On the Roles of Precipitation and Entrainment in Stratocumulus Transitions between Mesoscale States

Fabian Hoffmann aMeteorologisches Institut, Ludwig-Maximilans-Universität München, Munich, Germany

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Franziska Glassmeier bDelft University of Technology, Delft, Netherlands

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Takanobu Yamaguchi cCooperative Institute for Research in Environmental Sciences, University of Colorado Boulder, Boulder, Colorado
dChemical Sciences Laboratory, NOAA/Earth System Research Laboratories, Boulder, Colorado

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Graham Feingold dChemical Sciences Laboratory, NOAA/Earth System Research Laboratories, Boulder, Colorado

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Abstract

Stratocumulus occur in closed- or open-cell states, which tend to be associated with high or low cloud cover and the absence or presence of precipitation, respectively. Thus, the transition between these states has substantial implications for the role of this cloud type in Earth’s radiation budget. In this study, we analyze transitions between these states using an ensemble of 127 large-eddy simulations, covering a wide range of conditions. Our analysis is focused on the behavior of these clouds in a cloud fraction (fc) scene albedo (A) phase space, which has been shown in previous studies to be a useful framework for interpreting system behavior. For the transition from closed to open cells, we find that precipitation creates narrower clouds and scavenges cloud droplets for all fc. However, precipitation decreases the cloud depth for fc > 0.8 only, causing a rapid decrease in A. For fc < 0.8, the cloud depth actually increases due to mesoscale organization of the cloud field. As the cloud deepening balances the effects of cloud droplet scavenging in terms of influence on A, changes in A are determined by the decreasing fc only, causing a linear decrease in A for fc < 0.8. For the transition from open to closed cells, we find that longwave radiative cooling drives the cloud development, with cloud widening dominating for fc < 0.5. For fc > 0.5, clouds begin to deepen gradually due to the decreasing efficiency of lateral expansion. The smooth switch between cloud widening and deepening leads to a more gentle change in A compared to the transitions under precipitating conditions.

Significance Statement

By reflecting a substantial fraction of solar shortwave radiation back to space, shallow clouds constitute a major cooling agent in Earth’s radiation budget. To constrain this effect, a profound understanding of cloud cover and cloud albedo is necessary. In this study, we analyze the processes that drive the variability in these cloud properties in stratocumulus clouds, a very common cloud type covering approximately 20% of the globe. For these clouds, we show that changes from low to high or high to low cloud cover are different due to the underlying cloud micro- and macrophysics, elucidating this crucial aspect of aerosol–cloud–climate interactions.

© 2023 American Meteorological Society. This published article is licensed under the terms of the default AMS reuse license. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Fabian Hoffmann, fa.hoffmann@lmu.de

Abstract

Stratocumulus occur in closed- or open-cell states, which tend to be associated with high or low cloud cover and the absence or presence of precipitation, respectively. Thus, the transition between these states has substantial implications for the role of this cloud type in Earth’s radiation budget. In this study, we analyze transitions between these states using an ensemble of 127 large-eddy simulations, covering a wide range of conditions. Our analysis is focused on the behavior of these clouds in a cloud fraction (fc) scene albedo (A) phase space, which has been shown in previous studies to be a useful framework for interpreting system behavior. For the transition from closed to open cells, we find that precipitation creates narrower clouds and scavenges cloud droplets for all fc. However, precipitation decreases the cloud depth for fc > 0.8 only, causing a rapid decrease in A. For fc < 0.8, the cloud depth actually increases due to mesoscale organization of the cloud field. As the cloud deepening balances the effects of cloud droplet scavenging in terms of influence on A, changes in A are determined by the decreasing fc only, causing a linear decrease in A for fc < 0.8. For the transition from open to closed cells, we find that longwave radiative cooling drives the cloud development, with cloud widening dominating for fc < 0.5. For fc > 0.5, clouds begin to deepen gradually due to the decreasing efficiency of lateral expansion. The smooth switch between cloud widening and deepening leads to a more gentle change in A compared to the transitions under precipitating conditions.

Significance Statement

By reflecting a substantial fraction of solar shortwave radiation back to space, shallow clouds constitute a major cooling agent in Earth’s radiation budget. To constrain this effect, a profound understanding of cloud cover and cloud albedo is necessary. In this study, we analyze the processes that drive the variability in these cloud properties in stratocumulus clouds, a very common cloud type covering approximately 20% of the globe. For these clouds, we show that changes from low to high or high to low cloud cover are different due to the underlying cloud micro- and macrophysics, elucidating this crucial aspect of aerosol–cloud–climate interactions.

© 2023 American Meteorological Society. This published article is licensed under the terms of the default AMS reuse license. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Fabian Hoffmann, fa.hoffmann@lmu.de

1. Introduction

The planetary albedo is strongly affected by the presence of clouds that, in their net effect, increase the amount of shortwave radiation reflected back to space, constituting a major cooling agent in the Earth radiation budget (e.g., Loeb et al. 2018). Shallow boundary layer clouds, such as shallow cumulus and stratocumulus, primarily affect the climate system in this way due to their proximity to the surface, limiting potential counteracting effects via the emission of longwave radiation. While the ability of individual clouds to reflect shortwave radiation is primarily determined by their liquid water content and number of cloud droplets (e.g., Twomey 1974, 1977), the horizontal cloud cover is another important factor determining the radiative effect of clouds in the climate system (e.g., Albrecht 1989). Canonical examples for systematic cloud cover changes in shallow boundary layer clouds are the transition of closed- to open-cell or open- to closed-cell stratocumulus (e.g., Wang and Feingold 2009; Yamaguchi et al. 2015), as well as the transition from stratocumulus to shallow cumulus (e.g., Sandu and Stevens 2011; Goren et al. 2019).

In this study, we will focus on the transition of closed- to open-cell and open- to closed-cell stratocumulus. These stratocumulus mesoscale states are linked to the specific organization of the up- and downdraft regions in the cells in which this cloud type is organized (e.g., Helfand and Kalnay 1983). In closed-cell stratocumulus, broad updrafts dominate the center of the cells, causing approximately full cloud cover, while narrow bands of downdrafts are found on the edges of the cell, which are associated with a small reduction in cloud cover due to the entrainment of free-tropospheric air primarily taking place in these regions (Gerber et al. 2005). If these clouds start to precipitate, cold pools caused by evaporating raindrops drive the updrafts to the edges of the cells, where narrower and deeper clouds form on their tops, and downdrafts dominate the cell center. Following the direct dissipation of the cloud by precipitation, the subsequent stabilization of the subcloud layer limits the transport of moisture to the cloud layer such that the cloud cover of open-cell stratocumulus often reaches only a few tens of percent (Savic-Jovcic and Stevens 2008; Wang and Feingold 2009). Thus, this transition of closed- to open-cell stratocumulus is primarily caused by the initiation of precipitation, while the transition of open- to closed-cell stratocumulus requires not only the absence of precipitation but also the buildup of liquid water and hence radiative cooling to drive the underlying convection (Feingold et al. 2015). Beyond the scope of this study are transitions caused by changes in boundary layer depth or surface fluxes, as well as wind shear (e.g., Wood 2012).

The scene albedo A is often used to approximate the effect of clouds on the planetary albedo, and it is frequently expressed as
A=As(1fc)+Acfc,
where As is the surface albedo, Ac is the cloud albedo, and fc is the cloud fraction (Schneider and Dickinson 1976). The cloud albedo Ac can be determined by a simple two-stream approximation following Bohren (1987) as
Ac=τcγ+τc,
where γ ≈ 13.3 is a parameter that depends on the degree of forward scattering and τc is the cloud optical thickness:
τc=αNc1/3LWPc5/6,
with Nc being the cloud droplet concentration, LWPc=zbztqcdz being the liquid water path, i.e., the liquid water content qc integrated from cloud base zb to cloud top zt, and α ≈ 0.2 m8/3 kg−5/6, a temperature- and pressure-dependent parameter (e.g., Stephens 1978).

For the aforementioned examples of closed- and open-cell stratocumulus, but also stratocumulus transitioning to shallow cumulus, the relationship between A and fc has been found to obey a relatively universal functional relationship that was first documented by Bender et al. (2011), who analyzed satellite imagery of marine stratocumulus in selected subtropical regions. Engström et al. (2015) expanded their analysis by sampling all marine clouds between 60°N and 60°S over 12 years. The relationship discovered by Engström et al. (2015) has been described as exponential, superlinear, or by a power law and has been confirmed in various modeling studies and satellite observations subsequently (Feingold et al. 2016, 2017; McCoy et al. 2017; Rampal and Davies 2020). For instance, Feingold et al. (2017) showed that the shape of this relationship can be explained by the deepening of clouds while they widen, causing a higher LWPc and hence a larger τc, Ac, and A for increasing fc. Moreover, Feingold et al. (2016) showed a systematic increase in Nc with fc, which can also explain the increase in A with fc. Thus, the degree to which Nc and LWP modulate Ac with respect to fc remains uncertain.

To understand the transitions between stratocumulus mesoscale states and the associated changes in A as a function of fc further, this study compiles 127 large-eddy simulations (LESs) of stratocumulus-topped boundary layers. This ensemble enables us to understand the transitions of stratocumulus from a dynamical systems perspective, rather than individual case studies. This study will begin with a short summary of the simulations (section 2), followed by their analysis (section 3), beginning with a general overview of their behavior before precipitating, and nonprecipitating cases are analyzed individually. The study is concluded in section 4.

2. Setup, production, and evaluation of LES ensembles

The simulations for this study were conducted with the System for Atmospheric Modeling (SAM) (Khairoutdinov and Randall 2003), which uses the LES approach to solve the anelastic Navier–Stokes equations and transport equations for total water and liquid water static energy. Cloud microphysics are simulated with a bin-emulating, two-moment bulk scheme, covering droplet activation, condensation, and precipitation processes (Feingold et al. 1998).

The simulations are loosely based on the nocturnal, drizzling, marine stratocumulus case by Ackerman et al. (2009), as further detailed in our previous LES ensemble studies (Feingold et al. 2016; Glassmeier et al. 2019, 2021; Hoffmann et al. 2020; Feingold et al. 2022). In short, the simulation domain is set to 48 × 48 km2 in the horizontal direction and 2.5 km in the vertical. The horizontal extent is chosen to allow for adequate mesoscale organization (e.g., Kazil et al. 2017). The grid spacing is set to 200 m horizontally and 10 m vertically. While the grid spacing can be considered coarse for an individual simulation, it is a necessity to produce the large number of ensemble simulations for this study. While finer grid spacings tend to increase LWPc and fc, the applied anisotropic grid spacing can mitigate this dependency (e.g., Mellado et al. 2018), and the general sensitivities analyzed in this study are expected to be reliable. The simulation time step is 1 s, and simulations are run for 12 h. We disregard the first 2 h as model spinup. Precipitation is inhibited for the first hour. As the simulated cases are nocturnal, shortwave radiation has been neglected, while longwave emission is represented using the Rapid Radiative Transfer Model (RRTM) (Iacono et al. 2000). The sea surface temperature is set to 293.34 K, and the subsidence is determined from a fixed large-scale divergence of 3.75 × 10−6 s−1 (Ackerman et al. 2009). A surface aerosol source of 70 cm−2 s−1 (Yamaguchi et al. 2017) is added to represent various processes that result in an increase in aerosol (sea spray, new particle formation, advection), which is necessary to counter the runaway aerosol scavenging by precipitation. The simulations feature interactive surface sensible and latent heat fluxes that are determined using Monin–Obukhov similarity theory, which have been used in only one of our previous ensemble studies so far (Feingold et al. 2022). Note that these surface fluxes are somewhat smaller than those prescribed in our other ensemble studies with constant surface fluxes (Fig. 1) but within the range of previous measurements and simulations of stratocumulus (e.g., Large and Pond 1982; Hourston 1992; Kazil et al. 2014; Feingold et al. 2015).

Fig. 1.
Fig. 1.

Probability density distributions (PDFs) of sensible (blue lines) and latent (red lines) surface heat fluxes from this (continuous lines) and our previous (dashed lines) LES ensemble studies. Note that our previous studies assumed constant surface fluxes.

Citation: Journal of the Atmospheric Sciences 80, 12; 10.1175/JAS-D-22-0268.1

For initial conditions, we systematically varied five variables that are traditionally used to characterize a stratocumulus-topped boundary layer in a mixed-layer framework and one variable to determine cloud microphysics to initialize the simulations: the mixed-layer depth (500 m ≤ zi ≤ 1300 m), mixed-layer liquid water potential temperature (284 K ≤ θ1 ≤ 294 K), mixed-layer total water mixing ratio (6.5 g kg−1qt ≤ 10.5 g kg−1), liquid water potential temperature difference between mixed-layer and free troposphere (6 K ≤ Δθ1 ≤ 10 K), total water mixing ratio difference between mixed-layer and free troposphere (−10 g kg−1 ≤ Δqt ≤ −6 g kg−1), and the mixed-layer aerosol concentration (30 cm−3Na ≤ 500 cm−3). This variable space was examined using Latin-hypercube sampling to prevent correlations between these variables (e.g., Feingold et al. 2016). From all initialized cases, 127 simulations produced a cloud. These will be analyzed below.

From our simulations, we determine A using (1) with (2) and (3) for each column of the simulation domain individually to avoid any biases due to the inhomogeneity of the cloud field that may arise if Ac was determined from the domain-averaged LWPc and Nc (Glenn et al. 2020). We further assume As = 0.08, which is typical for oceans (e.g., Jin et al. 2004). In the following, the subscript c indicates that a variable (e.g., fc, τc, LWPc, or Nc) is evaluated only from cloudy columns in the simulation domain. To consider a column as cloudy, we apply a threshold of τc > 5 to exclude optically thin clouds. This value ensures that the analysis is focused on the most active regions of the clouds that drive their transitions by the production of precipitation or substantial longwave radiative cooling. However, we do not want to understate the importance of optically thin clouds on A. A sensitivity study on the τc threshold will be presented below.

3. Results

In this section, we will first lay out basic properties of the entire ensemble and describe how we separated the ensemble members into precipitating and nonprecipitating cases. These subensembles will be addressed in more detail in the subsequent subsections.

a. Overview

Figure 2a shows the trajectories of all analyzed simulations in the aforementioned Afc phase space. Based on details provided later, precipitating and nonprecipitating cases are colored in different shades of blue and red, respectively, while cases that do not fall into any of these categories are indicated by a thin black line. A thick black line shows the satellite reference from Engström et al. (2015), which will be used as a reference below. Generally, all simulated cases follow that reference, especially its curvature, albeit at somewhat higher A. As we will see below, this overestimation is partially due to the high threshold for τc used for analyzing the model output. Note further that the precipitating cases move predominantly from high to low fc, while the nonprecipitating cases move in the opposite direction (cf. Figs. 4b and 6b). This motion in the Afc phase space is primarily due to the transition between open and closed cells or closed and open cells, respectively, as analyzed in more depth below.

Fig. 2.
Fig. 2.

(a) All simulations as trajectories in an Afc phase space, with blue lines indicating precipitating cases and red lines indicating nonprecipitating cases. (The differently shaded blue and red lines are an aid to distinguishing the trajectories and have no further meaning.) A thin black line shows the trajectory that does not fall in the precipitating or nonprecipitating categories applied here. A thick black line shows the reference by Engström et al. (2015). (b) The same simulations in an Rcbfc phase space and (c) PDFs of Rcb. (d)–(f) Complement to (a) with corresponding joint frequency distributions for the cases classified as precipitating or nonprecipitating, as well as all cases combined. The respective blue, red, and orange lines show the average A¯ for τc = 5 (continuous lines), 2 (long-dashed lines), and 1 (short-dashed lines). Note that the threshold τc = 5 is used throughout the study.

Citation: Journal of the Atmospheric Sciences 80, 12; 10.1175/JAS-D-22-0268.1

To distinguish between precipitating and nonprecipitating cases, we assessed the cloud-base rain rate Rcb (Figs. 2b,c). Simulations with continuous Rcb > 1 mm day−1 during the analyzed time will be considered as precipitating (blue lines, 19 simulations), while simulations with continuous Rcb < 1 mm day−1 during the analyzed time will be considered nonprecipitating (red lines, 107 simulations). Only one simulation (thin black line) does not fall into these categories and will be disregarded in the subsequent analysis. A threshold for Rcb on the order of 1 mm day−1 is often applied to distinguish between heavy and weakly precipitating stratocumulus (cf. Wood 2012) and is indicative of the steady states in Nc that stratocumulus assume due to the competing effects of the surface source and precipitation scavenging (Baker and Charlson 1990).

Figures 2d and 2e show joint frequency distributions of all trajectories separated into precipitating and nonprecipitating cases, while Fig. 2f shows the joint frequency distribution for all cases. Only the analyzed time steps are considered. The corresponding average A¯ values are shown as continuous blue, red, and orange lines, respectively. As a reminder, these averages are always determined using a threshold of τc = 5 to discriminate between cloudy and noncloudy regions unless otherwise noted. Long- and short-dashed lines show A¯ for lower τc thresholds of 2 and 1. Unsurprisingly, smaller τc thresholds lead to a smaller A¯, while maintaining the general shape of A¯. Thus, the following analysis to understand the shape of A¯ is not substantially dependent on the applied threshold of τc.

What does A¯ show? For the nonprecipitating cases, which transition toward larger fc, A¯ exhibits a superlinear increase for all fc (Fig. 2e). This behavior is very similar to the satellite reference by Engström et al. (2015) (thick black line), while overestimating A for all fc slightly, which might be due to the higher τc threshold used for this study, as argued above. For the precipitating cases, which transition from high to low fc, one sees a rapid decrease in A¯ for fc > 0.8, followed by an almost linear and more gradual decrease for smaller fc (Fig. 2d). Again, the Engström et al. (2015) reference is exceeded, but now more distinctly. In addition to the τc-threshold bias, this is due to the generally higher LWPc in the precipitating cases (cf. Figs. 3b and 5b below). Most importantly, however, the shape of the precipitating A¯ differs substantially from the Engström et al. (2015) reference and hence the nonprecipitating cases. Note that these differences in A¯ for precipitating and nonprecipitating stratocumulus would be indistinguishable in the reference by Engström et al. (2015), which includes all marine clouds in the sampled regions.

In any case, the different shapes of A¯ for the precipitating and nonprecipitating cases indicate a hysteretic system, where different processes dominate the transitions from high to low (precipitating cases) and from low to high fc (nonprecipitating). Understanding the underlying processes will be the main subject of the next two subsections.

b. Precipitating cases

We will focus on the precipitating cases first, starting with a general overview of Ac, LWPc, Nc, and RWPc/LWPc in the Afc phase space introduced above (Fig. 3). In this and all the following depictions of the Afc phase space, each pixel represents the average of all precipitating (or nonprecipitating) trajectories passing through its boundaries, using all analyzed time steps. Here, RWPc is the vertically integrated rainwater path, analogous to LWPc but restricted to droplets with radii > 25 μm, a threshold which is often applied to discriminate between cloud and raindrops (e.g., Khairoutdinov and Kogan 2000). For a given fc, Ac must increase to cause a larger A per definition (1), while Ac also shows generally larger values at higher fc (Fig. 3a). These changes are determined by changes in LWPc and Nc, as expected from (2). Indeed, LWPc generally increases with A for a given fc (Fig. 3b). The distribution of Nc (Fig. 3c) is mostly determined by precipitation scavenging, reducing Nc by collision and coalescence, as indicated by the largely anticorrelated RWPc/LWPc (population Pearson correlation coefficient of −0.65), which marks the most active precipitation in this region of the phase space (Fig. 3d). Overall, Nc tends to be higher for larger fc, which is due to the less active precipitation in this part of the phase space, in agreement with Feingold et al. (2016).

Fig. 3.
Fig. 3.

For the precipitating cases, (a) Ac, (b) LWPc, (c) Nc, and (d) RWPc/LWPc are displayed in an Afc phase space. The black line shows the reference by Engström et al. (2015).

Citation: Journal of the Atmospheric Sciences 80, 12; 10.1175/JAS-D-22-0268.1

Figures 4a–c show the temporal changes in A, fc, and Ac, which are connected via
dAdt=(AcAs)dfcdt+dAcdtfc,
derived from differentiating (1) and assuming dAs/dt = 0. The temporal derivatives are determined using finite differences after applying a running average of 20 min to each trajectory to filter small-scale fluctuations. The dA/dt is negative throughout most of the phase space, with the strongest negative tendencies for fc ≈ 1 that approach zero for fc ≈ 0.1 (Fig. 4a). These changes are primarily determined by dfc/dt (Fig. 4b), which shows a similar distribution, although with slightly less negative values for fc ≈ 1. The onset of precipitation is most apparent in dAc/dt, which shows the strongest negative tendencies for fc > 0.8 (Fig. 4c) due to losses in LWPc and Nc. However, dAc/dt ≈ 0 for fc < 0.8. While this behavior is necessary to cause the aforementioned linear change in A¯ for fc < 0.8, it is surprising because precipitation and hence its potential effects on Ac do not disappear for fc < 0.8 (cf. Figs. 2b and 3d).
Fig. 4.
Fig. 4.

For the precipitating cases, the temporal change in (a) A, (b) fc, (c) Ac, (d) LWPc, (e) LWPc by precipitation, (g) Nc, (h) Nc by precipitation, and (i) Nc by surface sources is presented. (f) The cloud aspect ratio is shown. The black line indicates the reference by Engström et al. (2015).

Citation: Journal of the Atmospheric Sciences 80, 12; 10.1175/JAS-D-22-0268.1

To understand this, dAc/dt is expanded as
dAcdt=γAc2τc[13dln(Nc)dt+56dln(LWPc)dt],
using (2) and (3), with γAc2/τc0.2 for 5 < τc < 30, typical for stratocumulus (e.g., Pawlowska et al. 2000). Figures 4d and 4g show the total dln(LWPc)/dt and dln(Nc)/dt; the corresponding changes due to surface precipitation and precipitation scavenging only are depicted in Figs. 4e and 4h, respectively. Indeed, precipitation reduces LWPc and Nc for all fc, with the strongest reduction in Nc for fc > 0.8, which explains the rapid reduction in A¯ in this part of the phase space. However, the total dln(LWPc)/dt is positive for fc < 0.8. This corresponds to the aforementioned change in the mesoscale organization of the cloud field, where shallow closed-cell stratocumulus transition into deeper and narrower cloud bands (open-cell stratocumulus) due to convergence zones created by cold pools formed by evaporating precipitation (Savic-Jovcic and Stevens 2008; Wang and Feingold 2009). The commensurate change in the cloud aspect ratio, determined as the quotient of average cloud width to average cloud depth, confirms this (Fig. 4f). Combining the effects of cloud deepening [dln(LWPc)/dt > 0, Fig. 4d] and precipitation scavenging [dln(Nc)/dt < 0, Fig. 4g] yields the net-zero change in Ac for fc < 0.8 (Fig. 4c). While the cancellation of these two effects might be accidental here, the tendency of precipitation-induced cold pools to enable deeper clouds, and hence buffer the negative effects of precipitation scavenging of Nc on Ac, has been noted earlier (e.g., Stevens and Feingold 2009).

Finally, it is interesting to see that the low Nc steady state predicted by Baker and Charlson (1990), in which the surface source for Nc (Fig. 4i) matches the losses through precipitation (Fig. 4h), is reproduced at fc ≈ 0.1. Combined with the vanishing tendencies for LWPc (Fig. 4d), this indicates that fc ≈ 0.1 can constitute a steady state in the examined phase space for this set of simulations.

c. Nonprecipitating cases

The less understood transition from open- to closed-cell stratocumulus in the absence of precipitation is introduced in Fig. 5, showing the distribution of Ac, LWPc, Nc, and RWPc/LWPc in the Afc phase space. As in the precipitating cases in Fig. 3a, Ac exhibits larger values for higher A (Fig. 5a). In contrast to the precipitating cases, Nc shows no clear pattern in the Afc phase space (Fig. 5c), while LWPc increases substantially with A and fc (Fig. 5b). Per definition, there is no precipitation in the nonprecipitating cases (Fig. 5d).

Fig. 5.
Fig. 5.

For the nonprecipitating cases, (a) Ac, (b) LWPc, (c) Nc, and (d) RWPc/LWPc are displayed in an Afc phase space. The black line shows the reference by Engström et al. (2015).

Citation: Journal of the Atmospheric Sciences 80, 12; 10.1175/JAS-D-22-0268.1

Figures 6a–c show the temporal derivatives of A, fc, and Ac, respectively. For dA/dt and dfc/dt, we see a distinct band of positive values for all fc, representing the transition from open to closed cells in the absence of precipitation. Based on (4), we see that dA/dt is mainly driven by dfc/dt, while the contribution from dAc/dt to dA/dt is mostly negligible. Only for fc > 0.5 does dAc/dt exhibit a region of distinctly positive values, which are due to a temporal increase in LWPc (Fig. 6d), while there are no substantial changes in Nc (Fig. 6e). Nonetheless, this slight increase in LWPc is essential to explain the superlinear increase in A¯ discussed above. Figure 6f shows the buoyancy integral ratio, a decoupling index developed by Turton and Nicholls (1987), which is based on the ratio of buoyancy destruction below cloud base to the buoyancy production in the entire boundary layer [see (14) in Bretherton and Wyant 1997]. A value above 0.15 indicates a decoupled boundary layer. As the entire phase space is below this threshold, the nonprecipitating cases presented in this subsection can be considered well mixed, which is a necessary prerequisite for the mixed-layer analysis presented below.

Fig. 6.
Fig. 6.

For the nonprecipitating cases, the temporal change in (a) A, (b) fc, (c) Ac, (d) LWPc, (e) Nc, and (f) a decoupling index is presented. The black line shows the reference by Engström et al. (2015).

Citation: Journal of the Atmospheric Sciences 80, 12; 10.1175/JAS-D-22-0268.1

We focus on the changes in LWPc along the positive bands of dA/dt and dfc/dt first. The zero or slightly negative tendencies below the positive bands will be briefly addressed by the end of this subsection.

To analyze the behavior of LWPc more comprehensively, Fig. 7a shows dLWPc/dt directly from LES (thick black line) and mixed-layer model (MLM) tendencies diagnosed from the LESs using the approach presented in Hoffmann et al. (2020), which allows one to expand dLWPc/dt into contributions by cloud-top motion (blue line), cloud-top entrainment (green line), precipitation (cyan line), surface fluxes (purple line), and radiation (red line). For this, we determine the divergence of the corresponding fluxes of the total water mixing ratio and liquid water potential temperature across the LES mixed layer to determine the influence of precipitation, surface fluxes, and radiation. The effect of cloud-top motion is determined from the temporal change in cloud-top height. Cloud-top entrainment is diagnosed using the approach by Yamaguchi and Randall (2008, appendix E), which aims to minimize storage of total water mixing ratio and liquid water potential temperature in the inversion layer. A new term, which was not considered in Hoffmann et al. (2020), is the change in liquid water due to the horizontal development of the cloud layer, i.e., lateral entrainment (yellow line). For Fig. 7a, this term is determined as the difference between the sum of all the previously mentioned MLM tendencies (dashed black line) and the LES tendency (thick black line) as a residuum. This term will be discussed more deeply below, including direct estimates that are not based on determining a residuum. Note that all quantities are determined for regions with dfc/dt > 0 only to avoid the aforementioned regions that do not exhibit a transition from open to closed cells. Further note that the trajectories providing the data for these plots are binned in fc space, and then averaged.

Fig. 7.
Fig. 7.

(a) The temporal change in LWPc determined using MLM equations [cloud-top motion (blue line), cloud-top entrainment (green line), precipitation (cyan line), surface fluxes (purple line), longwave radiation (red line), and the total tendency (dashed black line)], the total LWPc tendency from the LES (thick black line), and the difference between the total LWPc tendencies of LES and MLM termed lateral entrainment (yellow line). (b) The temporal change in fc determined from LES (black line), the lateral entrainment rate (yellow line), and a theoretical estimate (blue line). (c) The LWPc (continuous black line) and the liquid water deficit δLWP (dashed black line). (d) The average cloud radius R. Quantities in (c) and (d) are derived from LESs.

Citation: Journal of the Atmospheric Sciences 80, 12; 10.1175/JAS-D-22-0268.1

The deepening of the boundary layer enables higher cloud tops and hence larger LWPc (cloud-top motion) (blue line in Fig. 7a), while the simultaneous mixing with free-tropospheric air evaporates the cloud and decreases LWPc (cloud-top entrainment) (green line). Together, these two terms represent the net effect of cloud-top entrainment on LWPc, which is slightly negative and becomes more negative for larger fc. This dependency on fc is expected because cloud-top entrainment requires the preconditioning of free-tropospheric air by cloud evaporation (Yamaguchi and Randall 2012), a process that naturally scales with fc. Consequently, a larger fc will accelerate cloud-top motion and cloud-top entrainment. The surface fluxes (purple line) are slightly negative for all fc, indicating that the influx of sensible heat, causing evaporation, exceeds the influx of water vapor, causing condensation, and thus leads to a lower LWPc. Longwave radiative cooling (red line) constitutes the largest positive LWPc tendency and increases with fc. Stronger radiative cooling with fc is expected due to the larger cloud amount contributing to the emission of longwave radiation. Combining all these MLM tendencies results in a positive impact on LWPc for all fc (dashed black line). While this MLM estimate agrees with the LES (thick black line) for fc = 1, it overestimates the LES tendency for all fc < 1.

We will show that the difference between the sum of all MLM tendencies and the LES tendency is due to lateral cloud development, which is traditionally not considered in MLMs but becomes a necessity for fc < 1 (yellow line in Fig. 7a). This thought is developed further in Fig. 7b, where dfc/dt is determined from the LESs directly (black line), a theoretical estimate (blue line), and the lateral entrainment tendency of Fig. 7a (yellow line). For the last approach, we assume that
dLWPcdt|lat.entr.=dfcdt(LWPc+δLWP),
where dLWPc/dt|lat.entr. is the lateral entrainment tendency from Fig. 7a, while LWPc and δLWP are shown in Fig. 7c. Here, δLWP=zbzt(qsqυ)dz is the vertically integrated liquid water deficit in the region between the clouds, where qυ is the water vapor density and qs is the corresponding saturation value. Note that (6) is an approximation of the underlying physics, considering only the amount of liquid water necessary to saturate a fraction of the environment (δLWP) and to adjust it to liquid water of the rest of the cloud deck (LWPc). In that sense, (6) represents the limiting case in which there is sufficient kinetic energy to sustain lateral expansion. Alternatively, it might be possible that the lateral transport is limited by the available kinetic energy, making it slower than predicted by (6) (e.g., MacVean and Mason 1990). However, Fig. 7b shows good agreement between (6) (yellow line) and the LES reference (black line), which supports the aforementioned limiting case driven by sufficient kinetic energy. This indicates that the excess in LWPc production predicted by the MLM, and here mostly due to longwave radiative cooling, is used for the lateral expansion. Only the decreasing efficiency of dfc/dt for fc > 0.5 enables cloud deepening and hence larger LWPc. Last, this analysis indicates that the excess in LWPc production predicted by the MLM is not due to inherent uncertainties in determining MLM tendencies from LES data (e.g., McMichael et al. 2019) but is indeed the signal of a physical process.
What determines the efficiency of dfc/dt? The dfc/dt is approximately zero for fc = 0 and 1 and exhibits a maximum in between. To analyze this behavior, we determine dfc/dt from the continuity equation
fctE+(fcwc)z=0,
which is the basis of many lateral entrainment parameterizations [cf. (6) in de Rooy et al. 2013]. Here, E is the net entrainment rate describing the horizontal cloud development, and ∂fcwc/∂z accounts for the vertical cloud development, with wc being the in-cloud vertical velocity. While one commonly uses a vertical profile of fc in (7), we restrict our analysis to the maximum of the fc profile, which corresponds to the two-dimensional cloud cover assessed in this study. Usually, the maximum of the fc profile coincides with a (local) maximum of the fcwc profile, and hence, the derivative ∂(fcwc)/∂z can be neglected in this study (cf. Stevens et al. 2001; Siebesma et al. 2003). Thus, we get
fct=EβfcR,
which uses a simple estimate for E based on an entraining plume (Morton et al. 1956), with R being the plume (or cloud) radius (Fig. 7d). Following (10) in de Rooy et al. (2013), R = 2ac/pc, the ratio of cloud area ac to cloud perimeter pc. The terms ac and pc are determined as bulk quantities of the two-dimensional projection of the entire cloud field, i.e., regions with τc > 5. Individual cloud elements are not considered explicitly, which is a simplification that is frequently applied in parameterizations of the entrainment process (e.g., Yanai et al. 1973). Thus, R needs to be interpreted as an average quantity of the cloud field rather than describing the radius of an individual cloud. With β ≈ 2800 m day−1, the estimate of ∂fc/∂t matches the general behavior of the LESs well (Fig. 7b). Based on (8), we understand that for fc = 0, dfc/dt is zero because there are no clouds from which new clouds can be generated. For fc = 1, dfc/dt approaches zero because of the increasing R, indicating a decreasing cloud perimeter to cloud area ratio that reduces the transport of liquid water to the lateral environment. This interplay naturally favors an intermediate fc for the most efficient transport of liquid water. Overall, this indicates that cloud geometry, introduced by fc and R, plays an important role in determining the temporal development of cloud fields (cf. Feingold et al. 2017; Rampal and Davies 2020).

Finally, we return to the regions of zero or slightly negative tendencies below the positive bands of dA/dt and dfc/dt in Figs. 6a and 6b, in which the stratocumulus are not transitioning. Figure 8a shows that these regions are characterized by a larger Δθ1. The associated stability limits entrainment and hence the vertical cloud development, resulting in the lower LWPc shown in Fig. 5b. While one might expect a commensurate increase in the horizontal cloud development when updrafts are blocked at a strong inversion and deflected laterally, dfc/dt ≈ 0 in this region of the phase space. As discussed above, radiative cooling is the primary driver for the transition of nonprecipitating stratocumulus from an open- to a closed-cell state, and the influence of radiative cooling is proportional to the cloud amount. Thus, the comparably low LWPc limits radiative cooling and hence the potential for a substantial increase in fc. While this halts the transition of the cloud deck (cf. Feingold et al. 2015), individual stratocumulus may be sustained for longer periods of time (e.g., McMichael et al. 2019). In contrast to Δθ1, Δqt varies only slightly in the analyzed phase space (Fig. 8b). A drier free troposphere could increase the evaporation of LWPc due to the entrainment of drier air. However, a drier free troposphere might also increase longwave radiative cooling of the cloud layer by decreasing the downward radiative flux reaching the cloud layer (e.g., Held and Soden 2000), which could cause a positive LWPc tendency. All in all, this last analysis indicates that the transitioning of stratocumulus is not only determined by the cloud layer intrinsically but is also dependent on external factors such as the lower tropospheric stability. This finding amends the work by Wood and Bretherton (2006), who showed that a higher lower tropospheric stability correlates well with high fc: While a higher lower tropospheric stability might indeed stabilize already high fc by decreasing the influence of entrainment, it might also prevent a system from reaching that high fc state by preventing the necessary buildup of liquid water.

Fig. 8.
Fig. 8.

For the nonprecipitating cases, differences between free-tropospheric and boundary layer thermodynamic quantities are shown for (a) Δθ1 and (b) Δqt; the black line shows the reference by Engström et al. (2015).

Citation: Journal of the Atmospheric Sciences 80, 12; 10.1175/JAS-D-22-0268.1

4. Summary

Stratocumulus clouds exist in two distinct states commonly referred to as open cell and closed cell, which are associated with lower and almost full cloud cover (fc), respectively, and substantial changes in the scene albedo (A). Thus, the transition between these states has important implications for the Earth radiation budget and hence the climate system. In this study, we used 127 large-eddy simulations (LESs) with bin-emulating cloud microphysics to understand the transitions in marine stratocumulus in a much wider phase space than possible with individual case studies (Feingold et al. 2016). In this study, transitions are primarily driven by the presence or absence of precipitation. Thus, the LESs are separated into precipitating (cloud-base rain rate Rcb > 1 mm day−1) and nonprecipitating cases (Rcb < 1 mm day−1). Beyond the scope of this study, but similarly important, are transitions caused by changes in boundary layer depth or surface fluxes, as well as wind shear (e.g., Wood 2012).

Based on previous satellite observations (Engström et al. 2015), we analyzed transitions in a reduced phase space employing the aforementioned A and fc as its dimensions. In this framework, observations and simulations populate a remarkably narrow region, with generally low A at low fc and large A at large fc, despite the wide range of initial and boundary conditions in our stratocumulus simulations.

Our study showed that the transitions follow different trajectories in the Afc phase space depending on the degree of precipitation. During their transition from closed to open cells, precipitating stratocumulus generally approach low fc from high fc, while nonprecipitating stratocumulus do the opposite during their transition from open to closed cells. The average trajectory of the precipitating cases exhibits a slightly higher A than the nonprecipitating cases and shows a strong initial decrease in A for fc > 0.8, followed by a scale break and a more gradual and almost linear decrease in A for fc < 0.8. The nonprecipitating cases show a continuous increase in A for all fc, without any scale breaks. This hysteretic behavior, previously emphasized by Feingold et al. (2015), is not apparent in the large statistical composite satellite reference by Engström et al. (2015), which is based on all marine clouds between 60°N and 60°S. In fact, the satellite reference is very similar to the average trajectory of the nonprecipitating stratocumulus cases, which might indicate that precipitating stratocumulus constitute a minority in the satellite data (e.g., Leon et al. 2008).

For the precipitating cases, we found that the reduction in fc through precipitation (cloud narrowing) is the main driver for the transition toward the open-cell state. To understand the concurrent changes in A, we analyzed the in-cloud liquid water path LWPc and cloud droplet concentration Nc. Precipitation losses in LWPc and Nc drive the initial reduction in A for fc > 0.8. For fc < 0.8, precipitation is still active and scavenges Nc, but LWPc increases due to the mesoscale organization of the cloud field which enables deeper clouds (Savic-Jovcic and Stevens 2008). Due to the opposite impacts of Nc scavenging and cloud deepening on the cloud albedo, the net effect of these two processes on A is negligible for fc < 0.8, which causes A to change linearly with fc for fc < 0.8.

For the nonprecipitating cases, we confirmed that the emission of longwave radiative cooling is the main driver for the transition toward larger fc (cloud widening) and higher LWPc (cloud deepening) (cf. Feingold et al. 2015). Our analysis showed that the cloud evolution is restricted to cloud widening for fc < 0.5. For fc > 0.5, however, cloud widening is successively replaced by cloud deepening until fc = 1 is reached. The continuous change from cloud widening to cloud deepening explains the steady increase in the cloud albedo and hence the steady superlinear increase in A with fc. We argued that this change in growth mode is caused by the decreasing efficiency of lateral entrainment at larger fc, where increasing cloud radii make the detrainment of liquid water to the environment less efficient. Overall, changes in Nc are negligible for the nonprecipitating cases.

Understanding the transitions of stratocumulus and the underlying micro- and macrophysical processes is essential to constrain the role of clouds in the climate system (e.g., Boucher et al. 2013). Given the high sensitivity of A on fc demonstrated above, this study emphasizes the necessity to extend our understanding of aerosol–cloud–climate interactions beyond the well-established effect of Nc on cloud reflectivity (Twomey 1974, 1977) and to include the more complex adjustments of LWPc (e.g., Glassmeier et al. 2021) and fc (e.g., Yamaguchi et al. 2017). To achieve this requires bridging the process-level and systemwide understanding of clouds attempted in this study, as well as an assessment of the frequency of occurrence of different stratocumulus mesoscale states and their transitions.

Acknowledgments.

FH appreciates support from the Emmy Noether Program of the German Research Foundation (DFG) under Grant HO 6588/1-1. FG acknowledges support from The Branco Weiss Fellowship—Society in Science, administered by ETH Zurich, and from an NWO Veni grant. GF acknowledges funding from NOAA’s ERB program (NOAA CPO Climate and CI 03-01-07-001). Marat Khairoutdinov graciously provided the SAM model.

Data availability statement.

The data that support the findings of this study are available from the corresponding author upon request.

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  • Fig. 1.

    Probability density distributions (PDFs) of sensible (blue lines) and latent (red lines) surface heat fluxes from this (continuous lines) and our previous (dashed lines) LES ensemble studies. Note that our previous studies assumed constant surface fluxes.

  • Fig. 2.

    (a) All simulations as trajectories in an Afc phase space, with blue lines indicating precipitating cases and red lines indicating nonprecipitating cases. (The differently shaded blue and red lines are an aid to distinguishing the trajectories and have no further meaning.) A thin black line shows the trajectory that does not fall in the precipitating or nonprecipitating categories applied here. A thick black line shows the reference by Engström et al. (2015). (b) The same simulations in an Rcbfc phase space and (c) PDFs of Rcb. (d)–(f) Complement to (a) with corresponding joint frequency distributions for the cases classified as precipitating or nonprecipitating, as well as all cases combined. The respective blue, red, and orange lines show the average A¯ for τc = 5 (continuous lines), 2 (long-dashed lines), and 1 (short-dashed lines). Note that the threshold τc = 5 is used throughout the study.

  • Fig. 3.

    For the precipitating cases, (a) Ac, (b) LWPc, (c) Nc, and (d) RWPc/LWPc are displayed in an Afc phase space. The black line shows the reference by Engström et al. (2015).

  • Fig. 4.

    For the precipitating cases, the temporal change in (a) A, (b) fc, (c) Ac, (d) LWPc, (e) LWPc by precipitation, (g) Nc, (h) Nc by precipitation, and (i) Nc by surface sources is presented. (f) The cloud aspect ratio is shown. The black line indicates the reference by Engström et al. (2015).

  • Fig. 5.

    For the nonprecipitating cases, (a) Ac, (b) LWPc, (c) Nc, and (d) RWPc/LWPc are displayed in an Afc phase space. The black line shows the reference by Engström et al. (2015).

  • Fig. 6.

    For the nonprecipitating cases, the temporal change in (a) A, (b) fc, (c) Ac, (d) LWPc, (e) Nc, and (f) a decoupling index is presented. The black line shows the reference by Engström et al. (2015).

  • Fig. 7.

    (a) The temporal change in LWPc determined using MLM equations [cloud-top motion (blue line), cloud-top entrainment (green line), precipitation (cyan line), surface fluxes (purple line), longwave radiation (red line), and the total tendency (dashed black line)], the total LWPc tendency from the LES (thick black line), and the difference between the total LWPc tendencies of LES and MLM termed lateral entrainment (yellow line). (b) The temporal change in fc determined from LES (black line), the lateral entrainment rate (yellow line), and a theoretical estimate (blue line). (c) The LWPc (continuous black line) and the liquid water deficit δLWP (dashed black line). (d) The average cloud radius R. Quantities in (c) and (d) are derived from LESs.

  • Fig. 8.

    For the nonprecipitating cases, differences between free-tropospheric and boundary layer thermodynamic quantities are shown for (a) Δθ1 and (b) Δqt; the black line shows the reference by Engström et al. (2015).

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