυ between the clouds with decaying neighboring clouds and with growing neighboring clouds. Here we only include the datasets in G0 stage with lifetime between 10 and 16 min. The shading in (a)–(c) represents the standard error. The subscript “Denv” donates to the group with decaying neighboring clouds.
Fig. 12.

Profiles of the anomalies of (a) buoyancy, (b) θ, (c) TKE, and (d) ql. Profiles of the differences of (e) buoyancy, (f) θ, (g) TKE, and (h) ql between the clouds with decaying neighboring clouds and with growing neighboring clouds. The shading in (a)–(c) represents the standard error. Here only includes the datasets in G0 stage with lifetime between 10 and 16 min.
Fig. 13.

Bowen ratio below the cloudy mask and neighboring air surrounding the clouds.
Fig. B1.

(a) PDF of the lifetime of all tracks and those tracks with G0 + D0 pattern. The median and 95% of the values correspond the 16 and 45 min. (b) PDF of the duration of G0 and D0 stage.
Fig. B2.

Time series of the sample size along relative time.
Fig. B3.

Local time of each group by lifetime and cloud growth state.
Fig. C1.

Distribution of environmental area growth rate.
Fig. C2.

(a) The ratio of neighboring clouds to the tracked clouds, where neighboring clouds include both clouds in other tracks and untracked clouds. (b) As in (a), but only considering clouds in other tracks in the neighboring clouds.
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